[
    {
        "sample_index": "1",
        "problem_index": "1",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC, it is known that angle A = 80.0, angle B = 60.0, point D is on AB and point E is on AC, DE parallel BC, then the size of angle CED is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:120\u00b0\nD:140\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC, it is known that angle A = 80.0, angle B = 60.0, point D is on AB and point E is on AC, DE parallel BC, then the size of angle CED is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:120\u00b0\nD:140\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC, it is known that angle A = 80.0, angle B = 60.0, point D is on AB and point E is on AC, DE parallel BC, then the size of angle CED is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:120\u00b0\nD:140\u00b0",
        "question_for_eval": "As shown in the figure, in triangle ABC, it is known that angle A = 80.0, angle B = 60.0, point D is on AB and point E is on AC, DE parallel BC, then the size of angle CED is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:120\u00b0\nD:140\u00b0"
    },
    {
        "sample_index": "2",
        "problem_index": "2",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, straight line EF intersects AB at point E, intersects CD at point F, EG bisects angle BEF, and it intersects CD at point G, angle 1 = 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:65\u00b0\nD:90\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, straight line EF intersects AB at point E, intersects CD at point F, EG bisects angle BEF, and it intersects CD at point G, angle 1 = 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:65\u00b0\nD:90\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, straight line EF intersects AB at point E, intersects CD at point F, EG bisects angle BEF, and it intersects CD at point G, angle 1 = 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:65\u00b0\nD:90\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, straight line EF intersects AB at point E, intersects CD at point F, EG bisects angle BEF, and it intersects CD at point G, angle 1 = 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:65\u00b0\nD:90\u00b0"
    },
    {
        "sample_index": "3",
        "problem_index": "3",
        "problem_version": "Text Only",
        "question": "As shown in the figure, BC and BA intersect at point B, BD bisects angle ABC, CD parallel AB, if angle BCD = 70.0, then the degree of angle CDB is ()\nChoices:\nA:55\u00b0\nB:50\u00b0\nC:45\u00b0\nD:30\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, BC and BA intersect at point B, BD bisects angle ABC, CD parallel AB, if angle BCD = 70.0, then the degree of angle CDB is ()\nChoices:\nA:55\u00b0\nB:50\u00b0\nC:45\u00b0\nD:30\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, BC and BA intersect at point B, BD bisects angle ABC, CD parallel AB, if angle BCD = 70.0, then the degree of angle CDB is ()\nChoices:\nA:55\u00b0\nB:50\u00b0\nC:45\u00b0\nD:30\u00b0",
        "question_for_eval": "As shown in the figure, BC and BA intersect at point B, BD bisects angle ABC, CD parallel AB, if angle BCD = 70.0, then the degree of angle CDB is ()\nChoices:\nA:55\u00b0\nB:50\u00b0\nC:45\u00b0\nD:30\u00b0"
    },
    {
        "sample_index": "4",
        "problem_index": "4",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is tangent to circle O at point B, and the extended line of AO intersects circle O at point C. Connect BC, if angle A = 36.0, then angle C is equal to ()\nChoices:\nA:36\u00b0\nB:54\u00b0\nC:60\u00b0\nD:27\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is tangent to circle O at point B, and the extended line of AO intersects circle O at point C. Connect BC, if angle A = 36.0, then angle C is equal to ()\nChoices:\nA:36\u00b0\nB:54\u00b0\nC:60\u00b0\nD:27\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is tangent to circle O at point B, and the extended line of AO intersects circle O at point C. Connect BC, if angle A = 36.0, then angle C is equal to ()\nChoices:\nA:36\u00b0\nB:54\u00b0\nC:60\u00b0\nD:27\u00b0",
        "question_for_eval": "As shown in the figure, AB is tangent to circle O at point B, and the extended line of AO intersects circle O at point C. Connect BC, if angle A = 36.0, then angle C is equal to ()\nChoices:\nA:36\u00b0\nB:54\u00b0\nC:60\u00b0\nD:27\u00b0"
    },
    {
        "sample_index": "5",
        "problem_index": "5",
        "problem_version": "Text Only",
        "question": "As shown in the figure, straight lines a and b intersect at point O. If angle 1 is equal to 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:140\u00b0\nD:130\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, straight lines a and b intersect at point O. If angle 1 is equal to 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:140\u00b0\nD:130\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, straight lines a and b intersect at point O. If angle 1 is equal to 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:140\u00b0\nD:130\u00b0",
        "question_for_eval": "As shown in the figure, straight lines a and b intersect at point O. If angle 1 is equal to 50.0, then angle 2 is equal to ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:140\u00b0\nD:130\u00b0"
    },
    {
        "sample_index": "6",
        "problem_index": "6",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB // CD, and EF intersects AB and CD at points E, F, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:50\u00b0\nB:120\u00b0\nC:130\u00b0\nD:150\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB // CD, and EF intersects AB and CD at points E, F, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:50\u00b0\nB:120\u00b0\nC:130\u00b0\nD:150\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB // CD, and EF intersects AB and CD at points E, F, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:50\u00b0\nB:120\u00b0\nC:130\u00b0\nD:150\u00b0",
        "question_for_eval": "As shown in the figure, AB // CD, and EF intersects AB and CD at points E, F, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:50\u00b0\nB:120\u00b0\nC:130\u00b0\nD:150\u00b0"
    },
    {
        "sample_index": "7",
        "problem_index": "7",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC congruent triangle ADE, Point A is their common vertex. if angle B = 70.0, angle C = 30.0, angle DAC = 35.0, then the degree of angle EAC is ()\nChoices:\nA:40\u00b0\nB:45\u00b0\nC:35\u00b0\nD:25\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC congruent triangle ADE, Point A is their common vertex. if angle B = 70.0, angle C = 30.0, angle DAC = 35.0, then the degree of angle EAC is ()\nChoices:\nA:40\u00b0\nB:45\u00b0\nC:35\u00b0\nD:25\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC congruent triangle ADE, Point A is their common vertex. if angle B = 70.0, angle C = 30.0, angle DAC = 35.0, then the degree of angle EAC is ()\nChoices:\nA:40\u00b0\nB:45\u00b0\nC:35\u00b0\nD:25\u00b0",
        "question_for_eval": "As shown in the figure, triangle ABC congruent triangle ADE, Point A is their common vertex. if angle B = 70.0, angle C = 30.0, angle DAC = 35.0, then the degree of angle EAC is ()\nChoices:\nA:40\u00b0\nB:45\u00b0\nC:35\u00b0\nD:25\u00b0"
    },
    {
        "sample_index": "8",
        "problem_index": "8",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC congruent triangle DEF, points A and D, B and E are the corresponding vertices, and the measured BC = 5.0, BF = 7.0, then the length of EC is ()\nChoices:\nA:1cm\nB:2cm\nC:3cm\nD:4cm",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC congruent triangle DEF, points A and D, B and E are the corresponding vertices, and the measured BC = 5.0, BF = 7.0, then the length of EC is ()\nChoices:\nA:1cm\nB:2cm\nC:3cm\nD:4cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC congruent triangle DEF, points A and D, B and E are the corresponding vertices, and the measured BC = 5.0, BF = 7.0, then the length of EC is ()\nChoices:\nA:1cm\nB:2cm\nC:3cm\nD:4cm",
        "question_for_eval": "As shown in the figure, triangle ABC congruent triangle DEF, points A and D, B and E are the corresponding vertices, and the measured BC = 5.0, BF = 7.0, then the length of EC is ()\nChoices:\nA:1cm\nB:2cm\nC:3cm\nD:4cm"
    },
    {
        "sample_index": "9",
        "problem_index": "9",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC, angle C = 90.0, AC = BC, AD bisects angle CAB and it intersects BC at D, DE perpendicular AB at E, if AB = 6.0, then the perimeter of triangle DBE is ()\nChoices:\nA:6cm\nB:7cm\nC:8cm\nD:9cm",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC, angle C = 90.0, AC = BC, AD bisects angle CAB and it intersects BC at D, DE perpendicular AB at E, if AB = 6.0, then the perimeter of triangle DBE is ()\nChoices:\nA:6cm\nB:7cm\nC:8cm\nD:9cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC, angle C = 90.0, AC = BC, AD bisects angle CAB and it intersects BC at D, DE perpendicular AB at E, if AB = 6.0, then the perimeter of triangle DBE is ()\nChoices:\nA:6cm\nB:7cm\nC:8cm\nD:9cm",
        "question_for_eval": "As shown in the figure, in triangle ABC, angle C = 90.0, AC = BC, AD bisects angle CAB and it intersects BC at D, DE perpendicular AB at E, if AB = 6.0, then the perimeter of triangle DBE is ()\nChoices:\nA:6cm\nB:7cm\nC:8cm\nD:9cm"
    },
    {
        "sample_index": "10",
        "problem_index": "10",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC, AB = AC, angle A = 36.0, the perpendicular bisector of AB intersects AC at D, and intersects AB at E, then the degree of angle BDC is ()\nChoices:\nA:72\u00b0\nB:36\u00b0\nC:60\u00b0\nD:82\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC, AB = AC, angle A = 36.0, the perpendicular bisector of AB intersects AC at D, and intersects AB at E, then the degree of angle BDC is ()\nChoices:\nA:72\u00b0\nB:36\u00b0\nC:60\u00b0\nD:82\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC, AB = AC, angle A = 36.0, the perpendicular bisector of AB intersects AC at D, and intersects AB at E, then the degree of angle BDC is ()\nChoices:\nA:72\u00b0\nB:36\u00b0\nC:60\u00b0\nD:82\u00b0",
        "question_for_eval": "As shown in the figure, in triangle ABC, AB = AC, angle A = 36.0, the perpendicular bisector of AB intersects AC at D, and intersects AB at E, then the degree of angle BDC is ()\nChoices:\nA:72\u00b0\nB:36\u00b0\nC:60\u00b0\nD:82\u00b0"
    },
    {
        "sample_index": "11",
        "problem_index": "11",
        "problem_version": "Text Only",
        "question": "As shown in the figure, angle C = 36.0, rotate triangle ABC anticlockwise around point A by 60.0 to get triangle AED, AD and BC intersect at point F, then the degree of angle AFC is ()\nChoices:\nA:84\u00b0\nB:80\u00b0\nC:60\u00b0\nD:90\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, angle C = 36.0, rotate triangle ABC anticlockwise around point A by 60.0 to get triangle AED, AD and BC intersect at point F, then the degree of angle AFC is ()\nChoices:\nA:84\u00b0\nB:80\u00b0\nC:60\u00b0\nD:90\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, angle C = 36.0, rotate triangle ABC anticlockwise around point A by 60.0 to get triangle AED, AD and BC intersect at point F, then the degree of angle AFC is ()\nChoices:\nA:84\u00b0\nB:80\u00b0\nC:60\u00b0\nD:90\u00b0",
        "question_for_eval": "As shown in the figure, angle C = 36.0, rotate triangle ABC anticlockwise around point A by 60.0 to get triangle AED, AD and BC intersect at point F, then the degree of angle AFC is ()\nChoices:\nA:84\u00b0\nB:80\u00b0\nC:60\u00b0\nD:90\u00b0"
    },
    {
        "sample_index": "12",
        "problem_index": "12",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line AB parallel CD, Rttriangle DEF is placed as shown, angle EDF = 90.0, if angle 1 + angle F = 70.0, then the degree of angle 2 is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:30\u00b0\nD:40\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line AB parallel CD, Rttriangle DEF is placed as shown, angle EDF = 90.0, if angle 1 + angle F = 70.0, then the degree of angle 2 is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:30\u00b0\nD:40\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line AB parallel CD, Rttriangle DEF is placed as shown, angle EDF = 90.0, if angle 1 + angle F = 70.0, then the degree of angle 2 is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:30\u00b0\nD:40\u00b0",
        "question_for_eval": "As shown in the figure, the straight line AB parallel CD, Rttriangle DEF is placed as shown, angle EDF = 90.0, if angle 1 + angle F = 70.0, then the degree of angle 2 is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:30\u00b0\nD:40\u00b0"
    },
    {
        "sample_index": "13",
        "problem_index": "13",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel EF, angle BAC = 50.0, then angle ACD = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:140\u00b0\nD:150\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel EF, angle BAC = 50.0, then angle ACD = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:140\u00b0\nD:150\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel EF, angle BAC = 50.0, then angle ACD = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:140\u00b0\nD:150\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel EF, angle BAC = 50.0, then angle ACD = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:140\u00b0\nD:150\u00b0"
    },
    {
        "sample_index": "14",
        "problem_index": "14",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle OAB = 35.0, then the degree of angle ACB is ()\nChoices:\nA:35\u00b0\nB:55\u00b0\nC:60\u00b0\nD:70\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle OAB = 35.0, then the degree of angle ACB is ()\nChoices:\nA:35\u00b0\nB:55\u00b0\nC:60\u00b0\nD:70\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle OAB = 35.0, then the degree of angle ACB is ()\nChoices:\nA:35\u00b0\nB:55\u00b0\nC:60\u00b0\nD:70\u00b0",
        "question_for_eval": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle OAB = 35.0, then the degree of angle ACB is ()\nChoices:\nA:35\u00b0\nB:55\u00b0\nC:60\u00b0\nD:70\u00b0"
    },
    {
        "sample_index": "15",
        "problem_index": "15",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line a and the straight line b are intercepted by the straight line c, b perpendicular  c, the foot of perpendicular is the point A, angle 1 = 70.0. If the line b is parallel to the line a, the line b can be rotated () clockwise around the point A \nChoices:\nA:70\u00b0\nB:50\u00b0\nC:30\u00b0\nD:20\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line a and the straight line b are intercepted by the straight line c, b perpendicular  c, the foot of perpendicular is the point A, angle 1 = 70.0. If the line b is parallel to the line a, the line b can be rotated () clockwise around the point A \nChoices:\nA:70\u00b0\nB:50\u00b0\nC:30\u00b0\nD:20\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line a and the straight line b are intercepted by the straight line c, b perpendicular  c, the foot of perpendicular is the point A, angle 1 = 70.0. If the line b is parallel to the line a, the line b can be rotated () clockwise around the point A \nChoices:\nA:70\u00b0\nB:50\u00b0\nC:30\u00b0\nD:20\u00b0",
        "question_for_eval": "As shown in the figure, the straight line a and the straight line b are intercepted by the straight line c, b perpendicular  c, the foot of perpendicular is the point A, angle 1 = 70.0. If the line b is parallel to the line a, the line b can be rotated () clockwise around the point A \nChoices:\nA:70\u00b0\nB:50\u00b0\nC:30\u00b0\nD:20\u00b0"
    },
    {
        "sample_index": "16",
        "problem_index": "16",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in circle O, chord AC parallel radius OB, angle BOC = 50.0, then the degree of angle OAB is ()\nChoices:\nA:25\u00b0\nB:50\u00b0\nC:60\u00b0\nD:30\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in circle O, chord AC parallel radius OB, angle BOC = 50.0, then the degree of angle OAB is ()\nChoices:\nA:25\u00b0\nB:50\u00b0\nC:60\u00b0\nD:30\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in circle O, chord AC parallel radius OB, angle BOC = 50.0, then the degree of angle OAB is ()\nChoices:\nA:25\u00b0\nB:50\u00b0\nC:60\u00b0\nD:30\u00b0",
        "question_for_eval": "As shown in the figure, in circle O, chord AC parallel radius OB, angle BOC = 50.0, then the degree of angle OAB is ()\nChoices:\nA:25\u00b0\nB:50\u00b0\nC:60\u00b0\nD:30\u00b0"
    },
    {
        "sample_index": "17",
        "problem_index": "17",
        "problem_version": "Text Only",
        "question": "In parallelogram ABCD, the diagonal AC and BD intersect at point O, angle DAC = 42.0, angle CBD = 23.0, then angle COD is ().\nChoices:\nA:61\u00b0\nB:63\u00b0\nC:65\u00b0\nD:67\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In parallelogram ABCD, the diagonal AC and BD intersect at point O, angle DAC = 42.0, angle CBD = 23.0, then angle COD is ().\nChoices:\nA:61\u00b0\nB:63\u00b0\nC:65\u00b0\nD:67\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In parallelogram ABCD, the diagonal AC and BD intersect at point O, angle DAC = 42.0, angle CBD = 23.0, then angle COD is ().\nChoices:\nA:61\u00b0\nB:63\u00b0\nC:65\u00b0\nD:67\u00b0",
        "question_for_eval": "In parallelogram ABCD, the diagonal AC and BD intersect at point O, angle DAC = 42.0, angle CBD = 23.0, then angle COD is ().\nChoices:\nA:61\u00b0\nB:63\u00b0\nC:65\u00b0\nD:67\u00b0"
    },
    {
        "sample_index": "18",
        "problem_index": "18",
        "problem_version": "Text Only",
        "question": "The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 58.0, angle 2 = 58.0, angle 3 = 70.0, then angle 4 is equal to ()\nChoices:\nA:58\u00b0\nB:70\u00b0\nC:110\u00b0\nD:116\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 58.0, angle 2 = 58.0, angle 3 = 70.0, then angle 4 is equal to ()\nChoices:\nA:58\u00b0\nB:70\u00b0\nC:110\u00b0\nD:116\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 58.0, angle 2 = 58.0, angle 3 = 70.0, then angle 4 is equal to ()\nChoices:\nA:58\u00b0\nB:70\u00b0\nC:110\u00b0\nD:116\u00b0",
        "question_for_eval": "The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 58.0, angle 2 = 58.0, angle 3 = 70.0, then angle 4 is equal to ()\nChoices:\nA:58\u00b0\nB:70\u00b0\nC:110\u00b0\nD:116\u00b0"
    },
    {
        "sample_index": "19",
        "problem_index": "19",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a parallel b, angle 1 = 158.0, angle 2 = 42.0, angle 4 = 50.0. Then angle 3 = ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:80\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a parallel b, angle 1 = 158.0, angle 2 = 42.0, angle 4 = 50.0. Then angle 3 = ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:80\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a parallel b, angle 1 = 158.0, angle 2 = 42.0, angle 4 = 50.0. Then angle 3 = ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:80\u00b0",
        "question_for_eval": "As shown in the figure, a parallel b, angle 1 = 158.0, angle 2 = 42.0, angle 4 = 50.0. Then angle 3 = ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:80\u00b0"
    },
    {
        "sample_index": "20",
        "problem_index": "20",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O. Connect AC, BC, CD, and OD respectively. If angle DOB = 140.0, then angle ACD = ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:40\u00b0\nD:.70\u00b0A70\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O. Connect AC, BC, CD, and OD respectively. If angle DOB = 140.0, then angle ACD = ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:40\u00b0\nD:.70\u00b0A70\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O. Connect AC, BC, CD, and OD respectively. If angle DOB = 140.0, then angle ACD = ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:40\u00b0\nD:.70\u00b0A70\u00b0",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O. Connect AC, BC, CD, and OD respectively. If angle DOB = 140.0, then angle ACD = ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:40\u00b0\nD:.70\u00b0A70\u00b0"
    },
    {
        "sample_index": "21",
        "problem_index": "21",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that angle 1 = angle 2 = angle 3 = 55.0, then the degree of angle 4 is ()\nChoices:\nA:110\u00b0\nB:115\u00b0\nC:120\u00b0\nD:125\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that angle 1 = angle 2 = angle 3 = 55.0, then the degree of angle 4 is ()\nChoices:\nA:110\u00b0\nB:115\u00b0\nC:120\u00b0\nD:125\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that angle 1 = angle 2 = angle 3 = 55.0, then the degree of angle 4 is ()\nChoices:\nA:110\u00b0\nB:115\u00b0\nC:120\u00b0\nD:125\u00b0",
        "question_for_eval": "As shown in the figure, it is known that angle 1 = angle 2 = angle 3 = 55.0, then the degree of angle 4 is ()\nChoices:\nA:110\u00b0\nB:115\u00b0\nC:120\u00b0\nD:125\u00b0"
    },
    {
        "sample_index": "22",
        "problem_index": "22",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in the diamond ABCD, M and N are respectively AB and CD, and AM = CN, MN and AC intersect at point O. Connect BO. If angle DAC = 28.0, then the degree of angle OBC is ()\nChoices:\nA:28\u00b0\nB:52\u00b0\nC:62\u00b0\nD:72\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in the diamond ABCD, M and N are respectively AB and CD, and AM = CN, MN and AC intersect at point O. Connect BO. If angle DAC = 28.0, then the degree of angle OBC is ()\nChoices:\nA:28\u00b0\nB:52\u00b0\nC:62\u00b0\nD:72\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in the diamond ABCD, M and N are respectively AB and CD, and AM = CN, MN and AC intersect at point O. Connect BO. If angle DAC = 28.0, then the degree of angle OBC is ()\nChoices:\nA:28\u00b0\nB:52\u00b0\nC:62\u00b0\nD:72\u00b0",
        "question_for_eval": "As shown in the figure, in the diamond ABCD, M and N are respectively AB and CD, and AM = CN, MN and AC intersect at point O. Connect BO. If angle DAC = 28.0, then the degree of angle OBC is ()\nChoices:\nA:28\u00b0\nB:52\u00b0\nC:62\u00b0\nD:72\u00b0"
    },
    {
        "sample_index": "23",
        "problem_index": "23",
        "problem_version": "Text Only",
        "question": "As shown in the figure, PA and PB are tangent to circle O at A and B respectively. If angle C = 65.0, then the degree of angle P is ()\nChoices:\nA:65\u00b0\nB:130\u00b0\nC:50\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, PA and PB are tangent to circle O at A and B respectively. If angle C = 65.0, then the degree of angle P is ()\nChoices:\nA:65\u00b0\nB:130\u00b0\nC:50\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, PA and PB are tangent to circle O at A and B respectively. If angle C = 65.0, then the degree of angle P is ()\nChoices:\nA:65\u00b0\nB:130\u00b0\nC:50\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, PA and PB are tangent to circle O at A and B respectively. If angle C = 65.0, then the degree of angle P is ()\nChoices:\nA:65\u00b0\nB:130\u00b0\nC:50\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "24",
        "problem_index": "24",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the line a parallel b and they intersect the line c at a and b respectively, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:150\u00b0\nB:130\u00b0\nC:100\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the line a parallel b and they intersect the line c at a and b respectively, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:150\u00b0\nB:130\u00b0\nC:100\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the line a parallel b and they intersect the line c at a and b respectively, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:150\u00b0\nB:130\u00b0\nC:100\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, the line a parallel b and they intersect the line c at a and b respectively, angle 1 = 50.0, then the degree of angle 2 is ()\nChoices:\nA:150\u00b0\nB:130\u00b0\nC:100\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "25",
        "problem_index": "25",
        "problem_version": "Text Only",
        "question": "As shown in the figure, EF parallel BC, AC bisects angle BAF, angle B = 50.0, then the degree of angle C is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, EF parallel BC, AC bisects angle BAF, angle B = 50.0, then the degree of angle C is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, EF parallel BC, AC bisects angle BAF, angle B = 50.0, then the degree of angle C is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "question_for_eval": "As shown in the figure, EF parallel BC, AC bisects angle BAF, angle B = 50.0, then the degree of angle C is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0"
    },
    {
        "sample_index": "26",
        "problem_index": "26",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in order to measure the height of the school flagpole, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool, and moves the bamboo pole so that the top of the bamboo pole and the shadow of the top of the flag pole fall on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0 , 22.0 from the flagpole, the height of the flagpole is ().\nChoices:\nA:8.8\nB:10\nC:12\nD:14",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in order to measure the height of the school flagpole, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool, and moves the bamboo pole so that the top of the bamboo pole and the shadow of the top of the flag pole fall on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0 , 22.0 from the flagpole, the height of the flagpole is ().\nChoices:\nA:8.8\nB:10\nC:12\nD:14",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in order to measure the height of the school flagpole, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool, and moves the bamboo pole so that the top of the bamboo pole and the shadow of the top of the flag pole fall on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0 , 22.0 from the flagpole, the height of the flagpole is ().\nChoices:\nA:8.8\nB:10\nC:12\nD:14",
        "question_for_eval": "As shown in the figure, in order to measure the height of the school flagpole, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool, and moves the bamboo pole so that the top of the bamboo pole and the shadow of the top of the flag pole fall on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0 , 22.0 from the flagpole, the height of the flagpole is ().\nChoices:\nA:8.8\nB:10\nC:12\nD:14"
    },
    {
        "sample_index": "27",
        "problem_index": "27",
        "problem_version": "Text Only",
        "question": "As shown in the figure, when planting trees on flat ground, the plant spacing (the horizontal distance between two adjacent trees) is required to be 4.0. If trees are planted on a hillside with a slope of 0.75, and the plant spacing is also required to be 4.0, then the slope distance between two adjacent trees is ()\nChoices:\nA:5m\nB:6m\nC:7m\nD:8m",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, when planting trees on flat ground, the plant spacing (the horizontal distance between two adjacent trees) is required to be 4.0. If trees are planted on a hillside with a slope of 0.75, and the plant spacing is also required to be 4.0, then the slope distance between two adjacent trees is ()\nChoices:\nA:5m\nB:6m\nC:7m\nD:8m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, when planting trees on flat ground, the plant spacing (the horizontal distance between two adjacent trees) is required to be 4.0. If trees are planted on a hillside with a slope of 0.75, and the plant spacing is also required to be 4.0, then the slope distance between two adjacent trees is ()\nChoices:\nA:5m\nB:6m\nC:7m\nD:8m",
        "question_for_eval": "As shown in the figure, when planting trees on flat ground, the plant spacing (the horizontal distance between two adjacent trees) is required to be 4.0. If trees are planted on a hillside with a slope of 0.75, and the plant spacing is also required to be 4.0, then the slope distance between two adjacent trees is ()\nChoices:\nA:5m\nB:6m\nC:7m\nD:8m"
    },
    {
        "sample_index": "28",
        "problem_index": "28",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the right triangle ABC and the equilateral triangle ABD are respectively drawn with the line segment AB as the edge, where angle ACB = 90.0. Connect CD, when the length of CD is the largest, the size of angle CAB is ()\nChoices:\nA:75\u00b0\nB:45\u00b0\nC:30\u00b0\nD:15\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the right triangle ABC and the equilateral triangle ABD are respectively drawn with the line segment AB as the edge, where angle ACB = 90.0. Connect CD, when the length of CD is the largest, the size of angle CAB is ()\nChoices:\nA:75\u00b0\nB:45\u00b0\nC:30\u00b0\nD:15\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the right triangle ABC and the equilateral triangle ABD are respectively drawn with the line segment AB as the edge, where angle ACB = 90.0. Connect CD, when the length of CD is the largest, the size of angle CAB is ()\nChoices:\nA:75\u00b0\nB:45\u00b0\nC:30\u00b0\nD:15\u00b0",
        "question_for_eval": "As shown in the figure, the right triangle ABC and the equilateral triangle ABD are respectively drawn with the line segment AB as the edge, where angle ACB = 90.0. Connect CD, when the length of CD is the largest, the size of angle CAB is ()\nChoices:\nA:75\u00b0\nB:45\u00b0\nC:30\u00b0\nD:15\u00b0"
    },
    {
        "sample_index": "29",
        "problem_index": "29",
        "problem_version": "Text Only",
        "question": "As shown in the figure, In the triangle ABC, D is the intersection point of the angular bisector BD and CD of triangle ABC. If angle A = 50.0, then angle D = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:115\u00b0\nD:110\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, In the triangle ABC, D is the intersection point of the angular bisector BD and CD of triangle ABC. If angle A = 50.0, then angle D = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:115\u00b0\nD:110\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, In the triangle ABC, D is the intersection point of the angular bisector BD and CD of triangle ABC. If angle A = 50.0, then angle D = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:115\u00b0\nD:110\u00b0",
        "question_for_eval": "As shown in the figure, In the triangle ABC, D is the intersection point of the angular bisector BD and CD of triangle ABC. If angle A = 50.0, then angle D = ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:115\u00b0\nD:110\u00b0"
    },
    {
        "sample_index": "30",
        "problem_index": "30",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that OA = OB = OC and angle ACB = 30.0, then the size of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:60\u00b0\nD:70\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that OA = OB = OC and angle ACB = 30.0, then the size of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:60\u00b0\nD:70\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that OA = OB = OC and angle ACB = 30.0, then the size of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:60\u00b0\nD:70\u00b0",
        "question_for_eval": "As shown in the figure, it is known that OA = OB = OC and angle ACB = 30.0, then the size of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:60\u00b0\nD:70\u00b0"
    },
    {
        "sample_index": "31",
        "problem_index": "31",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line a parallel b, the point B is on the straight line b, and AB perpendicular BC, angle 2 = 65.0, then the degree of angle 1 is ()\nChoices:\nA:65\u00b0\nB:25\u00b0\nC:35\u00b0\nD:45\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line a parallel b, the point B is on the straight line b, and AB perpendicular BC, angle 2 = 65.0, then the degree of angle 1 is ()\nChoices:\nA:65\u00b0\nB:25\u00b0\nC:35\u00b0\nD:45\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line a parallel b, the point B is on the straight line b, and AB perpendicular BC, angle 2 = 65.0, then the degree of angle 1 is ()\nChoices:\nA:65\u00b0\nB:25\u00b0\nC:35\u00b0\nD:45\u00b0",
        "question_for_eval": "As shown in the figure, the straight line a parallel b, the point B is on the straight line b, and AB perpendicular BC, angle 2 = 65.0, then the degree of angle 1 is ()\nChoices:\nA:65\u00b0\nB:25\u00b0\nC:35\u00b0\nD:45\u00b0"
    },
    {
        "sample_index": "32",
        "problem_index": "32",
        "problem_version": "Text Only",
        "question": "Circle I is the inscribed circle of triangle ABC, D, E, F are 3 tangent points, if angle DEF = 52.0, then the degree of angle A is ()\nChoices:\nA:68\u00b0\nB:52\u00b0\nC:76\u00b0\nD:38\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Circle I is the inscribed circle of triangle ABC, D, E, F are 3 tangent points, if angle DEF = 52.0, then the degree of angle A is ()\nChoices:\nA:68\u00b0\nB:52\u00b0\nC:76\u00b0\nD:38\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Circle I is the inscribed circle of triangle ABC, D, E, F are 3 tangent points, if angle DEF = 52.0, then the degree of angle A is ()\nChoices:\nA:68\u00b0\nB:52\u00b0\nC:76\u00b0\nD:38\u00b0",
        "question_for_eval": "Circle I is the inscribed circle of triangle ABC, D, E, F are 3 tangent points, if angle DEF = 52.0, then the degree of angle A is ()\nChoices:\nA:68\u00b0\nB:52\u00b0\nC:76\u00b0\nD:38\u00b0"
    },
    {
        "sample_index": "33",
        "problem_index": "33",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line AB parallel CD, angle 1 = 136.0, angle E is a right angle, then angle C is equal to ()\nChoices:\nA:42\u00b0\nB:44\u00b0\nC:46\u00b0\nD:48\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line AB parallel CD, angle 1 = 136.0, angle E is a right angle, then angle C is equal to ()\nChoices:\nA:42\u00b0\nB:44\u00b0\nC:46\u00b0\nD:48\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line AB parallel CD, angle 1 = 136.0, angle E is a right angle, then angle C is equal to ()\nChoices:\nA:42\u00b0\nB:44\u00b0\nC:46\u00b0\nD:48\u00b0",
        "question_for_eval": "As shown in the figure, the straight line AB parallel CD, angle 1 = 136.0, angle E is a right angle, then angle C is equal to ()\nChoices:\nA:42\u00b0\nB:44\u00b0\nC:46\u00b0\nD:48\u00b0"
    },
    {
        "sample_index": "34",
        "problem_index": "34",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight lines AB and CD are intercepted by the straight line EF. If AB parallel CD, angle 1 = 100.0, then the size of angle 2 is ()\nChoices:\nA:10\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight lines AB and CD are intercepted by the straight line EF. If AB parallel CD, angle 1 = 100.0, then the size of angle 2 is ()\nChoices:\nA:10\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight lines AB and CD are intercepted by the straight line EF. If AB parallel CD, angle 1 = 100.0, then the size of angle 2 is ()\nChoices:\nA:10\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, the straight lines AB and CD are intercepted by the straight line EF. If AB parallel CD, angle 1 = 100.0, then the size of angle 2 is ()\nChoices:\nA:10\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "35",
        "problem_index": "35",
        "problem_version": "Text Only",
        "question": "As shown in the figure: AB parallel DE, angle B = 30.0, angle C = 110.0, the degree of angle D is ()\nChoices:\nA:115\u00b0\nB:120\u00b0\nC:100\u00b0\nD:80\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure: AB parallel DE, angle B = 30.0, angle C = 110.0, the degree of angle D is ()\nChoices:\nA:115\u00b0\nB:120\u00b0\nC:100\u00b0\nD:80\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure: AB parallel DE, angle B = 30.0, angle C = 110.0, the degree of angle D is ()\nChoices:\nA:115\u00b0\nB:120\u00b0\nC:100\u00b0\nD:80\u00b0",
        "question_for_eval": "As shown in the figure: AB parallel DE, angle B = 30.0, angle C = 110.0, the degree of angle D is ()\nChoices:\nA:115\u00b0\nB:120\u00b0\nC:100\u00b0\nD:80\u00b0"
    },
    {
        "sample_index": "36",
        "problem_index": "36",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, point C is on circle O, passing point C to draw the tangent of circle O and it intersects the extended line of AB at point D. Connect AC. If angle D = 50.0, then the degree of angle A is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:.40\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, point C is on circle O, passing point C to draw the tangent of circle O and it intersects the extended line of AB at point D. Connect AC. If angle D = 50.0, then the degree of angle A is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:.40\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, point C is on circle O, passing point C to draw the tangent of circle O and it intersects the extended line of AB at point D. Connect AC. If angle D = 50.0, then the degree of angle A is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:.40\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, point C is on circle O, passing point C to draw the tangent of circle O and it intersects the extended line of AB at point D. Connect AC. If angle D = 50.0, then the degree of angle A is ()\nChoices:\nA:20\u00b0\nB:25\u00b0\nC:.40\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "37",
        "problem_index": "37",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, CP intersects AB at O, AO = PO, if angle C = 50.0, then the degree of angle A is ()\nChoices:\nA:25\u00b0\nB:35\u00b0\nC:15\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, CP intersects AB at O, AO = PO, if angle C = 50.0, then the degree of angle A is ()\nChoices:\nA:25\u00b0\nB:35\u00b0\nC:15\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, CP intersects AB at O, AO = PO, if angle C = 50.0, then the degree of angle A is ()\nChoices:\nA:25\u00b0\nB:35\u00b0\nC:15\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, CP intersects AB at O, AO = PO, if angle C = 50.0, then the degree of angle A is ()\nChoices:\nA:25\u00b0\nB:35\u00b0\nC:15\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "38",
        "problem_index": "38",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC, AB = AC, passing point A to draw AD parallel BC. If angle 1 = 70.0, then the size of angle BAC is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:.70\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC, AB = AC, passing point A to draw AD parallel BC. If angle 1 = 70.0, then the size of angle BAC is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:.70\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC, AB = AC, passing point A to draw AD parallel BC. If angle 1 = 70.0, then the size of angle BAC is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:.70\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, in triangle ABC, AB = AC, passing point A to draw AD parallel BC. If angle 1 = 70.0, then the size of angle BAC is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:.70\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "39",
        "problem_index": "39",
        "problem_version": "Text Only",
        "question": "Fold a rectangular piece of paper with equal width as shown in the figure. If angle 1 = 140.0, then the degree of angle 2 is ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:140\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Fold a rectangular piece of paper with equal width as shown in the figure. If angle 1 = 140.0, then the degree of angle 2 is ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:140\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Fold a rectangular piece of paper with equal width as shown in the figure. If angle 1 = 140.0, then the degree of angle 2 is ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:140\u00b0",
        "question_for_eval": "Fold a rectangular piece of paper with equal width as shown in the figure. If angle 1 = 140.0, then the degree of angle 2 is ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:140\u00b0"
    },
    {
        "sample_index": "40",
        "problem_index": "40",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that the straight lines a and b are intercepted by the straight line c, a parallel b, angle 1 = 50.0, then angle 2 = ()\nChoices:\nA:50\u00b0\nB:130\u00b0\nC:40\u00b0\nD:60\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that the straight lines a and b are intercepted by the straight line c, a parallel b, angle 1 = 50.0, then angle 2 = ()\nChoices:\nA:50\u00b0\nB:130\u00b0\nC:40\u00b0\nD:60\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that the straight lines a and b are intercepted by the straight line c, a parallel b, angle 1 = 50.0, then angle 2 = ()\nChoices:\nA:50\u00b0\nB:130\u00b0\nC:40\u00b0\nD:60\u00b0",
        "question_for_eval": "As shown in the figure, it is known that the straight lines a and b are intercepted by the straight line c, a parallel b, angle 1 = 50.0, then angle 2 = ()\nChoices:\nA:50\u00b0\nB:130\u00b0\nC:40\u00b0\nD:60\u00b0"
    },
    {
        "sample_index": "41",
        "problem_index": "41",
        "problem_version": "Text Only",
        "question": "The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 100.0, angle 2 = 100.0, angle 3 = 125.0, then angle 4 is equal to ()\nChoices:\nA:80\u00b0\nB:65\u00b0\nC:60\u00b0\nD:55\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 100.0, angle 2 = 100.0, angle 3 = 125.0, then angle 4 is equal to ()\nChoices:\nA:80\u00b0\nB:65\u00b0\nC:60\u00b0\nD:55\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 100.0, angle 2 = 100.0, angle 3 = 125.0, then angle 4 is equal to ()\nChoices:\nA:80\u00b0\nB:65\u00b0\nC:60\u00b0\nD:55\u00b0",
        "question_for_eval": "The positions of straight lines a, b, c, and d are shown in the figure. If angle 1 = 100.0, angle 2 = 100.0, angle 3 = 125.0, then angle 4 is equal to ()\nChoices:\nA:80\u00b0\nB:65\u00b0\nC:60\u00b0\nD:55\u00b0"
    },
    {
        "sample_index": "42",
        "problem_index": "42",
        "problem_version": "Text Only",
        "question": "The figure is a schematic diagram of a kite stand made by Xiao Liu. It is known that BC parallel PQ, AB:AP = 2.0:5.0, AQ = 20.0, then the length of CQ is ()\nChoices:\nA:8cm\nB:12cm\nC:30cm\nD:50cm",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure is a schematic diagram of a kite stand made by Xiao Liu. It is known that BC parallel PQ, AB:AP = 2.0:5.0, AQ = 20.0, then the length of CQ is ()\nChoices:\nA:8cm\nB:12cm\nC:30cm\nD:50cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure is a schematic diagram of a kite stand made by Xiao Liu. It is known that BC parallel PQ, AB:AP = 2.0:5.0, AQ = 20.0, then the length of CQ is ()\nChoices:\nA:8cm\nB:12cm\nC:30cm\nD:50cm",
        "question_for_eval": "The figure is a schematic diagram of a kite stand made by Xiao Liu. It is known that BC parallel PQ, AB:AP = 2.0:5.0, AQ = 20.0, then the length of CQ is ()\nChoices:\nA:8cm\nB:12cm\nC:30cm\nD:50cm"
    },
    {
        "sample_index": "43",
        "problem_index": "43",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ODC is the figure obtained by rotating triangle OAB clockwise around point O by 30.0. If point D happens to fall on AB, and the degree of angle AOC is 100.0, then the degree of angle DOB is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:38\u00b0\nD:15\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ODC is the figure obtained by rotating triangle OAB clockwise around point O by 30.0. If point D happens to fall on AB, and the degree of angle AOC is 100.0, then the degree of angle DOB is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:38\u00b0\nD:15\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ODC is the figure obtained by rotating triangle OAB clockwise around point O by 30.0. If point D happens to fall on AB, and the degree of angle AOC is 100.0, then the degree of angle DOB is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:38\u00b0\nD:15\u00b0",
        "question_for_eval": "As shown in the figure, triangle ODC is the figure obtained by rotating triangle OAB clockwise around point O by 30.0. If point D happens to fall on AB, and the degree of angle AOC is 100.0, then the degree of angle DOB is ()\nChoices:\nA:40\u00b0\nB:30\u00b0\nC:38\u00b0\nD:15\u00b0"
    },
    {
        "sample_index": "44",
        "problem_index": "44",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the two street lamps A and B are separated by 30.0. One night, when Xiaogang went straight 25.0 from the bottom of street lamp A to the bottom of street lamp B, he found that the top of his figure just touched the bottom of street lamp B. It is known that Xiaogang's height is 1.5, then the height of the street lamp is ()\nChoices:\nA:9\u7c73\nB:8\u7c73\nC:7\u7c73\nD:6\u7c73",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the two street lamps A and B are separated by 30.0. One night, when Xiaogang went straight 25.0 from the bottom of street lamp A to the bottom of street lamp B, he found that the top of his figure just touched the bottom of street lamp B. It is known that Xiaogang's height is 1.5, then the height of the street lamp is ()\nChoices:\nA:9\u7c73\nB:8\u7c73\nC:7\u7c73\nD:6\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the two street lamps A and B are separated by 30.0. One night, when Xiaogang went straight 25.0 from the bottom of street lamp A to the bottom of street lamp B, he found that the top of his figure just touched the bottom of street lamp B. It is known that Xiaogang's height is 1.5, then the height of the street lamp is ()\nChoices:\nA:9\u7c73\nB:8\u7c73\nC:7\u7c73\nD:6\u7c73",
        "question_for_eval": "As shown in the figure, the two street lamps A and B are separated by 30.0. One night, when Xiaogang went straight 25.0 from the bottom of street lamp A to the bottom of street lamp B, he found that the top of his figure just touched the bottom of street lamp B. It is known that Xiaogang's height is 1.5, then the height of the street lamp is ()\nChoices:\nA:9\u7c73\nB:8\u7c73\nC:7\u7c73\nD:6\u7c73"
    },
    {
        "sample_index": "45",
        "problem_index": "45",
        "problem_version": "Text Only",
        "question": "As shown in the figure, C is a point on circle O, O is the center of the circle, if angle C = 35.0, then the degree of angle AOB is ()\nChoices:\nA:35\u00b0\nB:70\u00b0\nC:105\u00b0\nD:150\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, C is a point on circle O, O is the center of the circle, if angle C = 35.0, then the degree of angle AOB is ()\nChoices:\nA:35\u00b0\nB:70\u00b0\nC:105\u00b0\nD:150\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, C is a point on circle O, O is the center of the circle, if angle C = 35.0, then the degree of angle AOB is ()\nChoices:\nA:35\u00b0\nB:70\u00b0\nC:105\u00b0\nD:150\u00b0",
        "question_for_eval": "As shown in the figure, C is a point on circle O, O is the center of the circle, if angle C = 35.0, then the degree of angle AOB is ()\nChoices:\nA:35\u00b0\nB:70\u00b0\nC:105\u00b0\nD:150\u00b0"
    },
    {
        "sample_index": "46",
        "problem_index": "46",
        "problem_version": "Text Only",
        "question": "As shown in the figure, if AB parallel CD, angle A = 70.0, then the degree of angle 1 is ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:70\u00b0\nD:110\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, if AB parallel CD, angle A = 70.0, then the degree of angle 1 is ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:70\u00b0\nD:110\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, if AB parallel CD, angle A = 70.0, then the degree of angle 1 is ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:70\u00b0\nD:110\u00b0",
        "question_for_eval": "As shown in the figure, if AB parallel CD, angle A = 70.0, then the degree of angle 1 is ()\nChoices:\nA:20\u00b0\nB:30\u00b0\nC:70\u00b0\nD:110\u00b0"
    },
    {
        "sample_index": "47",
        "problem_index": "47",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line AB parallel CD, angle C = 44.0, angle E is a right angle, then angle 1 is equal to ()\nChoices:\nA:132\u00b0\nB:134\u00b0\nC:136\u00b0\nD:138\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line AB parallel CD, angle C = 44.0, angle E is a right angle, then angle 1 is equal to ()\nChoices:\nA:132\u00b0\nB:134\u00b0\nC:136\u00b0\nD:138\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line AB parallel CD, angle C = 44.0, angle E is a right angle, then angle 1 is equal to ()\nChoices:\nA:132\u00b0\nB:134\u00b0\nC:136\u00b0\nD:138\u00b0",
        "question_for_eval": "As shown in the figure, the straight line AB parallel CD, angle C = 44.0, angle E is a right angle, then angle 1 is equal to ()\nChoices:\nA:132\u00b0\nB:134\u00b0\nC:136\u00b0\nD:138\u00b0"
    },
    {
        "sample_index": "48",
        "problem_index": "48",
        "problem_version": "Text Only",
        "question": "As shown in the figure, A, B, C are any three points on circle O, if angle BOC = 100.0, then the degree of angle BAC is ()\nChoices:\nA:50\u00b0\nB:80\u00b0\nC:100\u00b0\nD:130\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, A, B, C are any three points on circle O, if angle BOC = 100.0, then the degree of angle BAC is ()\nChoices:\nA:50\u00b0\nB:80\u00b0\nC:100\u00b0\nD:130\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, A, B, C are any three points on circle O, if angle BOC = 100.0, then the degree of angle BAC is ()\nChoices:\nA:50\u00b0\nB:80\u00b0\nC:100\u00b0\nD:130\u00b0",
        "question_for_eval": "As shown in the figure, A, B, C are any three points on circle O, if angle BOC = 100.0, then the degree of angle BAC is ()\nChoices:\nA:50\u00b0\nB:80\u00b0\nC:100\u00b0\nD:130\u00b0"
    },
    {
        "sample_index": "49",
        "problem_index": "49",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in the inscribed pentagon ABCDE of circle O, angle CAD = 35.0, angle AED = 115.0, then the degree of angle B is ()\nChoices:\nA:50\u00b0\nB:75\u00b0\nC:80\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in the inscribed pentagon ABCDE of circle O, angle CAD = 35.0, angle AED = 115.0, then the degree of angle B is ()\nChoices:\nA:50\u00b0\nB:75\u00b0\nC:80\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in the inscribed pentagon ABCDE of circle O, angle CAD = 35.0, angle AED = 115.0, then the degree of angle B is ()\nChoices:\nA:50\u00b0\nB:75\u00b0\nC:80\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, in the inscribed pentagon ABCDE of circle O, angle CAD = 35.0, angle AED = 115.0, then the degree of angle B is ()\nChoices:\nA:50\u00b0\nB:75\u00b0\nC:80\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "50",
        "problem_index": "50",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight lines AB and CD intersect at point O, EO perpendicular  AB, and the foot of perpendicular is point O, angle BOD = 50.0, then angle COE = ()\nChoices:\nA:30\u00b0\nB:140\u00b0\nC:50\u00b0\nD:60\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight lines AB and CD intersect at point O, EO perpendicular  AB, and the foot of perpendicular is point O, angle BOD = 50.0, then angle COE = ()\nChoices:\nA:30\u00b0\nB:140\u00b0\nC:50\u00b0\nD:60\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight lines AB and CD intersect at point O, EO perpendicular  AB, and the foot of perpendicular is point O, angle BOD = 50.0, then angle COE = ()\nChoices:\nA:30\u00b0\nB:140\u00b0\nC:50\u00b0\nD:60\u00b0",
        "question_for_eval": "As shown in the figure, the straight lines AB and CD intersect at point O, EO perpendicular  AB, and the foot of perpendicular is point O, angle BOD = 50.0, then angle COE = ()\nChoices:\nA:30\u00b0\nB:140\u00b0\nC:50\u00b0\nD:60\u00b0"
    },
    {
        "sample_index": "51",
        "problem_index": "51",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the points B, E, C, and F are on the same straight line, triangle ABC congruent  triangle DEF, angle B = 45.0, angle F = 65.0, then the degree of angle COE is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the points B, E, C, and F are on the same straight line, triangle ABC congruent  triangle DEF, angle B = 45.0, angle F = 65.0, then the degree of angle COE is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the points B, E, C, and F are on the same straight line, triangle ABC congruent  triangle DEF, angle B = 45.0, angle F = 65.0, then the degree of angle COE is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, the points B, E, C, and F are on the same straight line, triangle ABC congruent  triangle DEF, angle B = 45.0, angle F = 65.0, then the degree of angle COE is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "52",
        "problem_index": "52",
        "problem_version": "Text Only",
        "question": "As shown in the figure, put the two vertices of a right triangle plate with 45.0 angles on the opposite edges of the ruler. If angle 1 = 27.5, then angle 2 is equal to ()\nChoices:\nA:32.5\u00b0\nB:22.5\u00b0\nC:20.5\u00b0\nD:17.5\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, put the two vertices of a right triangle plate with 45.0 angles on the opposite edges of the ruler. If angle 1 = 27.5, then angle 2 is equal to ()\nChoices:\nA:32.5\u00b0\nB:22.5\u00b0\nC:20.5\u00b0\nD:17.5\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, put the two vertices of a right triangle plate with 45.0 angles on the opposite edges of the ruler. If angle 1 = 27.5, then angle 2 is equal to ()\nChoices:\nA:32.5\u00b0\nB:22.5\u00b0\nC:20.5\u00b0\nD:17.5\u00b0",
        "question_for_eval": "As shown in the figure, put the two vertices of a right triangle plate with 45.0 angles on the opposite edges of the ruler. If angle 1 = 27.5, then angle 2 is equal to ()\nChoices:\nA:32.5\u00b0\nB:22.5\u00b0\nC:20.5\u00b0\nD:17.5\u00b0"
    },
    {
        "sample_index": "53",
        "problem_index": "53",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line a parallel  b, the straight line c intersects a and b, angle 1 = 55.0, then angle 2 = ()\nChoices:\nA:55\u00b0\nB:35\u00b0\nC:125\u00b0\nD:65\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line a parallel  b, the straight line c intersects a and b, angle 1 = 55.0, then angle 2 = ()\nChoices:\nA:55\u00b0\nB:35\u00b0\nC:125\u00b0\nD:65\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line a parallel  b, the straight line c intersects a and b, angle 1 = 55.0, then angle 2 = ()\nChoices:\nA:55\u00b0\nB:35\u00b0\nC:125\u00b0\nD:65\u00b0",
        "question_for_eval": "As shown in the figure, the straight line a parallel  b, the straight line c intersects a and b, angle 1 = 55.0, then angle 2 = ()\nChoices:\nA:55\u00b0\nB:35\u00b0\nC:125\u00b0\nD:65\u00b0"
    },
    {
        "sample_index": "54",
        "problem_index": "54",
        "problem_version": "Text Only",
        "question": "Place a ruler and a triangular plate as shown in the figure, angle 1 = 40.0, then the degree of angle 2 is ()\nChoices:\nA:130\u00b0\nB:140\u00b0\nC:120\u00b0\nD:125\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Place a ruler and a triangular plate as shown in the figure, angle 1 = 40.0, then the degree of angle 2 is ()\nChoices:\nA:130\u00b0\nB:140\u00b0\nC:120\u00b0\nD:125\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Place a ruler and a triangular plate as shown in the figure, angle 1 = 40.0, then the degree of angle 2 is ()\nChoices:\nA:130\u00b0\nB:140\u00b0\nC:120\u00b0\nD:125\u00b0",
        "question_for_eval": "Place a ruler and a triangular plate as shown in the figure, angle 1 = 40.0, then the degree of angle 2 is ()\nChoices:\nA:130\u00b0\nB:140\u00b0\nC:120\u00b0\nD:125\u00b0"
    },
    {
        "sample_index": "55",
        "problem_index": "55",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight lines AB and CD intersect at point O, and the radial OM bisects angle AOC, ON perpendicular  OM. If angle AOC = 70.0, then the degree of angle CON is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight lines AB and CD intersect at point O, and the radial OM bisects angle AOC, ON perpendicular  OM. If angle AOC = 70.0, then the degree of angle CON is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight lines AB and CD intersect at point O, and the radial OM bisects angle AOC, ON perpendicular  OM. If angle AOC = 70.0, then the degree of angle CON is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0",
        "question_for_eval": "As shown in the figure, the straight lines AB and CD intersect at point O, and the radial OM bisects angle AOC, ON perpendicular  OM. If angle AOC = 70.0, then the degree of angle CON is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0"
    },
    {
        "sample_index": "56",
        "problem_index": "56",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the diameter CD of circle O crosses the midpoint G of chord EF, angle DCF = 20.0, then angle EOD is equal to ()\nChoices:\nA:10\u00b0\nB:20\u00b0\nC:40\u00b0\nD:80\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the diameter CD of circle O crosses the midpoint G of chord EF, angle DCF = 20.0, then angle EOD is equal to ()\nChoices:\nA:10\u00b0\nB:20\u00b0\nC:40\u00b0\nD:80\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the diameter CD of circle O crosses the midpoint G of chord EF, angle DCF = 20.0, then angle EOD is equal to ()\nChoices:\nA:10\u00b0\nB:20\u00b0\nC:40\u00b0\nD:80\u00b0",
        "question_for_eval": "As shown in the figure, the diameter CD of circle O crosses the midpoint G of chord EF, angle DCF = 20.0, then angle EOD is equal to ()\nChoices:\nA:10\u00b0\nB:20\u00b0\nC:40\u00b0\nD:80\u00b0"
    },
    {
        "sample_index": "57",
        "problem_index": "57",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is parallel to CD, if angle B = 20.0, then angle C is ()\nChoices:\nA:40\u00b0\nB:20\u00b0\nC:60\u00b0\nD:70\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is parallel to CD, if angle B = 20.0, then angle C is ()\nChoices:\nA:40\u00b0\nB:20\u00b0\nC:60\u00b0\nD:70\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is parallel to CD, if angle B = 20.0, then angle C is ()\nChoices:\nA:40\u00b0\nB:20\u00b0\nC:60\u00b0\nD:70\u00b0",
        "question_for_eval": "As shown in the figure, AB is parallel to CD, if angle B = 20.0, then angle C is ()\nChoices:\nA:40\u00b0\nB:20\u00b0\nC:60\u00b0\nD:70\u00b0"
    },
    {
        "sample_index": "58",
        "problem_index": "58",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, angle CED = 90.0, angle AEC = 35.0, then the size of angle D is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, angle CED = 90.0, angle AEC = 35.0, then the size of angle D is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, angle CED = 90.0, angle AEC = 35.0, then the size of angle D is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, angle CED = 90.0, angle AEC = 35.0, then the size of angle D is ()\nChoices:\nA:65\u00b0\nB:55\u00b0\nC:45\u00b0\nD:35\u00b0"
    },
    {
        "sample_index": "59",
        "problem_index": "59",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, AD bisects angle BAC, and angle C = 80.0, then the degree of angle D is ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, AD bisects angle BAC, and angle C = 80.0, then the degree of angle D is ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, AD bisects angle BAC, and angle C = 80.0, then the degree of angle D is ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, AD bisects angle BAC, and angle C = 80.0, then the degree of angle D is ()\nChoices:\nA:50\u00b0\nB:60\u00b0\nC:70\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "60",
        "problem_index": "60",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, if angle 2 = 135.0, then the degree of angle 1 is ()\nChoices:\nA:30\u00b0\nB:45\u00b0\nC:60\u00b0\nD:75\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, if angle 2 = 135.0, then the degree of angle 1 is ()\nChoices:\nA:30\u00b0\nB:45\u00b0\nC:60\u00b0\nD:75\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, if angle 2 = 135.0, then the degree of angle 1 is ()\nChoices:\nA:30\u00b0\nB:45\u00b0\nC:60\u00b0\nD:75\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, if angle 2 = 135.0, then the degree of angle 1 is ()\nChoices:\nA:30\u00b0\nB:45\u00b0\nC:60\u00b0\nD:75\u00b0"
    },
    {
        "sample_index": "61",
        "problem_index": "61",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, point E is on BC, and CD = CE, angle D = 74.0, then the degree of angle B is ()\nChoices:\nA:74\u00b0\nB:32\u00b0\nC:22\u00b0\nD:16\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, point E is on BC, and CD = CE, angle D = 74.0, then the degree of angle B is ()\nChoices:\nA:74\u00b0\nB:32\u00b0\nC:22\u00b0\nD:16\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, point E is on BC, and CD = CE, angle D = 74.0, then the degree of angle B is ()\nChoices:\nA:74\u00b0\nB:32\u00b0\nC:22\u00b0\nD:16\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, point E is on BC, and CD = CE, angle D = 74.0, then the degree of angle B is ()\nChoices:\nA:74\u00b0\nB:32\u00b0\nC:22\u00b0\nD:16\u00b0"
    },
    {
        "sample_index": "62",
        "problem_index": "62",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, point E is on the extended line of CA. If angle BAE = 40.0, then the size of angle ACD is ()\nChoices:\nA:150\u00b0\nB:140\u00b0\nC:130\u00b0\nD:120\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, point E is on the extended line of CA. If angle BAE = 40.0, then the size of angle ACD is ()\nChoices:\nA:150\u00b0\nB:140\u00b0\nC:130\u00b0\nD:120\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, point E is on the extended line of CA. If angle BAE = 40.0, then the size of angle ACD is ()\nChoices:\nA:150\u00b0\nB:140\u00b0\nC:130\u00b0\nD:120\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, point E is on the extended line of CA. If angle BAE = 40.0, then the size of angle ACD is ()\nChoices:\nA:150\u00b0\nB:140\u00b0\nC:130\u00b0\nD:120\u00b0"
    },
    {
        "sample_index": "63",
        "problem_index": "63",
        "problem_version": "Text Only",
        "question": "As shown in the figure, use the benchmark BE to measure the height of the tree CD. EB and DC are perpendicular to AC, If the length of the benchmark BE is 2.0, AB = 3.0, AC = 9.0, and the points A, E, and D are on a straight line, then the tree CD is ()\nChoices:\nA:6\u7c73\nB:7.5\u7c73\nC:8\u7c73\nD:8.5\u7c73",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, use the benchmark BE to measure the height of the tree CD. EB and DC are perpendicular to AC, If the length of the benchmark BE is 2.0, AB = 3.0, AC = 9.0, and the points A, E, and D are on a straight line, then the tree CD is ()\nChoices:\nA:6\u7c73\nB:7.5\u7c73\nC:8\u7c73\nD:8.5\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, use the benchmark BE to measure the height of the tree CD. EB and DC are perpendicular to AC, If the length of the benchmark BE is 2.0, AB = 3.0, AC = 9.0, and the points A, E, and D are on a straight line, then the tree CD is ()\nChoices:\nA:6\u7c73\nB:7.5\u7c73\nC:8\u7c73\nD:8.5\u7c73",
        "question_for_eval": "As shown in the figure, use the benchmark BE to measure the height of the tree CD. EB and DC are perpendicular to AC, If the length of the benchmark BE is 2.0, AB = 3.0, AC = 9.0, and the points A, E, and D are on a straight line, then the tree CD is ()\nChoices:\nA:6\u7c73\nB:7.5\u7c73\nC:8\u7c73\nD:8.5\u7c73"
    },
    {
        "sample_index": "64",
        "problem_index": "64",
        "problem_version": "Text Only",
        "question": "After filling some oil in a cylindrical oil tank with a diameter of 200.0, the cross section is shown in the figure. If the width of the oil surface AB = 160.0, the maximum depth of oil is ()\nChoices:\nA:40cm\nB:60cm\nC:80cm\nD:100cm",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: After filling some oil in a cylindrical oil tank with a diameter of 200.0, the cross section is shown in the figure. If the width of the oil surface AB = 160.0, the maximum depth of oil is ()\nChoices:\nA:40cm\nB:60cm\nC:80cm\nD:100cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: After filling some oil in a cylindrical oil tank with a diameter of 200.0, the cross section is shown in the figure. If the width of the oil surface AB = 160.0, the maximum depth of oil is ()\nChoices:\nA:40cm\nB:60cm\nC:80cm\nD:100cm",
        "question_for_eval": "After filling some oil in a cylindrical oil tank with a diameter of 200.0, the cross section is shown in the figure. If the width of the oil surface AB = 160.0, the maximum depth of oil is ()\nChoices:\nA:40cm\nB:60cm\nC:80cm\nD:100cm"
    },
    {
        "sample_index": "65",
        "problem_index": "65",
        "problem_version": "Text Only",
        "question": "As shown in the figure, angle 1 = angle 2, angle 4 = 30.0, then angle 3 is equal to ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:145\u00b0\nD:150\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, angle 1 = angle 2, angle 4 = 30.0, then angle 3 is equal to ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:145\u00b0\nD:150\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, angle 1 = angle 2, angle 4 = 30.0, then angle 3 is equal to ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:145\u00b0\nD:150\u00b0",
        "question_for_eval": "As shown in the figure, angle 1 = angle 2, angle 4 = 30.0, then angle 3 is equal to ()\nChoices:\nA:120\u00b0\nB:130\u00b0\nC:145\u00b0\nD:150\u00b0"
    },
    {
        "sample_index": "66",
        "problem_index": "66",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, angle B = 20.0, angle D = 60.0, then the degree of angle BED is ()\nChoices:\nA:40\u00b0\nB:80\u00b0\nC:90\u00b0\nD:l00\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, angle B = 20.0, angle D = 60.0, then the degree of angle BED is ()\nChoices:\nA:40\u00b0\nB:80\u00b0\nC:90\u00b0\nD:l00\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, angle B = 20.0, angle D = 60.0, then the degree of angle BED is ()\nChoices:\nA:40\u00b0\nB:80\u00b0\nC:90\u00b0\nD:l00\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, angle B = 20.0, angle D = 60.0, then the degree of angle BED is ()\nChoices:\nA:40\u00b0\nB:80\u00b0\nC:90\u00b0\nD:l00\u00b0"
    },
    {
        "sample_index": "67",
        "problem_index": "67",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line AB parallel CD, AE bisects angle CAB, angle ACD = 40.0, then the degree of angle AEC is ()\nChoices:\nA:40\u00b0\nB:70\u00b0\nC:80\u00b0\nD:140\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line AB parallel CD, AE bisects angle CAB, angle ACD = 40.0, then the degree of angle AEC is ()\nChoices:\nA:40\u00b0\nB:70\u00b0\nC:80\u00b0\nD:140\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line AB parallel CD, AE bisects angle CAB, angle ACD = 40.0, then the degree of angle AEC is ()\nChoices:\nA:40\u00b0\nB:70\u00b0\nC:80\u00b0\nD:140\u00b0",
        "question_for_eval": "As shown in the figure, the straight line AB parallel CD, AE bisects angle CAB, angle ACD = 40.0, then the degree of angle AEC is ()\nChoices:\nA:40\u00b0\nB:70\u00b0\nC:80\u00b0\nD:140\u00b0"
    },
    {
        "sample_index": "68",
        "problem_index": "68",
        "problem_version": "Text Only",
        "question": "Xuan Xuan and Kai Kai are in the same mathematics study group. In a math activity class, they each used a square piece of paper with a side length of 12.0 to make a pair of jigsaw puzzles, and cooperated to design the work shown in the picture. Help them calculate the sum of the area of the three figures circled in the figure, it is ()\nChoices:\nA:12cm\nB:24cm\nC:36cm\nD:48cm",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Xuan Xuan and Kai Kai are in the same mathematics study group. In a math activity class, they each used a square piece of paper with a side length of 12.0 to make a pair of jigsaw puzzles, and cooperated to design the work shown in the picture. Help them calculate the sum of the area of the three figures circled in the figure, it is ()\nChoices:\nA:12cm\nB:24cm\nC:36cm\nD:48cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Xuan Xuan and Kai Kai are in the same mathematics study group. In a math activity class, they each used a square piece of paper with a side length of 12.0 to make a pair of jigsaw puzzles, and cooperated to design the work shown in the picture. Help them calculate the sum of the area of the three figures circled in the figure, it is ()\nChoices:\nA:12cm\nB:24cm\nC:36cm\nD:48cm",
        "question_for_eval": "Xuan Xuan and Kai Kai are in the same mathematics study group. In a math activity class, they each used a square piece of paper with a side length of 12.0 to make a pair of jigsaw puzzles, and cooperated to design the work shown in the picture. Help them calculate the sum of the area of the three figures circled in the figure, it is ()\nChoices:\nA:12cm\nB:24cm\nC:36cm\nD:48cm"
    },
    {
        "sample_index": "69",
        "problem_index": "69",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line a parallel b, angle 2 = 35.0, angle 3 = 40.0, then the degree of angle 1 is ()\nChoices:\nA:75\u00b0\nB:105\u00b0\nC:140\u00b0\nD:145\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line a parallel b, angle 2 = 35.0, angle 3 = 40.0, then the degree of angle 1 is ()\nChoices:\nA:75\u00b0\nB:105\u00b0\nC:140\u00b0\nD:145\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line a parallel b, angle 2 = 35.0, angle 3 = 40.0, then the degree of angle 1 is ()\nChoices:\nA:75\u00b0\nB:105\u00b0\nC:140\u00b0\nD:145\u00b0",
        "question_for_eval": "As shown in the figure, the straight line a parallel b, angle 2 = 35.0, angle 3 = 40.0, then the degree of angle 1 is ()\nChoices:\nA:75\u00b0\nB:105\u00b0\nC:140\u00b0\nD:145\u00b0"
    },
    {
        "sample_index": "70",
        "problem_index": "70",
        "problem_version": "Text Only",
        "question": "As shown in the figure, BD is the angular bisector of triangle ABC, AE perpendicular BD, and the foot of perpendicular is F. If angle ABC = 35.0, angle C = 50.0, then the degree of angle CDE is ()\nChoices:\nA:35\u00b0\nB:40\u00b0\nC:45\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, BD is the angular bisector of triangle ABC, AE perpendicular BD, and the foot of perpendicular is F. If angle ABC = 35.0, angle C = 50.0, then the degree of angle CDE is ()\nChoices:\nA:35\u00b0\nB:40\u00b0\nC:45\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, BD is the angular bisector of triangle ABC, AE perpendicular BD, and the foot of perpendicular is F. If angle ABC = 35.0, angle C = 50.0, then the degree of angle CDE is ()\nChoices:\nA:35\u00b0\nB:40\u00b0\nC:45\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, BD is the angular bisector of triangle ABC, AE perpendicular BD, and the foot of perpendicular is F. If angle ABC = 35.0, angle C = 50.0, then the degree of angle CDE is ()\nChoices:\nA:35\u00b0\nB:40\u00b0\nC:45\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "71",
        "problem_index": "71",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line AD parallel BC, if angle 1 = 42.0, angle BAC = 78.0, then the degree of angle 2 is ()\nChoices:\nA:42\u00b0\nB:50\u00b0\nC:60\u00b0\nD:68\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line AD parallel BC, if angle 1 = 42.0, angle BAC = 78.0, then the degree of angle 2 is ()\nChoices:\nA:42\u00b0\nB:50\u00b0\nC:60\u00b0\nD:68\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line AD parallel BC, if angle 1 = 42.0, angle BAC = 78.0, then the degree of angle 2 is ()\nChoices:\nA:42\u00b0\nB:50\u00b0\nC:60\u00b0\nD:68\u00b0",
        "question_for_eval": "As shown in the figure, the straight line AD parallel BC, if angle 1 = 42.0, angle BAC = 78.0, then the degree of angle 2 is ()\nChoices:\nA:42\u00b0\nB:50\u00b0\nC:60\u00b0\nD:68\u00b0"
    },
    {
        "sample_index": "72",
        "problem_index": "72",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the perimeter of parallelogram ABCD is 16.0, AC and BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:10cm\nB:8cm\nC:6cm\nD:4cm",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the perimeter of parallelogram ABCD is 16.0, AC and BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:10cm\nB:8cm\nC:6cm\nD:4cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the perimeter of parallelogram ABCD is 16.0, AC and BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:10cm\nB:8cm\nC:6cm\nD:4cm",
        "question_for_eval": "As shown in the figure, the perimeter of parallelogram ABCD is 16.0, AC and BD intersect at point O, and OE perpendicular AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:10cm\nB:8cm\nC:6cm\nD:4cm"
    },
    {
        "sample_index": "73",
        "problem_index": "73",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O. If angle ABC = 70.0, then the degree of angle AOC is equal to ()\nChoices:\nA:140\u00b0\nB:130\u00b0\nC:120\u00b0\nD:110\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O. If angle ABC = 70.0, then the degree of angle AOC is equal to ()\nChoices:\nA:140\u00b0\nB:130\u00b0\nC:120\u00b0\nD:110\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O. If angle ABC = 70.0, then the degree of angle AOC is equal to ()\nChoices:\nA:140\u00b0\nB:130\u00b0\nC:120\u00b0\nD:110\u00b0",
        "question_for_eval": "As shown in the figure, triangle ABC is the inscribed triangle of circle O. If angle ABC = 70.0, then the degree of angle AOC is equal to ()\nChoices:\nA:140\u00b0\nB:130\u00b0\nC:120\u00b0\nD:110\u00b0"
    },
    {
        "sample_index": "74",
        "problem_index": "74",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, radial AE intersects CD at point F, if angle 1 = 115.0, then the degree of angle 2 is ()\nChoices:\nA:55\u00b0\nB:65\u00b0\nC:75\u00b0\nD:85\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, radial AE intersects CD at point F, if angle 1 = 115.0, then the degree of angle 2 is ()\nChoices:\nA:55\u00b0\nB:65\u00b0\nC:75\u00b0\nD:85\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, radial AE intersects CD at point F, if angle 1 = 115.0, then the degree of angle 2 is ()\nChoices:\nA:55\u00b0\nB:65\u00b0\nC:75\u00b0\nD:85\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, radial AE intersects CD at point F, if angle 1 = 115.0, then the degree of angle 2 is ()\nChoices:\nA:55\u00b0\nB:65\u00b0\nC:75\u00b0\nD:85\u00b0"
    },
    {
        "sample_index": "75",
        "problem_index": "75",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a // b, put the right-angled vertex of a triangular plate on the straight line a, angle 1 = 42.0, then the degree of angle 2 is ()\nChoices:\nA:46\u00b0\nB:48\u00b0\nC:56\u00b0\nD:72\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a // b, put the right-angled vertex of a triangular plate on the straight line a, angle 1 = 42.0, then the degree of angle 2 is ()\nChoices:\nA:46\u00b0\nB:48\u00b0\nC:56\u00b0\nD:72\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a // b, put the right-angled vertex of a triangular plate on the straight line a, angle 1 = 42.0, then the degree of angle 2 is ()\nChoices:\nA:46\u00b0\nB:48\u00b0\nC:56\u00b0\nD:72\u00b0",
        "question_for_eval": "As shown in the figure, a // b, put the right-angled vertex of a triangular plate on the straight line a, angle 1 = 42.0, then the degree of angle 2 is ()\nChoices:\nA:46\u00b0\nB:48\u00b0\nC:56\u00b0\nD:72\u00b0"
    },
    {
        "sample_index": "76",
        "problem_index": "76",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a parallel b, point B is on the straight line b, and AB perpendicular  BC, angle 1 = 36.0, then angle 2 = ()\nChoices:\nA:54\u00b0\nB:56\u00b0\nC:44\u00b0\nD:46\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a parallel b, point B is on the straight line b, and AB perpendicular  BC, angle 1 = 36.0, then angle 2 = ()\nChoices:\nA:54\u00b0\nB:56\u00b0\nC:44\u00b0\nD:46\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a parallel b, point B is on the straight line b, and AB perpendicular  BC, angle 1 = 36.0, then angle 2 = ()\nChoices:\nA:54\u00b0\nB:56\u00b0\nC:44\u00b0\nD:46\u00b0",
        "question_for_eval": "As shown in the figure, a parallel b, point B is on the straight line b, and AB perpendicular  BC, angle 1 = 36.0, then angle 2 = ()\nChoices:\nA:54\u00b0\nB:56\u00b0\nC:44\u00b0\nD:46\u00b0"
    },
    {
        "sample_index": "77",
        "problem_index": "77",
        "problem_version": "Text Only",
        "question": "As shown in the figure, if angle 1 = angle 3, angle 2 = 60.0, then the degree of angle 4 is ()\nChoices:\nA:60\u00b0\nB:100\u00b0\nC:120\u00b0\nD:130\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, if angle 1 = angle 3, angle 2 = 60.0, then the degree of angle 4 is ()\nChoices:\nA:60\u00b0\nB:100\u00b0\nC:120\u00b0\nD:130\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, if angle 1 = angle 3, angle 2 = 60.0, then the degree of angle 4 is ()\nChoices:\nA:60\u00b0\nB:100\u00b0\nC:120\u00b0\nD:130\u00b0",
        "question_for_eval": "As shown in the figure, if angle 1 = angle 3, angle 2 = 60.0, then the degree of angle 4 is ()\nChoices:\nA:60\u00b0\nB:100\u00b0\nC:120\u00b0\nD:130\u00b0"
    },
    {
        "sample_index": "78",
        "problem_index": "78",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB parallel CD, AE bisects angle CAB and CD at point E, if angle C = 70.0, then the degree of angle AED is ()\nChoices:\nA:110\u00b0\nB:125\u00b0\nC:135\u00b0\nD:140\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB parallel CD, AE bisects angle CAB and CD at point E, if angle C = 70.0, then the degree of angle AED is ()\nChoices:\nA:110\u00b0\nB:125\u00b0\nC:135\u00b0\nD:140\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB parallel CD, AE bisects angle CAB and CD at point E, if angle C = 70.0, then the degree of angle AED is ()\nChoices:\nA:110\u00b0\nB:125\u00b0\nC:135\u00b0\nD:140\u00b0",
        "question_for_eval": "As shown in the figure, AB parallel CD, AE bisects angle CAB and CD at point E, if angle C = 70.0, then the degree of angle AED is ()\nChoices:\nA:110\u00b0\nB:125\u00b0\nC:135\u00b0\nD:140\u00b0"
    },
    {
        "sample_index": "79",
        "problem_index": "79",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the perimeter of parallelogram ABCD is 32.0, AC, BD intersect at point O, and OE perpendicular  AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:8cm\nB:24cm\nC:10cm\nD:16cm",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the perimeter of parallelogram ABCD is 32.0, AC, BD intersect at point O, and OE perpendicular  AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:8cm\nB:24cm\nC:10cm\nD:16cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the perimeter of parallelogram ABCD is 32.0, AC, BD intersect at point O, and OE perpendicular  AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:8cm\nB:24cm\nC:10cm\nD:16cm",
        "question_for_eval": "As shown in the figure, the perimeter of parallelogram ABCD is 32.0, AC, BD intersect at point O, and OE perpendicular  AC and it intersects AD at point E, then the perimeter of triangle DCE is ()\nChoices:\nA:8cm\nB:24cm\nC:10cm\nD:16cm"
    },
    {
        "sample_index": "80",
        "problem_index": "80",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a cylinder with a bottom circumference of 24.0 and a height of 5.0, the shortest route that an ant passes along the surface from point A to point B is ()\nChoices:\nA:12m\nB:15m\nC:13m\nD:14m",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a cylinder with a bottom circumference of 24.0 and a height of 5.0, the shortest route that an ant passes along the surface from point A to point B is ()\nChoices:\nA:12m\nB:15m\nC:13m\nD:14m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a cylinder with a bottom circumference of 24.0 and a height of 5.0, the shortest route that an ant passes along the surface from point A to point B is ()\nChoices:\nA:12m\nB:15m\nC:13m\nD:14m",
        "question_for_eval": "As shown in the figure, a cylinder with a bottom circumference of 24.0 and a height of 5.0, the shortest route that an ant passes along the surface from point A to point B is ()\nChoices:\nA:12m\nB:15m\nC:13m\nD:14m"
    },
    {
        "sample_index": "81",
        "problem_index": "81",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular  BC at point D, AE bisects angle DAC, angle B = 50.0, so the degree of angle DAE is ()\nChoices:\nA:45\u00b0\nB:20\u00b0\nC:30\u00b0\nD:25\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular  BC at point D, AE bisects angle DAC, angle B = 50.0, so the degree of angle DAE is ()\nChoices:\nA:45\u00b0\nB:20\u00b0\nC:30\u00b0\nD:25\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular  BC at point D, AE bisects angle DAC, angle B = 50.0, so the degree of angle DAE is ()\nChoices:\nA:45\u00b0\nB:20\u00b0\nC:30\u00b0\nD:25\u00b0",
        "question_for_eval": "As shown in the figure, in triangle ABC, angle BAC = 90.0, AD perpendicular  BC at point D, AE bisects angle DAC, angle B = 50.0, so the degree of angle DAE is ()\nChoices:\nA:45\u00b0\nB:20\u00b0\nC:30\u00b0\nD:25\u00b0"
    },
    {
        "sample_index": "82",
        "problem_index": "82",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the line l parallel  m parallel  n, the vertices B and C of the triangle ABC are on the line n and line m, the angle between BC and the line n is 25.0, and angle ACB = 60.0, then the degree of angle a is ()\nChoices:\nA:25\u00b0\nB:30\u00b0\nC:35\u00b0\nD:45\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the line l parallel  m parallel  n, the vertices B and C of the triangle ABC are on the line n and line m, the angle between BC and the line n is 25.0, and angle ACB = 60.0, then the degree of angle a is ()\nChoices:\nA:25\u00b0\nB:30\u00b0\nC:35\u00b0\nD:45\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the line l parallel  m parallel  n, the vertices B and C of the triangle ABC are on the line n and line m, the angle between BC and the line n is 25.0, and angle ACB = 60.0, then the degree of angle a is ()\nChoices:\nA:25\u00b0\nB:30\u00b0\nC:35\u00b0\nD:45\u00b0",
        "question_for_eval": "As shown in the figure, the line l parallel  m parallel  n, the vertices B and C of the triangle ABC are on the line n and line m, the angle between BC and the line n is 25.0, and angle ACB = 60.0, then the degree of angle a is ()\nChoices:\nA:25\u00b0\nB:30\u00b0\nC:35\u00b0\nD:45\u00b0"
    },
    {
        "sample_index": "83",
        "problem_index": "83",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that in circle O, the central angle angle AOB = 100.0, then the angle of circumference angle ACB is equal to ().\nChoices:\nA:130\u00b0\nB:120\u00b0\nC:110\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that in circle O, the central angle angle AOB = 100.0, then the angle of circumference angle ACB is equal to ().\nChoices:\nA:130\u00b0\nB:120\u00b0\nC:110\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that in circle O, the central angle angle AOB = 100.0, then the angle of circumference angle ACB is equal to ().\nChoices:\nA:130\u00b0\nB:120\u00b0\nC:110\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, it is known that in circle O, the central angle angle AOB = 100.0, then the angle of circumference angle ACB is equal to ().\nChoices:\nA:130\u00b0\nB:120\u00b0\nC:110\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "84",
        "problem_index": "84",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC is inscribed in circle O with radius 1.0, if angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:2\nB:2\u221a{3}\nC:\u221a{3}\nD:2\u221a{2}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC is inscribed in circle O with radius 1.0, if angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:2\nB:2\u221a{3}\nC:\u221a{3}\nD:2\u221a{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC is inscribed in circle O with radius 1.0, if angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:2\nB:2\u221a{3}\nC:\u221a{3}\nD:2\u221a{2}",
        "question_for_eval": "As shown in the figure, triangle ABC is inscribed in circle O with radius 1.0, if angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:2\nB:2\u221a{3}\nC:\u221a{3}\nD:2\u221a{2}"
    },
    {
        "sample_index": "85",
        "problem_index": "85",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()\nChoices:\nA:4\u221a{3}+2\nB:4\u221a{3}+3\nC:8\u221a{3}+1\nD:8\u221a{3}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()\nChoices:\nA:4\u221a{3}+2\nB:4\u221a{3}+3\nC:8\u221a{3}+1\nD:8\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()\nChoices:\nA:4\u221a{3}+2\nB:4\u221a{3}+3\nC:8\u221a{3}+1\nD:8\u221a{3}",
        "question_for_eval": "As shown in the figure, the circle O is the circumscribed circle of triangle ABC, and the bisector of angle BAC and angle ABC intersects at point I. Extend AI and it intersects circle O at point D. Connect BD and DC. If the radius of circle O is 8.0, angle BAC = 120.0, then the length of DI is ()\nChoices:\nA:4\u221a{3}+2\nB:4\u221a{3}+3\nC:8\u221a{3}+1\nD:8\u221a{3}"
    },
    {
        "sample_index": "86",
        "problem_index": "86",
        "problem_version": "Text Only",
        "question": "As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OB and OC, if the radius of circle O is 2.0, angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:\u221a{3}\nB:2\u221a{3}\nC:4\nD:4\u221a{3}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OB and OC, if the radius of circle O is 2.0, angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:\u221a{3}\nB:2\u221a{3}\nC:4\nD:4\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OB and OC, if the radius of circle O is 2.0, angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:\u221a{3}\nB:2\u221a{3}\nC:4\nD:4\u221a{3}",
        "question_for_eval": "As shown in the figure, circle O is the circumscribed circle of triangle ABC. Connect OB and OC, if the radius of circle O is 2.0, angle BAC = 60.0, then the length of BC is ()\nChoices:\nA:\u221a{3}\nB:2\u221a{3}\nC:4\nD:4\u221a{3}"
    },
    {
        "sample_index": "87",
        "problem_index": "87",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB and CD are the two diameters of circle O, chord DE parallel  AB, arc DE is the arc of 50.0, then angle BOC is ()\nChoices:\nA:115\u00b0\nB:100\u00b0\nC:80\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB and CD are the two diameters of circle O, chord DE parallel  AB, arc DE is the arc of 50.0, then angle BOC is ()\nChoices:\nA:115\u00b0\nB:100\u00b0\nC:80\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB and CD are the two diameters of circle O, chord DE parallel  AB, arc DE is the arc of 50.0, then angle BOC is ()\nChoices:\nA:115\u00b0\nB:100\u00b0\nC:80\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, AB and CD are the two diameters of circle O, chord DE parallel  AB, arc DE is the arc of 50.0, then angle BOC is ()\nChoices:\nA:115\u00b0\nB:100\u00b0\nC:80\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "88",
        "problem_index": "88",
        "problem_version": "Text Only",
        "question": "As shown in the figure, points A, B, and C are on circle O, angle ABO = 22.0, angle ACO = 42.0, then angle BOC is equal to ()\nChoices:\nA:128\u00b0\nB:108\u00b0\nC:86\u00b0\nD:64\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, points A, B, and C are on circle O, angle ABO = 22.0, angle ACO = 42.0, then angle BOC is equal to ()\nChoices:\nA:128\u00b0\nB:108\u00b0\nC:86\u00b0\nD:64\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, points A, B, and C are on circle O, angle ABO = 22.0, angle ACO = 42.0, then angle BOC is equal to ()\nChoices:\nA:128\u00b0\nB:108\u00b0\nC:86\u00b0\nD:64\u00b0",
        "question_for_eval": "As shown in the figure, points A, B, and C are on circle O, angle ABO = 22.0, angle ACO = 42.0, then angle BOC is equal to ()\nChoices:\nA:128\u00b0\nB:108\u00b0\nC:86\u00b0\nD:64\u00b0"
    },
    {
        "sample_index": "89",
        "problem_index": "89",
        "problem_version": "Text Only",
        "question": "As shown in the figure, A, B, C are three points on circle O, angle ACB = 25.0, then the degree of angle BAO is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, A, B, C are three points on circle O, angle ACB = 25.0, then the degree of angle BAO is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, A, B, C are three points on circle O, angle ACB = 25.0, then the degree of angle BAO is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "question_for_eval": "As shown in the figure, A, B, C are three points on circle O, angle ACB = 25.0, then the degree of angle BAO is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0"
    },
    {
        "sample_index": "90",
        "problem_index": "90",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that in circle O, angle AOB = 50.0, then the degree of the angle of circumference angle ACB is ()\nChoices:\nA:50\u00b0\nB:25\u00b0\nC:100\u00b0\nD:30\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that in circle O, angle AOB = 50.0, then the degree of the angle of circumference angle ACB is ()\nChoices:\nA:50\u00b0\nB:25\u00b0\nC:100\u00b0\nD:30\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that in circle O, angle AOB = 50.0, then the degree of the angle of circumference angle ACB is ()\nChoices:\nA:50\u00b0\nB:25\u00b0\nC:100\u00b0\nD:30\u00b0",
        "question_for_eval": "As shown in the figure, it is known that in circle O, angle AOB = 50.0, then the degree of the angle of circumference angle ACB is ()\nChoices:\nA:50\u00b0\nB:25\u00b0\nC:100\u00b0\nD:30\u00b0"
    },
    {
        "sample_index": "91",
        "problem_index": "91",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, angle BAC = 30.0, arc AD = arc CD. Then angle DAC is equal to ()\nChoices:\nA:70\u00b0\nB:45\u00b0\nC:30\u00b0\nD:25\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, angle BAC = 30.0, arc AD = arc CD. Then angle DAC is equal to ()\nChoices:\nA:70\u00b0\nB:45\u00b0\nC:30\u00b0\nD:25\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, angle BAC = 30.0, arc AD = arc CD. Then angle DAC is equal to ()\nChoices:\nA:70\u00b0\nB:45\u00b0\nC:30\u00b0\nD:25\u00b0",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, C and D are two points on circle O, angle BAC = 30.0, arc AD = arc CD. Then angle DAC is equal to ()\nChoices:\nA:70\u00b0\nB:45\u00b0\nC:30\u00b0\nD:25\u00b0"
    },
    {
        "sample_index": "92",
        "problem_index": "92",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, C and D are two points on the circle, angle D = 34.0, then the degree of angle BOC is ()\nChoices:\nA:102\u00b0\nB:112\u00b0\nC:122\u00b0\nD:132\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, C and D are two points on the circle, angle D = 34.0, then the degree of angle BOC is ()\nChoices:\nA:102\u00b0\nB:112\u00b0\nC:122\u00b0\nD:132\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, C and D are two points on the circle, angle D = 34.0, then the degree of angle BOC is ()\nChoices:\nA:102\u00b0\nB:112\u00b0\nC:122\u00b0\nD:132\u00b0",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, C and D are two points on the circle, angle D = 34.0, then the degree of angle BOC is ()\nChoices:\nA:102\u00b0\nB:112\u00b0\nC:122\u00b0\nD:132\u00b0"
    },
    {
        "sample_index": "93",
        "problem_index": "93",
        "problem_version": "Text Only",
        "question": "As shown in the figure, points A, B, and C are all on circle O, when angle OBC = 40.0, the degree of angle A is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, points A, B, and C are all on circle O, when angle OBC = 40.0, the degree of angle A is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, points A, B, and C are all on circle O, when angle OBC = 40.0, the degree of angle A is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0",
        "question_for_eval": "As shown in the figure, points A, B, and C are all on circle O, when angle OBC = 40.0, the degree of angle A is ()\nChoices:\nA:50\u00b0\nB:55\u00b0\nC:60\u00b0\nD:65\u00b0"
    },
    {
        "sample_index": "94",
        "problem_index": "94",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, the foot of perpendicular is the point E, angle CAO = 22.5, OC = 6.0, then the length of CD is ()\nChoices:\nA:6\u221a{2}\nB:3\u221a{2}\nC:6\nD:12",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, the foot of perpendicular is the point E, angle CAO = 22.5, OC = 6.0, then the length of CD is ()\nChoices:\nA:6\u221a{2}\nB:3\u221a{2}\nC:6\nD:12",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, the foot of perpendicular is the point E, angle CAO = 22.5, OC = 6.0, then the length of CD is ()\nChoices:\nA:6\u221a{2}\nB:3\u221a{2}\nC:6\nD:12",
        "question_for_eval": "As shown in the figure, the diameter AB of circle O is perpendicular to the chord CD, the foot of perpendicular is the point E, angle CAO = 22.5, OC = 6.0, then the length of CD is ()\nChoices:\nA:6\u221a{2}\nB:3\u221a{2}\nC:6\nD:12"
    },
    {
        "sample_index": "95",
        "problem_index": "95",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in circle O, chord BC and radius OA intersect at point D. Connect AB and OC. If angle A = 60.0, angle ADC = 90.0, then the degree of angle C is ()\nChoices:\nA:25\u00b0\nB:27.5\u00b0\nC:30\u00b0\nD:35\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in circle O, chord BC and radius OA intersect at point D. Connect AB and OC. If angle A = 60.0, angle ADC = 90.0, then the degree of angle C is ()\nChoices:\nA:25\u00b0\nB:27.5\u00b0\nC:30\u00b0\nD:35\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in circle O, chord BC and radius OA intersect at point D. Connect AB and OC. If angle A = 60.0, angle ADC = 90.0, then the degree of angle C is ()\nChoices:\nA:25\u00b0\nB:27.5\u00b0\nC:30\u00b0\nD:35\u00b0",
        "question_for_eval": "As shown in the figure, in circle O, chord BC and radius OA intersect at point D. Connect AB and OC. If angle A = 60.0, angle ADC = 90.0, then the degree of angle C is ()\nChoices:\nA:25\u00b0\nB:27.5\u00b0\nC:30\u00b0\nD:35\u00b0"
    },
    {
        "sample_index": "96",
        "problem_index": "96",
        "problem_version": "Text Only",
        "question": "As shown in the figure, points A, B, and P are three points on circle O, if angle AOB = 40.0, then the degree of angle APB is ()\nChoices:\nA:80\u00b0\nB:140\u00b0\nC:20\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, points A, B, and P are three points on circle O, if angle AOB = 40.0, then the degree of angle APB is ()\nChoices:\nA:80\u00b0\nB:140\u00b0\nC:20\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, points A, B, and P are three points on circle O, if angle AOB = 40.0, then the degree of angle APB is ()\nChoices:\nA:80\u00b0\nB:140\u00b0\nC:20\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, points A, B, and P are three points on circle O, if angle AOB = 40.0, then the degree of angle APB is ()\nChoices:\nA:80\u00b0\nB:140\u00b0\nC:20\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "97",
        "problem_index": "97",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the chord of circle O, OC perpendicular  AB and it intersects circle O at point C. Connect OA, OB, BC, if angle ABC = 25.0, then the size of angle AOB is ()\nChoices:\nA:80\u00b0\nB:90\u00b0\nC:100\u00b0\nD:120\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the chord of circle O, OC perpendicular  AB and it intersects circle O at point C. Connect OA, OB, BC, if angle ABC = 25.0, then the size of angle AOB is ()\nChoices:\nA:80\u00b0\nB:90\u00b0\nC:100\u00b0\nD:120\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the chord of circle O, OC perpendicular  AB and it intersects circle O at point C. Connect OA, OB, BC, if angle ABC = 25.0, then the size of angle AOB is ()\nChoices:\nA:80\u00b0\nB:90\u00b0\nC:100\u00b0\nD:120\u00b0",
        "question_for_eval": "As shown in the figure, AB is the chord of circle O, OC perpendicular  AB and it intersects circle O at point C. Connect OA, OB, BC, if angle ABC = 25.0, then the size of angle AOB is ()\nChoices:\nA:80\u00b0\nB:90\u00b0\nC:100\u00b0\nD:120\u00b0"
    },
    {
        "sample_index": "98",
        "problem_index": "98",
        "problem_version": "Text Only",
        "question": "As shown in the figure, given the angle of circumference angle A = 50.0, then the size of angle OBC is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:130\u00b0\nD:80\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, given the angle of circumference angle A = 50.0, then the size of angle OBC is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:130\u00b0\nD:80\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, given the angle of circumference angle A = 50.0, then the size of angle OBC is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:130\u00b0\nD:80\u00b0",
        "question_for_eval": "As shown in the figure, given the angle of circumference angle A = 50.0, then the size of angle OBC is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:130\u00b0\nD:80\u00b0"
    },
    {
        "sample_index": "99",
        "problem_index": "99",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ADC = 26.0, then the degree of angle CAB is ()\nChoices:\nA:26\u00b0\nB:74\u00b0\nC:64\u00b0\nD:54\u00b0\n102",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ADC = 26.0, then the degree of angle CAB is ()\nChoices:\nA:26\u00b0\nB:74\u00b0\nC:64\u00b0\nD:54\u00b0\n102",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ADC = 26.0, then the degree of angle CAB is ()\nChoices:\nA:26\u00b0\nB:74\u00b0\nC:64\u00b0\nD:54\u00b0\n102",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, angle ADC = 26.0, then the degree of angle CAB is ()\nChoices:\nA:26\u00b0\nB:74\u00b0\nC:64\u00b0\nD:54\u00b0\n102"
    },
    {
        "sample_index": "100",
        "problem_index": "100",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in circle O, AB is the diameter, CD is the chord, AB perpendicular  CD, the foot of perpendicular is the point E. Connect CO and AD, if angle BOC = 30.0, then the degree of angle BAD is ()\nChoices:\nA:30\u00b0\nB:25\u00b0\nC:20\u00b0\nD:15\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in circle O, AB is the diameter, CD is the chord, AB perpendicular  CD, the foot of perpendicular is the point E. Connect CO and AD, if angle BOC = 30.0, then the degree of angle BAD is ()\nChoices:\nA:30\u00b0\nB:25\u00b0\nC:20\u00b0\nD:15\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in circle O, AB is the diameter, CD is the chord, AB perpendicular  CD, the foot of perpendicular is the point E. Connect CO and AD, if angle BOC = 30.0, then the degree of angle BAD is ()\nChoices:\nA:30\u00b0\nB:25\u00b0\nC:20\u00b0\nD:15\u00b0",
        "question_for_eval": "As shown in the figure, in circle O, AB is the diameter, CD is the chord, AB perpendicular  CD, the foot of perpendicular is the point E. Connect CO and AD, if angle BOC = 30.0, then the degree of angle BAD is ()\nChoices:\nA:30\u00b0\nB:25\u00b0\nC:20\u00b0\nD:15\u00b0"
    },
    {
        "sample_index": "101",
        "problem_index": "101",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = ()\nChoices:\nA:54\u00b0\nB:64\u00b0\nC:27\u00b0\nD:37\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = ()\nChoices:\nA:54\u00b0\nB:64\u00b0\nC:27\u00b0\nD:37\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = ()\nChoices:\nA:54\u00b0\nB:64\u00b0\nC:27\u00b0\nD:37\u00b0",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, points C and D are two points on the circle, and angle AOC = 126.0, then angle CDB = ()\nChoices:\nA:54\u00b0\nB:64\u00b0\nC:27\u00b0\nD:37\u00b0"
    },
    {
        "sample_index": "102",
        "problem_index": "102",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()\nChoices:\nA:3\nB:\\frac{20}{3}\nC:\\frac{12}{5}\nD:\\frac{16}{5}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()\nChoices:\nA:3\nB:\\frac{20}{3}\nC:\\frac{12}{5}\nD:\\frac{16}{5}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()\nChoices:\nA:3\nB:\\frac{20}{3}\nC:\\frac{12}{5}\nD:\\frac{16}{5}",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, points C and D are on circle O, and point C is the midpoint of arc BD, passing point C to draw the perpendicular line EF of AD and it intersects straight line AD at point E, if the radius of circle O is 2.5, the length of AC is 4.0, then the length of CE is ()\nChoices:\nA:3\nB:\\frac{20}{3}\nC:\\frac{12}{5}\nD:\\frac{16}{5}"
    },
    {
        "sample_index": "103",
        "problem_index": "103",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:130\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:130\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:130\u00b0",
        "question_for_eval": "As shown in the figure, the points A, B, and C are on circle O, and it is known that angle ABC = 130.0, then angle AOC = ()\nChoices:\nA:100\u00b0\nB:110\u00b0\nC:120\u00b0\nD:130\u00b0"
    },
    {
        "sample_index": "104",
        "problem_index": "104",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()\nChoices:\nA:6\nB:8\nC:5\u221a{2}\nD:5\u221a{3}",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()\nChoices:\nA:6\nB:8\nC:5\u221a{2}\nD:5\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()\nChoices:\nA:6\nB:8\nC:5\u221a{2}\nD:5\u221a{3}",
        "question_for_eval": "As shown in the figure, it is known that the radius of circle O is 5.0, the central angles of chords AB and CD are angle AOB, angle COD, and angle AOB is complementary to angle COD, chord CD = 8.0, then the length of chord AB is ()\nChoices:\nA:6\nB:8\nC:5\u221a{2}\nD:5\u221a{3}"
    },
    {
        "sample_index": "105",
        "problem_index": "105",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()\nChoices:\nA:32\u00b0\nB:24\u00b0\nC:16\u00b0\nD:48\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()\nChoices:\nA:32\u00b0\nB:24\u00b0\nC:16\u00b0\nD:48\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()\nChoices:\nA:32\u00b0\nB:24\u00b0\nC:16\u00b0\nD:48\u00b0",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, CD is the chord of circle O, and the extended lines of AB and CD intersect at point E. Given that AB = 2 DE, angle E = 16.0, then the degree of angle ABC is ()\nChoices:\nA:32\u00b0\nB:24\u00b0\nC:16\u00b0\nD:48\u00b0"
    },
    {
        "sample_index": "106",
        "problem_index": "106",
        "problem_version": "Text Only",
        "question": "This question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of circle O, C is the point on circle O (except A and B), angle AOD = 136.0, then the degree of angle C is ()\nChoices:\nA:44\u00b0\nB:22\u00b0\nC:46\u00b0\nD:36\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: This question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of circle O, C is the point on circle O (except A and B), angle AOD = 136.0, then the degree of angle C is ()\nChoices:\nA:44\u00b0\nB:22\u00b0\nC:46\u00b0\nD:36\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: This question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of circle O, C is the point on circle O (except A and B), angle AOD = 136.0, then the degree of angle C is ()\nChoices:\nA:44\u00b0\nB:22\u00b0\nC:46\u00b0\nD:36\u00b0",
        "question_for_eval": "This question examines the theorem of angle of circumference, the key is to answer it based on the relationship between the central angle and the angle of circumference of the same chord. 4.0. As shown in the figure, AB is the diameter of circle O, C is the point on circle O (except A and B), angle AOD = 136.0, then the degree of angle C is ()\nChoices:\nA:44\u00b0\nB:22\u00b0\nC:46\u00b0\nD:36\u00b0"
    },
    {
        "sample_index": "107",
        "problem_index": "107",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is ()\nChoices:\nA:50\u00b0\nB:30\u00b0\nC:25\u00b0\nD:20\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is ()\nChoices:\nA:50\u00b0\nB:30\u00b0\nC:25\u00b0\nD:20\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is ()\nChoices:\nA:50\u00b0\nB:30\u00b0\nC:25\u00b0\nD:20\u00b0",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If angle BOD = 130.0, then the degree of angle ACD is ()\nChoices:\nA:50\u00b0\nB:30\u00b0\nC:25\u00b0\nD:20\u00b0"
    },
    {
        "sample_index": "108",
        "problem_index": "108",
        "problem_version": "Text Only",
        "question": "Shaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()\nChoices:\nA:4m\nB:5m\nC:6m\nD:8m",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Shaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()\nChoices:\nA:4m\nB:5m\nC:6m\nD:8m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Shaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()\nChoices:\nA:4m\nB:5m\nC:6m\nD:8m",
        "question_for_eval": "Shaoxing is a famous bridge township. As shown in the figure, the distance CD from the top of the round arch bridge to the water surface is 8.0, and the arch radius OC is 5.0, so the width of the water surface AB is ()\nChoices:\nA:4m\nB:5m\nC:6m\nD:8m"
    },
    {
        "sample_index": "109",
        "problem_index": "109",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that angle \u03b1 = 130.0, then angle \u03b2 = ()\nChoices:\nA:30\u00b0\nB:40\u00b0\nC:50\u00b0\nD:65\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that angle \u03b1 = 130.0, then angle \u03b2 = ()\nChoices:\nA:30\u00b0\nB:40\u00b0\nC:50\u00b0\nD:65\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that angle \u03b1 = 130.0, then angle \u03b2 = ()\nChoices:\nA:30\u00b0\nB:40\u00b0\nC:50\u00b0\nD:65\u00b0",
        "question_for_eval": "As shown in the figure, it is known that angle \u03b1 = 130.0, then angle \u03b2 = ()\nChoices:\nA:30\u00b0\nB:40\u00b0\nC:50\u00b0\nD:65\u00b0"
    },
    {
        "sample_index": "110",
        "problem_index": "110",
        "problem_version": "Text Only",
        "question": "As shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A\u2032B\u2032 in the bridge hole is ()\nChoices:\nA:\u221a{15}\u7c73\nB:2\u221a{15}\u7c73\nC:2\u221a{17}\u7c73\nD:\u4e0d\u80fd\u8ba1\u7b97",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A\u2032B\u2032 in the bridge hole is ()\nChoices:\nA:\u221a{15}\u7c73\nB:2\u221a{15}\u7c73\nC:2\u221a{17}\u7c73\nD:\u4e0d\u80fd\u8ba1\u7b97",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A\u2032B\u2032 in the bridge hole is ()\nChoices:\nA:\u221a{15}\u7c73\nB:2\u221a{15}\u7c73\nC:2\u221a{17}\u7c73\nD:\u4e0d\u80fd\u8ba1\u7b97",
        "question_for_eval": "As shown in the figure, when the width of the water surface AB in the circular bridge hole is 8.0, the arc ACB is exactly a semicircle. When the water surface rises 1.0, the water surface width A\u2032B\u2032 in the bridge hole is ()\nChoices:\nA:\u221a{15}\u7c73\nB:2\u221a{15}\u7c73\nC:2\u221a{17}\u7c73\nD:\u4e0d\u80fd\u8ba1\u7b97"
    },
    {
        "sample_index": "111",
        "problem_index": "111",
        "problem_version": "Text Only",
        "question": "In the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()\nChoices:\nA:63\u00b0\nB:45\u00b0\nC:27\u00b0\nD:18\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()\nChoices:\nA:63\u00b0\nB:45\u00b0\nC:27\u00b0\nD:18\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()\nChoices:\nA:63\u00b0\nB:45\u00b0\nC:27\u00b0\nD:18\u00b0",
        "question_for_eval": "In the right triangle ABC, angle CAB = 90.0, angle ABC = 72.0, AD is the angle bisector of angle CAB, and the intersection BC is at point D, and crossing point C is the high line CE on the AD side in triangle ACD, then the degree of angle ECD is ()\nChoices:\nA:63\u00b0\nB:45\u00b0\nC:27\u00b0\nD:18\u00b0"
    },
    {
        "sample_index": "112",
        "problem_index": "112",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6",
        "question_for_eval": "As shown in the figure, AO is the height of the cone, the bottom radius of the cone OB = 0.7, the length of AB is 2.5, then the length of AO is ()\nChoices:\nA:2.4\nB:2.2\nC:1.8\nD:1.6"
    },
    {
        "sample_index": "113",
        "problem_index": "113",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()\nChoices:\nA:35\u00b0\nB:45\u00b0\nC:55\u00b0\nD:70\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()\nChoices:\nA:35\u00b0\nB:45\u00b0\nC:55\u00b0\nD:70\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()\nChoices:\nA:35\u00b0\nB:45\u00b0\nC:55\u00b0\nD:70\u00b0",
        "question_for_eval": "As shown in the figure, in circle O, chord AC and BD intersect at point E, arc AB = arc BC = arc CD, if angle BEC = 110.0, then angle BDC = ()\nChoices:\nA:35\u00b0\nB:45\u00b0\nC:55\u00b0\nD:70\u00b0"
    },
    {
        "sample_index": "114",
        "problem_index": "114",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of the shaded part in the figure is ()\nChoices:\nA:\u03c0cm\u00b2\nB:\\frac{2}{3}\u03c0cm\u00b2\nC:\\frac{1}{2}cm\u00b2\nD:\\frac{2}{3}cm\u00b2",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of the shaded part in the figure is ()\nChoices:\nA:\u03c0cm\u00b2\nB:\\frac{2}{3}\u03c0cm\u00b2\nC:\\frac{1}{2}cm\u00b2\nD:\\frac{2}{3}cm\u00b2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of the shaded part in the figure is ()\nChoices:\nA:\u03c0cm\u00b2\nB:\\frac{2}{3}\u03c0cm\u00b2\nC:\\frac{1}{2}cm\u00b2\nD:\\frac{2}{3}cm\u00b2",
        "question_for_eval": "As shown in the figure, in the sector OAB with a radius of 1.0 and a central angle of 90.0, OA and OB are the diameters respectively as a semicircle, and the area of the shaded part in the figure is ()\nChoices:\nA:\u03c0cm\u00b2\nB:\\frac{2}{3}\u03c0cm\u00b2\nC:\\frac{1}{2}cm\u00b2\nD:\\frac{2}{3}cm\u00b2"
    },
    {
        "sample_index": "115",
        "problem_index": "115",
        "problem_version": "Text Only",
        "question": "Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()\nChoices:\nA:2\u03c0cm\nB:3\u03c0cm\nC:4\u03c0cm\nD:5\u03c0cm",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()\nChoices:\nA:2\u03c0cm\nB:3\u03c0cm\nC:4\u03c0cm\nD:5\u03c0cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()\nChoices:\nA:2\u03c0cm\nB:3\u03c0cm\nC:4\u03c0cm\nD:5\u03c0cm",
        "question_for_eval": "Use a sector paper sheet with a central angle of 120.0 and a radius of 6.0 to roll into a conical bottomless paper cap (as shown in the picture), then the bottom perimeter of the paper cap is ()\nChoices:\nA:2\u03c0cm\nB:3\u03c0cm\nC:4\u03c0cm\nD:5\u03c0cm"
    },
    {
        "sample_index": "116",
        "problem_index": "116",
        "problem_version": "Text Only",
        "question": "The picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of \u200b\u200bpaper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60\u03c0\nB:65\u03c0\nC:78\u03c0\nD:156\u03c0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of \u200b\u200bpaper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60\u03c0\nB:65\u03c0\nC:78\u03c0\nD:156\u03c0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of \u200b\u200bpaper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60\u03c0\nB:65\u03c0\nC:78\u03c0\nD:156\u03c0",
        "question_for_eval": "The picture shows a small paper cap with a conical chimney. The length of its generatrix l is 13.0 and its height h is 12.0. The area of \u200b\u200bpaper required to make this paper cap is (the seams are ignored) ()\nChoices:\nA:60\u03c0\nB:65\u03c0\nC:78\u03c0\nD:156\u03c0"
    },
    {
        "sample_index": "117",
        "problem_index": "117",
        "problem_version": "Text Only",
        "question": "Use a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is ()\nChoices:\nA:3cm\nB:2\u221a{2}cm\nC:3\u221a{2}cm\nD:4\u221a{2}cm",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Use a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is ()\nChoices:\nA:3cm\nB:2\u221a{2}cm\nC:3\u221a{2}cm\nD:4\u221a{2}cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Use a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is ()\nChoices:\nA:3cm\nB:2\u221a{2}cm\nC:3\u221a{2}cm\nD:4\u221a{2}cm",
        "question_for_eval": "Use a sector piece of paper with a central angle of 120.0 and a radius of 3.0 to roll into a cone-shaped bottomless paper cap (as shown in the picture), then the height of the paper is ()\nChoices:\nA:3cm\nB:2\u221a{2}cm\nC:3\u221a{2}cm\nD:4\u221a{2}cm"
    },
    {
        "sample_index": "118",
        "problem_index": "118",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "question_for_eval": "As shown in the figure, the expanded figure of the lateral surface of a cone is a semicircle with a radius of 10.0, then the radius of its bottom is ()\nChoices:\nA:3\nB:4\nC:5\nD:6"
    },
    {
        "sample_index": "119",
        "problem_index": "119",
        "problem_version": "Text Only",
        "question": "As shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of \u200b\u200bthis sector cardboard is ()\nChoices:\nA:240\u03c0cm^{2}\nB:480\u03c0cm^{2}\nC:1200\u03c0cm^{2}\nD:2400\u03c0cm^{2}",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of \u200b\u200bthis sector cardboard is ()\nChoices:\nA:240\u03c0cm^{2}\nB:480\u03c0cm^{2}\nC:1200\u03c0cm^{2}\nD:2400\u03c0cm^{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of \u200b\u200bthis sector cardboard is ()\nChoices:\nA:240\u03c0cm^{2}\nB:480\u03c0cm^{2}\nC:1200\u03c0cm^{2}\nD:2400\u03c0cm^{2}",
        "question_for_eval": "As shown in the figure, use a sector cardboard with a radius of 24.0 to make a conical hat (the seams are ignored). If the radius of the bottom surface of the conical hat is 10.0, then the area of \u200b\u200bthis sector cardboard is ()\nChoices:\nA:240\u03c0cm^{2}\nB:480\u03c0cm^{2}\nC:1200\u03c0cm^{2}\nD:2400\u03c0cm^{2}"
    },
    {
        "sample_index": "120",
        "problem_index": "120",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of \u200b\u200bthe cone is ()\nChoices:\nA:3\u03c0cm^{2}\nB:9\u03c0cm^{2}\nC:16\u03c0cm^{2}\nD:25\u03c0cm^{2}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of \u200b\u200bthe cone is ()\nChoices:\nA:3\u03c0cm^{2}\nB:9\u03c0cm^{2}\nC:16\u03c0cm^{2}\nD:25\u03c0cm^{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of \u200b\u200bthe cone is ()\nChoices:\nA:3\u03c0cm^{2}\nB:9\u03c0cm^{2}\nC:16\u03c0cm^{2}\nD:25\u03c0cm^{2}",
        "question_for_eval": "As shown in the figure, the length of the generatrix of the cone is 5.0, and the length of the height line is 4.0, then the bottom area of \u200b\u200bthe cone is ()\nChoices:\nA:3\u03c0cm^{2}\nB:9\u03c0cm^{2}\nC:16\u03c0cm^{2}\nD:25\u03c0cm^{2}"
    },
    {
        "sample_index": "121",
        "problem_index": "121",
        "problem_version": "Text Only",
        "question": "The production process of paper umbrellas in our country is very ingenious. As shown in the figure, whether the umbrella is opened or closed, the handle AP always bisects the angle angle BAC formed by the two ribs in the same plane, and AE = AF, DE = DF, so as to ensure that the umbrella ring can slide along the handle. When a toy umbrella is opened, the BDC is on the same straight line. If AB = 50.0, AD = 14.0, then the area of \u200b\u200boil paper required to make such a paper umbrella is (don't remember the seam) ()\nChoices:\nA:48cm^{2}\nB:70\u03c0cm^{2}\nC:2400\u03c0cm^{2}\nD:2500\u03c0cm^{2}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The production process of paper umbrellas in our country is very ingenious. As shown in the figure, whether the umbrella is opened or closed, the handle AP always bisects the angle angle BAC formed by the two ribs in the same plane, and AE = AF, DE = DF, so as to ensure that the umbrella ring can slide along the handle. When a toy umbrella is opened, the BDC is on the same straight line. If AB = 50.0, AD = 14.0, then the area of \u200b\u200boil paper required to make such a paper umbrella is (don't remember the seam) ()\nChoices:\nA:48cm^{2}\nB:70\u03c0cm^{2}\nC:2400\u03c0cm^{2}\nD:2500\u03c0cm^{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The production process of paper umbrellas in our country is very ingenious. As shown in the figure, whether the umbrella is opened or closed, the handle AP always bisects the angle angle BAC formed by the two ribs in the same plane, and AE = AF, DE = DF, so as to ensure that the umbrella ring can slide along the handle. When a toy umbrella is opened, the BDC is on the same straight line. If AB = 50.0, AD = 14.0, then the area of \u200b\u200boil paper required to make such a paper umbrella is (don't remember the seam) ()\nChoices:\nA:48cm^{2}\nB:70\u03c0cm^{2}\nC:2400\u03c0cm^{2}\nD:2500\u03c0cm^{2}",
        "question_for_eval": "The production process of paper umbrellas in our country is very ingenious. As shown in the figure, whether the umbrella is opened or closed, the handle AP always bisects the angle angle BAC formed by the two ribs in the same plane, and AE = AF, DE = DF, so as to ensure that the umbrella ring can slide along the handle. When a toy umbrella is opened, the BDC is on the same straight line. If AB = 50.0, AD = 14.0, then the area of \u200b\u200boil paper required to make such a paper umbrella is (don't remember the seam) ()\nChoices:\nA:48cm^{2}\nB:70\u03c0cm^{2}\nC:2400\u03c0cm^{2}\nD:2500\u03c0cm^{2}"
    },
    {
        "sample_index": "122",
        "problem_index": "122",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a sector with a central angle of 120.0 and a radius of 6.0 encloses the side of a cone (the joints are ignored), then the height of the cone is ()\nChoices:\nA:6\nB:8\nC:3\u221a{3}\nD:4\u221a{2}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a sector with a central angle of 120.0 and a radius of 6.0 encloses the side of a cone (the joints are ignored), then the height of the cone is ()\nChoices:\nA:6\nB:8\nC:3\u221a{3}\nD:4\u221a{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a sector with a central angle of 120.0 and a radius of 6.0 encloses the side of a cone (the joints are ignored), then the height of the cone is ()\nChoices:\nA:6\nB:8\nC:3\u221a{3}\nD:4\u221a{2}",
        "question_for_eval": "As shown in the figure, a sector with a central angle of 120.0 and a radius of 6.0 encloses the side of a cone (the joints are ignored), then the height of the cone is ()\nChoices:\nA:6\nB:8\nC:3\u221a{3}\nD:4\u221a{2}"
    },
    {
        "sample_index": "123",
        "problem_index": "123",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, rotate triangle ABC around the line where AC is located to obtain a rotating body, then the lateral area of \u200b\u200bthe rotating body is ()\nChoices:\nA:12\u03c0\nB:15\u03c0\nC:30\u03c0\nD:60\u03c0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, rotate triangle ABC around the line where AC is located to obtain a rotating body, then the lateral area of \u200b\u200bthe rotating body is ()\nChoices:\nA:12\u03c0\nB:15\u03c0\nC:30\u03c0\nD:60\u03c0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, rotate triangle ABC around the line where AC is located to obtain a rotating body, then the lateral area of \u200b\u200bthe rotating body is ()\nChoices:\nA:12\u03c0\nB:15\u03c0\nC:30\u03c0\nD:60\u03c0",
        "question_for_eval": "As shown in the figure, in Rttriangle ABC, angle ACB = 90.0, AC = 4.0, BC = 3.0, rotate triangle ABC around the line where AC is located to obtain a rotating body, then the lateral area of \u200b\u200bthe rotating body is ()\nChoices:\nA:12\u03c0\nB:15\u03c0\nC:30\u03c0\nD:60\u03c0"
    },
    {
        "sample_index": "124",
        "problem_index": "124",
        "problem_version": "Text Only",
        "question": "As shown in the figure, cut a circle and a sector piece of paper on the paper so that it can form a cone model. If the radius of the circle is 1.0 and the central angle of the sector is equal to 90.0, then the radius of the sector is ()\nChoices:\nA:2\nB:4\nC:6\nD:8\n127",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, cut a circle and a sector piece of paper on the paper so that it can form a cone model. If the radius of the circle is 1.0 and the central angle of the sector is equal to 90.0, then the radius of the sector is ()\nChoices:\nA:2\nB:4\nC:6\nD:8\n127",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, cut a circle and a sector piece of paper on the paper so that it can form a cone model. If the radius of the circle is 1.0 and the central angle of the sector is equal to 90.0, then the radius of the sector is ()\nChoices:\nA:2\nB:4\nC:6\nD:8\n127",
        "question_for_eval": "As shown in the figure, cut a circle and a sector piece of paper on the paper so that it can form a cone model. If the radius of the circle is 1.0 and the central angle of the sector is equal to 90.0, then the radius of the sector is ()\nChoices:\nA:2\nB:4\nC:6\nD:8\n127"
    },
    {
        "sample_index": "125",
        "problem_index": "125",
        "problem_version": "Text Only",
        "question": "As shown in a sector iron sheet OAB, it is known that OA = 30.0, angle AOB = 120.0, the worker master combines OA and OB to form a conical chimney cap (the joints are ignored), then the radius of the bottom circle of the chimney cap is ()\nChoices:\nA:5cm\nB:12cm\nC:10cm\nD:15cm",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in a sector iron sheet OAB, it is known that OA = 30.0, angle AOB = 120.0, the worker master combines OA and OB to form a conical chimney cap (the joints are ignored), then the radius of the bottom circle of the chimney cap is ()\nChoices:\nA:5cm\nB:12cm\nC:10cm\nD:15cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in a sector iron sheet OAB, it is known that OA = 30.0, angle AOB = 120.0, the worker master combines OA and OB to form a conical chimney cap (the joints are ignored), then the radius of the bottom circle of the chimney cap is ()\nChoices:\nA:5cm\nB:12cm\nC:10cm\nD:15cm",
        "question_for_eval": "As shown in a sector iron sheet OAB, it is known that OA = 30.0, angle AOB = 120.0, the worker master combines OA and OB to form a conical chimney cap (the joints are ignored), then the radius of the bottom circle of the chimney cap is ()\nChoices:\nA:5cm\nB:12cm\nC:10cm\nD:15cm"
    },
    {
        "sample_index": "126",
        "problem_index": "126",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that the radius of the bottom surface of the cone is 6.0, and the length of the generatrix is \u200b\u200b10.0, then the lateral area of \u200b\u200bthe cone is ()\nChoices:\nA:60\u03c0\nB:80\u03c0\nC:10\u03c0\nD:96\u03c0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that the radius of the bottom surface of the cone is 6.0, and the length of the generatrix is \u200b\u200b10.0, then the lateral area of \u200b\u200bthe cone is ()\nChoices:\nA:60\u03c0\nB:80\u03c0\nC:10\u03c0\nD:96\u03c0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that the radius of the bottom surface of the cone is 6.0, and the length of the generatrix is \u200b\u200b10.0, then the lateral area of \u200b\u200bthe cone is ()\nChoices:\nA:60\u03c0\nB:80\u03c0\nC:10\u03c0\nD:96\u03c0",
        "question_for_eval": "As shown in the figure, it is known that the radius of the bottom surface of the cone is 6.0, and the length of the generatrix is \u200b\u200b10.0, then the lateral area of \u200b\u200bthe cone is ()\nChoices:\nA:60\u03c0\nB:80\u03c0\nC:10\u03c0\nD:96\u03c0"
    },
    {
        "sample_index": "127",
        "problem_index": "127",
        "problem_version": "Text Only",
        "question": "Lulu cuts a circle and a sector piece of paper from the paper (as shown in the picture), and uses them to form a cone model. If the radius of the circle is 1.0. The central angle of the sector is equal to 120.0, then the radius of the sector is ()\nChoices:\nA:\u221a{3}\nB:\u221a{6}\nC:3\nD:6",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Lulu cuts a circle and a sector piece of paper from the paper (as shown in the picture), and uses them to form a cone model. If the radius of the circle is 1.0. The central angle of the sector is equal to 120.0, then the radius of the sector is ()\nChoices:\nA:\u221a{3}\nB:\u221a{6}\nC:3\nD:6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Lulu cuts a circle and a sector piece of paper from the paper (as shown in the picture), and uses them to form a cone model. If the radius of the circle is 1.0. The central angle of the sector is equal to 120.0, then the radius of the sector is ()\nChoices:\nA:\u221a{3}\nB:\u221a{6}\nC:3\nD:6",
        "question_for_eval": "Lulu cuts a circle and a sector piece of paper from the paper (as shown in the picture), and uses them to form a cone model. If the radius of the circle is 1.0. The central angle of the sector is equal to 120.0, then the radius of the sector is ()\nChoices:\nA:\u221a{3}\nB:\u221a{6}\nC:3\nD:6"
    },
    {
        "sample_index": "128",
        "problem_index": "128",
        "problem_version": "Text Only",
        "question": "As shown in the figure, there is a sector with a central angle of 120.0 and a radius of 6.0. If OA and OB are overlapped to form a cone side, the diameter of the bottom of the cone is ()\nChoices:\nA:2cm\nB:4cm\nC:3cm\nD:5cm",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, there is a sector with a central angle of 120.0 and a radius of 6.0. If OA and OB are overlapped to form a cone side, the diameter of the bottom of the cone is ()\nChoices:\nA:2cm\nB:4cm\nC:3cm\nD:5cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, there is a sector with a central angle of 120.0 and a radius of 6.0. If OA and OB are overlapped to form a cone side, the diameter of the bottom of the cone is ()\nChoices:\nA:2cm\nB:4cm\nC:3cm\nD:5cm",
        "question_for_eval": "As shown in the figure, there is a sector with a central angle of 120.0 and a radius of 6.0. If OA and OB are overlapped to form a cone side, the diameter of the bottom of the cone is ()\nChoices:\nA:2cm\nB:4cm\nC:3cm\nD:5cm"
    },
    {
        "sample_index": "129",
        "problem_index": "129",
        "problem_version": "Text Only",
        "question": "As shown in the picture, the length of the generatrix of the cone-shaped tent roof is AB = 10.0, the bottom radius is BO = 5.0, and the lateral area of \u200b\u200bthe cone-shaped tent roof (excluding the seams) is ()\nChoices:\nA:15\u03c0m^{2}\nB:30\u03c0m^{2}\nC:50\u03c0m^{2}\nD:75\u03c0m^{2}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the picture, the length of the generatrix of the cone-shaped tent roof is AB = 10.0, the bottom radius is BO = 5.0, and the lateral area of \u200b\u200bthe cone-shaped tent roof (excluding the seams) is ()\nChoices:\nA:15\u03c0m^{2}\nB:30\u03c0m^{2}\nC:50\u03c0m^{2}\nD:75\u03c0m^{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the picture, the length of the generatrix of the cone-shaped tent roof is AB = 10.0, the bottom radius is BO = 5.0, and the lateral area of \u200b\u200bthe cone-shaped tent roof (excluding the seams) is ()\nChoices:\nA:15\u03c0m^{2}\nB:30\u03c0m^{2}\nC:50\u03c0m^{2}\nD:75\u03c0m^{2}",
        "question_for_eval": "As shown in the picture, the length of the generatrix of the cone-shaped tent roof is AB = 10.0, the bottom radius is BO = 5.0, and the lateral area of \u200b\u200bthe cone-shaped tent roof (excluding the seams) is ()\nChoices:\nA:15\u03c0m^{2}\nB:30\u03c0m^{2}\nC:50\u03c0m^{2}\nD:75\u03c0m^{2}"
    },
    {
        "sample_index": "130",
        "problem_index": "130",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in circle O, the length of chord AB is 10.0, and the angle of circumference angle ACB = 45.0, then the diameter of the circle AD is ()\nChoices:\nA:5\u221a{2}\nB:10\u221a{2}\nC:15\u221a{2}\nD:20\u221a{2}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in circle O, the length of chord AB is 10.0, and the angle of circumference angle ACB = 45.0, then the diameter of the circle AD is ()\nChoices:\nA:5\u221a{2}\nB:10\u221a{2}\nC:15\u221a{2}\nD:20\u221a{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in circle O, the length of chord AB is 10.0, and the angle of circumference angle ACB = 45.0, then the diameter of the circle AD is ()\nChoices:\nA:5\u221a{2}\nB:10\u221a{2}\nC:15\u221a{2}\nD:20\u221a{2}",
        "question_for_eval": "As shown in the figure, in circle O, the length of chord AB is 10.0, and the angle of circumference angle ACB = 45.0, then the diameter of the circle AD is ()\nChoices:\nA:5\u221a{2}\nB:10\u221a{2}\nC:15\u221a{2}\nD:20\u221a{2}"
    },
    {
        "sample_index": "131",
        "problem_index": "131",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC. angle C = 90.0, point D is a moving point on BC (point D does not coincide with point C). The circle with CD as the diameter intersects AD at point P. If AC = 6.0. The minimum length of the line segment BP is 2.0. Then the length of AB is ()\nChoices:\nA:8\nB:2\u221a{10}\nC:4\u221a{3}\nD:2\u221a{13}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC. angle C = 90.0, point D is a moving point on BC (point D does not coincide with point C). The circle with CD as the diameter intersects AD at point P. If AC = 6.0. The minimum length of the line segment BP is 2.0. Then the length of AB is ()\nChoices:\nA:8\nB:2\u221a{10}\nC:4\u221a{3}\nD:2\u221a{13}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC. angle C = 90.0, point D is a moving point on BC (point D does not coincide with point C). The circle with CD as the diameter intersects AD at point P. If AC = 6.0. The minimum length of the line segment BP is 2.0. Then the length of AB is ()\nChoices:\nA:8\nB:2\u221a{10}\nC:4\u221a{3}\nD:2\u221a{13}",
        "question_for_eval": "As shown in the figure, in triangle ABC. angle C = 90.0, point D is a moving point on BC (point D does not coincide with point C). The circle with CD as the diameter intersects AD at point P. If AC = 6.0. The minimum length of the line segment BP is 2.0. Then the length of AB is ()\nChoices:\nA:8\nB:2\u221a{10}\nC:4\u221a{3}\nD:2\u221a{13}"
    },
    {
        "sample_index": "132",
        "problem_index": "132",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in order to measure the height AB of a pavilion (the distance from the top A to the horizontal ground BD), Xiaoming placed a step DE (DE = BC = 0.6) that is the same height as the pavilion step BC beside the pavilion, find A, B, C Three points are collinear), place a mirror horizontally at point G on the platform, and measure CG = 12.0, and then move back along the straight line CG to point E. At this time, you can see the top A of the pavilion in the mirror, and measure GE = 2.0, Xiaoming's height EF = 1.6, then the height of the pavilion AB is approximately ()\nChoices:\nA:9\u7c73\nB:9.6\u7c73\nC:10\u7c73\nD:10.2\u7c73",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in order to measure the height AB of a pavilion (the distance from the top A to the horizontal ground BD), Xiaoming placed a step DE (DE = BC = 0.6) that is the same height as the pavilion step BC beside the pavilion, find A, B, C Three points are collinear), place a mirror horizontally at point G on the platform, and measure CG = 12.0, and then move back along the straight line CG to point E. At this time, you can see the top A of the pavilion in the mirror, and measure GE = 2.0, Xiaoming's height EF = 1.6, then the height of the pavilion AB is approximately ()\nChoices:\nA:9\u7c73\nB:9.6\u7c73\nC:10\u7c73\nD:10.2\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in order to measure the height AB of a pavilion (the distance from the top A to the horizontal ground BD), Xiaoming placed a step DE (DE = BC = 0.6) that is the same height as the pavilion step BC beside the pavilion, find A, B, C Three points are collinear), place a mirror horizontally at point G on the platform, and measure CG = 12.0, and then move back along the straight line CG to point E. At this time, you can see the top A of the pavilion in the mirror, and measure GE = 2.0, Xiaoming's height EF = 1.6, then the height of the pavilion AB is approximately ()\nChoices:\nA:9\u7c73\nB:9.6\u7c73\nC:10\u7c73\nD:10.2\u7c73",
        "question_for_eval": "As shown in the figure, in order to measure the height AB of a pavilion (the distance from the top A to the horizontal ground BD), Xiaoming placed a step DE (DE = BC = 0.6) that is the same height as the pavilion step BC beside the pavilion, find A, B, C Three points are collinear), place a mirror horizontally at point G on the platform, and measure CG = 12.0, and then move back along the straight line CG to point E. At this time, you can see the top A of the pavilion in the mirror, and measure GE = 2.0, Xiaoming's height EF = 1.6, then the height of the pavilion AB is approximately ()\nChoices:\nA:9\u7c73\nB:9.6\u7c73\nC:10\u7c73\nD:10.2\u7c73"
    },
    {
        "sample_index": "133",
        "problem_index": "133",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in order to estimate the width of the Jing River, a target point P is selected on the opposite bank of the Jing River, and points Q and S are taken near the bank, so that the points P, Q, and S are in a straight line, and the straight line PS is perpendicular to the river. Choose an appropriate point T on the straight line a passing point S and perpendicular to PS. The intersection of PT and the straight line b passing point Q and perpendicular to PS is R. If QS = 60.0, ST = 120.0, QR = 80.0, then the width of the river PQ is ()\nChoices:\nA:40m\nB:120m\nC:60m\nD:180m",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in order to estimate the width of the Jing River, a target point P is selected on the opposite bank of the Jing River, and points Q and S are taken near the bank, so that the points P, Q, and S are in a straight line, and the straight line PS is perpendicular to the river. Choose an appropriate point T on the straight line a passing point S and perpendicular to PS. The intersection of PT and the straight line b passing point Q and perpendicular to PS is R. If QS = 60.0, ST = 120.0, QR = 80.0, then the width of the river PQ is ()\nChoices:\nA:40m\nB:120m\nC:60m\nD:180m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in order to estimate the width of the Jing River, a target point P is selected on the opposite bank of the Jing River, and points Q and S are taken near the bank, so that the points P, Q, and S are in a straight line, and the straight line PS is perpendicular to the river. Choose an appropriate point T on the straight line a passing point S and perpendicular to PS. The intersection of PT and the straight line b passing point Q and perpendicular to PS is R. If QS = 60.0, ST = 120.0, QR = 80.0, then the width of the river PQ is ()\nChoices:\nA:40m\nB:120m\nC:60m\nD:180m",
        "question_for_eval": "As shown in the figure, in order to estimate the width of the Jing River, a target point P is selected on the opposite bank of the Jing River, and points Q and S are taken near the bank, so that the points P, Q, and S are in a straight line, and the straight line PS is perpendicular to the river. Choose an appropriate point T on the straight line a passing point S and perpendicular to PS. The intersection of PT and the straight line b passing point Q and perpendicular to PS is R. If QS = 60.0, ST = 120.0, QR = 80.0, then the width of the river PQ is ()\nChoices:\nA:40m\nB:120m\nC:60m\nD:180m"
    },
    {
        "sample_index": "134",
        "problem_index": "134",
        "problem_version": "Text Only",
        "question": "As shown in the picture, Xiaoying designed a flashlight to measure the height of an ancient city wall. Place a horizontal plane mirror at point P. The light starts from point A and is reflected by the plane mirror and hits the top C of the ancient city wall CD. It is known that AB perpendicular  BD, CD perpendicular  BD. And it is measured that AB = 1.4, BP = 2.1, PD = 12.0. Then the height of the ancient city wall CD is ()\nChoices:\nA:6\u7c73\nB:8\u7c73\nC:10\u7c73\nD:12\u7c73",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the picture, Xiaoying designed a flashlight to measure the height of an ancient city wall. Place a horizontal plane mirror at point P. The light starts from point A and is reflected by the plane mirror and hits the top C of the ancient city wall CD. It is known that AB perpendicular  BD, CD perpendicular  BD. And it is measured that AB = 1.4, BP = 2.1, PD = 12.0. Then the height of the ancient city wall CD is ()\nChoices:\nA:6\u7c73\nB:8\u7c73\nC:10\u7c73\nD:12\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the picture, Xiaoying designed a flashlight to measure the height of an ancient city wall. Place a horizontal plane mirror at point P. The light starts from point A and is reflected by the plane mirror and hits the top C of the ancient city wall CD. It is known that AB perpendicular  BD, CD perpendicular  BD. And it is measured that AB = 1.4, BP = 2.1, PD = 12.0. Then the height of the ancient city wall CD is ()\nChoices:\nA:6\u7c73\nB:8\u7c73\nC:10\u7c73\nD:12\u7c73",
        "question_for_eval": "As shown in the picture, Xiaoying designed a flashlight to measure the height of an ancient city wall. Place a horizontal plane mirror at point P. The light starts from point A and is reflected by the plane mirror and hits the top C of the ancient city wall CD. It is known that AB perpendicular  BD, CD perpendicular  BD. And it is measured that AB = 1.4, BP = 2.1, PD = 12.0. Then the height of the ancient city wall CD is ()\nChoices:\nA:6\u7c73\nB:8\u7c73\nC:10\u7c73\nD:12\u7c73"
    },
    {
        "sample_index": "135",
        "problem_index": "135",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in circle O, point M is the midpoint of arc AB. Connect MO and extend it to intersect circle O at point N, connect BN, if angle AOB = 140.0, then the degree of angle N is ()\nChoices:\nA:70\u00b0\nB:40\u00b0\nC:35\u00b0\nD:20\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in circle O, point M is the midpoint of arc AB. Connect MO and extend it to intersect circle O at point N, connect BN, if angle AOB = 140.0, then the degree of angle N is ()\nChoices:\nA:70\u00b0\nB:40\u00b0\nC:35\u00b0\nD:20\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in circle O, point M is the midpoint of arc AB. Connect MO and extend it to intersect circle O at point N, connect BN, if angle AOB = 140.0, then the degree of angle N is ()\nChoices:\nA:70\u00b0\nB:40\u00b0\nC:35\u00b0\nD:20\u00b0",
        "question_for_eval": "As shown in the figure, in circle O, point M is the midpoint of arc AB. Connect MO and extend it to intersect circle O at point N, connect BN, if angle AOB = 140.0, then the degree of angle N is ()\nChoices:\nA:70\u00b0\nB:40\u00b0\nC:35\u00b0\nD:20\u00b0"
    },
    {
        "sample_index": "136",
        "problem_index": "136",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in order to measure the degree of tree AB, a certain mathematics learning interest group measured the length of the tree's shadow BC in the sun as 9.0. At the same moment, they also measured the shadow length of Xiaoliang in the sun as 1.5. Knowing that Xiaoliang's height is 1.8, then the height of tree AB is ()\nChoices:\nA:10.8m\nB:9m\nC:7.5m\nD:0.3m",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in order to measure the degree of tree AB, a certain mathematics learning interest group measured the length of the tree's shadow BC in the sun as 9.0. At the same moment, they also measured the shadow length of Xiaoliang in the sun as 1.5. Knowing that Xiaoliang's height is 1.8, then the height of tree AB is ()\nChoices:\nA:10.8m\nB:9m\nC:7.5m\nD:0.3m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in order to measure the degree of tree AB, a certain mathematics learning interest group measured the length of the tree's shadow BC in the sun as 9.0. At the same moment, they also measured the shadow length of Xiaoliang in the sun as 1.5. Knowing that Xiaoliang's height is 1.8, then the height of tree AB is ()\nChoices:\nA:10.8m\nB:9m\nC:7.5m\nD:0.3m",
        "question_for_eval": "As shown in the figure, in order to measure the degree of tree AB, a certain mathematics learning interest group measured the length of the tree's shadow BC in the sun as 9.0. At the same moment, they also measured the shadow length of Xiaoliang in the sun as 1.5. Knowing that Xiaoliang's height is 1.8, then the height of tree AB is ()\nChoices:\nA:10.8m\nB:9m\nC:7.5m\nD:0.3m"
    },
    {
        "sample_index": "137",
        "problem_index": "137",
        "problem_version": "Text Only",
        "question": "As shown in the picture, it is an ancient masher in the countryside. It is known that the height of the support column AB is 0.3, the length of the pedal DE is 1.0, and the distance from the support point A to the foot D is 0.6. When foot D touches the ground, the head point E rises ()\nChoices:\nA:0.5\u7c73\nB:0.6\u7c73\nC:0.3\u7c73\nD:0.9\u7c73",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the picture, it is an ancient masher in the countryside. It is known that the height of the support column AB is 0.3, the length of the pedal DE is 1.0, and the distance from the support point A to the foot D is 0.6. When foot D touches the ground, the head point E rises ()\nChoices:\nA:0.5\u7c73\nB:0.6\u7c73\nC:0.3\u7c73\nD:0.9\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the picture, it is an ancient masher in the countryside. It is known that the height of the support column AB is 0.3, the length of the pedal DE is 1.0, and the distance from the support point A to the foot D is 0.6. When foot D touches the ground, the head point E rises ()\nChoices:\nA:0.5\u7c73\nB:0.6\u7c73\nC:0.3\u7c73\nD:0.9\u7c73",
        "question_for_eval": "As shown in the picture, it is an ancient masher in the countryside. It is known that the height of the support column AB is 0.3, the length of the pedal DE is 1.0, and the distance from the support point A to the foot D is 0.6. When foot D touches the ground, the head point E rises ()\nChoices:\nA:0.5\u7c73\nB:0.6\u7c73\nC:0.3\u7c73\nD:0.9\u7c73"
    },
    {
        "sample_index": "138",
        "problem_index": "138",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB parallel  CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is ().\nChoices:\nA:\\frac{6}{5}\nB:\\frac{7}{6}\nC:\\frac{9}{5}\nD:\\frac{15}{2}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB parallel  CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is ().\nChoices:\nA:\\frac{6}{5}\nB:\\frac{7}{6}\nC:\\frac{9}{5}\nD:\\frac{15}{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB parallel  CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is ().\nChoices:\nA:\\frac{6}{5}\nB:\\frac{7}{6}\nC:\\frac{9}{5}\nD:\\frac{15}{2}",
        "question_for_eval": "As shown in the figure, the light source P is directly above the crossbar AB, the shadow of AB under the light is CD, AB parallel  CD, AB = 2.0, CD = 5.0, the distance between point P and CD is 3.0, then the distance between AB and CD is ().\nChoices:\nA:\\frac{6}{5}\nB:\\frac{7}{6}\nC:\\frac{9}{5}\nD:\\frac{15}{2}"
    },
    {
        "sample_index": "139",
        "problem_index": "139",
        "problem_version": "Text Only",
        "question": "As shown in the figure, Xiaoqiang made a small hole imaging device in which the length of the paper tube is 15.0. He prepared a candle with a length of 20.0. To get an image with a height of 4.0, the distance between the candle and the paper tube should be ()\nChoices:\nA:60cm\nB:65cm\nC:70cm\nD:75cm",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, Xiaoqiang made a small hole imaging device in which the length of the paper tube is 15.0. He prepared a candle with a length of 20.0. To get an image with a height of 4.0, the distance between the candle and the paper tube should be ()\nChoices:\nA:60cm\nB:65cm\nC:70cm\nD:75cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, Xiaoqiang made a small hole imaging device in which the length of the paper tube is 15.0. He prepared a candle with a length of 20.0. To get an image with a height of 4.0, the distance between the candle and the paper tube should be ()\nChoices:\nA:60cm\nB:65cm\nC:70cm\nD:75cm",
        "question_for_eval": "As shown in the figure, Xiaoqiang made a small hole imaging device in which the length of the paper tube is 15.0. He prepared a candle with a length of 20.0. To get an image with a height of 4.0, the distance between the candle and the paper tube should be ()\nChoices:\nA:60cm\nB:65cm\nC:70cm\nD:75cm"
    },
    {
        "sample_index": "140",
        "problem_index": "140",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in a badminton game, Lin Dan, the athlete standing at M in the field, clicks the request from N to point B in the opponent. It is known that the net height OA = 1.52, OB = 4.0, OM = 5.0, then when Lin Dan takes off, the distance from the hitting point to the ground NM = ()\nChoices:\nA:3.42m\nB:1.9m\nC:3m\nD:3.24m",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in a badminton game, Lin Dan, the athlete standing at M in the field, clicks the request from N to point B in the opponent. It is known that the net height OA = 1.52, OB = 4.0, OM = 5.0, then when Lin Dan takes off, the distance from the hitting point to the ground NM = ()\nChoices:\nA:3.42m\nB:1.9m\nC:3m\nD:3.24m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in a badminton game, Lin Dan, the athlete standing at M in the field, clicks the request from N to point B in the opponent. It is known that the net height OA = 1.52, OB = 4.0, OM = 5.0, then when Lin Dan takes off, the distance from the hitting point to the ground NM = ()\nChoices:\nA:3.42m\nB:1.9m\nC:3m\nD:3.24m",
        "question_for_eval": "As shown in the figure, in a badminton game, Lin Dan, the athlete standing at M in the field, clicks the request from N to point B in the opponent. It is known that the net height OA = 1.52, OB = 4.0, OM = 5.0, then when Lin Dan takes off, the distance from the hitting point to the ground NM = ()\nChoices:\nA:3.42m\nB:1.9m\nC:3m\nD:3.24m"
    },
    {
        "sample_index": "141",
        "problem_index": "141",
        "problem_version": "Text Only",
        "question": "While measuring the height of the building, Xiao Ming first measured the shadow length BA of the building on the ground as 15.0 (as shown in the figure), and then set up a benchmark with a height of 2.0 at A, and measured the shadow length AC of the benchmark as 3.0, then the height of the building is ()\nChoices:\nA:10\u7c73\nB:12\u7c73\nC:15\u7c73\nD:22.5\u7c73",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: While measuring the height of the building, Xiao Ming first measured the shadow length BA of the building on the ground as 15.0 (as shown in the figure), and then set up a benchmark with a height of 2.0 at A, and measured the shadow length AC of the benchmark as 3.0, then the height of the building is ()\nChoices:\nA:10\u7c73\nB:12\u7c73\nC:15\u7c73\nD:22.5\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: While measuring the height of the building, Xiao Ming first measured the shadow length BA of the building on the ground as 15.0 (as shown in the figure), and then set up a benchmark with a height of 2.0 at A, and measured the shadow length AC of the benchmark as 3.0, then the height of the building is ()\nChoices:\nA:10\u7c73\nB:12\u7c73\nC:15\u7c73\nD:22.5\u7c73",
        "question_for_eval": "While measuring the height of the building, Xiao Ming first measured the shadow length BA of the building on the ground as 15.0 (as shown in the figure), and then set up a benchmark with a height of 2.0 at A, and measured the shadow length AC of the benchmark as 3.0, then the height of the building is ()\nChoices:\nA:10\u7c73\nB:12\u7c73\nC:15\u7c73\nD:22.5\u7c73"
    },
    {
        "sample_index": "142",
        "problem_index": "142",
        "problem_version": "Text Only",
        "question": "As shown in the figure: the length of two vertical telephone poles AB is 6.0, the length of CD is 3.0, AD intersects BC at point E, then the length of the distance from E to the ground EF is ()\nChoices:\nA:2\nB:2.2\nC:2.4\nD:2.5",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure: the length of two vertical telephone poles AB is 6.0, the length of CD is 3.0, AD intersects BC at point E, then the length of the distance from E to the ground EF is ()\nChoices:\nA:2\nB:2.2\nC:2.4\nD:2.5",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure: the length of two vertical telephone poles AB is 6.0, the length of CD is 3.0, AD intersects BC at point E, then the length of the distance from E to the ground EF is ()\nChoices:\nA:2\nB:2.2\nC:2.4\nD:2.5",
        "question_for_eval": "As shown in the figure: the length of two vertical telephone poles AB is 6.0, the length of CD is 3.0, AD intersects BC at point E, then the length of the distance from E to the ground EF is ()\nChoices:\nA:2\nB:2.2\nC:2.4\nD:2.5"
    },
    {
        "sample_index": "143",
        "problem_index": "143",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular  BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()\nChoices:\nA:\\frac{24}{5}cm\nB:4cm\nC:\\frac{24}{7}cm\nD:5cm",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular  BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()\nChoices:\nA:\\frac{24}{5}cm\nB:4cm\nC:\\frac{24}{7}cm\nD:5cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular  BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()\nChoices:\nA:\\frac{24}{5}cm\nB:4cm\nC:\\frac{24}{7}cm\nD:5cm",
        "question_for_eval": "As shown in the figure, a square DEFG model should be cut on a piece of triangle ABC paper. Among them, G and F are on BC, D and E are on AB and AC respectively, AH perpendicular  BC and it intersects DE at M, if BC = 12.0, AH = 8.0, then the edge length of the square DEFG is ()\nChoices:\nA:\\frac{24}{5}cm\nB:4cm\nC:\\frac{24}{7}cm\nD:5cm"
    },
    {
        "sample_index": "144",
        "problem_index": "144",
        "problem_version": "Text Only",
        "question": "On 27.0 2009.0, 10.0, 2009, Shanghai team player Wu Di came to the fore in the National Games and defeated the top-seeded men's singles player Zeng Shaoxuan with a score of 2.0:0.0, and won the men's singles championship in tennis at the National Games. The picture below is a ball played by Wu Di in the final. It is known that the net height is 0.8, and the horizontal distance from the hitting point to the net is 4.0. When the ball is played, the ball can hit the net and the landing point is exactly 6.0 away from the net. Then the height h of the racket hit is ()\nChoices:\nA:\\frac{8}{5}\u7c73\nB:\\frac{4}{3}\u7c73\nC:1\u7c73\nD:\\frac{8}{15}\u7c73",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: On 27.0 2009.0, 10.0, 2009, Shanghai team player Wu Di came to the fore in the National Games and defeated the top-seeded men's singles player Zeng Shaoxuan with a score of 2.0:0.0, and won the men's singles championship in tennis at the National Games. The picture below is a ball played by Wu Di in the final. It is known that the net height is 0.8, and the horizontal distance from the hitting point to the net is 4.0. When the ball is played, the ball can hit the net and the landing point is exactly 6.0 away from the net. Then the height h of the racket hit is ()\nChoices:\nA:\\frac{8}{5}\u7c73\nB:\\frac{4}{3}\u7c73\nC:1\u7c73\nD:\\frac{8}{15}\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: On 27.0 2009.0, 10.0, 2009, Shanghai team player Wu Di came to the fore in the National Games and defeated the top-seeded men's singles player Zeng Shaoxuan with a score of 2.0:0.0, and won the men's singles championship in tennis at the National Games. The picture below is a ball played by Wu Di in the final. It is known that the net height is 0.8, and the horizontal distance from the hitting point to the net is 4.0. When the ball is played, the ball can hit the net and the landing point is exactly 6.0 away from the net. Then the height h of the racket hit is ()\nChoices:\nA:\\frac{8}{5}\u7c73\nB:\\frac{4}{3}\u7c73\nC:1\u7c73\nD:\\frac{8}{15}\u7c73",
        "question_for_eval": "On 27.0 2009.0, 10.0, 2009, Shanghai team player Wu Di came to the fore in the National Games and defeated the top-seeded men's singles player Zeng Shaoxuan with a score of 2.0:0.0, and won the men's singles championship in tennis at the National Games. The picture below is a ball played by Wu Di in the final. It is known that the net height is 0.8, and the horizontal distance from the hitting point to the net is 4.0. When the ball is played, the ball can hit the net and the landing point is exactly 6.0 away from the net. Then the height h of the racket hit is ()\nChoices:\nA:\\frac{8}{5}\u7c73\nB:\\frac{4}{3}\u7c73\nC:1\u7c73\nD:\\frac{8}{15}\u7c73"
    },
    {
        "sample_index": "145",
        "problem_index": "145",
        "problem_version": "Text Only",
        "question": "As shown in the figure, points A, B, and C are on circle O, angle ABO = 40.0, angle ACO = 30.0, then the degree of angle BOC is ()\nChoices:\nA:60\u00b0\nB:70\u00b0\nC:120\u00b0\nD:140\u00b0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, points A, B, and C are on circle O, angle ABO = 40.0, angle ACO = 30.0, then the degree of angle BOC is ()\nChoices:\nA:60\u00b0\nB:70\u00b0\nC:120\u00b0\nD:140\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, points A, B, and C are on circle O, angle ABO = 40.0, angle ACO = 30.0, then the degree of angle BOC is ()\nChoices:\nA:60\u00b0\nB:70\u00b0\nC:120\u00b0\nD:140\u00b0",
        "question_for_eval": "As shown in the figure, points A, B, and C are on circle O, angle ABO = 40.0, angle ACO = 30.0, then the degree of angle BOC is ()\nChoices:\nA:60\u00b0\nB:70\u00b0\nC:120\u00b0\nD:140\u00b0"
    },
    {
        "sample_index": "146",
        "problem_index": "146",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is a ladder leaning against the wall, the foot of the ladder is away from the wall 2.0, the point D on the ladder is away from the wall 1.8, the length of BD is 0.6, then the length of the ladder is ()\nChoices:\nA:5.60\u7c73\nB:6.00\u7c73\nC:6.10\u7c73\nD:6.20\u7c73",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is a ladder leaning against the wall, the foot of the ladder is away from the wall 2.0, the point D on the ladder is away from the wall 1.8, the length of BD is 0.6, then the length of the ladder is ()\nChoices:\nA:5.60\u7c73\nB:6.00\u7c73\nC:6.10\u7c73\nD:6.20\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is a ladder leaning against the wall, the foot of the ladder is away from the wall 2.0, the point D on the ladder is away from the wall 1.8, the length of BD is 0.6, then the length of the ladder is ()\nChoices:\nA:5.60\u7c73\nB:6.00\u7c73\nC:6.10\u7c73\nD:6.20\u7c73",
        "question_for_eval": "As shown in the figure, AB is a ladder leaning against the wall, the foot of the ladder is away from the wall 2.0, the point D on the ladder is away from the wall 1.8, the length of BD is 0.6, then the length of the ladder is ()\nChoices:\nA:5.60\u7c73\nB:6.00\u7c73\nC:6.10\u7c73\nD:6.20\u7c73"
    },
    {
        "sample_index": "147",
        "problem_index": "147",
        "problem_version": "Text Only",
        "question": "In order to measure the height of the school flagpole AC, a school math interest group erected a benchmark DF with a length of 1.5 at point F. As shown in the figure, the length of the shadow EF of DF is measured as 1.0, and then measure the length of the shadow BC of the flagpole AC to be 6.0, then the height of the flagpole AC is ()\nChoices:\nA:6\u7c73\nB:7\u7c73\nC:8.5\u7c73\nD:9\u7c73",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In order to measure the height of the school flagpole AC, a school math interest group erected a benchmark DF with a length of 1.5 at point F. As shown in the figure, the length of the shadow EF of DF is measured as 1.0, and then measure the length of the shadow BC of the flagpole AC to be 6.0, then the height of the flagpole AC is ()\nChoices:\nA:6\u7c73\nB:7\u7c73\nC:8.5\u7c73\nD:9\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In order to measure the height of the school flagpole AC, a school math interest group erected a benchmark DF with a length of 1.5 at point F. As shown in the figure, the length of the shadow EF of DF is measured as 1.0, and then measure the length of the shadow BC of the flagpole AC to be 6.0, then the height of the flagpole AC is ()\nChoices:\nA:6\u7c73\nB:7\u7c73\nC:8.5\u7c73\nD:9\u7c73",
        "question_for_eval": "In order to measure the height of the school flagpole AC, a school math interest group erected a benchmark DF with a length of 1.5 at point F. As shown in the figure, the length of the shadow EF of DF is measured as 1.0, and then measure the length of the shadow BC of the flagpole AC to be 6.0, then the height of the flagpole AC is ()\nChoices:\nA:6\u7c73\nB:7\u7c73\nC:8.5\u7c73\nD:9\u7c73"
    },
    {
        "sample_index": "148",
        "problem_index": "148",
        "problem_version": "Text Only",
        "question": "As shown in the figure, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool to measure the height of the school flagpole, and moves the bamboo pole so that the shadow on the top of the pole and the flag pole falls on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0, and the distance from the flag pole is 22.0, then the height of the flag pole is ()\nChoices:\nA:12m\nB:10m\nC:8m\nD:7m",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool to measure the height of the school flagpole, and moves the bamboo pole so that the shadow on the top of the pole and the flag pole falls on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0, and the distance from the flag pole is 22.0, then the height of the flag pole is ()\nChoices:\nA:12m\nB:10m\nC:8m\nD:7m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool to measure the height of the school flagpole, and moves the bamboo pole so that the shadow on the top of the pole and the flag pole falls on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0, and the distance from the flag pole is 22.0, then the height of the flag pole is ()\nChoices:\nA:12m\nB:10m\nC:8m\nD:7m",
        "question_for_eval": "As shown in the figure, Xiaodong uses a bamboo pole with a length of 3.2 as a measuring tool to measure the height of the school flagpole, and moves the bamboo pole so that the shadow on the top of the pole and the flag pole falls on the same point on the ground. At this time, the distance between the bamboo pole and this point is 8.0, and the distance from the flag pole is 22.0, then the height of the flag pole is ()\nChoices:\nA:12m\nB:10m\nC:8m\nD:7m"
    },
    {
        "sample_index": "149",
        "problem_index": "149",
        "problem_version": "Text Only",
        "question": "As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is \u03b1, AC perpendicular  CD, BD perpendicular  CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()\nChoices:\nA:\\frac{20}{3}\nB:\\frac{10}{3}\nC:7\nD:\\frac{14}{3}",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is \u03b1, AC perpendicular  CD, BD perpendicular  CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()\nChoices:\nA:\\frac{20}{3}\nB:\\frac{10}{3}\nC:7\nD:\\frac{14}{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is \u03b1, AC perpendicular  CD, BD perpendicular  CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()\nChoices:\nA:\\frac{20}{3}\nB:\\frac{10}{3}\nC:7\nD:\\frac{14}{3}",
        "question_for_eval": "As shown in the figure, CD is a plane mirror, the light is emitted from point A, reflected by point E on CD, and irradiated to point B. If the incident angle is \u03b1, AC perpendicular  CD, BD perpendicular  CD, the feet of perpendicular are C, D, and AC = 3.0, BD = 6.0, CD = 10.0, then the length of the line segment ED is ()\nChoices:\nA:\\frac{20}{3}\nB:\\frac{10}{3}\nC:7\nD:\\frac{14}{3}"
    },
    {
        "sample_index": "150",
        "problem_index": "150",
        "problem_version": "Text Only",
        "question": "As shown in the figure, Xiaoming designed two right angles to measure the width of the river BC, he measured AB = 2.0, BD = frac {7.0}{3.0}, CE = 9.0, then the width of the river BC is ()\nChoices:\nA:\\frac{7}{2}\u7c73\nB:\\frac{17}{2}\u7c73\nC:\\frac{40}{7}\u7c73\nD:11\u7c73",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, Xiaoming designed two right angles to measure the width of the river BC, he measured AB = 2.0, BD = frac {7.0}{3.0}, CE = 9.0, then the width of the river BC is ()\nChoices:\nA:\\frac{7}{2}\u7c73\nB:\\frac{17}{2}\u7c73\nC:\\frac{40}{7}\u7c73\nD:11\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, Xiaoming designed two right angles to measure the width of the river BC, he measured AB = 2.0, BD = frac {7.0}{3.0}, CE = 9.0, then the width of the river BC is ()\nChoices:\nA:\\frac{7}{2}\u7c73\nB:\\frac{17}{2}\u7c73\nC:\\frac{40}{7}\u7c73\nD:11\u7c73",
        "question_for_eval": "As shown in the figure, Xiaoming designed two right angles to measure the width of the river BC, he measured AB = 2.0, BD = frac {7.0}{3.0}, CE = 9.0, then the width of the river BC is ()\nChoices:\nA:\\frac{7}{2}\u7c73\nB:\\frac{17}{2}\u7c73\nC:\\frac{40}{7}\u7c73\nD:11\u7c73"
    },
    {
        "sample_index": "151",
        "problem_index": "151",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a student saw a tree by the lake. He visually observed that the distance between himself and the tree is 20.0, and the reflection of the top of the tree in the water is 5.0 far away from him. The student's height is 1.7, and the height of the tree is ( ).\nChoices:\nA:3.4\nB:5.1\nC:6.8\nD:8.5",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a student saw a tree by the lake. He visually observed that the distance between himself and the tree is 20.0, and the reflection of the top of the tree in the water is 5.0 far away from him. The student's height is 1.7, and the height of the tree is ( ).\nChoices:\nA:3.4\nB:5.1\nC:6.8\nD:8.5",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a student saw a tree by the lake. He visually observed that the distance between himself and the tree is 20.0, and the reflection of the top of the tree in the water is 5.0 far away from him. The student's height is 1.7, and the height of the tree is ( ).\nChoices:\nA:3.4\nB:5.1\nC:6.8\nD:8.5",
        "question_for_eval": "As shown in the figure, a student saw a tree by the lake. He visually observed that the distance between himself and the tree is 20.0, and the reflection of the top of the tree in the water is 5.0 far away from him. The student's height is 1.7, and the height of the tree is ( ).\nChoices:\nA:3.4\nB:5.1\nC:6.8\nD:8.5"
    },
    {
        "sample_index": "152",
        "problem_index": "152",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is a fixed climbing ladder leaning on the wall, the distance from the foot of the ladder B to the foot of the wall C is 1.6, the distance from the point D on the ladder to the wall is 1.4, and the length of the ladder is 0.5, then the length of the ladder is ()\nChoices:\nA:3.5m\nB:4m\nC:4.5m\nD:5m",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is a fixed climbing ladder leaning on the wall, the distance from the foot of the ladder B to the foot of the wall C is 1.6, the distance from the point D on the ladder to the wall is 1.4, and the length of the ladder is 0.5, then the length of the ladder is ()\nChoices:\nA:3.5m\nB:4m\nC:4.5m\nD:5m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is a fixed climbing ladder leaning on the wall, the distance from the foot of the ladder B to the foot of the wall C is 1.6, the distance from the point D on the ladder to the wall is 1.4, and the length of the ladder is 0.5, then the length of the ladder is ()\nChoices:\nA:3.5m\nB:4m\nC:4.5m\nD:5m",
        "question_for_eval": "As shown in the figure, AB is a fixed climbing ladder leaning on the wall, the distance from the foot of the ladder B to the foot of the wall C is 1.6, the distance from the point D on the ladder to the wall is 1.4, and the length of the ladder is 0.5, then the length of the ladder is ()\nChoices:\nA:3.5m\nB:4m\nC:4.5m\nD:5m"
    },
    {
        "sample_index": "153",
        "problem_index": "153",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the sunlight enters the room from the windows of the classroom, the length of the shadow of the window frame AB on the ground DE = 1.8, the distance from the lower eaves of the window to the ground BC = 1.0, EC = 1.2, then the height of the window AB is ()\nChoices:\nA:1.5m\nB:1.6m\nC:1.86m\nD:2.16m",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the sunlight enters the room from the windows of the classroom, the length of the shadow of the window frame AB on the ground DE = 1.8, the distance from the lower eaves of the window to the ground BC = 1.0, EC = 1.2, then the height of the window AB is ()\nChoices:\nA:1.5m\nB:1.6m\nC:1.86m\nD:2.16m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the sunlight enters the room from the windows of the classroom, the length of the shadow of the window frame AB on the ground DE = 1.8, the distance from the lower eaves of the window to the ground BC = 1.0, EC = 1.2, then the height of the window AB is ()\nChoices:\nA:1.5m\nB:1.6m\nC:1.86m\nD:2.16m",
        "question_for_eval": "As shown in the figure, the sunlight enters the room from the windows of the classroom, the length of the shadow of the window frame AB on the ground DE = 1.8, the distance from the lower eaves of the window to the ground BC = 1.0, EC = 1.2, then the height of the window AB is ()\nChoices:\nA:1.5m\nB:1.6m\nC:1.86m\nD:2.16m"
    },
    {
        "sample_index": "154",
        "problem_index": "154",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()\nChoices:\nA:3.85\u7c73\nB:4.00\u7c73\nC:4.40\u7c73\nD:4.50\u7c73",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()\nChoices:\nA:3.85\u7c73\nB:4.00\u7c73\nC:4.40\u7c73\nD:4.50\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()\nChoices:\nA:3.85\u7c73\nB:4.00\u7c73\nC:4.40\u7c73\nD:4.50\u7c73",
        "question_for_eval": "As shown in the figure, AB is a long ladder leaning on the wall, the foot of the ladder B is away from the wall 1.6, the point D on the ladder is away from the wall 1.4, the length of BD is 0.55, then the length of the ladder is ()\nChoices:\nA:3.85\u7c73\nB:4.00\u7c73\nC:4.40\u7c73\nD:4.50\u7c73"
    },
    {
        "sample_index": "155",
        "problem_index": "155",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the student Xiao Li whose height is 1.6 wants to measure the height of the school's flagpole. When he stands at C, the shadow of the top of his head coincides with the shadow of the top of the flagpole, and AC = 2.0, BC = 8.0, then the height of the flagpole is ()\nChoices:\nA:6.4\u7c73\nB:7\u7c73\nC:8\u7c73\nD:9\u7c73",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the student Xiao Li whose height is 1.6 wants to measure the height of the school's flagpole. When he stands at C, the shadow of the top of his head coincides with the shadow of the top of the flagpole, and AC = 2.0, BC = 8.0, then the height of the flagpole is ()\nChoices:\nA:6.4\u7c73\nB:7\u7c73\nC:8\u7c73\nD:9\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the student Xiao Li whose height is 1.6 wants to measure the height of the school's flagpole. When he stands at C, the shadow of the top of his head coincides with the shadow of the top of the flagpole, and AC = 2.0, BC = 8.0, then the height of the flagpole is ()\nChoices:\nA:6.4\u7c73\nB:7\u7c73\nC:8\u7c73\nD:9\u7c73",
        "question_for_eval": "As shown in the figure, the student Xiao Li whose height is 1.6 wants to measure the height of the school's flagpole. When he stands at C, the shadow of the top of his head coincides with the shadow of the top of the flagpole, and AC = 2.0, BC = 8.0, then the height of the flagpole is ()\nChoices:\nA:6.4\u7c73\nB:7\u7c73\nC:8\u7c73\nD:9\u7c73"
    },
    {
        "sample_index": "156",
        "problem_index": "156",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the quadrilateral ABCD and A\u2032B\u2032C\u2032D\u2032 are similar figures with the similar center at point O. If OA\u2032: A\u2032A = 2.0:1.0, the area of \u200b\u200bthe quadrilateral A\u2032B\u2032C\u2032D\u2032 is 12.0 ^ 2, then the area of \u200b\u200bthe quadrilateral ABCD is ()\nChoices:\nA:24cm^{2}\nB:27cm^{2}\nC:36cm^{2}\nD:54cm^{2}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the quadrilateral ABCD and A\u2032B\u2032C\u2032D\u2032 are similar figures with the similar center at point O. If OA\u2032: A\u2032A = 2.0:1.0, the area of \u200b\u200bthe quadrilateral A\u2032B\u2032C\u2032D\u2032 is 12.0 ^ 2, then the area of \u200b\u200bthe quadrilateral ABCD is ()\nChoices:\nA:24cm^{2}\nB:27cm^{2}\nC:36cm^{2}\nD:54cm^{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the quadrilateral ABCD and A\u2032B\u2032C\u2032D\u2032 are similar figures with the similar center at point O. If OA\u2032: A\u2032A = 2.0:1.0, the area of \u200b\u200bthe quadrilateral A\u2032B\u2032C\u2032D\u2032 is 12.0 ^ 2, then the area of \u200b\u200bthe quadrilateral ABCD is ()\nChoices:\nA:24cm^{2}\nB:27cm^{2}\nC:36cm^{2}\nD:54cm^{2}",
        "question_for_eval": "As shown in the figure, the quadrilateral ABCD and A\u2032B\u2032C\u2032D\u2032 are similar figures with the similar center at point O. If OA\u2032: A\u2032A = 2.0:1.0, the area of \u200b\u200bthe quadrilateral A\u2032B\u2032C\u2032D\u2032 is 12.0 ^ 2, then the area of \u200b\u200bthe quadrilateral ABCD is ()\nChoices:\nA:24cm^{2}\nB:27cm^{2}\nC:36cm^{2}\nD:54cm^{2}"
    },
    {
        "sample_index": "157",
        "problem_index": "157",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC, angle C = 90.0, if AC = 4.0, BC = 3.0, then cosB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC, angle C = 90.0, if AC = 4.0, BC = 3.0, then cosB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC, angle C = 90.0, if AC = 4.0, BC = 3.0, then cosB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}",
        "question_for_eval": "As shown in the figure, in triangle ABC, angle C = 90.0, if AC = 4.0, BC = 3.0, then cosB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}"
    },
    {
        "sample_index": "158",
        "problem_index": "158",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, BC = 3.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{4}{3}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{3}{5}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, BC = 3.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{4}{3}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{3}{5}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, BC = 3.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{4}{3}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{3}{5}",
        "question_for_eval": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, BC = 3.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{4}{3}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{3}{5}"
    },
    {
        "sample_index": "159",
        "problem_index": "159",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 3.0, BC = 4.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{5}{3}\nC:\\frac{4}{5}\nD:\\frac{3}{4}",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 3.0, BC = 4.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{5}{3}\nC:\\frac{4}{5}\nD:\\frac{3}{4}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 3.0, BC = 4.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{5}{3}\nC:\\frac{4}{5}\nD:\\frac{3}{4}",
        "question_for_eval": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 3.0, BC = 4.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{5}{3}\nC:\\frac{4}{5}\nD:\\frac{3}{4}"
    },
    {
        "sample_index": "160",
        "problem_index": "160",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then the value of tanB is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then the value of tanB is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then the value of tanB is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}",
        "question_for_eval": "As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AB = 10.0, AC = 8.0, then the value of tanB is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{3}{4}\nC:\\frac{4}{5}\nD:\\frac{4}{3}"
    },
    {
        "sample_index": "161",
        "problem_index": "161",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the homothetic figures are composed of a triangle ruler and its center projection under the light. If the ratio of the distance from the bulb to the vertex of the triangle ruler to the distance from the bulb to the corresponding vertex of the triangular ruler projection is 2.0:5.0, and the length of one edge of the triangle ruler is 8.0, Then the corresponding edge length of the projection triangle is ()\nChoices:\nA:8cm\nB:20cm\nC:3.2cm\nD:10cm",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the homothetic figures are composed of a triangle ruler and its center projection under the light. If the ratio of the distance from the bulb to the vertex of the triangle ruler to the distance from the bulb to the corresponding vertex of the triangular ruler projection is 2.0:5.0, and the length of one edge of the triangle ruler is 8.0, Then the corresponding edge length of the projection triangle is ()\nChoices:\nA:8cm\nB:20cm\nC:3.2cm\nD:10cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the homothetic figures are composed of a triangle ruler and its center projection under the light. If the ratio of the distance from the bulb to the vertex of the triangle ruler to the distance from the bulb to the corresponding vertex of the triangular ruler projection is 2.0:5.0, and the length of one edge of the triangle ruler is 8.0, Then the corresponding edge length of the projection triangle is ()\nChoices:\nA:8cm\nB:20cm\nC:3.2cm\nD:10cm",
        "question_for_eval": "As shown in the figure, the homothetic figures are composed of a triangle ruler and its center projection under the light. If the ratio of the distance from the bulb to the vertex of the triangle ruler to the distance from the bulb to the corresponding vertex of the triangular ruler projection is 2.0:5.0, and the length of one edge of the triangle ruler is 8.0, Then the corresponding edge length of the projection triangle is ()\nChoices:\nA:8cm\nB:20cm\nC:3.2cm\nD:10cm"
    },
    {
        "sample_index": "162",
        "problem_index": "162",
        "problem_version": "Text Only",
        "question": "As shown in the figure, given the angle of circumference angle BAC = 40.0, then the degree of the central angle angle BOC is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:80\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, given the angle of circumference angle BAC = 40.0, then the degree of the central angle angle BOC is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:80\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, given the angle of circumference angle BAC = 40.0, then the degree of the central angle angle BOC is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:80\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, given the angle of circumference angle BAC = 40.0, then the degree of the central angle angle BOC is ()\nChoices:\nA:40\u00b0\nB:60\u00b0\nC:80\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "163",
        "problem_index": "163",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}",
        "question_for_eval": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of cosA is ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}"
    },
    {
        "sample_index": "164",
        "problem_index": "164",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in triangle ABC, angle C = Rtangle , AB = 5.0, AC = 4.0, then the value of sinA is ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{5}\nC:\\frac{3}{5}\nD:\\frac{5}{3}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in triangle ABC, angle C = Rtangle , AB = 5.0, AC = 4.0, then the value of sinA is ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{5}\nC:\\frac{3}{5}\nD:\\frac{5}{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in triangle ABC, angle C = Rtangle , AB = 5.0, AC = 4.0, then the value of sinA is ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{5}\nC:\\frac{3}{5}\nD:\\frac{5}{3}",
        "question_for_eval": "As shown in the figure, in triangle ABC, angle C = Rtangle , AB = 5.0, AC = 4.0, then the value of sinA is ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{5}\nC:\\frac{3}{5}\nD:\\frac{5}{3}"
    },
    {
        "sample_index": "165",
        "problem_index": "165",
        "problem_version": "Text Only",
        "question": "In Rttriangle ABC, angle C = 90.0, AB = 2.0, BC = 1.0, then the value of sinB is ()\nChoices:\nA:\\frac{1}{2}\nB:\\frac{\u221a{2}}{2}\nC:\\frac{\u221a{3}}{2}\nD:2",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In Rttriangle ABC, angle C = 90.0, AB = 2.0, BC = 1.0, then the value of sinB is ()\nChoices:\nA:\\frac{1}{2}\nB:\\frac{\u221a{2}}{2}\nC:\\frac{\u221a{3}}{2}\nD:2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In Rttriangle ABC, angle C = 90.0, AB = 2.0, BC = 1.0, then the value of sinB is ()\nChoices:\nA:\\frac{1}{2}\nB:\\frac{\u221a{2}}{2}\nC:\\frac{\u221a{3}}{2}\nD:2",
        "question_for_eval": "In Rttriangle ABC, angle C = 90.0, AB = 2.0, BC = 1.0, then the value of sinB is ()\nChoices:\nA:\\frac{1}{2}\nB:\\frac{\u221a{2}}{2}\nC:\\frac{\u221a{3}}{2}\nD:2"
    },
    {
        "sample_index": "166",
        "problem_index": "166",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in Rttriangle ABC, it is known that angle A = 90.0, AC = 3.0, AB = 4.0, then sinB is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{3}{5}\nC:\\frac{4}{5}\nD:\\frac{5}{4}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in Rttriangle ABC, it is known that angle A = 90.0, AC = 3.0, AB = 4.0, then sinB is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{3}{5}\nC:\\frac{4}{5}\nD:\\frac{5}{4}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in Rttriangle ABC, it is known that angle A = 90.0, AC = 3.0, AB = 4.0, then sinB is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{3}{5}\nC:\\frac{4}{5}\nD:\\frac{5}{4}",
        "question_for_eval": "As shown in the figure, in Rttriangle ABC, it is known that angle A = 90.0, AC = 3.0, AB = 4.0, then sinB is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{3}{5}\nC:\\frac{4}{5}\nD:\\frac{5}{4}"
    },
    {
        "sample_index": "167",
        "problem_index": "167",
        "problem_version": "Text Only",
        "question": "As shown in the figure: In Rttriangle ABC, angle C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure: In Rttriangle ABC, angle C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure: In Rttriangle ABC, angle C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}",
        "question_for_eval": "As shown in the figure: In Rttriangle ABC, angle C = 90.0, AC = 8.0, AB = 10.0, then the value of sinB is equal to ()\nChoices:\nA:\\frac{3}{5}\nB:\\frac{4}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{3}"
    },
    {
        "sample_index": "168",
        "problem_index": "168",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (2.0,3.0), then the value of tan\u03b1 is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{2}\nC:\\frac{2\u221a{13}}{13}\nD:\\frac{3\u221a{13}}{13}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (2.0,3.0), then the value of tan\u03b1 is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{2}\nC:\\frac{2\u221a{13}}{13}\nD:\\frac{3\u221a{13}}{13}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (2.0,3.0), then the value of tan\u03b1 is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{2}\nC:\\frac{2\u221a{13}}{13}\nD:\\frac{3\u221a{13}}{13}",
        "question_for_eval": "As shown in the figure, in the plane rectangular coordinate system, the coordinates of point A are (2.0,3.0), then the value of tan\u03b1 is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{2}\nC:\\frac{2\u221a{13}}{13}\nD:\\frac{3\u221a{13}}{13}"
    },
    {
        "sample_index": "169",
        "problem_index": "169",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 4.0, tanA = frac {1.0}{2.0}, then the length of BC is ()\nChoices:\nA:2\nB:8\nC:2\u221a{5}\nD:4\u221a{5}",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 4.0, tanA = frac {1.0}{2.0}, then the length of BC is ()\nChoices:\nA:2\nB:8\nC:2\u221a{5}\nD:4\u221a{5}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 4.0, tanA = frac {1.0}{2.0}, then the length of BC is ()\nChoices:\nA:2\nB:8\nC:2\u221a{5}\nD:4\u221a{5}",
        "question_for_eval": "As shown in the figure, it is known that in Rttriangle ABC, angle C = 90.0, AC = 4.0, tanA = frac {1.0}{2.0}, then the length of BC is ()\nChoices:\nA:2\nB:8\nC:2\u221a{5}\nD:4\u221a{5}"
    },
    {
        "sample_index": "170",
        "problem_index": "170",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{5}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{5}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{5}",
        "question_for_eval": "As shown in the figure, in Rttriangle ABC, angle C = 90.0, AC = 4.0, AB = 5.0, then the value of sinB is ()\nChoices:\nA:\\frac{2}{3}\nB:\\frac{3}{5}\nC:\\frac{3}{4}\nD:\\frac{4}{5}"
    },
    {
        "sample_index": "171",
        "problem_index": "171",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the hypotenuse of Rttriangle ABC AB = 10.0, cosA = frac {3.0}{5.0}, then the length of BC is ()\nChoices:\nA:5cm\nB:6cm\nC:3cm\nD:8cm",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the hypotenuse of Rttriangle ABC AB = 10.0, cosA = frac {3.0}{5.0}, then the length of BC is ()\nChoices:\nA:5cm\nB:6cm\nC:3cm\nD:8cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the hypotenuse of Rttriangle ABC AB = 10.0, cosA = frac {3.0}{5.0}, then the length of BC is ()\nChoices:\nA:5cm\nB:6cm\nC:3cm\nD:8cm",
        "question_for_eval": "As shown in the figure, the hypotenuse of Rttriangle ABC AB = 10.0, cosA = frac {3.0}{5.0}, then the length of BC is ()\nChoices:\nA:5cm\nB:6cm\nC:3cm\nD:8cm"
    },
    {
        "sample_index": "172",
        "problem_index": "172",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in the quadrilateral ABCD, E and F are the midpoints of AB and AD respectively. If EF = 2.0, BC = 5.0, CD = 3.0, then tanC is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{3}\nC:\\frac{3}{5}\nD:\\frac{4}{5}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in the quadrilateral ABCD, E and F are the midpoints of AB and AD respectively. If EF = 2.0, BC = 5.0, CD = 3.0, then tanC is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{3}\nC:\\frac{3}{5}\nD:\\frac{4}{5}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in the quadrilateral ABCD, E and F are the midpoints of AB and AD respectively. If EF = 2.0, BC = 5.0, CD = 3.0, then tanC is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{3}\nC:\\frac{3}{5}\nD:\\frac{4}{5}",
        "question_for_eval": "As shown in the figure, in the quadrilateral ABCD, E and F are the midpoints of AB and AD respectively. If EF = 2.0, BC = 5.0, CD = 3.0, then tanC is equal to ()\nChoices:\nA:\\frac{3}{4}\nB:\\frac{4}{3}\nC:\\frac{3}{5}\nD:\\frac{4}{5}"
    },
    {
        "sample_index": "173",
        "problem_index": "173",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that AB and AD are the chords of circle O, angle BOD = 50.0, then the degree of angle BAD is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:25\u00b0\nD:35\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that AB and AD are the chords of circle O, angle BOD = 50.0, then the degree of angle BAD is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:25\u00b0\nD:35\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that AB and AD are the chords of circle O, angle BOD = 50.0, then the degree of angle BAD is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:25\u00b0\nD:35\u00b0",
        "question_for_eval": "As shown in the figure, it is known that AB and AD are the chords of circle O, angle BOD = 50.0, then the degree of angle BAD is ()\nChoices:\nA:50\u00b0\nB:40\u00b0\nC:25\u00b0\nD:35\u00b0"
    },
    {
        "sample_index": "174",
        "problem_index": "174",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that O is a point in the quadrilateral ABCD, OA = OB = OC, angle ABC = angle ADC = 65.0, then angle DAO + angle DCO = ()\nChoices:\nA:90\u00b0\nB:110\u00b0\nC:120\u00b0\nD:165\u00b0",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that O is a point in the quadrilateral ABCD, OA = OB = OC, angle ABC = angle ADC = 65.0, then angle DAO + angle DCO = ()\nChoices:\nA:90\u00b0\nB:110\u00b0\nC:120\u00b0\nD:165\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that O is a point in the quadrilateral ABCD, OA = OB = OC, angle ABC = angle ADC = 65.0, then angle DAO + angle DCO = ()\nChoices:\nA:90\u00b0\nB:110\u00b0\nC:120\u00b0\nD:165\u00b0",
        "question_for_eval": "As shown in the figure, it is known that O is a point in the quadrilateral ABCD, OA = OB = OC, angle ABC = angle ADC = 65.0, then angle DAO + angle DCO = ()\nChoices:\nA:90\u00b0\nB:110\u00b0\nC:120\u00b0\nD:165\u00b0"
    },
    {
        "sample_index": "175",
        "problem_index": "175",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AC is the diameter of circle O, if angle OBC = 40.0, then the degree of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AC is the diameter of circle O, if angle OBC = 40.0, then the degree of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AC is the diameter of circle O, if angle OBC = 40.0, then the degree of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0",
        "question_for_eval": "As shown in the figure, AC is the diameter of circle O, if angle OBC = 40.0, then the degree of angle AOB is ()\nChoices:\nA:40\u00b0\nB:50\u00b0\nC:80\u00b0\nD:100\u00b0"
    },
    {
        "sample_index": "176",
        "problem_index": "176",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in circle A, the known chord BC = 8.0, DE = 6.0, angle BAC + angle EAD = 180.0, then the radius of circle A is ()\nChoices:\nA:10\nB:6\nC:5\nD:8",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in circle A, the known chord BC = 8.0, DE = 6.0, angle BAC + angle EAD = 180.0, then the radius of circle A is ()\nChoices:\nA:10\nB:6\nC:5\nD:8",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in circle A, the known chord BC = 8.0, DE = 6.0, angle BAC + angle EAD = 180.0, then the radius of circle A is ()\nChoices:\nA:10\nB:6\nC:5\nD:8",
        "question_for_eval": "As shown in the figure, in circle A, the known chord BC = 8.0, DE = 6.0, angle BAC + angle EAD = 180.0, then the radius of circle A is ()\nChoices:\nA:10\nB:6\nC:5\nD:8"
    },
    {
        "sample_index": "177",
        "problem_index": "177",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the cross section of a tunnel is a semicircle with a radius of 3.4, and a truck with a width of 3.2 can pass through the tunnel.\nChoices:\nA:3m\nB:3.4m\nC:4m\nD:2.8m",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the cross section of a tunnel is a semicircle with a radius of 3.4, and a truck with a width of 3.2 can pass through the tunnel.\nChoices:\nA:3m\nB:3.4m\nC:4m\nD:2.8m",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the cross section of a tunnel is a semicircle with a radius of 3.4, and a truck with a width of 3.2 can pass through the tunnel.\nChoices:\nA:3m\nB:3.4m\nC:4m\nD:2.8m",
        "question_for_eval": "As shown in the figure, the cross section of a tunnel is a semicircle with a radius of 3.4, and a truck with a width of 3.2 can pass through the tunnel.\nChoices:\nA:3m\nB:3.4m\nC:4m\nD:2.8m"
    },
    {
        "sample_index": "178",
        "problem_index": "178",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, if angle ACB = 30.0, AB = 6.0, then the radius of circle O is ()\nChoices:\nA:3\nB:2\u221a{3}\nC:6\nD:4\u221a{3}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O, if angle ACB = 30.0, AB = 6.0, then the radius of circle O is ()\nChoices:\nA:3\nB:2\u221a{3}\nC:6\nD:4\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O, if angle ACB = 30.0, AB = 6.0, then the radius of circle O is ()\nChoices:\nA:3\nB:2\u221a{3}\nC:6\nD:4\u221a{3}",
        "question_for_eval": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, if angle ACB = 30.0, AB = 6.0, then the radius of circle O is ()\nChoices:\nA:3\nB:2\u221a{3}\nC:6\nD:4\u221a{3}"
    },
    {
        "sample_index": "179",
        "problem_index": "179",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle C = 30.0, the radius of circle O is 5.0, if point P is a point on circle O, in triangle ABP, PB = AB, then the length of PA is ( )\nChoices:\nA:5\nB:\\frac{5\u221a{3}}{2}\nC:5\u221a{2}\nD:5\u221a{3}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle C = 30.0, the radius of circle O is 5.0, if point P is a point on circle O, in triangle ABP, PB = AB, then the length of PA is ( )\nChoices:\nA:5\nB:\\frac{5\u221a{3}}{2}\nC:5\u221a{2}\nD:5\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle C = 30.0, the radius of circle O is 5.0, if point P is a point on circle O, in triangle ABP, PB = AB, then the length of PA is ( )\nChoices:\nA:5\nB:\\frac{5\u221a{3}}{2}\nC:5\u221a{2}\nD:5\u221a{3}",
        "question_for_eval": "As shown in the figure, triangle ABC is the inscribed triangle of circle O, angle C = 30.0, the radius of circle O is 5.0, if point P is a point on circle O, in triangle ABP, PB = AB, then the length of PA is ( )\nChoices:\nA:5\nB:\\frac{5\u221a{3}}{2}\nC:5\u221a{2}\nD:5\u221a{3}"
    },
    {
        "sample_index": "180",
        "problem_index": "180",
        "problem_version": "Text Only",
        "question": "As shown in the figure, triangle ABC is inscribed in circle O, OC perpendicular  OB, OD perpendicular  AB intersects AC at point E. Knowing that the radius of circle O is 1.0, then the value of AE^ 2 + CE^ 2 is ()\nChoices:\nA:1\nB:2\nC:3\nD:4",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, triangle ABC is inscribed in circle O, OC perpendicular  OB, OD perpendicular  AB intersects AC at point E. Knowing that the radius of circle O is 1.0, then the value of AE^ 2 + CE^ 2 is ()\nChoices:\nA:1\nB:2\nC:3\nD:4",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, triangle ABC is inscribed in circle O, OC perpendicular  OB, OD perpendicular  AB intersects AC at point E. Knowing that the radius of circle O is 1.0, then the value of AE^ 2 + CE^ 2 is ()\nChoices:\nA:1\nB:2\nC:3\nD:4",
        "question_for_eval": "As shown in the figure, triangle ABC is inscribed in circle O, OC perpendicular  OB, OD perpendicular  AB intersects AC at point E. Knowing that the radius of circle O is 1.0, then the value of AE^ 2 + CE^ 2 is ()\nChoices:\nA:1\nB:2\nC:3\nD:4"
    },
    {
        "sample_index": "181",
        "problem_index": "181",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, and AB is the diameter of circle O, if OC = 5.0, AC = 6.0, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:\u65e0\u6cd5\u786e\u5b9a",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, and AB is the diameter of circle O, if OC = 5.0, AC = 6.0, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:\u65e0\u6cd5\u786e\u5b9a",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, and AB is the diameter of circle O, if OC = 5.0, AC = 6.0, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:\u65e0\u6cd5\u786e\u5b9a",
        "question_for_eval": "As shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, and AB is the diameter of circle O, if OC = 5.0, AC = 6.0, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:\u65e0\u6cd5\u786e\u5b9a"
    },
    {
        "sample_index": "182",
        "problem_index": "182",
        "problem_version": "Text Only",
        "question": "As shown in the figure, angle XOY = 45.0, the two vertices A and B of a right triangle ABC move on OX and OY respectively, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8\u221a{2}\nD:10\u221a{2}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, angle XOY = 45.0, the two vertices A and B of a right triangle ABC move on OX and OY respectively, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8\u221a{2}\nD:10\u221a{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, angle XOY = 45.0, the two vertices A and B of a right triangle ABC move on OX and OY respectively, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8\u221a{2}\nD:10\u221a{2}",
        "question_for_eval": "As shown in the figure, angle XOY = 45.0, the two vertices A and B of a right triangle ABC move on OX and OY respectively, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8\u221a{2}\nD:10\u221a{2}"
    },
    {
        "sample_index": "183",
        "problem_index": "183",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that the angle between the diameter AB of circle O and the chord AC is 30.0, the tangent PC passing through point C and the extended line of AB intersect at point P, the radius of circle O is 2.0, then PC is ()\nChoices:\nA:4\nB:4\u221a{3}\nC:6\nD:2\u221a{3}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that the angle between the diameter AB of circle O and the chord AC is 30.0, the tangent PC passing through point C and the extended line of AB intersect at point P, the radius of circle O is 2.0, then PC is ()\nChoices:\nA:4\nB:4\u221a{3}\nC:6\nD:2\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that the angle between the diameter AB of circle O and the chord AC is 30.0, the tangent PC passing through point C and the extended line of AB intersect at point P, the radius of circle O is 2.0, then PC is ()\nChoices:\nA:4\nB:4\u221a{3}\nC:6\nD:2\u221a{3}",
        "question_for_eval": "As shown in the figure, it is known that the angle between the diameter AB of circle O and the chord AC is 30.0, the tangent PC passing through point C and the extended line of AB intersect at point P, the radius of circle O is 2.0, then PC is ()\nChoices:\nA:4\nB:4\u221a{3}\nC:6\nD:2\u221a{3}"
    },
    {
        "sample_index": "184",
        "problem_index": "184",
        "problem_version": "Text Only",
        "question": "As shown in the figure, in the circle O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that angle DAC = 30.0, the length of the line segment CD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, in the circle O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that angle DAC = 30.0, the length of the line segment CD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, in the circle O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that angle DAC = 30.0, the length of the line segment CD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}",
        "question_for_eval": "As shown in the figure, in the circle O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that angle DAC = 30.0, the length of the line segment CD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}"
    },
    {
        "sample_index": "185",
        "problem_index": "185",
        "problem_version": "Text Only",
        "question": "As shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, draw a tangent of circle O through any point P on the straight line L , and the tangent point is Q; if PQ is taken as the edge to make the square PQRS, then the minimum area of the square PQRS is ()\nChoices:\nA:7\nB:8\nC:9\nD:10",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, draw a tangent of circle O through any point P on the straight line L , and the tangent point is Q; if PQ is taken as the edge to make the square PQRS, then the minimum area of the square PQRS is ()\nChoices:\nA:7\nB:8\nC:9\nD:10",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, draw a tangent of circle O through any point P on the straight line L , and the tangent point is Q; if PQ is taken as the edge to make the square PQRS, then the minimum area of the square PQRS is ()\nChoices:\nA:7\nB:8\nC:9\nD:10",
        "question_for_eval": "As shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, draw a tangent of circle O through any point P on the straight line L , and the tangent point is Q; if PQ is taken as the edge to make the square PQRS, then the minimum area of the square PQRS is ()\nChoices:\nA:7\nB:8\nC:9\nD:10"
    },
    {
        "sample_index": "186",
        "problem_index": "186",
        "problem_version": "Text Only",
        "question": "As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular  AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular  AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular  AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}",
        "question_for_eval": "As shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular  AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:2\u221a{3}"
    },
    {
        "sample_index": "187",
        "problem_index": "187",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the straight line AB is tangent to circle O at point A, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:\u221a{3}\nD:2\u221a{3}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the straight line AB is tangent to circle O at point A, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:\u221a{3}\nD:2\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the straight line AB is tangent to circle O at point A, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:\u221a{3}\nD:2\u221a{3}",
        "question_for_eval": "As shown in the figure, the straight line AB is tangent to circle O at point A, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:\u221a{3}\nD:2\u221a{3}"
    },
    {
        "sample_index": "188",
        "problem_index": "188",
        "problem_version": "Text Only",
        "question": "As shown in the figure, it is known that BA is the tangent of circle O, and connect OB to intersect circle O at point C. If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()\nChoices:\nA:2\u221a{2}-1\nB:\u221a{2}\nC:2\u221a{2}-2\nD:2-\u221a{2}",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, it is known that BA is the tangent of circle O, and connect OB to intersect circle O at point C. If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()\nChoices:\nA:2\u221a{2}-1\nB:\u221a{2}\nC:2\u221a{2}-2\nD:2-\u221a{2}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, it is known that BA is the tangent of circle O, and connect OB to intersect circle O at point C. If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()\nChoices:\nA:2\u221a{2}-1\nB:\u221a{2}\nC:2\u221a{2}-2\nD:2-\u221a{2}",
        "question_for_eval": "As shown in the figure, it is known that BA is the tangent of circle O, and connect OB to intersect circle O at point C. If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()\nChoices:\nA:2\u221a{2}-1\nB:\u221a{2}\nC:2\u221a{2}-2\nD:2-\u221a{2}"
    },
    {
        "sample_index": "189",
        "problem_index": "189",
        "problem_version": "Text Only",
        "question": "As shown in the figure, point A is a point outside circle O, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5\nD:3",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, point A is a point outside circle O, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5\nD:3",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, point A is a point outside circle O, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5\nD:3",
        "question_for_eval": "As shown in the figure, point A is a point outside circle O, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5\nD:3"
    },
    {
        "sample_index": "190",
        "problem_index": "190",
        "problem_version": "Text Only",
        "question": "As shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, AC is the diameter of circle O, given that angle P = 50.0, then the size of angle ACB is ()\nChoices:\nA:65\u00b0\nB:60\u00b0\nC:55\u00b0\nD:50\u00b0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, AC is the diameter of circle O, given that angle P = 50.0, then the size of angle ACB is ()\nChoices:\nA:65\u00b0\nB:60\u00b0\nC:55\u00b0\nD:50\u00b0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, AC is the diameter of circle O, given that angle P = 50.0, then the size of angle ACB is ()\nChoices:\nA:65\u00b0\nB:60\u00b0\nC:55\u00b0\nD:50\u00b0",
        "question_for_eval": "As shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, AC is the diameter of circle O, given that angle P = 50.0, then the size of angle ACB is ()\nChoices:\nA:65\u00b0\nB:60\u00b0\nC:55\u00b0\nD:50\u00b0"
    },
    {
        "sample_index": "191",
        "problem_index": "191",
        "problem_version": "Text Only",
        "question": "As shown in the figure, points A, B, and C are on circle O, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()\nChoices:\nA:3\nB:\\frac{3}{2}\nC:\\frac{2}{3}\u221a{3}\nD:\\frac{3}{2}\u221a{3}",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, points A, B, and C are on circle O, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()\nChoices:\nA:3\nB:\\frac{3}{2}\nC:\\frac{2}{3}\u221a{3}\nD:\\frac{3}{2}\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, points A, B, and C are on circle O, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()\nChoices:\nA:3\nB:\\frac{3}{2}\nC:\\frac{2}{3}\u221a{3}\nD:\\frac{3}{2}\u221a{3}",
        "question_for_eval": "As shown in the figure, points A, B, and C are on circle O, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()\nChoices:\nA:3\nB:\\frac{3}{2}\nC:\\frac{2}{3}\u221a{3}\nD:\\frac{3}{2}\u221a{3}"
    },
    {
        "sample_index": "192",
        "problem_index": "192",
        "problem_version": "Text Only",
        "question": "As shown in the figure, point P is outside circle O. PA and PB are connected. the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()\nChoices:\nA:5\nB:10\nC:10\u221a{3}\nD:5\u221a{3}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, point P is outside circle O. PA and PB are connected. the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()\nChoices:\nA:5\nB:10\nC:10\u221a{3}\nD:5\u221a{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, point P is outside circle O. PA and PB are connected. the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()\nChoices:\nA:5\nB:10\nC:10\u221a{3}\nD:5\u221a{3}",
        "question_for_eval": "As shown in the figure, point P is outside circle O. PA and PB are connected. the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()\nChoices:\nA:5\nB:10\nC:10\u221a{3}\nD:5\u221a{3}"
    },
    {
        "sample_index": "193",
        "problem_index": "193",
        "problem_version": "Text Only",
        "question": "As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively, and the tangent point C is on the arc AB. If the length of PA is 2.0, then the perimeter of triangle PEF is ()\nChoices:\nA:8\nB:6\nC:4\nD:2",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively, and the tangent point C is on the arc AB. If the length of PA is 2.0, then the perimeter of triangle PEF is ()\nChoices:\nA:8\nB:6\nC:4\nD:2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively, and the tangent point C is on the arc AB. If the length of PA is 2.0, then the perimeter of triangle PEF is ()\nChoices:\nA:8\nB:6\nC:4\nD:2",
        "question_for_eval": "As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively, and the tangent point C is on the arc AB. If the length of PA is 2.0, then the perimeter of triangle PEF is ()\nChoices:\nA:8\nB:6\nC:4\nD:2"
    },
    {
        "sample_index": "194",
        "problem_index": "194",
        "problem_version": "Text Only",
        "question": "Put the ruler, the triangle ruler and the round nut on the desktop as shown in the figure, angle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6\u221a{3}cm\nD:12\u221a{3}cm",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Put the ruler, the triangle ruler and the round nut on the desktop as shown in the figure, angle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6\u221a{3}cm\nD:12\u221a{3}cm",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Put the ruler, the triangle ruler and the round nut on the desktop as shown in the figure, angle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6\u221a{3}cm\nD:12\u221a{3}cm",
        "question_for_eval": "Put the ruler, the triangle ruler and the round nut on the desktop as shown in the figure, angle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6\u221a{3}cm\nD:12\u221a{3}cm"
    },
    {
        "sample_index": "195",
        "problem_index": "195",
        "problem_version": "Text Only",
        "question": "As shown in the figure, point P is a point on the extended line AB of the diameter of circle O, passing point P to draw the tangent PC of circle O, and the tangent point is C. If AO = OB = PB = 1.0, then the length of PC is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:\u221a{5}",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, point P is a point on the extended line AB of the diameter of circle O, passing point P to draw the tangent PC of circle O, and the tangent point is C. If AO = OB = PB = 1.0, then the length of PC is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:\u221a{5}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, point P is a point on the extended line AB of the diameter of circle O, passing point P to draw the tangent PC of circle O, and the tangent point is C. If AO = OB = PB = 1.0, then the length of PC is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:\u221a{5}",
        "question_for_eval": "As shown in the figure, point P is a point on the extended line AB of the diameter of circle O, passing point P to draw the tangent PC of circle O, and the tangent point is C. If AO = OB = PB = 1.0, then the length of PC is ()\nChoices:\nA:1\nB:\u221a{3}\nC:2\nD:\u221a{5}"
    },
    {
        "sample_index": "196",
        "problem_index": "196",
        "problem_version": "Text Only",
        "question": "As shown in the figure, a torus carpet is to be laid in the lobby of a hotel. The worker only measures the length of the chord AB of the great circle that is tangent to the small circle, and then calculates the area of \u200b\u200bthe torus. If the measured length of AB is 8.0, the area of \u200b\u200bthe torus is ()\nChoices:\nA:16\u5e73\u65b9\u7c73\nB:8\u03c0\u5e73\u65b9\u7c73\nC:64\u5e73\u65b9\u7c73\nD:16\u03c0\u5e73\u65b9\u7c73",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, a torus carpet is to be laid in the lobby of a hotel. The worker only measures the length of the chord AB of the great circle that is tangent to the small circle, and then calculates the area of \u200b\u200bthe torus. If the measured length of AB is 8.0, the area of \u200b\u200bthe torus is ()\nChoices:\nA:16\u5e73\u65b9\u7c73\nB:8\u03c0\u5e73\u65b9\u7c73\nC:64\u5e73\u65b9\u7c73\nD:16\u03c0\u5e73\u65b9\u7c73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, a torus carpet is to be laid in the lobby of a hotel. The worker only measures the length of the chord AB of the great circle that is tangent to the small circle, and then calculates the area of \u200b\u200bthe torus. If the measured length of AB is 8.0, the area of \u200b\u200bthe torus is ()\nChoices:\nA:16\u5e73\u65b9\u7c73\nB:8\u03c0\u5e73\u65b9\u7c73\nC:64\u5e73\u65b9\u7c73\nD:16\u03c0\u5e73\u65b9\u7c73",
        "question_for_eval": "As shown in the figure, a torus carpet is to be laid in the lobby of a hotel. The worker only measures the length of the chord AB of the great circle that is tangent to the small circle, and then calculates the area of \u200b\u200bthe torus. If the measured length of AB is 8.0, the area of \u200b\u200bthe torus is ()\nChoices:\nA:16\u5e73\u65b9\u7c73\nB:8\u03c0\u5e73\u65b9\u7c73\nC:64\u5e73\u65b9\u7c73\nD:16\u03c0\u5e73\u65b9\u7c73"
    },
    {
        "sample_index": "197",
        "problem_index": "197",
        "problem_version": "Text Only",
        "question": "As shown in the figure, circle O is the circumcircle of triangle ABC, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()\nChoices:\nA:6\u221a{5}\nB:6\u221a{3}\nC:6\u221a{2}\nD:6",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GeoQA",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, circle O is the circumcircle of triangle ABC, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()\nChoices:\nA:6\u221a{5}\nB:6\u221a{3}\nC:6\u221a{2}\nD:6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, circle O is the circumcircle of triangle ABC, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()\nChoices:\nA:6\u221a{5}\nB:6\u221a{3}\nC:6\u221a{2}\nD:6",
        "question_for_eval": "As shown in the figure, circle O is the circumcircle of triangle ABC, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()\nChoices:\nA:6\u221a{5}\nB:6\u221a{3}\nC:6\u221a{2}\nD:6"
    },
    {
        "sample_index": "198",
        "problem_index": "198",
        "problem_version": "Text Only",
        "question": "There is an isosceles triangle with side length 13 and base length 10. Find the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is an isosceles triangle with side length 13 and base length 10. Find the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is an isosceles triangle with side length 13 and base length 10. Find the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240",
        "question_for_eval": "There is an isosceles triangle with side length 13 and base length 10. Find the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240"
    },
    {
        "sample_index": "199",
        "problem_index": "199",
        "problem_version": "Text Only",
        "question": "Circle O has a radius of 13 inches, which is the length of O C. Radius O B is perpendicular at point X to chord C D which is 24 inches long. Find O X.\nChoices:\nA:5\nB:12\nC:13\nD:26",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Circle O has a radius of 13 inches, which is the length of O C. Radius O B is perpendicular at point X to chord C D which is 24 inches long. Find O X.\nChoices:\nA:5\nB:12\nC:13\nD:26",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Circle O has a radius of 13 inches, which is the length of O C. Radius O B is perpendicular at point X to chord C D which is 24 inches long. Find O X.\nChoices:\nA:5\nB:12\nC:13\nD:26",
        "question_for_eval": "Circle O has a radius of 13 inches, which is the length of O C. Radius O B is perpendicular at point X to chord C D which is 24 inches long. Find O X.\nChoices:\nA:5\nB:12\nC:13\nD:26"
    },
    {
        "sample_index": "200",
        "problem_index": "200",
        "problem_version": "Text Only",
        "question": "There is an isosceles triangle with side length 32. The base angle is 54 degrees. x is half of the base. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is an isosceles triangle with side length 32. The base angle is 54 degrees. x is half of the base. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is an isosceles triangle with side length 32. The base angle is 54 degrees. x is half of the base. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0",
        "question_for_eval": "There is an isosceles triangle with side length 32. The base angle is 54 degrees. x is half of the base. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0"
    },
    {
        "sample_index": "201",
        "problem_index": "201",
        "problem_version": "Text Only",
        "question": "There is a circle with center M and two chords A C and T N. The distences between M and the two chords are equal. Find m \\angle C A M.\nChoices:\nA:14\nB:28\nC:36\nD:90",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a circle with center M and two chords A C and T N. The distences between M and the two chords are equal. Find m \\angle C A M.\nChoices:\nA:14\nB:28\nC:36\nD:90",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a circle with center M and two chords A C and T N. The distences between M and the two chords are equal. Find m \\angle C A M.\nChoices:\nA:14\nB:28\nC:36\nD:90",
        "question_for_eval": "There is a circle with center M and two chords A C and T N. The distences between M and the two chords are equal. Find m \\angle C A M.\nChoices:\nA:14\nB:28\nC:36\nD:90"
    },
    {
        "sample_index": "202",
        "problem_index": "202",
        "problem_version": "Text Only",
        "question": "In the figure below, \\angle A B C is intersected by parallel lines l and m at points A and C, respectively. What is the measure of \\angle A B C? Express your answer in degrees.\nChoices:\nA:33\nB:38\nC:61\nD:71",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure below, \\angle A B C is intersected by parallel lines l and m at points A and C, respectively. What is the measure of \\angle A B C? Express your answer in degrees.\nChoices:\nA:33\nB:38\nC:61\nD:71",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure below, \\angle A B C is intersected by parallel lines l and m at points A and C, respectively. What is the measure of \\angle A B C? Express your answer in degrees.\nChoices:\nA:33\nB:38\nC:61\nD:71",
        "question_for_eval": "In the figure below, \\angle A B C is intersected by parallel lines l and m at points A and C, respectively. What is the measure of \\angle A B C? Express your answer in degrees.\nChoices:\nA:33\nB:38\nC:61\nD:71"
    },
    {
        "sample_index": "203",
        "problem_index": "203",
        "problem_version": "Text Only",
        "question": "There are four rays with four different included angles. Find the value of x in the diagram.\nChoices:\nA:68\nB:78\nC:79\nD:136",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There are four rays with four different included angles. Find the value of x in the diagram.\nChoices:\nA:68\nB:78\nC:79\nD:136",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There are four rays with four different included angles. Find the value of x in the diagram.\nChoices:\nA:68\nB:78\nC:79\nD:136",
        "question_for_eval": "There are four rays with four different included angles. Find the value of x in the diagram.\nChoices:\nA:68\nB:78\nC:79\nD:136"
    },
    {
        "sample_index": "204",
        "problem_index": "204",
        "problem_version": "Text Only",
        "question": "Two triangles X N M and X Z Y are similar with a shared vertex X. M N and Y Z are parallel. If X N = 6, X M = 2, and X Y = 10, find N Z.\nChoices:\nA:12\nB:16\nC:24\nD:32",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles X N M and X Z Y are similar with a shared vertex X. M N and Y Z are parallel. If X N = 6, X M = 2, and X Y = 10, find N Z.\nChoices:\nA:12\nB:16\nC:24\nD:32",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles X N M and X Z Y are similar with a shared vertex X. M N and Y Z are parallel. If X N = 6, X M = 2, and X Y = 10, find N Z.\nChoices:\nA:12\nB:16\nC:24\nD:32",
        "question_for_eval": "Two triangles X N M and X Z Y are similar with a shared vertex X. M N and Y Z are parallel. If X N = 6, X M = 2, and X Y = 10, find N Z.\nChoices:\nA:12\nB:16\nC:24\nD:32"
    },
    {
        "sample_index": "205",
        "problem_index": "205",
        "problem_version": "Text Only",
        "question": "There is a right triangle with two angles 30 and 60 degrees. The length of hypotenuse is x and other sides are y and 21. Find y.\nChoices:\nA:21\nB:21 \\sqrt { 2 }\nC:21 \\sqrt { 3 }\nD:42",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a right triangle with two angles 30 and 60 degrees. The length of hypotenuse is x and other sides are y and 21. Find y.\nChoices:\nA:21\nB:21 \\sqrt { 2 }\nC:21 \\sqrt { 3 }\nD:42",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a right triangle with two angles 30 and 60 degrees. The length of hypotenuse is x and other sides are y and 21. Find y.\nChoices:\nA:21\nB:21 \\sqrt { 2 }\nC:21 \\sqrt { 3 }\nD:42",
        "question_for_eval": "There is a right triangle with two angles 30 and 60 degrees. The length of hypotenuse is x and other sides are y and 21. Find y.\nChoices:\nA:21\nB:21 \\sqrt { 2 }\nC:21 \\sqrt { 3 }\nD:42"
    },
    {
        "sample_index": "206",
        "problem_index": "206",
        "problem_version": "Text Only",
        "question": "Two triangles A B C and A E D are similar with a shared vertex A. B C and E D are parallel. Find C D if A C = x - 3, B E = 20, A B = 16, and C D = x + 5.\nChoices:\nA:32\nB:35\nC:36\nD:40",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles A B C and A E D are similar with a shared vertex A. B C and E D are parallel. Find C D if A C = x - 3, B E = 20, A B = 16, and C D = x + 5.\nChoices:\nA:32\nB:35\nC:36\nD:40",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles A B C and A E D are similar with a shared vertex A. B C and E D are parallel. Find C D if A C = x - 3, B E = 20, A B = 16, and C D = x + 5.\nChoices:\nA:32\nB:35\nC:36\nD:40",
        "question_for_eval": "Two triangles A B C and A E D are similar with a shared vertex A. B C and E D are parallel. Find C D if A C = x - 3, B E = 20, A B = 16, and C D = x + 5.\nChoices:\nA:32\nB:35\nC:36\nD:40"
    },
    {
        "sample_index": "207",
        "problem_index": "207",
        "problem_version": "Text Only",
        "question": "Two small circles are inscribed to the biggest circle. The diameter of the biggest circle is 20. Find the area of the shaded region. Round to the nearest tenth.\nChoices:\nA:104.7\nB:157.1\nC:235.6\nD:314.2",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two small circles are inscribed to the biggest circle. The diameter of the biggest circle is 20. Find the area of the shaded region. Round to the nearest tenth.\nChoices:\nA:104.7\nB:157.1\nC:235.6\nD:314.2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two small circles are inscribed to the biggest circle. The diameter of the biggest circle is 20. Find the area of the shaded region. Round to the nearest tenth.\nChoices:\nA:104.7\nB:157.1\nC:235.6\nD:314.2",
        "question_for_eval": "Two small circles are inscribed to the biggest circle. The diameter of the biggest circle is 20. Find the area of the shaded region. Round to the nearest tenth.\nChoices:\nA:104.7\nB:157.1\nC:235.6\nD:314.2"
    },
    {
        "sample_index": "208",
        "problem_index": "208",
        "problem_version": "Text Only",
        "question": "J K L M is a rectangle. M L P R is a rhombus. M L equals M R. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K M L.\nChoices:\nA:35\nB:70\nC:110\nD:140",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: J K L M is a rectangle. M L P R is a rhombus. M L equals M R. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K M L.\nChoices:\nA:35\nB:70\nC:110\nD:140",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: J K L M is a rectangle. M L P R is a rhombus. M L equals M R. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K M L.\nChoices:\nA:35\nB:70\nC:110\nD:140",
        "question_for_eval": "J K L M is a rectangle. M L P R is a rhombus. M L equals M R. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K M L.\nChoices:\nA:35\nB:70\nC:110\nD:140"
    },
    {
        "sample_index": "209",
        "problem_index": "209",
        "problem_version": "Text Only",
        "question": "In rhombus A B C D, m \\angle D A B = 2, m \\angle A D C and C B = 6. D B and A C intersect at point E. Find m \\angle A C D.\nChoices:\nA:45\nB:60\nC:90\nD:180",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In rhombus A B C D, m \\angle D A B = 2, m \\angle A D C and C B = 6. D B and A C intersect at point E. Find m \\angle A C D.\nChoices:\nA:45\nB:60\nC:90\nD:180",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In rhombus A B C D, m \\angle D A B = 2, m \\angle A D C and C B = 6. D B and A C intersect at point E. Find m \\angle A C D.\nChoices:\nA:45\nB:60\nC:90\nD:180",
        "question_for_eval": "In rhombus A B C D, m \\angle D A B = 2, m \\angle A D C and C B = 6. D B and A C intersect at point E. Find m \\angle A C D.\nChoices:\nA:45\nB:60\nC:90\nD:180"
    },
    {
        "sample_index": "210",
        "problem_index": "210",
        "problem_version": "Text Only",
        "question": "Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. Find A E if A B = 12, A C = 16, and E D = 5.\nChoices:\nA:12\nB:15\nC:16\nD:20",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. Find A E if A B = 12, A C = 16, and E D = 5.\nChoices:\nA:12\nB:15\nC:16\nD:20",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. Find A E if A B = 12, A C = 16, and E D = 5.\nChoices:\nA:12\nB:15\nC:16\nD:20",
        "question_for_eval": "Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. Find A E if A B = 12, A C = 16, and E D = 5.\nChoices:\nA:12\nB:15\nC:16\nD:20"
    },
    {
        "sample_index": "211",
        "problem_index": "211",
        "problem_version": "Text Only",
        "question": "In parallelogram M N P R, M P and R N intersect at Q. M N = 3x - 4. N P = 2y + 5. R P = 20. M R = 17.9. Find m \\angle R N P.\nChoices:\nA:38\nB:52\nC:52\nD:62",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In parallelogram M N P R, M P and R N intersect at Q. M N = 3x - 4. N P = 2y + 5. R P = 20. M R = 17.9. Find m \\angle R N P.\nChoices:\nA:38\nB:52\nC:52\nD:62",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In parallelogram M N P R, M P and R N intersect at Q. M N = 3x - 4. N P = 2y + 5. R P = 20. M R = 17.9. Find m \\angle R N P.\nChoices:\nA:38\nB:52\nC:52\nD:62",
        "question_for_eval": "In parallelogram M N P R, M P and R N intersect at Q. M N = 3x - 4. N P = 2y + 5. R P = 20. M R = 17.9. Find m \\angle R N P.\nChoices:\nA:38\nB:52\nC:52\nD:62"
    },
    {
        "sample_index": "212",
        "problem_index": "212",
        "problem_version": "Text Only",
        "question": "Three rays intersect at two points. Two shorter rays are parallel. Find y in the figure.\nChoices:\nA:5\nB:6\nC:7\nD:8",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Three rays intersect at two points. Two shorter rays are parallel. Find y in the figure.\nChoices:\nA:5\nB:6\nC:7\nD:8",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Three rays intersect at two points. Two shorter rays are parallel. Find y in the figure.\nChoices:\nA:5\nB:6\nC:7\nD:8",
        "question_for_eval": "Three rays intersect at two points. Two shorter rays are parallel. Find y in the figure.\nChoices:\nA:5\nB:6\nC:7\nD:8"
    },
    {
        "sample_index": "213",
        "problem_index": "213",
        "problem_version": "Text Only",
        "question": "In \\odot P, the radius is 2 inches. \\angle Q P T is 112 degrees, and \\angle RPS is 130 degrees. Find the length of \\widehat R S. Round to the nearest hundredth.\nChoices:\nA:2.27\nB:3.91\nC:4.54\nD:7.82",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot P, the radius is 2 inches. \\angle Q P T is 112 degrees, and \\angle RPS is 130 degrees. Find the length of \\widehat R S. Round to the nearest hundredth.\nChoices:\nA:2.27\nB:3.91\nC:4.54\nD:7.82",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot P, the radius is 2 inches. \\angle Q P T is 112 degrees, and \\angle RPS is 130 degrees. Find the length of \\widehat R S. Round to the nearest hundredth.\nChoices:\nA:2.27\nB:3.91\nC:4.54\nD:7.82",
        "question_for_eval": "In \\odot P, the radius is 2 inches. \\angle Q P T is 112 degrees, and \\angle RPS is 130 degrees. Find the length of \\widehat R S. Round to the nearest hundredth.\nChoices:\nA:2.27\nB:3.91\nC:4.54\nD:7.82"
    },
    {
        "sample_index": "214",
        "problem_index": "214",
        "problem_version": "Text Only",
        "question": "In parallelogram A B C D, AD = 9 and A B = 6. Find m \\angle A D C.\nChoices:\nA:42\nB:52\nC:72\nD:128",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In parallelogram A B C D, AD = 9 and A B = 6. Find m \\angle A D C.\nChoices:\nA:42\nB:52\nC:72\nD:128",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In parallelogram A B C D, AD = 9 and A B = 6. Find m \\angle A D C.\nChoices:\nA:42\nB:52\nC:72\nD:128",
        "question_for_eval": "In parallelogram A B C D, AD = 9 and A B = 6. Find m \\angle A D C.\nChoices:\nA:42\nB:52\nC:72\nD:128"
    },
    {
        "sample_index": "215",
        "problem_index": "215",
        "problem_version": "Text Only",
        "question": "The rectangle is inscribed into the circle with two sides 8 and 6 inches. Find the exact circumference of the circle.\nChoices:\nA:8 \\pi\nB:10 \\pi\nC:16 \\pi\nD:20 \\pi",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The rectangle is inscribed into the circle with two sides 8 and 6 inches. Find the exact circumference of the circle.\nChoices:\nA:8 \\pi\nB:10 \\pi\nC:16 \\pi\nD:20 \\pi",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The rectangle is inscribed into the circle with two sides 8 and 6 inches. Find the exact circumference of the circle.\nChoices:\nA:8 \\pi\nB:10 \\pi\nC:16 \\pi\nD:20 \\pi",
        "question_for_eval": "The rectangle is inscribed into the circle with two sides 8 and 6 inches. Find the exact circumference of the circle.\nChoices:\nA:8 \\pi\nB:10 \\pi\nC:16 \\pi\nD:20 \\pi"
    },
    {
        "sample_index": "216",
        "problem_index": "216",
        "problem_version": "Text Only",
        "question": "There are two right triangles D F E and A C B. Find D E.\nChoices:\nA:3\nB:4\nC:6\nD:9",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There are two right triangles D F E and A C B. Find D E.\nChoices:\nA:3\nB:4\nC:6\nD:9",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There are two right triangles D F E and A C B. Find D E.\nChoices:\nA:3\nB:4\nC:6\nD:9",
        "question_for_eval": "There are two right triangles D F E and A C B. Find D E.\nChoices:\nA:3\nB:4\nC:6\nD:9"
    },
    {
        "sample_index": "217",
        "problem_index": "217",
        "problem_version": "Text Only",
        "question": "There is a parallelogram with two sides 20 and 12 cm. Find its perimeter. Round to the nearest tenth if necessary.\nChoices:\nA:60\nB:62\nC:64\nD:66",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a parallelogram with two sides 20 and 12 cm. Find its perimeter. Round to the nearest tenth if necessary.\nChoices:\nA:60\nB:62\nC:64\nD:66",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a parallelogram with two sides 20 and 12 cm. Find its perimeter. Round to the nearest tenth if necessary.\nChoices:\nA:60\nB:62\nC:64\nD:66",
        "question_for_eval": "There is a parallelogram with two sides 20 and 12 cm. Find its perimeter. Round to the nearest tenth if necessary.\nChoices:\nA:60\nB:62\nC:64\nD:66"
    },
    {
        "sample_index": "218",
        "problem_index": "218",
        "problem_version": "Text Only",
        "question": "In \\odot O, the diameter is 14, and \\angle A O B is 80 degrees. Find the length of \\widehat A B. Round to the nearest hundredth.\nChoices:\nA:7.63\nB:9.77\nC:11.13\nD:14.83",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot O, the diameter is 14, and \\angle A O B is 80 degrees. Find the length of \\widehat A B. Round to the nearest hundredth.\nChoices:\nA:7.63\nB:9.77\nC:11.13\nD:14.83",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot O, the diameter is 14, and \\angle A O B is 80 degrees. Find the length of \\widehat A B. Round to the nearest hundredth.\nChoices:\nA:7.63\nB:9.77\nC:11.13\nD:14.83",
        "question_for_eval": "In \\odot O, the diameter is 14, and \\angle A O B is 80 degrees. Find the length of \\widehat A B. Round to the nearest hundredth.\nChoices:\nA:7.63\nB:9.77\nC:11.13\nD:14.83"
    },
    {
        "sample_index": "219",
        "problem_index": "219",
        "problem_version": "Text Only",
        "question": "Find A B if \\triangle A B C is an isosceles triangle with A B \\cong B C.\nChoices:\nA:3\nB:4\nC:7\nD:11",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Find A B if \\triangle A B C is an isosceles triangle with A B \\cong B C.\nChoices:\nA:3\nB:4\nC:7\nD:11",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Find A B if \\triangle A B C is an isosceles triangle with A B \\cong B C.\nChoices:\nA:3\nB:4\nC:7\nD:11",
        "question_for_eval": "Find A B if \\triangle A B C is an isosceles triangle with A B \\cong B C.\nChoices:\nA:3\nB:4\nC:7\nD:11"
    },
    {
        "sample_index": "220",
        "problem_index": "220",
        "problem_version": "Text Only",
        "question": "In \\odot G, CE and AB are diameters. \\angle A G D is a right angle and \\angle A G C is 60 degrees. Find m \\angle B G E.\nChoices:\nA:60\nB:120\nC:240\nD:360",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot G, CE and AB are diameters. \\angle A G D is a right angle and \\angle A G C is 60 degrees. Find m \\angle B G E.\nChoices:\nA:60\nB:120\nC:240\nD:360",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot G, CE and AB are diameters. \\angle A G D is a right angle and \\angle A G C is 60 degrees. Find m \\angle B G E.\nChoices:\nA:60\nB:120\nC:240\nD:360",
        "question_for_eval": "In \\odot G, CE and AB are diameters. \\angle A G D is a right angle and \\angle A G C is 60 degrees. Find m \\angle B G E.\nChoices:\nA:60\nB:120\nC:240\nD:360"
    },
    {
        "sample_index": "221",
        "problem_index": "221",
        "problem_version": "Text Only",
        "question": "In the triangle, there are two angles as 60 and 55 degrees. Find x. Round the side measure to the nearest tenth.\nChoices:\nA:69.0\nB:69.8\nC:76.4\nD:77.2",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the triangle, there are two angles as 60 and 55 degrees. Find x. Round the side measure to the nearest tenth.\nChoices:\nA:69.0\nB:69.8\nC:76.4\nD:77.2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the triangle, there are two angles as 60 and 55 degrees. Find x. Round the side measure to the nearest tenth.\nChoices:\nA:69.0\nB:69.8\nC:76.4\nD:77.2",
        "question_for_eval": "In the triangle, there are two angles as 60 and 55 degrees. Find x. Round the side measure to the nearest tenth.\nChoices:\nA:69.0\nB:69.8\nC:76.4\nD:77.2"
    },
    {
        "sample_index": "222",
        "problem_index": "222",
        "problem_version": "Text Only",
        "question": "For the pair of similar figures in blue and green, use the given areas to find x.\nChoices:\nA:1\nB:2\nC:8\nD:16",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: For the pair of similar figures in blue and green, use the given areas to find x.\nChoices:\nA:1\nB:2\nC:8\nD:16",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: For the pair of similar figures in blue and green, use the given areas to find x.\nChoices:\nA:1\nB:2\nC:8\nD:16",
        "question_for_eval": "For the pair of similar figures in blue and green, use the given areas to find x.\nChoices:\nA:1\nB:2\nC:8\nD:16"
    },
    {
        "sample_index": "223",
        "problem_index": "223",
        "problem_version": "Text Only",
        "question": "There is a right triangle with the length of hypotenuse as 5 and other sides as x and 3 \\sqrt { 2 }. Find x.\nChoices:\nA:\\sqrt { 7 }\nB:3 \\sqrt { 2 }\nC:3 \\sqrt { 3 }\nD:3 \\sqrt { 6 }",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a right triangle with the length of hypotenuse as 5 and other sides as x and 3 \\sqrt { 2 }. Find x.\nChoices:\nA:\\sqrt { 7 }\nB:3 \\sqrt { 2 }\nC:3 \\sqrt { 3 }\nD:3 \\sqrt { 6 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a right triangle with the length of hypotenuse as 5 and other sides as x and 3 \\sqrt { 2 }. Find x.\nChoices:\nA:\\sqrt { 7 }\nB:3 \\sqrt { 2 }\nC:3 \\sqrt { 3 }\nD:3 \\sqrt { 6 }",
        "question_for_eval": "There is a right triangle with the length of hypotenuse as 5 and other sides as x and 3 \\sqrt { 2 }. Find x.\nChoices:\nA:\\sqrt { 7 }\nB:3 \\sqrt { 2 }\nC:3 \\sqrt { 3 }\nD:3 \\sqrt { 6 }"
    },
    {
        "sample_index": "224",
        "problem_index": "224",
        "problem_version": "Text Only",
        "question": "In the figure, a regular polygon is inscribed in a circle with center R. R S is perpendicular to K L. Find the measure of a central angle.\nChoices:\nA:30\nB:60\nC:90\nD:120",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure, a regular polygon is inscribed in a circle with center R. R S is perpendicular to K L. Find the measure of a central angle.\nChoices:\nA:30\nB:60\nC:90\nD:120",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure, a regular polygon is inscribed in a circle with center R. R S is perpendicular to K L. Find the measure of a central angle.\nChoices:\nA:30\nB:60\nC:90\nD:120",
        "question_for_eval": "In the figure, a regular polygon is inscribed in a circle with center R. R S is perpendicular to K L. Find the measure of a central angle.\nChoices:\nA:30\nB:60\nC:90\nD:120"
    },
    {
        "sample_index": "225",
        "problem_index": "225",
        "problem_version": "Text Only",
        "question": "In triangle X Y Z, Z W and W Y are equal. X W is perpendicular to Z Y. X Y and X Z are 18 + 2y and 5y - 6, respectively. Find X Z.\nChoices:\nA:5\nB:17\nC:18\nD:34",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle X Y Z, Z W and W Y are equal. X W is perpendicular to Z Y. X Y and X Z are 18 + 2y and 5y - 6, respectively. Find X Z.\nChoices:\nA:5\nB:17\nC:18\nD:34",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle X Y Z, Z W and W Y are equal. X W is perpendicular to Z Y. X Y and X Z are 18 + 2y and 5y - 6, respectively. Find X Z.\nChoices:\nA:5\nB:17\nC:18\nD:34",
        "question_for_eval": "In triangle X Y Z, Z W and W Y are equal. X W is perpendicular to Z Y. X Y and X Z are 18 + 2y and 5y - 6, respectively. Find X Z.\nChoices:\nA:5\nB:17\nC:18\nD:34"
    },
    {
        "sample_index": "226",
        "problem_index": "226",
        "problem_version": "Text Only",
        "question": "In regular hexagon U V W X Y Z, W Y is perpendicular to X U, and the side is 12 centimeters long. Find W Y.\nChoices:\nA:12\nB:6 \\sqrt { 6 }\nC:12 \\sqrt { 3 }\nD:36",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In regular hexagon U V W X Y Z, W Y is perpendicular to X U, and the side is 12 centimeters long. Find W Y.\nChoices:\nA:12\nB:6 \\sqrt { 6 }\nC:12 \\sqrt { 3 }\nD:36",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In regular hexagon U V W X Y Z, W Y is perpendicular to X U, and the side is 12 centimeters long. Find W Y.\nChoices:\nA:12\nB:6 \\sqrt { 6 }\nC:12 \\sqrt { 3 }\nD:36",
        "question_for_eval": "In regular hexagon U V W X Y Z, W Y is perpendicular to X U, and the side is 12 centimeters long. Find W Y.\nChoices:\nA:12\nB:6 \\sqrt { 6 }\nC:12 \\sqrt { 3 }\nD:36"
    },
    {
        "sample_index": "227",
        "problem_index": "227",
        "problem_version": "Text Only",
        "question": "Find the area of the rectangle, whose sides are 9 and 16 inches.\nChoices:\nA:25\nB:50\nC:72\nD:144",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Find the area of the rectangle, whose sides are 9 and 16 inches.\nChoices:\nA:25\nB:50\nC:72\nD:144",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Find the area of the rectangle, whose sides are 9 and 16 inches.\nChoices:\nA:25\nB:50\nC:72\nD:144",
        "question_for_eval": "Find the area of the rectangle, whose sides are 9 and 16 inches.\nChoices:\nA:25\nB:50\nC:72\nD:144"
    },
    {
        "sample_index": "228",
        "problem_index": "228",
        "problem_version": "Text Only",
        "question": "There is a right triangle with hypotenuse length 17. Find x.\nChoices:\nA:\\frac { 17 } { 2 }\nB:\\frac { 17 } { 2 } \\sqrt { 2 }\nC:\\frac { 17 } { 2 } \\sqrt { 3 }\nD:17",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a right triangle with hypotenuse length 17. Find x.\nChoices:\nA:\\frac { 17 } { 2 }\nB:\\frac { 17 } { 2 } \\sqrt { 2 }\nC:\\frac { 17 } { 2 } \\sqrt { 3 }\nD:17",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a right triangle with hypotenuse length 17. Find x.\nChoices:\nA:\\frac { 17 } { 2 }\nB:\\frac { 17 } { 2 } \\sqrt { 2 }\nC:\\frac { 17 } { 2 } \\sqrt { 3 }\nD:17",
        "question_for_eval": "There is a right triangle with hypotenuse length 17. Find x.\nChoices:\nA:\\frac { 17 } { 2 }\nB:\\frac { 17 } { 2 } \\sqrt { 2 }\nC:\\frac { 17 } { 2 } \\sqrt { 3 }\nD:17"
    },
    {
        "sample_index": "229",
        "problem_index": "229",
        "problem_version": "Text Only",
        "question": "Let A B be the median of trapezoid R S T Q. R A equals A Q, and S B equals B T. R S = 54 and Q T = 86. Find A B.\nChoices:\nA:27\nB:54\nC:70\nD:86",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Let A B be the median of trapezoid R S T Q. R A equals A Q, and S B equals B T. R S = 54 and Q T = 86. Find A B.\nChoices:\nA:27\nB:54\nC:70\nD:86",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Let A B be the median of trapezoid R S T Q. R A equals A Q, and S B equals B T. R S = 54 and Q T = 86. Find A B.\nChoices:\nA:27\nB:54\nC:70\nD:86",
        "question_for_eval": "Let A B be the median of trapezoid R S T Q. R A equals A Q, and S B equals B T. R S = 54 and Q T = 86. Find A B.\nChoices:\nA:27\nB:54\nC:70\nD:86"
    },
    {
        "sample_index": "230",
        "problem_index": "230",
        "problem_version": "Text Only",
        "question": "In the circle, two chords A C and B D intersect. Find m \\angle 2 if m \\widehat B C = 30 and m \\widehat A D = 20.\nChoices:\nA:20\nB:25\nC:30\nD:155",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the circle, two chords A C and B D intersect. Find m \\angle 2 if m \\widehat B C = 30 and m \\widehat A D = 20.\nChoices:\nA:20\nB:25\nC:30\nD:155",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the circle, two chords A C and B D intersect. Find m \\angle 2 if m \\widehat B C = 30 and m \\widehat A D = 20.\nChoices:\nA:20\nB:25\nC:30\nD:155",
        "question_for_eval": "In the circle, two chords A C and B D intersect. Find m \\angle 2 if m \\widehat B C = 30 and m \\widehat A D = 20.\nChoices:\nA:20\nB:25\nC:30\nD:155"
    },
    {
        "sample_index": "231",
        "problem_index": "231",
        "problem_version": "Text Only",
        "question": "In \\odot X, Z W and Y V are diameters. Find m \\angle V X W.\nChoices:\nA:25\nB:65\nC:115\nD:180",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot X, Z W and Y V are diameters. Find m \\angle V X W.\nChoices:\nA:25\nB:65\nC:115\nD:180",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot X, Z W and Y V are diameters. Find m \\angle V X W.\nChoices:\nA:25\nB:65\nC:115\nD:180",
        "question_for_eval": "In \\odot X, Z W and Y V are diameters. Find m \\angle V X W.\nChoices:\nA:25\nB:65\nC:115\nD:180"
    },
    {
        "sample_index": "232",
        "problem_index": "232",
        "problem_version": "Text Only",
        "question": "Two triangles W S R and T V R are similar. W S and V T are parallel. W S is 8, and V T is 10. Find W R.\nChoices:\nA:6\nB:8\nC:10\nD:12",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles W S R and T V R are similar. W S and V T are parallel. W S is 8, and V T is 10. Find W R.\nChoices:\nA:6\nB:8\nC:10\nD:12",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles W S R and T V R are similar. W S and V T are parallel. W S is 8, and V T is 10. Find W R.\nChoices:\nA:6\nB:8\nC:10\nD:12",
        "question_for_eval": "Two triangles W S R and T V R are similar. W S and V T are parallel. W S is 8, and V T is 10. Find W R.\nChoices:\nA:6\nB:8\nC:10\nD:12"
    },
    {
        "sample_index": "233",
        "problem_index": "233",
        "problem_version": "Text Only",
        "question": "In isosceles triangle R S T, \\angle S R T is 70 degrees. Find m \\angle R S T.\nChoices:\nA:55\nB:70\nC:75\nD:80",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In isosceles triangle R S T, \\angle S R T is 70 degrees. Find m \\angle R S T.\nChoices:\nA:55\nB:70\nC:75\nD:80",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In isosceles triangle R S T, \\angle S R T is 70 degrees. Find m \\angle R S T.\nChoices:\nA:55\nB:70\nC:75\nD:80",
        "question_for_eval": "In isosceles triangle R S T, \\angle S R T is 70 degrees. Find m \\angle R S T.\nChoices:\nA:55\nB:70\nC:75\nD:80"
    },
    {
        "sample_index": "234",
        "problem_index": "234",
        "problem_version": "Text Only",
        "question": "Polygon A B C D \\sim polygon A E F G, m \\angle A G F = 108, G F = 14, A D = 12, D G = 4.5, E F = 8, and A B = 26. Find m \\angle A D C.\nChoices:\nA:14\nB:72\nC:108\nD:120",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Polygon A B C D \\sim polygon A E F G, m \\angle A G F = 108, G F = 14, A D = 12, D G = 4.5, E F = 8, and A B = 26. Find m \\angle A D C.\nChoices:\nA:14\nB:72\nC:108\nD:120",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Polygon A B C D \\sim polygon A E F G, m \\angle A G F = 108, G F = 14, A D = 12, D G = 4.5, E F = 8, and A B = 26. Find m \\angle A D C.\nChoices:\nA:14\nB:72\nC:108\nD:120",
        "question_for_eval": "Polygon A B C D \\sim polygon A E F G, m \\angle A G F = 108, G F = 14, A D = 12, D G = 4.5, E F = 8, and A B = 26. Find m \\angle A D C.\nChoices:\nA:14\nB:72\nC:108\nD:120"
    },
    {
        "sample_index": "235",
        "problem_index": "235",
        "problem_version": "Text Only",
        "question": "In the figure, four rays intersect and form 16 angles, and two upright rays are parallel. m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 1.\nChoices:\nA:55\nB:110\nC:125\nD:135",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure, four rays intersect and form 16 angles, and two upright rays are parallel. m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 1.\nChoices:\nA:55\nB:110\nC:125\nD:135",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure, four rays intersect and form 16 angles, and two upright rays are parallel. m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 1.\nChoices:\nA:55\nB:110\nC:125\nD:135",
        "question_for_eval": "In the figure, four rays intersect and form 16 angles, and two upright rays are parallel. m \\angle 3 = 110 and m \\angle 12 = 55. Find the measure of \\angle 1.\nChoices:\nA:55\nB:110\nC:125\nD:135"
    },
    {
        "sample_index": "236",
        "problem_index": "236",
        "problem_version": "Text Only",
        "question": "Two rays intersect and form four angles all as x degrees. Find x.\nChoices:\nA:60\nB:80\nC:90\nD:120",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two rays intersect and form four angles all as x degrees. Find x.\nChoices:\nA:60\nB:80\nC:90\nD:120",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two rays intersect and form four angles all as x degrees. Find x.\nChoices:\nA:60\nB:80\nC:90\nD:120",
        "question_for_eval": "Two rays intersect and form four angles all as x degrees. Find x.\nChoices:\nA:60\nB:80\nC:90\nD:120"
    },
    {
        "sample_index": "237",
        "problem_index": "237",
        "problem_version": "Text Only",
        "question": "In the right triangle Q P R, \\angle Q R P is 33 degrees, and \\angle P Q S is 51 degrees. Connect Q S. Find m \\angle 1.\nChoices:\nA:39\nB:84\nC:108\nD:129",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle Q P R, \\angle Q R P is 33 degrees, and \\angle P Q S is 51 degrees. Connect Q S. Find m \\angle 1.\nChoices:\nA:39\nB:84\nC:108\nD:129",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle Q P R, \\angle Q R P is 33 degrees, and \\angle P Q S is 51 degrees. Connect Q S. Find m \\angle 1.\nChoices:\nA:39\nB:84\nC:108\nD:129",
        "question_for_eval": "In the right triangle Q P R, \\angle Q R P is 33 degrees, and \\angle P Q S is 51 degrees. Connect Q S. Find m \\angle 1.\nChoices:\nA:39\nB:84\nC:108\nD:129"
    },
    {
        "sample_index": "238",
        "problem_index": "238",
        "problem_version": "Text Only",
        "question": "In the triangle with height x, two acute angles are 45 and 30 degrees. One of a right-angle side is bisected by a line from the top vertex. Find x.\nChoices:\nA:4\nB:4 \\sqrt { 2 }\nC:4 \\sqrt { 3 }\nD:8",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the triangle with height x, two acute angles are 45 and 30 degrees. One of a right-angle side is bisected by a line from the top vertex. Find x.\nChoices:\nA:4\nB:4 \\sqrt { 2 }\nC:4 \\sqrt { 3 }\nD:8",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the triangle with height x, two acute angles are 45 and 30 degrees. One of a right-angle side is bisected by a line from the top vertex. Find x.\nChoices:\nA:4\nB:4 \\sqrt { 2 }\nC:4 \\sqrt { 3 }\nD:8",
        "question_for_eval": "In the triangle with height x, two acute angles are 45 and 30 degrees. One of a right-angle side is bisected by a line from the top vertex. Find x.\nChoices:\nA:4\nB:4 \\sqrt { 2 }\nC:4 \\sqrt { 3 }\nD:8"
    },
    {
        "sample_index": "239",
        "problem_index": "239",
        "problem_version": "Text Only",
        "question": "In triangle A B C, R, S, T are midpoints of A C, A B, and C B. A T, B R, and C S intersect at M. M C = 7, R M = 4, and A T = 16. Find M B.\nChoices:\nA:6\nB:8\nC:10\nD:12",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle A B C, R, S, T are midpoints of A C, A B, and C B. A T, B R, and C S intersect at M. M C = 7, R M = 4, and A T = 16. Find M B.\nChoices:\nA:6\nB:8\nC:10\nD:12",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle A B C, R, S, T are midpoints of A C, A B, and C B. A T, B R, and C S intersect at M. M C = 7, R M = 4, and A T = 16. Find M B.\nChoices:\nA:6\nB:8\nC:10\nD:12",
        "question_for_eval": "In triangle A B C, R, S, T are midpoints of A C, A B, and C B. A T, B R, and C S intersect at M. M C = 7, R M = 4, and A T = 16. Find M B.\nChoices:\nA:6\nB:8\nC:10\nD:12"
    },
    {
        "sample_index": "240",
        "problem_index": "240",
        "problem_version": "Text Only",
        "question": "Find the value of the variable y in the right trapezoid.\nChoices:\nA:10\nB:20\nC:30\nD:70",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Find the value of the variable y in the right trapezoid.\nChoices:\nA:10\nB:20\nC:30\nD:70",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Find the value of the variable y in the right trapezoid.\nChoices:\nA:10\nB:20\nC:30\nD:70",
        "question_for_eval": "Find the value of the variable y in the right trapezoid.\nChoices:\nA:10\nB:20\nC:30\nD:70"
    },
    {
        "sample_index": "241",
        "problem_index": "241",
        "problem_version": "Text Only",
        "question": "In the right triangle, the hypotenuse is 20 and two sides are y and x. Find y.\nChoices:\nA:4\nB:6\nC:8\nD:10",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle, the hypotenuse is 20 and two sides are y and x. Find y.\nChoices:\nA:4\nB:6\nC:8\nD:10",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle, the hypotenuse is 20 and two sides are y and x. Find y.\nChoices:\nA:4\nB:6\nC:8\nD:10",
        "question_for_eval": "In the right triangle, the hypotenuse is 20 and two sides are y and x. Find y.\nChoices:\nA:4\nB:6\nC:8\nD:10"
    },
    {
        "sample_index": "242",
        "problem_index": "242",
        "problem_version": "Text Only",
        "question": "In a pentagon UVWYZ, angle W is x + 8 degrees. Find m \\angle W.\nChoices:\nA:38\nB:38\nC:76\nD:152",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In a pentagon UVWYZ, angle W is x + 8 degrees. Find m \\angle W.\nChoices:\nA:38\nB:38\nC:76\nD:152",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In a pentagon UVWYZ, angle W is x + 8 degrees. Find m \\angle W.\nChoices:\nA:38\nB:38\nC:76\nD:152",
        "question_for_eval": "In a pentagon UVWYZ, angle W is x + 8 degrees. Find m \\angle W.\nChoices:\nA:38\nB:38\nC:76\nD:152"
    },
    {
        "sample_index": "243",
        "problem_index": "243",
        "problem_version": "Text Only",
        "question": "A plane travels from Des Moines to Phoenix with a distance 110x + 53, on to Atlanta with a distance 150x + 91, and back to Des Moines with a distance 73.8x, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.\nChoices:\nA:53\nB:73.8\nC:110\nD:1591",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A plane travels from Des Moines to Phoenix with a distance 110x + 53, on to Atlanta with a distance 150x + 91, and back to Des Moines with a distance 73.8x, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.\nChoices:\nA:53\nB:73.8\nC:110\nD:1591",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A plane travels from Des Moines to Phoenix with a distance 110x + 53, on to Atlanta with a distance 150x + 91, and back to Des Moines with a distance 73.8x, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.\nChoices:\nA:53\nB:73.8\nC:110\nD:1591",
        "question_for_eval": "A plane travels from Des Moines to Phoenix with a distance 110x + 53, on to Atlanta with a distance 150x + 91, and back to Des Moines with a distance 73.8x, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.\nChoices:\nA:53\nB:73.8\nC:110\nD:1591"
    },
    {
        "sample_index": "244",
        "problem_index": "244",
        "problem_version": "Text Only",
        "question": "In the figure, m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. EC and AB are parallel. Connect B E. Find the measure of \\angle 5.\nChoices:\nA:43\nB:47\nC:58\nD:73",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure, m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. EC and AB are parallel. Connect B E. Find the measure of \\angle 5.\nChoices:\nA:43\nB:47\nC:58\nD:73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure, m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. EC and AB are parallel. Connect B E. Find the measure of \\angle 5.\nChoices:\nA:43\nB:47\nC:58\nD:73",
        "question_for_eval": "In the figure, m \\angle 1 = 58, m \\angle 2 = 47, and m \\angle 3 = 26. EC and AB are parallel. Connect B E. Find the measure of \\angle 5.\nChoices:\nA:43\nB:47\nC:58\nD:73"
    },
    {
        "sample_index": "245",
        "problem_index": "245",
        "problem_version": "Text Only",
        "question": "The diagonals of rhombus F G H J intersect at K. If G H = x + 9 and J H = 5 x - 2, find x.\nChoices:\nA:2.75\nB:3\nC:5.5\nD:9",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The diagonals of rhombus F G H J intersect at K. If G H = x + 9 and J H = 5 x - 2, find x.\nChoices:\nA:2.75\nB:3\nC:5.5\nD:9",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The diagonals of rhombus F G H J intersect at K. If G H = x + 9 and J H = 5 x - 2, find x.\nChoices:\nA:2.75\nB:3\nC:5.5\nD:9",
        "question_for_eval": "The diagonals of rhombus F G H J intersect at K. If G H = x + 9 and J H = 5 x - 2, find x.\nChoices:\nA:2.75\nB:3\nC:5.5\nD:9"
    },
    {
        "sample_index": "246",
        "problem_index": "246",
        "problem_version": "Text Only",
        "question": "The diameter of the circle is 6.2 cm. Find the circumference of the figure. Round to the nearest tenth.\nChoices:\nA:18.6\nB:19.5\nC:37.7\nD:39.0",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The diameter of the circle is 6.2 cm. Find the circumference of the figure. Round to the nearest tenth.\nChoices:\nA:18.6\nB:19.5\nC:37.7\nD:39.0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The diameter of the circle is 6.2 cm. Find the circumference of the figure. Round to the nearest tenth.\nChoices:\nA:18.6\nB:19.5\nC:37.7\nD:39.0",
        "question_for_eval": "The diameter of the circle is 6.2 cm. Find the circumference of the figure. Round to the nearest tenth.\nChoices:\nA:18.6\nB:19.5\nC:37.7\nD:39.0"
    },
    {
        "sample_index": "247",
        "problem_index": "247",
        "problem_version": "Text Only",
        "question": "D is an external point to the circle, and A, C, F, E, B are on the circle. If m \\widehat F E = 118, m \\widehat A B = 108, m \\angle E G B = 52, and m \\angle E F B = 30, find m \\widehat C F.\nChoices:\nA:30\nB:44\nC:108\nD:118",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: D is an external point to the circle, and A, C, F, E, B are on the circle. If m \\widehat F E = 118, m \\widehat A B = 108, m \\angle E G B = 52, and m \\angle E F B = 30, find m \\widehat C F.\nChoices:\nA:30\nB:44\nC:108\nD:118",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: D is an external point to the circle, and A, C, F, E, B are on the circle. If m \\widehat F E = 118, m \\widehat A B = 108, m \\angle E G B = 52, and m \\angle E F B = 30, find m \\widehat C F.\nChoices:\nA:30\nB:44\nC:108\nD:118",
        "question_for_eval": "D is an external point to the circle, and A, C, F, E, B are on the circle. If m \\widehat F E = 118, m \\widehat A B = 108, m \\angle E G B = 52, and m \\angle E F B = 30, find m \\widehat C F.\nChoices:\nA:30\nB:44\nC:108\nD:118"
    },
    {
        "sample_index": "248",
        "problem_index": "248",
        "problem_version": "Text Only",
        "question": "In the right triangle with hypotenuse length 74 and two sides length 24 and x, use a Pythagorean Triple to find x.\nChoices:\nA:66\nB:68\nC:70\nD:72",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle with hypotenuse length 74 and two sides length 24 and x, use a Pythagorean Triple to find x.\nChoices:\nA:66\nB:68\nC:70\nD:72",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle with hypotenuse length 74 and two sides length 24 and x, use a Pythagorean Triple to find x.\nChoices:\nA:66\nB:68\nC:70\nD:72",
        "question_for_eval": "In the right triangle with hypotenuse length 74 and two sides length 24 and x, use a Pythagorean Triple to find x.\nChoices:\nA:66\nB:68\nC:70\nD:72"
    },
    {
        "sample_index": "249",
        "problem_index": "249",
        "problem_version": "Text Only",
        "question": "\\angle B F C is 72 degrees, and B, C, D, A are on the circle. Find the measure of \\angle C F D on \\odot F with diameter A C.\nChoices:\nA:115\nB:119\nC:120\nD:123",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: \\angle B F C is 72 degrees, and B, C, D, A are on the circle. Find the measure of \\angle C F D on \\odot F with diameter A C.\nChoices:\nA:115\nB:119\nC:120\nD:123",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: \\angle B F C is 72 degrees, and B, C, D, A are on the circle. Find the measure of \\angle C F D on \\odot F with diameter A C.\nChoices:\nA:115\nB:119\nC:120\nD:123",
        "question_for_eval": "\\angle B F C is 72 degrees, and B, C, D, A are on the circle. Find the measure of \\angle C F D on \\odot F with diameter A C.\nChoices:\nA:115\nB:119\nC:120\nD:123"
    },
    {
        "sample_index": "250",
        "problem_index": "250",
        "problem_version": "Text Only",
        "question": "J K L M is a rectangle. M L P R is a rhombus. Connect M K and connect M P. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K L P.\nChoices:\nA:20\nB:110\nC:140\nD:160",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: J K L M is a rectangle. M L P R is a rhombus. Connect M K and connect M P. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K L P.\nChoices:\nA:20\nB:110\nC:140\nD:160",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: J K L M is a rectangle. M L P R is a rhombus. Connect M K and connect M P. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K L P.\nChoices:\nA:20\nB:110\nC:140\nD:160",
        "question_for_eval": "J K L M is a rectangle. M L P R is a rhombus. Connect M K and connect M P. \\angle J M K \\cong \\angle R M P, m \\angle J M K = 55, and m \\angle M R P = 70. Find m \\angle K L P.\nChoices:\nA:20\nB:110\nC:140\nD:160"
    },
    {
        "sample_index": "251",
        "problem_index": "251",
        "problem_version": "Text Only",
        "question": "In a triangle with three sides length 29, 50, and 61. Find x. Round the angle measure to the nearest degree.\nChoices:\nA:98\nB:103\nC:108\nD:113",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In a triangle with three sides length 29, 50, and 61. Find x. Round the angle measure to the nearest degree.\nChoices:\nA:98\nB:103\nC:108\nD:113",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In a triangle with three sides length 29, 50, and 61. Find x. Round the angle measure to the nearest degree.\nChoices:\nA:98\nB:103\nC:108\nD:113",
        "question_for_eval": "In a triangle with three sides length 29, 50, and 61. Find x. Round the angle measure to the nearest degree.\nChoices:\nA:98\nB:103\nC:108\nD:113"
    },
    {
        "sample_index": "252",
        "problem_index": "252",
        "problem_version": "Text Only",
        "question": "In triangle A B C, A D, B E, and C F intersect at point Q. Q is the centroid and B E = 9. Find B Q.\nChoices:\nA:3\nB:6\nC:9\nD:12",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle A B C, A D, B E, and C F intersect at point Q. Q is the centroid and B E = 9. Find B Q.\nChoices:\nA:3\nB:6\nC:9\nD:12",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle A B C, A D, B E, and C F intersect at point Q. Q is the centroid and B E = 9. Find B Q.\nChoices:\nA:3\nB:6\nC:9\nD:12",
        "question_for_eval": "In triangle A B C, A D, B E, and C F intersect at point Q. Q is the centroid and B E = 9. Find B Q.\nChoices:\nA:3\nB:6\nC:9\nD:12"
    },
    {
        "sample_index": "253",
        "problem_index": "253",
        "problem_version": "Text Only",
        "question": "A B is a diameter, A C = 8 inches, and B C = 15 inches. Find the radius of the circle.\nChoices:\nA:7.5\nB:8\nC:8.5\nD:17",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A B is a diameter, A C = 8 inches, and B C = 15 inches. Find the radius of the circle.\nChoices:\nA:7.5\nB:8\nC:8.5\nD:17",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A B is a diameter, A C = 8 inches, and B C = 15 inches. Find the radius of the circle.\nChoices:\nA:7.5\nB:8\nC:8.5\nD:17",
        "question_for_eval": "A B is a diameter, A C = 8 inches, and B C = 15 inches. Find the radius of the circle.\nChoices:\nA:7.5\nB:8\nC:8.5\nD:17"
    },
    {
        "sample_index": "254",
        "problem_index": "254",
        "problem_version": "Text Only",
        "question": "In the right triangle with hypotenuse length 12 and two sides length x and z, find y.\nChoices:\nA:\\frac { \\sqrt { 2 } } { 2 }\nB:\\sqrt { 2 }\nC:2 \\sqrt { 2 }\nD:4 \\sqrt { 2 }",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle with hypotenuse length 12 and two sides length x and z, find y.\nChoices:\nA:\\frac { \\sqrt { 2 } } { 2 }\nB:\\sqrt { 2 }\nC:2 \\sqrt { 2 }\nD:4 \\sqrt { 2 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle with hypotenuse length 12 and two sides length x and z, find y.\nChoices:\nA:\\frac { \\sqrt { 2 } } { 2 }\nB:\\sqrt { 2 }\nC:2 \\sqrt { 2 }\nD:4 \\sqrt { 2 }",
        "question_for_eval": "In the right triangle with hypotenuse length 12 and two sides length x and z, find y.\nChoices:\nA:\\frac { \\sqrt { 2 } } { 2 }\nB:\\sqrt { 2 }\nC:2 \\sqrt { 2 }\nD:4 \\sqrt { 2 }"
    },
    {
        "sample_index": "255",
        "problem_index": "255",
        "problem_version": "Text Only",
        "question": "m is the perpendicular bisector of X Z, W Z = 14.9. Find W X.\nChoices:\nA:7.45\nB:14.9\nC:22.4\nD:25.3",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: m is the perpendicular bisector of X Z, W Z = 14.9. Find W X.\nChoices:\nA:7.45\nB:14.9\nC:22.4\nD:25.3",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: m is the perpendicular bisector of X Z, W Z = 14.9. Find W X.\nChoices:\nA:7.45\nB:14.9\nC:22.4\nD:25.3",
        "question_for_eval": "m is the perpendicular bisector of X Z, W Z = 14.9. Find W X.\nChoices:\nA:7.45\nB:14.9\nC:22.4\nD:25.3"
    },
    {
        "sample_index": "256",
        "problem_index": "256",
        "problem_version": "Text Only",
        "question": "Lines l, m, and n are perpendicular bisectors of \\triangle P Q R and meet at T. If T Q = 2 x, P T = 3 y - 1, T Q = 2 x, and T R = 8, find z.\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Lines l, m, and n are perpendicular bisectors of \\triangle P Q R and meet at T. If T Q = 2 x, P T = 3 y - 1, T Q = 2 x, and T R = 8, find z.\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Lines l, m, and n are perpendicular bisectors of \\triangle P Q R and meet at T. If T Q = 2 x, P T = 3 y - 1, T Q = 2 x, and T R = 8, find z.\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "question_for_eval": "Lines l, m, and n are perpendicular bisectors of \\triangle P Q R and meet at T. If T Q = 2 x, P T = 3 y - 1, T Q = 2 x, and T R = 8, find z.\nChoices:\nA:3\nB:4\nC:5\nD:6"
    },
    {
        "sample_index": "257",
        "problem_index": "257",
        "problem_version": "Text Only",
        "question": "Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. If A B = 12, A C = 16, and E D = 5, find A E.\nChoices:\nA:10\nB:12\nC:15\nD:16",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. If A B = 12, A C = 16, and E D = 5, find A E.\nChoices:\nA:10\nB:12\nC:15\nD:16",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. If A B = 12, A C = 16, and E D = 5, find A E.\nChoices:\nA:10\nB:12\nC:15\nD:16",
        "question_for_eval": "Two triangles A B E and A C D are similar with a shared vertex A. B E and C D are parallel. If A B = 12, A C = 16, and E D = 5, find A E.\nChoices:\nA:10\nB:12\nC:15\nD:16"
    },
    {
        "sample_index": "258",
        "problem_index": "258",
        "problem_version": "Text Only",
        "question": "In \\odot C, \\angle R C M is x - 1 degrees, \\angle R C L is 3 x + 5 degrees, and \\angle M C N is 60 degrees. Find m \\angle N C L.\nChoices:\nA:60\nB:120\nC:240\nD:360",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot C, \\angle R C M is x - 1 degrees, \\angle R C L is 3 x + 5 degrees, and \\angle M C N is 60 degrees. Find m \\angle N C L.\nChoices:\nA:60\nB:120\nC:240\nD:360",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot C, \\angle R C M is x - 1 degrees, \\angle R C L is 3 x + 5 degrees, and \\angle M C N is 60 degrees. Find m \\angle N C L.\nChoices:\nA:60\nB:120\nC:240\nD:360",
        "question_for_eval": "In \\odot C, \\angle R C M is x - 1 degrees, \\angle R C L is 3 x + 5 degrees, and \\angle M C N is 60 degrees. Find m \\angle N C L.\nChoices:\nA:60\nB:120\nC:240\nD:360"
    },
    {
        "sample_index": "259",
        "problem_index": "259",
        "problem_version": "Text Only",
        "question": "In a right triangle G E F, the hypotenuse G F is 16 and H F is 12. E H is the altitude of triangle G E F. Find the measure of the altitude drawn to the hypotenuse.\nChoices:\nA:2 \\sqrt { 3 }\nB:2 \\sqrt { 6 }\nC:4 \\sqrt { 3 }\nD:4 \\sqrt { 6 }",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In a right triangle G E F, the hypotenuse G F is 16 and H F is 12. E H is the altitude of triangle G E F. Find the measure of the altitude drawn to the hypotenuse.\nChoices:\nA:2 \\sqrt { 3 }\nB:2 \\sqrt { 6 }\nC:4 \\sqrt { 3 }\nD:4 \\sqrt { 6 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In a right triangle G E F, the hypotenuse G F is 16 and H F is 12. E H is the altitude of triangle G E F. Find the measure of the altitude drawn to the hypotenuse.\nChoices:\nA:2 \\sqrt { 3 }\nB:2 \\sqrt { 6 }\nC:4 \\sqrt { 3 }\nD:4 \\sqrt { 6 }",
        "question_for_eval": "In a right triangle G E F, the hypotenuse G F is 16 and H F is 12. E H is the altitude of triangle G E F. Find the measure of the altitude drawn to the hypotenuse.\nChoices:\nA:2 \\sqrt { 3 }\nB:2 \\sqrt { 6 }\nC:4 \\sqrt { 3 }\nD:4 \\sqrt { 6 }"
    },
    {
        "sample_index": "260",
        "problem_index": "260",
        "problem_version": "Text Only",
        "question": "In triangle A B C, AB = AC. \\angle C A B and \\angle A B C are both 2 x degrees. A B and B C are 3 and 4 y - 5 inches, respectively. Find x.\nChoices:\nA:20\nB:30\nC:40\nD:50",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle A B C, AB = AC. \\angle C A B and \\angle A B C are both 2 x degrees. A B and B C are 3 and 4 y - 5 inches, respectively. Find x.\nChoices:\nA:20\nB:30\nC:40\nD:50",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle A B C, AB = AC. \\angle C A B and \\angle A B C are both 2 x degrees. A B and B C are 3 and 4 y - 5 inches, respectively. Find x.\nChoices:\nA:20\nB:30\nC:40\nD:50",
        "question_for_eval": "In triangle A B C, AB = AC. \\angle C A B and \\angle A B C are both 2 x degrees. A B and B C are 3 and 4 y - 5 inches, respectively. Find x.\nChoices:\nA:20\nB:30\nC:40\nD:50"
    },
    {
        "sample_index": "261",
        "problem_index": "261",
        "problem_version": "Text Only",
        "question": "In rhombus L M P Q, diagonal P L and Q M intersect at R. m \\angle Q L M = 2 x^ { 2 } - 10, m \\angle Q P M = 8 x, and M P = 10. Find the perimeter of L M P Q.\nChoices:\nA:10\nB:40\nC:70\nD:140",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In rhombus L M P Q, diagonal P L and Q M intersect at R. m \\angle Q L M = 2 x^ { 2 } - 10, m \\angle Q P M = 8 x, and M P = 10. Find the perimeter of L M P Q.\nChoices:\nA:10\nB:40\nC:70\nD:140",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In rhombus L M P Q, diagonal P L and Q M intersect at R. m \\angle Q L M = 2 x^ { 2 } - 10, m \\angle Q P M = 8 x, and M P = 10. Find the perimeter of L M P Q.\nChoices:\nA:10\nB:40\nC:70\nD:140",
        "question_for_eval": "In rhombus L M P Q, diagonal P L and Q M intersect at R. m \\angle Q L M = 2 x^ { 2 } - 10, m \\angle Q P M = 8 x, and M P = 10. Find the perimeter of L M P Q.\nChoices:\nA:10\nB:40\nC:70\nD:140"
    },
    {
        "sample_index": "262",
        "problem_index": "262",
        "problem_version": "Text Only",
        "question": "The top and bottom sides of the quadrilateral are 22 and 37 ft. It's altitude is 23 ft. Find the area of the trapezoid.\nChoices:\nA:506\nB:667\nC:678.5\nD:851",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The top and bottom sides of the quadrilateral are 22 and 37 ft. It's altitude is 23 ft. Find the area of the trapezoid.\nChoices:\nA:506\nB:667\nC:678.5\nD:851",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The top and bottom sides of the quadrilateral are 22 and 37 ft. It's altitude is 23 ft. Find the area of the trapezoid.\nChoices:\nA:506\nB:667\nC:678.5\nD:851",
        "question_for_eval": "The top and bottom sides of the quadrilateral are 22 and 37 ft. It's altitude is 23 ft. Find the area of the trapezoid.\nChoices:\nA:506\nB:667\nC:678.5\nD:851"
    },
    {
        "sample_index": "263",
        "problem_index": "263",
        "problem_version": "Text Only",
        "question": "Triangle L M N is equilateral, and M P bisects L N. L M is 3 x + 1 and M N is 4 x - 2. Find the measure of the side of \\triangle L M N.\nChoices:\nA:9\nB:10\nC:11\nD:12",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Triangle L M N is equilateral, and M P bisects L N. L M is 3 x + 1 and M N is 4 x - 2. Find the measure of the side of \\triangle L M N.\nChoices:\nA:9\nB:10\nC:11\nD:12",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Triangle L M N is equilateral, and M P bisects L N. L M is 3 x + 1 and M N is 4 x - 2. Find the measure of the side of \\triangle L M N.\nChoices:\nA:9\nB:10\nC:11\nD:12",
        "question_for_eval": "Triangle L M N is equilateral, and M P bisects L N. L M is 3 x + 1 and M N is 4 x - 2. Find the measure of the side of \\triangle L M N.\nChoices:\nA:9\nB:10\nC:11\nD:12"
    },
    {
        "sample_index": "264",
        "problem_index": "264",
        "problem_version": "Text Only",
        "question": "Parallelogram M N P Q with m \\angle M = 10 x and m \\angle N = 20 x, \\angle M = \\angle P and \\angle N = \\angle Q. Find \\angle M.\nChoices:\nA:30\nB:45\nC:60\nD:120",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Parallelogram M N P Q with m \\angle M = 10 x and m \\angle N = 20 x, \\angle M = \\angle P and \\angle N = \\angle Q. Find \\angle M.\nChoices:\nA:30\nB:45\nC:60\nD:120",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Parallelogram M N P Q with m \\angle M = 10 x and m \\angle N = 20 x, \\angle M = \\angle P and \\angle N = \\angle Q. Find \\angle M.\nChoices:\nA:30\nB:45\nC:60\nD:120",
        "question_for_eval": "Parallelogram M N P Q with m \\angle M = 10 x and m \\angle N = 20 x, \\angle M = \\angle P and \\angle N = \\angle Q. Find \\angle M.\nChoices:\nA:30\nB:45\nC:60\nD:120"
    },
    {
        "sample_index": "265",
        "problem_index": "265",
        "problem_version": "Text Only",
        "question": "Three lines l, m, and p intersect at two points and form eights angles. Line l and m are parallel. If m \\angle 5 = 7 x - 5 and m \\angle 4 = 2 x + 23, find x.\nChoices:\nA:5.6\nB:18\nC:20\nD:22",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Three lines l, m, and p intersect at two points and form eights angles. Line l and m are parallel. If m \\angle 5 = 7 x - 5 and m \\angle 4 = 2 x + 23, find x.\nChoices:\nA:5.6\nB:18\nC:20\nD:22",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Three lines l, m, and p intersect at two points and form eights angles. Line l and m are parallel. If m \\angle 5 = 7 x - 5 and m \\angle 4 = 2 x + 23, find x.\nChoices:\nA:5.6\nB:18\nC:20\nD:22",
        "question_for_eval": "Three lines l, m, and p intersect at two points and form eights angles. Line l and m are parallel. If m \\angle 5 = 7 x - 5 and m \\angle 4 = 2 x + 23, find x.\nChoices:\nA:5.6\nB:18\nC:20\nD:22"
    },
    {
        "sample_index": "266",
        "problem_index": "266",
        "problem_version": "Text Only",
        "question": "In parallelogram M N P R, diagonals M P and R N intersect at Q. M N = 3 x - 4, N P = 2 y + 5, R P = 20, and M R = 17.9. Find m \\angle R M N.\nChoices:\nA:33\nB:38\nC:71\nD:109",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In parallelogram M N P R, diagonals M P and R N intersect at Q. M N = 3 x - 4, N P = 2 y + 5, R P = 20, and M R = 17.9. Find m \\angle R M N.\nChoices:\nA:33\nB:38\nC:71\nD:109",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In parallelogram M N P R, diagonals M P and R N intersect at Q. M N = 3 x - 4, N P = 2 y + 5, R P = 20, and M R = 17.9. Find m \\angle R M N.\nChoices:\nA:33\nB:38\nC:71\nD:109",
        "question_for_eval": "In parallelogram M N P R, diagonals M P and R N intersect at Q. M N = 3 x - 4, N P = 2 y + 5, R P = 20, and M R = 17.9. Find m \\angle R M N.\nChoices:\nA:33\nB:38\nC:71\nD:109"
    },
    {
        "sample_index": "267",
        "problem_index": "267",
        "problem_version": "Text Only",
        "question": "Point A, B, and C are on the circle. The radius angle of A C is 122 degrees. Find m \\angle B.\nChoices:\nA:29\nB:58\nC:61\nD:122",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Point A, B, and C are on the circle. The radius angle of A C is 122 degrees. Find m \\angle B.\nChoices:\nA:29\nB:58\nC:61\nD:122",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Point A, B, and C are on the circle. The radius angle of A C is 122 degrees. Find m \\angle B.\nChoices:\nA:29\nB:58\nC:61\nD:122",
        "question_for_eval": "Point A, B, and C are on the circle. The radius angle of A C is 122 degrees. Find m \\angle B.\nChoices:\nA:29\nB:58\nC:61\nD:122"
    },
    {
        "sample_index": "268",
        "problem_index": "268",
        "problem_version": "Text Only",
        "question": "If \\triangle L M N \\sim \\triangle Q R S, Q R = 35, R S = 37, S Q = 12, and N L = 5, find the perimeter of \\triangle L M N.\nChoices:\nA:35\nB:42\nC:63\nD:84",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: If \\triangle L M N \\sim \\triangle Q R S, Q R = 35, R S = 37, S Q = 12, and N L = 5, find the perimeter of \\triangle L M N.\nChoices:\nA:35\nB:42\nC:63\nD:84",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: If \\triangle L M N \\sim \\triangle Q R S, Q R = 35, R S = 37, S Q = 12, and N L = 5, find the perimeter of \\triangle L M N.\nChoices:\nA:35\nB:42\nC:63\nD:84",
        "question_for_eval": "If \\triangle L M N \\sim \\triangle Q R S, Q R = 35, R S = 37, S Q = 12, and N L = 5, find the perimeter of \\triangle L M N.\nChoices:\nA:35\nB:42\nC:63\nD:84"
    },
    {
        "sample_index": "269",
        "problem_index": "269",
        "problem_version": "Text Only",
        "question": "The two polygons are similar. R V = x m, R T = 18 m, A E = 3 m, C D = 5m, and B C = 4m. Find U T.\nChoices:\nA:12\nB:20.5\nC:22.5\nD:35",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The two polygons are similar. R V = x m, R T = 18 m, A E = 3 m, C D = 5m, and B C = 4m. Find U T.\nChoices:\nA:12\nB:20.5\nC:22.5\nD:35",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The two polygons are similar. R V = x m, R T = 18 m, A E = 3 m, C D = 5m, and B C = 4m. Find U T.\nChoices:\nA:12\nB:20.5\nC:22.5\nD:35",
        "question_for_eval": "The two polygons are similar. R V = x m, R T = 18 m, A E = 3 m, C D = 5m, and B C = 4m. Find U T.\nChoices:\nA:12\nB:20.5\nC:22.5\nD:35"
    },
    {
        "sample_index": "270",
        "problem_index": "270",
        "problem_version": "Text Only",
        "question": "Several triangles are combined together with 6 annotated angles. Find m \\angle 6.\nChoices:\nA:25\nB:28\nC:35\nD:55",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Several triangles are combined together with 6 annotated angles. Find m \\angle 6.\nChoices:\nA:25\nB:28\nC:35\nD:55",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Several triangles are combined together with 6 annotated angles. Find m \\angle 6.\nChoices:\nA:25\nB:28\nC:35\nD:55",
        "question_for_eval": "Several triangles are combined together with 6 annotated angles. Find m \\angle 6.\nChoices:\nA:25\nB:28\nC:35\nD:55"
    },
    {
        "sample_index": "271",
        "problem_index": "271",
        "problem_version": "Text Only",
        "question": "\\odot P \\cong \\odot Q. Chord R S is on \\odot P with length 3x and chord T U is on \\odot Q with length 7 x - 44. Find x.\nChoices:\nA:7\nB:11\nC:22\nD:44",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: \\odot P \\cong \\odot Q. Chord R S is on \\odot P with length 3x and chord T U is on \\odot Q with length 7 x - 44. Find x.\nChoices:\nA:7\nB:11\nC:22\nD:44",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: \\odot P \\cong \\odot Q. Chord R S is on \\odot P with length 3x and chord T U is on \\odot Q with length 7 x - 44. Find x.\nChoices:\nA:7\nB:11\nC:22\nD:44",
        "question_for_eval": "\\odot P \\cong \\odot Q. Chord R S is on \\odot P with length 3x and chord T U is on \\odot Q with length 7 x - 44. Find x.\nChoices:\nA:7\nB:11\nC:22\nD:44"
    },
    {
        "sample_index": "272",
        "problem_index": "272",
        "problem_version": "Text Only",
        "question": "There is a right triangle with hypotenuse length x. One of the acute is 45 degrees and one of the side is 4. Find x.\nChoices:\nA:4 \\sqrt { 2 }\nB:4 \\sqrt { 3 }\nC:8\nD:4 \\sqrt { 5 }",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a right triangle with hypotenuse length x. One of the acute is 45 degrees and one of the side is 4. Find x.\nChoices:\nA:4 \\sqrt { 2 }\nB:4 \\sqrt { 3 }\nC:8\nD:4 \\sqrt { 5 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a right triangle with hypotenuse length x. One of the acute is 45 degrees and one of the side is 4. Find x.\nChoices:\nA:4 \\sqrt { 2 }\nB:4 \\sqrt { 3 }\nC:8\nD:4 \\sqrt { 5 }",
        "question_for_eval": "There is a right triangle with hypotenuse length x. One of the acute is 45 degrees and one of the side is 4. Find x.\nChoices:\nA:4 \\sqrt { 2 }\nB:4 \\sqrt { 3 }\nC:8\nD:4 \\sqrt { 5 }"
    },
    {
        "sample_index": "273",
        "problem_index": "273",
        "problem_version": "Text Only",
        "question": "Two triangles M Q N and M P O are similar with a shared vertex M. Q N and P O are parallel. M Q = 5, M N = 6, and Q P = x. Find Q P.\nChoices:\nA:2\nB:3.6\nC:5\nD:6",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles M Q N and M P O are similar with a shared vertex M. Q N and P O are parallel. M Q = 5, M N = 6, and Q P = x. Find Q P.\nChoices:\nA:2\nB:3.6\nC:5\nD:6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles M Q N and M P O are similar with a shared vertex M. Q N and P O are parallel. M Q = 5, M N = 6, and Q P = x. Find Q P.\nChoices:\nA:2\nB:3.6\nC:5\nD:6",
        "question_for_eval": "Two triangles M Q N and M P O are similar with a shared vertex M. Q N and P O are parallel. M Q = 5, M N = 6, and Q P = x. Find Q P.\nChoices:\nA:2\nB:3.6\nC:5\nD:6"
    },
    {
        "sample_index": "274",
        "problem_index": "274",
        "problem_version": "Text Only",
        "question": "There is a right triangle with hypotenuse length 42. The two sides are x and 38. Find x.\nChoices:\nA:8 \\sqrt { 2 }\nB:8 \\sqrt { 3 }\nC:8 \\sqrt { 5 }\nD:8 \\sqrt { 7 }",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a right triangle with hypotenuse length 42. The two sides are x and 38. Find x.\nChoices:\nA:8 \\sqrt { 2 }\nB:8 \\sqrt { 3 }\nC:8 \\sqrt { 5 }\nD:8 \\sqrt { 7 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a right triangle with hypotenuse length 42. The two sides are x and 38. Find x.\nChoices:\nA:8 \\sqrt { 2 }\nB:8 \\sqrt { 3 }\nC:8 \\sqrt { 5 }\nD:8 \\sqrt { 7 }",
        "question_for_eval": "There is a right triangle with hypotenuse length 42. The two sides are x and 38. Find x.\nChoices:\nA:8 \\sqrt { 2 }\nB:8 \\sqrt { 3 }\nC:8 \\sqrt { 5 }\nD:8 \\sqrt { 7 }"
    },
    {
        "sample_index": "275",
        "problem_index": "275",
        "problem_version": "Text Only",
        "question": "In rhombus A B C D, diagonals A C and B D intersect at point E. A B = 2 x + 3 and B C = 5 x. Find m \\angle A E B.\nChoices:\nA:45\nB:60\nC:90\nD:180",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In rhombus A B C D, diagonals A C and B D intersect at point E. A B = 2 x + 3 and B C = 5 x. Find m \\angle A E B.\nChoices:\nA:45\nB:60\nC:90\nD:180",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In rhombus A B C D, diagonals A C and B D intersect at point E. A B = 2 x + 3 and B C = 5 x. Find m \\angle A E B.\nChoices:\nA:45\nB:60\nC:90\nD:180",
        "question_for_eval": "In rhombus A B C D, diagonals A C and B D intersect at point E. A B = 2 x + 3 and B C = 5 x. Find m \\angle A E B.\nChoices:\nA:45\nB:60\nC:90\nD:180"
    },
    {
        "sample_index": "276",
        "problem_index": "276",
        "problem_version": "Text Only",
        "question": "Circle O has a radius of 13 inches, such as O C and O B. Radius O B is perpendicular to chord C D which is 24 inches long. If m \\widehat C D = 134, find m \\widehat C B.\nChoices:\nA:24\nB:33\nC:67\nD:134",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Circle O has a radius of 13 inches, such as O C and O B. Radius O B is perpendicular to chord C D which is 24 inches long. If m \\widehat C D = 134, find m \\widehat C B.\nChoices:\nA:24\nB:33\nC:67\nD:134",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Circle O has a radius of 13 inches, such as O C and O B. Radius O B is perpendicular to chord C D which is 24 inches long. If m \\widehat C D = 134, find m \\widehat C B.\nChoices:\nA:24\nB:33\nC:67\nD:134",
        "question_for_eval": "Circle O has a radius of 13 inches, such as O C and O B. Radius O B is perpendicular to chord C D which is 24 inches long. If m \\widehat C D = 134, find m \\widehat C B.\nChoices:\nA:24\nB:33\nC:67\nD:134"
    },
    {
        "sample_index": "277",
        "problem_index": "277",
        "problem_version": "Text Only",
        "question": "Circles G, J, and K all intersect at L. F H is the diameter of \\odot G and G H is the radius. If G H = 10, find F H.\nChoices:\nA:5\nB:10\nC:20\nD:25",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Circles G, J, and K all intersect at L. F H is the diameter of \\odot G and G H is the radius. If G H = 10, find F H.\nChoices:\nA:5\nB:10\nC:20\nD:25",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Circles G, J, and K all intersect at L. F H is the diameter of \\odot G and G H is the radius. If G H = 10, find F H.\nChoices:\nA:5\nB:10\nC:20\nD:25",
        "question_for_eval": "Circles G, J, and K all intersect at L. F H is the diameter of \\odot G and G H is the radius. If G H = 10, find F H.\nChoices:\nA:5\nB:10\nC:20\nD:25"
    },
    {
        "sample_index": "278",
        "problem_index": "278",
        "problem_version": "Text Only",
        "question": "Two triangles W in green and W' in blue are similar according to a reference point F. Find the scale factor from W to W'.\nChoices:\nA:\\frac { 1 } { 3 }\nB:\\frac { 2 } { 3 }\nC:\\frac { 3 } { 4 }\nD:\\frac { 3 } { 2 }",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles W in green and W' in blue are similar according to a reference point F. Find the scale factor from W to W'.\nChoices:\nA:\\frac { 1 } { 3 }\nB:\\frac { 2 } { 3 }\nC:\\frac { 3 } { 4 }\nD:\\frac { 3 } { 2 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles W in green and W' in blue are similar according to a reference point F. Find the scale factor from W to W'.\nChoices:\nA:\\frac { 1 } { 3 }\nB:\\frac { 2 } { 3 }\nC:\\frac { 3 } { 4 }\nD:\\frac { 3 } { 2 }",
        "question_for_eval": "Two triangles W in green and W' in blue are similar according to a reference point F. Find the scale factor from W to W'.\nChoices:\nA:\\frac { 1 } { 3 }\nB:\\frac { 2 } { 3 }\nC:\\frac { 3 } { 4 }\nD:\\frac { 3 } { 2 }"
    },
    {
        "sample_index": "279",
        "problem_index": "279",
        "problem_version": "Text Only",
        "question": "In quadrilateral R Q T S, \\angle R = \\angle T = x degrees. Find m \\angle R.\nChoices:\nA:58\nB:60\nC:122\nD:124",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In quadrilateral R Q T S, \\angle R = \\angle T = x degrees. Find m \\angle R.\nChoices:\nA:58\nB:60\nC:122\nD:124",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In quadrilateral R Q T S, \\angle R = \\angle T = x degrees. Find m \\angle R.\nChoices:\nA:58\nB:60\nC:122\nD:124",
        "question_for_eval": "In quadrilateral R Q T S, \\angle R = \\angle T = x degrees. Find m \\angle R.\nChoices:\nA:58\nB:60\nC:122\nD:124"
    },
    {
        "sample_index": "280",
        "problem_index": "280",
        "problem_version": "Text Only",
        "question": "There are two annotated angles of 5y and 60 degrees, and two annotated length x + 4 and 3 x - 6. Find x so that the quadrilateral is a parallelogram.\nChoices:\nA:3\nB:5\nC:12\nD:18",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There are two annotated angles of 5y and 60 degrees, and two annotated length x + 4 and 3 x - 6. Find x so that the quadrilateral is a parallelogram.\nChoices:\nA:3\nB:5\nC:12\nD:18",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There are two annotated angles of 5y and 60 degrees, and two annotated length x + 4 and 3 x - 6. Find x so that the quadrilateral is a parallelogram.\nChoices:\nA:3\nB:5\nC:12\nD:18",
        "question_for_eval": "There are two annotated angles of 5y and 60 degrees, and two annotated length x + 4 and 3 x - 6. Find x so that the quadrilateral is a parallelogram.\nChoices:\nA:3\nB:5\nC:12\nD:18"
    },
    {
        "sample_index": "281",
        "problem_index": "281",
        "problem_version": "Text Only",
        "question": "In the right trangle A B C, \\angle C = 90 degrees. A C = 24, A B = 26, and B C = 10. Express the ratio of \\cos B as a decimal to the nearest hundredth.\nChoices:\nA:0.38\nB:0.42\nC:0.92\nD:2.40",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right trangle A B C, \\angle C = 90 degrees. A C = 24, A B = 26, and B C = 10. Express the ratio of \\cos B as a decimal to the nearest hundredth.\nChoices:\nA:0.38\nB:0.42\nC:0.92\nD:2.40",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right trangle A B C, \\angle C = 90 degrees. A C = 24, A B = 26, and B C = 10. Express the ratio of \\cos B as a decimal to the nearest hundredth.\nChoices:\nA:0.38\nB:0.42\nC:0.92\nD:2.40",
        "question_for_eval": "In the right trangle A B C, \\angle C = 90 degrees. A C = 24, A B = 26, and B C = 10. Express the ratio of \\cos B as a decimal to the nearest hundredth.\nChoices:\nA:0.38\nB:0.42\nC:0.92\nD:2.40"
    },
    {
        "sample_index": "282",
        "problem_index": "282",
        "problem_version": "Text Only",
        "question": "A B \\cong D F. C E is perpendicular to A B and D F. C B = 9 x and D E = 2 x + 14. Find x.\nChoices:\nA:1\nB:2\nC:3\nD:4",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A B \\cong D F. C E is perpendicular to A B and D F. C B = 9 x and D E = 2 x + 14. Find x.\nChoices:\nA:1\nB:2\nC:3\nD:4",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A B \\cong D F. C E is perpendicular to A B and D F. C B = 9 x and D E = 2 x + 14. Find x.\nChoices:\nA:1\nB:2\nC:3\nD:4",
        "question_for_eval": "A B \\cong D F. C E is perpendicular to A B and D F. C B = 9 x and D E = 2 x + 14. Find x.\nChoices:\nA:1\nB:2\nC:3\nD:4"
    },
    {
        "sample_index": "283",
        "problem_index": "283",
        "problem_version": "Text Only",
        "question": "In \\odot M, M K and M P are radii and perpendicular to chords F G and H J, respectively. F L = 24, H J = 48, and m \\widehat H P = 65. Find F G.\nChoices:\nA:24\nB:32\nC:48\nD:65",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot M, M K and M P are radii and perpendicular to chords F G and H J, respectively. F L = 24, H J = 48, and m \\widehat H P = 65. Find F G.\nChoices:\nA:24\nB:32\nC:48\nD:65",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot M, M K and M P are radii and perpendicular to chords F G and H J, respectively. F L = 24, H J = 48, and m \\widehat H P = 65. Find F G.\nChoices:\nA:24\nB:32\nC:48\nD:65",
        "question_for_eval": "In \\odot M, M K and M P are radii and perpendicular to chords F G and H J, respectively. F L = 24, H J = 48, and m \\widehat H P = 65. Find F G.\nChoices:\nA:24\nB:32\nC:48\nD:65"
    },
    {
        "sample_index": "284",
        "problem_index": "284",
        "problem_version": "Text Only",
        "question": "There are five lines shown. Three lines are parallel and the other two lines intersect with them. The spacing of the parallel lines is equal. Find x.\nChoices:\nA:0.5\nB:1\nC:1.5\nD:2",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There are five lines shown. Three lines are parallel and the other two lines intersect with them. The spacing of the parallel lines is equal. Find x.\nChoices:\nA:0.5\nB:1\nC:1.5\nD:2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There are five lines shown. Three lines are parallel and the other two lines intersect with them. The spacing of the parallel lines is equal. Find x.\nChoices:\nA:0.5\nB:1\nC:1.5\nD:2",
        "question_for_eval": "There are five lines shown. Three lines are parallel and the other two lines intersect with them. The spacing of the parallel lines is equal. Find x.\nChoices:\nA:0.5\nB:1\nC:1.5\nD:2"
    },
    {
        "sample_index": "285",
        "problem_index": "285",
        "problem_version": "Text Only",
        "question": "In the right triangle, the hypotenuse is x length with an altitule of 8 length. The other two sides are y and z length. Find z.\nChoices:\nA:10\nB:\\frac { 32 } { 3 }\nC:\\frac { 40 } { 3 }\nD:\\frac { 50 } { 3 }",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle, the hypotenuse is x length with an altitule of 8 length. The other two sides are y and z length. Find z.\nChoices:\nA:10\nB:\\frac { 32 } { 3 }\nC:\\frac { 40 } { 3 }\nD:\\frac { 50 } { 3 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle, the hypotenuse is x length with an altitule of 8 length. The other two sides are y and z length. Find z.\nChoices:\nA:10\nB:\\frac { 32 } { 3 }\nC:\\frac { 40 } { 3 }\nD:\\frac { 50 } { 3 }",
        "question_for_eval": "In the right triangle, the hypotenuse is x length with an altitule of 8 length. The other two sides are y and z length. Find z.\nChoices:\nA:10\nB:\\frac { 32 } { 3 }\nC:\\frac { 40 } { 3 }\nD:\\frac { 50 } { 3 }"
    },
    {
        "sample_index": "286",
        "problem_index": "286",
        "problem_version": "Text Only",
        "question": "In H, the diameter is 18, L M = 12, and m \\widehat L M = 84. J K is hypotenuse to L M at P. Find H P. Round to the nearest hundredth.\nChoices:\nA:2.29\nB:3.35\nC:5.65\nD:6.71",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In H, the diameter is 18, L M = 12, and m \\widehat L M = 84. J K is hypotenuse to L M at P. Find H P. Round to the nearest hundredth.\nChoices:\nA:2.29\nB:3.35\nC:5.65\nD:6.71",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In H, the diameter is 18, L M = 12, and m \\widehat L M = 84. J K is hypotenuse to L M at P. Find H P. Round to the nearest hundredth.\nChoices:\nA:2.29\nB:3.35\nC:5.65\nD:6.71",
        "question_for_eval": "In H, the diameter is 18, L M = 12, and m \\widehat L M = 84. J K is hypotenuse to L M at P. Find H P. Round to the nearest hundredth.\nChoices:\nA:2.29\nB:3.35\nC:5.65\nD:6.71"
    },
    {
        "sample_index": "287",
        "problem_index": "287",
        "problem_version": "Text Only",
        "question": "There is a triangle with two acute angles of 27 and 52 degrees, along with an external angle as \\angle 1. Find m \\angle 1.\nChoices:\nA:21\nB:27\nC:52\nD:79",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a triangle with two acute angles of 27 and 52 degrees, along with an external angle as \\angle 1. Find m \\angle 1.\nChoices:\nA:21\nB:27\nC:52\nD:79",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a triangle with two acute angles of 27 and 52 degrees, along with an external angle as \\angle 1. Find m \\angle 1.\nChoices:\nA:21\nB:27\nC:52\nD:79",
        "question_for_eval": "There is a triangle with two acute angles of 27 and 52 degrees, along with an external angle as \\angle 1. Find m \\angle 1.\nChoices:\nA:21\nB:27\nC:52\nD:79"
    },
    {
        "sample_index": "288",
        "problem_index": "288",
        "problem_version": "Text Only",
        "question": "There is a right triangle A B F on top of a rectangle C D E F. \\angle C F D is labeled as \\angle 2. Find m \\angle 2.\nChoices:\nA:39\nB:42\nC:48\nD:51",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a right triangle A B F on top of a rectangle C D E F. \\angle C F D is labeled as \\angle 2. Find m \\angle 2.\nChoices:\nA:39\nB:42\nC:48\nD:51",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a right triangle A B F on top of a rectangle C D E F. \\angle C F D is labeled as \\angle 2. Find m \\angle 2.\nChoices:\nA:39\nB:42\nC:48\nD:51",
        "question_for_eval": "There is a right triangle A B F on top of a rectangle C D E F. \\angle C F D is labeled as \\angle 2. Find m \\angle 2.\nChoices:\nA:39\nB:42\nC:48\nD:51"
    },
    {
        "sample_index": "289",
        "problem_index": "289",
        "problem_version": "Text Only",
        "question": "In \\triangle P Q R, S T \\parallel R Q. Triangle P S T is similar to triangle P R Q with a shared vertex P. If P S = 12.5, S R = 5, and P T = 15, find T Q.\nChoices:\nA:5\nB:6\nC:6.5\nD:12.5",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\triangle P Q R, S T \\parallel R Q. Triangle P S T is similar to triangle P R Q with a shared vertex P. If P S = 12.5, S R = 5, and P T = 15, find T Q.\nChoices:\nA:5\nB:6\nC:6.5\nD:12.5",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\triangle P Q R, S T \\parallel R Q. Triangle P S T is similar to triangle P R Q with a shared vertex P. If P S = 12.5, S R = 5, and P T = 15, find T Q.\nChoices:\nA:5\nB:6\nC:6.5\nD:12.5",
        "question_for_eval": "In \\triangle P Q R, S T \\parallel R Q. Triangle P S T is similar to triangle P R Q with a shared vertex P. If P S = 12.5, S R = 5, and P T = 15, find T Q.\nChoices:\nA:5\nB:6\nC:6.5\nD:12.5"
    },
    {
        "sample_index": "290",
        "problem_index": "290",
        "problem_version": "Text Only",
        "question": "In the right triangle, an acute angle is labeled as \\angle 4 with an external angle of 123 degrees. Find m \\angle 4.\nChoices:\nA:33\nB:43\nC:57\nD:123",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle, an acute angle is labeled as \\angle 4 with an external angle of 123 degrees. Find m \\angle 4.\nChoices:\nA:33\nB:43\nC:57\nD:123",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle, an acute angle is labeled as \\angle 4 with an external angle of 123 degrees. Find m \\angle 4.\nChoices:\nA:33\nB:43\nC:57\nD:123",
        "question_for_eval": "In the right triangle, an acute angle is labeled as \\angle 4 with an external angle of 123 degrees. Find m \\angle 4.\nChoices:\nA:33\nB:43\nC:57\nD:123"
    },
    {
        "sample_index": "291",
        "problem_index": "291",
        "problem_version": "Text Only",
        "question": "A triangle with an acute angle of 30 degrees is within a circle, which forms the shaded region. Find the area of the shaded region. \nChoices:\nA:35.2\nB:43.2\nC:53.5\nD:56.9",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A triangle with an acute angle of 30 degrees is within a circle, which forms the shaded region. Find the area of the shaded region. \nChoices:\nA:35.2\nB:43.2\nC:53.5\nD:56.9",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A triangle with an acute angle of 30 degrees is within a circle, which forms the shaded region. Find the area of the shaded region. \nChoices:\nA:35.2\nB:43.2\nC:53.5\nD:56.9",
        "question_for_eval": "A triangle with an acute angle of 30 degrees is within a circle, which forms the shaded region. Find the area of the shaded region. \nChoices:\nA:35.2\nB:43.2\nC:53.5\nD:56.9"
    },
    {
        "sample_index": "292",
        "problem_index": "292",
        "problem_version": "Text Only",
        "question": "In the right triangle, an acute angle is 70 degrees and the hypotenuse is x length. Find x to the nearest hundredth.\nChoices:\nA:5.13\nB:5.46\nC:15.96\nD:43.86",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle, an acute angle is 70 degrees and the hypotenuse is x length. Find x to the nearest hundredth.\nChoices:\nA:5.13\nB:5.46\nC:15.96\nD:43.86",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle, an acute angle is 70 degrees and the hypotenuse is x length. Find x to the nearest hundredth.\nChoices:\nA:5.13\nB:5.46\nC:15.96\nD:43.86",
        "question_for_eval": "In the right triangle, an acute angle is 70 degrees and the hypotenuse is x length. Find x to the nearest hundredth.\nChoices:\nA:5.13\nB:5.46\nC:15.96\nD:43.86"
    },
    {
        "sample_index": "293",
        "problem_index": "293",
        "problem_version": "Text Only",
        "question": "There is a rhombus in blue. Find the area of the rhombus.\nChoices:\nA:38\nB:84\nC:168\nD:336",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a rhombus in blue. Find the area of the rhombus.\nChoices:\nA:38\nB:84\nC:168\nD:336",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a rhombus in blue. Find the area of the rhombus.\nChoices:\nA:38\nB:84\nC:168\nD:336",
        "question_for_eval": "There is a rhombus in blue. Find the area of the rhombus.\nChoices:\nA:38\nB:84\nC:168\nD:336"
    },
    {
        "sample_index": "294",
        "problem_index": "294",
        "problem_version": "Text Only",
        "question": "In parallelogram J K L M, diagonals J L and K M intersect at point R, and ML is 45, KL is 21. Find m \\angle K J L if J K = 2 b + 3 and J M = 3 a.\nChoices:\nA:30\nB:70\nC:80\nD:100",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In parallelogram J K L M, diagonals J L and K M intersect at point R, and ML is 45, KL is 21. Find m \\angle K J L if J K = 2 b + 3 and J M = 3 a.\nChoices:\nA:30\nB:70\nC:80\nD:100",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In parallelogram J K L M, diagonals J L and K M intersect at point R, and ML is 45, KL is 21. Find m \\angle K J L if J K = 2 b + 3 and J M = 3 a.\nChoices:\nA:30\nB:70\nC:80\nD:100",
        "question_for_eval": "In parallelogram J K L M, diagonals J L and K M intersect at point R, and ML is 45, KL is 21. Find m \\angle K J L if J K = 2 b + 3 and J M = 3 a.\nChoices:\nA:30\nB:70\nC:80\nD:100"
    },
    {
        "sample_index": "295",
        "problem_index": "295",
        "problem_version": "Text Only",
        "question": "In triangle T Q S, TQ = 2, S Q = 5, and T S = 3. Find x if \\triangle J L M \\sim \\triangle Q S T.\nChoices:\nA:1.5\nB:2\nC:3\nD:4",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle T Q S, TQ = 2, S Q = 5, and T S = 3. Find x if \\triangle J L M \\sim \\triangle Q S T.\nChoices:\nA:1.5\nB:2\nC:3\nD:4",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle T Q S, TQ = 2, S Q = 5, and T S = 3. Find x if \\triangle J L M \\sim \\triangle Q S T.\nChoices:\nA:1.5\nB:2\nC:3\nD:4",
        "question_for_eval": "In triangle T Q S, TQ = 2, S Q = 5, and T S = 3. Find x if \\triangle J L M \\sim \\triangle Q S T.\nChoices:\nA:1.5\nB:2\nC:3\nD:4"
    },
    {
        "sample_index": "296",
        "problem_index": "296",
        "problem_version": "Text Only",
        "question": "There is an equilateral triangle with two sides 2 x + 11 and 6 x - 9. Find x.\nChoices:\nA:2\nB:5\nC:6\nD:9",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is an equilateral triangle with two sides 2 x + 11 and 6 x - 9. Find x.\nChoices:\nA:2\nB:5\nC:6\nD:9",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is an equilateral triangle with two sides 2 x + 11 and 6 x - 9. Find x.\nChoices:\nA:2\nB:5\nC:6\nD:9",
        "question_for_eval": "There is an equilateral triangle with two sides 2 x + 11 and 6 x - 9. Find x.\nChoices:\nA:2\nB:5\nC:6\nD:9"
    },
    {
        "sample_index": "297",
        "problem_index": "297",
        "problem_version": "Text Only",
        "question": "In the figure, there are four lines intersect at four points. Two pairs of lines are parallel to each other. m \\angle 1 = 123. Find the measure of \\angle 14.\nChoices:\nA:47\nB:57\nC:67\nD:123",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure, there are four lines intersect at four points. Two pairs of lines are parallel to each other. m \\angle 1 = 123. Find the measure of \\angle 14.\nChoices:\nA:47\nB:57\nC:67\nD:123",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure, there are four lines intersect at four points. Two pairs of lines are parallel to each other. m \\angle 1 = 123. Find the measure of \\angle 14.\nChoices:\nA:47\nB:57\nC:67\nD:123",
        "question_for_eval": "In the figure, there are four lines intersect at four points. Two pairs of lines are parallel to each other. m \\angle 1 = 123. Find the measure of \\angle 14.\nChoices:\nA:47\nB:57\nC:67\nD:123"
    },
    {
        "sample_index": "298",
        "problem_index": "298",
        "problem_version": "Text Only",
        "question": "The diameters of \\odot J and \\odot K are on the same line with points A, B, C, and D. Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and B C = 5.4 units. Find J K.\nChoices:\nA:12.6\nB:14.6\nC:20.6\nD:30.6",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The diameters of \\odot J and \\odot K are on the same line with points A, B, C, and D. Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and B C = 5.4 units. Find J K.\nChoices:\nA:12.6\nB:14.6\nC:20.6\nD:30.6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The diameters of \\odot J and \\odot K are on the same line with points A, B, C, and D. Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and B C = 5.4 units. Find J K.\nChoices:\nA:12.6\nB:14.6\nC:20.6\nD:30.6",
        "question_for_eval": "The diameters of \\odot J and \\odot K are on the same line with points A, B, C, and D. Circle J has a radius of 10 units, \\odot K has a radius of 8 units, and B C = 5.4 units. Find J K.\nChoices:\nA:12.6\nB:14.6\nC:20.6\nD:30.6"
    },
    {
        "sample_index": "299",
        "problem_index": "299",
        "problem_version": "Text Only",
        "question": "In the right isosceles triangle, the hypotenuse is 20. Find x. Round to the nearest tenth.\nChoices:\nA:1.4\nB:7.1\nC:14.1\nD:15.6",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right isosceles triangle, the hypotenuse is 20. Find x. Round to the nearest tenth.\nChoices:\nA:1.4\nB:7.1\nC:14.1\nD:15.6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right isosceles triangle, the hypotenuse is 20. Find x. Round to the nearest tenth.\nChoices:\nA:1.4\nB:7.1\nC:14.1\nD:15.6",
        "question_for_eval": "In the right isosceles triangle, the hypotenuse is 20. Find x. Round to the nearest tenth.\nChoices:\nA:1.4\nB:7.1\nC:14.1\nD:15.6"
    },
    {
        "sample_index": "300",
        "problem_index": "300",
        "problem_version": "Text Only",
        "question": "In the right triangle, the two sides are y and 12 with an altitude of x. Find x.\nChoices:\nA:5\nB:2 \\sqrt { 11 }\nC:10\nD:4 \\sqrt { 11 }",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the right triangle, the two sides are y and 12 with an altitude of x. Find x.\nChoices:\nA:5\nB:2 \\sqrt { 11 }\nC:10\nD:4 \\sqrt { 11 }",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the right triangle, the two sides are y and 12 with an altitude of x. Find x.\nChoices:\nA:5\nB:2 \\sqrt { 11 }\nC:10\nD:4 \\sqrt { 11 }",
        "question_for_eval": "In the right triangle, the two sides are y and 12 with an altitude of x. Find x.\nChoices:\nA:5\nB:2 \\sqrt { 11 }\nC:10\nD:4 \\sqrt { 11 }"
    },
    {
        "sample_index": "301",
        "problem_index": "301",
        "problem_version": "Text Only",
        "question": "In triangle A B C, A B = x, B C = 16. \\angle B A C = 97 degrees and \\angle A C B = 21 degrees. Find x. Round to the nearest tenth.\nChoices:\nA:5.8\nB:6.5\nC:14.2\nD:44.3",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle A B C, A B = x, B C = 16. \\angle B A C = 97 degrees and \\angle A C B = 21 degrees. Find x. Round to the nearest tenth.\nChoices:\nA:5.8\nB:6.5\nC:14.2\nD:44.3",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle A B C, A B = x, B C = 16. \\angle B A C = 97 degrees and \\angle A C B = 21 degrees. Find x. Round to the nearest tenth.\nChoices:\nA:5.8\nB:6.5\nC:14.2\nD:44.3",
        "question_for_eval": "In triangle A B C, A B = x, B C = 16. \\angle B A C = 97 degrees and \\angle A C B = 21 degrees. Find x. Round to the nearest tenth.\nChoices:\nA:5.8\nB:6.5\nC:14.2\nD:44.3"
    },
    {
        "sample_index": "302",
        "problem_index": "302",
        "problem_version": "Text Only",
        "question": "Two triangles G J I and G K H are similar with a shared vertex G. K H and J I are parallel. Find K J if G J = 8, G H = 12, and H I = 4.\nChoices:\nA:2\nB:4\nC:6\nD:8",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles G J I and G K H are similar with a shared vertex G. K H and J I are parallel. Find K J if G J = 8, G H = 12, and H I = 4.\nChoices:\nA:2\nB:4\nC:6\nD:8",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles G J I and G K H are similar with a shared vertex G. K H and J I are parallel. Find K J if G J = 8, G H = 12, and H I = 4.\nChoices:\nA:2\nB:4\nC:6\nD:8",
        "question_for_eval": "Two triangles G J I and G K H are similar with a shared vertex G. K H and J I are parallel. Find K J if G J = 8, G H = 12, and H I = 4.\nChoices:\nA:2\nB:4\nC:6\nD:8"
    },
    {
        "sample_index": "303",
        "problem_index": "303",
        "problem_version": "Text Only",
        "question": "\\triangle R S T \\cong \\triangle A B C. \\angle R S T = \\angle C B A. S T = 2y - 8, and C B = y + 13. Find x.\nChoices:\nA:8\nB:10\nC:13\nD:21",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: \\triangle R S T \\cong \\triangle A B C. \\angle R S T = \\angle C B A. S T = 2y - 8, and C B = y + 13. Find x.\nChoices:\nA:8\nB:10\nC:13\nD:21",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: \\triangle R S T \\cong \\triangle A B C. \\angle R S T = \\angle C B A. S T = 2y - 8, and C B = y + 13. Find x.\nChoices:\nA:8\nB:10\nC:13\nD:21",
        "question_for_eval": "\\triangle R S T \\cong \\triangle A B C. \\angle R S T = \\angle C B A. S T = 2y - 8, and C B = y + 13. Find x.\nChoices:\nA:8\nB:10\nC:13\nD:21"
    },
    {
        "sample_index": "304",
        "problem_index": "304",
        "problem_version": "Text Only",
        "question": "\\triangle R S V \\cong \\triangle T V S, and they share a side S V. S V is perpendicular to S R and \\angle R V S = 78 degrees. Find x.\nChoices:\nA:11\nB:11.5\nC:12\nD:12.5",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: \\triangle R S V \\cong \\triangle T V S, and they share a side S V. S V is perpendicular to S R and \\angle R V S = 78 degrees. Find x.\nChoices:\nA:11\nB:11.5\nC:12\nD:12.5",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: \\triangle R S V \\cong \\triangle T V S, and they share a side S V. S V is perpendicular to S R and \\angle R V S = 78 degrees. Find x.\nChoices:\nA:11\nB:11.5\nC:12\nD:12.5",
        "question_for_eval": "\\triangle R S V \\cong \\triangle T V S, and they share a side S V. S V is perpendicular to S R and \\angle R V S = 78 degrees. Find x.\nChoices:\nA:11\nB:11.5\nC:12\nD:12.5"
    },
    {
        "sample_index": "305",
        "problem_index": "305",
        "problem_version": "Text Only",
        "question": "There are four rays B A, B D, B F, and B C with a shared starting point B. \\overrightarrow B A and \\overrightarrow B C are opposite rays and \\overrightarrow B D bisects \\angle A B F. If m \\angle F B C = 2 x + 25 and m \\angle A B F = 10 x - 1, find m \\angle D B F.\nChoices:\nA:25.5\nB:50\nC:54\nD:64.5",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There are four rays B A, B D, B F, and B C with a shared starting point B. \\overrightarrow B A and \\overrightarrow B C are opposite rays and \\overrightarrow B D bisects \\angle A B F. If m \\angle F B C = 2 x + 25 and m \\angle A B F = 10 x - 1, find m \\angle D B F.\nChoices:\nA:25.5\nB:50\nC:54\nD:64.5",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There are four rays B A, B D, B F, and B C with a shared starting point B. \\overrightarrow B A and \\overrightarrow B C are opposite rays and \\overrightarrow B D bisects \\angle A B F. If m \\angle F B C = 2 x + 25 and m \\angle A B F = 10 x - 1, find m \\angle D B F.\nChoices:\nA:25.5\nB:50\nC:54\nD:64.5",
        "question_for_eval": "There are four rays B A, B D, B F, and B C with a shared starting point B. \\overrightarrow B A and \\overrightarrow B C are opposite rays and \\overrightarrow B D bisects \\angle A B F. If m \\angle F B C = 2 x + 25 and m \\angle A B F = 10 x - 1, find m \\angle D B F.\nChoices:\nA:25.5\nB:50\nC:54\nD:64.5"
    },
    {
        "sample_index": "306",
        "problem_index": "306",
        "problem_version": "Text Only",
        "question": "There is a right triangle V X W, the hypotenuse V X is 75, and V W = 72, X W = 21. Express the ratio of \\cos X as a decimal to the nearest hundredth.\nChoices:\nA:0.28\nB:0.29\nC:0.96\nD:3.43",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a right triangle V X W, the hypotenuse V X is 75, and V W = 72, X W = 21. Express the ratio of \\cos X as a decimal to the nearest hundredth.\nChoices:\nA:0.28\nB:0.29\nC:0.96\nD:3.43",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a right triangle V X W, the hypotenuse V X is 75, and V W = 72, X W = 21. Express the ratio of \\cos X as a decimal to the nearest hundredth.\nChoices:\nA:0.28\nB:0.29\nC:0.96\nD:3.43",
        "question_for_eval": "There is a right triangle V X W, the hypotenuse V X is 75, and V W = 72, X W = 21. Express the ratio of \\cos X as a decimal to the nearest hundredth.\nChoices:\nA:0.28\nB:0.29\nC:0.96\nD:3.43"
    },
    {
        "sample_index": "307",
        "problem_index": "307",
        "problem_version": "Text Only",
        "question": "In \\odot C, point R, M, N, L are on the circle, and M L is the diameter. \\angle M C R = x - 1 degrees and \\angle R C L = 3x + 5 degrees. Find m \\angle R C M.\nChoices:\nA:27\nB:43\nC:47\nD:67",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot C, point R, M, N, L are on the circle, and M L is the diameter. \\angle M C R = x - 1 degrees and \\angle R C L = 3x + 5 degrees. Find m \\angle R C M.\nChoices:\nA:27\nB:43\nC:47\nD:67",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot C, point R, M, N, L are on the circle, and M L is the diameter. \\angle M C R = x - 1 degrees and \\angle R C L = 3x + 5 degrees. Find m \\angle R C M.\nChoices:\nA:27\nB:43\nC:47\nD:67",
        "question_for_eval": "In \\odot C, point R, M, N, L are on the circle, and M L is the diameter. \\angle M C R = x - 1 degrees and \\angle R C L = 3x + 5 degrees. Find m \\angle R C M.\nChoices:\nA:27\nB:43\nC:47\nD:67"
    },
    {
        "sample_index": "308",
        "problem_index": "308",
        "problem_version": "Text Only",
        "question": "A B \\perp D C and G H \\perp F E. A C = 4.4, G H = 3.15, and G E = 6.3. If \\triangle A C D \\sim \\triangle G E F, find A B.\nChoices:\nA:2.2\nB:3.6\nC:4.4\nD:6.3",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A B \\perp D C and G H \\perp F E. A C = 4.4, G H = 3.15, and G E = 6.3. If \\triangle A C D \\sim \\triangle G E F, find A B.\nChoices:\nA:2.2\nB:3.6\nC:4.4\nD:6.3",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A B \\perp D C and G H \\perp F E. A C = 4.4, G H = 3.15, and G E = 6.3. If \\triangle A C D \\sim \\triangle G E F, find A B.\nChoices:\nA:2.2\nB:3.6\nC:4.4\nD:6.3",
        "question_for_eval": "A B \\perp D C and G H \\perp F E. A C = 4.4, G H = 3.15, and G E = 6.3. If \\triangle A C D \\sim \\triangle G E F, find A B.\nChoices:\nA:2.2\nB:3.6\nC:4.4\nD:6.3"
    },
    {
        "sample_index": "309",
        "problem_index": "309",
        "problem_version": "Text Only",
        "question": "Find x for the equilateral triangle R S T if R S = x + 9, S T = 2 x, and R T = 3 x - 9.\nChoices:\nA:3\nB:6\nC:9\nD:12",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Find x for the equilateral triangle R S T if R S = x + 9, S T = 2 x, and R T = 3 x - 9.\nChoices:\nA:3\nB:6\nC:9\nD:12",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Find x for the equilateral triangle R S T if R S = x + 9, S T = 2 x, and R T = 3 x - 9.\nChoices:\nA:3\nB:6\nC:9\nD:12",
        "question_for_eval": "Find x for the equilateral triangle R S T if R S = x + 9, S T = 2 x, and R T = 3 x - 9.\nChoices:\nA:3\nB:6\nC:9\nD:12"
    },
    {
        "sample_index": "310",
        "problem_index": "310",
        "problem_version": "Text Only",
        "question": "Two triangles A E B and A D C are similar with a shared vertex A. E B and D C are parallel. Find x if A E = 3, A B = 2, B C = 6, and E D = 2 x - 3.\nChoices:\nA:5\nB:6\nC:8\nD:9",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles A E B and A D C are similar with a shared vertex A. E B and D C are parallel. Find x if A E = 3, A B = 2, B C = 6, and E D = 2 x - 3.\nChoices:\nA:5\nB:6\nC:8\nD:9",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles A E B and A D C are similar with a shared vertex A. E B and D C are parallel. Find x if A E = 3, A B = 2, B C = 6, and E D = 2 x - 3.\nChoices:\nA:5\nB:6\nC:8\nD:9",
        "question_for_eval": "Two triangles A E B and A D C are similar with a shared vertex A. E B and D C are parallel. Find x if A E = 3, A B = 2, B C = 6, and E D = 2 x - 3.\nChoices:\nA:5\nB:6\nC:8\nD:9"
    },
    {
        "sample_index": "311",
        "problem_index": "311",
        "problem_version": "Text Only",
        "question": "In \\odot Z, points V, U, Y, X, W are on the circle. \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U = 4 x, m \\angle U Z Y = 2 x + 24, and V Y and W U are diameters. Find m \\widehat W U X.\nChoices:\nA:52\nB:104\nC:154\nD:308",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot Z, points V, U, Y, X, W are on the circle. \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U = 4 x, m \\angle U Z Y = 2 x + 24, and V Y and W U are diameters. Find m \\widehat W U X.\nChoices:\nA:52\nB:104\nC:154\nD:308",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot Z, points V, U, Y, X, W are on the circle. \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U = 4 x, m \\angle U Z Y = 2 x + 24, and V Y and W U are diameters. Find m \\widehat W U X.\nChoices:\nA:52\nB:104\nC:154\nD:308",
        "question_for_eval": "In \\odot Z, points V, U, Y, X, W are on the circle. \\angle W Z X \\cong \\angle X Z Y, m \\angle V Z U = 4 x, m \\angle U Z Y = 2 x + 24, and V Y and W U are diameters. Find m \\widehat W U X.\nChoices:\nA:52\nB:104\nC:154\nD:308"
    },
    {
        "sample_index": "312",
        "problem_index": "312",
        "problem_version": "Text Only",
        "question": "Two triangles have a shared vertex with three annotated points A, B, and C. Find the measure of \\angle 2 if A B \\perp B C.\nChoices:\nA:64\nB:68\nC:72\nD:76",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles have a shared vertex with three annotated points A, B, and C. Find the measure of \\angle 2 if A B \\perp B C.\nChoices:\nA:64\nB:68\nC:72\nD:76",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles have a shared vertex with three annotated points A, B, and C. Find the measure of \\angle 2 if A B \\perp B C.\nChoices:\nA:64\nB:68\nC:72\nD:76",
        "question_for_eval": "Two triangles have a shared vertex with three annotated points A, B, and C. Find the measure of \\angle 2 if A B \\perp B C.\nChoices:\nA:64\nB:68\nC:72\nD:76"
    },
    {
        "sample_index": "313",
        "problem_index": "313",
        "problem_version": "Text Only",
        "question": "Find the area of the circle with a diameter 6.2 cm. Round to the nearest tenth.\nChoices:\nA:19.5\nB:30.2\nC:60.4\nD:120.8",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Find the area of the circle with a diameter 6.2 cm. Round to the nearest tenth.\nChoices:\nA:19.5\nB:30.2\nC:60.4\nD:120.8",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Find the area of the circle with a diameter 6.2 cm. Round to the nearest tenth.\nChoices:\nA:19.5\nB:30.2\nC:60.4\nD:120.8",
        "question_for_eval": "Find the area of the circle with a diameter 6.2 cm. Round to the nearest tenth.\nChoices:\nA:19.5\nB:30.2\nC:60.4\nD:120.8"
    },
    {
        "sample_index": "314",
        "problem_index": "314",
        "problem_version": "Text Only",
        "question": "In trapezoid J K L M, J K is parallel to M L. J M = 6, K L = 6, and \\angle J M L is 80 degrees. Find m \\angle K.\nChoices:\nA:6\nB:60\nC:100\nD:180",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In trapezoid J K L M, J K is parallel to M L. J M = 6, K L = 6, and \\angle J M L is 80 degrees. Find m \\angle K.\nChoices:\nA:6\nB:60\nC:100\nD:180",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In trapezoid J K L M, J K is parallel to M L. J M = 6, K L = 6, and \\angle J M L is 80 degrees. Find m \\angle K.\nChoices:\nA:6\nB:60\nC:100\nD:180",
        "question_for_eval": "In trapezoid J K L M, J K is parallel to M L. J M = 6, K L = 6, and \\angle J M L is 80 degrees. Find m \\angle K.\nChoices:\nA:6\nB:60\nC:100\nD:180"
    },
    {
        "sample_index": "315",
        "problem_index": "315",
        "problem_version": "Text Only",
        "question": "Find the perimeter of the isosceles triangle in yellow with a base length 3.5 ft. Round to the nearest hundredth.\nChoices:\nA:5.84\nB:6.65\nC:8.21\nD:8.73",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Find the perimeter of the isosceles triangle in yellow with a base length 3.5 ft. Round to the nearest hundredth.\nChoices:\nA:5.84\nB:6.65\nC:8.21\nD:8.73",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Find the perimeter of the isosceles triangle in yellow with a base length 3.5 ft. Round to the nearest hundredth.\nChoices:\nA:5.84\nB:6.65\nC:8.21\nD:8.73",
        "question_for_eval": "Find the perimeter of the isosceles triangle in yellow with a base length 3.5 ft. Round to the nearest hundredth.\nChoices:\nA:5.84\nB:6.65\nC:8.21\nD:8.73"
    },
    {
        "sample_index": "316",
        "problem_index": "316",
        "problem_version": "Text Only",
        "question": "Two triangles A E B and A D C are similar with a shared vertex A. E B \\parallel D C.  A B = x - 2 and B C = 5. Find x.\nChoices:\nA:5\nB:7.5\nC:9.5\nD:10",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two triangles A E B and A D C are similar with a shared vertex A. E B \\parallel D C.  A B = x - 2 and B C = 5. Find x.\nChoices:\nA:5\nB:7.5\nC:9.5\nD:10",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two triangles A E B and A D C are similar with a shared vertex A. E B \\parallel D C.  A B = x - 2 and B C = 5. Find x.\nChoices:\nA:5\nB:7.5\nC:9.5\nD:10",
        "question_for_eval": "Two triangles A E B and A D C are similar with a shared vertex A. E B \\parallel D C.  A B = x - 2 and B C = 5. Find x.\nChoices:\nA:5\nB:7.5\nC:9.5\nD:10"
    },
    {
        "sample_index": "317",
        "problem_index": "317",
        "problem_version": "Text Only",
        "question": "In \\odot F, B, C, D, A are on the circle and A C is a diameter. \\angle C F D is 4 a - 1 degrees. Find the measure of \\angle A F B.\nChoices:\nA:72\nB:108\nC:120\nD:144",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In \\odot F, B, C, D, A are on the circle and A C is a diameter. \\angle C F D is 4 a - 1 degrees. Find the measure of \\angle A F B.\nChoices:\nA:72\nB:108\nC:120\nD:144",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In \\odot F, B, C, D, A are on the circle and A C is a diameter. \\angle C F D is 4 a - 1 degrees. Find the measure of \\angle A F B.\nChoices:\nA:72\nB:108\nC:120\nD:144",
        "question_for_eval": "In \\odot F, B, C, D, A are on the circle and A C is a diameter. \\angle C F D is 4 a - 1 degrees. Find the measure of \\angle A F B.\nChoices:\nA:72\nB:108\nC:120\nD:144"
    },
    {
        "sample_index": "318",
        "problem_index": "318",
        "problem_version": "Text Only",
        "question": "The figure shows three parallel horizontal lines, with a diagonal line running through them on the left and a vertical line on the right. The diagonal line on the left intersects with three horizontal lines, with a length of 2x+6 for the lower section and 20-5x for the upper section. The vertical line on the right intersects with three horizontal lines, with a length of y for the upper section and 3/5y+2 for the lower section. The two short line segments cut by the left line are of equal length, and the two short line segments cut by the right line are of equal lengthFind y.\nChoices:\nA:3\nB:4.5\nC:5\nD:6",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure shows three parallel horizontal lines, with a diagonal line running through them on the left and a vertical line on the right. The diagonal line on the left intersects with three horizontal lines, with a length of 2x+6 for the lower section and 20-5x for the upper section. The vertical line on the right intersects with three horizontal lines, with a length of y for the upper section and 3/5y+2 for the lower section. The two short line segments cut by the left line are of equal length, and the two short line segments cut by the right line are of equal lengthFind y.\nChoices:\nA:3\nB:4.5\nC:5\nD:6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure shows three parallel horizontal lines, with a diagonal line running through them on the left and a vertical line on the right. The diagonal line on the left intersects with three horizontal lines, with a length of 2x+6 for the lower section and 20-5x for the upper section. The vertical line on the right intersects with three horizontal lines, with a length of y for the upper section and 3/5y+2 for the lower section. The two short line segments cut by the left line are of equal length, and the two short line segments cut by the right line are of equal lengthFind y.\nChoices:\nA:3\nB:4.5\nC:5\nD:6",
        "question_for_eval": "The figure shows three parallel horizontal lines, with a diagonal line running through them on the left and a vertical line on the right. The diagonal line on the left intersects with three horizontal lines, with a length of 2x+6 for the lower section and 20-5x for the upper section. The vertical line on the right intersects with three horizontal lines, with a length of y for the upper section and 3/5y+2 for the lower section. The two short line segments cut by the left line are of equal length, and the two short line segments cut by the right line are of equal lengthFind y.\nChoices:\nA:3\nB:4.5\nC:5\nD:6"
    },
    {
        "sample_index": "319",
        "problem_index": "319",
        "problem_version": "Text Only",
        "question": "The diagonal length of the blue quadrilateral is 8yd, the diagonal length of the green quadrilateral is 4yd, and the area of the blue quadrilateral is 36yd ^ 2. For the pair of similar figures, find the area of the green figure.\nChoices:\nA:9\nB:18\nC:72\nD:144",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The diagonal length of the blue quadrilateral is 8yd, the diagonal length of the green quadrilateral is 4yd, and the area of the blue quadrilateral is 36yd ^ 2. For the pair of similar figures, find the area of the green figure.\nChoices:\nA:9\nB:18\nC:72\nD:144",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The diagonal length of the blue quadrilateral is 8yd, the diagonal length of the green quadrilateral is 4yd, and the area of the blue quadrilateral is 36yd ^ 2. For the pair of similar figures, find the area of the green figure.\nChoices:\nA:9\nB:18\nC:72\nD:144",
        "question_for_eval": "The diagonal length of the blue quadrilateral is 8yd, the diagonal length of the green quadrilateral is 4yd, and the area of the blue quadrilateral is 36yd ^ 2. For the pair of similar figures, find the area of the green figure.\nChoices:\nA:9\nB:18\nC:72\nD:144"
    },
    {
        "sample_index": "320",
        "problem_index": "320",
        "problem_version": "Text Only",
        "question": "The figure shows a quadrilateral ABCD, with S on AC and T on BD. For trapezoid A B C D, S and T are midpoints of the legs. If A B = x + 4, C D = 3 x + 2, and S T = 9, find A B.\nChoices:\nA:3\nB:5\nC:7\nD:9",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure shows a quadrilateral ABCD, with S on AC and T on BD. For trapezoid A B C D, S and T are midpoints of the legs. If A B = x + 4, C D = 3 x + 2, and S T = 9, find A B.\nChoices:\nA:3\nB:5\nC:7\nD:9",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure shows a quadrilateral ABCD, with S on AC and T on BD. For trapezoid A B C D, S and T are midpoints of the legs. If A B = x + 4, C D = 3 x + 2, and S T = 9, find A B.\nChoices:\nA:3\nB:5\nC:7\nD:9",
        "question_for_eval": "The figure shows a quadrilateral ABCD, with S on AC and T on BD. For trapezoid A B C D, S and T are midpoints of the legs. If A B = x + 4, C D = 3 x + 2, and S T = 9, find A B.\nChoices:\nA:3\nB:5\nC:7\nD:9"
    },
    {
        "sample_index": "321",
        "problem_index": "321",
        "problem_version": "Text Only",
        "question": "The figure shows a \\parallelogram ABCD, with BD connected, BD perpendicular to AB, and BD also perpendicular to DC. The length of BD is 6m, and the length of AD is 10m. What is the area of \\parallelogram ABCD?\nChoices:\nA:24\nB:30\nC:48\nD:60",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure shows a \\parallelogram ABCD, with BD connected, BD perpendicular to AB, and BD also perpendicular to DC. The length of BD is 6m, and the length of AD is 10m. What is the area of \\parallelogram ABCD?\nChoices:\nA:24\nB:30\nC:48\nD:60",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure shows a \\parallelogram ABCD, with BD connected, BD perpendicular to AB, and BD also perpendicular to DC. The length of BD is 6m, and the length of AD is 10m. What is the area of \\parallelogram ABCD?\nChoices:\nA:24\nB:30\nC:48\nD:60",
        "question_for_eval": "The figure shows a \\parallelogram ABCD, with BD connected, BD perpendicular to AB, and BD also perpendicular to DC. The length of BD is 6m, and the length of AD is 10m. What is the area of \\parallelogram ABCD?\nChoices:\nA:24\nB:30\nC:48\nD:60"
    },
    {
        "sample_index": "322",
        "problem_index": "322",
        "problem_version": "Text Only",
        "question": "QM is perpendicular to MN, QP is perpendicular to NP, the length of MQ is 2x+2, and the length of QP is 4x-8, NQ is the angular bisector of angle MNP. Find Q M.\nChoices:\nA:4\nB:8\nC:12\nD:16",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: QM is perpendicular to MN, QP is perpendicular to NP, the length of MQ is 2x+2, and the length of QP is 4x-8, NQ is the angular bisector of angle MNP. Find Q M.\nChoices:\nA:4\nB:8\nC:12\nD:16",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: QM is perpendicular to MN, QP is perpendicular to NP, the length of MQ is 2x+2, and the length of QP is 4x-8, NQ is the angular bisector of angle MNP. Find Q M.\nChoices:\nA:4\nB:8\nC:12\nD:16",
        "question_for_eval": "QM is perpendicular to MN, QP is perpendicular to NP, the length of MQ is 2x+2, and the length of QP is 4x-8, NQ is the angular bisector of angle MNP. Find Q M.\nChoices:\nA:4\nB:8\nC:12\nD:16"
    },
    {
        "sample_index": "323",
        "problem_index": "323",
        "problem_version": "Text Only",
        "question": "The diagram is a quadrilateral with intersecting diagonals and perpendicular to each other. Where AB=AD, BC=DC, and the length from D to the diagonal intersection point is 5, and the length from C to the diagonal intersection point is 12. Find B C.\nChoices:\nA:5\nB:9\nC:12\nD:13",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The diagram is a quadrilateral with intersecting diagonals and perpendicular to each other. Where AB=AD, BC=DC, and the length from D to the diagonal intersection point is 5, and the length from C to the diagonal intersection point is 12. Find B C.\nChoices:\nA:5\nB:9\nC:12\nD:13",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The diagram is a quadrilateral with intersecting diagonals and perpendicular to each other. Where AB=AD, BC=DC, and the length from D to the diagonal intersection point is 5, and the length from C to the diagonal intersection point is 12. Find B C.\nChoices:\nA:5\nB:9\nC:12\nD:13",
        "question_for_eval": "The diagram is a quadrilateral with intersecting diagonals and perpendicular to each other. Where AB=AD, BC=DC, and the length from D to the diagonal intersection point is 5, and the length from C to the diagonal intersection point is 12. Find B C.\nChoices:\nA:5\nB:9\nC:12\nD:13"
    },
    {
        "sample_index": "324",
        "problem_index": "324",
        "problem_version": "Text Only",
        "question": "The figure shows a regular octagon, with a distance of 6cm from the vertex of the central path of the octagon. Find the area of the regular polygon figure. Round to the nearest tenth.\nChoices:\nA:12.7\nB:25.5\nC:101.8\nD:203.6",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure shows a regular octagon, with a distance of 6cm from the vertex of the central path of the octagon. Find the area of the regular polygon figure. Round to the nearest tenth.\nChoices:\nA:12.7\nB:25.5\nC:101.8\nD:203.6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure shows a regular octagon, with a distance of 6cm from the vertex of the central path of the octagon. Find the area of the regular polygon figure. Round to the nearest tenth.\nChoices:\nA:12.7\nB:25.5\nC:101.8\nD:203.6",
        "question_for_eval": "The figure shows a regular octagon, with a distance of 6cm from the vertex of the central path of the octagon. Find the area of the regular polygon figure. Round to the nearest tenth.\nChoices:\nA:12.7\nB:25.5\nC:101.8\nD:203.6"
    },
    {
        "sample_index": "325",
        "problem_index": "325",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the parallelogram with 2sides of 13yd and 10yd respectively. Find the area of the parallelogram. Round to the nearest tenth if necessary.\nChoices:\nA:65\nB:91.9\nC:112.6\nD:130",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: As shown in the figure, the parallelogram with 2sides of 13yd and 10yd respectively. Find the area of the parallelogram. Round to the nearest tenth if necessary.\nChoices:\nA:65\nB:91.9\nC:112.6\nD:130",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: As shown in the figure, the parallelogram with 2sides of 13yd and 10yd respectively. Find the area of the parallelogram. Round to the nearest tenth if necessary.\nChoices:\nA:65\nB:91.9\nC:112.6\nD:130",
        "question_for_eval": "As shown in the figure, the parallelogram with 2sides of 13yd and 10yd respectively. Find the area of the parallelogram. Round to the nearest tenth if necessary.\nChoices:\nA:65\nB:91.9\nC:112.6\nD:130"
    },
    {
        "sample_index": "326",
        "problem_index": "326",
        "problem_version": "Text Only",
        "question": "The diagram shows a triangle with a perpendicular length of 7ft and base length is 10.2ft. Find the area of the figure. Round to the nearest tenth if necessary.\nChoices:\nA:35.7\nB:49\nC:71.4\nD:104.0",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geometry3K",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The diagram shows a triangle with a perpendicular length of 7ft and base length is 10.2ft. Find the area of the figure. Round to the nearest tenth if necessary.\nChoices:\nA:35.7\nB:49\nC:71.4\nD:104.0",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The diagram shows a triangle with a perpendicular length of 7ft and base length is 10.2ft. Find the area of the figure. Round to the nearest tenth if necessary.\nChoices:\nA:35.7\nB:49\nC:71.4\nD:104.0",
        "question_for_eval": "The diagram shows a triangle with a perpendicular length of 7ft and base length is 10.2ft. Find the area of the figure. Round to the nearest tenth if necessary.\nChoices:\nA:35.7\nB:49\nC:71.4\nD:104.0"
    },
    {
        "sample_index": "327",
        "problem_index": "327",
        "problem_version": "Text Only",
        "question": "During a rescue search, a helicopter flew b kilometres west from point X to point Y, then changed course and flew 10.7 kilometres north to point Z. If point Z is on a bearing of 335\u00b0 T from point X:\n\nNow, if the distance that the helicopter must fly between point Z and point X is d kilometres, calculate d to one decimal place.",
        "image": "",
        "answer": "11.8",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: During a rescue search, a helicopter flew b kilometres west from point X to point Y, then changed course and flew 10.7 kilometres north to point Z. If point Z is on a bearing of 335\u00b0 T from point X:\n\nNow, if the distance that the helicopter must fly between point Z and point X is d kilometres, calculate d to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: During a rescue search, a helicopter flew b kilometres west from point X to point Y, then changed course and flew 10.7 kilometres north to point Z. If point Z is on a bearing of 335\u00b0 T from point X:\n\nNow, if the distance that the helicopter must fly between point Z and point X is d kilometres, calculate d to one decimal place.",
        "question_for_eval": "During a rescue search, a helicopter flew b kilometres west from point X to point Y, then changed course and flew 10.7 kilometres north to point Z. If point Z is on a bearing of 335\u00b0 T from point X:\n\nNow, if the distance that the helicopter must fly between point Z and point X is d kilometres, calculate d to one decimal place."
    },
    {
        "sample_index": "328",
        "problem_index": "328",
        "problem_version": "Text Only",
        "question": "Three television presenters are practising their navigation skills before heading off on an expedition to a remote location. Amelia at point B is positioned 17.6 metres south of Ned at point A. Bart at point C is due east of Amelia and on a bearing of S 38^\\circ E from Ned. If Ned and Bart are d metres apart, find d to one decimal place.",
        "image": "",
        "answer": "22.3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Three television presenters are practising their navigation skills before heading off on an expedition to a remote location. Amelia at point B is positioned 17.6 metres south of Ned at point A. Bart at point C is due east of Amelia and on a bearing of S 38^\\circ E from Ned. If Ned and Bart are d metres apart, find d to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Three television presenters are practising their navigation skills before heading off on an expedition to a remote location. Amelia at point B is positioned 17.6 metres south of Ned at point A. Bart at point C is due east of Amelia and on a bearing of S 38^\\circ E from Ned. If Ned and Bart are d metres apart, find d to one decimal place.",
        "question_for_eval": "Three television presenters are practising their navigation skills before heading off on an expedition to a remote location. Amelia at point B is positioned 17.6 metres south of Ned at point A. Bart at point C is due east of Amelia and on a bearing of S 38^\\circ E from Ned. If Ned and Bart are d metres apart, find d to one decimal place."
    },
    {
        "sample_index": "329",
        "problem_index": "329",
        "problem_version": "Text Only",
        "question": "In remote locations, photographers must keep track of their position from their base. One morning a photographer sets out from base, represented by point B, to the edge of an ice shelf at point S on a bearing of 055\u00b0. She then walked on a bearing of 145\u00b0 to point P, which is 916 metres due east of base.\n\nIf the photographer were to walk back to her base from point P, what is the total distance she would have travelled? Round your answer to one decimal place.",
        "image": "",
        "answer": "2191.7 metres",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In remote locations, photographers must keep track of their position from their base. One morning a photographer sets out from base, represented by point B, to the edge of an ice shelf at point S on a bearing of 055\u00b0. She then walked on a bearing of 145\u00b0 to point P, which is 916 metres due east of base.\n\nIf the photographer were to walk back to her base from point P, what is the total distance she would have travelled? Round your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In remote locations, photographers must keep track of their position from their base. One morning a photographer sets out from base, represented by point B, to the edge of an ice shelf at point S on a bearing of 055\u00b0. She then walked on a bearing of 145\u00b0 to point P, which is 916 metres due east of base.\n\nIf the photographer were to walk back to her base from point P, what is the total distance she would have travelled? Round your answer to one decimal place.",
        "question_for_eval": "In remote locations, photographers must keep track of their position from their base. One morning a photographer sets out from base, represented by point B, to the edge of an ice shelf at point S on a bearing of 055\u00b0. She then walked on a bearing of 145\u00b0 to point P, which is 916 metres due east of base.\n\nIf the photographer were to walk back to her base from point P, what is the total distance she would have travelled? Round your answer to one decimal place."
    },
    {
        "sample_index": "330",
        "problem_index": "330",
        "problem_version": "Text Only",
        "question": "A rally car starts at point P and races 191 kilometres south to point Q. Here the car turns west and races for 83 kilometres to point R. At point R the car must turn to head directly back to point P.\n\nWhat is the compass bearing of R from P? Give your answer to one decimal place.",
        "image": "",
        "answer": "S 23.5 ^\\circ W",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A rally car starts at point P and races 191 kilometres south to point Q. Here the car turns west and races for 83 kilometres to point R. At point R the car must turn to head directly back to point P.\n\nWhat is the compass bearing of R from P? Give your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A rally car starts at point P and races 191 kilometres south to point Q. Here the car turns west and races for 83 kilometres to point R. At point R the car must turn to head directly back to point P.\n\nWhat is the compass bearing of R from P? Give your answer to one decimal place.",
        "question_for_eval": "A rally car starts at point P and races 191 kilometres south to point Q. Here the car turns west and races for 83 kilometres to point R. At point R the car must turn to head directly back to point P.\n\nWhat is the compass bearing of R from P? Give your answer to one decimal place."
    },
    {
        "sample_index": "331",
        "problem_index": "331",
        "problem_version": "Text Only",
        "question": "Consider the points on the diagram P, A and N where N denotes the north cardinal point. Angle PAN is 45\u00b0.\n\nUsing the diagram, find the true bearing of P from A.",
        "image": "",
        "answer": "315^\\circT",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the points on the diagram P, A and N where N denotes the north cardinal point. Angle PAN is 45\u00b0.\n\nUsing the diagram, find the true bearing of P from A.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the points on the diagram P, A and N where N denotes the north cardinal point. Angle PAN is 45\u00b0.\n\nUsing the diagram, find the true bearing of P from A.",
        "question_for_eval": "Consider the points on the diagram P, A and N where N denotes the north cardinal point. Angle PAN is 45\u00b0.\n\nUsing the diagram, find the true bearing of P from A."
    },
    {
        "sample_index": "332",
        "problem_index": "332",
        "problem_version": "Text Only",
        "question": "Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 50\u00b0.\n\nUsing the diagram, find the true bearing of P from M.",
        "image": "",
        "answer": "230 ^\\circ T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 50\u00b0.\n\nUsing the diagram, find the true bearing of P from M.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 50\u00b0.\n\nUsing the diagram, find the true bearing of P from M.",
        "question_for_eval": "Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 50\u00b0.\n\nUsing the diagram, find the true bearing of P from M."
    },
    {
        "sample_index": "333",
        "problem_index": "333",
        "problem_version": "Text Only",
        "question": "Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 37\u00b0.\n\nUsing the diagram, find the true bearing of P from M.",
        "image": "",
        "answer": "217 ^\\circ T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 37\u00b0.\n\nUsing the diagram, find the true bearing of P from M.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 37\u00b0.\n\nUsing the diagram, find the true bearing of P from M.",
        "question_for_eval": "Consider the points on the diagram P, M and S where S denotes the south cardinal point. Angle PMS is 37\u00b0.\n\nUsing the diagram, find the true bearing of P from M."
    },
    {
        "sample_index": "334",
        "problem_index": "334",
        "problem_version": "Text Only",
        "question": "Consider the point A. The angle between line OA and the positive direction of the x-axis is 28\u00b0.\n\nFind the true bearing of A from O.",
        "image": "",
        "answer": "118\u63b3T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the point A. The angle between line OA and the positive direction of the x-axis is 28\u00b0.\n\nFind the true bearing of A from O.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the point A. The angle between line OA and the positive direction of the x-axis is 28\u00b0.\n\nFind the true bearing of A from O.",
        "question_for_eval": "Consider the point A. The angle between line OA and the positive direction of the x-axis is 28\u00b0.\n\nFind the true bearing of A from O."
    },
    {
        "sample_index": "335",
        "problem_index": "335",
        "problem_version": "Text Only",
        "question": "Consider the point A. The angle between line OA and the south direction is 32\u00b0.\n\nWhat is the true bearing of A from O?",
        "image": "",
        "answer": "212\u00b0T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the point A. The angle between line OA and the south direction is 32\u00b0.\n\nWhat is the true bearing of A from O?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the point A. The angle between line OA and the south direction is 32\u00b0.\n\nWhat is the true bearing of A from O?",
        "question_for_eval": "Consider the point A. The angle between line OA and the south direction is 32\u00b0.\n\nWhat is the true bearing of A from O?"
    },
    {
        "sample_index": "336",
        "problem_index": "336",
        "problem_version": "Text Only",
        "question": "Consider the point A. The angle between line OA and the north direction is 31\u00b0.\n\nFind the true bearing of point A from O.",
        "image": "",
        "answer": "329\u00b0 T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the point A. The angle between line OA and the north direction is 31\u00b0.\n\nFind the true bearing of point A from O.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the point A. The angle between line OA and the north direction is 31\u00b0.\n\nFind the true bearing of point A from O.",
        "question_for_eval": "Consider the point A. The angle between line OA and the north direction is 31\u00b0.\n\nFind the true bearing of point A from O."
    },
    {
        "sample_index": "337",
        "problem_index": "337",
        "problem_version": "Text Only",
        "question": "In the figure above, triangle ABC formed by the dashed line, angle A is 37\u00b0 and angle B is 48\u00b0. Find the true bearing of point A from point B.",
        "image": "",
        "answer": "270 ^\\circ T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the figure above, triangle ABC formed by the dashed line, angle A is 37\u00b0 and angle B is 48\u00b0. Find the true bearing of point A from point B.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the figure above, triangle ABC formed by the dashed line, angle A is 37\u00b0 and angle B is 48\u00b0. Find the true bearing of point A from point B.",
        "question_for_eval": "In the figure above, triangle ABC formed by the dashed line, angle A is 37\u00b0 and angle B is 48\u00b0. Find the true bearing of point A from point B."
    },
    {
        "sample_index": "338",
        "problem_index": "338",
        "problem_version": "Text Only",
        "question": "In the figure below, point B is due East of point A. We want to find the position of point A relative to point C. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 39\u00b0.\n\nFind the true bearing of point A from point C.",
        "image": "",
        "answer": "319 ^\\circ T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the figure below, point B is due East of point A. We want to find the position of point A relative to point C. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 39\u00b0.\n\nFind the true bearing of point A from point C.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the figure below, point B is due East of point A. We want to find the position of point A relative to point C. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 39\u00b0.\n\nFind the true bearing of point A from point C.",
        "question_for_eval": "In the figure below, point B is due East of point A. We want to find the position of point A relative to point C. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 39\u00b0.\n\nFind the true bearing of point A from point C."
    },
    {
        "sample_index": "339",
        "problem_index": "339",
        "problem_version": "Text Only",
        "question": "In the figure below, point B is due East of point A. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0. Find the true bearing of point B from point A.\nChoice:\nA. 090^\\circ T\nB. 180^\\circ T\nC. 049^\\circ T\nD. 041^\\circ T",
        "image": "",
        "answer": "090^\\circ T",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure below, point B is due East of point A. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0. Find the true bearing of point B from point A.\nChoice:\nA. 090^\\circ T\nB. 180^\\circ T\nC. 049^\\circ T\nD. 041^\\circ T",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure below, point B is due East of point A. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0. Find the true bearing of point B from point A.\nChoice:\nA. 090^\\circ T\nB. 180^\\circ T\nC. 049^\\circ T\nD. 041^\\circ T",
        "question_for_eval": "In the figure below, point B is due East of point A. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0. Find the true bearing of point B from point A.\nChoice:\nA. 090^\\circ T\nB. 180^\\circ T\nC. 049^\\circ T\nD. 041^\\circ T"
    },
    {
        "sample_index": "340",
        "problem_index": "340",
        "problem_version": "Text Only",
        "question": "Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0.\n\nFind the true bearing of point B from point C.\nChoice:\nA. 053 ^\\circ T\nB. 082 ^\\circ T\nC. 045 ^\\circ T\nD. 037 ^\\circ T",
        "image": "",
        "answer": "053 ^\\circ T",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0.\n\nFind the true bearing of point B from point C.\nChoice:\nA. 053 ^\\circ T\nB. 082 ^\\circ T\nC. 045 ^\\circ T\nD. 037 ^\\circ T",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0.\n\nFind the true bearing of point B from point C.\nChoice:\nA. 053 ^\\circ T\nB. 082 ^\\circ T\nC. 045 ^\\circ T\nD. 037 ^\\circ T",
        "question_for_eval": "Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 49\u00b0 and angle B is 41\u00b0.\n\nFind the true bearing of point B from point C.\nChoice:\nA. 053 ^\\circ T\nB. 082 ^\\circ T\nC. 045 ^\\circ T\nD. 037 ^\\circ T"
    },
    {
        "sample_index": "341",
        "problem_index": "341",
        "problem_version": "Text Only",
        "question": "Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 42\u00b0 and angle B is 53\u00b0.\n\n\nFind the true bearing of point C from point A.",
        "image": "",
        "answer": "132 ^\\circT",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 42\u00b0 and angle B is 53\u00b0.\n\n\nFind the true bearing of point C from point A.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 42\u00b0 and angle B is 53\u00b0.\n\n\nFind the true bearing of point C from point A.",
        "question_for_eval": "Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 42\u00b0 and angle B is 53\u00b0.\n\n\nFind the true bearing of point C from point A."
    },
    {
        "sample_index": "342",
        "problem_index": "342",
        "problem_version": "Text Only",
        "question": "Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 38\u00b0 and angle B is 49\u00b0.\n\nFind the true bearing of point C from point B.",
        "image": "",
        "answer": "221 ^\\circ T",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 38\u00b0 and angle B is 49\u00b0.\n\nFind the true bearing of point C from point B.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 38\u00b0 and angle B is 49\u00b0.\n\nFind the true bearing of point C from point B.",
        "question_for_eval": "Consider the following diagram. Triangle ABC formed by the dashed line, angle A is 38\u00b0 and angle B is 49\u00b0.\n\nFind the true bearing of point C from point B."
    },
    {
        "sample_index": "343",
        "problem_index": "343",
        "problem_version": "Text Only",
        "question": "Given the diagram shown, if the bearing of the clearing from the town is a\u00b0. Starting from town, heading 3.2 kilometers due north and then 5.9 kilometers due east is clearing. Find a to the nearest degree.",
        "image": "",
        "answer": "62^\\circ ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Given the diagram shown, if the bearing of the clearing from the town is a\u00b0. Starting from town, heading 3.2 kilometers due north and then 5.9 kilometers due east is clearing. Find a to the nearest degree.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Given the diagram shown, if the bearing of the clearing from the town is a\u00b0. Starting from town, heading 3.2 kilometers due north and then 5.9 kilometers due east is clearing. Find a to the nearest degree.",
        "question_for_eval": "Given the diagram shown, if the bearing of the clearing from the town is a\u00b0. Starting from town, heading 3.2 kilometers due north and then 5.9 kilometers due east is clearing. Find a to the nearest degree."
    },
    {
        "sample_index": "344",
        "problem_index": "344",
        "problem_version": "Text Only",
        "question": "At a point during the flight, a plane is 42 kilometres south and 57 kilometres west of the airport it left from.\n\n\nFind the size of the angle marked b to one decimal place.",
        "image": "",
        "answer": "53.6^\\circ ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: At a point during the flight, a plane is 42 kilometres south and 57 kilometres west of the airport it left from.\n\n\nFind the size of the angle marked b to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: At a point during the flight, a plane is 42 kilometres south and 57 kilometres west of the airport it left from.\n\n\nFind the size of the angle marked b to one decimal place.",
        "question_for_eval": "At a point during the flight, a plane is 42 kilometres south and 57 kilometres west of the airport it left from.\n\n\nFind the size of the angle marked b to one decimal place."
    },
    {
        "sample_index": "345",
        "problem_index": "345",
        "problem_version": "Text Only",
        "question": "Luke sailed for 116 kilometres on a bearing of 231^\\circ .\n\nIf w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place.",
        "image": "",
        "answer": "90.1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Luke sailed for 116 kilometres on a bearing of 231^\\circ .\n\nIf w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Luke sailed for 116 kilometres on a bearing of 231^\\circ .\n\nIf w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place.",
        "question_for_eval": "Luke sailed for 116 kilometres on a bearing of 231^\\circ .\n\nIf w is how many kilometres west he has sailed from his starting point, find $w$ to one decimal place."
    },
    {
        "sample_index": "346",
        "problem_index": "346",
        "problem_version": "Text Only",
        "question": "Considering the diagram below, find x, the angle of elevation to point A from point C. The picture shows a right angled triangle with a base length of 25 and a height of 19.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "37.23",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Considering the diagram below, find x, the angle of elevation to point A from point C. The picture shows a right angled triangle with a base length of 25 and a height of 19.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Considering the diagram below, find x, the angle of elevation to point A from point C. The picture shows a right angled triangle with a base length of 25 and a height of 19.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Considering the diagram below, find x, the angle of elevation to point A from point C. The picture shows a right angled triangle with a base length of 25 and a height of 19.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "347",
        "problem_index": "347",
        "problem_version": "Text Only",
        "question": "Sally measures the angle of elevation to the top of a tree from a point $20$m away to be 43^\\circ . If the height of the tree is H m, find the value of H.\n\nRound your answer to the nearest whole number.",
        "image": "",
        "answer": "19",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Sally measures the angle of elevation to the top of a tree from a point $20$m away to be 43^\\circ . If the height of the tree is H m, find the value of H.\n\nRound your answer to the nearest whole number.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Sally measures the angle of elevation to the top of a tree from a point $20$m away to be 43^\\circ . If the height of the tree is H m, find the value of H.\n\nRound your answer to the nearest whole number.",
        "question_for_eval": "Sally measures the angle of elevation to the top of a tree from a point $20$m away to be 43^\\circ . If the height of the tree is H m, find the value of H.\n\nRound your answer to the nearest whole number."
    },
    {
        "sample_index": "348",
        "problem_index": "348",
        "problem_version": "Text Only",
        "question": "A helicopter is flying at an altitude of 198 metres, at an angle of depression of 44\u00b0 to its landing pad. What is the distance d between the helicopter and the landing pad?\n\nRound your answer to the nearest whole number.",
        "image": "",
        "answer": "285",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A helicopter is flying at an altitude of 198 metres, at an angle of depression of 44\u00b0 to its landing pad. What is the distance d between the helicopter and the landing pad?\n\nRound your answer to the nearest whole number.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A helicopter is flying at an altitude of 198 metres, at an angle of depression of 44\u00b0 to its landing pad. What is the distance d between the helicopter and the landing pad?\n\nRound your answer to the nearest whole number.",
        "question_for_eval": "A helicopter is flying at an altitude of 198 metres, at an angle of depression of 44\u00b0 to its landing pad. What is the distance d between the helicopter and the landing pad?\n\nRound your answer to the nearest whole number."
    },
    {
        "sample_index": "349",
        "problem_index": "349",
        "problem_version": "Text Only",
        "question": "Considering the diagram below, ABCD is a rectangle, find x, the angle of depression from point B to point C. The lengths of AC and BC are 3 and 5, respectively.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "53.13",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Considering the diagram below, ABCD is a rectangle, find x, the angle of depression from point B to point C. The lengths of AC and BC are 3 and 5, respectively.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Considering the diagram below, ABCD is a rectangle, find x, the angle of depression from point B to point C. The lengths of AC and BC are 3 and 5, respectively.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Considering the diagram below, ABCD is a rectangle, find x, the angle of depression from point B to point C. The lengths of AC and BC are 3 and 5, respectively.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "350",
        "problem_index": "350",
        "problem_version": "Text Only",
        "question": "A fighter jet, flying at an altitude of 2000 m is approaching a target. At a particular time the pilot measures the angle of depression to the target to be 13^\\circ . After a minute, the pilot measures the angle of depression again and finds it to be 16^\\circ .\nNow find the distance covered by the jet in one minute.\n\nRound your answer to the nearest meter.",
        "image": "",
        "answer": "1688",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A fighter jet, flying at an altitude of 2000 m is approaching a target. At a particular time the pilot measures the angle of depression to the target to be 13^\\circ . After a minute, the pilot measures the angle of depression again and finds it to be 16^\\circ .\nNow find the distance covered by the jet in one minute.\n\nRound your answer to the nearest meter.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A fighter jet, flying at an altitude of 2000 m is approaching a target. At a particular time the pilot measures the angle of depression to the target to be 13^\\circ . After a minute, the pilot measures the angle of depression again and finds it to be 16^\\circ .\nNow find the distance covered by the jet in one minute.\n\nRound your answer to the nearest meter.",
        "question_for_eval": "A fighter jet, flying at an altitude of 2000 m is approaching a target. At a particular time the pilot measures the angle of depression to the target to be 13^\\circ . After a minute, the pilot measures the angle of depression again and finds it to be 16^\\circ .\nNow find the distance covered by the jet in one minute.\n\nRound your answer to the nearest meter."
    },
    {
        "sample_index": "351",
        "problem_index": "351",
        "problem_version": "Text Only",
        "question": "A man stands at point A looking at the top of two poles. Pole 1 has height 8 m and angle of elevation 34^\\circ  and Pole 2 has height 25 m and angle of elevation 57^\\circ . The man wishes to find the distance between the two poles.\nHence find BC, the distance between the two poles in metres.\n\nRound your answer to one decimal place.",
        "image": "",
        "answer": "4.4 m",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A man stands at point A looking at the top of two poles. Pole 1 has height 8 m and angle of elevation 34^\\circ  and Pole 2 has height 25 m and angle of elevation 57^\\circ . The man wishes to find the distance between the two poles.\nHence find BC, the distance between the two poles in metres.\n\nRound your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A man stands at point A looking at the top of two poles. Pole 1 has height 8 m and angle of elevation 34^\\circ  and Pole 2 has height 25 m and angle of elevation 57^\\circ . The man wishes to find the distance between the two poles.\nHence find BC, the distance between the two poles in metres.\n\nRound your answer to one decimal place.",
        "question_for_eval": "A man stands at point A looking at the top of two poles. Pole 1 has height 8 m and angle of elevation 34^\\circ  and Pole 2 has height 25 m and angle of elevation 57^\\circ . The man wishes to find the distance between the two poles.\nHence find BC, the distance between the two poles in metres.\n\nRound your answer to one decimal place."
    },
    {
        "sample_index": "352",
        "problem_index": "352",
        "problem_version": "Text Only",
        "question": "From the cockpit of an aeroplane flying at an altitude of 3000 m, the angle of depression to the airport is 57\u00b0. The aeroplane continues to fly in the same straight line, and after a few minutes the angle of depression to the airport becomes 67\u00b0.\nNow find the distance between the two sightings.\n\nRound your answer to the nearest metre.",
        "image": "",
        "answer": "675 m",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: From the cockpit of an aeroplane flying at an altitude of 3000 m, the angle of depression to the airport is 57\u00b0. The aeroplane continues to fly in the same straight line, and after a few minutes the angle of depression to the airport becomes 67\u00b0.\nNow find the distance between the two sightings.\n\nRound your answer to the nearest metre.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: From the cockpit of an aeroplane flying at an altitude of 3000 m, the angle of depression to the airport is 57\u00b0. The aeroplane continues to fly in the same straight line, and after a few minutes the angle of depression to the airport becomes 67\u00b0.\nNow find the distance between the two sightings.\n\nRound your answer to the nearest metre.",
        "question_for_eval": "From the cockpit of an aeroplane flying at an altitude of 3000 m, the angle of depression to the airport is 57\u00b0. The aeroplane continues to fly in the same straight line, and after a few minutes the angle of depression to the airport becomes 67\u00b0.\nNow find the distance between the two sightings.\n\nRound your answer to the nearest metre."
    },
    {
        "sample_index": "353",
        "problem_index": "353",
        "problem_version": "Text Only",
        "question": "An airplane is currently flying 35^\\circ  south of east, as shown in the image.\n\nThe control tower orders the plane to change course by turning 7^\\circ  to the left. How many degrees south of east is the new course that the plane is ordered to fly?",
        "image": "",
        "answer": "28",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: An airplane is currently flying 35^\\circ  south of east, as shown in the image.\n\nThe control tower orders the plane to change course by turning 7^\\circ  to the left. How many degrees south of east is the new course that the plane is ordered to fly?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: An airplane is currently flying 35^\\circ  south of east, as shown in the image.\n\nThe control tower orders the plane to change course by turning 7^\\circ  to the left. How many degrees south of east is the new course that the plane is ordered to fly?",
        "question_for_eval": "An airplane is currently flying 35^\\circ  south of east, as shown in the image.\n\nThe control tower orders the plane to change course by turning 7^\\circ  to the left. How many degrees south of east is the new course that the plane is ordered to fly?"
    },
    {
        "sample_index": "354",
        "problem_index": "354",
        "problem_version": "Text Only",
        "question": "In triangle ABD, BC is the perpendicular to AD, with AB length of 32 and BD length of 35. Angle A is 50\u00b0, angle D is 45\u00b0. Consider the following diagram. Hence, find the length of AD correct to two decimal places.",
        "image": "",
        "answer": "45.32",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In triangle ABD, BC is the perpendicular to AD, with AB length of 32 and BD length of 35. Angle A is 50\u00b0, angle D is 45\u00b0. Consider the following diagram. Hence, find the length of AD correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In triangle ABD, BC is the perpendicular to AD, with AB length of 32 and BD length of 35. Angle A is 50\u00b0, angle D is 45\u00b0. Consider the following diagram. Hence, find the length of AD correct to two decimal places.",
        "question_for_eval": "In triangle ABD, BC is the perpendicular to AD, with AB length of 32 and BD length of 35. Angle A is 50\u00b0, angle D is 45\u00b0. Consider the following diagram. Hence, find the length of AD correct to two decimal places."
    },
    {
        "sample_index": "355",
        "problem_index": "355",
        "problem_version": "Text Only",
        "question": "In triangle ABD, BC is the perpendicular to AD, with AB length of 58 and BD length of 72. Angle A is 57\u00b0, angle D is 31\u00b0. Consider the following diagram. Hence, find AD correct to two decimal places.",
        "image": "",
        "answer": "93.31",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In triangle ABD, BC is the perpendicular to AD, with AB length of 58 and BD length of 72. Angle A is 57\u00b0, angle D is 31\u00b0. Consider the following diagram. Hence, find AD correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In triangle ABD, BC is the perpendicular to AD, with AB length of 58 and BD length of 72. Angle A is 57\u00b0, angle D is 31\u00b0. Consider the following diagram. Hence, find AD correct to two decimal places.",
        "question_for_eval": "In triangle ABD, BC is the perpendicular to AD, with AB length of 58 and BD length of 72. Angle A is 57\u00b0, angle D is 31\u00b0. Consider the following diagram. Hence, find AD correct to two decimal places."
    },
    {
        "sample_index": "356",
        "problem_index": "356",
        "problem_version": "Text Only",
        "question": "In triangle ABC, angle A is 60\u00b0, angle B is 35\u00b0, and the length of the perpendicular CD of AB is 9. Consider the following diagram.Hence, find the length of AB correct to two decimal places.",
        "image": "",
        "answer": "18.05",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In triangle ABC, angle A is 60\u00b0, angle B is 35\u00b0, and the length of the perpendicular CD of AB is 9. Consider the following diagram.Hence, find the length of AB correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In triangle ABC, angle A is 60\u00b0, angle B is 35\u00b0, and the length of the perpendicular CD of AB is 9. Consider the following diagram.Hence, find the length of AB correct to two decimal places.",
        "question_for_eval": "In triangle ABC, angle A is 60\u00b0, angle B is 35\u00b0, and the length of the perpendicular CD of AB is 9. Consider the following diagram.Hence, find the length of AB correct to two decimal places."
    },
    {
        "sample_index": "357",
        "problem_index": "357",
        "problem_version": "Text Only",
        "question": "The quadrilateral ABCD in the figure is composed of two right angled triangles ABC and ACD, angle B is 35\u00b0, angle BCD is a right angle, the length of BC is 13. Consider the following diagram:Find the size of \\angle ACD.",
        "image": "",
        "answer": "35\u63b3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The quadrilateral ABCD in the figure is composed of two right angled triangles ABC and ACD, angle B is 35\u00b0, angle BCD is a right angle, the length of BC is 13. Consider the following diagram:Find the size of \\angle ACD.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The quadrilateral ABCD in the figure is composed of two right angled triangles ABC and ACD, angle B is 35\u00b0, angle BCD is a right angle, the length of BC is 13. Consider the following diagram:Find the size of \\angle ACD.",
        "question_for_eval": "The quadrilateral ABCD in the figure is composed of two right angled triangles ABC and ACD, angle B is 35\u00b0, angle BCD is a right angle, the length of BC is 13. Consider the following diagram:Find the size of \\angle ACD."
    },
    {
        "sample_index": "358",
        "problem_index": "358",
        "problem_version": "Text Only",
        "question": "Consider the following diagram. The height of the dashed line in the figure is 68. The angle enclosed by the blue arc is 46\u00b0, and the angle enclosed by the red arc is 37\u00b0. Hence, use the rounded values of y and w to find x, correct to 1 decimal place.",
        "image": "",
        "answer": "24.6",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following diagram. The height of the dashed line in the figure is 68. The angle enclosed by the blue arc is 46\u00b0, and the angle enclosed by the red arc is 37\u00b0. Hence, use the rounded values of y and w to find x, correct to 1 decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following diagram. The height of the dashed line in the figure is 68. The angle enclosed by the blue arc is 46\u00b0, and the angle enclosed by the red arc is 37\u00b0. Hence, use the rounded values of y and w to find x, correct to 1 decimal place.",
        "question_for_eval": "Consider the following diagram. The height of the dashed line in the figure is 68. The angle enclosed by the blue arc is 46\u00b0, and the angle enclosed by the red arc is 37\u00b0. Hence, use the rounded values of y and w to find x, correct to 1 decimal place."
    },
    {
        "sample_index": "359",
        "problem_index": "359",
        "problem_version": "Text Only",
        "question": "Consider the following diagram. The height of the rectangle in the picture is 63, the angle enclosed by the purple arc is 67\u00b0 and the angle pointed by the arrow is 39\u00b0. Hence, find x, correct to one decimal place.",
        "image": "",
        "answer": "51.1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following diagram. The height of the rectangle in the picture is 63, the angle enclosed by the purple arc is 67\u00b0 and the angle pointed by the arrow is 39\u00b0. Hence, find x, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following diagram. The height of the rectangle in the picture is 63, the angle enclosed by the purple arc is 67\u00b0 and the angle pointed by the arrow is 39\u00b0. Hence, find x, correct to one decimal place.",
        "question_for_eval": "Consider the following diagram. The height of the rectangle in the picture is 63, the angle enclosed by the purple arc is 67\u00b0 and the angle pointed by the arrow is 39\u00b0. Hence, find x, correct to one decimal place."
    },
    {
        "sample_index": "360",
        "problem_index": "360",
        "problem_version": "Text Only",
        "question": "In the following diagram, \\angle CAE=61^\\circ , \\angle CBE=73^\\circ and CE=25.\nFind the length of BD, correct to one decimal place.",
        "image": "",
        "answer": "6.3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the following diagram, \\angle CAE=61^\\circ , \\angle CBE=73^\\circ and CE=25.\nFind the length of BD, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the following diagram, \\angle CAE=61^\\circ , \\angle CBE=73^\\circ and CE=25.\nFind the length of BD, correct to one decimal place.",
        "question_for_eval": "In the following diagram, \\angle CAE=61^\\circ , \\angle CBE=73^\\circ and CE=25.\nFind the length of BD, correct to one decimal place."
    },
    {
        "sample_index": "361",
        "problem_index": "361",
        "problem_version": "Text Only",
        "question": "A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. At point A, the surveyor takes an angle measurement to the top of the tower of 10\u00b0. She then walks 29 meters towards the tower and takes another reading of 22\u00b0 at point B.\nHence or otherwise, find the value of h to the nearest metre.",
        "image": "",
        "answer": "9",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. At point A, the surveyor takes an angle measurement to the top of the tower of 10\u00b0. She then walks 29 meters towards the tower and takes another reading of 22\u00b0 at point B.\nHence or otherwise, find the value of h to the nearest metre.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. At point A, the surveyor takes an angle measurement to the top of the tower of 10\u00b0. She then walks 29 meters towards the tower and takes another reading of 22\u00b0 at point B.\nHence or otherwise, find the value of h to the nearest metre.",
        "question_for_eval": "A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. At point A, the surveyor takes an angle measurement to the top of the tower of 10\u00b0. She then walks 29 meters towards the tower and takes another reading of 22\u00b0 at point B.\nHence or otherwise, find the value of h to the nearest metre."
    },
    {
        "sample_index": "362",
        "problem_index": "362",
        "problem_version": "Text Only",
        "question": "The final approach of an aeroplane when landing requires the pilot to adjust their angle of descent to about 3\u00b0. If the plane is 12 metres above the runway and has d metres until touchdown, find d to the nearest metre.",
        "image": "",
        "answer": "229",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The final approach of an aeroplane when landing requires the pilot to adjust their angle of descent to about 3\u00b0. If the plane is 12 metres above the runway and has d metres until touchdown, find d to the nearest metre.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The final approach of an aeroplane when landing requires the pilot to adjust their angle of descent to about 3\u00b0. If the plane is 12 metres above the runway and has d metres until touchdown, find d to the nearest metre.",
        "question_for_eval": "The final approach of an aeroplane when landing requires the pilot to adjust their angle of descent to about 3\u00b0. If the plane is 12 metres above the runway and has d metres until touchdown, find d to the nearest metre."
    },
    {
        "sample_index": "363",
        "problem_index": "363",
        "problem_version": "Text Only",
        "question": "Two flag posts of height 13 m and 18 m are erected 21 m apart. Find l, the length of the string (in metres) needed to join the tops of the two posts, correct to one decimal place.",
        "image": "",
        "answer": "21.6",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Two flag posts of height 13 m and 18 m are erected 21 m apart. Find l, the length of the string (in metres) needed to join the tops of the two posts, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Two flag posts of height 13 m and 18 m are erected 21 m apart. Find l, the length of the string (in metres) needed to join the tops of the two posts, correct to one decimal place.",
        "question_for_eval": "Two flag posts of height 13 m and 18 m are erected 21 m apart. Find l, the length of the string (in metres) needed to join the tops of the two posts, correct to one decimal place."
    },
    {
        "sample_index": "364",
        "problem_index": "364",
        "problem_version": "Text Only",
        "question": "A suspension bridge is being built. The top of the concrete tower is 35.5 metres above the bridge and the connection point for the main cable is 65.9 metres from the tower.\n\nAssume that the concrete tower and the bridge are perpendicular to each other.\n\nIf the length of the cable is h metres, find h to two decimal places.",
        "image": "",
        "answer": "74.85",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A suspension bridge is being built. The top of the concrete tower is 35.5 metres above the bridge and the connection point for the main cable is 65.9 metres from the tower.\n\nAssume that the concrete tower and the bridge are perpendicular to each other.\n\nIf the length of the cable is h metres, find h to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A suspension bridge is being built. The top of the concrete tower is 35.5 metres above the bridge and the connection point for the main cable is 65.9 metres from the tower.\n\nAssume that the concrete tower and the bridge are perpendicular to each other.\n\nIf the length of the cable is h metres, find h to two decimal places.",
        "question_for_eval": "A suspension bridge is being built. The top of the concrete tower is 35.5 metres above the bridge and the connection point for the main cable is 65.9 metres from the tower.\n\nAssume that the concrete tower and the bridge are perpendicular to each other.\n\nIf the length of the cable is h metres, find h to two decimal places."
    },
    {
        "sample_index": "365",
        "problem_index": "365",
        "problem_version": "Text Only",
        "question": "The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10369 metres above the ground and is still 23444 metres from the runway. If \\theta \u00b0 is the angle at which the plane should approach, find \\theta  to one decimal place.",
        "image": "",
        "answer": "23.9",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10369 metres above the ground and is still 23444 metres from the runway. If \\theta \u00b0 is the angle at which the plane should approach, find \\theta  to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10369 metres above the ground and is still 23444 metres from the runway. If \\theta \u00b0 is the angle at which the plane should approach, find \\theta  to one decimal place.",
        "question_for_eval": "The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10369 metres above the ground and is still 23444 metres from the runway. If \\theta \u00b0 is the angle at which the plane should approach, find \\theta  to one decimal place."
    },
    {
        "sample_index": "366",
        "problem_index": "366",
        "problem_version": "Text Only",
        "question": "A ship is 27m away from the bottom of a cliff. A lighthouse is located at the top of the cliff. The ship's distance is 34m from the bottom of the lighthouse and 37m from the top of the lighthouse.\nHence find the height of the lighthouse to the nearest tenth of a metre.",
        "image": "",
        "answer": "4.6 m",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A ship is 27m away from the bottom of a cliff. A lighthouse is located at the top of the cliff. The ship's distance is 34m from the bottom of the lighthouse and 37m from the top of the lighthouse.\nHence find the height of the lighthouse to the nearest tenth of a metre.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A ship is 27m away from the bottom of a cliff. A lighthouse is located at the top of the cliff. The ship's distance is 34m from the bottom of the lighthouse and 37m from the top of the lighthouse.\nHence find the height of the lighthouse to the nearest tenth of a metre.",
        "question_for_eval": "A ship is 27m away from the bottom of a cliff. A lighthouse is located at the top of the cliff. The ship's distance is 34m from the bottom of the lighthouse and 37m from the top of the lighthouse.\nHence find the height of the lighthouse to the nearest tenth of a metre."
    },
    {
        "sample_index": "367",
        "problem_index": "367",
        "problem_version": "Text Only",
        "question": "Sand has an angle of friction of about 40\u00b0. This means once it gets over this it slides down the side of the sand pile. Mae is getting a delivery of sand to her home, but the area where the sand will be delivered is only 10.6 metres wide. If h metres is the maximum height of the sandpile, find h to one decimal place.",
        "image": "",
        "answer": "4.4",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Sand has an angle of friction of about 40\u00b0. This means once it gets over this it slides down the side of the sand pile. Mae is getting a delivery of sand to her home, but the area where the sand will be delivered is only 10.6 metres wide. If h metres is the maximum height of the sandpile, find h to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Sand has an angle of friction of about 40\u00b0. This means once it gets over this it slides down the side of the sand pile. Mae is getting a delivery of sand to her home, but the area where the sand will be delivered is only 10.6 metres wide. If h metres is the maximum height of the sandpile, find h to one decimal place.",
        "question_for_eval": "Sand has an angle of friction of about 40\u00b0. This means once it gets over this it slides down the side of the sand pile. Mae is getting a delivery of sand to her home, but the area where the sand will be delivered is only 10.6 metres wide. If h metres is the maximum height of the sandpile, find h to one decimal place."
    },
    {
        "sample_index": "368",
        "problem_index": "368",
        "problem_version": "Text Only",
        "question": "A farmer wants to build a fence around the entire perimeter of his land, as shown in the diagram. The fencing costs \u00a337 per metre. the lengths of EF and CD are x metre and y metre.\nAt \u00a337 per metre of fencing, how much will it cost him to build the fence along the entire perimeter of the land?",
        "image": "",
        "answer": "777 ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A farmer wants to build a fence around the entire perimeter of his land, as shown in the diagram. The fencing costs \u00a337 per metre. the lengths of EF and CD are x metre and y metre.\nAt \u00a337 per metre of fencing, how much will it cost him to build the fence along the entire perimeter of the land?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A farmer wants to build a fence around the entire perimeter of his land, as shown in the diagram. The fencing costs \u00a337 per metre. the lengths of EF and CD are x metre and y metre.\nAt \u00a337 per metre of fencing, how much will it cost him to build the fence along the entire perimeter of the land?",
        "question_for_eval": "A farmer wants to build a fence around the entire perimeter of his land, as shown in the diagram. The fencing costs \u00a337 per metre. the lengths of EF and CD are x metre and y metre.\nAt \u00a337 per metre of fencing, how much will it cost him to build the fence along the entire perimeter of the land?"
    },
    {
        "sample_index": "369",
        "problem_index": "369",
        "problem_version": "Text Only",
        "question": "In a right angled triangle ABC, angle A is 30\u00b0, angle B is 60\u00b0, the length of AB is sqrt{3}, and the length of BC is h. Find the length of side h.",
        "image": "",
        "answer": "1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In a right angled triangle ABC, angle A is 30\u00b0, angle B is 60\u00b0, the length of AB is sqrt{3}, and the length of BC is h. Find the length of side h.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In a right angled triangle ABC, angle A is 30\u00b0, angle B is 60\u00b0, the length of AB is sqrt{3}, and the length of BC is h. Find the length of side h.",
        "question_for_eval": "In a right angled triangle ABC, angle A is 30\u00b0, angle B is 60\u00b0, the length of AB is sqrt{3}, and the length of BC is h. Find the length of side h."
    },
    {
        "sample_index": "370",
        "problem_index": "370",
        "problem_version": "Text Only",
        "question": "In the right angled triangle, a marked right angled line has a length of 4 and a slanted line has a length of 4*sqrt{2}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees.",
        "image": "",
        "answer": "45^\\circ ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the right angled triangle, a marked right angled line has a length of 4 and a slanted line has a length of 4*sqrt{2}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the right angled triangle, a marked right angled line has a length of 4 and a slanted line has a length of 4*sqrt{2}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees.",
        "question_for_eval": "In the right angled triangle, a marked right angled line has a length of 4 and a slanted line has a length of 4*sqrt{2}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees."
    },
    {
        "sample_index": "371",
        "problem_index": "371",
        "problem_version": "Text Only",
        "question": "In the right angled triangle, the marked angle is 60\u00b0, the marked right angled side has a length of 11, and the diagonal side has a length of w. Consider the adjacent figure:\n\nSolve for the unknown w.",
        "image": "",
        "answer": "22",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the right angled triangle, the marked angle is 60\u00b0, the marked right angled side has a length of 11, and the diagonal side has a length of w. Consider the adjacent figure:\n\nSolve for the unknown w.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the right angled triangle, the marked angle is 60\u00b0, the marked right angled side has a length of 11, and the diagonal side has a length of w. Consider the adjacent figure:\n\nSolve for the unknown w.",
        "question_for_eval": "In the right angled triangle, the marked angle is 60\u00b0, the marked right angled side has a length of 11, and the diagonal side has a length of w. Consider the adjacent figure:\n\nSolve for the unknown w."
    },
    {
        "sample_index": "372",
        "problem_index": "372",
        "problem_version": "Text Only",
        "question": "In the right angled triangle, the marked angle is \\theta, the marked right angled side has a length of 12, and the diagonal side has a length of 8*sqrt{3}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees.",
        "image": "",
        "answer": "60^\\circ ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the right angled triangle, the marked angle is \\theta, the marked right angled side has a length of 12, and the diagonal side has a length of 8*sqrt{3}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the right angled triangle, the marked angle is \\theta, the marked right angled side has a length of 12, and the diagonal side has a length of 8*sqrt{3}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees.",
        "question_for_eval": "In the right angled triangle, the marked angle is \\theta, the marked right angled side has a length of 12, and the diagonal side has a length of 8*sqrt{3}. Consider the adjacent figure:\n\nSolve for the unknown \\theta . Leave your answer in degrees."
    },
    {
        "sample_index": "373",
        "problem_index": "373",
        "problem_version": "Text Only",
        "question": "In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of 8.5, and the diagonal side has a length of P. Consider the adjacent figure:\n\nSolve for the unknown P.",
        "image": "",
        "answer": "17",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of 8.5, and the diagonal side has a length of P. Consider the adjacent figure:\n\nSolve for the unknown P.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of 8.5, and the diagonal side has a length of P. Consider the adjacent figure:\n\nSolve for the unknown P.",
        "question_for_eval": "In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of 8.5, and the diagonal side has a length of P. Consider the adjacent figure:\n\nSolve for the unknown P."
    },
    {
        "sample_index": "374",
        "problem_index": "374",
        "problem_version": "Text Only",
        "question": "In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of x, and the diagonal side has a length of sqrt{10}. Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "image": "",
        "answer": "\\frac{\\sqrt{30}}{2}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of x, and the diagonal side has a length of sqrt{10}. Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of x, and the diagonal side has a length of sqrt{10}. Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "question_for_eval": "In the right angled triangle, the marked angle is 30\u00b0, the marked right angled side has a length of x, and the diagonal side has a length of sqrt{10}. Consider the adjacent figure:\n\nSolve for the exact value of x."
    },
    {
        "sample_index": "375",
        "problem_index": "375",
        "problem_version": "Text Only",
        "question": "In the right angled triangle, the marked angle is 45\u00b0, the lengths of the two right angled edges are 4*sqrt{3} and y respectively, and the diagonal side has a length of x. Consider the adjacent figure:\n\n\nSolve for the exact value of x.",
        "image": "",
        "answer": "4\\sqrt{6}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the right angled triangle, the marked angle is 45\u00b0, the lengths of the two right angled edges are 4*sqrt{3} and y respectively, and the diagonal side has a length of x. Consider the adjacent figure:\n\n\nSolve for the exact value of x.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the right angled triangle, the marked angle is 45\u00b0, the lengths of the two right angled edges are 4*sqrt{3} and y respectively, and the diagonal side has a length of x. Consider the adjacent figure:\n\n\nSolve for the exact value of x.",
        "question_for_eval": "In the right angled triangle, the marked angle is 45\u00b0, the lengths of the two right angled edges are 4*sqrt{3} and y respectively, and the diagonal side has a length of x. Consider the adjacent figure:\n\n\nSolve for the exact value of x."
    },
    {
        "sample_index": "376",
        "problem_index": "376",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:Solve for the exact value of y.",
        "image": "",
        "answer": "4\\sqrt{3}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:Solve for the exact value of y.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:Solve for the exact value of y.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:Solve for the exact value of y."
    },
    {
        "sample_index": "377",
        "problem_index": "377",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 9. Consider the adjacent figure:\n\nSolve for the unknown a.",
        "image": "",
        "answer": "\\frac{9\\sqrt{3}}{2}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 9. Consider the adjacent figure:\n\nSolve for the unknown a.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 9. Consider the adjacent figure:\n\nSolve for the unknown a.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 9. Consider the adjacent figure:\n\nSolve for the unknown a."
    },
    {
        "sample_index": "378",
        "problem_index": "378",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 8\\sqrt{5}. Consider the adjacent figure:Find the exact value of y.",
        "image": "",
        "answer": "4\\sqrt{5}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 8\\sqrt{5}. Consider the adjacent figure:Find the exact value of y.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 8\\sqrt{5}. Consider the adjacent figure:Find the exact value of y.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 60^\\circ, the hypotenuse measures 8\\sqrt{5}. Consider the adjacent figure:Find the exact value of y."
    },
    {
        "sample_index": "379",
        "problem_index": "379",
        "problem_version": "Text Only",
        "question": "A right trapezoid, with one of its base angles measuring 30^\\circ, has an adjacent leg length of 8 to this angle. The length of the shorter base of the trapezoid is 4. Find t.",
        "image": "",
        "answer": "4+4\\sqrt{3}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A right trapezoid, with one of its base angles measuring 30^\\circ, has an adjacent leg length of 8 to this angle. The length of the shorter base of the trapezoid is 4. Find t.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A right trapezoid, with one of its base angles measuring 30^\\circ, has an adjacent leg length of 8 to this angle. The length of the shorter base of the trapezoid is 4. Find t.",
        "question_for_eval": "A right trapezoid, with one of its base angles measuring 30^\\circ, has an adjacent leg length of 8 to this angle. The length of the shorter base of the trapezoid is 4. Find t."
    },
    {
        "sample_index": "380",
        "problem_index": "380",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side h.",
        "image": "",
        "answer": "1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side h.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side h.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side h."
    },
    {
        "sample_index": "381",
        "problem_index": "381",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring 11. Solve for the unknown w.",
        "image": "",
        "answer": "22 ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring 11. Solve for the unknown w.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring 11. Solve for the unknown w.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring 11. Solve for the unknown w."
    },
    {
        "sample_index": "382",
        "problem_index": "382",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one leg measuring 12, the hypotenuse measures 8\\sqrt{3}. Solve for the unknown \\theta . Leave your answer in degrees.",
        "image": "",
        "answer": "60^\\circ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one leg measuring 12, the hypotenuse measures 8\\sqrt{3}. Solve for the unknown \\theta . Leave your answer in degrees.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one leg measuring 12, the hypotenuse measures 8\\sqrt{3}. Solve for the unknown \\theta . Leave your answer in degrees.",
        "question_for_eval": "In this right-angled triangle, one leg measuring 12, the hypotenuse measures 8\\sqrt{3}. Solve for the unknown \\theta . Leave your answer in degrees."
    },
    {
        "sample_index": "383",
        "problem_index": "383",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side x, leaving your answer as an exact value.",
        "image": "",
        "answer": "2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side x, leaving your answer as an exact value.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side x, leaving your answer as an exact value.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 60^\\circ, one leg measuring \\sqrt{3}. Find the length of side x, leaving your answer as an exact value."
    },
    {
        "sample_index": "384",
        "problem_index": "384",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring 8.5. Consider the adjacent figure:\n\nSolve for the unknown P.",
        "image": "",
        "answer": "17",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring 8.5. Consider the adjacent figure:\n\nSolve for the unknown P.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring 8.5. Consider the adjacent figure:\n\nSolve for the unknown P.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring 8.5. Consider the adjacent figure:\n\nSolve for the unknown P."
    },
    {
        "sample_index": "385",
        "problem_index": "385",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring \\sqrt{10}.Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "image": "",
        "answer": "\\frac{\\sqrt{30}}{2}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring \\sqrt{10}.Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring \\sqrt{10}.Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 30^\\circ, one leg measuring \\sqrt{10}.Consider the adjacent figure:\n\nSolve for the exact value of x."
    },
    {
        "sample_index": "386",
        "problem_index": "386",
        "problem_version": "Text Only",
        "question": "In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "image": "",
        "answer": "4\\sqrt{6}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:\n\nSolve for the exact value of x.",
        "question_for_eval": "In this right-angled triangle, one of the acute angles measures 45^\\circ, one leg measuring 4\\sqrt{3}. Consider the adjacent figure:\n\nSolve for the exact value of x."
    },
    {
        "sample_index": "387",
        "problem_index": "387",
        "problem_version": "Text Only",
        "question": "A circle with a radius of $8 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places.",
        "image": "",
        "answer": "Circumference $=50.27 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a radius of $8 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a radius of $8 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places.",
        "question_for_eval": "A circle with a radius of $8 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places."
    },
    {
        "sample_index": "388",
        "problem_index": "388",
        "problem_version": "Text Only",
        "question": "A circle with a radius of $18 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to one decimal place.",
        "image": "",
        "answer": "Circumference $=113.1 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a radius of $18 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a radius of $18 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to one decimal place.",
        "question_for_eval": "A circle with a radius of $18 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to one decimal place."
    },
    {
        "sample_index": "389",
        "problem_index": "389",
        "problem_version": "Text Only",
        "question": "A circle with a diameter of $13 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places.",
        "image": "",
        "answer": "$C=40.84 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a diameter of $13 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a diameter of $13 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places.",
        "question_for_eval": "A circle with a diameter of $13 \\mathrm{~cm}$. Find the circumference of the circle shown, correct to two decimal places."
    },
    {
        "sample_index": "390",
        "problem_index": "390",
        "problem_version": "Text Only",
        "question": "A circle with a circumference of $44 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the radius $r$ of the circle?\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "$$r=7.00$$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a circumference of $44 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the radius $r$ of the circle?\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a circumference of $44 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the radius $r$ of the circle?\n\nRound your answer to two decimal places.",
        "question_for_eval": "A circle with a circumference of $44 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the radius $r$ of the circle?\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "391",
        "problem_index": "391",
        "problem_version": "Text Only",
        "question": "A circle with a circumference of $42 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the diameter $D$ of the circle?\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "$D=13.37$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a circumference of $42 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the diameter $D$ of the circle?\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a circumference of $42 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the diameter $D$ of the circle?\n\nRound your answer to two decimal places.",
        "question_for_eval": "A circle with a circumference of $42 \\mathrm{~cm}$. Consider the circle below.\n\nWhat is the diameter $D$ of the circle?\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "392",
        "problem_index": "392",
        "problem_version": "Text Only",
        "question": "The radius of a quarter circle is $10 \\mathrm{~mm}$. Calculate the total perimeter of the following figure, correct to one decimal place.",
        "image": "",
        "answer": "Perimeter $=35.7 \\mathrm{~mm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of a quarter circle is $10 \\mathrm{~mm}$. Calculate the total perimeter of the following figure, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of a quarter circle is $10 \\mathrm{~mm}$. Calculate the total perimeter of the following figure, correct to one decimal place.",
        "question_for_eval": "The radius of a quarter circle is $10 \\mathrm{~mm}$. Calculate the total perimeter of the following figure, correct to one decimal place."
    },
    {
        "sample_index": "393",
        "problem_index": "393",
        "problem_version": "Text Only",
        "question": "A circle with a radius of $6 \\mathrm{~cm}$. Find the area of the circle shown, correct to one decimal place.",
        "image": "",
        "answer": "Area $=113.1 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a radius of $6 \\mathrm{~cm}$. Find the area of the circle shown, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a radius of $6 \\mathrm{~cm}$. Find the area of the circle shown, correct to one decimal place.",
        "question_for_eval": "A circle with a radius of $6 \\mathrm{~cm}$. Find the area of the circle shown, correct to one decimal place."
    },
    {
        "sample_index": "394",
        "problem_index": "394",
        "problem_version": "Text Only",
        "question": "The radius of the following figure is $2 \\mathrm{~cm}$. Calculate the area of the following figure, correct to one decimal place.",
        "image": "",
        "answer": "Area $=9.4 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the following figure is $2 \\mathrm{~cm}$. Calculate the area of the following figure, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the following figure is $2 \\mathrm{~cm}$. Calculate the area of the following figure, correct to one decimal place.",
        "question_for_eval": "The radius of the following figure is $2 \\mathrm{~cm}$. Calculate the area of the following figure, correct to one decimal place."
    },
    {
        "sample_index": "395",
        "problem_index": "395",
        "problem_version": "Text Only",
        "question": "A circle with a radius of $3 \\mathrm{~cm}$. Find the exact area of the circle shown.\n\nGive your answer as an exact value in terms of $\\pi $.",
        "image": "",
        "answer": "Area $=9 \\pi \\mathrm{cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a radius of $3 \\mathrm{~cm}$. Find the exact area of the circle shown.\n\nGive your answer as an exact value in terms of $\\pi $.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a radius of $3 \\mathrm{~cm}$. Find the exact area of the circle shown.\n\nGive your answer as an exact value in terms of $\\pi $.",
        "question_for_eval": "A circle with a radius of $3 \\mathrm{~cm}$. Find the exact area of the circle shown.\n\nGive your answer as an exact value in terms of $\\pi $."
    },
    {
        "sample_index": "396",
        "problem_index": "396",
        "problem_version": "Text Only",
        "question": "A circle with a radius of $11 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "image": "",
        "answer": "Area $=121 \\pi \\mathrm{cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a radius of $11 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a radius of $11 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "question_for_eval": "A circle with a radius of $11 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value."
    },
    {
        "sample_index": "397",
        "problem_index": "397",
        "problem_version": "Text Only",
        "question": "A circle with a radius of $50 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "image": "",
        "answer": "Area $=2500 \\pi \\mathrm{cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a radius of $50 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a radius of $50 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "question_for_eval": "A circle with a radius of $50 \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value."
    },
    {
        "sample_index": "398",
        "problem_index": "398",
        "problem_version": "Text Only",
        "question": "A circle with a radius of $ \\frac{1}{5} \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "image": "",
        "answer": "Area $=\\frac{\\pi}{25} \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A circle with a radius of $ \\frac{1}{5} \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A circle with a radius of $ \\frac{1}{5} \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value.",
        "question_for_eval": "A circle with a radius of $ \\frac{1}{5} \\mathrm{~cm}$. Find the area of the circle shown.\n\nGive your answer as an exact value."
    },
    {
        "sample_index": "399",
        "problem_index": "399",
        "problem_version": "Text Only",
        "question": "A figure with a radius of $ 5 \\mathrm{~mm}$. Find the exact area of the given figure:",
        "image": "",
        "answer": "Area $=\\frac{25 \\pi}{4} \\mathrm{~mm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A figure with a radius of $ 5 \\mathrm{~mm}$. Find the exact area of the given figure:",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A figure with a radius of $ 5 \\mathrm{~mm}$. Find the exact area of the given figure:",
        "question_for_eval": "A figure with a radius of $ 5 \\mathrm{~mm}$. Find the exact area of the given figure:"
    },
    {
        "sample_index": "400",
        "problem_index": "400",
        "problem_version": "Text Only",
        "question": "A figure with a radius of $ 11 \\mathrm{~m}$. Find the area of the shape shown.\n\nGive your answer as an exact value.",
        "image": "",
        "answer": "Area $=\\frac{121 \\pi}{4} \\mathrm{~m}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A figure with a radius of $ 11 \\mathrm{~m}$. Find the area of the shape shown.\n\nGive your answer as an exact value.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A figure with a radius of $ 11 \\mathrm{~m}$. Find the area of the shape shown.\n\nGive your answer as an exact value.",
        "question_for_eval": "A figure with a radius of $ 11 \\mathrm{~m}$. Find the area of the shape shown.\n\nGive your answer as an exact value."
    },
    {
        "sample_index": "401",
        "problem_index": "401",
        "problem_version": "Text Only",
        "question": "Area of the figure is a $=\\frac{3}{4}$ of area of the circle. Calculate the area of the following figure.\n\nGive your answer as an exact value.",
        "image": "",
        "answer": "Area $=\\frac{147 \\pi}{4} \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Area of the figure is a $=\\frac{3}{4}$ of area of the circle. Calculate the area of the following figure.\n\nGive your answer as an exact value.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Area of the figure is a $=\\frac{3}{4}$ of area of the circle. Calculate the area of the following figure.\n\nGive your answer as an exact value.",
        "question_for_eval": "Area of the figure is a $=\\frac{3}{4}$ of area of the circle. Calculate the area of the following figure.\n\nGive your answer as an exact value."
    },
    {
        "sample_index": "402",
        "problem_index": "402",
        "problem_version": "Text Only",
        "question": "The diameter of the figure is $ 52.72 \\mathrm{~cm}$. The figure follows that half of a circle has area $\\frac{1}{2} \\pi r^{2}$. Find the exact area of the shape shown.",
        "image": "",
        "answer": "Area $=347.4248 \\pi \\mathrm{cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The diameter of the figure is $ 52.72 \\mathrm{~cm}$. The figure follows that half of a circle has area $\\frac{1}{2} \\pi r^{2}$. Find the exact area of the shape shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The diameter of the figure is $ 52.72 \\mathrm{~cm}$. The figure follows that half of a circle has area $\\frac{1}{2} \\pi r^{2}$. Find the exact area of the shape shown.",
        "question_for_eval": "The diameter of the figure is $ 52.72 \\mathrm{~cm}$. The figure follows that half of a circle has area $\\frac{1}{2} \\pi r^{2}$. Find the exact area of the shape shown."
    },
    {
        "sample_index": "403",
        "problem_index": "403",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 13 \\mathrm{~mm}$. It follows that a two thirds of a circle has area $\\frac{2}{3} \\pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle.",
        "image": "",
        "answer": "Area $=\\frac{338 \\pi}{3} \\mathrm{~mm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 13 \\mathrm{~mm}$. It follows that a two thirds of a circle has area $\\frac{2}{3} \\pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 13 \\mathrm{~mm}$. It follows that a two thirds of a circle has area $\\frac{2}{3} \\pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle.",
        "question_for_eval": "The radius of the figure is $ 13 \\mathrm{~mm}$. It follows that a two thirds of a circle has area $\\frac{2}{3} \\pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle."
    },
    {
        "sample_index": "404",
        "problem_index": "404",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 96.4 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to four decimal places.",
        "image": "",
        "answer": "7298.6737 \\mathrm{~mm}^{2}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 96.4 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to four decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 96.4 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to four decimal places.",
        "question_for_eval": "The radius of the figure is $ 96.4 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to four decimal places."
    },
    {
        "sample_index": "405",
        "problem_index": "405",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 59.6 \\mathrm{~cm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places.",
        "image": "",
        "answer": "Area $=1115.94 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 59.6 \\mathrm{~cm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 59.6 \\mathrm{~cm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places.",
        "question_for_eval": "The radius of the figure is $ 59.6 \\mathrm{~cm}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places."
    },
    {
        "sample_index": "406",
        "problem_index": "406",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 56.5 \\mathrm{~m}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places.",
        "image": "",
        "answer": "Area $=3426.49 \\mathrm{~m}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 56.5 \\mathrm{~m}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 56.5 \\mathrm{~m}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places.",
        "question_for_eval": "The radius of the figure is $ 56.5 \\mathrm{~m}$. Consider the sector below.\n\nCalculate the area. Give your answer correct to two decimal places."
    },
    {
        "sample_index": "407",
        "problem_index": "407",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 8 \\mathrm{~cm}$. Perimeter=lengths of the two equal segments + the length of the arc.Calculate the total perimeter of the sector shown, correct to one decimal place.",
        "image": "",
        "answer": "Perimeter $=18.8 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 8 \\mathrm{~cm}$. Perimeter=lengths of the two equal segments + the length of the arc.Calculate the total perimeter of the sector shown, correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 8 \\mathrm{~cm}$. Perimeter=lengths of the two equal segments + the length of the arc.Calculate the total perimeter of the sector shown, correct to one decimal place.",
        "question_for_eval": "The radius of the figure is $ 8 \\mathrm{~cm}$. Perimeter=lengths of the two equal segments + the length of the arc.Calculate the total perimeter of the sector shown, correct to one decimal place."
    },
    {
        "sample_index": "408",
        "problem_index": "408",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 7 \\mathrm{~cm}$. Find the perimeter of the sector shown, correct to two decimal places.",
        "image": "",
        "answer": "Perimeter $=18.89 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 7 \\mathrm{~cm}$. Find the perimeter of the sector shown, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 7 \\mathrm{~cm}$. Find the perimeter of the sector shown, correct to two decimal places.",
        "question_for_eval": "The radius of the figure is $ 7 \\mathrm{~cm}$. Find the perimeter of the sector shown, correct to two decimal places."
    },
    {
        "sample_index": "409",
        "problem_index": "409",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 8 \\mathrm{~cm}$. Find the perimeter of the figure shown, correct to two decimal places.",
        "image": "",
        "answer": "Perimeter $=60.68 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 8 \\mathrm{~cm}$. Find the perimeter of the figure shown, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 8 \\mathrm{~cm}$. Find the perimeter of the figure shown, correct to two decimal places.",
        "question_for_eval": "The radius of the figure is $ 8 \\mathrm{~cm}$. Find the perimeter of the figure shown, correct to two decimal places."
    },
    {
        "sample_index": "410",
        "problem_index": "410",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 80.2 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the perimeter. Round your answer to two decimal places.",
        "image": "",
        "answer": "Perimeter $=492.14 \\mathrm{~mm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 80.2 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the perimeter. Round your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 80.2 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the perimeter. Round your answer to two decimal places.",
        "question_for_eval": "The radius of the figure is $ 80.2 \\mathrm{~mm}$. Consider the sector below.\n\nCalculate the perimeter. Round your answer to two decimal places."
    },
    {
        "sample_index": "411",
        "problem_index": "411",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $ 32.2 \\mathrm{~m}$. The marked angle measures 344\u00b0. Consider the sector below. The marked angle measures 344\u00b0.\n\nCalculate the perimeter of the sector. Round your answer to two decimal places.",
        "image": "",
        "answer": "Perimeter $=257.73 \\mathrm{~m}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $ 32.2 \\mathrm{~m}$. The marked angle measures 344\u00b0. Consider the sector below. The marked angle measures 344\u00b0.\n\nCalculate the perimeter of the sector. Round your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $ 32.2 \\mathrm{~m}$. The marked angle measures 344\u00b0. Consider the sector below. The marked angle measures 344\u00b0.\n\nCalculate the perimeter of the sector. Round your answer to two decimal places.",
        "question_for_eval": "The radius of the figure is $ 32.2 \\mathrm{~m}$. The marked angle measures 344\u00b0. Consider the sector below. The marked angle measures 344\u00b0.\n\nCalculate the perimeter of the sector. Round your answer to two decimal places."
    },
    {
        "sample_index": "412",
        "problem_index": "412",
        "problem_version": "Text Only",
        "question": "This is part of a piece of jewellery. It is made out of a metal plate base, and gold plated wire (of negligible thickness) runs around the outside.\n\nWhat is the area covered by the metal plate base?\n\nGive your answer correct to two decimal places.",
        "image": "",
        "answer": "Area $=70.69 \\mathrm{~mm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: This is part of a piece of jewellery. It is made out of a metal plate base, and gold plated wire (of negligible thickness) runs around the outside.\n\nWhat is the area covered by the metal plate base?\n\nGive your answer correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: This is part of a piece of jewellery. It is made out of a metal plate base, and gold plated wire (of negligible thickness) runs around the outside.\n\nWhat is the area covered by the metal plate base?\n\nGive your answer correct to two decimal places.",
        "question_for_eval": "This is part of a piece of jewellery. It is made out of a metal plate base, and gold plated wire (of negligible thickness) runs around the outside.\n\nWhat is the area covered by the metal plate base?\n\nGive your answer correct to two decimal places."
    },
    {
        "sample_index": "413",
        "problem_index": "413",
        "problem_version": "Text Only",
        "question": "The area $A$ of the sector below is 140.28 (cm)^2. We wish to find the length of the radius, then the perimeter.\n\nFind the length of the radius, $r$. (You may let \\theta  represent the angle of the sector). Give your answer correct to one decimal place.",
        "image": "",
        "answer": "$r=24.4$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The area $A$ of the sector below is 140.28 (cm)^2. We wish to find the length of the radius, then the perimeter.\n\nFind the length of the radius, $r$. (You may let \\theta  represent the angle of the sector). Give your answer correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The area $A$ of the sector below is 140.28 (cm)^2. We wish to find the length of the radius, then the perimeter.\n\nFind the length of the radius, $r$. (You may let \\theta  represent the angle of the sector). Give your answer correct to one decimal place.",
        "question_for_eval": "The area $A$ of the sector below is 140.28 (cm)^2. We wish to find the length of the radius, then the perimeter.\n\nFind the length of the radius, $r$. (You may let \\theta  represent the angle of the sector). Give your answer correct to one decimal place."
    },
    {
        "sample_index": "414",
        "problem_index": "414",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $5\\mathrm{~cm}$. Find the area of the sector shown.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Area $=73.52\\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $5\\mathrm{~cm}$. Find the area of the sector shown.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $5\\mathrm{~cm}$. Find the area of the sector shown.\n\nRound your answer to two decimal places.",
        "question_for_eval": "The radius of the figure is $5\\mathrm{~cm}$. Find the area of the sector shown.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "415",
        "problem_index": "415",
        "problem_version": "Text Only",
        "question": "The radius of the figure is $22.1\\mathrm{~m}$. Calculate the area of the following sector.\n\nRound your answer to one decimal place.",
        "image": "",
        "answer": "Area $=315.4 \\mathrm{~m}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the figure is $22.1\\mathrm{~m}$. Calculate the area of the following sector.\n\nRound your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the figure is $22.1\\mathrm{~m}$. Calculate the area of the following sector.\n\nRound your answer to one decimal place.",
        "question_for_eval": "The radius of the figure is $22.1\\mathrm{~m}$. Calculate the area of the following sector.\n\nRound your answer to one decimal place."
    },
    {
        "sample_index": "416",
        "problem_index": "416",
        "problem_version": "Text Only",
        "question": "In the diagram, $O$ is the center of a circle with radius 6 cm. Arc $JK$ has a length measuring 2\\pi  cm. Determine the exact area of sector $OJK$.",
        "image": "",
        "answer": "Area of sector $=6 \\pi \\mathrm{cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the diagram, $O$ is the center of a circle with radius 6 cm. Arc $JK$ has a length measuring 2\\pi  cm. Determine the exact area of sector $OJK$.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the diagram, $O$ is the center of a circle with radius 6 cm. Arc $JK$ has a length measuring 2\\pi  cm. Determine the exact area of sector $OJK$.",
        "question_for_eval": "In the diagram, $O$ is the center of a circle with radius 6 cm. Arc $JK$ has a length measuring 2\\pi  cm. Determine the exact area of sector $OJK$."
    },
    {
        "sample_index": "417",
        "problem_index": "417",
        "problem_version": "Text Only",
        "question": "The perimeter is the total length of all sides of a figure.Find the perimeter of the parallelogram shown.",
        "image": "",
        "answer": "Perimeter $=94 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The perimeter is the total length of all sides of a figure.Find the perimeter of the parallelogram shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The perimeter is the total length of all sides of a figure.Find the perimeter of the parallelogram shown.",
        "question_for_eval": "The perimeter is the total length of all sides of a figure.Find the perimeter of the parallelogram shown."
    },
    {
        "sample_index": "418",
        "problem_index": "418",
        "problem_version": "Text Only",
        "question": "The perimeter is the total length of all sides of a figure.Find the perimeter of the kite shown.",
        "image": "",
        "answer": " Perimeter $=74 \\mathrm{~mm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The perimeter is the total length of all sides of a figure.Find the perimeter of the kite shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The perimeter is the total length of all sides of a figure.Find the perimeter of the kite shown.",
        "question_for_eval": "The perimeter is the total length of all sides of a figure.Find the perimeter of the kite shown."
    },
    {
        "sample_index": "419",
        "problem_index": "419",
        "problem_version": "Text Only",
        "question": "The perimeter is the total length of all sides of a figure.Find the perimeter of the rhombus shown.",
        "image": "",
        "answer": "Perimeter $=28 \\mathrm{~mm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The perimeter is the total length of all sides of a figure.Find the perimeter of the rhombus shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The perimeter is the total length of all sides of a figure.Find the perimeter of the rhombus shown.",
        "question_for_eval": "The perimeter is the total length of all sides of a figure.Find the perimeter of the rhombus shown."
    },
    {
        "sample_index": "420",
        "problem_index": "420",
        "problem_version": "Text Only",
        "question": "The perimeter is equal to the sum of the four side lengths of the trapezium. Find the length of the missing side of the trapezium shown.",
        "image": "",
        "answer": "$5=s$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The perimeter is equal to the sum of the four side lengths of the trapezium. Find the length of the missing side of the trapezium shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The perimeter is equal to the sum of the four side lengths of the trapezium. Find the length of the missing side of the trapezium shown.",
        "question_for_eval": "The perimeter is equal to the sum of the four side lengths of the trapezium. Find the length of the missing side of the trapezium shown."
    },
    {
        "sample_index": "421",
        "problem_index": "421",
        "problem_version": "Text Only",
        "question": "The total area is 6096. How much area is remaining?",
        "image": "",
        "answer": "96",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The total area is 6096. How much area is remaining?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The total area is 6096. How much area is remaining?",
        "question_for_eval": "The total area is 6096. How much area is remaining?"
    },
    {
        "sample_index": "422",
        "problem_index": "422",
        "problem_version": "Text Only",
        "question": "The total area is 6096. How much area is remaining?",
        "image": "",
        "answer": "36",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The total area is 6096. How much area is remaining?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The total area is 6096. How much area is remaining?",
        "question_for_eval": "The total area is 6096. How much area is remaining?"
    },
    {
        "sample_index": "423",
        "problem_index": "423",
        "problem_version": "Text Only",
        "question": "After two meteoroids collide at point A, one starts travelling in the direction of point B, while the other starts travelling in the direction of point C, with an angle of 53^\\circ  between the two directions. The meteoroid projected in the direction of B is moving at a speed of 7860 km/h, while the other is moving at a speed of 10170 km/h.\n\n\nWhat distance will the meteoroid travelling towards point B have covered after 29 minutes?",
        "image": "",
        "answer": "3799 km",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: After two meteoroids collide at point A, one starts travelling in the direction of point B, while the other starts travelling in the direction of point C, with an angle of 53^\\circ  between the two directions. The meteoroid projected in the direction of B is moving at a speed of 7860 km/h, while the other is moving at a speed of 10170 km/h.\n\n\nWhat distance will the meteoroid travelling towards point B have covered after 29 minutes?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: After two meteoroids collide at point A, one starts travelling in the direction of point B, while the other starts travelling in the direction of point C, with an angle of 53^\\circ  between the two directions. The meteoroid projected in the direction of B is moving at a speed of 7860 km/h, while the other is moving at a speed of 10170 km/h.\n\n\nWhat distance will the meteoroid travelling towards point B have covered after 29 minutes?",
        "question_for_eval": "After two meteoroids collide at point A, one starts travelling in the direction of point B, while the other starts travelling in the direction of point C, with an angle of 53^\\circ  between the two directions. The meteoroid projected in the direction of B is moving at a speed of 7860 km/h, while the other is moving at a speed of 10170 km/h.\n\n\nWhat distance will the meteoroid travelling towards point B have covered after 29 minutes?"
    },
    {
        "sample_index": "424",
        "problem_index": "424",
        "problem_version": "Text Only",
        "question": "As shown in the figure above, a triangle has an angle of 50\u00b0 and two sides of 12m and 13.1m. Calculate the area of the following triangle.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "60.21 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure above, a triangle has an angle of 50\u00b0 and two sides of 12m and 13.1m. Calculate the area of the following triangle.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure above, a triangle has an angle of 50\u00b0 and two sides of 12m and 13.1m. Calculate the area of the following triangle.\n\nRound your answer to two decimal places.",
        "question_for_eval": "As shown in the figure above, a triangle has an angle of 50\u00b0 and two sides of 12m and 13.1m. Calculate the area of the following triangle.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "425",
        "problem_index": "425",
        "problem_version": "Text Only",
        "question": "An industrial site in the shape of a triangle is to take up the space between where three roads intersect. The triangle has an angle of 44\u00b0 and two sides of 50m and 80m.\n\nCalculate the area of the site.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "1389.32 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: An industrial site in the shape of a triangle is to take up the space between where three roads intersect. The triangle has an angle of 44\u00b0 and two sides of 50m and 80m.\n\nCalculate the area of the site.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: An industrial site in the shape of a triangle is to take up the space between where three roads intersect. The triangle has an angle of 44\u00b0 and two sides of 50m and 80m.\n\nCalculate the area of the site.\n\nRound your answer to two decimal places.",
        "question_for_eval": "An industrial site in the shape of a triangle is to take up the space between where three roads intersect. The triangle has an angle of 44\u00b0 and two sides of 50m and 80m.\n\nCalculate the area of the site.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "426",
        "problem_index": "426",
        "problem_version": "Text Only",
        "question": "On an orienteering course, Valentina runs 550 metres north from point A to point B, then turns east and runs to point C. If the true bearing of C from A is 041 ^\\circ T and the direct distance Valentina must run to get back to point A is d metres, find d to the nearest metre.",
        "image": "",
        "answer": "729",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: On an orienteering course, Valentina runs 550 metres north from point A to point B, then turns east and runs to point C. If the true bearing of C from A is 041 ^\\circ T and the direct distance Valentina must run to get back to point A is d metres, find d to the nearest metre.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: On an orienteering course, Valentina runs 550 metres north from point A to point B, then turns east and runs to point C. If the true bearing of C from A is 041 ^\\circ T and the direct distance Valentina must run to get back to point A is d metres, find d to the nearest metre.",
        "question_for_eval": "On an orienteering course, Valentina runs 550 metres north from point A to point B, then turns east and runs to point C. If the true bearing of C from A is 041 ^\\circ T and the direct distance Valentina must run to get back to point A is d metres, find d to the nearest metre."
    },
    {
        "sample_index": "427",
        "problem_index": "427",
        "problem_version": "Text Only",
        "question": "A boat travels S 14^\\circ E for 12 km and then changes direction to S 49^\\circ E for another 16 km.\n\nHence write down the bearing that the boat should travel on to return to the starting point.",
        "image": "",
        "answer": "N 34\u00b0 W",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A boat travels S 14^\\circ E for 12 km and then changes direction to S 49^\\circ E for another 16 km.\n\nHence write down the bearing that the boat should travel on to return to the starting point.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A boat travels S 14^\\circ E for 12 km and then changes direction to S 49^\\circ E for another 16 km.\n\nHence write down the bearing that the boat should travel on to return to the starting point.",
        "question_for_eval": "A boat travels S 14^\\circ E for 12 km and then changes direction to S 49^\\circ E for another 16 km.\n\nHence write down the bearing that the boat should travel on to return to the starting point."
    },
    {
        "sample_index": "428",
        "problem_index": "428",
        "problem_version": "Text Only",
        "question": "The logo of a shop consists of five semicircles; four small semicircles each with the same radius, and one large semicircle. The perimeter of the whole shape is 14\\pi  units.\nThe entire shape is to be enlarged by a factor of 5 to form a logo sticker on the window of a shop front. What area of the shop front window will the sticker take up?",
        "image": "",
        "answer": "\\frac{1225\\pi }{2} \\text { units }^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The logo of a shop consists of five semicircles; four small semicircles each with the same radius, and one large semicircle. The perimeter of the whole shape is 14\\pi  units.\nThe entire shape is to be enlarged by a factor of 5 to form a logo sticker on the window of a shop front. What area of the shop front window will the sticker take up?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The logo of a shop consists of five semicircles; four small semicircles each with the same radius, and one large semicircle. The perimeter of the whole shape is 14\\pi  units.\nThe entire shape is to be enlarged by a factor of 5 to form a logo sticker on the window of a shop front. What area of the shop front window will the sticker take up?",
        "question_for_eval": "The logo of a shop consists of five semicircles; four small semicircles each with the same radius, and one large semicircle. The perimeter of the whole shape is 14\\pi  units.\nThe entire shape is to be enlarged by a factor of 5 to form a logo sticker on the window of a shop front. What area of the shop front window will the sticker take up?"
    },
    {
        "sample_index": "429",
        "problem_index": "429",
        "problem_version": "Text Only",
        "question": "A driver glances up at the top of a building.\n\nTrue or false: According to the angle A, the distance from the driver to the building would be the opposite side.\nChoice:\nA. True\nB. False",
        "image": "",
        "answer": "False",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A driver glances up at the top of a building.\n\nTrue or false: According to the angle A, the distance from the driver to the building would be the opposite side.\nChoice:\nA. True\nB. False",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A driver glances up at the top of a building.\n\nTrue or false: According to the angle A, the distance from the driver to the building would be the opposite side.\nChoice:\nA. True\nB. False",
        "question_for_eval": "A driver glances up at the top of a building.\n\nTrue or false: According to the angle A, the distance from the driver to the building would be the opposite side.\nChoice:\nA. True\nB. False"
    },
    {
        "sample_index": "430",
        "problem_index": "430",
        "problem_version": "Text Only",
        "question": "Sally needs to walk from the school to the bus stop.\n\nTrue or False : The quickest way to get there will be through the playground.\nChoice:\nA. False\nB. True",
        "image": "",
        "answer": "False",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Sally needs to walk from the school to the bus stop.\n\nTrue or False : The quickest way to get there will be through the playground.\nChoice:\nA. False\nB. True",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Sally needs to walk from the school to the bus stop.\n\nTrue or False : The quickest way to get there will be through the playground.\nChoice:\nA. False\nB. True",
        "question_for_eval": "Sally needs to walk from the school to the bus stop.\n\nTrue or False : The quickest way to get there will be through the playground.\nChoice:\nA. False\nB. True"
    },
    {
        "sample_index": "431",
        "problem_index": "431",
        "problem_version": "Text Only",
        "question": "Iain\u2019s car has run out of petrol. He walks 12 km west and then 9 km south looking for a petrol station.\n\nIf he is now $h$ km directly from his starting point, find the value of $h$.",
        "image": "",
        "answer": "$h=15$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Iain\u2019s car has run out of petrol. He walks 12 km west and then 9 km south looking for a petrol station.\n\nIf he is now $h$ km directly from his starting point, find the value of $h$.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Iain\u2019s car has run out of petrol. He walks 12 km west and then 9 km south looking for a petrol station.\n\nIf he is now $h$ km directly from his starting point, find the value of $h$.",
        "question_for_eval": "Iain\u2019s car has run out of petrol. He walks 12 km west and then 9 km south looking for a petrol station.\n\nIf he is now $h$ km directly from his starting point, find the value of $h$."
    },
    {
        "sample_index": "432",
        "problem_index": "432",
        "problem_version": "Text Only",
        "question": "Find the distance between the two endpoints using the distance formula. The two end points of the line are (-3, 4) and (5, 2), respectively. Round to three decimal places.\n",
        "image": "",
        "answer": "8.246",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the distance between the two endpoints using the distance formula. The two end points of the line are (-3, 4) and (5, 2), respectively. Round to three decimal places.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the distance between the two endpoints using the distance formula. The two end points of the line are (-3, 4) and (5, 2), respectively. Round to three decimal places.\n",
        "question_for_eval": "Find the distance between the two endpoints using the distance formula. The two end points of the line are (-3, 4) and (5, 2), respectively. Round to three decimal places.\n"
    },
    {
        "sample_index": "433",
        "problem_index": "433",
        "problem_version": "Text Only",
        "question": "There is a blue rectangular with four vertexes (-6,5), (-6,-1), (10,5), (10,-1). The two diagonals are red and intersect with each other at (2,2). Find the coordinates of the midpoint for each diagonal.\n",
        "image": "",
        "answer": "(2,-2)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a blue rectangular with four vertexes (-6,5), (-6,-1), (10,5), (10,-1). The two diagonals are red and intersect with each other at (2,2). Find the coordinates of the midpoint for each diagonal.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a blue rectangular with four vertexes (-6,5), (-6,-1), (10,5), (10,-1). The two diagonals are red and intersect with each other at (2,2). Find the coordinates of the midpoint for each diagonal.\n",
        "question_for_eval": "There is a blue rectangular with four vertexes (-6,5), (-6,-1), (10,5), (10,-1). The two diagonals are red and intersect with each other at (2,2). Find the coordinates of the midpoint for each diagonal.\n"
    },
    {
        "sample_index": "434",
        "problem_index": "434",
        "problem_version": "Text Only",
        "question": "Given the graph of the ellipse that intersects with x-axis at 9 and -9 and with y-axis at 3 and -3, determine its equation.\n",
        "image": "",
        "answer": "\\frac{x^2}{81}+\\frac{y^2}{9}=1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Given the graph of the ellipse that intersects with x-axis at 9 and -9 and with y-axis at 3 and -3, determine its equation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Given the graph of the ellipse that intersects with x-axis at 9 and -9 and with y-axis at 3 and -3, determine its equation.\n",
        "question_for_eval": "Given the graph of the ellipse that intersects with x-axis at 9 and -9 and with y-axis at 3 and -3, determine its equation.\n"
    },
    {
        "sample_index": "435",
        "problem_index": "435",
        "problem_version": "Text Only",
        "question": "Given the graph of the ellipse that intersects with x-axis at -0.5 and -3.5 and with y-axis at 2, determine its equation.\n",
        "image": "",
        "answer": "\\frac{(x+2)^2}{4}+\\frac{(y-2)^2}{9}=1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Given the graph of the ellipse that intersects with x-axis at -0.5 and -3.5 and with y-axis at 2, determine its equation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Given the graph of the ellipse that intersects with x-axis at -0.5 and -3.5 and with y-axis at 2, determine its equation.\n",
        "question_for_eval": "Given the graph of the ellipse that intersects with x-axis at -0.5 and -3.5 and with y-axis at 2, determine its equation.\n"
    },
    {
        "sample_index": "436",
        "problem_index": "436",
        "problem_version": "Text Only",
        "question": "There is a hyperbola in blue with double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. Find the equation of the hyperbola.\n",
        "image": "",
        "answer": "\\frac{y^2}{16}-\\frac{x^2}{25}=1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a hyperbola in blue with double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. Find the equation of the hyperbola.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a hyperbola in blue with double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. Find the equation of the hyperbola.\n",
        "question_for_eval": "There is a hyperbola in blue with double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. Find the equation of the hyperbola.\n"
    },
    {
        "sample_index": "437",
        "problem_index": "437",
        "problem_version": "Text Only",
        "question": "There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\\sqrt{2}$) and (-1, -$3\\sqrt{2}$). Find the equation of the hyperbola.\n",
        "image": "",
        "answer": "\\frac{y^2}{9}-\\frac{(x+1)^2}{9}=1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\\sqrt{2}$) and (-1, -$3\\sqrt{2}$). Find the equation of the hyperbola.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\\sqrt{2}$) and (-1, -$3\\sqrt{2}$). Find the equation of the hyperbola.\n",
        "question_for_eval": "There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\\sqrt{2}$) and (-1, -$3\\sqrt{2}$). Find the equation of the hyperbola.\n"
    },
    {
        "sample_index": "438",
        "problem_index": "438",
        "problem_version": "Text Only",
        "question": "There is a hyperbola in blue with two vertices highlighted at (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\\sqrt{2}$,-3) and ($-3+5\\sqrt{2}$,-3). Find the equation of the hyperbola.\n",
        "image": "",
        "answer": "\\frac{(x+3)^2}{25}-\\frac{(y+3)^2}{25}=1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a hyperbola in blue with two vertices highlighted at (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\\sqrt{2}$,-3) and ($-3+5\\sqrt{2}$,-3). Find the equation of the hyperbola.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a hyperbola in blue with two vertices highlighted at (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\\sqrt{2}$,-3) and ($-3+5\\sqrt{2}$,-3). Find the equation of the hyperbola.\n",
        "question_for_eval": "There is a hyperbola in blue with two vertices highlighted at (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\\sqrt{2}$,-3) and ($-3+5\\sqrt{2}$,-3). Find the equation of the hyperbola.\n"
    },
    {
        "sample_index": "439",
        "problem_index": "439",
        "problem_version": "Text Only",
        "question": "Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\\frac{\\pi}{4}$. What are the coordinates of point $A$ ?\nEnter an exact value or round to the nearest hundredth.\n",
        "image": "",
        "answer": "$\\left(\\frac{\\sqrt{2}}{2}, \\frac{\\sqrt{2}}{2}\\right)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\\frac{\\pi}{4}$. What are the coordinates of point $A$ ?\nEnter an exact value or round to the nearest hundredth.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\\frac{\\pi}{4}$. What are the coordinates of point $A$ ?\nEnter an exact value or round to the nearest hundredth.\n",
        "question_for_eval": "Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\\frac{\\pi}{4}$. What are the coordinates of point $A$ ?\nEnter an exact value or round to the nearest hundredth.\n"
    },
    {
        "sample_index": "440",
        "problem_index": "440",
        "problem_version": "Text Only",
        "question": "On the following unit circle, an angle $\\theta$ is formed by a radius and x-axis. Which two of the following expressions are OPPOSITE of $\\tan (\\theta)$ ?\nChoose 2 answers:\nChoices:\nA:$\\tan (\\pi+\\theta)$\nB:$\\tan \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\tan (2 \\pi-\\theta)$\nD:$\\tan (\\pi-\\theta)$",
        "image": "",
        "answer": "C\nD",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: On the following unit circle, an angle $\\theta$ is formed by a radius and x-axis. Which two of the following expressions are OPPOSITE of $\\tan (\\theta)$ ?\nChoose 2 answers:\nChoices:\nA:$\\tan (\\pi+\\theta)$\nB:$\\tan \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\tan (2 \\pi-\\theta)$\nD:$\\tan (\\pi-\\theta)$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: On the following unit circle, an angle $\\theta$ is formed by a radius and x-axis. Which two of the following expressions are OPPOSITE of $\\tan (\\theta)$ ?\nChoose 2 answers:\nChoices:\nA:$\\tan (\\pi+\\theta)$\nB:$\\tan \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\tan (2 \\pi-\\theta)$\nD:$\\tan (\\pi-\\theta)$",
        "question_for_eval": "On the following unit circle, an angle $\\theta$ is formed by a radius and x-axis. Which two of the following expressions are OPPOSITE of $\\tan (\\theta)$ ?\nChoose 2 answers:\nChoices:\nA:$\\tan (\\pi+\\theta)$\nB:$\\tan \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\tan (2 \\pi-\\theta)$\nD:$\\tan (\\pi-\\theta)$"
    },
    {
        "sample_index": "441",
        "problem_index": "441",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n",
        "image": "",
        "answer": "$\\frac{4}{5}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n"
    },
    {
        "sample_index": "442",
        "problem_index": "442",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "image": "",
        "answer": "$\\frac{4}{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{3}{5}, \\frac{4}{5}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n"
    },
    {
        "sample_index": "443",
        "problem_index": "443",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "image": "",
        "answer": "$-\\frac{21}{29}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n"
    },
    {
        "sample_index": "444",
        "problem_index": "444",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "image": "",
        "answer": "$-\\frac{20}{21}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n"
    },
    {
        "sample_index": "445",
        "problem_index": "445",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n",
        "image": "",
        "answer": "$\\frac{20}{29}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\sin a$.\n"
    },
    {
        "sample_index": "446",
        "problem_index": "446",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "image": "",
        "answer": "$-\\frac{21}{29}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(-\\frac{21}{29}, \\frac{20}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n"
    },
    {
        "sample_index": "447",
        "problem_index": "447",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "image": "",
        "answer": "$\\frac{20}{29}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\cos a$.\n"
    },
    {
        "sample_index": "448",
        "problem_index": "448",
        "problem_version": "Text Only",
        "question": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "image": "",
        "answer": "$-\\frac{21}{20}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n",
        "question_for_eval": "The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\\left(\\frac{20}{29},-\\frac{21}{29}\\right)$. The center of the circle is the origin and the radius of the circle is 1.\n\nFind the value of $\\tan a$.\n"
    },
    {
        "sample_index": "449",
        "problem_index": "449",
        "problem_version": "Text Only",
        "question": "A circle the center of the circle is the origin and the radius of the circle is 1. The point $P$ on the unit circle has the coordinates $(x, y)$. What is the value of $\\sec \\theta$ ?\nChoices:\nA:$\\frac{1}{x}$\nB:$x$\nC:$y$\nD:$\\frac{1}{y}$",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A circle the center of the circle is the origin and the radius of the circle is 1. The point $P$ on the unit circle has the coordinates $(x, y)$. What is the value of $\\sec \\theta$ ?\nChoices:\nA:$\\frac{1}{x}$\nB:$x$\nC:$y$\nD:$\\frac{1}{y}$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A circle the center of the circle is the origin and the radius of the circle is 1. The point $P$ on the unit circle has the coordinates $(x, y)$. What is the value of $\\sec \\theta$ ?\nChoices:\nA:$\\frac{1}{x}$\nB:$x$\nC:$y$\nD:$\\frac{1}{y}$",
        "question_for_eval": "A circle the center of the circle is the origin and the radius of the circle is 1. The point $P$ on the unit circle has the coordinates $(x, y)$. What is the value of $\\sec \\theta$ ?\nChoices:\nA:$\\frac{1}{x}$\nB:$x$\nC:$y$\nD:$\\frac{1}{y}$"
    },
    {
        "sample_index": "450",
        "problem_index": "450",
        "problem_version": "Text Only",
        "question": "The line passes (0,5) and (2.5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n",
        "image": "",
        "answer": "y=-2 x+5",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (0,5) and (2.5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (0,5) and (2.5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n",
        "question_for_eval": "The line passes (0,5) and (2.5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n"
    },
    {
        "sample_index": "451",
        "problem_index": "451",
        "problem_version": "Text Only",
        "question": "The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n",
        "image": "",
        "answer": "$y+3=\\frac{3}{4}(x-2)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n",
        "question_for_eval": "The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n"
    },
    {
        "sample_index": "452",
        "problem_index": "452",
        "problem_version": "Text Only",
        "question": "The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n",
        "image": "",
        "answer": "$y-3=\\frac{2}{3}(x-8)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n",
        "question_for_eval": "The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n"
    },
    {
        "sample_index": "453",
        "problem_index": "453",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the coordinates of the centre in the form $(a, b)$.\n",
        "image": "",
        "answer": "(0,0)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the coordinates of the centre in the form $(a, b)$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the coordinates of the centre in the form $(a, b)$.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the coordinates of the centre in the form $(a, b)$.\n"
    },
    {
        "sample_index": "454",
        "problem_index": "454",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the radius.\n",
        "image": "",
        "answer": "2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the radius.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the radius.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the radius.\n"
    },
    {
        "sample_index": "455",
        "problem_index": "455",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n",
        "image": "",
        "answer": "8",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n"
    },
    {
        "sample_index": "456",
        "problem_index": "456",
        "problem_version": "Text Only",
        "question": "Consider the circle on the graph. Its center at the origin and its radius is 7. State the equation of the circle.\n",
        "image": "",
        "answer": "$x^{2}+y^{2}=49$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle on the graph. Its center at the origin and its radius is 7. State the equation of the circle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle on the graph. Its center at the origin and its radius is 7. State the equation of the circle.\n",
        "question_for_eval": "Consider the circle on the graph. Its center at the origin and its radius is 7. State the equation of the circle.\n"
    },
    {
        "sample_index": "457",
        "problem_index": "457",
        "problem_version": "Text Only",
        "question": "Consider the circle on the graph. Its center is at (1,3) and its radius is 6.\n\nFind the equation of the circle in standard form.\n",
        "image": "",
        "answer": "$(x-1)^{2}+(y-3)^{2}=36$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle on the graph. Its center is at (1,3) and its radius is 6.\n\nFind the equation of the circle in standard form.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle on the graph. Its center is at (1,3) and its radius is 6.\n\nFind the equation of the circle in standard form.\n",
        "question_for_eval": "Consider the circle on the graph. Its center is at (1,3) and its radius is 6.\n\nFind the equation of the circle in standard form.\n"
    },
    {
        "sample_index": "458",
        "problem_index": "458",
        "problem_version": "Text Only",
        "question": "The terminal side of an angle, $\\theta$ passes through the point $(-4,-6)$. Use the diagram to answer the following question.\n\nFind the value of $\\cos \\theta$. Rationalise the denominator if necessary.\n",
        "image": "",
        "answer": "$\\frac{-2 \\sqrt{13}}{13}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The terminal side of an angle, $\\theta$ passes through the point $(-4,-6)$. Use the diagram to answer the following question.\n\nFind the value of $\\cos \\theta$. Rationalise the denominator if necessary.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The terminal side of an angle, $\\theta$ passes through the point $(-4,-6)$. Use the diagram to answer the following question.\n\nFind the value of $\\cos \\theta$. Rationalise the denominator if necessary.\n",
        "question_for_eval": "The terminal side of an angle, $\\theta$ passes through the point $(-4,-6)$. Use the diagram to answer the following question.\n\nFind the value of $\\cos \\theta$. Rationalise the denominator if necessary.\n"
    },
    {
        "sample_index": "459",
        "problem_index": "459",
        "problem_version": "Text Only",
        "question": "Consider the graph of the circle, which has 4 intersection points with axes, shown below.\n\nComplete the statement.\n\nEvery point on the circle is exactly _ units away from the point\n\n( _ , _ ).\n",
        "image": "",
        "answer": "Complete the statement.Every point on the circle is exactly 5 units away from the point (0,0).",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the graph of the circle, which has 4 intersection points with axes, shown below.\n\nComplete the statement.\n\nEvery point on the circle is exactly _ units away from the point\n\n( _ , _ ).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the graph of the circle, which has 4 intersection points with axes, shown below.\n\nComplete the statement.\n\nEvery point on the circle is exactly _ units away from the point\n\n( _ , _ ).\n",
        "question_for_eval": "Consider the graph of the circle, which has 4 intersection points with axes, shown below.\n\nComplete the statement.\n\nEvery point on the circle is exactly _ units away from the point\n\n( _ , _ ).\n"
    },
    {
        "sample_index": "460",
        "problem_index": "460",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 2 intersection points with axes, on the graph.\n\n\nFind the centre of the circle. Write your answer in the form ( _ , _ )\n",
        "image": "",
        "answer": "(-3,-3)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 2 intersection points with axes, on the graph.\n\n\nFind the centre of the circle. Write your answer in the form ( _ , _ )\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 2 intersection points with axes, on the graph.\n\n\nFind the centre of the circle. Write your answer in the form ( _ , _ )\n",
        "question_for_eval": "Consider the circle, which has 2 intersection points with axes, on the graph.\n\n\nFind the centre of the circle. Write your answer in the form ( _ , _ )\n"
    },
    {
        "sample_index": "461",
        "problem_index": "461",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n",
        "image": "",
        "answer": "3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n",
        "question_for_eval": "Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n"
    },
    {
        "sample_index": "462",
        "problem_index": "462",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n",
        "image": "",
        "answer": "6",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, on the graph.\n\nFind the radius of the circle.\n"
    },
    {
        "sample_index": "463",
        "problem_index": "463",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the centre of the circle. Write your answer in the form ( _ , _ ).\n",
        "image": "",
        "answer": "(-3,-3)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the centre of the circle. Write your answer in the form ( _ , _ ).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the centre of the circle. Write your answer in the form ( _ , _ ).\n",
        "question_for_eval": "Consider the circle, which has 2 intersection points with axes, on the graph.\n\nFind the centre of the circle. Write your answer in the form ( _ , _ ).\n"
    },
    {
        "sample_index": "464",
        "problem_index": "464",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, on the graph.\nFind the radius of the circle.\n",
        "image": "",
        "answer": "3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\nFind the radius of the circle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\nFind the radius of the circle.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, on the graph.\nFind the radius of the circle.\n"
    },
    {
        "sample_index": "465",
        "problem_index": "465",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, on the graph.\n\nWrite the equation of the circle in the form \\left(x-h\\right)^2+\\left(y-k\\right)^2=r^2.\n",
        "image": "",
        "answer": "(x+3)^2+(y+3)^2=9",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\n\nWrite the equation of the circle in the form \\left(x-h\\right)^2+\\left(y-k\\right)^2=r^2.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\n\nWrite the equation of the circle in the form \\left(x-h\\right)^2+\\left(y-k\\right)^2=r^2.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, on the graph.\n\nWrite the equation of the circle in the form \\left(x-h\\right)^2+\\left(y-k\\right)^2=r^2.\n"
    },
    {
        "sample_index": "466",
        "problem_index": "466",
        "problem_version": "Text Only",
        "question": "Consider the graph of the circle, which has 2 intersection points with axes, below.\n\n\nDescribe the translation to get from x^2+y^2=4^2 to the circle shown.\nChoices:\nA:The graph has been translated 4 units downwards.\nB:The graph has been translated 4 units right.\nC:The graph has been translated 4 units left.\nD:The graph has been translated 4 units upwards.",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Consider the graph of the circle, which has 2 intersection points with axes, below.\n\n\nDescribe the translation to get from x^2+y^2=4^2 to the circle shown.\nChoices:\nA:The graph has been translated 4 units downwards.\nB:The graph has been translated 4 units right.\nC:The graph has been translated 4 units left.\nD:The graph has been translated 4 units upwards.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Consider the graph of the circle, which has 2 intersection points with axes, below.\n\n\nDescribe the translation to get from x^2+y^2=4^2 to the circle shown.\nChoices:\nA:The graph has been translated 4 units downwards.\nB:The graph has been translated 4 units right.\nC:The graph has been translated 4 units left.\nD:The graph has been translated 4 units upwards.",
        "question_for_eval": "Consider the graph of the circle, which has 2 intersection points with axes, below.\n\n\nDescribe the translation to get from x^2+y^2=4^2 to the circle shown.\nChoices:\nA:The graph has been translated 4 units downwards.\nB:The graph has been translated 4 units right.\nC:The graph has been translated 4 units left.\nD:The graph has been translated 4 units upwards."
    },
    {
        "sample_index": "467",
        "problem_index": "467",
        "problem_version": "Text Only",
        "question": "Consider the graph of the circle, which has 2 intersection points with axes, below.\n\nState the equation of the circle shown in the graph.\n",
        "image": "",
        "answer": "x^2+(y+4)^2=4^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the graph of the circle, which has 2 intersection points with axes, below.\n\nState the equation of the circle shown in the graph.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the graph of the circle, which has 2 intersection points with axes, below.\n\nState the equation of the circle shown in the graph.\n",
        "question_for_eval": "Consider the graph of the circle, which has 2 intersection points with axes, below.\n\nState the equation of the circle shown in the graph.\n"
    },
    {
        "sample_index": "468",
        "problem_index": "468",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, on the graph.\n\n\nFind the centre of the circle.\n",
        "image": "",
        "answer": "(1,3)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\n\n\nFind the centre of the circle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, on the graph.\n\n\nFind the centre of the circle.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, on the graph.\n\n\nFind the centre of the circle.\n"
    },
    {
        "sample_index": "469",
        "problem_index": "469",
        "problem_version": "Text Only",
        "question": "The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\n\nState the centre of the semicircle.\n",
        "image": "",
        "answer": "(0,0)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\n\nState the centre of the semicircle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\n\nState the centre of the semicircle.\n",
        "question_for_eval": "The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\n\nState the centre of the semicircle.\n"
    },
    {
        "sample_index": "470",
        "problem_index": "470",
        "problem_version": "Text Only",
        "question": "The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nState the radius of the semicircle.\n\nRadius = _ units\n",
        "image": "",
        "answer": "7",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nState the radius of the semicircle.\n\nRadius = _ units\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nState the radius of the semicircle.\n\nRadius = _ units\n",
        "question_for_eval": "The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nState the radius of the semicircle.\n\nRadius = _ units\n"
    },
    {
        "sample_index": "471",
        "problem_index": "471",
        "problem_version": "Text Only",
        "question": "The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nFind the equation of this semicircle.\n",
        "image": "",
        "answer": "y=\\sqrt{49-x^2}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nFind the equation of this semicircle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nFind the equation of this semicircle.\n",
        "question_for_eval": "The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).\n\nFind the equation of this semicircle.\n"
    },
    {
        "sample_index": "472",
        "problem_index": "472",
        "problem_version": "Text Only",
        "question": "The following graph shows a semicircle which passes (-7,0), (-5,-5), (0,7), (5,-5), (7,0).\n\nState the centre of the semicircle.\n",
        "image": "",
        "answer": "(0,0)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,-5), (0,7), (5,-5), (7,0).\n\nState the centre of the semicircle.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The following graph shows a semicircle which passes (-7,0), (-5,-5), (0,7), (5,-5), (7,0).\n\nState the centre of the semicircle.\n",
        "question_for_eval": "The following graph shows a semicircle which passes (-7,0), (-5,-5), (0,7), (5,-5), (7,0).\n\nState the centre of the semicircle.\n"
    },
    {
        "sample_index": "473",
        "problem_index": "473",
        "problem_version": "Text Only",
        "question": "A rectangle contains an ellipse. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). The center of the ellipse is (20,10), and its four vertices are (0,10), (20,10), (20,20), (40,10). A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n",
        "image": "",
        "answer": "Center $=(20,10)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo2D_collected",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A rectangle contains an ellipse. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). The center of the ellipse is (20,10), and its four vertices are (0,10), (20,10), (20,20), (40,10). A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A rectangle contains an ellipse. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). The center of the ellipse is (20,10), and its four vertices are (0,10), (20,10), (20,20), (40,10). A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n",
        "question_for_eval": "A rectangle contains an ellipse. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). The center of the ellipse is (20,10), and its four vertices are (0,10), (20,10), (20,20), (40,10). A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n"
    },
    {
        "sample_index": "474",
        "problem_index": "474",
        "problem_version": "Text Only",
        "question": "There are two points at -2 and 1 on the number line. Write the set of numbers represented on the number line in interval notation.\n",
        "image": "",
        "answer": "(-2,1]",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There are two points at -2 and 1 on the number line. Write the set of numbers represented on the number line in interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There are two points at -2 and 1 on the number line. Write the set of numbers represented on the number line in interval notation.\n",
        "question_for_eval": "There are two points at -2 and 1 on the number line. Write the set of numbers represented on the number line in interval notation.\n"
    },
    {
        "sample_index": "475",
        "problem_index": "475",
        "problem_version": "Text Only",
        "question": "There is a point at 4 and a blue arrow goes to left from that point. Write the set of numbers represented on the number line in interval notation.\n",
        "image": "",
        "answer": "(-\\infty, 4]",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a point at 4 and a blue arrow goes to left from that point. Write the set of numbers represented on the number line in interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a point at 4 and a blue arrow goes to left from that point. Write the set of numbers represented on the number line in interval notation.\n",
        "question_for_eval": "There is a point at 4 and a blue arrow goes to left from that point. Write the set of numbers represented on the number line in interval notation.\n"
    },
    {
        "sample_index": "476",
        "problem_index": "476",
        "problem_version": "Text Only",
        "question": "Two curves are symmetrical about the x-axis. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Two curves are symmetrical about the x-axis. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Two curves are symmetrical about the x-axis. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function",
        "question_for_eval": "Two curves are symmetrical about the x-axis. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function"
    },
    {
        "sample_index": "477",
        "problem_index": "477",
        "problem_version": "Text Only",
        "question": "There is a curve goes through the origin. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a curve goes through the origin. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a curve goes through the origin. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function",
        "question_for_eval": "There is a curve goes through the origin. Use the vertical line test to determine if this relation is a function.\nChoices:\nA:This is a function\nB:This is not a function"
    },
    {
        "sample_index": "478",
        "problem_index": "478",
        "problem_version": "Text Only",
        "question": "There is an ellipse, for which the domain is from -3 to -1 and the range is from -1 to 3. Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is an ellipse, for which the domain is from -3 to -1 and the range is from -1 to 3. Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is an ellipse, for which the domain is from -3 to -1 and the range is from -1 to 3. Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "question_for_eval": "There is an ellipse, for which the domain is from -3 to -1 and the range is from -1 to 3. Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function"
    },
    {
        "sample_index": "479",
        "problem_index": "479",
        "problem_version": "Text Only",
        "question": "There is a curve that goes through (-3,0), (-2,1), and (-1,2). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a curve that goes through (-3,0), (-2,1), and (-1,2). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a curve that goes through (-3,0), (-2,1), and (-1,2). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "question_for_eval": "There is a curve that goes through (-3,0), (-2,1), and (-1,2). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function"
    },
    {
        "sample_index": "480",
        "problem_index": "480",
        "problem_version": "Text Only",
        "question": "There are 4 labels on the x-axis $-\\pi$, $-\\frac{2}{\\pi}$, $\\frac{2}{\\pi}$, $\\pi$ and a curve that goes through ($\\frac{2}{\\pi}$,0). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There are 4 labels on the x-axis $-\\pi$, $-\\frac{2}{\\pi}$, $\\frac{2}{\\pi}$, $\\pi$ and a curve that goes through ($\\frac{2}{\\pi}$,0). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There are 4 labels on the x-axis $-\\pi$, $-\\frac{2}{\\pi}$, $\\frac{2}{\\pi}$, $\\pi$ and a curve that goes through ($\\frac{2}{\\pi}$,0). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function",
        "question_for_eval": "There are 4 labels on the x-axis $-\\pi$, $-\\frac{2}{\\pi}$, $\\frac{2}{\\pi}$, $\\pi$ and a curve that goes through ($\\frac{2}{\\pi}$,0). Determine if this relation is a one-to-one function.\nChoices:\nA:This is a one-to-one function\nB:This is not a one-to-one function"
    },
    {
        "sample_index": "481",
        "problem_index": "481",
        "problem_version": "Text Only",
        "question": "Find the domain and range of the function f using interval notation, which goes through (-2,-4), (-1,-2), (0,0), (1,-4), with a hollow point (-3,0).\n",
        "image": "",
        "answer": "domain: [-4, 0) and range: (-3, 1]",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the domain and range of the function f using interval notation, which goes through (-2,-4), (-1,-2), (0,0), (1,-4), with a hollow point (-3,0).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the domain and range of the function f using interval notation, which goes through (-2,-4), (-1,-2), (0,0), (1,-4), with a hollow point (-3,0).\n",
        "question_for_eval": "Find the domain and range of the function f using interval notation, which goes through (-2,-4), (-1,-2), (0,0), (1,-4), with a hollow point (-3,0).\n"
    },
    {
        "sample_index": "482",
        "problem_index": "482",
        "problem_version": "Text Only",
        "question": "There is a line goes through a hollow point (2,8) and a solid point (8,6). Write the domain and range of each function using interval notation.\n",
        "image": "",
        "answer": "domain: (2,8] and range: [6,8)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a line goes through a hollow point (2,8) and a solid point (8,6). Write the domain and range of each function using interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a line goes through a hollow point (2,8) and a solid point (8,6). Write the domain and range of each function using interval notation.\n",
        "question_for_eval": "There is a line goes through a hollow point (2,8) and a solid point (8,6). Write the domain and range of each function using interval notation.\n"
    },
    {
        "sample_index": "483",
        "problem_index": "483",
        "problem_version": "Text Only",
        "question": "There is a curve goes through (-4,0), (0,2), and (4,0). The points at (-4,0) and (4,0) are both solid points. Write the domain and range of the function using interval notation.\n",
        "image": "",
        "answer": "domain: [-4,4] and range: [0,2]",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a curve goes through (-4,0), (0,2), and (4,0). The points at (-4,0) and (4,0) are both solid points. Write the domain and range of the function using interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a curve goes through (-4,0), (0,2), and (4,0). The points at (-4,0) and (4,0) are both solid points. Write the domain and range of the function using interval notation.\n",
        "question_for_eval": "There is a curve goes through (-4,0), (0,2), and (4,0). The points at (-4,0) and (4,0) are both solid points. Write the domain and range of the function using interval notation.\n"
    },
    {
        "sample_index": "484",
        "problem_index": "484",
        "problem_version": "Text Only",
        "question": "There is a curve goes through (-5,2), (-1,0), and (3,2). The point at (-5,2) and (3,2) are respectively solid and hollow. Write the domain and range of the function using interval notation.\n",
        "image": "",
        "answer": "domain: [-5,3) and range: [0,2]",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a curve goes through (-5,2), (-1,0), and (3,2). The point at (-5,2) and (3,2) are respectively solid and hollow. Write the domain and range of the function using interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a curve goes through (-5,2), (-1,0), and (3,2). The point at (-5,2) and (3,2) are respectively solid and hollow. Write the domain and range of the function using interval notation.\n",
        "question_for_eval": "There is a curve goes through (-5,2), (-1,0), and (3,2). The point at (-5,2) and (3,2) are respectively solid and hollow. Write the domain and range of the function using interval notation.\n"
    },
    {
        "sample_index": "485",
        "problem_index": "485",
        "problem_version": "Text Only",
        "question": "There is a curve start from a solid point (1,0) with an end arrow going through (-4,4). Write the domain and range of the function using interval notation.\n",
        "image": "",
        "answer": "domain: (-\\infty, 1] and range: [0, \\infty)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a curve start from a solid point (1,0) with an end arrow going through (-4,4). Write the domain and range of the function using interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a curve start from a solid point (1,0) with an end arrow going through (-4,4). Write the domain and range of the function using interval notation.\n",
        "question_for_eval": "There is a curve start from a solid point (1,0) with an end arrow going through (-4,4). Write the domain and range of the function using interval notation.\n"
    },
    {
        "sample_index": "486",
        "problem_index": "486",
        "problem_version": "Text Only",
        "question": "There is a hyperbolic function with its center at the origin. The graph approaches zero as $\u2223x\u2223$ increases, and the function is undefined at x=0. There are four points labeled at (1/6,6), (6,1/6), (-1/6,-6), (-6,-1/6). Write the domain and range of the function using interval notation.\n",
        "image": "",
        "answer": "domain: [-6,-\\frac{1}{6}] \\cup[\\frac{1}{6}, 6] and range: [-6,-\\frac{1}{6}\\right] \\cup[\\frac{1}{6}, 6]",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a hyperbolic function with its center at the origin. The graph approaches zero as $\u2223x\u2223$ increases, and the function is undefined at x=0. There are four points labeled at (1/6,6), (6,1/6), (-1/6,-6), (-6,-1/6). Write the domain and range of the function using interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a hyperbolic function with its center at the origin. The graph approaches zero as $\u2223x\u2223$ increases, and the function is undefined at x=0. There are four points labeled at (1/6,6), (6,1/6), (-1/6,-6), (-6,-1/6). Write the domain and range of the function using interval notation.\n",
        "question_for_eval": "There is a hyperbolic function with its center at the origin. The graph approaches zero as $\u2223x\u2223$ increases, and the function is undefined at x=0. There are four points labeled at (1/6,6), (6,1/6), (-1/6,-6), (-6,-1/6). Write the domain and range of the function using interval notation.\n"
    },
    {
        "sample_index": "487",
        "problem_index": "487",
        "problem_version": "Text Only",
        "question": "There is a piecewise function going through points (-3, 0), (0, 5), and (3, 5). Write the domain and range of the function using interval notation.\n",
        "image": "",
        "answer": "domain: [-3, \\infty) and range: [0, \\infty)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a piecewise function going through points (-3, 0), (0, 5), and (3, 5). Write the domain and range of the function using interval notation.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a piecewise function going through points (-3, 0), (0, 5), and (3, 5). Write the domain and range of the function using interval notation.\n",
        "question_for_eval": "There is a piecewise function going through points (-3, 0), (0, 5), and (3, 5). Write the domain and range of the function using interval notation.\n"
    },
    {
        "sample_index": "488",
        "problem_index": "488",
        "problem_version": "Text Only",
        "question": "There is a curve goes through (-4,1), (-1,3), and (0,0). Estimate the intervals on which the function is increasing or decreasing.\n",
        "image": "",
        "answer": "The function is increasing on (-\\infty,-2.5) \\cup(1, \\infty), and decreasing on (-2.5,1)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a curve goes through (-4,1), (-1,3), and (0,0). Estimate the intervals on which the function is increasing or decreasing.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a curve goes through (-4,1), (-1,3), and (0,0). Estimate the intervals on which the function is increasing or decreasing.\n",
        "question_for_eval": "There is a curve goes through (-4,1), (-1,3), and (0,0). Estimate the intervals on which the function is increasing or decreasing.\n"
    },
    {
        "sample_index": "489",
        "problem_index": "489",
        "problem_version": "Text Only",
        "question": "There are two curves with a vertical asymptote x=3. One curve passes (1,0), and another curve passes (4,0). Estimate the intervals on which the function is increasing or decreasing.\n",
        "image": "",
        "answer": "\\text { increasing on }(-\\infty, 1) \\cup(3,4) \\text {, decreasing on }(1,3) \\cup(4, \\infty)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There are two curves with a vertical asymptote x=3. One curve passes (1,0), and another curve passes (4,0). Estimate the intervals on which the function is increasing or decreasing.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There are two curves with a vertical asymptote x=3. One curve passes (1,0), and another curve passes (4,0). Estimate the intervals on which the function is increasing or decreasing.\n",
        "question_for_eval": "There are two curves with a vertical asymptote x=3. One curve passes (1,0), and another curve passes (4,0). Estimate the intervals on which the function is increasing or decreasing.\n"
    },
    {
        "sample_index": "490",
        "problem_index": "490",
        "problem_version": "Text Only",
        "question": "There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n",
        "image": "",
        "answer": "\\text { local maximum: }(-3,60) \\text {, local minimum: }(3, -60)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n",
        "question_for_eval": "There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n"
    },
    {
        "sample_index": "491",
        "problem_index": "491",
        "problem_version": "Text Only",
        "question": "There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n",
        "image": "",
        "answer": "\\text { Local minimum at }(-2,-2) \\text {, decreasing on }(-3,-2) \\text {, increasing on }(-2, \\infty)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n",
        "question_for_eval": "There is an odd function f going through (0,0). Estimate the point(s) at which the graph of f has a local maximum or a local minimum.\n"
    },
    {
        "sample_index": "492",
        "problem_index": "492",
        "problem_version": "Text Only",
        "question": "The graph of a cubic function  f  is shown in Figure 18 with a labeled point (1.333, 5.185) at its right part. Based on the calculator screen shot, the point  (1.333,5.185)  is which of the following?\nChoices:\nA.a relative (local) maximum of the function\nB.the vertex of the function\nC.the absolute maximum of the function\nD.a zero of the function",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph of a cubic function  f  is shown in Figure 18 with a labeled point (1.333, 5.185) at its right part. Based on the calculator screen shot, the point  (1.333,5.185)  is which of the following?\nChoices:\nA.a relative (local) maximum of the function\nB.the vertex of the function\nC.the absolute maximum of the function\nD.a zero of the function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph of a cubic function  f  is shown in Figure 18 with a labeled point (1.333, 5.185) at its right part. Based on the calculator screen shot, the point  (1.333,5.185)  is which of the following?\nChoices:\nA.a relative (local) maximum of the function\nB.the vertex of the function\nC.the absolute maximum of the function\nD.a zero of the function",
        "question_for_eval": "The graph of a cubic function  f  is shown in Figure 18 with a labeled point (1.333, 5.185) at its right part. Based on the calculator screen shot, the point  (1.333,5.185)  is which of the following?\nChoices:\nA.a relative (local) maximum of the function\nB.the vertex of the function\nC.the absolute maximum of the function\nD.a zero of the function"
    },
    {
        "sample_index": "493",
        "problem_index": "493",
        "problem_version": "Text Only",
        "question": "There is a piecewise function combind by straight lines going through (3, -2), (1, 0), and (0,1). Write an equation for the graphed function f.\n",
        "image": "",
        "answer": "When x<=3 $f(x)=-x+1$, when x>3, $f(x)=x-5$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a piecewise function combind by straight lines going through (3, -2), (1, 0), and (0,1). Write an equation for the graphed function f.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a piecewise function combind by straight lines going through (3, -2), (1, 0), and (0,1). Write an equation for the graphed function f.\n",
        "question_for_eval": "There is a piecewise function combind by straight lines going through (3, -2), (1, 0), and (0,1). Write an equation for the graphed function f.\n"
    },
    {
        "sample_index": "494",
        "problem_index": "494",
        "problem_version": "Text Only",
        "question": "There is a piecewise function combind by straight lines, which goes through (-3, -2), (0, 1), and (-1, 0). Write an equation for the graphed function f.\n",
        "image": "",
        "answer": "When x<=-3 $f(x) = -x-5$, when x>3, $f(x)=x+1$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a piecewise function combind by straight lines, which goes through (-3, -2), (0, 1), and (-1, 0). Write an equation for the graphed function f.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a piecewise function combind by straight lines, which goes through (-3, -2), (0, 1), and (-1, 0). Write an equation for the graphed function f.\n",
        "question_for_eval": "There is a piecewise function combind by straight lines, which goes through (-3, -2), (0, 1), and (-1, 0). Write an equation for the graphed function f.\n"
    },
    {
        "sample_index": "495",
        "problem_index": "495",
        "problem_version": "Text Only",
        "question": "There is a quadratic function going through (-2,1), (-1,2), (0,1). Write an equation for the graphed function f.\n",
        "image": "",
        "answer": "f(x)=-(x+1)^2+2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a quadratic function going through (-2,1), (-1,2), (0,1). Write an equation for the graphed function f.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a quadratic function going through (-2,1), (-1,2), (0,1). Write an equation for the graphed function f.\n",
        "question_for_eval": "There is a quadratic function going through (-2,1), (-1,2), (0,1). Write an equation for the graphed function f.\n"
    },
    {
        "sample_index": "496",
        "problem_index": "496",
        "problem_version": "Text Only",
        "question": "There is a quadratic function, which goes through (0,0), (20,0) and opens upward. Determine whether the graph represents a one-to-one function.\nChoices:\nA.This is a one-to-one function\nB.This is not a one-to-one function",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a quadratic function, which goes through (0,0), (20,0) and opens upward. Determine whether the graph represents a one-to-one function.\nChoices:\nA.This is a one-to-one function\nB.This is not a one-to-one function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a quadratic function, which goes through (0,0), (20,0) and opens upward. Determine whether the graph represents a one-to-one function.\nChoices:\nA.This is a one-to-one function\nB.This is not a one-to-one function",
        "question_for_eval": "There is a quadratic function, which goes through (0,0), (20,0) and opens upward. Determine whether the graph represents a one-to-one function.\nChoices:\nA.This is a one-to-one function\nB.This is not a one-to-one function"
    },
    {
        "sample_index": "497",
        "problem_index": "497",
        "problem_version": "Text Only",
        "question": "There is a linear function with a y-intercept of 3 and a x-intercept of 2. Determine the function expression of f shown in the figure.\n",
        "image": "",
        "answer": "$-\\frac{3}{2}x+3$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a linear function with a y-intercept of 3 and a x-intercept of 2. Determine the function expression of f shown in the figure.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a linear function with a y-intercept of 3 and a x-intercept of 2. Determine the function expression of f shown in the figure.\n",
        "question_for_eval": "There is a linear function with a y-intercept of 3 and a x-intercept of 2. Determine the function expression of f shown in the figure.\n"
    },
    {
        "sample_index": "498",
        "problem_index": "498",
        "problem_version": "Text Only",
        "question": "There is a curve goes through (-2,0), (0,0), (2,0). Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a curve goes through (-2,0), (0,0), (2,0). Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a curve goes through (-2,0), (0,0), (2,0). Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function",
        "question_for_eval": "There is a curve goes through (-2,0), (0,0), (2,0). Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function"
    },
    {
        "sample_index": "499",
        "problem_index": "499",
        "problem_version": "Text Only",
        "question": "There are two curves symmetric to the orign and lie in the second and fourth quadrant. Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There are two curves symmetric to the orign and lie in the second and fourth quadrant. Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There are two curves symmetric to the orign and lie in the second and fourth quadrant. Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function",
        "question_for_eval": "There are two curves symmetric to the orign and lie in the second and fourth quadrant. Use the vertical line test to determine if this relation is a function.\nChoices:\nA.This is a function\nB.This is not a function"
    },
    {
        "sample_index": "500",
        "problem_index": "500",
        "problem_version": "Text Only",
        "question": "There is a quadratic function that opens upwards symmetric with respect to x=2. The vertex of the parabola is at the point (2,-2). Determine the intervals on which the functions are increasing, decreasing, or constant.\n",
        "image": "",
        "answer": "Increasing at (2, \\infty) and decreasing at (-\\infty, 2)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a quadratic function that opens upwards symmetric with respect to x=2. The vertex of the parabola is at the point (2,-2). Determine the intervals on which the functions are increasing, decreasing, or constant.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a quadratic function that opens upwards symmetric with respect to x=2. The vertex of the parabola is at the point (2,-2). Determine the intervals on which the functions are increasing, decreasing, or constant.\n",
        "question_for_eval": "There is a quadratic function that opens upwards symmetric with respect to x=2. The vertex of the parabola is at the point (2,-2). Determine the intervals on which the functions are increasing, decreasing, or constant.\n"
    },
    {
        "sample_index": "501",
        "problem_index": "501",
        "problem_version": "Text Only",
        "question": "There is a piecewise function going through (-3, -4), (-1, 0), (0, 2), and (1, 4). Determine the intervals on which the functions are increasing, decreasing, or constant.\n",
        "image": "",
        "answer": "\\text { increasing } \\quad(-3,1) ; \\quad \\text { constant }(-\\infty,-3) \\cup(1, \\infty)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a piecewise function going through (-3, -4), (-1, 0), (0, 2), and (1, 4). Determine the intervals on which the functions are increasing, decreasing, or constant.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a piecewise function going through (-3, -4), (-1, 0), (0, 2), and (1, 4). Determine the intervals on which the functions are increasing, decreasing, or constant.\n",
        "question_for_eval": "There is a piecewise function going through (-3, -4), (-1, 0), (0, 2), and (1, 4). Determine the intervals on which the functions are increasing, decreasing, or constant.\n"
    },
    {
        "sample_index": "502",
        "problem_index": "502",
        "problem_version": "Text Only",
        "question": "There is a cubic function that passes (0,0). Find the absolute maximum of the function.\n",
        "image": "",
        "answer": "(-1.8,10)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a cubic function that passes (0,0). Find the absolute maximum of the function.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a cubic function that passes (0,0). Find the absolute maximum of the function.\n",
        "question_for_eval": "There is a cubic function that passes (0,0). Find the absolute maximum of the function.\n"
    },
    {
        "sample_index": "503",
        "problem_index": "503",
        "problem_version": "Text Only",
        "question": "Write the equation for the piecewise function symmetric to x=3, which goes through (3,0) and (0, 3).\n",
        "image": "",
        "answer": "f(x)=|x-3|",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Write the equation for the piecewise function symmetric to x=3, which goes through (3,0) and (0, 3).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Write the equation for the piecewise function symmetric to x=3, which goes through (3,0) and (0, 3).\n",
        "question_for_eval": "Write the equation for the piecewise function symmetric to x=3, which goes through (3,0) and (0, 3).\n"
    },
    {
        "sample_index": "504",
        "problem_index": "504",
        "problem_version": "Text Only",
        "question": "There is a U-shape curve opens upwards and passes (0,0). Determine whether the graphed function is even, odd, or neither.\n",
        "image": "",
        "answer": "even",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There is a U-shape curve opens upwards and passes (0,0). Determine whether the graphed function is even, odd, or neither.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There is a U-shape curve opens upwards and passes (0,0). Determine whether the graphed function is even, odd, or neither.\n",
        "question_for_eval": "There is a U-shape curve opens upwards and passes (0,0). Determine whether the graphed function is even, odd, or neither.\n"
    },
    {
        "sample_index": "505",
        "problem_index": "505",
        "problem_version": "Text Only",
        "question": "Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (-2, 1) and are piecewise.\n",
        "image": "",
        "answer": "f(x)=\\frac{1}{2}|x+2|+1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (-2, 1) and are piecewise.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (-2, 1) and are piecewise.\n",
        "question_for_eval": "Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (-2, 1) and are piecewise.\n"
    },
    {
        "sample_index": "506",
        "problem_index": "506",
        "problem_version": "Text Only",
        "question": "Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (3, 3) and are piecewise.\n",
        "image": "",
        "answer": "f(x)=-3|x-3|+3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (3, 3) and are piecewise.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (3, 3) and are piecewise.\n",
        "question_for_eval": "Write an equation for the transformation of f(x)=|x| as shown in the figure, which passes (3, 3) and are piecewise.\n"
    },
    {
        "sample_index": "507",
        "problem_index": "507",
        "problem_version": "Text Only",
        "question": "Which of the following could be the equation of the graphed line, whose y-intercept is 3 and x-intercept is -8?\nChoices:\nA.$3 x-8 y=24$\nB.$3 x-8 y=-24$\nC.$3 x+8 y=24$\nD.$3 x+8 y=-24$",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Which of the following could be the equation of the graphed line, whose y-intercept is 3 and x-intercept is -8?\nChoices:\nA.$3 x-8 y=24$\nB.$3 x-8 y=-24$\nC.$3 x+8 y=24$\nD.$3 x+8 y=-24$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Which of the following could be the equation of the graphed line, whose y-intercept is 3 and x-intercept is -8?\nChoices:\nA.$3 x-8 y=24$\nB.$3 x-8 y=-24$\nC.$3 x+8 y=24$\nD.$3 x+8 y=-24$",
        "question_for_eval": "Which of the following could be the equation of the graphed line, whose y-intercept is 3 and x-intercept is -8?\nChoices:\nA.$3 x-8 y=24$\nB.$3 x-8 y=-24$\nC.$3 x+8 y=24$\nD.$3 x+8 y=-24$"
    },
    {
        "sample_index": "508",
        "problem_index": "508",
        "problem_version": "Text Only",
        "question": "Consider the graph of the line whose x-intercept is 0.5 and y-intercept is 2. What is the slope of the line?\n",
        "image": "",
        "answer": "slope =-4",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the graph of the line whose x-intercept is 0.5 and y-intercept is 2. What is the slope of the line?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the graph of the line whose x-intercept is 0.5 and y-intercept is 2. What is the slope of the line?\n",
        "question_for_eval": "Consider the graph of the line whose x-intercept is 0.5 and y-intercept is 2. What is the slope of the line?\n"
    },
    {
        "sample_index": "509",
        "problem_index": "509",
        "problem_version": "Text Only",
        "question": "A line is parallel to x-axis at y=5. Write the inequality that describes the points in the shaded region.\n",
        "image": "",
        "answer": "$y \\leq 5$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A line is parallel to x-axis at y=5. Write the inequality that describes the points in the shaded region.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A line is parallel to x-axis at y=5. Write the inequality that describes the points in the shaded region.\n",
        "question_for_eval": "A line is parallel to x-axis at y=5. Write the inequality that describes the points in the shaded region.\n"
    },
    {
        "sample_index": "510",
        "problem_index": "510",
        "problem_version": "Text Only",
        "question": "The x-intercept of the line is -3 and the y-intercept is -6. State the inequality that describes the region drawn in the number plane.\n",
        "image": "",
        "answer": "$y \\geq-2 x-6$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The x-intercept of the line is -3 and the y-intercept is -6. State the inequality that describes the region drawn in the number plane.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The x-intercept of the line is -3 and the y-intercept is -6. State the inequality that describes the region drawn in the number plane.\n",
        "question_for_eval": "The x-intercept of the line is -3 and the y-intercept is -6. State the inequality that describes the region drawn in the number plane.\n"
    },
    {
        "sample_index": "511",
        "problem_index": "511",
        "problem_version": "Text Only",
        "question": "The x-intercept of the line is -3 and the y-intercept is 6. State the inequality that describes the region drawn in the number plane.\n",
        "image": "",
        "answer": "$y<2 x+6$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The x-intercept of the line is -3 and the y-intercept is 6. State the inequality that describes the region drawn in the number plane.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The x-intercept of the line is -3 and the y-intercept is 6. State the inequality that describes the region drawn in the number plane.\n",
        "question_for_eval": "The x-intercept of the line is -3 and the y-intercept is 6. State the inequality that describes the region drawn in the number plane.\n"
    },
    {
        "sample_index": "512",
        "problem_index": "512",
        "problem_version": "Text Only",
        "question": "The line goes through the origin. State the inequality that describes the region drawn in the number plane.\n",
        "image": "",
        "answer": "$y>-3 x$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line goes through the origin. State the inequality that describes the region drawn in the number plane.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line goes through the origin. State the inequality that describes the region drawn in the number plane.\n",
        "question_for_eval": "The line goes through the origin. State the inequality that describes the region drawn in the number plane.\n"
    },
    {
        "sample_index": "513",
        "problem_index": "513",
        "problem_version": "Text Only",
        "question": "The x-intercept of the line is -1.5 and the y-intercept is 3. State the inequality that describes the region drawn in the number plane.\n",
        "image": "",
        "answer": "$y \\leq 2 x+3$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The x-intercept of the line is -1.5 and the y-intercept is 3. State the inequality that describes the region drawn in the number plane.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The x-intercept of the line is -1.5 and the y-intercept is 3. State the inequality that describes the region drawn in the number plane.\n",
        "question_for_eval": "The x-intercept of the line is -1.5 and the y-intercept is 3. State the inequality that describes the region drawn in the number plane.\n"
    },
    {
        "sample_index": "514",
        "problem_index": "514",
        "problem_version": "Text Only",
        "question": "The graph shows the temperature of a room after the heater has been turned on. What is the slope of the shown function that passes the point (0, 1)?\n",
        "image": "",
        "answer": "Slope $=\\frac{1}{5}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows the temperature of a room after the heater has been turned on. What is the slope of the shown function that passes the point (0, 1)?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows the temperature of a room after the heater has been turned on. What is the slope of the shown function that passes the point (0, 1)?\n",
        "question_for_eval": "The graph shows the temperature of a room after the heater has been turned on. What is the slope of the shown function that passes the point (0, 1)?\n"
    },
    {
        "sample_index": "515",
        "problem_index": "515",
        "problem_version": "Text Only",
        "question": "The graph shows the amount of water remaining in a bucket that was initially full before a hole was made in its side. What is the slope of the shown function that passes (0, 30)?\n",
        "image": "",
        "answer": "Slope $=-\\frac{1}{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows the amount of water remaining in a bucket that was initially full before a hole was made in its side. What is the slope of the shown function that passes (0, 30)?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows the amount of water remaining in a bucket that was initially full before a hole was made in its side. What is the slope of the shown function that passes (0, 30)?\n",
        "question_for_eval": "The graph shows the amount of water remaining in a bucket that was initially full before a hole was made in its side. What is the slope of the shown function that passes (0, 30)?\n"
    },
    {
        "sample_index": "516",
        "problem_index": "516",
        "problem_version": "Text Only",
        "question": "Consider the graph of the exponential function $y=4^{x}$. What can we say about the $y$-value of every point on the graph?\nChoices:\nA.The $y$-value of most points of the graph is greater than 1.\nB.The $y$-value of every point on the graph is positive.\nC.The $y$-value of every point on the graph is an integer.\nD.The $y$-value of most points on the graph is positive, and the $y$-value at one point is 0.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Consider the graph of the exponential function $y=4^{x}$. What can we say about the $y$-value of every point on the graph?\nChoices:\nA.The $y$-value of most points of the graph is greater than 1.\nB.The $y$-value of every point on the graph is positive.\nC.The $y$-value of every point on the graph is an integer.\nD.The $y$-value of most points on the graph is positive, and the $y$-value at one point is 0.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Consider the graph of the exponential function $y=4^{x}$. What can we say about the $y$-value of every point on the graph?\nChoices:\nA.The $y$-value of most points of the graph is greater than 1.\nB.The $y$-value of every point on the graph is positive.\nC.The $y$-value of every point on the graph is an integer.\nD.The $y$-value of most points on the graph is positive, and the $y$-value at one point is 0.",
        "question_for_eval": "Consider the graph of the exponential function $y=4^{x}$. What can we say about the $y$-value of every point on the graph?\nChoices:\nA.The $y$-value of most points of the graph is greater than 1.\nB.The $y$-value of every point on the graph is positive.\nC.The $y$-value of every point on the graph is an integer.\nD.The $y$-value of most points on the graph is positive, and the $y$-value at one point is 0."
    },
    {
        "sample_index": "517",
        "problem_index": "517",
        "problem_version": "Text Only",
        "question": "Consider the graphs of the functions $y=4^{x}$ and $y=\\left(\\frac{1}{4}\\right)^{x}$. How would you describe the rate of increase of $y=4^{x}$ ?\nChoices:\nA.$y$ is increasing at a constant rate\nB.$y$ is increasing at a decreasing rate\nC.$y$ is increasing at an increasing rate",
        "image": "",
        "answer": "(C)",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Consider the graphs of the functions $y=4^{x}$ and $y=\\left(\\frac{1}{4}\\right)^{x}$. How would you describe the rate of increase of $y=4^{x}$ ?\nChoices:\nA.$y$ is increasing at a constant rate\nB.$y$ is increasing at a decreasing rate\nC.$y$ is increasing at an increasing rate",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Consider the graphs of the functions $y=4^{x}$ and $y=\\left(\\frac{1}{4}\\right)^{x}$. How would you describe the rate of increase of $y=4^{x}$ ?\nChoices:\nA.$y$ is increasing at a constant rate\nB.$y$ is increasing at a decreasing rate\nC.$y$ is increasing at an increasing rate",
        "question_for_eval": "Consider the graphs of the functions $y=4^{x}$ and $y=\\left(\\frac{1}{4}\\right)^{x}$. How would you describe the rate of increase of $y=4^{x}$ ?\nChoices:\nA.$y$ is increasing at a constant rate\nB.$y$ is increasing at a decreasing rate\nC.$y$ is increasing at an increasing rate"
    },
    {
        "sample_index": "518",
        "problem_index": "518",
        "problem_version": "Text Only",
        "question": "The graph of $y=2^{x}$ is displayed here, whose y-intercept=1 and all values > 0. Which single option below gives us the graph's domain?\nChoices:\nA.$x \\geq 0$\nB.$x>0$\nC.All real $x$\nD.$x<0$",
        "image": "",
        "answer": "(C)",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph of $y=2^{x}$ is displayed here, whose y-intercept=1 and all values > 0. Which single option below gives us the graph's domain?\nChoices:\nA.$x \\geq 0$\nB.$x>0$\nC.All real $x$\nD.$x<0$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph of $y=2^{x}$ is displayed here, whose y-intercept=1 and all values > 0. Which single option below gives us the graph's domain?\nChoices:\nA.$x \\geq 0$\nB.$x>0$\nC.All real $x$\nD.$x<0$",
        "question_for_eval": "The graph of $y=2^{x}$ is displayed here, whose y-intercept=1 and all values > 0. Which single option below gives us the graph's domain?\nChoices:\nA.$x \\geq 0$\nB.$x>0$\nC.All real $x$\nD.$x<0$"
    },
    {
        "sample_index": "519",
        "problem_index": "519",
        "problem_version": "Text Only",
        "question": "The function $f(x)=5 x-x^2$ in blue gives the number of mosquitos in the forest (in millions), and the function $g(x)=3 x-0.5 x^2$ in red gives the number of bats (in millions). In both equations $x$ represents rainfall (in centimeters). $g(x)$ goes through (0,0), (3,6), (6,0) and opens downward. $f(x)$ in blue goes through (0,0), (2,6), (3,6), (5,0) and opens downsward. When there is $0 \\mathrm{~cm}$ of rainfall, the number of mosquitos is the same as the number of bats. What is another rainfall amount where the number of mosquitos is the same as the number of bats?\nRound your answer to the nearest half centimeter.\n",
        "image": "",
        "answer": "4",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The function $f(x)=5 x-x^2$ in blue gives the number of mosquitos in the forest (in millions), and the function $g(x)=3 x-0.5 x^2$ in red gives the number of bats (in millions). In both equations $x$ represents rainfall (in centimeters). $g(x)$ goes through (0,0), (3,6), (6,0) and opens downward. $f(x)$ in blue goes through (0,0), (2,6), (3,6), (5,0) and opens downsward. When there is $0 \\mathrm{~cm}$ of rainfall, the number of mosquitos is the same as the number of bats. What is another rainfall amount where the number of mosquitos is the same as the number of bats?\nRound your answer to the nearest half centimeter.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The function $f(x)=5 x-x^2$ in blue gives the number of mosquitos in the forest (in millions), and the function $g(x)=3 x-0.5 x^2$ in red gives the number of bats (in millions). In both equations $x$ represents rainfall (in centimeters). $g(x)$ goes through (0,0), (3,6), (6,0) and opens downward. $f(x)$ in blue goes through (0,0), (2,6), (3,6), (5,0) and opens downsward. When there is $0 \\mathrm{~cm}$ of rainfall, the number of mosquitos is the same as the number of bats. What is another rainfall amount where the number of mosquitos is the same as the number of bats?\nRound your answer to the nearest half centimeter.\n",
        "question_for_eval": "The function $f(x)=5 x-x^2$ in blue gives the number of mosquitos in the forest (in millions), and the function $g(x)=3 x-0.5 x^2$ in red gives the number of bats (in millions). In both equations $x$ represents rainfall (in centimeters). $g(x)$ goes through (0,0), (3,6), (6,0) and opens downward. $f(x)$ in blue goes through (0,0), (2,6), (3,6), (5,0) and opens downsward. When there is $0 \\mathrm{~cm}$ of rainfall, the number of mosquitos is the same as the number of bats. What is another rainfall amount where the number of mosquitos is the same as the number of bats?\nRound your answer to the nearest half centimeter.\n"
    },
    {
        "sample_index": "520",
        "problem_index": "520",
        "problem_version": "Text Only",
        "question": "Esteban's account balance can be modeled by $f(t)=1000 \\cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \\cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?\nRound your answer to the nearest integer. \n",
        "image": "",
        "answer": "7",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Esteban's account balance can be modeled by $f(t)=1000 \\cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \\cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?\nRound your answer to the nearest integer. \n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Esteban's account balance can be modeled by $f(t)=1000 \\cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \\cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?\nRound your answer to the nearest integer. \n",
        "question_for_eval": "Esteban's account balance can be modeled by $f(t)=1000 \\cdot e^{(0.08 t)}$ and Anna's account balance can be modeled by $g(t)=750 \\cdot e^{(0.12 t)}$, where $t$ is the number of years since they opened their accounts. $f(x)$ in blue goes through (0,1000), (5,1500), and $g(x)$ in red goes through (6,1500), (8,2000). When do the accounts have the same balance?\nRound your answer to the nearest integer. \n"
    },
    {
        "sample_index": "521",
        "problem_index": "521",
        "problem_version": "Text Only",
        "question": "This is the graph of $y=x^3-x^2-x$ that goes through (-1,-1), (0,0), (1,-1), (2,2). Use the graph to determine how many solutions the equation $x^3-x^2-x=-2$ has.\nChoices:\nA.No solutions\nB.One solution\nC.Two solutions\nD.Three solutions",
        "image": "",
        "answer": "(B)",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: This is the graph of $y=x^3-x^2-x$ that goes through (-1,-1), (0,0), (1,-1), (2,2). Use the graph to determine how many solutions the equation $x^3-x^2-x=-2$ has.\nChoices:\nA.No solutions\nB.One solution\nC.Two solutions\nD.Three solutions",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: This is the graph of $y=x^3-x^2-x$ that goes through (-1,-1), (0,0), (1,-1), (2,2). Use the graph to determine how many solutions the equation $x^3-x^2-x=-2$ has.\nChoices:\nA.No solutions\nB.One solution\nC.Two solutions\nD.Three solutions",
        "question_for_eval": "This is the graph of $y=x^3-x^2-x$ that goes through (-1,-1), (0,0), (1,-1), (2,2). Use the graph to determine how many solutions the equation $x^3-x^2-x=-2$ has.\nChoices:\nA.No solutions\nB.One solution\nC.Two solutions\nD.Three solutions"
    },
    {
        "sample_index": "522",
        "problem_index": "522",
        "problem_version": "Text Only",
        "question": "This is the graph of $y=\\sqrt{6 x+7}$, which goes through (-1,1), (3,5), (5,6), (7,7). Use the graph to find an approximate solution to $\\sqrt{6 x+7}=6$. Round your answer to the nearest integer.\n",
        "image": "",
        "answer": "5",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: This is the graph of $y=\\sqrt{6 x+7}$, which goes through (-1,1), (3,5), (5,6), (7,7). Use the graph to find an approximate solution to $\\sqrt{6 x+7}=6$. Round your answer to the nearest integer.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: This is the graph of $y=\\sqrt{6 x+7}$, which goes through (-1,1), (3,5), (5,6), (7,7). Use the graph to find an approximate solution to $\\sqrt{6 x+7}=6$. Round your answer to the nearest integer.\n",
        "question_for_eval": "This is the graph of $y=\\sqrt{6 x+7}$, which goes through (-1,1), (3,5), (5,6), (7,7). Use the graph to find an approximate solution to $\\sqrt{6 x+7}=6$. Round your answer to the nearest integer.\n"
    },
    {
        "sample_index": "523",
        "problem_index": "523",
        "problem_version": "Text Only",
        "question": "Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?\nChoices:\nA.They mean that one airplane was initially higher than the other airplane.\nB.They mean that the airplanes reached the same height when they were both at 10,000 meters.\nC.They give the solutions to the equation $f(t)=0$.\nD.They give the solutions to the equation $f(t)=g(t)$.",
        "image": "",
        "answer": "(B)",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?\nChoices:\nA.They mean that one airplane was initially higher than the other airplane.\nB.They mean that the airplanes reached the same height when they were both at 10,000 meters.\nC.They give the solutions to the equation $f(t)=0$.\nD.They give the solutions to the equation $f(t)=g(t)$.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?\nChoices:\nA.They mean that one airplane was initially higher than the other airplane.\nB.They mean that the airplanes reached the same height when they were both at 10,000 meters.\nC.They give the solutions to the equation $f(t)=0$.\nD.They give the solutions to the equation $f(t)=g(t)$.",
        "question_for_eval": "Piecewise functions $f$ and $g$ can model the heights (in meters) of two airplanes. $g$ is purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), and $f$ is blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). $t$ is the number of minutes that have passed since noon at a local airport. Which statements represent the meaning of the intersection points of the graphs?\nChoices:\nA.They mean that one airplane was initially higher than the other airplane.\nB.They mean that the airplanes reached the same height when they were both at 10,000 meters.\nC.They give the solutions to the equation $f(t)=0$.\nD.They give the solutions to the equation $f(t)=g(t)$."
    },
    {
        "sample_index": "524",
        "problem_index": "524",
        "problem_version": "Text Only",
        "question": "There is a function representing a circle centered at the origin with a radius of 1 unit. Point A is on the circle. What is the value of the y-coordinate of point A?\nChoices:\nA:$\\sin \\left(0^{\\circ}\\right)$\nB:$\\cos \\left(0^{\\circ}\\right)$\nC:$\\sin \\left(90^{\\circ}\\right)$\nD:$\\cos \\left(90^{\\circ}\\right)$\nE:$\\hline \\sin \\left(270^{\\circ}\\right)$\nF:$\\cos \\left(270^{\\circ}\\right)$",
        "image": "",
        "answer": "E",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a function representing a circle centered at the origin with a radius of 1 unit. Point A is on the circle. What is the value of the y-coordinate of point A?\nChoices:\nA:$\\sin \\left(0^{\\circ}\\right)$\nB:$\\cos \\left(0^{\\circ}\\right)$\nC:$\\sin \\left(90^{\\circ}\\right)$\nD:$\\cos \\left(90^{\\circ}\\right)$\nE:$\\hline \\sin \\left(270^{\\circ}\\right)$\nF:$\\cos \\left(270^{\\circ}\\right)$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a function representing a circle centered at the origin with a radius of 1 unit. Point A is on the circle. What is the value of the y-coordinate of point A?\nChoices:\nA:$\\sin \\left(0^{\\circ}\\right)$\nB:$\\cos \\left(0^{\\circ}\\right)$\nC:$\\sin \\left(90^{\\circ}\\right)$\nD:$\\cos \\left(90^{\\circ}\\right)$\nE:$\\hline \\sin \\left(270^{\\circ}\\right)$\nF:$\\cos \\left(270^{\\circ}\\right)$",
        "question_for_eval": "There is a function representing a circle centered at the origin with a radius of 1 unit. Point A is on the circle. What is the value of the y-coordinate of point A?\nChoices:\nA:$\\sin \\left(0^{\\circ}\\right)$\nB:$\\cos \\left(0^{\\circ}\\right)$\nC:$\\sin \\left(90^{\\circ}\\right)$\nD:$\\cos \\left(90^{\\circ}\\right)$\nE:$\\hline \\sin \\left(270^{\\circ}\\right)$\nF:$\\cos \\left(270^{\\circ}\\right)$"
    },
    {
        "sample_index": "525",
        "problem_index": "525",
        "problem_version": "Text Only",
        "question": "There is a function representing a circle centered at the origin with a radius of 1 unit. Points A,B, and C are plotted on the unit circle. Which of the coordinates is equal to \\sin \\left(310^{\\circ}\\right) ?\nChoices:\nA:x-coordinate of point A\nB:y-coordinate of point A\nC:x-coordinate of point B\nD:y-coordinate of point B\nE:x-coordinate of point C\nF:y-coordinate of point C",
        "image": "",
        "answer": "F",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a function representing a circle centered at the origin with a radius of 1 unit. Points A,B, and C are plotted on the unit circle. Which of the coordinates is equal to \\sin \\left(310^{\\circ}\\right) ?\nChoices:\nA:x-coordinate of point A\nB:y-coordinate of point A\nC:x-coordinate of point B\nD:y-coordinate of point B\nE:x-coordinate of point C\nF:y-coordinate of point C",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a function representing a circle centered at the origin with a radius of 1 unit. Points A,B, and C are plotted on the unit circle. Which of the coordinates is equal to \\sin \\left(310^{\\circ}\\right) ?\nChoices:\nA:x-coordinate of point A\nB:y-coordinate of point A\nC:x-coordinate of point B\nD:y-coordinate of point B\nE:x-coordinate of point C\nF:y-coordinate of point C",
        "question_for_eval": "There is a function representing a circle centered at the origin with a radius of 1 unit. Points A,B, and C are plotted on the unit circle. Which of the coordinates is equal to \\sin \\left(310^{\\circ}\\right) ?\nChoices:\nA:x-coordinate of point A\nB:y-coordinate of point A\nC:x-coordinate of point B\nD:y-coordinate of point B\nE:x-coordinate of point C\nF:y-coordinate of point C"
    },
    {
        "sample_index": "526",
        "problem_index": "526",
        "problem_version": "Text Only",
        "question": "The function represents a circle centered at the origin with a radius of 1 unit. There is a point A with an angle to the negative x-axis of $50^\\circ$. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(50^{\\circ}\\right)$\nB:$\\cos \\left(50^{\\circ}\\right)$\nC:$\\sin \\left(140^{\\circ}\\right)$\nD:$\\cos \\left(140^{\\circ}\\right)$\nE:$\\sin \\left(230^{\\circ}\\right)$\nF:$\\cos \\left(230^{\\circ}\\right)$",
        "image": "",
        "answer": "F",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The function represents a circle centered at the origin with a radius of 1 unit. There is a point A with an angle to the negative x-axis of $50^\\circ$. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(50^{\\circ}\\right)$\nB:$\\cos \\left(50^{\\circ}\\right)$\nC:$\\sin \\left(140^{\\circ}\\right)$\nD:$\\cos \\left(140^{\\circ}\\right)$\nE:$\\sin \\left(230^{\\circ}\\right)$\nF:$\\cos \\left(230^{\\circ}\\right)$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The function represents a circle centered at the origin with a radius of 1 unit. There is a point A with an angle to the negative x-axis of $50^\\circ$. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(50^{\\circ}\\right)$\nB:$\\cos \\left(50^{\\circ}\\right)$\nC:$\\sin \\left(140^{\\circ}\\right)$\nD:$\\cos \\left(140^{\\circ}\\right)$\nE:$\\sin \\left(230^{\\circ}\\right)$\nF:$\\cos \\left(230^{\\circ}\\right)$",
        "question_for_eval": "The function represents a circle centered at the origin with a radius of 1 unit. There is a point A with an angle to the negative x-axis of $50^\\circ$. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(50^{\\circ}\\right)$\nB:$\\cos \\left(50^{\\circ}\\right)$\nC:$\\sin \\left(140^{\\circ}\\right)$\nD:$\\cos \\left(140^{\\circ}\\right)$\nE:$\\sin \\left(230^{\\circ}\\right)$\nF:$\\cos \\left(230^{\\circ}\\right)$"
    },
    {
        "sample_index": "527",
        "problem_index": "527",
        "problem_version": "Text Only",
        "question": "There is a function representing a circle centered at the origin with a radius of 1 unit. There is a point A on the circle with an angle of $\\frac{\\pi}{5}$ to the negative x-axis. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(\\frac{\\pi}{5}\\right)$\nB:$\\cos \\left(\\frac{\\pi}{5}\\right)$\nC:$\\sin \\left(\\frac{6 \\pi}{5}\\right)$\nD:$\\cos \\left(\\frac{6 \\pi}{5}\\right)$\nE:$\\sin \\left(\\frac{9 \\pi}{5}\\right)$\nF:$\\cos \\left(\\frac{9 \\pi}{5}\\right)$",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: There is a function representing a circle centered at the origin with a radius of 1 unit. There is a point A on the circle with an angle of $\\frac{\\pi}{5}$ to the negative x-axis. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(\\frac{\\pi}{5}\\right)$\nB:$\\cos \\left(\\frac{\\pi}{5}\\right)$\nC:$\\sin \\left(\\frac{6 \\pi}{5}\\right)$\nD:$\\cos \\left(\\frac{6 \\pi}{5}\\right)$\nE:$\\sin \\left(\\frac{9 \\pi}{5}\\right)$\nF:$\\cos \\left(\\frac{9 \\pi}{5}\\right)$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: There is a function representing a circle centered at the origin with a radius of 1 unit. There is a point A on the circle with an angle of $\\frac{\\pi}{5}$ to the negative x-axis. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(\\frac{\\pi}{5}\\right)$\nB:$\\cos \\left(\\frac{\\pi}{5}\\right)$\nC:$\\sin \\left(\\frac{6 \\pi}{5}\\right)$\nD:$\\cos \\left(\\frac{6 \\pi}{5}\\right)$\nE:$\\sin \\left(\\frac{9 \\pi}{5}\\right)$\nF:$\\cos \\left(\\frac{9 \\pi}{5}\\right)$",
        "question_for_eval": "There is a function representing a circle centered at the origin with a radius of 1 unit. There is a point A on the circle with an angle of $\\frac{\\pi}{5}$ to the negative x-axis. What is the value of the x-coordinate of point A?\nChoices:\nA:$\\sin \\left(\\frac{\\pi}{5}\\right)$\nB:$\\cos \\left(\\frac{\\pi}{5}\\right)$\nC:$\\sin \\left(\\frac{6 \\pi}{5}\\right)$\nD:$\\cos \\left(\\frac{6 \\pi}{5}\\right)$\nE:$\\sin \\left(\\frac{9 \\pi}{5}\\right)$\nF:$\\cos \\left(\\frac{9 \\pi}{5}\\right)$"
    },
    {
        "sample_index": "528",
        "problem_index": "528",
        "problem_version": "Text Only",
        "question": "Points $A, B$, and $C$ are plotted on the unit circle and also on the x-axis and y-axis. Which of the coordinates is equal to $\\cos (\\pi)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$",
        "image": "",
        "answer": "E",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Points $A, B$, and $C$ are plotted on the unit circle and also on the x-axis and y-axis. Which of the coordinates is equal to $\\cos (\\pi)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Points $A, B$, and $C$ are plotted on the unit circle and also on the x-axis and y-axis. Which of the coordinates is equal to $\\cos (\\pi)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$",
        "question_for_eval": "Points $A, B$, and $C$ are plotted on the unit circle and also on the x-axis and y-axis. Which of the coordinates is equal to $\\cos (\\pi)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$"
    },
    {
        "sample_index": "529",
        "problem_index": "529",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function with a yellow point labeled ($-\\frac{\\pi}{3},2). It has a maximum point at $\\left(-\\frac{\\pi}{3}, 2\\right)$ and an amplitude of 1.8 . What is the midline equation of the function?\n",
        "image": "",
        "answer": "0.2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function with a yellow point labeled ($-\\frac{\\pi}{3},2). It has a maximum point at $\\left(-\\frac{\\pi}{3}, 2\\right)$ and an amplitude of 1.8 . What is the midline equation of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function with a yellow point labeled ($-\\frac{\\pi}{3},2). It has a maximum point at $\\left(-\\frac{\\pi}{3}, 2\\right)$ and an amplitude of 1.8 . What is the midline equation of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function with a yellow point labeled ($-\\frac{\\pi}{3},2). It has a maximum point at $\\left(-\\frac{\\pi}{3}, 2\\right)$ and an amplitude of 1.8 . What is the midline equation of the function?\n"
    },
    {
        "sample_index": "530",
        "problem_index": "530",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the midline equation of the function?\n",
        "image": "",
        "answer": "-5.35",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the midline equation of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the midline equation of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the midline equation of the function?\n"
    },
    {
        "sample_index": "531",
        "problem_index": "531",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a maximum point at $(1.2,5.5)$ and an amplitude of 3.5 . What is the midline equation of the function?\n",
        "image": "",
        "answer": "2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $(1.2,5.5)$ and an amplitude of 3.5 . What is the midline equation of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $(1.2,5.5)$ and an amplitude of 3.5 . What is the midline equation of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a maximum point at $(1.2,5.5)$ and an amplitude of 3.5 . What is the midline equation of the function?\n"
    },
    {
        "sample_index": "532",
        "problem_index": "532",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the midline equation of the function? Give an exact expression.\n",
        "image": "",
        "answer": "7.7",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the midline equation of the function? Give an exact expression.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the midline equation of the function? Give an exact expression.\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the midline equation of the function? Give an exact expression.\n"
    },
    {
        "sample_index": "533",
        "problem_index": "533",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It intersects its midline at $(-3.5,-0.8)$, and it has a maximum point at $(4.1,0.7)$. What is the amplitude of the function?\n",
        "image": "",
        "answer": "1.5",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $(-3.5,-0.8)$, and it has a maximum point at $(4.1,0.7)$. What is the amplitude of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $(-3.5,-0.8)$, and it has a maximum point at $(4.1,0.7)$. What is the amplitude of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It intersects its midline at $(-3.5,-0.8)$, and it has a maximum point at $(4.1,0.7)$. What is the amplitude of the function?\n"
    },
    {
        "sample_index": "534",
        "problem_index": "534",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the amplitude of the function?\n",
        "image": "",
        "answer": "3.15",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the amplitude of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the amplitude of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the amplitude of the function?\n"
    },
    {
        "sample_index": "535",
        "problem_index": "535",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{2}{3} \\pi, 1.2\\right)$, and it has a minimum point at $\\left(\\frac{4}{3} \\pi,-3.4\\right)$. What is the amplitude of the function?\n",
        "image": "",
        "answer": "4.6",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{2}{3} \\pi, 1.2\\right)$, and it has a minimum point at $\\left(\\frac{4}{3} \\pi,-3.4\\right)$. What is the amplitude of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{2}{3} \\pi, 1.2\\right)$, and it has a minimum point at $\\left(\\frac{4}{3} \\pi,-3.4\\right)$. What is the amplitude of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{2}{3} \\pi, 1.2\\right)$, and it has a minimum point at $\\left(\\frac{4}{3} \\pi,-3.4\\right)$. What is the amplitude of the function?\n"
    },
    {
        "sample_index": "536",
        "problem_index": "536",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the amplitude of the function?\n",
        "image": "",
        "answer": "5.3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the amplitude of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the amplitude of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the amplitude of the function?\n"
    },
    {
        "sample_index": "537",
        "problem_index": "537",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the period of the function? Give an exact value.\n",
        "image": "",
        "answer": "\\pi",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the period of the function? Give an exact value.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the period of the function? Give an exact value.\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a maximum point at $\\left(\\frac{1}{4} \\pi,-2.2\\right)$ and a minimum point at $\\left(\\frac{3}{4} \\pi,-8.5\\right)$. What is the period of the function? Give an exact value.\n"
    },
    {
        "sample_index": "538",
        "problem_index": "538",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{3}{5} \\pi, 8\\right)$ and again at $\\left(\\frac{7}{5} \\pi, 8\\right)$. What is the period of the function? Give an exact value.\n",
        "image": "",
        "answer": "{8}{5} \\pi",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{3}{5} \\pi, 8\\right)$ and again at $\\left(\\frac{7}{5} \\pi, 8\\right)$. What is the period of the function? Give an exact value.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{3}{5} \\pi, 8\\right)$ and again at $\\left(\\frac{7}{5} \\pi, 8\\right)$. What is the period of the function? Give an exact value.\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It intersects its midline at $\\left(\\frac{3}{5} \\pi, 8\\right)$ and again at $\\left(\\frac{7}{5} \\pi, 8\\right)$. What is the period of the function? Give an exact value.\n"
    },
    {
        "sample_index": "539",
        "problem_index": "539",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the period of the function? Give an exact value.\n",
        "image": "",
        "answer": "4 \\pi",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the period of the function? Give an exact value.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the period of the function? Give an exact value.\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a minimum point at $\\left(-\\frac{1}{2} \\pi, 2.4\\right)$ and a maximum point at $\\left(\\frac{3}{2} \\pi, 13\\right)$. What is the period of the function? Give an exact value.\n"
    },
    {
        "sample_index": "540",
        "problem_index": "540",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It intersects its midline at $(1.25,-2.75)$ and it has a minimum point at $(4.75,-6.25)$. What is the period of the function? Give an exact value.\n$+\\stackrel{x}{=}$ units\n",
        "image": "",
        "answer": "14",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $(1.25,-2.75)$ and it has a minimum point at $(4.75,-6.25)$. What is the period of the function? Give an exact value.\n$+\\stackrel{x}{=}$ units\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $(1.25,-2.75)$ and it has a minimum point at $(4.75,-6.25)$. What is the period of the function? Give an exact value.\n$+\\stackrel{x}{=}$ units\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It intersects its midline at $(1.25,-2.75)$ and it has a minimum point at $(4.75,-6.25)$. What is the period of the function? Give an exact value.\n$+\\stackrel{x}{=}$ units\n"
    },
    {
        "sample_index": "541",
        "problem_index": "541",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It has a minimum point at $(1,1.5)$ and an amplitude of 1.5. What is the midline equation of the function?\n",
        "image": "",
        "answer": "3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $(1,1.5)$ and an amplitude of 1.5. What is the midline equation of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It has a minimum point at $(1,1.5)$ and an amplitude of 1.5. What is the midline equation of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It has a minimum point at $(1,1.5)$ and an amplitude of 1.5. What is the midline equation of the function?\n"
    },
    {
        "sample_index": "542",
        "problem_index": "542",
        "problem_version": "Text Only",
        "question": "Below is the graph of a trigonometric function. It intersects its midline at $\\left(-\\frac{1}{2} \\pi, 3.3\\right)$, and it has a maximum point at $(-2 \\pi, 9.8)$. What is the amplitude of the function?\n",
        "image": "",
        "answer": "6.5",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $\\left(-\\frac{1}{2} \\pi, 3.3\\right)$, and it has a maximum point at $(-2 \\pi, 9.8)$. What is the amplitude of the function?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Below is the graph of a trigonometric function. It intersects its midline at $\\left(-\\frac{1}{2} \\pi, 3.3\\right)$, and it has a maximum point at $(-2 \\pi, 9.8)$. What is the amplitude of the function?\n",
        "question_for_eval": "Below is the graph of a trigonometric function. It intersects its midline at $\\left(-\\frac{1}{2} \\pi, 3.3\\right)$, and it has a maximum point at $(-2 \\pi, 9.8)$. What is the amplitude of the function?\n"
    },
    {
        "sample_index": "543",
        "problem_index": "543",
        "problem_version": "Text Only",
        "question": "$f$ is a trigonometric function of the form $f(x)=a \\cos (b x+c)+d$.\nBelow is the graph of $f(x)$. The function has a maximum point at $(-2,-3)$ and a minimum point at $(-2.5,-9)$. Find a formula for $f(x)$. Give an exact expression.\n",
        "image": "",
        "answer": "3 \\cos (2 \\pi x+4 \\pi)-6",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: $f$ is a trigonometric function of the form $f(x)=a \\cos (b x+c)+d$.\nBelow is the graph of $f(x)$. The function has a maximum point at $(-2,-3)$ and a minimum point at $(-2.5,-9)$. Find a formula for $f(x)$. Give an exact expression.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: $f$ is a trigonometric function of the form $f(x)=a \\cos (b x+c)+d$.\nBelow is the graph of $f(x)$. The function has a maximum point at $(-2,-3)$ and a minimum point at $(-2.5,-9)$. Find a formula for $f(x)$. Give an exact expression.\n",
        "question_for_eval": "$f$ is a trigonometric function of the form $f(x)=a \\cos (b x+c)+d$.\nBelow is the graph of $f(x)$. The function has a maximum point at $(-2,-3)$ and a minimum point at $(-2.5,-9)$. Find a formula for $f(x)$. Give an exact expression.\n"
    },
    {
        "sample_index": "544",
        "problem_index": "544",
        "problem_version": "Text Only",
        "question": "Kai is swinging on a trapeze in a circus show. The horizontal distance between Kai and the edge of the stage, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (5,21) to (15,21). What is the meaning of the highlighted segment?\nChoices:\nA:Kai completes 10 swing cycles per second.\nB:The trapeze is hung $\\mathbf{1 0}$ meters from the edge of the stage.\nC:Kai completes a single swing cycle in 10 seconds.\nD:The trapeze is $\\mathbf{1 0}$ meters long.",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Kai is swinging on a trapeze in a circus show. The horizontal distance between Kai and the edge of the stage, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (5,21) to (15,21). What is the meaning of the highlighted segment?\nChoices:\nA:Kai completes 10 swing cycles per second.\nB:The trapeze is hung $\\mathbf{1 0}$ meters from the edge of the stage.\nC:Kai completes a single swing cycle in 10 seconds.\nD:The trapeze is $\\mathbf{1 0}$ meters long.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Kai is swinging on a trapeze in a circus show. The horizontal distance between Kai and the edge of the stage, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (5,21) to (15,21). What is the meaning of the highlighted segment?\nChoices:\nA:Kai completes 10 swing cycles per second.\nB:The trapeze is hung $\\mathbf{1 0}$ meters from the edge of the stage.\nC:Kai completes a single swing cycle in 10 seconds.\nD:The trapeze is $\\mathbf{1 0}$ meters long.",
        "question_for_eval": "Kai is swinging on a trapeze in a circus show. The horizontal distance between Kai and the edge of the stage, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (5,21) to (15,21). What is the meaning of the highlighted segment?\nChoices:\nA:Kai completes 10 swing cycles per second.\nB:The trapeze is hung $\\mathbf{1 0}$ meters from the edge of the stage.\nC:Kai completes a single swing cycle in 10 seconds.\nD:The trapeze is $\\mathbf{1 0}$ meters long."
    },
    {
        "sample_index": "545",
        "problem_index": "545",
        "problem_version": "Text Only",
        "question": "Sia is swinging from a chandelier. The horizontal distance between Sia and the wall, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (3.75,3), (3.75,5). What is the meaning of the highlighted segment?\nChoices:\nA:The chandelier is hung 2 meters from the wall.\nB:The furthest Sia gets from the point where the chandelier hangs is 2 meters.\nC:The chandelier is 2 meters wide.\nD:Sia completes 2 swing cycles per second.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Sia is swinging from a chandelier. The horizontal distance between Sia and the wall, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (3.75,3), (3.75,5). What is the meaning of the highlighted segment?\nChoices:\nA:The chandelier is hung 2 meters from the wall.\nB:The furthest Sia gets from the point where the chandelier hangs is 2 meters.\nC:The chandelier is 2 meters wide.\nD:Sia completes 2 swing cycles per second.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Sia is swinging from a chandelier. The horizontal distance between Sia and the wall, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (3.75,3), (3.75,5). What is the meaning of the highlighted segment?\nChoices:\nA:The chandelier is hung 2 meters from the wall.\nB:The furthest Sia gets from the point where the chandelier hangs is 2 meters.\nC:The chandelier is 2 meters wide.\nD:Sia completes 2 swing cycles per second.",
        "question_for_eval": "Sia is swinging from a chandelier. The horizontal distance between Sia and the wall, in meters, is modeled by $D(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (3.75,3), (3.75,5). What is the meaning of the highlighted segment?\nChoices:\nA:The chandelier is hung 2 meters from the wall.\nB:The furthest Sia gets from the point where the chandelier hangs is 2 meters.\nC:The chandelier is 2 meters wide.\nD:Sia completes 2 swing cycles per second."
    },
    {
        "sample_index": "546",
        "problem_index": "546",
        "problem_version": "Text Only",
        "question": "A fly is standing on a bike wheel in motion. The vertical distance between the fly and the ground, in centimeters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (1,50) to (5,50). What is the meaning of the highlighted segment?\nChoices:\nA:The wheel completes a single cycle in 4 seconds.\nB:The height of the wheel's center is 4 centimeters.\nC:The radius of the wheel is 4 centimeters.\nD:The bike's speed is 4 centimeters per second.",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A fly is standing on a bike wheel in motion. The vertical distance between the fly and the ground, in centimeters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (1,50) to (5,50). What is the meaning of the highlighted segment?\nChoices:\nA:The wheel completes a single cycle in 4 seconds.\nB:The height of the wheel's center is 4 centimeters.\nC:The radius of the wheel is 4 centimeters.\nD:The bike's speed is 4 centimeters per second.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A fly is standing on a bike wheel in motion. The vertical distance between the fly and the ground, in centimeters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (1,50) to (5,50). What is the meaning of the highlighted segment?\nChoices:\nA:The wheel completes a single cycle in 4 seconds.\nB:The height of the wheel's center is 4 centimeters.\nC:The radius of the wheel is 4 centimeters.\nD:The bike's speed is 4 centimeters per second.",
        "question_for_eval": "A fly is standing on a bike wheel in motion. The vertical distance between the fly and the ground, in centimeters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted, a red double arrow from (1,50) to (5,50). What is the meaning of the highlighted segment?\nChoices:\nA:The wheel completes a single cycle in 4 seconds.\nB:The height of the wheel's center is 4 centimeters.\nC:The radius of the wheel is 4 centimeters.\nD:The bike's speed is 4 centimeters per second."
    },
    {
        "sample_index": "547",
        "problem_index": "547",
        "problem_version": "Text Only",
        "question": "$h$ is a trigonometric function of the form $h(x)=a \\cos (b x+c)+d$. Below is the graph of $h(x)$. The function has a maximum point at $(-2 \\pi, 3)$ and a minimum point at $\\left(-\\frac{\\pi}{2},-4\\right)$. Find a formula for $h(x)$. Give an exact expression.\n",
        "image": "",
        "answer": "3.5 \\cos \\left(\\frac{2}{3} x+\\frac{4 \\pi}{3}\\right)-0.5",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: $h$ is a trigonometric function of the form $h(x)=a \\cos (b x+c)+d$. Below is the graph of $h(x)$. The function has a maximum point at $(-2 \\pi, 3)$ and a minimum point at $\\left(-\\frac{\\pi}{2},-4\\right)$. Find a formula for $h(x)$. Give an exact expression.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: $h$ is a trigonometric function of the form $h(x)=a \\cos (b x+c)+d$. Below is the graph of $h(x)$. The function has a maximum point at $(-2 \\pi, 3)$ and a minimum point at $\\left(-\\frac{\\pi}{2},-4\\right)$. Find a formula for $h(x)$. Give an exact expression.\n",
        "question_for_eval": "$h$ is a trigonometric function of the form $h(x)=a \\cos (b x+c)+d$. Below is the graph of $h(x)$. The function has a maximum point at $(-2 \\pi, 3)$ and a minimum point at $\\left(-\\frac{\\pi}{2},-4\\right)$. Find a formula for $h(x)$. Give an exact expression.\n"
    },
    {
        "sample_index": "548",
        "problem_index": "548",
        "problem_version": "Text Only",
        "question": "Emile is observing a wind turbine. The vertical distance between the ground and the tip of one of the turbine's blades, in meters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted. What is the meaning of the highlighted segment?\nChoices:\nA:The turbine's center is 35 meters above the ground.\nB:The turbine completes a single cycle in 35 seconds.\nC:The length of the blade is 35 meters.\nD:The turbine has 35 blades.",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Emile is observing a wind turbine. The vertical distance between the ground and the tip of one of the turbine's blades, in meters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted. What is the meaning of the highlighted segment?\nChoices:\nA:The turbine's center is 35 meters above the ground.\nB:The turbine completes a single cycle in 35 seconds.\nC:The length of the blade is 35 meters.\nD:The turbine has 35 blades.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Emile is observing a wind turbine. The vertical distance between the ground and the tip of one of the turbine's blades, in meters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted. What is the meaning of the highlighted segment?\nChoices:\nA:The turbine's center is 35 meters above the ground.\nB:The turbine completes a single cycle in 35 seconds.\nC:The length of the blade is 35 meters.\nD:The turbine has 35 blades.",
        "question_for_eval": "Emile is observing a wind turbine. The vertical distance between the ground and the tip of one of the turbine's blades, in meters, is modeled by $H(t)$ where $t$ is the time in seconds. The function is graphed below, along with one segment highlighted. What is the meaning of the highlighted segment?\nChoices:\nA:The turbine's center is 35 meters above the ground.\nB:The turbine completes a single cycle in 35 seconds.\nC:The length of the blade is 35 meters.\nD:The turbine has 35 blades."
    },
    {
        "sample_index": "549",
        "problem_index": "549",
        "problem_version": "Text Only",
        "question": "Takoda is watching the tides off the coast of Cape Cod. For two days, Takoda records the height of the water, $h$, in feet. His results are shown in the graph below, where $t$ corresponds to the number of hours after 12:00 a.m. According to Takoda's research, approximately how much time passes between two consecutive high tides?\n",
        "image": "",
        "answer": "12.5",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Takoda is watching the tides off the coast of Cape Cod. For two days, Takoda records the height of the water, $h$, in feet. His results are shown in the graph below, where $t$ corresponds to the number of hours after 12:00 a.m. According to Takoda's research, approximately how much time passes between two consecutive high tides?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Takoda is watching the tides off the coast of Cape Cod. For two days, Takoda records the height of the water, $h$, in feet. His results are shown in the graph below, where $t$ corresponds to the number of hours after 12:00 a.m. According to Takoda's research, approximately how much time passes between two consecutive high tides?\n",
        "question_for_eval": "Takoda is watching the tides off the coast of Cape Cod. For two days, Takoda records the height of the water, $h$, in feet. His results are shown in the graph below, where $t$ corresponds to the number of hours after 12:00 a.m. According to Takoda's research, approximately how much time passes between two consecutive high tides?\n"
    },
    {
        "sample_index": "550",
        "problem_index": "550",
        "problem_version": "Text Only",
        "question": "Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden. The graph below represents the widths that correspond to possible lengths of Lea's garden, which decreases when $w$ increases and goes through (5,20), (10,10), (20,5). As the possible width of Lea's garden increases, what does its possible length approach?\nChoices:\nA:$\\infty$\nB:$\\hline 0$\nC:$\\hline 10$\nD:$\\hline 120$",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden. The graph below represents the widths that correspond to possible lengths of Lea's garden, which decreases when $w$ increases and goes through (5,20), (10,10), (20,5). As the possible width of Lea's garden increases, what does its possible length approach?\nChoices:\nA:$\\infty$\nB:$\\hline 0$\nC:$\\hline 10$\nD:$\\hline 120$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden. The graph below represents the widths that correspond to possible lengths of Lea's garden, which decreases when $w$ increases and goes through (5,20), (10,10), (20,5). As the possible width of Lea's garden increases, what does its possible length approach?\nChoices:\nA:$\\infty$\nB:$\\hline 0$\nC:$\\hline 10$\nD:$\\hline 120$",
        "question_for_eval": "Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden. The graph below represents the widths that correspond to possible lengths of Lea's garden, which decreases when $w$ increases and goes through (5,20), (10,10), (20,5). As the possible width of Lea's garden increases, what does its possible length approach?\nChoices:\nA:$\\infty$\nB:$\\hline 0$\nC:$\\hline 10$\nD:$\\hline 120$"
    },
    {
        "sample_index": "551",
        "problem_index": "551",
        "problem_version": "Text Only",
        "question": "Catalina opened a new restaurant. She modeled the relationship between the number of months $T$ since she opened the restaurant and its profit $P$ (in dollars, measured as income minus expenses) as\n$$\nP=80(T-4)^2-300 \\text {. }\n$$ She wanted to create a graph to show the restaurant's profits over the first year. From month=0 to month=2, the profit decreases when months increase. From month=6 to month =13, profit increases when months increase. Here is her work: What mistakes did Catalina make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Catalina didn't make any mistake",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Catalina opened a new restaurant. She modeled the relationship between the number of months $T$ since she opened the restaurant and its profit $P$ (in dollars, measured as income minus expenses) as\n$$\nP=80(T-4)^2-300 \\text {. }\n$$ She wanted to create a graph to show the restaurant's profits over the first year. From month=0 to month=2, the profit decreases when months increase. From month=6 to month =13, profit increases when months increase. Here is her work: What mistakes did Catalina make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Catalina didn't make any mistake",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Catalina opened a new restaurant. She modeled the relationship between the number of months $T$ since she opened the restaurant and its profit $P$ (in dollars, measured as income minus expenses) as\n$$\nP=80(T-4)^2-300 \\text {. }\n$$ She wanted to create a graph to show the restaurant's profits over the first year. From month=0 to month=2, the profit decreases when months increase. From month=6 to month =13, profit increases when months increase. Here is her work: What mistakes did Catalina make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Catalina didn't make any mistake",
        "question_for_eval": "Catalina opened a new restaurant. She modeled the relationship between the number of months $T$ since she opened the restaurant and its profit $P$ (in dollars, measured as income minus expenses) as\n$$\nP=80(T-4)^2-300 \\text {. }\n$$ She wanted to create a graph to show the restaurant's profits over the first year. From month=0 to month=2, the profit decreases when months increase. From month=6 to month =13, profit increases when months increase. Here is her work: What mistakes did Catalina make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Catalina didn't make any mistake"
    },
    {
        "sample_index": "552",
        "problem_index": "552",
        "problem_version": "Text Only",
        "question": "Ashlynn models the relationship between the temperature $C$ of a hot cup of tea (in degrees Celsius) and time $T$ since the tea was poured into the cup (in minutes) as $C=20+20 \\cdot 0.88^T$. The temperature decreases when time increases, and passes points(0, 40). She wanted to graph the relationship over the first half hour. Here is her work: What mistakes did Ashlynn make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Ashlynn didn't make any mistake",
        "image": "",
        "answer": "E",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Ashlynn models the relationship between the temperature $C$ of a hot cup of tea (in degrees Celsius) and time $T$ since the tea was poured into the cup (in minutes) as $C=20+20 \\cdot 0.88^T$. The temperature decreases when time increases, and passes points(0, 40). She wanted to graph the relationship over the first half hour. Here is her work: What mistakes did Ashlynn make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Ashlynn didn't make any mistake",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Ashlynn models the relationship between the temperature $C$ of a hot cup of tea (in degrees Celsius) and time $T$ since the tea was poured into the cup (in minutes) as $C=20+20 \\cdot 0.88^T$. The temperature decreases when time increases, and passes points(0, 40). She wanted to graph the relationship over the first half hour. Here is her work: What mistakes did Ashlynn make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Ashlynn didn't make any mistake",
        "question_for_eval": "Ashlynn models the relationship between the temperature $C$ of a hot cup of tea (in degrees Celsius) and time $T$ since the tea was poured into the cup (in minutes) as $C=20+20 \\cdot 0.88^T$. The temperature decreases when time increases, and passes points(0, 40). She wanted to graph the relationship over the first half hour. Here is her work: What mistakes did Ashlynn make when drawing the graph?\nChoices:\nA:Inappropriate scale for $x$-axis\nB:Inappropriate scale for $y$-axis\nC:Wrong/missing label for $x$-axis\nD:Wrong/missing label for $y$-axis\nE:Ashlynn didn't make any mistake"
    },
    {
        "sample_index": "553",
        "problem_index": "553",
        "problem_version": "Text Only",
        "question": "Points $A, B$, and $C$ are plotted on the unit circle, the eqution of which is $x^2+y^2=1$. Which of the coordinates is equal to $\\sin \\left(200^{\\circ}\\right)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Points $A, B$, and $C$ are plotted on the unit circle, the eqution of which is $x^2+y^2=1$. Which of the coordinates is equal to $\\sin \\left(200^{\\circ}\\right)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Points $A, B$, and $C$ are plotted on the unit circle, the eqution of which is $x^2+y^2=1$. Which of the coordinates is equal to $\\sin \\left(200^{\\circ}\\right)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$",
        "question_for_eval": "Points $A, B$, and $C$ are plotted on the unit circle, the eqution of which is $x^2+y^2=1$. Which of the coordinates is equal to $\\sin \\left(200^{\\circ}\\right)$ ?\nChoices:\nA:$x$-coordinate of point $A$\nB:$y$-coordinate of point $A$\nC:$x$-coordinate of point $B$\nD:$y$-coordinate of point $B$\nE:$x$-coordinate of point $C$\nF:$y$-coordinate of point $C$"
    },
    {
        "sample_index": "554",
        "problem_index": "554",
        "problem_version": "Text Only",
        "question": "A polynomial $p$ is graphed, which goes through (-2.5,0), (-1,0), (3,0). What could be the equation of $p$ ?\nChoices:\nA:$p(x)=(x+1)^2(2 x+5)^2(x-3)^2$\nB:$p(x)=(x+1)^2(2 x+5)(x-3)^2$\nC:$p(x)=(x+1)^2(2 x+5)(x-3)$\nD:$p(x)=(x+1)(2 x+5)(x-3)^2$",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A polynomial $p$ is graphed, which goes through (-2.5,0), (-1,0), (3,0). What could be the equation of $p$ ?\nChoices:\nA:$p(x)=(x+1)^2(2 x+5)^2(x-3)^2$\nB:$p(x)=(x+1)^2(2 x+5)(x-3)^2$\nC:$p(x)=(x+1)^2(2 x+5)(x-3)$\nD:$p(x)=(x+1)(2 x+5)(x-3)^2$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A polynomial $p$ is graphed, which goes through (-2.5,0), (-1,0), (3,0). What could be the equation of $p$ ?\nChoices:\nA:$p(x)=(x+1)^2(2 x+5)^2(x-3)^2$\nB:$p(x)=(x+1)^2(2 x+5)(x-3)^2$\nC:$p(x)=(x+1)^2(2 x+5)(x-3)$\nD:$p(x)=(x+1)(2 x+5)(x-3)^2$",
        "question_for_eval": "A polynomial $p$ is graphed, which goes through (-2.5,0), (-1,0), (3,0). What could be the equation of $p$ ?\nChoices:\nA:$p(x)=(x+1)^2(2 x+5)^2(x-3)^2$\nB:$p(x)=(x+1)^2(2 x+5)(x-3)^2$\nC:$p(x)=(x+1)^2(2 x+5)(x-3)$\nD:$p(x)=(x+1)(2 x+5)(x-3)^2$"
    },
    {
        "sample_index": "555",
        "problem_index": "555",
        "problem_version": "Text Only",
        "question": "On the following unit circle, an acute angle $\\theta$ is formed by a radius and x-axis.. Which two of the following expressions are OPPOSITE of $\\cos (\\theta)$ ? Choose 2 answers:\nChoices:\nA:$\\cos (\\pi+\\theta)$\nB:$\\cos \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\cos (\\pi-\\theta)$\nD:$\\cos (2 \\pi-\\theta)$",
        "image": "",
        "answer": "A\nC",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: On the following unit circle, an acute angle $\\theta$ is formed by a radius and x-axis.. Which two of the following expressions are OPPOSITE of $\\cos (\\theta)$ ? Choose 2 answers:\nChoices:\nA:$\\cos (\\pi+\\theta)$\nB:$\\cos \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\cos (\\pi-\\theta)$\nD:$\\cos (2 \\pi-\\theta)$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: On the following unit circle, an acute angle $\\theta$ is formed by a radius and x-axis.. Which two of the following expressions are OPPOSITE of $\\cos (\\theta)$ ? Choose 2 answers:\nChoices:\nA:$\\cos (\\pi+\\theta)$\nB:$\\cos \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\cos (\\pi-\\theta)$\nD:$\\cos (2 \\pi-\\theta)$",
        "question_for_eval": "On the following unit circle, an acute angle $\\theta$ is formed by a radius and x-axis.. Which two of the following expressions are OPPOSITE of $\\cos (\\theta)$ ? Choose 2 answers:\nChoices:\nA:$\\cos (\\pi+\\theta)$\nB:$\\cos \\left(\\frac{\\pi}{2}-\\theta\\right)$\nC:$\\cos (\\pi-\\theta)$\nD:$\\cos (2 \\pi-\\theta)$"
    },
    {
        "sample_index": "556",
        "problem_index": "556",
        "problem_version": "Text Only",
        "question": "On the following unit circle, $\\theta$ is in radians and $\\tan (\\theta)=\\frac{0.98}{0.2}=4.9$. Without a calculator, evaluate the following expressions to the nearest hundredth or as an exact ratio.\n",
        "image": "",
        "answer": "-4.9\n-4.9",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: On the following unit circle, $\\theta$ is in radians and $\\tan (\\theta)=\\frac{0.98}{0.2}=4.9$. Without a calculator, evaluate the following expressions to the nearest hundredth or as an exact ratio.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: On the following unit circle, $\\theta$ is in radians and $\\tan (\\theta)=\\frac{0.98}{0.2}=4.9$. Without a calculator, evaluate the following expressions to the nearest hundredth or as an exact ratio.\n",
        "question_for_eval": "On the following unit circle, $\\theta$ is in radians and $\\tan (\\theta)=\\frac{0.98}{0.2}=4.9$. Without a calculator, evaluate the following expressions to the nearest hundredth or as an exact ratio.\n"
    },
    {
        "sample_index": "557",
        "problem_index": "557",
        "problem_version": "Text Only",
        "question": "There are two piecewise functions in the graph. Line $y=g(x)$ is a purple line and line $y=f(x)$ is a blue line. The range of $g(x)$ is (-2,6) and the range of $f(x)$ is (-5,1). 10 \\cdot f(7) + 9 \\cdot g(-1) =\n",
        "image": "",
        "answer": "-1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There are two piecewise functions in the graph. Line $y=g(x)$ is a purple line and line $y=f(x)$ is a blue line. The range of $g(x)$ is (-2,6) and the range of $f(x)$ is (-5,1). 10 \\cdot f(7) + 9 \\cdot g(-1) =\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There are two piecewise functions in the graph. Line $y=g(x)$ is a purple line and line $y=f(x)$ is a blue line. The range of $g(x)$ is (-2,6) and the range of $f(x)$ is (-5,1). 10 \\cdot f(7) + 9 \\cdot g(-1) =\n",
        "question_for_eval": "There are two piecewise functions in the graph. Line $y=g(x)$ is a purple line and line $y=f(x)$ is a blue line. The range of $g(x)$ is (-2,6) and the range of $f(x)$ is (-5,1). 10 \\cdot f(7) + 9 \\cdot g(-1) =\n"
    },
    {
        "sample_index": "558",
        "problem_index": "558",
        "problem_version": "Text Only",
        "question": "h is a piecewise function, and goes through (-5,4), (3,3), (0,7), (3,1), (5,-5). What is the domain of h?\nChoices:\nA:-5 \\leq x \\leq 7\nB:-5 \\leq x \\leq 4\nC:-5 \\leq x \\leq 5\nD:-5 \\leq x \\leq 6",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: h is a piecewise function, and goes through (-5,4), (3,3), (0,7), (3,1), (5,-5). What is the domain of h?\nChoices:\nA:-5 \\leq x \\leq 7\nB:-5 \\leq x \\leq 4\nC:-5 \\leq x \\leq 5\nD:-5 \\leq x \\leq 6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: h is a piecewise function, and goes through (-5,4), (3,3), (0,7), (3,1), (5,-5). What is the domain of h?\nChoices:\nA:-5 \\leq x \\leq 7\nB:-5 \\leq x \\leq 4\nC:-5 \\leq x \\leq 5\nD:-5 \\leq x \\leq 6",
        "question_for_eval": "h is a piecewise function, and goes through (-5,4), (3,3), (0,7), (3,1), (5,-5). What is the domain of h?\nChoices:\nA:-5 \\leq x \\leq 7\nB:-5 \\leq x \\leq 4\nC:-5 \\leq x \\leq 5\nD:-5 \\leq x \\leq 6"
    },
    {
        "sample_index": "559",
        "problem_index": "559",
        "problem_version": "Text Only",
        "question": "g is a piecewise function. One segment is from (-5,0) to (-2,9). Another segment is from (-2,9) to (4,-4). What is the range of g?\nChoices:\nA:-4 \\leq g(x) \\leq 9\nB:The $g(x)$-values $-5,-2,1,3$, and 4\nC:The $g(x)$-values $-4,0$, and 9\nD:-5 \\leq g(x) \\leq 4",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: g is a piecewise function. One segment is from (-5,0) to (-2,9). Another segment is from (-2,9) to (4,-4). What is the range of g?\nChoices:\nA:-4 \\leq g(x) \\leq 9\nB:The $g(x)$-values $-5,-2,1,3$, and 4\nC:The $g(x)$-values $-4,0$, and 9\nD:-5 \\leq g(x) \\leq 4",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: g is a piecewise function. One segment is from (-5,0) to (-2,9). Another segment is from (-2,9) to (4,-4). What is the range of g?\nChoices:\nA:-4 \\leq g(x) \\leq 9\nB:The $g(x)$-values $-5,-2,1,3$, and 4\nC:The $g(x)$-values $-4,0$, and 9\nD:-5 \\leq g(x) \\leq 4",
        "question_for_eval": "g is a piecewise function. One segment is from (-5,0) to (-2,9). Another segment is from (-2,9) to (4,-4). What is the range of g?\nChoices:\nA:-4 \\leq g(x) \\leq 9\nB:The $g(x)$-values $-5,-2,1,3$, and 4\nC:The $g(x)$-values $-4,0$, and 9\nD:-5 \\leq g(x) \\leq 4"
    },
    {
        "sample_index": "560",
        "problem_index": "560",
        "problem_version": "Text Only",
        "question": "This is a quadratic function. The y-axis labels mosquitoes (millions), and x-axis labels rainfall (centimeters). The vertex of the function is (2,4) and the function intersects with x-axis at (0,0) and (4,0). Which of these statements are true?\nChoices:\nA:The largest possible number of mosquitoes is 2 million mosquitoes.\nB:The largest possible number of mosquitoes is 4 million mosquitoes.\nC:More rainfall always relates to less mosquitoes.\nD:More rainfall relates to less mosquitoes as long as rainfall is less than $2 \\mathrm{~cm}$.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: This is a quadratic function. The y-axis labels mosquitoes (millions), and x-axis labels rainfall (centimeters). The vertex of the function is (2,4) and the function intersects with x-axis at (0,0) and (4,0). Which of these statements are true?\nChoices:\nA:The largest possible number of mosquitoes is 2 million mosquitoes.\nB:The largest possible number of mosquitoes is 4 million mosquitoes.\nC:More rainfall always relates to less mosquitoes.\nD:More rainfall relates to less mosquitoes as long as rainfall is less than $2 \\mathrm{~cm}$.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: This is a quadratic function. The y-axis labels mosquitoes (millions), and x-axis labels rainfall (centimeters). The vertex of the function is (2,4) and the function intersects with x-axis at (0,0) and (4,0). Which of these statements are true?\nChoices:\nA:The largest possible number of mosquitoes is 2 million mosquitoes.\nB:The largest possible number of mosquitoes is 4 million mosquitoes.\nC:More rainfall always relates to less mosquitoes.\nD:More rainfall relates to less mosquitoes as long as rainfall is less than $2 \\mathrm{~cm}$.",
        "question_for_eval": "This is a quadratic function. The y-axis labels mosquitoes (millions), and x-axis labels rainfall (centimeters). The vertex of the function is (2,4) and the function intersects with x-axis at (0,0) and (4,0). Which of these statements are true?\nChoices:\nA:The largest possible number of mosquitoes is 2 million mosquitoes.\nB:The largest possible number of mosquitoes is 4 million mosquitoes.\nC:More rainfall always relates to less mosquitoes.\nD:More rainfall relates to less mosquitoes as long as rainfall is less than $2 \\mathrm{~cm}$."
    },
    {
        "sample_index": "561",
        "problem_index": "561",
        "problem_version": "Text Only",
        "question": "Quadratic function g opens downward, and goes through (4,-5), (8,-5) with a vertex (6,-1). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Quadratic function g opens downward, and goes through (4,-5), (8,-5) with a vertex (6,-1). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Quadratic function g opens downward, and goes through (4,-5), (8,-5) with a vertex (6,-1). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "question_for_eval": "Quadratic function g opens downward, and goes through (4,-5), (8,-5) with a vertex (6,-1). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative"
    },
    {
        "sample_index": "562",
        "problem_index": "562",
        "problem_version": "Text Only",
        "question": "Quadratic function g opens upward, and goes through (2,4), (6,4) with a vertex of (4,0). Is the discriminant of f positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Quadratic function g opens upward, and goes through (2,4), (6,4) with a vertex of (4,0). Is the discriminant of f positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Quadratic function g opens upward, and goes through (2,4), (6,4) with a vertex of (4,0). Is the discriminant of f positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "question_for_eval": "Quadratic function g opens upward, and goes through (2,4), (6,4) with a vertex of (4,0). Is the discriminant of f positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative"
    },
    {
        "sample_index": "563",
        "problem_index": "563",
        "problem_version": "Text Only",
        "question": "Quadratic function g opens downward, and goes through (-1,-4), (-5,-4) with a vertex of (-3,0). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Quadratic function g opens downward, and goes through (-1,-4), (-5,-4) with a vertex of (-3,0). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Quadratic function g opens downward, and goes through (-1,-4), (-5,-4) with a vertex of (-3,0). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative",
        "question_for_eval": "Quadratic function g opens downward, and goes through (-1,-4), (-5,-4) with a vertex of (-3,0). Is the discriminant of g positive, zero, or negative?\nChoices:\nA:Positivie\nB:Zero\nC:Negative"
    },
    {
        "sample_index": "564",
        "problem_index": "564",
        "problem_version": "Text Only",
        "question": "g(x) is shown in the figure, which is a quadratic function going through (0,7), (-4,7) with a vertex (-2,3). f(x)=4(x-5)^2+2. Which function has a greater minimum?\nChoices:\nA:$f$ has a greater minimum than $g$.\nB:$g$ has a greater minimum than $f$.\nC:$f$ and $g$ share the same minimum.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: g(x) is shown in the figure, which is a quadratic function going through (0,7), (-4,7) with a vertex (-2,3). f(x)=4(x-5)^2+2. Which function has a greater minimum?\nChoices:\nA:$f$ has a greater minimum than $g$.\nB:$g$ has a greater minimum than $f$.\nC:$f$ and $g$ share the same minimum.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: g(x) is shown in the figure, which is a quadratic function going through (0,7), (-4,7) with a vertex (-2,3). f(x)=4(x-5)^2+2. Which function has a greater minimum?\nChoices:\nA:$f$ has a greater minimum than $g$.\nB:$g$ has a greater minimum than $f$.\nC:$f$ and $g$ share the same minimum.",
        "question_for_eval": "g(x) is shown in the figure, which is a quadratic function going through (0,7), (-4,7) with a vertex (-2,3). f(x)=4(x-5)^2+2. Which function has a greater minimum?\nChoices:\nA:$f$ has a greater minimum than $g$.\nB:$g$ has a greater minimum than $f$.\nC:$f$ and $g$ share the same minimum."
    },
    {
        "sample_index": "565",
        "problem_index": "565",
        "problem_version": "Text Only",
        "question": "g(x) is shown in the figure, which is a quadratic function going through (0,-2), (-1,0), (2,0), (3,4), (-2,4). f(x)=x^2+x-6. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: g(x) is shown in the figure, which is a quadratic function going through (0,-2), (-1,0), (2,0), (3,4), (-2,4). f(x)=x^2+x-6. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: g(x) is shown in the figure, which is a quadratic function going through (0,-2), (-1,0), (2,0), (3,4), (-2,4). f(x)=x^2+x-6. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common.",
        "question_for_eval": "g(x) is shown in the figure, which is a quadratic function going through (0,-2), (-1,0), (2,0), (3,4), (-2,4). f(x)=x^2+x-6. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common."
    },
    {
        "sample_index": "566",
        "problem_index": "566",
        "problem_version": "Text Only",
        "question": "g(x) is shown in the figure, which is a quadratic function opening upward with a vertex of (3,\u22128) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?\nChoices:\nA:$f$ has a greater $y$-intercept than $g$.\nB:$g$ has a greater $y$-intercept than $f$.\nC:$f$ and $g$ share the same $y$-intercept.",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening upward with a vertex of (3,\u22128) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?\nChoices:\nA:$f$ has a greater $y$-intercept than $g$.\nB:$g$ has a greater $y$-intercept than $f$.\nC:$f$ and $g$ share the same $y$-intercept.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening upward with a vertex of (3,\u22128) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?\nChoices:\nA:$f$ has a greater $y$-intercept than $g$.\nB:$g$ has a greater $y$-intercept than $f$.\nC:$f$ and $g$ share the same $y$-intercept.",
        "question_for_eval": "g(x) is shown in the figure, which is a quadratic function opening upward with a vertex of (3,\u22128) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?\nChoices:\nA:$f$ has a greater $y$-intercept than $g$.\nB:$g$ has a greater $y$-intercept than $f$.\nC:$f$ and $g$ share the same $y$-intercept."
    },
    {
        "sample_index": "567",
        "problem_index": "567",
        "problem_version": "Text Only",
        "question": "g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-5,6). f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?\nChoices:\nA:Yes, $f$ and $g$ are both concave down.\nB:Yes, $f$ and $g$ are both concave up.\nC:No, $f$ is concave up and $g$ is concave down.\nD:No, $f$ is concave down and $g$ is concave up.",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-5,6). f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?\nChoices:\nA:Yes, $f$ and $g$ are both concave down.\nB:Yes, $f$ and $g$ are both concave up.\nC:No, $f$ is concave up and $g$ is concave down.\nD:No, $f$ is concave down and $g$ is concave up.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-5,6). f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?\nChoices:\nA:Yes, $f$ and $g$ are both concave down.\nB:Yes, $f$ and $g$ are both concave up.\nC:No, $f$ is concave up and $g$ is concave down.\nD:No, $f$ is concave down and $g$ is concave up.",
        "question_for_eval": "g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-5,6). f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?\nChoices:\nA:Yes, $f$ and $g$ are both concave down.\nB:Yes, $f$ and $g$ are both concave up.\nC:No, $f$ is concave up and $g$ is concave down.\nD:No, $f$ is concave down and $g$ is concave up."
    },
    {
        "sample_index": "568",
        "problem_index": "568",
        "problem_version": "Text Only",
        "question": "Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n",
        "image": "",
        "answer": "\\[g(x)=(x + 4)^2 - 5\\].",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n",
        "question_for_eval": "Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n"
    },
    {
        "sample_index": "569",
        "problem_index": "569",
        "problem_version": "Text Only",
        "question": "Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n",
        "image": "",
        "answer": "g(x)=x^2-3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n",
        "question_for_eval": "Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a translated (shifted) version of f(x)=x^2. Write the equation for g(x).\n"
    },
    {
        "sample_index": "570",
        "problem_index": "570",
        "problem_version": "Text Only",
        "question": "Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a scaled version of f(x)=x^2. Write the equation for g(x).\n",
        "image": "",
        "answer": "0.75 x^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a scaled version of f(x)=x^2. Write the equation for g(x).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a scaled version of f(x)=x^2. Write the equation for g(x).\n",
        "question_for_eval": "Function f in blue is a parabola as $y=x^2$. Function g in red can be thought of as a scaled version of f(x)=x^2. Write the equation for g(x).\n"
    },
    {
        "sample_index": "571",
        "problem_index": "571",
        "problem_version": "Text Only",
        "question": "There are two quadratic functions. The red one is g(x) that goes through the origin and point (2, -4). Find the equation of the dashed line in red. Use exact numbers.\n",
        "image": "",
        "answer": "g(x)=-x^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: There are two quadratic functions. The red one is g(x) that goes through the origin and point (2, -4). Find the equation of the dashed line in red. Use exact numbers.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: There are two quadratic functions. The red one is g(x) that goes through the origin and point (2, -4). Find the equation of the dashed line in red. Use exact numbers.\n",
        "question_for_eval": "There are two quadratic functions. The red one is g(x) that goes through the origin and point (2, -4). Find the equation of the dashed line in red. Use exact numbers.\n"
    },
    {
        "sample_index": "572",
        "problem_index": "572",
        "problem_version": "Text Only",
        "question": "g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-8,8). f(x)=-5(x+4)^2+8. Which function has a greater maximum?\nChoices:\nA:$f$ has a greater maximum than $g$.\nB:$g$ has a greater maximum than $f$.\nC:$f$ and $g$ share the same maximum.",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-8,8). f(x)=-5(x+4)^2+8. Which function has a greater maximum?\nChoices:\nA:$f$ has a greater maximum than $g$.\nB:$g$ has a greater maximum than $f$.\nC:$f$ and $g$ share the same maximum.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-8,8). f(x)=-5(x+4)^2+8. Which function has a greater maximum?\nChoices:\nA:$f$ has a greater maximum than $g$.\nB:$g$ has a greater maximum than $f$.\nC:$f$ and $g$ share the same maximum.",
        "question_for_eval": "g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-8,8). f(x)=-5(x+4)^2+8. Which function has a greater maximum?\nChoices:\nA:$f$ has a greater maximum than $g$.\nB:$g$ has a greater maximum than $f$.\nC:$f$ and $g$ share the same maximum."
    },
    {
        "sample_index": "573",
        "problem_index": "573",
        "problem_version": "Text Only",
        "question": "Function g in red can be thought of as a translated (shifted) version of f(x)=x^2 in blue. Write the equation for g(x).\n",
        "image": "",
        "answer": "g(x)=(x+2)^2+1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Function g in red can be thought of as a translated (shifted) version of f(x)=x^2 in blue. Write the equation for g(x).\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Function g in red can be thought of as a translated (shifted) version of f(x)=x^2 in blue. Write the equation for g(x).\n",
        "question_for_eval": "Function g in red can be thought of as a translated (shifted) version of f(x)=x^2 in blue. Write the equation for g(x).\n"
    },
    {
        "sample_index": "574",
        "problem_index": "574",
        "problem_version": "Text Only",
        "question": "Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?\nChoices:\nA:Greater width always relates to smaller area.\nB:Greater width relates to smaller area as long as the width is less than $10 \\mathrm{~m}$.\nC:When there is no width, the area is $20 \\mathrm{~m}^2$.\nD:When there is no width, the area is $0 \\mathrm{~m}^2$.",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?\nChoices:\nA:Greater width always relates to smaller area.\nB:Greater width relates to smaller area as long as the width is less than $10 \\mathrm{~m}$.\nC:When there is no width, the area is $20 \\mathrm{~m}^2$.\nD:When there is no width, the area is $0 \\mathrm{~m}^2$.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?\nChoices:\nA:Greater width always relates to smaller area.\nB:Greater width relates to smaller area as long as the width is less than $10 \\mathrm{~m}$.\nC:When there is no width, the area is $20 \\mathrm{~m}^2$.\nD:When there is no width, the area is $0 \\mathrm{~m}^2$.",
        "question_for_eval": "Simon has a certain length of fencing to enclose a rectangular area. The quadratic function A with a vertec of (10, 100) models the rectangle's area (in square meters) as a function of its width (in meters). It intersects with x-axis at (0,0) and (20,0). Which of these statements are true?\nChoices:\nA:Greater width always relates to smaller area.\nB:Greater width relates to smaller area as long as the width is less than $10 \\mathrm{~m}$.\nC:When there is no width, the area is $20 \\mathrm{~m}^2$.\nD:When there is no width, the area is $0 \\mathrm{~m}^2$."
    },
    {
        "sample_index": "575",
        "problem_index": "575",
        "problem_version": "Text Only",
        "question": "g(x) is shown in the figure, which is a quadratic function opening upward and goes through (-3,0) and (4,0). f(x)=x^2+4x. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common.",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening upward and goes through (-3,0) and (4,0). f(x)=x^2+4x. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: g(x) is shown in the figure, which is a quadratic function opening upward and goes through (-3,0) and (4,0). f(x)=x^2+4x. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common.",
        "question_for_eval": "g(x) is shown in the figure, which is a quadratic function opening upward and goes through (-3,0) and (4,0). f(x)=x^2+4x. How many roots do the functions have in common?\nChoices:\nA:$f$ and $g$ share the same root(s).\nB:$f$ and $g$ share one root in common but each have another root that is not shared.\nC:$f$ and $g$ share no roots in common."
    },
    {
        "sample_index": "576",
        "problem_index": "576",
        "problem_version": "Text Only",
        "question": "A polynomial function p is graphed, which goes through (-5,0), (-1.5,0), (2,0). What could be the equation of p?\nChoices:\nA:p(x)=(x+5)(2 x+3)(x-2)\nB:p(x)=(x-5)(2 x-3)(x+2)\nC:p(x)=(-5 x)\\left(-\\frac{3}{2} x\\right)(2 x)\nD:p(x)=(5 x)\\left(\\frac{3}{2} x\\right)(-2 x)",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A polynomial function p is graphed, which goes through (-5,0), (-1.5,0), (2,0). What could be the equation of p?\nChoices:\nA:p(x)=(x+5)(2 x+3)(x-2)\nB:p(x)=(x-5)(2 x-3)(x+2)\nC:p(x)=(-5 x)\\left(-\\frac{3}{2} x\\right)(2 x)\nD:p(x)=(5 x)\\left(\\frac{3}{2} x\\right)(-2 x)",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A polynomial function p is graphed, which goes through (-5,0), (-1.5,0), (2,0). What could be the equation of p?\nChoices:\nA:p(x)=(x+5)(2 x+3)(x-2)\nB:p(x)=(x-5)(2 x-3)(x+2)\nC:p(x)=(-5 x)\\left(-\\frac{3}{2} x\\right)(2 x)\nD:p(x)=(5 x)\\left(\\frac{3}{2} x\\right)(-2 x)",
        "question_for_eval": "A polynomial function p is graphed, which goes through (-5,0), (-1.5,0), (2,0). What could be the equation of p?\nChoices:\nA:p(x)=(x+5)(2 x+3)(x-2)\nB:p(x)=(x-5)(2 x-3)(x+2)\nC:p(x)=(-5 x)\\left(-\\frac{3}{2} x\\right)(2 x)\nD:p(x)=(5 x)\\left(\\frac{3}{2} x\\right)(-2 x)"
    },
    {
        "sample_index": "577",
        "problem_index": "577",
        "problem_version": "Text Only",
        "question": "A polynomial p is graphed, which goes through (-3.5,0), (0,0), (3,0). What could be the equation of p?\nChoices:\nA:p(x)=x(x-3)^2(2 x+7)\nB:p(x)=x^2(x-3)(2 x+7)\nC:p(x)=x(x-3)^2(2 x+7)^2\nD:p(x)=x(x-3)(2 x+7)^2",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A polynomial p is graphed, which goes through (-3.5,0), (0,0), (3,0). What could be the equation of p?\nChoices:\nA:p(x)=x(x-3)^2(2 x+7)\nB:p(x)=x^2(x-3)(2 x+7)\nC:p(x)=x(x-3)^2(2 x+7)^2\nD:p(x)=x(x-3)(2 x+7)^2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A polynomial p is graphed, which goes through (-3.5,0), (0,0), (3,0). What could be the equation of p?\nChoices:\nA:p(x)=x(x-3)^2(2 x+7)\nB:p(x)=x^2(x-3)(2 x+7)\nC:p(x)=x(x-3)^2(2 x+7)^2\nD:p(x)=x(x-3)(2 x+7)^2",
        "question_for_eval": "A polynomial p is graphed, which goes through (-3.5,0), (0,0), (3,0). What could be the equation of p?\nChoices:\nA:p(x)=x(x-3)^2(2 x+7)\nB:p(x)=x^2(x-3)(2 x+7)\nC:p(x)=x(x-3)^2(2 x+7)^2\nD:p(x)=x(x-3)(2 x+7)^2"
    },
    {
        "sample_index": "578",
        "problem_index": "578",
        "problem_version": "Text Only",
        "question": "Peter received a lump sum payment of $\\$ 50000$ for an insurance claim (and decided not to put it in a savings account).\n\nEvery month, he withdraws $5 \\%$ of the remaining funds.\n\nThe funds after $x$ months is shown below. The curve in the graph passes (0,5). y-axis labels\"y('0000s)\"\n\nHow much would the first withdrawal be?\n",
        "image": "",
        "answer": "2500",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Peter received a lump sum payment of $\\$ 50000$ for an insurance claim (and decided not to put it in a savings account).\n\nEvery month, he withdraws $5 \\%$ of the remaining funds.\n\nThe funds after $x$ months is shown below. The curve in the graph passes (0,5). y-axis labels\"y('0000s)\"\n\nHow much would the first withdrawal be?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Peter received a lump sum payment of $\\$ 50000$ for an insurance claim (and decided not to put it in a savings account).\n\nEvery month, he withdraws $5 \\%$ of the remaining funds.\n\nThe funds after $x$ months is shown below. The curve in the graph passes (0,5). y-axis labels\"y('0000s)\"\n\nHow much would the first withdrawal be?\n",
        "question_for_eval": "Peter received a lump sum payment of $\\$ 50000$ for an insurance claim (and decided not to put it in a savings account).\n\nEvery month, he withdraws $5 \\%$ of the remaining funds.\n\nThe funds after $x$ months is shown below. The curve in the graph passes (0,5). y-axis labels\"y('0000s)\"\n\nHow much would the first withdrawal be?\n"
    },
    {
        "sample_index": "579",
        "problem_index": "579",
        "problem_version": "Text Only",
        "question": "In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nWhich of the following could model the percentage that Lucy can still recall after $t$ days?\nChoices:\nA:$Q=(0.85)^{t}$\nB:$Q=(0.83)^{t}$\nC:$Q=(0.87)^{t}$",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nWhich of the following could model the percentage that Lucy can still recall after $t$ days?\nChoices:\nA:$Q=(0.85)^{t}$\nB:$Q=(0.83)^{t}$\nC:$Q=(0.87)^{t}$",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nWhich of the following could model the percentage that Lucy can still recall after $t$ days?\nChoices:\nA:$Q=(0.85)^{t}$\nB:$Q=(0.83)^{t}$\nC:$Q=(0.87)^{t}$",
        "question_for_eval": "In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nWhich of the following could model the percentage that Lucy can still recall after $t$ days?\nChoices:\nA:$Q=(0.85)^{t}$\nB:$Q=(0.83)^{t}$\nC:$Q=(0.87)^{t}$"
    },
    {
        "sample_index": "580",
        "problem_index": "580",
        "problem_version": "Text Only",
        "question": "In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nOn each day, what percentage of the previous day's content did Lucy forget?\n",
        "image": "",
        "answer": "$13 \\%$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nOn each day, what percentage of the previous day's content did Lucy forget?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nOn each day, what percentage of the previous day's content did Lucy forget?\n",
        "question_for_eval": "In a memory study, subjects are asked to memorize some content and recall as much as they can remember each day thereafter. Each day, Maximilian finds that he has forgotten $15 \\%$ of what he could recount the day before. Lucy also took part in the study. The given graphs represent the percentage of content that Maximilian (gray) and Lucy (black) could remember after $t$ days. y-axis labels \"days\" and x-axis labels \"recall percentage\"\n\nOn each day, what percentage of the previous day's content did Lucy forget?\n"
    },
    {
        "sample_index": "581",
        "problem_index": "581",
        "problem_version": "Text Only",
        "question": "For function graphed below, it passes (0,-2) and (3,0) and starts from (-1,-5). Determine if it has an inverse function.\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: For function graphed below, it passes (0,-2) and (3,0) and starts from (-1,-5). Determine if it has an inverse function.\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: For function graphed below, it passes (0,-2) and (3,0) and starts from (-1,-5). Determine if it has an inverse function.\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "For function graphed below, it passes (0,-2) and (3,0) and starts from (-1,-5). Determine if it has an inverse function.\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "582",
        "problem_index": "582",
        "problem_version": "Text Only",
        "question": "For function graphed below, which is a curve whose asymptote is x-axis and x=4, determine if it has an inverse function.\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: For function graphed below, which is a curve whose asymptote is x-axis and x=4, determine if it has an inverse function.\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: For function graphed below, which is a curve whose asymptote is x-axis and x=4, determine if it has an inverse function.\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "For function graphed below, which is a curve whose asymptote is x-axis and x=4, determine if it has an inverse function.\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "583",
        "problem_index": "583",
        "problem_version": "Text Only",
        "question": "Do the following graph, a line which passes (-6,0) and (0,2) and the slope of the line > 0, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Do the following graph, a line which passes (-6,0) and (0,2) and the slope of the line > 0, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Do the following graph, a line which passes (-6,0) and (0,2) and the slope of the line > 0, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "Do the following graph, a line which passes (-6,0) and (0,2) and the slope of the line > 0, have inverse functions?\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "584",
        "problem_index": "584",
        "problem_version": "Text Only",
        "question": "Do the following graph, which is a parabola passing (0,2) and it opens upwards, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Do the following graph, which is a parabola passing (0,2) and it opens upwards, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Do the following graph, which is a parabola passing (0,2) and it opens upwards, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "Do the following graph, which is a parabola passing (0,2) and it opens upwards, have inverse functions?\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "585",
        "problem_index": "585",
        "problem_version": "Text Only",
        "question": "Do the following graph, which is a curve passes (0,1) and when the value of x increases the value of y increases, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Do the following graph, which is a curve passes (0,1) and when the value of x increases the value of y increases, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Do the following graph, which is a curve passes (0,1) and when the value of x increases the value of y increases, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "Do the following graph, which is a curve passes (0,1) and when the value of x increases the value of y increases, have inverse functions?\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "586",
        "problem_index": "586",
        "problem_version": "Text Only",
        "question": "Do the following graph, which is a curve passes (0,0) and the value of y increases by the increase of the value of x, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Do the following graph, which is a curve passes (0,0) and the value of y increases by the increase of the value of x, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Do the following graph, which is a curve passes (0,0) and the value of y increases by the increase of the value of x, have inverse functions?\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "Do the following graph, which is a curve passes (0,0) and the value of y increases by the increase of the value of x, have inverse functions?\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "587",
        "problem_index": "587",
        "problem_version": "Text Only",
        "question": "Do the following graph, which is a curve passes (-1,0), (0,8), (2,0), (4,0), have inverse functions?\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Do the following graph, which is a curve passes (-1,0), (0,8), (2,0), (4,0), have inverse functions?\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Do the following graph, which is a curve passes (-1,0), (0,8), (2,0), (4,0), have inverse functions?\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "Do the following graph, which is a curve passes (-1,0), (0,8), (2,0), (4,0), have inverse functions?\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "588",
        "problem_index": "588",
        "problem_version": "Text Only",
        "question": "The graphs of logarithm function $f(x)=\\ln x$ passing (1,4) and logarithm function $g(x)$ passing (1,0) are shown below. $g(x)$ is a transformation of $f(x)$.\n\nHence state the equation of $g(x)$.\n",
        "image": "",
        "answer": "$g(x)=\\ln x+4$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graphs of logarithm function $f(x)=\\ln x$ passing (1,4) and logarithm function $g(x)$ passing (1,0) are shown below. $g(x)$ is a transformation of $f(x)$.\n\nHence state the equation of $g(x)$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graphs of logarithm function $f(x)=\\ln x$ passing (1,4) and logarithm function $g(x)$ passing (1,0) are shown below. $g(x)$ is a transformation of $f(x)$.\n\nHence state the equation of $g(x)$.\n",
        "question_for_eval": "The graphs of logarithm function $f(x)=\\ln x$ passing (1,4) and logarithm function $g(x)$ passing (1,0) are shown below. $g(x)$ is a transformation of $f(x)$.\n\nHence state the equation of $g(x)$.\n"
    },
    {
        "sample_index": "589",
        "problem_index": "589",
        "problem_version": "Text Only",
        "question": "The graph of logarithm function $f(x)=\\ln x$ (gray) and logarithm function $g(x)$ (black) is drawn below. $g(x)$ is a transformation of $f(x)$.\n\nWhat sort of transformation is $g(x)$ of $f(x)$ ?\nChoices:\nA:Vertical dilation\nB:Vertical translation\nC:Reflection\nD:Horizontal translation",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph of logarithm function $f(x)=\\ln x$ (gray) and logarithm function $g(x)$ (black) is drawn below. $g(x)$ is a transformation of $f(x)$.\n\nWhat sort of transformation is $g(x)$ of $f(x)$ ?\nChoices:\nA:Vertical dilation\nB:Vertical translation\nC:Reflection\nD:Horizontal translation",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph of logarithm function $f(x)=\\ln x$ (gray) and logarithm function $g(x)$ (black) is drawn below. $g(x)$ is a transformation of $f(x)$.\n\nWhat sort of transformation is $g(x)$ of $f(x)$ ?\nChoices:\nA:Vertical dilation\nB:Vertical translation\nC:Reflection\nD:Horizontal translation",
        "question_for_eval": "The graph of logarithm function $f(x)=\\ln x$ (gray) and logarithm function $g(x)$ (black) is drawn below. $g(x)$ is a transformation of $f(x)$.\n\nWhat sort of transformation is $g(x)$ of $f(x)$ ?\nChoices:\nA:Vertical dilation\nB:Vertical translation\nC:Reflection\nD:Horizontal translation"
    },
    {
        "sample_index": "590",
        "problem_index": "590",
        "problem_version": "Text Only",
        "question": "The line, which is parallel to y-axis, passes (6,0). What is the slope of the line?\nChoices:\nA:0\nB:1\nC:6\nD:Undefined",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The line, which is parallel to y-axis, passes (6,0). What is the slope of the line?\nChoices:\nA:0\nB:1\nC:6\nD:Undefined",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The line, which is parallel to y-axis, passes (6,0). What is the slope of the line?\nChoices:\nA:0\nB:1\nC:6\nD:Undefined",
        "question_for_eval": "The line, which is parallel to y-axis, passes (6,0). What is the slope of the line?\nChoices:\nA:0\nB:1\nC:6\nD:Undefined"
    },
    {
        "sample_index": "591",
        "problem_index": "591",
        "problem_version": "Text Only",
        "question": "The line passes (0,2), (1,0). What is the slope of the line?\n",
        "image": "",
        "answer": "-2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (0,2), (1,0). What is the slope of the line?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (0,2), (1,0). What is the slope of the line?\n",
        "question_for_eval": "The line passes (0,2), (1,0). What is the slope of the line?\n"
    },
    {
        "sample_index": "592",
        "problem_index": "592",
        "problem_version": "Text Only",
        "question": "The line passes (3,4) and (-1,-3). What is the slope of the line?\n",
        "image": "",
        "answer": "=\\frac{7}{4}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (3,4) and (-1,-3). What is the slope of the line?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (3,4) and (-1,-3). What is the slope of the line?\n",
        "question_for_eval": "The line passes (3,4) and (-1,-3). What is the slope of the line?\n"
    },
    {
        "sample_index": "593",
        "problem_index": "593",
        "problem_version": "Text Only",
        "question": "A vertical blue line in the graph. What is the equation of the line?\n",
        "image": "",
        "answer": "$x=0$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A vertical blue line in the graph. What is the equation of the line?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A vertical blue line in the graph. What is the equation of the line?\n",
        "question_for_eval": "A vertical blue line in the graph. What is the equation of the line?\n"
    },
    {
        "sample_index": "594",
        "problem_index": "594",
        "problem_version": "Text Only",
        "question": "Mio bought a tablet and pays monthly for internet service for it. She graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it. x-axis labels \"Time (months)\", and y-axis labels \"Total cost (dollars)\"\nWhat does the y-intercept represent in this context?\nChoose 1 answer:\nChoices:\nA:The number of months after which the total cost is 0 dollars.\nB:The cost of buying the tablet\nC:The cost per month of internet service\nD:None of the above",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Mio bought a tablet and pays monthly for internet service for it. She graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it. x-axis labels \"Time (months)\", and y-axis labels \"Total cost (dollars)\"\nWhat does the y-intercept represent in this context?\nChoose 1 answer:\nChoices:\nA:The number of months after which the total cost is 0 dollars.\nB:The cost of buying the tablet\nC:The cost per month of internet service\nD:None of the above",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Mio bought a tablet and pays monthly for internet service for it. She graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it. x-axis labels \"Time (months)\", and y-axis labels \"Total cost (dollars)\"\nWhat does the y-intercept represent in this context?\nChoose 1 answer:\nChoices:\nA:The number of months after which the total cost is 0 dollars.\nB:The cost of buying the tablet\nC:The cost per month of internet service\nD:None of the above",
        "question_for_eval": "Mio bought a tablet and pays monthly for internet service for it. She graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it. x-axis labels \"Time (months)\", and y-axis labels \"Total cost (dollars)\"\nWhat does the y-intercept represent in this context?\nChoose 1 answer:\nChoices:\nA:The number of months after which the total cost is 0 dollars.\nB:The cost of buying the tablet\nC:The cost per month of internet service\nD:None of the above"
    },
    {
        "sample_index": "595",
        "problem_index": "595",
        "problem_version": "Text Only",
        "question": "The line passes (0,-5) and (5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n",
        "image": "",
        "answer": "$y=x-5$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (0,-5) and (5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (0,-5) and (5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n",
        "question_for_eval": "The line passes (0,-5) and (5,0). Find the equation of the line.\nUse exact numbers.\ny = _ x + _\n"
    },
    {
        "sample_index": "596",
        "problem_index": "596",
        "problem_version": "Text Only",
        "question": "The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n",
        "image": "",
        "answer": "$y+3=\\frac{3}{4}(x-2)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n",
        "question_for_eval": "The line passes (-2,-6) and (2,-3). Write an equation that represents the line.\nUse exact numbers.\n"
    },
    {
        "sample_index": "597",
        "problem_index": "597",
        "problem_version": "Text Only",
        "question": "A system of two equations: $x^2+y^2=9$ and $y=x^2-4$ and their graphs in the \nxy-plane are shown above. How many solutions \ndoes the system have?\nChoices:\nA:One\nB:Two\nC:Three\nD:Four",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: A system of two equations: $x^2+y^2=9$ and $y=x^2-4$ and their graphs in the \nxy-plane are shown above. How many solutions \ndoes the system have?\nChoices:\nA:One\nB:Two\nC:Three\nD:Four",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: A system of two equations: $x^2+y^2=9$ and $y=x^2-4$ and their graphs in the \nxy-plane are shown above. How many solutions \ndoes the system have?\nChoices:\nA:One\nB:Two\nC:Three\nD:Four",
        "question_for_eval": "A system of two equations: $x^2+y^2=9$ and $y=x^2-4$ and their graphs in the \nxy-plane are shown above. How many solutions \ndoes the system have?\nChoices:\nA:One\nB:Two\nC:Three\nD:Four"
    },
    {
        "sample_index": "598",
        "problem_index": "598",
        "problem_version": "Text Only",
        "question": "The figure has two segments. Use the vertical line test to determine whether the curve is the graph of a function.\nChoices:\nA:Yes\nB:No",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure has two segments. Use the vertical line test to determine whether the curve is the graph of a function.\nChoices:\nA:Yes\nB:No",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure has two segments. Use the vertical line test to determine whether the curve is the graph of a function.\nChoices:\nA:Yes\nB:No",
        "question_for_eval": "The figure has two segments. Use the vertical line test to determine whether the curve is the graph of a function.\nChoices:\nA:Yes\nB:No"
    },
    {
        "sample_index": "599",
        "problem_index": "599",
        "problem_version": "Text Only",
        "question": "The graph shows $y_1=x^3$ passing (0,0) and a vertical or horizontal translation $y_2$ passing (-2,0). The blue line is solid while the red line is dotted. Write an equation for $y_2$ as shown in the graph.\n",
        "image": "",
        "answer": "$y_2=(x+2)^3=y_1(x+2)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows $y_1=x^3$ passing (0,0) and a vertical or horizontal translation $y_2$ passing (-2,0). The blue line is solid while the red line is dotted. Write an equation for $y_2$ as shown in the graph.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows $y_1=x^3$ passing (0,0) and a vertical or horizontal translation $y_2$ passing (-2,0). The blue line is solid while the red line is dotted. Write an equation for $y_2$ as shown in the graph.\n",
        "question_for_eval": "The graph shows $y_1=x^3$ passing (0,0) and a vertical or horizontal translation $y_2$ passing (-2,0). The blue line is solid while the red line is dotted. Write an equation for $y_2$ as shown in the graph.\n"
    },
    {
        "sample_index": "600",
        "problem_index": "600",
        "problem_version": "Text Only",
        "question": "A rectangle is inscribed between the $x$-axis and the parabola $y=36-x^2$ with one side along the $x$-axis, as shown in the figure below. Let $x$ denote the $x$-coordinate of the point highlighted in the figure. Write the area $A$ of the rectangle as a function of $x$.\n",
        "image": "",
        "answer": "$72 x-2 x^3$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Expression"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A rectangle is inscribed between the $x$-axis and the parabola $y=36-x^2$ with one side along the $x$-axis, as shown in the figure below. Let $x$ denote the $x$-coordinate of the point highlighted in the figure. Write the area $A$ of the rectangle as a function of $x$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A rectangle is inscribed between the $x$-axis and the parabola $y=36-x^2$ with one side along the $x$-axis, as shown in the figure below. Let $x$ denote the $x$-coordinate of the point highlighted in the figure. Write the area $A$ of the rectangle as a function of $x$.\n",
        "question_for_eval": "A rectangle is inscribed between the $x$-axis and the parabola $y=36-x^2$ with one side along the $x$-axis, as shown in the figure below. Let $x$ denote the $x$-coordinate of the point highlighted in the figure. Write the area $A$ of the rectangle as a function of $x$.\n"
    },
    {
        "sample_index": "601",
        "problem_index": "601",
        "problem_version": "Text Only",
        "question": "The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n",
        "image": "",
        "answer": "$y-3=\\frac{2}{3}(x-8)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n",
        "question_for_eval": "The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .\n"
    },
    {
        "sample_index": "602",
        "problem_index": "602",
        "problem_version": "Text Only",
        "question": "A piecewise function, with 2 segments constructed by a line passing (-5,1), (-3,2), and (-1,4) and a line passing (-1,5), (3,3), and (5,1), as shown in the figure. Let $f$ be the function given by the following graph. What is the domain of $f$? \n",
        "image": "",
        "answer": "$[-5,-3) \\cup(-3,5]$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A piecewise function, with 2 segments constructed by a line passing (-5,1), (-3,2), and (-1,4) and a line passing (-1,5), (3,3), and (5,1), as shown in the figure. Let $f$ be the function given by the following graph. What is the domain of $f$? \n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A piecewise function, with 2 segments constructed by a line passing (-5,1), (-3,2), and (-1,4) and a line passing (-1,5), (3,3), and (5,1), as shown in the figure. Let $f$ be the function given by the following graph. What is the domain of $f$? \n",
        "question_for_eval": "A piecewise function, with 2 segments constructed by a line passing (-5,1), (-3,2), and (-1,4) and a line passing (-1,5), (3,3), and (5,1), as shown in the figure. Let $f$ be the function given by the following graph. What is the domain of $f$? \n"
    },
    {
        "sample_index": "603",
        "problem_index": "603",
        "problem_version": "Text Only",
        "question": "The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nWho is traveling faster?\nChoices:\nA:Justin\nB:Oliver",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nWho is traveling faster?\nChoices:\nA:Justin\nB:Oliver",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nWho is traveling faster?\nChoices:\nA:Justin\nB:Oliver",
        "question_for_eval": "The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nWho is traveling faster?\nChoices:\nA:Justin\nB:Oliver"
    },
    {
        "sample_index": "604",
        "problem_index": "604",
        "problem_version": "Text Only",
        "question": "The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nHow much faster is Oliver traveling?\n",
        "image": "",
        "answer": "$10km / h$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nHow much faster is Oliver traveling?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nHow much faster is Oliver traveling?\n",
        "question_for_eval": "The graph with 2 linear functions shows the progress of two competitors in a cycling race. In the graph, the x-axis represents Time and the y-axis represents Distance.\n\nHow much faster is Oliver traveling?\n"
    },
    {
        "sample_index": "605",
        "problem_index": "605",
        "problem_version": "Text Only",
        "question": "The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).\n\nPedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.\n",
        "image": "",
        "answer": "1.6",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).\n\nPedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).\n\nPedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.\n",
        "question_for_eval": "The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road. The bridge meets the road at coordinates $(0,0)$ and $(100,0)$, with the vertex at (50,50).\n\nPedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.\n"
    },
    {
        "sample_index": "606",
        "problem_index": "606",
        "problem_version": "Text Only",
        "question": "The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat is the average rate of change?\n",
        "image": "",
        "answer": "$\\frac{9}{10}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat is the average rate of change?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat is the average rate of change?\n",
        "question_for_eval": "The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat is the average rate of change?\n"
    },
    {
        "sample_index": "607",
        "problem_index": "607",
        "problem_version": "Text Only",
        "question": "The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat does this tell you?\nChoices:\nA:The cost of a call increases by $\\$ 0.90$ for each additional minute\nB:Each additional dollar will buy an additional 0.9 minutes of call time\nC:The cost of a call decreases by $\\$ 0.90$ for each additional minute\nD:Each additional dollar will buy 0.9 minutes less of call time than the previous dollar",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat does this tell you?\nChoices:\nA:The cost of a call increases by $\\$ 0.90$ for each additional minute\nB:Each additional dollar will buy an additional 0.9 minutes of call time\nC:The cost of a call decreases by $\\$ 0.90$ for each additional minute\nD:Each additional dollar will buy 0.9 minutes less of call time than the previous dollar",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat does this tell you?\nChoices:\nA:The cost of a call increases by $\\$ 0.90$ for each additional minute\nB:Each additional dollar will buy an additional 0.9 minutes of call time\nC:The cost of a call decreases by $\\$ 0.90$ for each additional minute\nD:Each additional dollar will buy 0.9 minutes less of call time than the previous dollar",
        "question_for_eval": "The graph shows the cost, in dollars, of a phone call for different call durations. The x-axis represents call length (minutes), and the y-axis represents call cost.\n\nWhat does this tell you?\nChoices:\nA:The cost of a call increases by $\\$ 0.90$ for each additional minute\nB:Each additional dollar will buy an additional 0.9 minutes of call time\nC:The cost of a call decreases by $\\$ 0.90$ for each additional minute\nD:Each additional dollar will buy 0.9 minutes less of call time than the previous dollar"
    },
    {
        "sample_index": "608",
        "problem_index": "608",
        "problem_version": "Text Only",
        "question": "The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat is the average rate of change?\n",
        "image": "",
        "answer": "$\\frac{1}{2000}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat is the average rate of change?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat is the average rate of change?\n",
        "question_for_eval": "The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat is the average rate of change?\n"
    },
    {
        "sample_index": "609",
        "problem_index": "609",
        "problem_version": "Text Only",
        "question": "The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat does the average rate of change tell you?\nChoices:\nA:An increase in demand of 500 units will decrease the price of each toy by $\\$ 1$\nB:An increase in demand of 500 units will increase the price of each toy by $\\$ 1$\nC:The price of each toy increases by $\\$ 0.50$ for each additional 1000 units demanded\nD:The price of each toy decreases by $\\$ 0.50$ for each additional 1000 units demanded",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat does the average rate of change tell you?\nChoices:\nA:An increase in demand of 500 units will decrease the price of each toy by $\\$ 1$\nB:An increase in demand of 500 units will increase the price of each toy by $\\$ 1$\nC:The price of each toy increases by $\\$ 0.50$ for each additional 1000 units demanded\nD:The price of each toy decreases by $\\$ 0.50$ for each additional 1000 units demanded",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat does the average rate of change tell you?\nChoices:\nA:An increase in demand of 500 units will decrease the price of each toy by $\\$ 1$\nB:An increase in demand of 500 units will increase the price of each toy by $\\$ 1$\nC:The price of each toy increases by $\\$ 0.50$ for each additional 1000 units demanded\nD:The price of each toy decreases by $\\$ 0.50$ for each additional 1000 units demanded",
        "question_for_eval": "The graph shows the price change, in dollars, of a toy for different levels of demand. The x-axis represents quantity (thousand units), and the y-axis represents price.\n\nWhat does the average rate of change tell you?\nChoices:\nA:An increase in demand of 500 units will decrease the price of each toy by $\\$ 1$\nB:An increase in demand of 500 units will increase the price of each toy by $\\$ 1$\nC:The price of each toy increases by $\\$ 0.50$ for each additional 1000 units demanded\nD:The price of each toy decreases by $\\$ 0.50$ for each additional 1000 units demanded"
    },
    {
        "sample_index": "610",
        "problem_index": "610",
        "problem_version": "Text Only",
        "question": "The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat is the average rate of change?\n",
        "image": "",
        "answer": "0",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat is the average rate of change?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat is the average rate of change?\n",
        "question_for_eval": "The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat is the average rate of change?\n"
    },
    {
        "sample_index": "611",
        "problem_index": "611",
        "problem_version": "Text Only",
        "question": "The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat does the average rate of change tell you?\nChoices:\nA:The number of earthquakes per year increased by 6 each year.\nB:The number of earthquakes per year did not change.\nC:There were a total of 6 earthquakes over the 4 years.\nD:The number of earthquakes per year decreased by 6 each year.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat does the average rate of change tell you?\nChoices:\nA:The number of earthquakes per year increased by 6 each year.\nB:The number of earthquakes per year did not change.\nC:There were a total of 6 earthquakes over the 4 years.\nD:The number of earthquakes per year decreased by 6 each year.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat does the average rate of change tell you?\nChoices:\nA:The number of earthquakes per year increased by 6 each year.\nB:The number of earthquakes per year did not change.\nC:There were a total of 6 earthquakes over the 4 years.\nD:The number of earthquakes per year decreased by 6 each year.",
        "question_for_eval": "The graph shows the number of earthquakes in a particular country. The x-axis represents years, and the y-axis represents the number of earthquakes.\n\nWhat does the average rate of change tell you?\nChoices:\nA:The number of earthquakes per year increased by 6 each year.\nB:The number of earthquakes per year did not change.\nC:There were a total of 6 earthquakes over the 4 years.\nD:The number of earthquakes per year decreased by 6 each year."
    },
    {
        "sample_index": "612",
        "problem_index": "612",
        "problem_version": "Text Only",
        "question": "The curve shown in the figure is a quadratic function opening upwards and passes through the origin. Does the graphed function have an even or odd power?\nChoices:\nA:Odd\nB:Even",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Property"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The curve shown in the figure is a quadratic function opening upwards and passes through the origin. Does the graphed function have an even or odd power?\nChoices:\nA:Odd\nB:Even",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The curve shown in the figure is a quadratic function opening upwards and passes through the origin. Does the graphed function have an even or odd power?\nChoices:\nA:Odd\nB:Even",
        "question_for_eval": "The curve shown in the figure is a quadratic function opening upwards and passes through the origin. Does the graphed function have an even or odd power?\nChoices:\nA:Odd\nB:Even"
    },
    {
        "sample_index": "613",
        "problem_index": "613",
        "problem_version": "Text Only",
        "question": "The graph, which is a linear function and passes the origin, shows Charlie's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Charlie starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed steadily until the end of the race\nB:Charlie starts off at a constant speed and then increases his speed at a steady rate\nC:Charlie hits his maximum speed about halfway through the race\nD:Charlie increases his speed at a constant rate throughout",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph, which is a linear function and passes the origin, shows Charlie's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Charlie starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed steadily until the end of the race\nB:Charlie starts off at a constant speed and then increases his speed at a steady rate\nC:Charlie hits his maximum speed about halfway through the race\nD:Charlie increases his speed at a constant rate throughout",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph, which is a linear function and passes the origin, shows Charlie's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Charlie starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed steadily until the end of the race\nB:Charlie starts off at a constant speed and then increases his speed at a steady rate\nC:Charlie hits his maximum speed about halfway through the race\nD:Charlie increases his speed at a constant rate throughout",
        "question_for_eval": "The graph, which is a linear function and passes the origin, shows Charlie's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Charlie starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed steadily until the end of the race\nB:Charlie starts off at a constant speed and then increases his speed at a steady rate\nC:Charlie hits his maximum speed about halfway through the race\nD:Charlie increases his speed at a constant rate throughout"
    },
    {
        "sample_index": "614",
        "problem_index": "614",
        "problem_version": "Text Only",
        "question": "The graph, which is a piecewise function and passes through the origin, shows John's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:John increases his speed for the first half of the race and then decreases his speed in the second half\nB:John increases his speed at a constant rate throughout the entire race\nC:John starts off by increasing his pace gradually and then stops as he trips over a stick, but then recovers and is able to increase his speed steadily until the end of the race\nD:John starts off by increasing his pace gradually and then continues to steadily increase his pace at a faster rate",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows John's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:John increases his speed for the first half of the race and then decreases his speed in the second half\nB:John increases his speed at a constant rate throughout the entire race\nC:John starts off by increasing his pace gradually and then stops as he trips over a stick, but then recovers and is able to increase his speed steadily until the end of the race\nD:John starts off by increasing his pace gradually and then continues to steadily increase his pace at a faster rate",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows John's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:John increases his speed for the first half of the race and then decreases his speed in the second half\nB:John increases his speed at a constant rate throughout the entire race\nC:John starts off by increasing his pace gradually and then stops as he trips over a stick, but then recovers and is able to increase his speed steadily until the end of the race\nD:John starts off by increasing his pace gradually and then continues to steadily increase his pace at a faster rate",
        "question_for_eval": "The graph, which is a piecewise function and passes through the origin, shows John's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:John increases his speed for the first half of the race and then decreases his speed in the second half\nB:John increases his speed at a constant rate throughout the entire race\nC:John starts off by increasing his pace gradually and then stops as he trips over a stick, but then recovers and is able to increase his speed steadily until the end of the race\nD:John starts off by increasing his pace gradually and then continues to steadily increase his pace at a faster rate"
    },
    {
        "sample_index": "615",
        "problem_index": "615",
        "problem_version": "Text Only",
        "question": "The graph, which is a piecewise function and passes through the origin, shows Jimmy's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Jimmy starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed until the end of the race\nB:Jimmy starts off at a constant speed and then increases his speed at a steady rate\nC:Jimmy starts off by increasing his pace gradually and then maintains a constant speed\nD:Jimmy hits his maximum speed about halfway through the race",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows Jimmy's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Jimmy starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed until the end of the race\nB:Jimmy starts off at a constant speed and then increases his speed at a steady rate\nC:Jimmy starts off by increasing his pace gradually and then maintains a constant speed\nD:Jimmy hits his maximum speed about halfway through the race",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows Jimmy's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Jimmy starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed until the end of the race\nB:Jimmy starts off at a constant speed and then increases his speed at a steady rate\nC:Jimmy starts off by increasing his pace gradually and then maintains a constant speed\nD:Jimmy hits his maximum speed about halfway through the race",
        "question_for_eval": "The graph, which is a piecewise function and passes through the origin, shows Jimmy's speed while he is competing in a bike race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Jimmy starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed until the end of the race\nB:Jimmy starts off at a constant speed and then increases his speed at a steady rate\nC:Jimmy starts off by increasing his pace gradually and then maintains a constant speed\nD:Jimmy hits his maximum speed about halfway through the race"
    },
    {
        "sample_index": "616",
        "problem_index": "616",
        "problem_version": "Text Only",
        "question": "The graph, which is a piecewise function and passes through the origin, shows Bart's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Bart increases his speed for the first half of the race and then slows in the second half\nB:Bart starts off by increasing his pace gradually and then maintains a constant speed\nC:Bart starts off at a constant speed and then increases his speed at a steady rate\nD:Bart increases his speed at a constant rate throughout the entire race",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows Bart's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Bart increases his speed for the first half of the race and then slows in the second half\nB:Bart starts off by increasing his pace gradually and then maintains a constant speed\nC:Bart starts off at a constant speed and then increases his speed at a steady rate\nD:Bart increases his speed at a constant rate throughout the entire race",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows Bart's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Bart increases his speed for the first half of the race and then slows in the second half\nB:Bart starts off by increasing his pace gradually and then maintains a constant speed\nC:Bart starts off at a constant speed and then increases his speed at a steady rate\nD:Bart increases his speed at a constant rate throughout the entire race",
        "question_for_eval": "The graph, which is a piecewise function and passes through the origin, shows Bart's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Bart increases his speed for the first half of the race and then slows in the second half\nB:Bart starts off by increasing his pace gradually and then maintains a constant speed\nC:Bart starts off at a constant speed and then increases his speed at a steady rate\nD:Bart increases his speed at a constant rate throughout the entire race"
    },
    {
        "sample_index": "617",
        "problem_index": "617",
        "problem_version": "Text Only",
        "question": "The graph, which is a piecewise function and passes through the origin, shows Frank's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Frank starts off at a constant speed and then increases his speed at a steady rate\nB:Frank starts off by increasing his pace gradually and then maintains a constant speed\nC:Frank starts off by increasing his pace gradually, then increases his pace at a faster rate as he sees his arch rival beside him and finally increases his pace at a more gradual pace\nD:Frank increases his speed at a constant rate throughout the entire race",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows Frank's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Frank starts off at a constant speed and then increases his speed at a steady rate\nB:Frank starts off by increasing his pace gradually and then maintains a constant speed\nC:Frank starts off by increasing his pace gradually, then increases his pace at a faster rate as he sees his arch rival beside him and finally increases his pace at a more gradual pace\nD:Frank increases his speed at a constant rate throughout the entire race",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The graph, which is a piecewise function and passes through the origin, shows Frank's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Frank starts off at a constant speed and then increases his speed at a steady rate\nB:Frank starts off by increasing his pace gradually and then maintains a constant speed\nC:Frank starts off by increasing his pace gradually, then increases his pace at a faster rate as he sees his arch rival beside him and finally increases his pace at a more gradual pace\nD:Frank increases his speed at a constant rate throughout the entire race",
        "question_for_eval": "The graph, which is a piecewise function and passes through the origin, shows Frank's speed while he is competing in a walking race, the x-axis representing Time and the y-axis representing Speed. Which situation corresponds to the graph?\nChoices:\nA:Frank starts off at a constant speed and then increases his speed at a steady rate\nB:Frank starts off by increasing his pace gradually and then maintains a constant speed\nC:Frank starts off by increasing his pace gradually, then increases his pace at a faster rate as he sees his arch rival beside him and finally increases his pace at a more gradual pace\nD:Frank increases his speed at a constant rate throughout the entire race"
    },
    {
        "sample_index": "618",
        "problem_index": "618",
        "problem_version": "Text Only",
        "question": "Consider the graph, where it is an exponential function and passes through (0,1), (1,2), (2,4), and (3,8), shown.\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of people $(y)$ attending a parent/teacher conference when there are $x$ parents, each bringing 2 children.\nB:The number of layers $(y)$ resulting from a rectangular piece of paper being folded in half $x$ times.\nC:The number of handshakes $(y)$ made by $x$ people in a room if every person shakes hands with every other person.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Consider the graph, where it is an exponential function and passes through (0,1), (1,2), (2,4), and (3,8), shown.\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of people $(y)$ attending a parent/teacher conference when there are $x$ parents, each bringing 2 children.\nB:The number of layers $(y)$ resulting from a rectangular piece of paper being folded in half $x$ times.\nC:The number of handshakes $(y)$ made by $x$ people in a room if every person shakes hands with every other person.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Consider the graph, where it is an exponential function and passes through (0,1), (1,2), (2,4), and (3,8), shown.\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of people $(y)$ attending a parent/teacher conference when there are $x$ parents, each bringing 2 children.\nB:The number of layers $(y)$ resulting from a rectangular piece of paper being folded in half $x$ times.\nC:The number of handshakes $(y)$ made by $x$ people in a room if every person shakes hands with every other person.",
        "question_for_eval": "Consider the graph, where it is an exponential function and passes through (0,1), (1,2), (2,4), and (3,8), shown.\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of people $(y)$ attending a parent/teacher conference when there are $x$ parents, each bringing 2 children.\nB:The number of layers $(y)$ resulting from a rectangular piece of paper being folded in half $x$ times.\nC:The number of handshakes $(y)$ made by $x$ people in a room if every person shakes hands with every other person."
    },
    {
        "sample_index": "619",
        "problem_index": "619",
        "problem_version": "Text Only",
        "question": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n",
        "image": "",
        "answer": "8",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Plane Geometry",
            "subfield": "Analytic"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n",
        "question_for_eval": "Consider the circle, which has 4 intersection points with axes, in the graph.\n\nState the diameter.\n"
    },
    {
        "sample_index": "620",
        "problem_index": "620",
        "problem_version": "Text Only",
        "question": "This graph shows the relationship between the current (in amperes) and resistance (in ohms) in an electrical circuit, when the voltage provided to the circuit is 240 V. The equation could be described as \\frac{240}{\\text{Resistance}}=\\text{Current}\n\nWhat happens to the current as the resistance increases?\nChoices:\nA:The current increases.\nB:The current decreases.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: This graph shows the relationship between the current (in amperes) and resistance (in ohms) in an electrical circuit, when the voltage provided to the circuit is 240 V. The equation could be described as \\frac{240}{\\text{Resistance}}=\\text{Current}\n\nWhat happens to the current as the resistance increases?\nChoices:\nA:The current increases.\nB:The current decreases.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: This graph shows the relationship between the current (in amperes) and resistance (in ohms) in an electrical circuit, when the voltage provided to the circuit is 240 V. The equation could be described as \\frac{240}{\\text{Resistance}}=\\text{Current}\n\nWhat happens to the current as the resistance increases?\nChoices:\nA:The current increases.\nB:The current decreases.",
        "question_for_eval": "This graph shows the relationship between the current (in amperes) and resistance (in ohms) in an electrical circuit, when the voltage provided to the circuit is 240 V. The equation could be described as \\frac{240}{\\text{Resistance}}=\\text{Current}\n\nWhat happens to the current as the resistance increases?\nChoices:\nA:The current increases.\nB:The current decreases."
    },
    {
        "sample_index": "621",
        "problem_index": "621",
        "problem_version": "Text Only",
        "question": "Consider the graph shown. A curve passes (0,1), (1,2), (2,4), (3,8). As x increases, y increases.\n\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.\nB:The number of layers, y, resulting from a rectangular piece of paper being folded in half x times.\nC:The number of people, y, attending a parent/teacher conference when there are x parents who each bring 2 children.",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Consider the graph shown. A curve passes (0,1), (1,2), (2,4), (3,8). As x increases, y increases.\n\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.\nB:The number of layers, y, resulting from a rectangular piece of paper being folded in half x times.\nC:The number of people, y, attending a parent/teacher conference when there are x parents who each bring 2 children.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Consider the graph shown. A curve passes (0,1), (1,2), (2,4), (3,8). As x increases, y increases.\n\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.\nB:The number of layers, y, resulting from a rectangular piece of paper being folded in half x times.\nC:The number of people, y, attending a parent/teacher conference when there are x parents who each bring 2 children.",
        "question_for_eval": "Consider the graph shown. A curve passes (0,1), (1,2), (2,4), (3,8). As x increases, y increases.\n\n\nWhich of the following relationships could be represented by the given graph?\nChoices:\nA:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.\nB:The number of layers, y, resulting from a rectangular piece of paper being folded in half x times.\nC:The number of people, y, attending a parent/teacher conference when there are x parents who each bring 2 children."
    },
    {
        "sample_index": "622",
        "problem_index": "622",
        "problem_version": "Text Only",
        "question": "The logarithm function and a line are graphed. Logarithm function $f$ is graphed in blue and it goes through (30,4), (5,2), (55,5). Line $y=4$ is graphed in red and parallel to x-axis. A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.\n\nThe amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.\n\nWhich statements represent the meaning of the intersection point of the graphs?\n\nChoose all answers that apply:\nChoices:\nA:It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \\mathrm{mg}$.\nB:\nC:It gives the solution to the equation $-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)=4$.\nD:It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.\nE:\nF:It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours.",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The logarithm function and a line are graphed. Logarithm function $f$ is graphed in blue and it goes through (30,4), (5,2), (55,5). Line $y=4$ is graphed in red and parallel to x-axis. A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.\n\nThe amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.\n\nWhich statements represent the meaning of the intersection point of the graphs?\n\nChoose all answers that apply:\nChoices:\nA:It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \\mathrm{mg}$.\nB:\nC:It gives the solution to the equation $-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)=4$.\nD:It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.\nE:\nF:It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The logarithm function and a line are graphed. Logarithm function $f$ is graphed in blue and it goes through (30,4), (5,2), (55,5). Line $y=4$ is graphed in red and parallel to x-axis. A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.\n\nThe amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.\n\nWhich statements represent the meaning of the intersection point of the graphs?\n\nChoose all answers that apply:\nChoices:\nA:It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \\mathrm{mg}$.\nB:\nC:It gives the solution to the equation $-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)=4$.\nD:It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.\nE:\nF:It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours.",
        "question_for_eval": "The logarithm function and a line are graphed. Logarithm function $f$ is graphed in blue and it goes through (30,4), (5,2), (55,5). Line $y=4$ is graphed in red and parallel to x-axis. A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.\n\nThe amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.\n\nWhich statements represent the meaning of the intersection point of the graphs?\n\nChoose all answers that apply:\nChoices:\nA:It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \\mathrm{mg}$.\nB:\nC:It gives the solution to the equation $-1.25 \\cdot \\ln \\left(\\frac{1}{x}\\right)=4$.\nD:It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.\nE:\nF:It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours."
    },
    {
        "sample_index": "623",
        "problem_index": "623",
        "problem_version": "Text Only",
        "question": "Two piecewirse function $g$ and $f$ are graphed, $g$ is graphed in purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), $f$ is graphed in blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). t is the number of minutes that have passed since noon at a local airport.\nThe airplanes have the same height about 9 minutes after noon.\nWhat is the other time the airplanes have the same height?\nRound your answer to the nearest ten minutes.\nAbout _ minutes after noon\n",
        "image": "",
        "answer": "90",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Two piecewirse function $g$ and $f$ are graphed, $g$ is graphed in purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), $f$ is graphed in blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). t is the number of minutes that have passed since noon at a local airport.\nThe airplanes have the same height about 9 minutes after noon.\nWhat is the other time the airplanes have the same height?\nRound your answer to the nearest ten minutes.\nAbout _ minutes after noon\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Two piecewirse function $g$ and $f$ are graphed, $g$ is graphed in purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), $f$ is graphed in blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). t is the number of minutes that have passed since noon at a local airport.\nThe airplanes have the same height about 9 minutes after noon.\nWhat is the other time the airplanes have the same height?\nRound your answer to the nearest ten minutes.\nAbout _ minutes after noon\n",
        "question_for_eval": "Two piecewirse function $g$ and $f$ are graphed, $g$ is graphed in purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), $f$ is graphed in blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). t is the number of minutes that have passed since noon at a local airport.\nThe airplanes have the same height about 9 minutes after noon.\nWhat is the other time the airplanes have the same height?\nRound your answer to the nearest ten minutes.\nAbout _ minutes after noon\n"
    },
    {
        "sample_index": "624",
        "problem_index": "624",
        "problem_version": "Text Only",
        "question": "For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980. The line chart is begin from (15,150) and goes to (25,130).\n\nFind the linear function  y,  where  y  depends on  t,  the number of years since 1980.\n",
        "image": "",
        "answer": "y=-2 t+180",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980. The line chart is begin from (15,150) and goes to (25,130).\n\nFind the linear function  y,  where  y  depends on  t,  the number of years since 1980.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980. The line chart is begin from (15,150) and goes to (25,130).\n\nFind the linear function  y,  where  y  depends on  t,  the number of years since 1980.\n",
        "question_for_eval": "For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980. The line chart is begin from (15,150) and goes to (25,130).\n\nFind the linear function  y,  where  y  depends on  t,  the number of years since 1980.\n"
    },
    {
        "sample_index": "625",
        "problem_index": "625",
        "problem_version": "Text Only",
        "question": "A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n",
        "image": "",
        "answer": "Center $=(20,10)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n",
        "question_for_eval": "A cake maker has rectangular boxes measuring $40 \\mathrm{~cm}$ in length and 20 $\\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.\n\nState the coordinates of the center of the cake in the form $(a, b)$.\n"
    },
    {
        "sample_index": "626",
        "problem_index": "626",
        "problem_version": "Text Only",
        "question": "The linear function is graphed. The slope is less than 0. It passes through (0,4) and (4,0). Consider the graph of $y=4-x$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n",
        "image": "",
        "answer": "$=(4,0)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The linear function is graphed. The slope is less than 0. It passes through (0,4) and (4,0). Consider the graph of $y=4-x$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The linear function is graphed. The slope is less than 0. It passes through (0,4) and (4,0). Consider the graph of $y=4-x$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n",
        "question_for_eval": "The linear function is graphed. The slope is less than 0. It passes through (0,4) and (4,0). Consider the graph of $y=4-x$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n"
    },
    {
        "sample_index": "627",
        "problem_index": "627",
        "problem_version": "Text Only",
        "question": "Two linear functions are graphed. The slope of function is greater than 0. It intersects the x-axis and the y-axis at (0,-4). Consider the graph of $y=x-4$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n",
        "image": "",
        "answer": "$(4,0)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Two linear functions are graphed. The slope of function is greater than 0. It intersects the x-axis and the y-axis at (0,-4). Consider the graph of $y=x-4$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Two linear functions are graphed. The slope of function is greater than 0. It intersects the x-axis and the y-axis at (0,-4). Consider the graph of $y=x-4$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n",
        "question_for_eval": "Two linear functions are graphed. The slope of function is greater than 0. It intersects the x-axis and the y-axis at (0,-4). Consider the graph of $y=x-4$.\n\nState the coordinates of the $x$-intercept in the form $(a, b)$.\n"
    },
    {
        "sample_index": "628",
        "problem_index": "628",
        "problem_version": "Text Only",
        "question": "Two linear functions are graphed. The slope of function is less than 0. It intersects the x-axis at (4,0) and the y-axis at (0,4). Consider the graph of $y=4-x$.\n\nIf the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?\n\nState the coordinates in the form $(a, b)$.\n",
        "image": "",
        "answer": "$(0,14)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Two linear functions are graphed. The slope of function is less than 0. It intersects the x-axis at (4,0) and the y-axis at (0,4). Consider the graph of $y=4-x$.\n\nIf the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?\n\nState the coordinates in the form $(a, b)$.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Two linear functions are graphed. The slope of function is less than 0. It intersects the x-axis at (4,0) and the y-axis at (0,4). Consider the graph of $y=4-x$.\n\nIf the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?\n\nState the coordinates in the form $(a, b)$.\n",
        "question_for_eval": "Two linear functions are graphed. The slope of function is less than 0. It intersects the x-axis at (4,0) and the y-axis at (0,4). Consider the graph of $y=4-x$.\n\nIf the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?\n\nState the coordinates in the form $(a, b)$.\n"
    },
    {
        "sample_index": "629",
        "problem_index": "629",
        "problem_version": "Text Only",
        "question": "The linear function is graphed. The x-axis represents Time (minutes) and the y-axis represents Water (liters). The slope is less than 0. It intersects the x-axis at (5,0) and the y-axis at (0,360). Archimedes drained the water in his tub.\nThe amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.\nHow much water was initially in the tub?\n",
        "image": "",
        "answer": "Bugs Bunny",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The linear function is graphed. The x-axis represents Time (minutes) and the y-axis represents Water (liters). The slope is less than 0. It intersects the x-axis at (5,0) and the y-axis at (0,360). Archimedes drained the water in his tub.\nThe amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.\nHow much water was initially in the tub?\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The linear function is graphed. The x-axis represents Time (minutes) and the y-axis represents Water (liters). The slope is less than 0. It intersects the x-axis at (5,0) and the y-axis at (0,360). Archimedes drained the water in his tub.\nThe amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.\nHow much water was initially in the tub?\n",
        "question_for_eval": "The linear function is graphed. The x-axis represents Time (minutes) and the y-axis represents Water (liters). The slope is less than 0. It intersects the x-axis at (5,0) and the y-axis at (0,360). Archimedes drained the water in his tub.\nThe amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.\nHow much water was initially in the tub?\n"
    },
    {
        "sample_index": "630",
        "problem_index": "630",
        "problem_version": "Text Only",
        "question": "The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of y=\\sin x. Its first maximum point for x\\ge 0 is at \\left(90^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=5\\sin x\n",
        "image": "",
        "answer": "y=\\sin x=\\left(90^\\circ ,5\\right)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of y=\\sin x. Its first maximum point for x\\ge 0 is at \\left(90^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=5\\sin x\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of y=\\sin x. Its first maximum point for x\\ge 0 is at \\left(90^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=5\\sin x\n",
        "question_for_eval": "The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of y=\\sin x. Its first maximum point for x\\ge 0 is at \\left(90^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=5\\sin x\n"
    },
    {
        "sample_index": "631",
        "problem_index": "631",
        "problem_version": "Text Only",
        "question": "The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=-5\\sin x\n",
        "image": "",
        "answer": "\\left(x,y\\right)=\\left(270^\\circ ,5\\right)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=-5\\sin x\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=-5\\sin x\n",
        "question_for_eval": "The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\n\ny=-5\\sin x\n"
    },
    {
        "sample_index": "632",
        "problem_index": "632",
        "problem_version": "Text Only",
        "question": "The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of y=\\cos x. Its first maximum point for x\\ge 0 is at \\left(0^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\ny=\\cos \\left(x+45^\\circ \\right)\n",
        "image": "",
        "answer": "\\left(315^\\circ ,1\\right)",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of y=\\cos x. Its first maximum point for x\\ge 0 is at \\left(0^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\ny=\\cos \\left(x+45^\\circ \\right)\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of y=\\cos x. Its first maximum point for x\\ge 0 is at \\left(0^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\ny=\\cos \\left(x+45^\\circ \\right)\n",
        "question_for_eval": "The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of y=\\cos x. Its first maximum point for x\\ge 0 is at \\left(0^\\circ ,1\\right).\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\\ge 0.\ny=\\cos \\left(x+45^\\circ \\right)\n"
    },
    {
        "sample_index": "633",
        "problem_index": "633",
        "problem_version": "Text Only",
        "question": "The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of $y=\\sin x$. Its first maximum point for $x \\geq 0$ is at $\\left(90^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=5 \\sin x$\n",
        "image": "",
        "answer": "$(x, y)=\\left(90^{\\circ}, 5\\right)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of $y=\\sin x$. Its first maximum point for $x \\geq 0$ is at $\\left(90^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=5 \\sin x$\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of $y=\\sin x$. Its first maximum point for $x \\geq 0$ is at $\\left(90^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=5 \\sin x$\n",
        "question_for_eval": "The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of $y=\\sin x$. Its first maximum point for $x \\geq 0$ is at $\\left(90^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=5 \\sin x$\n"
    },
    {
        "sample_index": "634",
        "problem_index": "634",
        "problem_version": "Text Only",
        "question": "The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of $y=\\cos x$. Its first maximum point for $x \\geq 0$ is at $\\left(0^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=\\cos \\left(x+45^{\\circ}\\right)$\n",
        "image": "",
        "answer": "$(x, y)=\\left(315^{\\circ}, 1\\right)$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Functions_collected",
            "subject": "Functions",
            "subfield": "Coordinate"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of $y=\\cos x$. Its first maximum point for $x \\geq 0$ is at $\\left(0^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=\\cos \\left(x+45^{\\circ}\\right)$\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of $y=\\cos x$. Its first maximum point for $x \\geq 0$ is at $\\left(0^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=\\cos \\left(x+45^{\\circ}\\right)$\n",
        "question_for_eval": "The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of $y=\\cos x$. Its first maximum point for $x \\geq 0$ is at $\\left(0^{\\circ}, 1\\right)$.\n\nBy considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \\geq 0$.\n\n$y=\\cos \\left(x+45^{\\circ}\\right)$\n"
    },
    {
        "sample_index": "635",
        "problem_index": "635",
        "problem_version": "Text Only",
        "question": "Consider a cone with slant height 13m and perpendicular height 12m.\n\nHence, find the length of the diameter of the cone's base.",
        "image": "",
        "answer": "diameter $=10 \\mathrm{~m}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider a cone with slant height 13m and perpendicular height 12m.\n\nHence, find the length of the diameter of the cone's base.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider a cone with slant height 13m and perpendicular height 12m.\n\nHence, find the length of the diameter of the cone's base.",
        "question_for_eval": "Consider a cone with slant height 13m and perpendicular height 12m.\n\nHence, find the length of the diameter of the cone's base."
    },
    {
        "sample_index": "636",
        "problem_index": "636",
        "problem_version": "Text Only",
        "question": "The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.\n\nFind the value of $r$.",
        "image": "",
        "answer": "$r=5$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.\n\nFind the value of $r$.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.\n\nFind the value of $r$.",
        "question_for_eval": "The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.\n\nFind the value of $r$."
    },
    {
        "sample_index": "637",
        "problem_index": "637",
        "problem_version": "Text Only",
        "question": "A square prism has sides of length 11cm, 11cm and 15cm as shown.\n\nNow, we want to find $y$, the length of the diagonal $DF$.\n\nCalculate $y$ to two decimal places.\n",
        "image": "",
        "answer": "$y=21.61$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A square prism has sides of length 11cm, 11cm and 15cm as shown.\n\nNow, we want to find $y$, the length of the diagonal $DF$.\n\nCalculate $y$ to two decimal places.\n",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A square prism has sides of length 11cm, 11cm and 15cm as shown.\n\nNow, we want to find $y$, the length of the diagonal $DF$.\n\nCalculate $y$ to two decimal places.\n",
        "question_for_eval": "A square prism has sides of length 11cm, 11cm and 15cm as shown.\n\nNow, we want to find $y$, the length of the diagonal $DF$.\n\nCalculate $y$ to two decimal places.\n"
    },
    {
        "sample_index": "638",
        "problem_index": "638",
        "problem_version": "Text Only",
        "question": "A triangular divider has been placed into a box, as shown in the diagram. The box has sides of length 12cm, 12cm and 17cm. \n\nCalculate the area of the triangular divider correct to two decimal places.",
        "image": "",
        "answer": "Area $=124.85 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A triangular divider has been placed into a box, as shown in the diagram. The box has sides of length 12cm, 12cm and 17cm. \n\nCalculate the area of the triangular divider correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A triangular divider has been placed into a box, as shown in the diagram. The box has sides of length 12cm, 12cm and 17cm. \n\nCalculate the area of the triangular divider correct to two decimal places.",
        "question_for_eval": "A triangular divider has been placed into a box, as shown in the diagram. The box has sides of length 12cm, 12cm and 17cm. \n\nCalculate the area of the triangular divider correct to two decimal places."
    },
    {
        "sample_index": "639",
        "problem_index": "639",
        "problem_version": "Text Only",
        "question": "Find the volume of a concrete pipe with outer radius 7 metres, inner radius 3 metres and length 13 metres. Write your answer correct to two decimal places.",
        "image": "",
        "answer": "Volume $=1633.63 \\mathrm{~m}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of a concrete pipe with outer radius 7 metres, inner radius 3 metres and length 13 metres. Write your answer correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of a concrete pipe with outer radius 7 metres, inner radius 3 metres and length 13 metres. Write your answer correct to two decimal places.",
        "question_for_eval": "Find the volume of a concrete pipe with outer radius 7 metres, inner radius 3 metres and length 13 metres. Write your answer correct to two decimal places."
    },
    {
        "sample_index": "640",
        "problem_index": "640",
        "problem_version": "Text Only",
        "question": "A hollow cylindrical pipe has the dimensions shown in the figure. The outer diameter is 2.1 centimeters. The inner diameter is 1.8 centimeters. The length is 13 centimeters.\n\nThe pipe is made of a particularly strong metal.\n\nCalculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer correct to one decimal place.",
        "image": "",
        "answer": "Weight $=63.3 \\mathrm{~g}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A hollow cylindrical pipe has the dimensions shown in the figure. The outer diameter is 2.1 centimeters. The inner diameter is 1.8 centimeters. The length is 13 centimeters.\n\nThe pipe is made of a particularly strong metal.\n\nCalculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A hollow cylindrical pipe has the dimensions shown in the figure. The outer diameter is 2.1 centimeters. The inner diameter is 1.8 centimeters. The length is 13 centimeters.\n\nThe pipe is made of a particularly strong metal.\n\nCalculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer correct to one decimal place.",
        "question_for_eval": "A hollow cylindrical pipe has the dimensions shown in the figure. The outer diameter is 2.1 centimeters. The inner diameter is 1.8 centimeters. The length is 13 centimeters.\n\nThe pipe is made of a particularly strong metal.\n\nCalculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer correct to one decimal place."
    },
    {
        "sample_index": "641",
        "problem_index": "641",
        "problem_version": "Text Only",
        "question": "The figure shows a cylinder with height of 8 centimeters and radius of 6 centimeters. The volume of a cylinder is given by $V=\\pi r^2h$. \n\nFind the volume of the cylinder, rounding your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=904.78 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The figure shows a cylinder with height of 8 centimeters and radius of 6 centimeters. The volume of a cylinder is given by $V=\\pi r^2h$. \n\nFind the volume of the cylinder, rounding your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The figure shows a cylinder with height of 8 centimeters and radius of 6 centimeters. The volume of a cylinder is given by $V=\\pi r^2h$. \n\nFind the volume of the cylinder, rounding your answer to two decimal places.",
        "question_for_eval": "The figure shows a cylinder with height of 8 centimeters and radius of 6 centimeters. The volume of a cylinder is given by $V=\\pi r^2h$. \n\nFind the volume of the cylinder, rounding your answer to two decimal places."
    },
    {
        "sample_index": "642",
        "problem_index": "642",
        "problem_version": "Text Only",
        "question": "The figure shows $\\frac{3}{4}$ of a cylinder. The height is 15 centimeters and radius is 5 centimeters. Find the volume of the figure shown, correct to two decimal places.",
        "image": "",
        "answer": "Volume $=883.57 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The figure shows $\\frac{3}{4}$ of a cylinder. The height is 15 centimeters and radius is 5 centimeters. Find the volume of the figure shown, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The figure shows $\\frac{3}{4}$ of a cylinder. The height is 15 centimeters and radius is 5 centimeters. Find the volume of the figure shown, correct to two decimal places.",
        "question_for_eval": "The figure shows $\\frac{3}{4}$ of a cylinder. The height is 15 centimeters and radius is 5 centimeters. Find the volume of the figure shown, correct to two decimal places."
    },
    {
        "sample_index": "643",
        "problem_index": "643",
        "problem_version": "Text Only",
        "question": "Find the volume of the cone shown. The perpendicular height is 6 centimeters and radius is 2 centimeters.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=25.13 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the cone shown. The perpendicular height is 6 centimeters and radius is 2 centimeters.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the cone shown. The perpendicular height is 6 centimeters and radius is 2 centimeters.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the volume of the cone shown. The perpendicular height is 6 centimeters and radius is 2 centimeters.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "644",
        "problem_index": "644",
        "problem_version": "Text Only",
        "question": "Find the volume of the cone shown. The slant height is 8 centimeters and radius is 2 centimeters. \n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=32.45 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the cone shown. The slant height is 8 centimeters and radius is 2 centimeters. \n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the cone shown. The slant height is 8 centimeters and radius is 2 centimeters. \n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the volume of the cone shown. The slant height is 8 centimeters and radius is 2 centimeters. \n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "645",
        "problem_index": "645",
        "problem_version": "Text Only",
        "question": "A cone is sliced in half to produce the solid shown. The slant height is 9 centimeters and diameter is 3 centimeters.\n\nFind the volume of the solid, correct to two decimal places.",
        "image": "",
        "answer": "Volume $=10.45 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A cone is sliced in half to produce the solid shown. The slant height is 9 centimeters and diameter is 3 centimeters.\n\nFind the volume of the solid, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A cone is sliced in half to produce the solid shown. The slant height is 9 centimeters and diameter is 3 centimeters.\n\nFind the volume of the solid, correct to two decimal places.",
        "question_for_eval": "A cone is sliced in half to produce the solid shown. The slant height is 9 centimeters and diameter is 3 centimeters.\n\nFind the volume of the solid, correct to two decimal places."
    },
    {
        "sample_index": "646",
        "problem_index": "646",
        "problem_version": "Text Only",
        "question": "Find the volume of the cone pictured here. The perpendicular height is 12.5 centimeters and radius is 4.1 centimeters.\n\n(Give your answer correct to 1 decimal place.)",
        "image": "",
        "answer": "220.0 \\mathrm{~cm}^{3}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the cone pictured here. The perpendicular height is 12.5 centimeters and radius is 4.1 centimeters.\n\n(Give your answer correct to 1 decimal place.)",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the cone pictured here. The perpendicular height is 12.5 centimeters and radius is 4.1 centimeters.\n\n(Give your answer correct to 1 decimal place.)",
        "question_for_eval": "Find the volume of the cone pictured here. The perpendicular height is 12.5 centimeters and radius is 4.1 centimeters.\n\n(Give your answer correct to 1 decimal place.)"
    },
    {
        "sample_index": "647",
        "problem_index": "647",
        "problem_version": "Text Only",
        "question": "Find the volume of the cone pictured. The perpendicular height is 6 and radius is 3.\n\n(Give your answer correct to 2 decimal places.)",
        "image": "",
        "answer": "56.55 units $^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the cone pictured. The perpendicular height is 6 and radius is 3.\n\n(Give your answer correct to 2 decimal places.)",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the cone pictured. The perpendicular height is 6 and radius is 3.\n\n(Give your answer correct to 2 decimal places.)",
        "question_for_eval": "Find the volume of the cone pictured. The perpendicular height is 6 and radius is 3.\n\n(Give your answer correct to 2 decimal places.)"
    },
    {
        "sample_index": "648",
        "problem_index": "648",
        "problem_version": "Text Only",
        "question": "Find the volume of the sphere shown. The radius is 3 centimeters.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=113.10 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the sphere shown. The radius is 3 centimeters.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the sphere shown. The radius is 3 centimeters.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the volume of the sphere shown. The radius is 3 centimeters.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "649",
        "problem_index": "649",
        "problem_version": "Text Only",
        "question": "Find the volume of the sphere shown. The diameter is 4 centimeters.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=33.51 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the sphere shown. The diameter is 4 centimeters.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the sphere shown. The diameter is 4 centimeters.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the volume of the sphere shown. The diameter is 4 centimeters.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "650",
        "problem_index": "650",
        "problem_version": "Text Only",
        "question": "The composite solid consists of two hemispheres stuck together. The diameter of large hemisphere is 12 centimeters and small hemisphere is 6 centimeters. Find the volume of the solid.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=508.94 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The composite solid consists of two hemispheres stuck together. The diameter of large hemisphere is 12 centimeters and small hemisphere is 6 centimeters. Find the volume of the solid.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The composite solid consists of two hemispheres stuck together. The diameter of large hemisphere is 12 centimeters and small hemisphere is 6 centimeters. Find the volume of the solid.\n\nRound your answer to two decimal places.",
        "question_for_eval": "The composite solid consists of two hemispheres stuck together. The diameter of large hemisphere is 12 centimeters and small hemisphere is 6 centimeters. Find the volume of the solid.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "651",
        "problem_index": "651",
        "problem_version": "Text Only",
        "question": "The radius of the sphere is 8.8 centimeters. Find the volume of the sphere, giving your answer correct to two decimal places.",
        "image": "",
        "answer": "Volume $=2854.54 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the sphere is 8.8 centimeters. Find the volume of the sphere, giving your answer correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the sphere is 8.8 centimeters. Find the volume of the sphere, giving your answer correct to two decimal places.",
        "question_for_eval": "The radius of the sphere is 8.8 centimeters. Find the volume of the sphere, giving your answer correct to two decimal places."
    },
    {
        "sample_index": "652",
        "problem_index": "652",
        "problem_version": "Text Only",
        "question": "The radius of the sphere is 22.36 millimeters. Find the volume of the sphere shown, giving your answer correct to two decimal places.",
        "image": "",
        "answer": "Volume $=46827.83 \\mathrm{~mm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The radius of the sphere is 22.36 millimeters. Find the volume of the sphere shown, giving your answer correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The radius of the sphere is 22.36 millimeters. Find the volume of the sphere shown, giving your answer correct to two decimal places.",
        "question_for_eval": "The radius of the sphere is 22.36 millimeters. Find the volume of the sphere shown, giving your answer correct to two decimal places."
    },
    {
        "sample_index": "653",
        "problem_index": "653",
        "problem_version": "Text Only",
        "question": "Find the volume of the following hemisphere. The radius is 6.\n\nRound your answer to three decimal places.",
        "image": "",
        "answer": "Volume $=452.389$ cubic units",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the following hemisphere. The radius is 6.\n\nRound your answer to three decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the following hemisphere. The radius is 6.\n\nRound your answer to three decimal places.",
        "question_for_eval": "Find the volume of the following hemisphere. The radius is 6.\n\nRound your answer to three decimal places."
    },
    {
        "sample_index": "654",
        "problem_index": "654",
        "problem_version": "Text Only",
        "question": "Find the volume of the following hemisphere. The radius is 25.36 centimeters.\n\nRound your answer to three decimal places.",
        "image": "",
        "answer": "Volume $=34159.095 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the following hemisphere. The radius is 25.36 centimeters.\n\nRound your answer to three decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the following hemisphere. The radius is 25.36 centimeters.\n\nRound your answer to three decimal places.",
        "question_for_eval": "Find the volume of the following hemisphere. The radius is 25.36 centimeters.\n\nRound your answer to three decimal places."
    },
    {
        "sample_index": "655",
        "problem_index": "655",
        "problem_version": "Text Only",
        "question": "Consider the following cylinder with a height of 35 cm and base radius of 10 cm. Find the surface area of the cylinder.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=2827.43 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following cylinder with a height of 35 cm and base radius of 10 cm. Find the surface area of the cylinder.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following cylinder with a height of 35 cm and base radius of 10 cm. Find the surface area of the cylinder.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Consider the following cylinder with a height of 35 cm and base radius of 10 cm. Find the surface area of the cylinder.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "656",
        "problem_index": "656",
        "problem_version": "Text Only",
        "question": "The following cylinder has a height of 49 m and a base radius of 21 m.\n\nFind the surface area.\n\nGive your answer to the nearest two decimal places.",
        "image": "",
        "answer": "Surface Area $=9236.28 \\mathrm{~m}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The following cylinder has a height of 49 m and a base radius of 21 m.\n\nFind the surface area.\n\nGive your answer to the nearest two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The following cylinder has a height of 49 m and a base radius of 21 m.\n\nFind the surface area.\n\nGive your answer to the nearest two decimal places.",
        "question_for_eval": "The following cylinder has a height of 49 m and a base radius of 21 m.\n\nFind the surface area.\n\nGive your answer to the nearest two decimal places."
    },
    {
        "sample_index": "657",
        "problem_index": "657",
        "problem_version": "Text Only",
        "question": "Find the surface area of the given cylinder. The height is 80 and radius is 98. All measurements in the diagram are in mm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=109603.88 \\mathrm{~mm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the given cylinder. The height is 80 and radius is 98. All measurements in the diagram are in mm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the given cylinder. The height is 80 and radius is 98. All measurements in the diagram are in mm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the given cylinder. The height is 80 and radius is 98. All measurements in the diagram are in mm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "658",
        "problem_index": "658",
        "problem_version": "Text Only",
        "question": "The diagram shows a water trough in the shape of a half cylinder. The height is 2.49 m and radius is 0.92 m.\n\nFind the surface area of the outside of this water trough.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=9.86 \\mathrm{~m}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The diagram shows a water trough in the shape of a half cylinder. The height is 2.49 m and radius is 0.92 m.\n\nFind the surface area of the outside of this water trough.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The diagram shows a water trough in the shape of a half cylinder. The height is 2.49 m and radius is 0.92 m.\n\nFind the surface area of the outside of this water trough.\n\nRound your answer to two decimal places.",
        "question_for_eval": "The diagram shows a water trough in the shape of a half cylinder. The height is 2.49 m and radius is 0.92 m.\n\nFind the surface area of the outside of this water trough.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "659",
        "problem_index": "659",
        "problem_version": "Text Only",
        "question": "Find the height $h$ mm of this closed cylinder if its surface area (S) is 27288(mm)^2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number.",
        "image": "",
        "answer": "$h=58$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the height $h$ mm of this closed cylinder if its surface area (S) is 27288(mm)^2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the height $h$ mm of this closed cylinder if its surface area (S) is 27288(mm)^2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number.",
        "question_for_eval": "Find the height $h$ mm of this closed cylinder if its surface area (S) is 27288(mm)^2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number."
    },
    {
        "sample_index": "660",
        "problem_index": "660",
        "problem_version": "Text Only",
        "question": "A cylinder has a surface area of 54105(mm)^2 and a radius of 79 mm.\n\nWhat must the height $h$ mm of the cylinder be?\n\nRound your answer to the nearest whole number.",
        "image": "",
        "answer": "$h=30$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A cylinder has a surface area of 54105(mm)^2 and a radius of 79 mm.\n\nWhat must the height $h$ mm of the cylinder be?\n\nRound your answer to the nearest whole number.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A cylinder has a surface area of 54105(mm)^2 and a radius of 79 mm.\n\nWhat must the height $h$ mm of the cylinder be?\n\nRound your answer to the nearest whole number.",
        "question_for_eval": "A cylinder has a surface area of 54105(mm)^2 and a radius of 79 mm.\n\nWhat must the height $h$ mm of the cylinder be?\n\nRound your answer to the nearest whole number."
    },
    {
        "sample_index": "661",
        "problem_index": "661",
        "problem_version": "Text Only",
        "question": "Find the surface area of the cylinder shown. The height is 10 cm and radius is 6 cm.\n\nGive your answer to the nearest two decimal places.",
        "image": "",
        "answer": "Surface Area $=603.19 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the cylinder shown. The height is 10 cm and radius is 6 cm.\n\nGive your answer to the nearest two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the cylinder shown. The height is 10 cm and radius is 6 cm.\n\nGive your answer to the nearest two decimal places.",
        "question_for_eval": "Find the surface area of the cylinder shown. The height is 10 cm and radius is 6 cm.\n\nGive your answer to the nearest two decimal places."
    },
    {
        "sample_index": "662",
        "problem_index": "662",
        "problem_version": "Text Only",
        "question": "Consider the solid pictured and answer the following:\n\nHence what is the total surface area? The outer radius is 11 cm, inner radius is 10 cm and length 24 cm.\n\nGive your answer to the nearest two decimal places.",
        "image": "",
        "answer": "$\\mathrm{SA}=3298.67 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the solid pictured and answer the following:\n\nHence what is the total surface area? The outer radius is 11 cm, inner radius is 10 cm and length 24 cm.\n\nGive your answer to the nearest two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the solid pictured and answer the following:\n\nHence what is the total surface area? The outer radius is 11 cm, inner radius is 10 cm and length 24 cm.\n\nGive your answer to the nearest two decimal places.",
        "question_for_eval": "Consider the solid pictured and answer the following:\n\nHence what is the total surface area? The outer radius is 11 cm, inner radius is 10 cm and length 24 cm.\n\nGive your answer to the nearest two decimal places."
    },
    {
        "sample_index": "663",
        "problem_index": "663",
        "problem_version": "Text Only",
        "question": "Write an equation for the surface area of the above cylinder if the length is $L$, the major radius $R$ and minor radius $r$. You must factorise this expression fully.",
        "image": "",
        "answer": "Surface area $=2 \\pi(R+r)(L+R-r)$ square units",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Write an equation for the surface area of the above cylinder if the length is $L$, the major radius $R$ and minor radius $r$. You must factorise this expression fully.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Write an equation for the surface area of the above cylinder if the length is $L$, the major radius $R$ and minor radius $r$. You must factorise this expression fully.",
        "question_for_eval": "Write an equation for the surface area of the above cylinder if the length is $L$, the major radius $R$ and minor radius $r$. You must factorise this expression fully."
    },
    {
        "sample_index": "664",
        "problem_index": "664",
        "problem_version": "Text Only",
        "question": "Find the surface area of the sphere shown. The radius is 11 cm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=1520.53 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the sphere shown. The radius is 11 cm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the sphere shown. The radius is 11 cm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the sphere shown. The radius is 11 cm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "665",
        "problem_index": "665",
        "problem_version": "Text Only",
        "question": "Find the surface area of the sphere shown. The diameter is 9 cm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=254.47 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the sphere shown. The diameter is 9 cm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the sphere shown. The diameter is 9 cm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the sphere shown. The diameter is 9 cm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "666",
        "problem_index": "666",
        "problem_version": "Text Only",
        "question": "Find the surface area of the following sphere. The radius is 56.17 mm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=39647.77 \\mathrm{~mm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the following sphere. The radius is 56.17 mm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the following sphere. The radius is 56.17 mm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the following sphere. The radius is 56.17 mm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "667",
        "problem_index": "667",
        "problem_version": "Text Only",
        "question": "In this question we will find the surface area of the following solid hemispher with a radius of 6:\n\nWhat is the area of the circular base of the hemisphere?\n\nRound your answer to three decimal places.",
        "image": "",
        "answer": "Area $=113.097$ units $^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In this question we will find the surface area of the following solid hemispher with a radius of 6:\n\nWhat is the area of the circular base of the hemisphere?\n\nRound your answer to three decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In this question we will find the surface area of the following solid hemispher with a radius of 6:\n\nWhat is the area of the circular base of the hemisphere?\n\nRound your answer to three decimal places.",
        "question_for_eval": "In this question we will find the surface area of the following solid hemispher with a radius of 6:\n\nWhat is the area of the circular base of the hemisphere?\n\nRound your answer to three decimal places."
    },
    {
        "sample_index": "668",
        "problem_index": "668",
        "problem_version": "Text Only",
        "question": "Consider the following hemisphere with a radius of 8. Find the total surface area.\n\nRound your answer to three decimal places.",
        "image": "",
        "answer": "Surface Area $=603.186$ units $^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following hemisphere with a radius of 8. Find the total surface area.\n\nRound your answer to three decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following hemisphere with a radius of 8. Find the total surface area.\n\nRound your answer to three decimal places.",
        "question_for_eval": "Consider the following hemisphere with a radius of 8. Find the total surface area.\n\nRound your answer to three decimal places."
    },
    {
        "sample_index": "669",
        "problem_index": "669",
        "problem_version": "Text Only",
        "question": "Find the surface area of the following hemisphere. The radius is 74.74 m,\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=52647.45$ units $^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the following hemisphere. The radius is 74.74 m,\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the following hemisphere. The radius is 74.74 m,\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the following hemisphere. The radius is 74.74 m,\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "670",
        "problem_index": "670",
        "problem_version": "Text Only",
        "question": "A solid consists of a cylinder (of radius 5mm and height 11mm) attached to a rectangular prism on one of its faces. The rectangular prism has sides of length 21mm, 10mm and 65mm. We wish to find the surface area of the entire solid. Note that an area is called 'exposed' if it is not covered by the other object.\nWhat is the exposed surface area of the rectangular prism? Give your answer correct to two decimal places.",
        "image": "",
        "answer": "S.A. of rectangular prism $=4371.46 \\mathrm{~mm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A solid consists of a cylinder (of radius 5mm and height 11mm) attached to a rectangular prism on one of its faces. The rectangular prism has sides of length 21mm, 10mm and 65mm. We wish to find the surface area of the entire solid. Note that an area is called 'exposed' if it is not covered by the other object.\nWhat is the exposed surface area of the rectangular prism? Give your answer correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A solid consists of a cylinder (of radius 5mm and height 11mm) attached to a rectangular prism on one of its faces. The rectangular prism has sides of length 21mm, 10mm and 65mm. We wish to find the surface area of the entire solid. Note that an area is called 'exposed' if it is not covered by the other object.\nWhat is the exposed surface area of the rectangular prism? Give your answer correct to two decimal places.",
        "question_for_eval": "A solid consists of a cylinder (of radius 5mm and height 11mm) attached to a rectangular prism on one of its faces. The rectangular prism has sides of length 21mm, 10mm and 65mm. We wish to find the surface area of the entire solid. Note that an area is called 'exposed' if it is not covered by the other object.\nWhat is the exposed surface area of the rectangular prism? Give your answer correct to two decimal places."
    },
    {
        "sample_index": "671",
        "problem_index": "671",
        "problem_version": "Text Only",
        "question": "We want to find the surface area of this shape. Assume that both boxes are identical in size. The box has sides of length 25, 20 and 33. The cylinder has a radius of 6 and a height of 11.\n\nFind the surface area of the solid.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=8128.50$ units $^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: We want to find the surface area of this shape. Assume that both boxes are identical in size. The box has sides of length 25, 20 and 33. The cylinder has a radius of 6 and a height of 11.\n\nFind the surface area of the solid.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: We want to find the surface area of this shape. Assume that both boxes are identical in size. The box has sides of length 25, 20 and 33. The cylinder has a radius of 6 and a height of 11.\n\nFind the surface area of the solid.\n\nRound your answer to two decimal places.",
        "question_for_eval": "We want to find the surface area of this shape. Assume that both boxes are identical in size. The box has sides of length 25, 20 and 33. The cylinder has a radius of 6 and a height of 11.\n\nFind the surface area of the solid.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "672",
        "problem_index": "672",
        "problem_version": "Text Only",
        "question": "Find the surface area of the composite figure shown, which consists of a cone and a hemisphere joined at their bases. The radius is 4 cm. The perpendicular height of cone is 10cm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Surface Area $=235.87 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the composite figure shown, which consists of a cone and a hemisphere joined at their bases. The radius is 4 cm. The perpendicular height of cone is 10cm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the composite figure shown, which consists of a cone and a hemisphere joined at their bases. The radius is 4 cm. The perpendicular height of cone is 10cm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the composite figure shown, which consists of a cone and a hemisphere joined at their bases. The radius is 4 cm. The perpendicular height of cone is 10cm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "673",
        "problem_index": "673",
        "problem_version": "Text Only",
        "question": "We wish to find the surface area of the shape given, consisting of a hemisphere and a cylinder. The radius is 10.55 mm. The height of cylinder is 33.1 mm.\n\nHence find the total surface area of the shape, correct to two decimal places.",
        "image": "",
        "answer": "Total S.A. $=3222.80 \\mathrm{~mm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: We wish to find the surface area of the shape given, consisting of a hemisphere and a cylinder. The radius is 10.55 mm. The height of cylinder is 33.1 mm.\n\nHence find the total surface area of the shape, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: We wish to find the surface area of the shape given, consisting of a hemisphere and a cylinder. The radius is 10.55 mm. The height of cylinder is 33.1 mm.\n\nHence find the total surface area of the shape, correct to two decimal places.",
        "question_for_eval": "We wish to find the surface area of the shape given, consisting of a hemisphere and a cylinder. The radius is 10.55 mm. The height of cylinder is 33.1 mm.\n\nHence find the total surface area of the shape, correct to two decimal places."
    },
    {
        "sample_index": "674",
        "problem_index": "674",
        "problem_version": "Text Only",
        "question": "A cylinder with a radius of 2.5cm and a height of 10cm contains two identical spherical balls that fit exactly inside it. What is the surface area of each ball? Give your answer correct to one decimal place.",
        "image": "",
        "answer": "Surface area $=78.5 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A cylinder with a radius of 2.5cm and a height of 10cm contains two identical spherical balls that fit exactly inside it. What is the surface area of each ball? Give your answer correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A cylinder with a radius of 2.5cm and a height of 10cm contains two identical spherical balls that fit exactly inside it. What is the surface area of each ball? Give your answer correct to one decimal place.",
        "question_for_eval": "A cylinder with a radius of 2.5cm and a height of 10cm contains two identical spherical balls that fit exactly inside it. What is the surface area of each ball? Give your answer correct to one decimal place."
    },
    {
        "sample_index": "675",
        "problem_index": "675",
        "problem_version": "Text Only",
        "question": "Let us find the surface area of the solid given (constructed by removing a hemisphere from a cylinder). The radius is 15 cm. The height of cylinder is 22 cm.\n\nHence, find the total surface area of the shape.\n\nGive our answer to two decimal places.",
        "image": "",
        "answer": "Total surface area $=4194.03 \\mathrm{~cm}^{2}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Let us find the surface area of the solid given (constructed by removing a hemisphere from a cylinder). The radius is 15 cm. The height of cylinder is 22 cm.\n\nHence, find the total surface area of the shape.\n\nGive our answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Let us find the surface area of the solid given (constructed by removing a hemisphere from a cylinder). The radius is 15 cm. The height of cylinder is 22 cm.\n\nHence, find the total surface area of the shape.\n\nGive our answer to two decimal places.",
        "question_for_eval": "Let us find the surface area of the solid given (constructed by removing a hemisphere from a cylinder). The radius is 15 cm. The height of cylinder is 22 cm.\n\nHence, find the total surface area of the shape.\n\nGive our answer to two decimal places."
    },
    {
        "sample_index": "676",
        "problem_index": "676",
        "problem_version": "Text Only",
        "question": "The solid shown is constructed by cutting out a quarter of a sphere from a cube. Find its surface area if the side length is 14.2 and the radius is half that.",
        "image": "",
        "answer": "S.A. $=1209.84$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The solid shown is constructed by cutting out a quarter of a sphere from a cube. Find its surface area if the side length is 14.2 and the radius is half that.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The solid shown is constructed by cutting out a quarter of a sphere from a cube. Find its surface area if the side length is 14.2 and the radius is half that.",
        "question_for_eval": "The solid shown is constructed by cutting out a quarter of a sphere from a cube. Find its surface area if the side length is 14.2 and the radius is half that."
    },
    {
        "sample_index": "677",
        "problem_index": "677",
        "problem_version": "Text Only",
        "question": "A square prism has sides of length 3cm, 3cm and 14cm as shown.\n\nIf the size of \\angle DFH is \\theta \u00b0, find theta to two decimal places.",
        "image": "",
        "answer": "11.83",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A square prism has sides of length 3cm, 3cm and 14cm as shown.\n\nIf the size of \\angle DFH is \\theta \u00b0, find theta to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A square prism has sides of length 3cm, 3cm and 14cm as shown.\n\nIf the size of \\angle DFH is \\theta \u00b0, find theta to two decimal places.",
        "question_for_eval": "A square prism has sides of length 3cm, 3cm and 14cm as shown.\n\nIf the size of \\angle DFH is \\theta \u00b0, find theta to two decimal places."
    },
    {
        "sample_index": "678",
        "problem_index": "678",
        "problem_version": "Text Only",
        "question": "The following is a right pyramid on a square base with side length 12cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 23cm.\nNow, if the size of \\angle VAW is \\theta \u00b0, find \\theta  to two decimal places.",
        "image": "",
        "answer": "68.34",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The following is a right pyramid on a square base with side length 12cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 23cm.\nNow, if the size of \\angle VAW is \\theta \u00b0, find \\theta  to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The following is a right pyramid on a square base with side length 12cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 23cm.\nNow, if the size of \\angle VAW is \\theta \u00b0, find \\theta  to two decimal places.",
        "question_for_eval": "The following is a right pyramid on a square base with side length 12cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 23cm.\nNow, if the size of \\angle VAW is \\theta \u00b0, find \\theta  to two decimal places."
    },
    {
        "sample_index": "679",
        "problem_index": "679",
        "problem_version": "Text Only",
        "question": "All edges of the following cube are 7 cm long.Find z, the size of \\angle AGH, correct to 2 decimal places.",
        "image": "",
        "answer": "54.74",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: All edges of the following cube are 7 cm long.Find z, the size of \\angle AGH, correct to 2 decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: All edges of the following cube are 7 cm long.Find z, the size of \\angle AGH, correct to 2 decimal places.",
        "question_for_eval": "All edges of the following cube are 7 cm long.Find z, the size of \\angle AGH, correct to 2 decimal places."
    },
    {
        "sample_index": "680",
        "problem_index": "680",
        "problem_version": "Text Only",
        "question": "A triangular prism has as dimensions those labelled on the diagram. The AB edge has length of 10. The BC edge has length of 3. The CF edge has length of 15. The EX edge and FX edge have the equal length. Find z, the size of \\angle BXC, correct to 2 decimal places.",
        "image": "",
        "answer": "10.74",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A triangular prism has as dimensions those labelled on the diagram. The AB edge has length of 10. The BC edge has length of 3. The CF edge has length of 15. The EX edge and FX edge have the equal length. Find z, the size of \\angle BXC, correct to 2 decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A triangular prism has as dimensions those labelled on the diagram. The AB edge has length of 10. The BC edge has length of 3. The CF edge has length of 15. The EX edge and FX edge have the equal length. Find z, the size of \\angle BXC, correct to 2 decimal places.",
        "question_for_eval": "A triangular prism has as dimensions those labelled on the diagram. The AB edge has length of 10. The BC edge has length of 3. The CF edge has length of 15. The EX edge and FX edge have the equal length. Find z, the size of \\angle BXC, correct to 2 decimal places."
    },
    {
        "sample_index": "681",
        "problem_index": "681",
        "problem_version": "Text Only",
        "question": "This box is to have a divider placed in as shown. The box has sides of length 19 cm, 10 cm and 7 cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.",
        "image": "",
        "answer": "75.15 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: This box is to have a divider placed in as shown. The box has sides of length 19 cm, 10 cm and 7 cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: This box is to have a divider placed in as shown. The box has sides of length 19 cm, 10 cm and 7 cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.",
        "question_for_eval": "This box is to have a divider placed in as shown. The box has sides of length 19 cm, 10 cm and 7 cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part."
    },
    {
        "sample_index": "682",
        "problem_index": "682",
        "problem_version": "Text Only",
        "question": "All edges of the base of the following square pyramid are 8 cm long, while all the sloping edges are 12 cm long. The CN edge and DN edge have the equal length.\nFind Y, the size of \\angle PNM, correct to two decimal places.",
        "image": "",
        "answer": "69.30",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: All edges of the base of the following square pyramid are 8 cm long, while all the sloping edges are 12 cm long. The CN edge and DN edge have the equal length.\nFind Y, the size of \\angle PNM, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: All edges of the base of the following square pyramid are 8 cm long, while all the sloping edges are 12 cm long. The CN edge and DN edge have the equal length.\nFind Y, the size of \\angle PNM, correct to two decimal places.",
        "question_for_eval": "All edges of the base of the following square pyramid are 8 cm long, while all the sloping edges are 12 cm long. The CN edge and DN edge have the equal length.\nFind Y, the size of \\angle PNM, correct to two decimal places."
    },
    {
        "sample_index": "683",
        "problem_index": "683",
        "problem_version": "Text Only",
        "question": "This triangular prism shaped box labelled ABCDEF needs a diagonal support inserted as shown. Find the length AF of this support.\nHence, find the length of AF in terms of AB, BD and DF.",
        "image": "",
        "answer": "\\sqrt{AB^2+BD^2+DF^2}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: This triangular prism shaped box labelled ABCDEF needs a diagonal support inserted as shown. Find the length AF of this support.\nHence, find the length of AF in terms of AB, BD and DF.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: This triangular prism shaped box labelled ABCDEF needs a diagonal support inserted as shown. Find the length AF of this support.\nHence, find the length of AF in terms of AB, BD and DF.",
        "question_for_eval": "This triangular prism shaped box labelled ABCDEF needs a diagonal support inserted as shown. Find the length AF of this support.\nHence, find the length of AF in terms of AB, BD and DF."
    },
    {
        "sample_index": "684",
        "problem_index": "684",
        "problem_version": "Text Only",
        "question": "This box is to have a divider placed in as shown. The box has sides of length 9cm, 9cm and 19cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.",
        "image": "",
        "answer": "94.59 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: This box is to have a divider placed in as shown. The box has sides of length 9cm, 9cm and 19cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: This box is to have a divider placed in as shown. The box has sides of length 9cm, 9cm and 19cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.",
        "question_for_eval": "This box is to have a divider placed in as shown. The box has sides of length 9cm, 9cm and 19cm.\nCalculate the area of the divider correct to two decimal places, using your rounded answer from the previous part."
    },
    {
        "sample_index": "685",
        "problem_index": "685",
        "problem_version": "Text Only",
        "question": "A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can.",
        "image": "",
        "answer": "14",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can.",
        "question_for_eval": "A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can."
    },
    {
        "sample_index": "686",
        "problem_index": "686",
        "problem_version": "Text Only",
        "question": "Find the volume of the cylinder shown. The height is 13 cm and radius is 3 cm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=367.57 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the cylinder shown. The height is 13 cm and radius is 3 cm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the cylinder shown. The height is 13 cm and radius is 3 cm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the volume of the cylinder shown. The height is 13 cm and radius is 3 cm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "687",
        "problem_index": "687",
        "problem_version": "Text Only",
        "question": "Calculate the volume of the cylinder. Correct to one decimal place. The height is 10 cm and diameter is 3 cm.",
        "image": "",
        "answer": "Volume $=70.7 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Calculate the volume of the cylinder. Correct to one decimal place. The height is 10 cm and diameter is 3 cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Calculate the volume of the cylinder. Correct to one decimal place. The height is 10 cm and diameter is 3 cm.",
        "question_for_eval": "Calculate the volume of the cylinder. Correct to one decimal place. The height is 10 cm and diameter is 3 cm."
    },
    {
        "sample_index": "688",
        "problem_index": "688",
        "problem_version": "Text Only",
        "question": "Calculate the volume of the half cylinder correct to one decimal place. The height is 9 cm and diameter is 6 cm.",
        "image": "",
        "answer": "Volume $=127.2 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Calculate the volume of the half cylinder correct to one decimal place. The height is 9 cm and diameter is 6 cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Calculate the volume of the half cylinder correct to one decimal place. The height is 9 cm and diameter is 6 cm.",
        "question_for_eval": "Calculate the volume of the half cylinder correct to one decimal place. The height is 9 cm and diameter is 6 cm."
    },
    {
        "sample_index": "689",
        "problem_index": "689",
        "problem_version": "Text Only",
        "question": "Calculate the volume of the half cylinder with a diameter of 6 cm and a height of 12 cm. Correct to one decimal place.",
        "image": "",
        "answer": "Volume $=169.6 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Calculate the volume of the half cylinder with a diameter of 6 cm and a height of 12 cm. Correct to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Calculate the volume of the half cylinder with a diameter of 6 cm and a height of 12 cm. Correct to one decimal place.",
        "question_for_eval": "Calculate the volume of the half cylinder with a diameter of 6 cm and a height of 12 cm. Correct to one decimal place."
    },
    {
        "sample_index": "690",
        "problem_index": "690",
        "problem_version": "Text Only",
        "question": "Consider the halfpipe with a diameter of 8 cm.\n\nFind its volume, rounding to two decimal places.",
        "image": "",
        "answer": "Volume $=502.65 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the halfpipe with a diameter of 8 cm.\n\nFind its volume, rounding to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the halfpipe with a diameter of 8 cm.\n\nFind its volume, rounding to two decimal places.",
        "question_for_eval": "Consider the halfpipe with a diameter of 8 cm.\n\nFind its volume, rounding to two decimal places."
    },
    {
        "sample_index": "691",
        "problem_index": "691",
        "problem_version": "Text Only",
        "question": "Calculate the volume of the solid. Assume that the solid is a quarter of a cylinder. The height is 15 cm and radius is 7 cm.\n\nRound your answer to one decimal place.",
        "image": "",
        "answer": "Volume $=577.3 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Calculate the volume of the solid. Assume that the solid is a quarter of a cylinder. The height is 15 cm and radius is 7 cm.\n\nRound your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Calculate the volume of the solid. Assume that the solid is a quarter of a cylinder. The height is 15 cm and radius is 7 cm.\n\nRound your answer to one decimal place.",
        "question_for_eval": "Calculate the volume of the solid. Assume that the solid is a quarter of a cylinder. The height is 15 cm and radius is 7 cm.\n\nRound your answer to one decimal place."
    },
    {
        "sample_index": "692",
        "problem_index": "692",
        "problem_version": "Text Only",
        "question": "A 13 cm concrete cylindrical pipe has an outer radius of 6 cm and an inner radius of 4 cm as shown. Find the volume of concrete required to make the pipe, correct to two decimal places.",
        "image": "",
        "answer": "Volume $=816.81 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A 13 cm concrete cylindrical pipe has an outer radius of 6 cm and an inner radius of 4 cm as shown. Find the volume of concrete required to make the pipe, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A 13 cm concrete cylindrical pipe has an outer radius of 6 cm and an inner radius of 4 cm as shown. Find the volume of concrete required to make the pipe, correct to two decimal places.",
        "question_for_eval": "A 13 cm concrete cylindrical pipe has an outer radius of 6 cm and an inner radius of 4 cm as shown. Find the volume of concrete required to make the pipe, correct to two decimal places."
    },
    {
        "sample_index": "693",
        "problem_index": "693",
        "problem_version": "Text Only",
        "question": "An empty glass jar weighing 250g is in the shape of a cylinder which has a radius (r) of 15 cm and a height (h) of 26 cm.\n\nCalculate its total weight when it is filled with water, correct to 2 decimal places.",
        "image": "",
        "answer": "Weight $=18.63 \\mathrm{~kg}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: An empty glass jar weighing 250g is in the shape of a cylinder which has a radius (r) of 15 cm and a height (h) of 26 cm.\n\nCalculate its total weight when it is filled with water, correct to 2 decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: An empty glass jar weighing 250g is in the shape of a cylinder which has a radius (r) of 15 cm and a height (h) of 26 cm.\n\nCalculate its total weight when it is filled with water, correct to 2 decimal places.",
        "question_for_eval": "An empty glass jar weighing 250g is in the shape of a cylinder which has a radius (r) of 15 cm and a height (h) of 26 cm.\n\nCalculate its total weight when it is filled with water, correct to 2 decimal places."
    },
    {
        "sample_index": "694",
        "problem_index": "694",
        "problem_version": "Text Only",
        "question": "Xavier's mother told him to drink 4 glasses of water each day. She gave him a cylindrical glass with radius 4 cm.\n\nIf Xavier follows this drinking routine for a week, how many litres of water would he drink altogether?\n\nRound your answer to one decimal place.",
        "image": "",
        "answer": "Weekly water intake $=15.5$ Litres",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Xavier's mother told him to drink 4 glasses of water each day. She gave him a cylindrical glass with radius 4 cm.\n\nIf Xavier follows this drinking routine for a week, how many litres of water would he drink altogether?\n\nRound your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Xavier's mother told him to drink 4 glasses of water each day. She gave him a cylindrical glass with radius 4 cm.\n\nIf Xavier follows this drinking routine for a week, how many litres of water would he drink altogether?\n\nRound your answer to one decimal place.",
        "question_for_eval": "Xavier's mother told him to drink 4 glasses of water each day. She gave him a cylindrical glass with radius 4 cm.\n\nIf Xavier follows this drinking routine for a week, how many litres of water would he drink altogether?\n\nRound your answer to one decimal place."
    },
    {
        "sample_index": "695",
        "problem_index": "695",
        "problem_version": "Text Only",
        "question": "In the diagram, the solid is 3 cm thick. The edge is 9 cm and the angle is 45\u00b0. Calculate the volume of the solid, correct to one decimal places.",
        "image": "",
        "answer": "Volume $=89.1 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the diagram, the solid is 3 cm thick. The edge is 9 cm and the angle is 45\u00b0. Calculate the volume of the solid, correct to one decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the diagram, the solid is 3 cm thick. The edge is 9 cm and the angle is 45\u00b0. Calculate the volume of the solid, correct to one decimal places.",
        "question_for_eval": "In the diagram, the solid is 3 cm thick. The edge is 9 cm and the angle is 45\u00b0. Calculate the volume of the solid, correct to one decimal places."
    },
    {
        "sample_index": "696",
        "problem_index": "696",
        "problem_version": "Text Only",
        "question": "Find the volume of the figure shown, correct to two decimal places. The inner cylinder has a radius of 4 cm and the outer cylinder has a radius of 9 cm. The height of both cylinders is 2 cm.",
        "image": "",
        "answer": "Volume $=609.47 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the figure shown, correct to two decimal places. The inner cylinder has a radius of 4 cm and the outer cylinder has a radius of 9 cm. The height of both cylinders is 2 cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the figure shown, correct to two decimal places. The inner cylinder has a radius of 4 cm and the outer cylinder has a radius of 9 cm. The height of both cylinders is 2 cm.",
        "question_for_eval": "Find the volume of the figure shown, correct to two decimal places. The inner cylinder has a radius of 4 cm and the outer cylinder has a radius of 9 cm. The height of both cylinders is 2 cm."
    },
    {
        "sample_index": "697",
        "problem_index": "697",
        "problem_version": "Text Only",
        "question": "Find the volume of the figure shown. The top and bottom cylinder are the same size with a radius of 8 cm and height of 2 cm. The middle cylinder has a diameter of 3 cm and height of 10 cm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=874.93 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the figure shown. The top and bottom cylinder are the same size with a radius of 8 cm and height of 2 cm. The middle cylinder has a diameter of 3 cm and height of 10 cm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the figure shown. The top and bottom cylinder are the same size with a radius of 8 cm and height of 2 cm. The middle cylinder has a diameter of 3 cm and height of 10 cm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the volume of the figure shown. The top and bottom cylinder are the same size with a radius of 8 cm and height of 2 cm. The middle cylinder has a diameter of 3 cm and height of 10 cm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "698",
        "problem_index": "698",
        "problem_version": "Text Only",
        "question": "A hole is drilled through a rectangular box forming the solid shown. The box has sides of length 10cm, 8cm and 14cm. The radius of hole is 2cm. Find the volume of the solid, correct to two decimal places.",
        "image": "",
        "answer": "Volume $=944.07 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A hole is drilled through a rectangular box forming the solid shown. The box has sides of length 10cm, 8cm and 14cm. The radius of hole is 2cm. Find the volume of the solid, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A hole is drilled through a rectangular box forming the solid shown. The box has sides of length 10cm, 8cm and 14cm. The radius of hole is 2cm. Find the volume of the solid, correct to two decimal places.",
        "question_for_eval": "A hole is drilled through a rectangular box forming the solid shown. The box has sides of length 10cm, 8cm and 14cm. The radius of hole is 2cm. Find the volume of the solid, correct to two decimal places."
    },
    {
        "sample_index": "699",
        "problem_index": "699",
        "problem_version": "Text Only",
        "question": "Consider the following cube with a side length equal to 6 cm. The nine marked edges have the same length. Find the total surface area.",
        "image": "",
        "answer": "216.\\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following cube with a side length equal to 6 cm. The nine marked edges have the same length. Find the total surface area.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following cube with a side length equal to 6 cm. The nine marked edges have the same length. Find the total surface area.",
        "question_for_eval": "Consider the following cube with a side length equal to 6 cm. The nine marked edges have the same length. Find the total surface area."
    },
    {
        "sample_index": "700",
        "problem_index": "700",
        "problem_version": "Text Only",
        "question": "Consider the following rectangular prism with length width and height equal to 12 m, 6 m and 4 m respectively.\n\nFind the surface area of the prism.",
        "image": "",
        "answer": "288 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following rectangular prism with length width and height equal to 12 m, 6 m and 4 m respectively.\n\nFind the surface area of the prism.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following rectangular prism with length width and height equal to 12 m, 6 m and 4 m respectively.\n\nFind the surface area of the prism.",
        "question_for_eval": "Consider the following rectangular prism with length width and height equal to 12 m, 6 m and 4 m respectively.\n\nFind the surface area of the prism."
    },
    {
        "sample_index": "701",
        "problem_index": "701",
        "problem_version": "Text Only",
        "question": "Find the surface area of the triangular prism shown. The height is 21 cm. The base is an isosceles triangle with waist length of 10 cm and base length of 12 cm.",
        "image": "",
        "answer": "768 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the triangular prism shown. The height is 21 cm. The base is an isosceles triangle with waist length of 10 cm and base length of 12 cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the triangular prism shown. The height is 21 cm. The base is an isosceles triangle with waist length of 10 cm and base length of 12 cm.",
        "question_for_eval": "Find the surface area of the triangular prism shown. The height is 21 cm. The base is an isosceles triangle with waist length of 10 cm and base length of 12 cm."
    },
    {
        "sample_index": "702",
        "problem_index": "702",
        "problem_version": "Text Only",
        "question": "Find the surface area of the triangular prism shown. The height is 20 cm. The base is right triangle with edges of length 6 cm, 8 cm and 10 cm.",
        "image": "",
        "answer": "528 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the triangular prism shown. The height is 20 cm. The base is right triangle with edges of length 6 cm, 8 cm and 10 cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the triangular prism shown. The height is 20 cm. The base is right triangle with edges of length 6 cm, 8 cm and 10 cm.",
        "question_for_eval": "Find the surface area of the triangular prism shown. The height is 20 cm. The base is right triangle with edges of length 6 cm, 8 cm and 10 cm."
    },
    {
        "sample_index": "703",
        "problem_index": "703",
        "problem_version": "Text Only",
        "question": "The dimensions of a trapezoidal prism are given in the following diagram (not drawn to scale). A trapezoidal prism consists of two trapezium faces and four rectangular faces. The trapezium face has edges of 10cm, 5cm and 18cm and height of 3cm. The bottom face has edges of 18cm and 8cm.\n\nFind the surface area of the trapezoidal prism.",
        "image": "",
        "answer": "338 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The dimensions of a trapezoidal prism are given in the following diagram (not drawn to scale). A trapezoidal prism consists of two trapezium faces and four rectangular faces. The trapezium face has edges of 10cm, 5cm and 18cm and height of 3cm. The bottom face has edges of 18cm and 8cm.\n\nFind the surface area of the trapezoidal prism.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The dimensions of a trapezoidal prism are given in the following diagram (not drawn to scale). A trapezoidal prism consists of two trapezium faces and four rectangular faces. The trapezium face has edges of 10cm, 5cm and 18cm and height of 3cm. The bottom face has edges of 18cm and 8cm.\n\nFind the surface area of the trapezoidal prism.",
        "question_for_eval": "The dimensions of a trapezoidal prism are given in the following diagram (not drawn to scale). A trapezoidal prism consists of two trapezium faces and four rectangular faces. The trapezium face has edges of 10cm, 5cm and 18cm and height of 3cm. The bottom face has edges of 18cm and 8cm.\n\nFind the surface area of the trapezoidal prism."
    },
    {
        "sample_index": "704",
        "problem_index": "704",
        "problem_version": "Text Only",
        "question": "Find the surface area of this prism. The prism consists of 10 different rectangles with edges. The thickness of the prism is 3cm.",
        "image": "",
        "answer": "534 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of this prism. The prism consists of 10 different rectangles with edges. The thickness of the prism is 3cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of this prism. The prism consists of 10 different rectangles with edges. The thickness of the prism is 3cm.",
        "question_for_eval": "Find the surface area of this prism. The prism consists of 10 different rectangles with edges. The thickness of the prism is 3cm."
    },
    {
        "sample_index": "705",
        "problem_index": "705",
        "problem_version": "Text Only",
        "question": "Consider the following trapezoidal prism. The right rectangle surface has edges of 3cm and 10cm. The trapezoid surface has edges of 3cm, 10cm and 13cm.  Find the surface area of the trapezoidal prism.\n\nGive your answer to the nearest one decimal place.",
        "image": "",
        "answer": "577.0 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following trapezoidal prism. The right rectangle surface has edges of 3cm and 10cm. The trapezoid surface has edges of 3cm, 10cm and 13cm.  Find the surface area of the trapezoidal prism.\n\nGive your answer to the nearest one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following trapezoidal prism. The right rectangle surface has edges of 3cm and 10cm. The trapezoid surface has edges of 3cm, 10cm and 13cm.  Find the surface area of the trapezoidal prism.\n\nGive your answer to the nearest one decimal place.",
        "question_for_eval": "Consider the following trapezoidal prism. The right rectangle surface has edges of 3cm and 10cm. The trapezoid surface has edges of 3cm, 10cm and 13cm.  Find the surface area of the trapezoidal prism.\n\nGive your answer to the nearest one decimal place."
    },
    {
        "sample_index": "706",
        "problem_index": "706",
        "problem_version": "Text Only",
        "question": "Consider the following figure.Find the total surface area of the triangular prism shown. The height is 16cm. The base is an isosceles triangle with waist length of 10cm and base length of 12cm.",
        "image": "",
        "answer": "608 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following figure.Find the total surface area of the triangular prism shown. The height is 16cm. The base is an isosceles triangle with waist length of 10cm and base length of 12cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following figure.Find the total surface area of the triangular prism shown. The height is 16cm. The base is an isosceles triangle with waist length of 10cm and base length of 12cm.",
        "question_for_eval": "Consider the following figure.Find the total surface area of the triangular prism shown. The height is 16cm. The base is an isosceles triangle with waist length of 10cm and base length of 12cm."
    },
    {
        "sample_index": "707",
        "problem_index": "707",
        "problem_version": "Text Only",
        "question": "Find the surface area of the figure shown. The trapezoid surface has edges of 9cm, 12cm and 5cm. The height is 3 cm.\n\nGive your answer to the nearest two decimal places.",
        "image": "",
        "answer": "200.49 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the figure shown. The trapezoid surface has edges of 9cm, 12cm and 5cm. The height is 3 cm.\n\nGive your answer to the nearest two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the figure shown. The trapezoid surface has edges of 9cm, 12cm and 5cm. The height is 3 cm.\n\nGive your answer to the nearest two decimal places.",
        "question_for_eval": "Find the surface area of the figure shown. The trapezoid surface has edges of 9cm, 12cm and 5cm. The height is 3 cm.\n\nGive your answer to the nearest two decimal places."
    },
    {
        "sample_index": "708",
        "problem_index": "708",
        "problem_version": "Text Only",
        "question": "Find the surface area of the figure shown. The two marked edges have the same length. The top rectangular prism has sides length of 12cm, 1cm and 1cm. The bottom rectangular prism has sides length of 7cm, 4cm and 1cm.",
        "image": "",
        "answer": "120 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the figure shown. The two marked edges have the same length. The top rectangular prism has sides length of 12cm, 1cm and 1cm. The bottom rectangular prism has sides length of 7cm, 4cm and 1cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the figure shown. The two marked edges have the same length. The top rectangular prism has sides length of 12cm, 1cm and 1cm. The bottom rectangular prism has sides length of 7cm, 4cm and 1cm.",
        "question_for_eval": "Find the surface area of the figure shown. The two marked edges have the same length. The top rectangular prism has sides length of 12cm, 1cm and 1cm. The bottom rectangular prism has sides length of 7cm, 4cm and 1cm."
    },
    {
        "sample_index": "709",
        "problem_index": "709",
        "problem_version": "Text Only",
        "question": "Find the surface area of the square pyramid. The four marked edges have the same length. The perpendicular height is 6 cm. The side length of base is 10cm. Make sure to include all faces in your calculations.\n\nRound your answer to one decimal place.",
        "image": "",
        "answer": "256.2 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the square pyramid. The four marked edges have the same length. The perpendicular height is 6 cm. The side length of base is 10cm. Make sure to include all faces in your calculations.\n\nRound your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the square pyramid. The four marked edges have the same length. The perpendicular height is 6 cm. The side length of base is 10cm. Make sure to include all faces in your calculations.\n\nRound your answer to one decimal place.",
        "question_for_eval": "Find the surface area of the square pyramid. The four marked edges have the same length. The perpendicular height is 6 cm. The side length of base is 10cm. Make sure to include all faces in your calculations.\n\nRound your answer to one decimal place."
    },
    {
        "sample_index": "710",
        "problem_index": "710",
        "problem_version": "Text Only",
        "question": "Find the surface area of the cone shown. The radius is 3cm. The slant height is 10cm.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "122.52 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the cone shown. The radius is 3cm. The slant height is 10cm.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the cone shown. The radius is 3cm. The slant height is 10cm.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the cone shown. The radius is 3cm. The slant height is 10cm.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "711",
        "problem_index": "711",
        "problem_version": "Text Only",
        "question": "The top of a solid cone was sawed off to form the solid attached. The top cone has a diameter of 8cm and slant height of 8cm. The solid cone has a diameter of 4cm. The solid left has a slant height of 8cm. Find the surface area of the solid formed, correct to two decimal places.",
        "image": "",
        "answer": "91.11 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The top of a solid cone was sawed off to form the solid attached. The top cone has a diameter of 8cm and slant height of 8cm. The solid cone has a diameter of 4cm. The solid left has a slant height of 8cm. Find the surface area of the solid formed, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The top of a solid cone was sawed off to form the solid attached. The top cone has a diameter of 8cm and slant height of 8cm. The solid cone has a diameter of 4cm. The solid left has a slant height of 8cm. Find the surface area of the solid formed, correct to two decimal places.",
        "question_for_eval": "The top of a solid cone was sawed off to form the solid attached. The top cone has a diameter of 8cm and slant height of 8cm. The solid cone has a diameter of 4cm. The solid left has a slant height of 8cm. Find the surface area of the solid formed, correct to two decimal places."
    },
    {
        "sample_index": "712",
        "problem_index": "712",
        "problem_version": "Text Only",
        "question": "Find the surface area of the pyramid. The perpendicular height is 8mm. The base is a square with the edge of 10mm. Include all faces in your calculations.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "288.6 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the pyramid. The perpendicular height is 8mm. The base is a square with the edge of 10mm. Include all faces in your calculations.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the pyramid. The perpendicular height is 8mm. The base is a square with the edge of 10mm. Include all faces in your calculations.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the pyramid. The perpendicular height is 8mm. The base is a square with the edge of 10mm. Include all faces in your calculations.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "713",
        "problem_index": "713",
        "problem_version": "Text Only",
        "question": "Find the surface area of the cone given. The radius is 9.1cm. The slant height is 13.7cm.\n\nGive your answer correct to 2 decimal places.",
        "image": "",
        "answer": "651.82 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the cone given. The radius is 9.1cm. The slant height is 13.7cm.\n\nGive your answer correct to 2 decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the cone given. The radius is 9.1cm. The slant height is 13.7cm.\n\nGive your answer correct to 2 decimal places.",
        "question_for_eval": "Find the surface area of the cone given. The radius is 9.1cm. The slant height is 13.7cm.\n\nGive your answer correct to 2 decimal places."
    },
    {
        "sample_index": "714",
        "problem_index": "714",
        "problem_version": "Text Only",
        "question": "Find the surface area of the prism shown. The bottom is a rectangular prism with edges of 6m, 5m and 10m. The top is a triangular prism. The marked edges are the same length.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "323.10 \\mathrm{m}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the prism shown. The bottom is a rectangular prism with edges of 6m, 5m and 10m. The top is a triangular prism. The marked edges are the same length.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the prism shown. The bottom is a rectangular prism with edges of 6m, 5m and 10m. The top is a triangular prism. The marked edges are the same length.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Find the surface area of the prism shown. The bottom is a rectangular prism with edges of 6m, 5m and 10m. The top is a triangular prism. The marked edges are the same length.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "715",
        "problem_index": "715",
        "problem_version": "Text Only",
        "question": "Find the surface area of the figure shown, rounded to two decimal places. Assume that the solid is three quarters of a cylinder. The height is 12 cm and radius is 5 cm.",
        "image": "",
        "answer": "520.55 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the surface area of the figure shown, rounded to two decimal places. Assume that the solid is three quarters of a cylinder. The height is 12 cm and radius is 5 cm.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the surface area of the figure shown, rounded to two decimal places. Assume that the solid is three quarters of a cylinder. The height is 12 cm and radius is 5 cm.",
        "question_for_eval": "Find the surface area of the figure shown, rounded to two decimal places. Assume that the solid is three quarters of a cylinder. The height is 12 cm and radius is 5 cm."
    },
    {
        "sample_index": "716",
        "problem_index": "716",
        "problem_version": "Text Only",
        "question": "Assume that both boxes are identical in size. The box has edges of length 20, 25 and 33. The middle cylinder has radius of 6 and height of 11.\nFind the surface area of the solid.\n\nRound your answer to two decimal places.",
        "image": "",
        "answer": "8128.50 \\text { units }^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Assume that both boxes are identical in size. The box has edges of length 20, 25 and 33. The middle cylinder has radius of 6 and height of 11.\nFind the surface area of the solid.\n\nRound your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Assume that both boxes are identical in size. The box has edges of length 20, 25 and 33. The middle cylinder has radius of 6 and height of 11.\nFind the surface area of the solid.\n\nRound your answer to two decimal places.",
        "question_for_eval": "Assume that both boxes are identical in size. The box has edges of length 20, 25 and 33. The middle cylinder has radius of 6 and height of 11.\nFind the surface area of the solid.\n\nRound your answer to two decimal places."
    },
    {
        "sample_index": "717",
        "problem_index": "717",
        "problem_version": "Text Only",
        "question": "Given the following square pyramid. The height of the square pyramid is 6cm. The length of the base is 10cm.\nFind the volume of the square pyramid.",
        "image": "",
        "answer": "200 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Given the following square pyramid. The height of the square pyramid is 6cm. The length of the base is 10cm.\nFind the volume of the square pyramid.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Given the following square pyramid. The height of the square pyramid is 6cm. The length of the base is 10cm.\nFind the volume of the square pyramid.",
        "question_for_eval": "Given the following square pyramid. The height of the square pyramid is 6cm. The length of the base is 10cm.\nFind the volume of the square pyramid."
    },
    {
        "sample_index": "718",
        "problem_index": "718",
        "problem_version": "Text Only",
        "question": "Consider the two similar spheres shown. The smaller sphere has radius $3$ cm while the larger sphere has a radius of 12 cm.\n\n\nFind the volume of Sphere A, in simplest exact form.",
        "image": "",
        "answer": "36\\pi \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the two similar spheres shown. The smaller sphere has radius $3$ cm while the larger sphere has a radius of 12 cm.\n\n\nFind the volume of Sphere A, in simplest exact form.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the two similar spheres shown. The smaller sphere has radius $3$ cm while the larger sphere has a radius of 12 cm.\n\n\nFind the volume of Sphere A, in simplest exact form.",
        "question_for_eval": "Consider the two similar spheres shown. The smaller sphere has radius $3$ cm while the larger sphere has a radius of 12 cm.\n\n\nFind the volume of Sphere A, in simplest exact form."
    },
    {
        "sample_index": "719",
        "problem_index": "719",
        "problem_version": "Text Only",
        "question": "Consider the two similar spheres shown. The smaller sphere has radius 3 cm while the larger sphere has a radius of 12 cm.\nWhat is the ratio of the volume of Sphere A to Sphere B?",
        "image": "",
        "answer": "1:64",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the two similar spheres shown. The smaller sphere has radius 3 cm while the larger sphere has a radius of 12 cm.\nWhat is the ratio of the volume of Sphere A to Sphere B?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the two similar spheres shown. The smaller sphere has radius 3 cm while the larger sphere has a radius of 12 cm.\nWhat is the ratio of the volume of Sphere A to Sphere B?",
        "question_for_eval": "Consider the two similar spheres shown. The smaller sphere has radius 3 cm while the larger sphere has a radius of 12 cm.\nWhat is the ratio of the volume of Sphere A to Sphere B?"
    },
    {
        "sample_index": "720",
        "problem_index": "720",
        "problem_version": "Text Only",
        "question": "Two similar cylinders have volumes of 5760\\mathrm{cm}^3 and 90\\mathrm{cm}^3.\n\n\nFind the fully simplified ratio of the volume of the larger cylinder to the volume of the smaller cylinder.",
        "image": "",
        "answer": "100",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Two similar cylinders have volumes of 5760\\mathrm{cm}^3 and 90\\mathrm{cm}^3.\n\n\nFind the fully simplified ratio of the volume of the larger cylinder to the volume of the smaller cylinder.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Two similar cylinders have volumes of 5760\\mathrm{cm}^3 and 90\\mathrm{cm}^3.\n\n\nFind the fully simplified ratio of the volume of the larger cylinder to the volume of the smaller cylinder.",
        "question_for_eval": "Two similar cylinders have volumes of 5760\\mathrm{cm}^3 and 90\\mathrm{cm}^3.\n\n\nFind the fully simplified ratio of the volume of the larger cylinder to the volume of the smaller cylinder."
    },
    {
        "sample_index": "721",
        "problem_index": "721",
        "problem_version": "Text Only",
        "question": "Consider the rectangular prism shown with its height is 12m and the length of its base is $(x+4)m$ and $(x+8)m$ respectively.\n\nWrite a fully expanded and simplified expression for the volume of the prism.",
        "image": "",
        "answer": "12x^2+144x+384 \\mathrm{m}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the rectangular prism shown with its height is 12m and the length of its base is $(x+4)m$ and $(x+8)m$ respectively.\n\nWrite a fully expanded and simplified expression for the volume of the prism.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the rectangular prism shown with its height is 12m and the length of its base is $(x+4)m$ and $(x+8)m$ respectively.\n\nWrite a fully expanded and simplified expression for the volume of the prism.",
        "question_for_eval": "Consider the rectangular prism shown with its height is 12m and the length of its base is $(x+4)m$ and $(x+8)m$ respectively.\n\nWrite a fully expanded and simplified expression for the volume of the prism."
    },
    {
        "sample_index": "722",
        "problem_index": "722",
        "problem_version": "Text Only",
        "question": "A square pyramid is shown with the following dimensions. The height of the square pyramid is 5x+7. Length L is the side of the base of the pyramid.\n\nFind an expression for L, in terms of the variable, x.",
        "image": "",
        "answer": "\\frac{5\\left(5x+7\\right)}{2x+3} units",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A square pyramid is shown with the following dimensions. The height of the square pyramid is 5x+7. Length L is the side of the base of the pyramid.\n\nFind an expression for L, in terms of the variable, x.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A square pyramid is shown with the following dimensions. The height of the square pyramid is 5x+7. Length L is the side of the base of the pyramid.\n\nFind an expression for L, in terms of the variable, x.",
        "question_for_eval": "A square pyramid is shown with the following dimensions. The height of the square pyramid is 5x+7. Length L is the side of the base of the pyramid.\n\nFind an expression for L, in terms of the variable, x."
    },
    {
        "sample_index": "723",
        "problem_index": "723",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the height of the cylindrical water tank is 3x and the radius of its base is 5x+3. The cylindrical water tank is leaking at a constant rate of 3\\pi x litres per second (where x is a fixed unknown). If the water tank was initially full, calculate the amount of water remaining after \\left(2x+2\\right)^2 seconds. Give your simplified answer in expanded form.",
        "image": "",
        "answer": "63\\pi x^3+66\\pi x^2+15\\pi x litres",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the height of the cylindrical water tank is 3x and the radius of its base is 5x+3. The cylindrical water tank is leaking at a constant rate of 3\\pi x litres per second (where x is a fixed unknown). If the water tank was initially full, calculate the amount of water remaining after \\left(2x+2\\right)^2 seconds. Give your simplified answer in expanded form.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the height of the cylindrical water tank is 3x and the radius of its base is 5x+3. The cylindrical water tank is leaking at a constant rate of 3\\pi x litres per second (where x is a fixed unknown). If the water tank was initially full, calculate the amount of water remaining after \\left(2x+2\\right)^2 seconds. Give your simplified answer in expanded form.",
        "question_for_eval": "As shown in the figure, the height of the cylindrical water tank is 3x and the radius of its base is 5x+3. The cylindrical water tank is leaking at a constant rate of 3\\pi x litres per second (where x is a fixed unknown). If the water tank was initially full, calculate the amount of water remaining after \\left(2x+2\\right)^2 seconds. Give your simplified answer in expanded form."
    },
    {
        "sample_index": "724",
        "problem_index": "724",
        "problem_version": "Text Only",
        "question": "Consider the cube shown. Its length of side is $x+4$.\n\nFind the polynomial that represents the volume of the cube.",
        "image": "",
        "answer": "$x^{3}+12 x^{2}+48 x+64$ ",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the cube shown. Its length of side is $x+4$.\n\nFind the polynomial that represents the volume of the cube.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the cube shown. Its length of side is $x+4$.\n\nFind the polynomial that represents the volume of the cube.",
        "question_for_eval": "Consider the cube shown. Its length of side is $x+4$.\n\nFind the polynomial that represents the volume of the cube."
    },
    {
        "sample_index": "725",
        "problem_index": "725",
        "problem_version": "Text Only",
        "question": "The volume of a cylinder is given by $V=\\pi r^{2} h$. The radius of its circle face is 6cm. The height of it is 8cm. \n\nFind the volume of the cylinder shown, rounding your answer to two decimal places.",
        "image": "",
        "answer": "Volume $=904.78 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The volume of a cylinder is given by $V=\\pi r^{2} h$. The radius of its circle face is 6cm. The height of it is 8cm. \n\nFind the volume of the cylinder shown, rounding your answer to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The volume of a cylinder is given by $V=\\pi r^{2} h$. The radius of its circle face is 6cm. The height of it is 8cm. \n\nFind the volume of the cylinder shown, rounding your answer to two decimal places.",
        "question_for_eval": "The volume of a cylinder is given by $V=\\pi r^{2} h$. The radius of its circle face is 6cm. The height of it is 8cm. \n\nFind the volume of the cylinder shown, rounding your answer to two decimal places."
    },
    {
        "sample_index": "726",
        "problem_index": "726",
        "problem_version": "Text Only",
        "question": "Find the volume of the prism shown. The height of the prism is 2cm. The Volume of any prism= area of cross section $\\times$ depth.",
        "image": "",
        "answer": "$299 \\mathrm{~cm}^{3}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the volume of the prism shown. The height of the prism is 2cm. The Volume of any prism= area of cross section $\\times$ depth.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the volume of the prism shown. The height of the prism is 2cm. The Volume of any prism= area of cross section $\\times$ depth.",
        "question_for_eval": "Find the volume of the prism shown. The height of the prism is 2cm. The Volume of any prism= area of cross section $\\times$ depth."
    },
    {
        "sample_index": "727",
        "problem_index": "727",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the height of the rectangular prism is 10cm. The base of the rectangular prism is a square with length of side of 13cm. Calculate the volume of the rectangular prism in the figure.",
        "image": "",
        "answer": "$1690cm^2$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the height of the rectangular prism is 10cm. The base of the rectangular prism is a square with length of side of 13cm. Calculate the volume of the rectangular prism in the figure.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the height of the rectangular prism is 10cm. The base of the rectangular prism is a square with length of side of 13cm. Calculate the volume of the rectangular prism in the figure.",
        "question_for_eval": "As shown in the figure, the height of the rectangular prism is 10cm. The base of the rectangular prism is a square with length of side of 13cm. Calculate the volume of the rectangular prism in the figure."
    },
    {
        "sample_index": "728",
        "problem_index": "728",
        "problem_version": "Text Only",
        "question": "Each side length of the cube is equal to 12cm. Find the volume of the cube shown.",
        "image": "",
        "answer": "$144cm^3$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Each side length of the cube is equal to 12cm. Find the volume of the cube shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Each side length of the cube is equal to 12cm. Find the volume of the cube shown.",
        "question_for_eval": "Each side length of the cube is equal to 12cm. Find the volume of the cube shown."
    },
    {
        "sample_index": "729",
        "problem_index": "729",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the length, width and height of the rectangular prism are 2cm, 8cm, 3cm respectively. Find the volume of the rectangular prism.",
        "image": "",
        "answer": "48 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the length, width and height of the rectangular prism are 2cm, 8cm, 3cm respectively. Find the volume of the rectangular prism.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the length, width and height of the rectangular prism are 2cm, 8cm, 3cm respectively. Find the volume of the rectangular prism.",
        "question_for_eval": "As shown in the figure, the length, width and height of the rectangular prism are 2cm, 8cm, 3cm respectively. Find the volume of the rectangular prism."
    },
    {
        "sample_index": "730",
        "problem_index": "730",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the height of the triangular prism is 8cm and the length of its right triangle's sides are 2cm and 4cm respectively. Find the volume of the triangular prism.",
        "image": "",
        "answer": "32 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the height of the triangular prism is 8cm and the length of its right triangle's sides are 2cm and 4cm respectively. Find the volume of the triangular prism.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the height of the triangular prism is 8cm and the length of its right triangle's sides are 2cm and 4cm respectively. Find the volume of the triangular prism.",
        "question_for_eval": "As shown in the figure, the height of the triangular prism is 8cm and the length of its right triangle's sides are 2cm and 4cm respectively. Find the volume of the triangular prism."
    },
    {
        "sample_index": "731",
        "problem_index": "731",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the width and height of the base are 4cm, 8cm respectively. The height of the prism is 2cm. Find the volume of the prism.",
        "image": "",
        "answer": "32 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the width and height of the base are 4cm, 8cm respectively. The height of the prism is 2cm. Find the volume of the prism.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the width and height of the base are 4cm, 8cm respectively. The height of the prism is 2cm. Find the volume of the prism.",
        "question_for_eval": "As shown in the figure, the width and height of the base are 4cm, 8cm respectively. The height of the prism is 2cm. Find the volume of the prism."
    },
    {
        "sample_index": "732",
        "problem_index": "732",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the base of the prism is $30cm^2$ and the height of the prism is 9cm. Find the volume of the prism shown.",
        "image": "",
        "answer": "270 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the base of the prism is $30cm^2$ and the height of the prism is 9cm. Find the volume of the prism shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the base of the prism is $30cm^2$ and the height of the prism is 9cm. Find the volume of the prism shown.",
        "question_for_eval": "As shown in the figure, the base of the prism is $30cm^2$ and the height of the prism is 9cm. Find the volume of the prism shown."
    },
    {
        "sample_index": "733",
        "problem_index": "733",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the height of the base is 14cm. The height of the prism is 3 cm. Find the volume of the prism.",
        "image": "",
        "answer": "399 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the height of the base is 14cm. The height of the prism is 3 cm. Find the volume of the prism.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the height of the base is 14cm. The height of the prism is 3 cm. Find the volume of the prism.",
        "question_for_eval": "As shown in the figure, the height of the base is 14cm. The height of the prism is 3 cm. Find the volume of the prism."
    },
    {
        "sample_index": "734",
        "problem_index": "734",
        "problem_version": "Text Only",
        "question": "The solid in the figure is constructed by 3 segments, 2 of segments are same cylinder on each side of the solid with radius of 11. The cylinder in the middle has radius of 4. Calculate the volume of the solid. Round your answer to one decimal place.",
        "image": "",
        "answer": "1608.5",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The solid in the figure is constructed by 3 segments, 2 of segments are same cylinder on each side of the solid with radius of 11. The cylinder in the middle has radius of 4. Calculate the volume of the solid. Round your answer to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The solid in the figure is constructed by 3 segments, 2 of segments are same cylinder on each side of the solid with radius of 11. The cylinder in the middle has radius of 4. Calculate the volume of the solid. Round your answer to one decimal place.",
        "question_for_eval": "The solid in the figure is constructed by 3 segments, 2 of segments are same cylinder on each side of the solid with radius of 11. The cylinder in the middle has radius of 4. Calculate the volume of the solid. Round your answer to one decimal place."
    },
    {
        "sample_index": "735",
        "problem_index": "735",
        "problem_version": "Text Only",
        "question": "As the solid shown in the figure, the seven marked edges have the same length. The height of the prism of 16 cm. Find the volume of the composite solid shown.",
        "image": "",
        "answer": "3136 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As the solid shown in the figure, the seven marked edges have the same length. The height of the prism of 16 cm. Find the volume of the composite solid shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As the solid shown in the figure, the seven marked edges have the same length. The height of the prism of 16 cm. Find the volume of the composite solid shown.",
        "question_for_eval": "As the solid shown in the figure, the seven marked edges have the same length. The height of the prism of 16 cm. Find the volume of the composite solid shown."
    },
    {
        "sample_index": "736",
        "problem_index": "736",
        "problem_version": "Text Only",
        "question": "The length and width of the base of the pyramid in the figure are 3cm and 9cm respectively. Find the volume of the pyramid to one decimal place.",
        "image": "",
        "answer": "125.3 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The length and width of the base of the pyramid in the figure are 3cm and 9cm respectively. Find the volume of the pyramid to one decimal place.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The length and width of the base of the pyramid in the figure are 3cm and 9cm respectively. Find the volume of the pyramid to one decimal place.",
        "question_for_eval": "The length and width of the base of the pyramid in the figure are 3cm and 9cm respectively. Find the volume of the pyramid to one decimal place."
    },
    {
        "sample_index": "737",
        "problem_index": "737",
        "problem_version": "Text Only",
        "question": "The height of the right pyramid is 7mm, the length of its base's side is 11mm. Find the exact volume of the right pyramid pictured.",
        "image": "",
        "answer": "\\frac{847}{3} \\mathrm{mm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The height of the right pyramid is 7mm, the length of its base's side is 11mm. Find the exact volume of the right pyramid pictured.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The height of the right pyramid is 7mm, the length of its base's side is 11mm. Find the exact volume of the right pyramid pictured.",
        "question_for_eval": "The height of the right pyramid is 7mm, the length of its base's side is 11mm. Find the exact volume of the right pyramid pictured."
    },
    {
        "sample_index": "738",
        "problem_index": "738",
        "problem_version": "Text Only",
        "question": "As shown in the figure, the solid is constructed by a cone and semi-sphere. The radius of the cone is 3cm and its height is 12cm. Find the volume of the composite figure shown, correct to two decimal places.",
        "image": "",
        "answer": "169.65 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: As shown in the figure, the solid is constructed by a cone and semi-sphere. The radius of the cone is 3cm and its height is 12cm. Find the volume of the composite figure shown, correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: As shown in the figure, the solid is constructed by a cone and semi-sphere. The radius of the cone is 3cm and its height is 12cm. Find the volume of the composite figure shown, correct to two decimal places.",
        "question_for_eval": "As shown in the figure, the solid is constructed by a cone and semi-sphere. The radius of the cone is 3cm and its height is 12cm. Find the volume of the composite figure shown, correct to two decimal places."
    },
    {
        "sample_index": "739",
        "problem_index": "739",
        "problem_version": "Text Only",
        "question": "A pyramid has been removed from a rectangular prism, as shown in the figure. The height of the rectangular prism is 8cm, its length and width are 15cm and 9cm respectively. Find the volume of this composite solid.",
        "image": "",
        "answer": "720 \\mathrm{cm}^3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Volume"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A pyramid has been removed from a rectangular prism, as shown in the figure. The height of the rectangular prism is 8cm, its length and width are 15cm and 9cm respectively. Find the volume of this composite solid.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A pyramid has been removed from a rectangular prism, as shown in the figure. The height of the rectangular prism is 8cm, its length and width are 15cm and 9cm respectively. Find the volume of this composite solid.",
        "question_for_eval": "A pyramid has been removed from a rectangular prism, as shown in the figure. The height of the rectangular prism is 8cm, its length and width are 15cm and 9cm respectively. Find the volume of this composite solid."
    },
    {
        "sample_index": "740",
        "problem_index": "740",
        "problem_version": "Text Only",
        "question": "Find the height h mm of this closed cylinder if its surface area (S) is $27288$mm2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number.",
        "image": "",
        "answer": "58",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Find the height h mm of this closed cylinder if its surface area (S) is $27288$mm2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Find the height h mm of this closed cylinder if its surface area (S) is $27288$mm2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number.",
        "question_for_eval": "Find the height h mm of this closed cylinder if its surface area (S) is $27288$mm2 and the radius (r) of its circular faces is 43mm.\n\nRound your answer to the nearest whole number."
    },
    {
        "sample_index": "741",
        "problem_index": "741",
        "problem_version": "Text Only",
        "question": "A cylinder has a surface area of 54105 \\mathrm{mm}^2 and a radius of 79 mm.\n\nWhat must the height h mm of the cylinder be?\n\nRound your answer to the nearest whole number.",
        "image": "",
        "answer": "30",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A cylinder has a surface area of 54105 \\mathrm{mm}^2 and a radius of 79 mm.\n\nWhat must the height h mm of the cylinder be?\n\nRound your answer to the nearest whole number.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A cylinder has a surface area of 54105 \\mathrm{mm}^2 and a radius of 79 mm.\n\nWhat must the height h mm of the cylinder be?\n\nRound your answer to the nearest whole number.",
        "question_for_eval": "A cylinder has a surface area of 54105 \\mathrm{mm}^2 and a radius of 79 mm.\n\nWhat must the height h mm of the cylinder be?\n\nRound your answer to the nearest whole number."
    },
    {
        "sample_index": "742",
        "problem_index": "742",
        "problem_version": "Text Only",
        "question": "A wedding cake consists of three cylinders stacked on top of each other. The top layer has a radius and height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.\n\nAll the sides and top surfaces are to be covered in icing, but not the bottom.\n\nWhat is the surface area of the cake that needs to be iced?\n\nGive your answer to the nearest cm2.",
        "image": "",
        "answer": "33929 \\mathrm{cm}^2",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A wedding cake consists of three cylinders stacked on top of each other. The top layer has a radius and height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.\n\nAll the sides and top surfaces are to be covered in icing, but not the bottom.\n\nWhat is the surface area of the cake that needs to be iced?\n\nGive your answer to the nearest cm2.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A wedding cake consists of three cylinders stacked on top of each other. The top layer has a radius and height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.\n\nAll the sides and top surfaces are to be covered in icing, but not the bottom.\n\nWhat is the surface area of the cake that needs to be iced?\n\nGive your answer to the nearest cm2.",
        "question_for_eval": "A wedding cake consists of three cylinders stacked on top of each other. The top layer has a radius and height of 20 cm, the middle layer has a radius double this, and the same height and the bottom layer has a radius three times as big, and is twice as high.\n\nAll the sides and top surfaces are to be covered in icing, but not the bottom.\n\nWhat is the surface area of the cake that needs to be iced?\n\nGive your answer to the nearest cm2."
    },
    {
        "sample_index": "743",
        "problem_index": "743",
        "problem_version": "Text Only",
        "question": "A square pyramid is shown with the following dimensions, splitted by a middle base. Length of middle base is 8, height of upper square pyramid is 2x+3, height of whole square pyramid is 6x+9.\n\nFind an expression for the length L of the base of the pyramid in terms of the variable, x.",
        "image": "",
        "answer": "24 units",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A square pyramid is shown with the following dimensions, splitted by a middle base. Length of middle base is 8, height of upper square pyramid is 2x+3, height of whole square pyramid is 6x+9.\n\nFind an expression for the length L of the base of the pyramid in terms of the variable, x.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A square pyramid is shown with the following dimensions, splitted by a middle base. Length of middle base is 8, height of upper square pyramid is 2x+3, height of whole square pyramid is 6x+9.\n\nFind an expression for the length L of the base of the pyramid in terms of the variable, x.",
        "question_for_eval": "A square pyramid is shown with the following dimensions, splitted by a middle base. Length of middle base is 8, height of upper square pyramid is 2x+3, height of whole square pyramid is 6x+9.\n\nFind an expression for the length L of the base of the pyramid in terms of the variable, x."
    },
    {
        "sample_index": "744",
        "problem_index": "744",
        "problem_version": "Text Only",
        "question": "The volume of a cylinder that fits exactly into a sphere is given by the formula:\n\nV=\\frac{1}{4}\\pi h\\left(4r^2-h^2\\right)\n\nwhere r is the radius of the sphere and h is the height of the cylinder.\n\nWhat is the radius of the sphere if the volume of the cylinder is 13.75\\pi cm3 and the height of the cylinder is 5 cm?",
        "image": "",
        "answer": "3",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The volume of a cylinder that fits exactly into a sphere is given by the formula:\n\nV=\\frac{1}{4}\\pi h\\left(4r^2-h^2\\right)\n\nwhere r is the radius of the sphere and h is the height of the cylinder.\n\nWhat is the radius of the sphere if the volume of the cylinder is 13.75\\pi cm3 and the height of the cylinder is 5 cm?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The volume of a cylinder that fits exactly into a sphere is given by the formula:\n\nV=\\frac{1}{4}\\pi h\\left(4r^2-h^2\\right)\n\nwhere r is the radius of the sphere and h is the height of the cylinder.\n\nWhat is the radius of the sphere if the volume of the cylinder is 13.75\\pi cm3 and the height of the cylinder is 5 cm?",
        "question_for_eval": "The volume of a cylinder that fits exactly into a sphere is given by the formula:\n\nV=\\frac{1}{4}\\pi h\\left(4r^2-h^2\\right)\n\nwhere r is the radius of the sphere and h is the height of the cylinder.\n\nWhat is the radius of the sphere if the volume of the cylinder is 13.75\\pi cm3 and the height of the cylinder is 5 cm?"
    },
    {
        "sample_index": "745",
        "problem_index": "745",
        "problem_version": "Text Only",
        "question": "A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can.",
        "image": "",
        "answer": "14",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can.",
        "question_for_eval": "A soft drink can has a height of 13 cm and a radius of 3 cm. Find L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).\n\nGive your answer rounded down to the nearest cm, to ensure it fits inside the can."
    },
    {
        "sample_index": "746",
        "problem_index": "746",
        "problem_version": "Text Only",
        "question": "Consider the triangular prism below. Lengths of AB, CF are 10, 4, 15. EX and XF have same length.\nFind the length of CX correct to two decimal places.",
        "image": "",
        "answer": "15.81",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the triangular prism below. Lengths of AB, CF are 10, 4, 15. EX and XF have same length.\nFind the length of CX correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the triangular prism below. Lengths of AB, CF are 10, 4, 15. EX and XF have same length.\nFind the length of CX correct to two decimal places.",
        "question_for_eval": "Consider the triangular prism below. Lengths of AB, CF are 10, 4, 15. EX and XF have same length.\nFind the length of CX correct to two decimal places."
    },
    {
        "sample_index": "747",
        "problem_index": "747",
        "problem_version": "Text Only",
        "question": "All edges of the following cube are 7 cm long.\n\nFind the exact length of AG in simplest surd form.",
        "image": "",
        "answer": "\\sqrt{147}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: All edges of the following cube are 7 cm long.\n\nFind the exact length of AG in simplest surd form.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: All edges of the following cube are 7 cm long.\n\nFind the exact length of AG in simplest surd form.",
        "question_for_eval": "All edges of the following cube are 7 cm long.\n\nFind the exact length of AG in simplest surd form."
    },
    {
        "sample_index": "748",
        "problem_index": "748",
        "problem_version": "Text Only",
        "question": "The following is a right pyramid on a square base with side length 16cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 26cm.\nFind the length of VW, the perpendicular height of the pyramid correct to two decimal places.",
        "image": "",
        "answer": "23.41",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The following is a right pyramid on a square base with side length 16cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 26cm.\nFind the length of VW, the perpendicular height of the pyramid correct to two decimal places.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The following is a right pyramid on a square base with side length 16cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 26cm.\nFind the length of VW, the perpendicular height of the pyramid correct to two decimal places.",
        "question_for_eval": "The following is a right pyramid on a square base with side length 16cm. A right pyramid has its apex aligned directly above the centre of its base.\n\nThe edge length VA is 26cm.\nFind the length of VW, the perpendicular height of the pyramid correct to two decimal places."
    },
    {
        "sample_index": "749",
        "problem_index": "749",
        "problem_version": "Text Only",
        "question": "A rectangular prism has dimensions as labelled on the diagram. The length, width and height are 9, 4, 5.\nFind the length of AG. Leave your answer in surd form.",
        "image": "",
        "answer": "\\sqrt{122}",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: A rectangular prism has dimensions as labelled on the diagram. The length, width and height are 9, 4, 5.\nFind the length of AG. Leave your answer in surd form.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: A rectangular prism has dimensions as labelled on the diagram. The length, width and height are 9, 4, 5.\nFind the length of AG. Leave your answer in surd form.",
        "question_for_eval": "A rectangular prism has dimensions as labelled on the diagram. The length, width and height are 9, 4, 5.\nFind the length of AG. Leave your answer in surd form."
    },
    {
        "sample_index": "750",
        "problem_index": "750",
        "problem_version": "Text Only",
        "question": "Consider the following figure. The base is a triangle with two side of the same length 10cm and one side of length 12cm. The height of the prism is 16cm.\n\nUse Pythagoras' Theorem to find the unknown height $x$ in the triangular prism shown.",
        "image": "",
        "answer": "$x=8 \\mathrm{~cm}$",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: Consider the following figure. The base is a triangle with two side of the same length 10cm and one side of length 12cm. The height of the prism is 16cm.\n\nUse Pythagoras' Theorem to find the unknown height $x$ in the triangular prism shown.",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: Consider the following figure. The base is a triangle with two side of the same length 10cm and one side of length 12cm. The height of the prism is 16cm.\n\nUse Pythagoras' Theorem to find the unknown height $x$ in the triangular prism shown.",
        "question_for_eval": "Consider the following figure. The base is a triangle with two side of the same length 10cm and one side of length 12cm. The height of the prism is 16cm.\n\nUse Pythagoras' Theorem to find the unknown height $x$ in the triangular prism shown."
    },
    {
        "sample_index": "751",
        "problem_index": "751",
        "problem_version": "Text Only",
        "question": "In the cylindrical tube shown above, the height of the tube is 30 and the circumference of the circular base is 32 . If the tube is cut along $\\overline{A B}$ and laid out flat to make a rectangle, what is the length of $\\overline{A C}$ to the nearest whole number?\nChoices:\nA:24\nB:30\nC:34\nD:38",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the cylindrical tube shown above, the height of the tube is 30 and the circumference of the circular base is 32 . If the tube is cut along $\\overline{A B}$ and laid out flat to make a rectangle, what is the length of $\\overline{A C}$ to the nearest whole number?\nChoices:\nA:24\nB:30\nC:34\nD:38",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the cylindrical tube shown above, the height of the tube is 30 and the circumference of the circular base is 32 . If the tube is cut along $\\overline{A B}$ and laid out flat to make a rectangle, what is the length of $\\overline{A C}$ to the nearest whole number?\nChoices:\nA:24\nB:30\nC:34\nD:38",
        "question_for_eval": "In the cylindrical tube shown above, the height of the tube is 30 and the circumference of the circular base is 32 . If the tube is cut along $\\overline{A B}$ and laid out flat to make a rectangle, what is the length of $\\overline{A C}$ to the nearest whole number?\nChoices:\nA:24\nB:30\nC:34\nD:38"
    },
    {
        "sample_index": "752",
        "problem_index": "752",
        "problem_version": "Text Only",
        "question": "The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\\sqrt{3} x$. If the volume of the prism is $\\frac{81}{4}$, what is the value of $x$ ?\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\\sqrt{3} x$. If the volume of the prism is $\\frac{81}{4}$, what is the value of $x$ ?\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\\sqrt{3} x$. If the volume of the prism is $\\frac{81}{4}$, what is the value of $x$ ?\nChoices:\nA:3\nB:4\nC:5\nD:6",
        "question_for_eval": "The figure above shows a triangular prism whose base is a equilateral triangle with side lengths $x$ and height $\\sqrt{3} x$. If the volume of the prism is $\\frac{81}{4}$, what is the value of $x$ ?\nChoices:\nA:3\nB:4\nC:5\nD:6"
    },
    {
        "sample_index": "753",
        "problem_index": "753",
        "problem_version": "Text Only",
        "question": "In the figure shown above, the rectangular container has length, width and height of 6, 5, and 4, and the cylinder has radius of 3. If all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?\nChoices:\nA:3\nB:3.4\nC:3.8\nD:4.2",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "Geo3D_collected",
            "subject": "Solid Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure shown above, the rectangular container has length, width and height of 6, 5, and 4, and the cylinder has radius of 3. If all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?\nChoices:\nA:3\nB:3.4\nC:3.8\nD:4.2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure shown above, the rectangular container has length, width and height of 6, 5, and 4, and the cylinder has radius of 3. If all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?\nChoices:\nA:3\nB:3.4\nC:3.8\nD:4.2",
        "question_for_eval": "In the figure shown above, the rectangular container has length, width and height of 6, 5, and 4, and the cylinder has radius of 3. If all the water in the rectangular container is poured into the cylinder, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?\nChoices:\nA:3\nB:3.4\nC:3.8\nD:4.2"
    },
    {
        "sample_index": "754",
        "problem_index": "754",
        "problem_version": "Text Only",
        "question": "In the figure above, there is a triangle and two line segments in the figure, and the angle formed by the two segments is x. The two angles labeled in the figure are 55\u00b0 and 75\u00b0 respectively. What is the value of x?\nChoices:\nA.35\nB.40\nC.50\nD.65\nE.130",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, there is a triangle and two line segments in the figure, and the angle formed by the two segments is x. The two angles labeled in the figure are 55\u00b0 and 75\u00b0 respectively. What is the value of x?\nChoices:\nA.35\nB.40\nC.50\nD.65\nE.130",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, there is a triangle and two line segments in the figure, and the angle formed by the two segments is x. The two angles labeled in the figure are 55\u00b0 and 75\u00b0 respectively. What is the value of x?\nChoices:\nA.35\nB.40\nC.50\nD.65\nE.130",
        "question_for_eval": "In the figure above, there is a triangle and two line segments in the figure, and the angle formed by the two segments is x. The two angles labeled in the figure are 55\u00b0 and 75\u00b0 respectively. What is the value of x?\nChoices:\nA.35\nB.40\nC.50\nD.65\nE.130"
    },
    {
        "sample_index": "755",
        "problem_index": "755",
        "problem_version": "Text Only",
        "question": "The figure above shows six right triangles. They are put together to form an irregular figure. What is the value of x^2 + y^2?\nChoices:\nA.21\nB.27\nC.33\nD.\\sqrt{593} (approximately 24.35)\nE.\\sqrt{611} (approximately 24.72)",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The figure above shows six right triangles. They are put together to form an irregular figure. What is the value of x^2 + y^2?\nChoices:\nA.21\nB.27\nC.33\nD.\\sqrt{593} (approximately 24.35)\nE.\\sqrt{611} (approximately 24.72)",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The figure above shows six right triangles. They are put together to form an irregular figure. What is the value of x^2 + y^2?\nChoices:\nA.21\nB.27\nC.33\nD.\\sqrt{593} (approximately 24.35)\nE.\\sqrt{611} (approximately 24.72)",
        "question_for_eval": "The figure above shows six right triangles. They are put together to form an irregular figure. What is the value of x^2 + y^2?\nChoices:\nA.21\nB.27\nC.33\nD.\\sqrt{593} (approximately 24.35)\nE.\\sqrt{611} (approximately 24.72)"
    },
    {
        "sample_index": "756",
        "problem_index": "756",
        "problem_version": "Text Only",
        "question": "In quadrilateral PQRS above, the length of QR is 3 and the length of SR is 4. Angle P and angle R are right angles. The length of QP and PS are respectively a and b. What is the value of a^2 + b^2?\nChoices:\nA.8\nB.10\nC.11\nD.12\nE.13",
        "image": "",
        "answer": "E",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In quadrilateral PQRS above, the length of QR is 3 and the length of SR is 4. Angle P and angle R are right angles. The length of QP and PS are respectively a and b. What is the value of a^2 + b^2?\nChoices:\nA.8\nB.10\nC.11\nD.12\nE.13",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In quadrilateral PQRS above, the length of QR is 3 and the length of SR is 4. Angle P and angle R are right angles. The length of QP and PS are respectively a and b. What is the value of a^2 + b^2?\nChoices:\nA.8\nB.10\nC.11\nD.12\nE.13",
        "question_for_eval": "In quadrilateral PQRS above, the length of QR is 3 and the length of SR is 4. Angle P and angle R are right angles. The length of QP and PS are respectively a and b. What is the value of a^2 + b^2?\nChoices:\nA.8\nB.10\nC.11\nD.12\nE.13"
    },
    {
        "sample_index": "757",
        "problem_index": "757",
        "problem_version": "Text Only",
        "question": "In the figure above, point O lies on line AB. There are four angles in the figure, which are \\frac{x}{6}, \\frac{x}{4}, \\frac{x}{3}, and \\frac{x}{2}. What is the value of x?\nChoices:\nA.90\nB.120\nC.144\nD.156\nE.168",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, point O lies on line AB. There are four angles in the figure, which are \\frac{x}{6}, \\frac{x}{4}, \\frac{x}{3}, and \\frac{x}{2}. What is the value of x?\nChoices:\nA.90\nB.120\nC.144\nD.156\nE.168",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, point O lies on line AB. There are four angles in the figure, which are \\frac{x}{6}, \\frac{x}{4}, \\frac{x}{3}, and \\frac{x}{2}. What is the value of x?\nChoices:\nA.90\nB.120\nC.144\nD.156\nE.168",
        "question_for_eval": "In the figure above, point O lies on line AB. There are four angles in the figure, which are \\frac{x}{6}, \\frac{x}{4}, \\frac{x}{3}, and \\frac{x}{2}. What is the value of x?\nChoices:\nA.90\nB.120\nC.144\nD.156\nE.168"
    },
    {
        "sample_index": "758",
        "problem_index": "758",
        "problem_version": "Text Only",
        "question": "In triangle ABC above, the bisector of angle BAC is perpendicular to BC at point D. The length of AB is equal to the length of AC. If AB = 6 and BD = 3, what is the measure of angle BAC?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.75*\\degree",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle ABC above, the bisector of angle BAC is perpendicular to BC at point D. The length of AB is equal to the length of AC. If AB = 6 and BD = 3, what is the measure of angle BAC?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.75*\\degree",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle ABC above, the bisector of angle BAC is perpendicular to BC at point D. The length of AB is equal to the length of AC. If AB = 6 and BD = 3, what is the measure of angle BAC?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.75*\\degree",
        "question_for_eval": "In triangle ABC above, the bisector of angle BAC is perpendicular to BC at point D. The length of AB is equal to the length of AC. If AB = 6 and BD = 3, what is the measure of angle BAC?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.75*\\degree"
    },
    {
        "sample_index": "759",
        "problem_index": "759",
        "problem_version": "Text Only",
        "question": "In the figure above, three lines intersect at a point. The graph consists of the intersection of three lines, two of the angles are y\u00b0, and one of the angles is 50\u00b0. What is the value of y?\nChoices:\nA.65\nB.70\nC.75\nD.80\nE.85",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, three lines intersect at a point. The graph consists of the intersection of three lines, two of the angles are y\u00b0, and one of the angles is 50\u00b0. What is the value of y?\nChoices:\nA.65\nB.70\nC.75\nD.80\nE.85",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, three lines intersect at a point. The graph consists of the intersection of three lines, two of the angles are y\u00b0, and one of the angles is 50\u00b0. What is the value of y?\nChoices:\nA.65\nB.70\nC.75\nD.80\nE.85",
        "question_for_eval": "In the figure above, three lines intersect at a point. The graph consists of the intersection of three lines, two of the angles are y\u00b0, and one of the angles is 50\u00b0. What is the value of y?\nChoices:\nA.65\nB.70\nC.75\nD.80\nE.85"
    },
    {
        "sample_index": "760",
        "problem_index": "760",
        "problem_version": "Text Only",
        "question": "In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?\nChoices:\nA.r + 1\nB.2*r\nC.r*\\sqrt{2}\nD.r*\\sqrt{3}\nE.r*\\sqrt{5}",
        "image": "",
        "answer": "E",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?\nChoices:\nA.r + 1\nB.2*r\nC.r*\\sqrt{2}\nD.r*\\sqrt{3}\nE.r*\\sqrt{5}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?\nChoices:\nA.r + 1\nB.2*r\nC.r*\\sqrt{2}\nD.r*\\sqrt{3}\nE.r*\\sqrt{5}",
        "question_for_eval": "In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?\nChoices:\nA.r + 1\nB.2*r\nC.r*\\sqrt{2}\nD.r*\\sqrt{3}\nE.r*\\sqrt{5}"
    },
    {
        "sample_index": "761",
        "problem_index": "761",
        "problem_version": "Text Only",
        "question": "In the triangle above, angle M is 80 degrees and angle Q is 30 degrees. The length of MN is 4. Which of the following must be true?\nChoices:\nA.p=r\nB.p<r\nC.p>r\nD.p=4\nE.p>4",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the triangle above, angle M is 80 degrees and angle Q is 30 degrees. The length of MN is 4. Which of the following must be true?\nChoices:\nA.p=r\nB.p<r\nC.p>r\nD.p=4\nE.p>4",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the triangle above, angle M is 80 degrees and angle Q is 30 degrees. The length of MN is 4. Which of the following must be true?\nChoices:\nA.p=r\nB.p<r\nC.p>r\nD.p=4\nE.p>4",
        "question_for_eval": "In the triangle above, angle M is 80 degrees and angle Q is 30 degrees. The length of MN is 4. Which of the following must be true?\nChoices:\nA.p=r\nB.p<r\nC.p>r\nD.p=4\nE.p>4"
    },
    {
        "sample_index": "762",
        "problem_index": "762",
        "problem_version": "Text Only",
        "question": "In the figure above, the length of CD is 7, the length of CF is 15, and CDEF is a rectangle. If the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD?\nChoices:\nA.7/2\nB.5\nC.7\nD.15/2\nE.15",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, the length of CD is 7, the length of CF is 15, and CDEF is a rectangle. If the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD?\nChoices:\nA.7/2\nB.5\nC.7\nD.15/2\nE.15",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, the length of CD is 7, the length of CF is 15, and CDEF is a rectangle. If the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD?\nChoices:\nA.7/2\nB.5\nC.7\nD.15/2\nE.15",
        "question_for_eval": "In the figure above, the length of CD is 7, the length of CF is 15, and CDEF is a rectangle. If the area of triangle CAF is equal to the area of rectangle CDEF, what is the length of segment AD?\nChoices:\nA.7/2\nB.5\nC.7\nD.15/2\nE.15"
    },
    {
        "sample_index": "763",
        "problem_index": "763",
        "problem_version": "Text Only",
        "question": "In the figure above, the four circles have the same center and their radii are 1, 2, 3, and 4, respectively. They form two shaded rings and two write rings. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?\nChoices:\nA.1:2\nB.1:4\nC.3:5\nD.3:7\nE.5:7",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, the four circles have the same center and their radii are 1, 2, 3, and 4, respectively. They form two shaded rings and two write rings. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?\nChoices:\nA.1:2\nB.1:4\nC.3:5\nD.3:7\nE.5:7",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, the four circles have the same center and their radii are 1, 2, 3, and 4, respectively. They form two shaded rings and two write rings. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?\nChoices:\nA.1:2\nB.1:4\nC.3:5\nD.3:7\nE.5:7",
        "question_for_eval": "In the figure above, the four circles have the same center and their radii are 1, 2, 3, and 4, respectively. They form two shaded rings and two write rings. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?\nChoices:\nA.1:2\nB.1:4\nC.3:5\nD.3:7\nE.5:7"
    },
    {
        "sample_index": "764",
        "problem_index": "764",
        "problem_version": "Text Only",
        "question": "In the figure above, this is a rectangle and the lengths of the sides are x-3 and x+3 respectively. If the perimeter of the rectangle above is 72, what is the value of x?\nChoices:\nA.9\nB.15\nC.18\nD.21\nE.36",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, this is a rectangle and the lengths of the sides are x-3 and x+3 respectively. If the perimeter of the rectangle above is 72, what is the value of x?\nChoices:\nA.9\nB.15\nC.18\nD.21\nE.36",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, this is a rectangle and the lengths of the sides are x-3 and x+3 respectively. If the perimeter of the rectangle above is 72, what is the value of x?\nChoices:\nA.9\nB.15\nC.18\nD.21\nE.36",
        "question_for_eval": "In the figure above, this is a rectangle and the lengths of the sides are x-3 and x+3 respectively. If the perimeter of the rectangle above is 72, what is the value of x?\nChoices:\nA.9\nB.15\nC.18\nD.21\nE.36"
    },
    {
        "sample_index": "765",
        "problem_index": "765",
        "problem_version": "Text Only",
        "question": "The graph consists of the rectangle QRPS and the line segment RT, and the point T is on PS. The area of triangle RST is 7 and PT=2/5*PS. What is the area of PQRS?",
        "image": "",
        "answer": "23",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The graph consists of the rectangle QRPS and the line segment RT, and the point T is on PS. The area of triangle RST is 7 and PT=2/5*PS. What is the area of PQRS?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The graph consists of the rectangle QRPS and the line segment RT, and the point T is on PS. The area of triangle RST is 7 and PT=2/5*PS. What is the area of PQRS?",
        "question_for_eval": "The graph consists of the rectangle QRPS and the line segment RT, and the point T is on PS. The area of triangle RST is 7 and PT=2/5*PS. What is the area of PQRS?"
    },
    {
        "sample_index": "766",
        "problem_index": "766",
        "problem_version": "Text Only",
        "question": "In the figure above, point B lies on side AC. This figure consists of triangles BCD and BAD. If 55 < x < 60, what is one possible value of y ?",
        "image": "",
        "answer": "123",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the figure above, point B lies on side AC. This figure consists of triangles BCD and BAD. If 55 < x < 60, what is one possible value of y ?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the figure above, point B lies on side AC. This figure consists of triangles BCD and BAD. If 55 < x < 60, what is one possible value of y ?",
        "question_for_eval": "In the figure above, point B lies on side AC. This figure consists of triangles BCD and BAD. If 55 < x < 60, what is one possible value of y ?"
    },
    {
        "sample_index": "767",
        "problem_index": "767",
        "problem_version": "Text Only",
        "question": "In rectangle ABDF above, point C lies on side BD,point E lies on side DF, C and E are midpoints of sides BD and DF, respectively. What fraction of the area of the rectangle is shaded?",
        "image": "",
        "answer": "0",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In rectangle ABDF above, point C lies on side BD,point E lies on side DF, C and E are midpoints of sides BD and DF, respectively. What fraction of the area of the rectangle is shaded?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In rectangle ABDF above, point C lies on side BD,point E lies on side DF, C and E are midpoints of sides BD and DF, respectively. What fraction of the area of the rectangle is shaded?",
        "question_for_eval": "In rectangle ABDF above, point C lies on side BD,point E lies on side DF, C and E are midpoints of sides BD and DF, respectively. What fraction of the area of the rectangle is shaded?"
    },
    {
        "sample_index": "768",
        "problem_index": "768",
        "problem_version": "Text Only",
        "question": "In rectangle ABCD above, the length of BC is l and the length of DC is w. The area of the shaded region is given by \\pi*l*w/4. If the area of the shaded region is 7*\\pi, what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD ?\nChoices:\nA.4\nB.6\nC.8\nD.9\nE.10",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In rectangle ABCD above, the length of BC is l and the length of DC is w. The area of the shaded region is given by \\pi*l*w/4. If the area of the shaded region is 7*\\pi, what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD ?\nChoices:\nA.4\nB.6\nC.8\nD.9\nE.10",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In rectangle ABCD above, the length of BC is l and the length of DC is w. The area of the shaded region is given by \\pi*l*w/4. If the area of the shaded region is 7*\\pi, what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD ?\nChoices:\nA.4\nB.6\nC.8\nD.9\nE.10",
        "question_for_eval": "In rectangle ABCD above, the length of BC is l and the length of DC is w. The area of the shaded region is given by \\pi*l*w/4. If the area of the shaded region is 7*\\pi, what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD ?\nChoices:\nA.4\nB.6\nC.8\nD.9\nE.10"
    },
    {
        "sample_index": "769",
        "problem_index": "769",
        "problem_version": "Text Only",
        "question": "Four lines are drawn through the center of the rectangle shown above.The rectangle is divided into eight triangles. What fraction of the area of the rectangle is shaded?\nChoices:\nA.3/8\nB.1/4\nC.1/8\nD.1/10\nE.1/16",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Four lines are drawn through the center of the rectangle shown above.The rectangle is divided into eight triangles. What fraction of the area of the rectangle is shaded?\nChoices:\nA.3/8\nB.1/4\nC.1/8\nD.1/10\nE.1/16",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Four lines are drawn through the center of the rectangle shown above.The rectangle is divided into eight triangles. What fraction of the area of the rectangle is shaded?\nChoices:\nA.3/8\nB.1/4\nC.1/8\nD.1/10\nE.1/16",
        "question_for_eval": "Four lines are drawn through the center of the rectangle shown above.The rectangle is divided into eight triangles. What fraction of the area of the rectangle is shaded?\nChoices:\nA.3/8\nB.1/4\nC.1/8\nD.1/10\nE.1/16"
    },
    {
        "sample_index": "770",
        "problem_index": "770",
        "problem_version": "Text Only",
        "question": "In the figure above, the seven small circles, which have equal radii, and the large circle share only those points on the circles that are marked. Point P is the center of the large circle and PA and PB are radii. The area of the shaded portion is how many times the area of one of the small circles?",
        "image": "",
        "answer": "1",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the figure above, the seven small circles, which have equal radii, and the large circle share only those points on the circles that are marked. Point P is the center of the large circle and PA and PB are radii. The area of the shaded portion is how many times the area of one of the small circles?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the figure above, the seven small circles, which have equal radii, and the large circle share only those points on the circles that are marked. Point P is the center of the large circle and PA and PB are radii. The area of the shaded portion is how many times the area of one of the small circles?",
        "question_for_eval": "In the figure above, the seven small circles, which have equal radii, and the large circle share only those points on the circles that are marked. Point P is the center of the large circle and PA and PB are radii. The area of the shaded portion is how many times the area of one of the small circles?"
    },
    {
        "sample_index": "771",
        "problem_index": "771",
        "problem_version": "Text Only",
        "question": "In the figure above, the circle with center O has radius 7, AB is a diameter, and AC = BC. What is the area of triangle ABC?",
        "image": "",
        "answer": "49",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the figure above, the circle with center O has radius 7, AB is a diameter, and AC = BC. What is the area of triangle ABC?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the figure above, the circle with center O has radius 7, AB is a diameter, and AC = BC. What is the area of triangle ABC?",
        "question_for_eval": "In the figure above, the circle with center O has radius 7, AB is a diameter, and AC = BC. What is the area of triangle ABC?"
    },
    {
        "sample_index": "772",
        "problem_index": "772",
        "problem_version": "Text Only",
        "question": "In the figure above,line k and line l intersect perpendicularly, and line k and line m intersect at an angle of x\u00b0. Lines l and m are not parallel. Which of the following cannot be the value of x?\nChoices:\nA.89\nB.90\nC.91\nD.92\nE.93",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above,line k and line l intersect perpendicularly, and line k and line m intersect at an angle of x\u00b0. Lines l and m are not parallel. Which of the following cannot be the value of x?\nChoices:\nA.89\nB.90\nC.91\nD.92\nE.93",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above,line k and line l intersect perpendicularly, and line k and line m intersect at an angle of x\u00b0. Lines l and m are not parallel. Which of the following cannot be the value of x?\nChoices:\nA.89\nB.90\nC.91\nD.92\nE.93",
        "question_for_eval": "In the figure above,line k and line l intersect perpendicularly, and line k and line m intersect at an angle of x\u00b0. Lines l and m are not parallel. Which of the following cannot be the value of x?\nChoices:\nA.89\nB.90\nC.91\nD.92\nE.93"
    },
    {
        "sample_index": "773",
        "problem_index": "773",
        "problem_version": "Text Only",
        "question": "This graph consists of three lines. Lines l and k intersect at point Q. If m = 40 and p = 25, what is the value of x?\nChoices:\nA.15\nB.20\nC.25\nD.40\nE.65",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: This graph consists of three lines. Lines l and k intersect at point Q. If m = 40 and p = 25, what is the value of x?\nChoices:\nA.15\nB.20\nC.25\nD.40\nE.65",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: This graph consists of three lines. Lines l and k intersect at point Q. If m = 40 and p = 25, what is the value of x?\nChoices:\nA.15\nB.20\nC.25\nD.40\nE.65",
        "question_for_eval": "This graph consists of three lines. Lines l and k intersect at point Q. If m = 40 and p = 25, what is the value of x?\nChoices:\nA.15\nB.20\nC.25\nD.40\nE.65"
    },
    {
        "sample_index": "774",
        "problem_index": "774",
        "problem_version": "Text Only",
        "question": "In the figure above, a+b = 54, and one of the angles is 126\u00b0. What is the value of x?\nChoices:\nA.72\nB.70\nC.68\nD.66\nE.64",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, a+b = 54, and one of the angles is 126\u00b0. What is the value of x?\nChoices:\nA.72\nB.70\nC.68\nD.66\nE.64",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, a+b = 54, and one of the angles is 126\u00b0. What is the value of x?\nChoices:\nA.72\nB.70\nC.68\nD.66\nE.64",
        "question_for_eval": "In the figure above, a+b = 54, and one of the angles is 126\u00b0. What is the value of x?\nChoices:\nA.72\nB.70\nC.68\nD.66\nE.64"
    },
    {
        "sample_index": "775",
        "problem_index": "775",
        "problem_version": "Text Only",
        "question": "The perimeter of the rectangle above is p and the area of the rectangle is 36. If l and w are integers, what is one possible value of p?",
        "image": "",
        "answer": "24",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: The perimeter of the rectangle above is p and the area of the rectangle is 36. If l and w are integers, what is one possible value of p?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: The perimeter of the rectangle above is p and the area of the rectangle is 36. If l and w are integers, what is one possible value of p?",
        "question_for_eval": "The perimeter of the rectangle above is p and the area of the rectangle is 36. If l and w are integers, what is one possible value of p?"
    },
    {
        "sample_index": "776",
        "problem_index": "776",
        "problem_version": "Text Only",
        "question": "In the figure above. The graph consists of four lines l,m,n,p intersecting each other. Line l and line p are perpendicular. If the angle (not shown) where lines n and p intersect is twice as large as the angle (also not shown) where lines l and m intersect, what is the value of x?",
        "image": "",
        "answer": "50",
        "question_type": "free-form",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.\nQuestion: In the figure above. The graph consists of four lines l,m,n,p intersecting each other. Line l and line p are perpendicular. If the angle (not shown) where lines n and p intersect is twice as large as the angle (also not shown) where lines l and m intersect, what is the value of x?",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.\nQuestion: In the figure above. The graph consists of four lines l,m,n,p intersecting each other. Line l and line p are perpendicular. If the angle (not shown) where lines n and p intersect is twice as large as the angle (also not shown) where lines l and m intersect, what is the value of x?",
        "question_for_eval": "In the figure above. The graph consists of four lines l,m,n,p intersecting each other. Line l and line p are perpendicular. If the angle (not shown) where lines n and p intersect is twice as large as the angle (also not shown) where lines l and m intersect, what is the value of x?"
    },
    {
        "sample_index": "777",
        "problem_index": "777",
        "problem_version": "Text Only",
        "question": "In the figure above, points A and B lie on the circle with center O. If x = 80, what is the value of z?\nChoices:\nA.80\nB.60\nC.50\nD.40\nE.10",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, points A and B lie on the circle with center O. If x = 80, what is the value of z?\nChoices:\nA.80\nB.60\nC.50\nD.40\nE.10",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, points A and B lie on the circle with center O. If x = 80, what is the value of z?\nChoices:\nA.80\nB.60\nC.50\nD.40\nE.10",
        "question_for_eval": "In the figure above, points A and B lie on the circle with center O. If x = 80, what is the value of z?\nChoices:\nA.80\nB.60\nC.50\nD.40\nE.10"
    },
    {
        "sample_index": "778",
        "problem_index": "778",
        "problem_version": "Text Only",
        "question": "In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO, what is the degree measure of angle ABO?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.90*\\degree",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO, what is the degree measure of angle ABO?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.90*\\degree",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO, what is the degree measure of angle ABO?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.90*\\degree",
        "question_for_eval": "In the figure above, triangle ABC is inscribed in the circle with center O and diameter AC. If AB = AO, what is the degree measure of angle ABO?\nChoices:\nA.15*\\degree\nB.30*\\degree\nC.45*\\degree\nD.60*\\degree\nE.90*\\degree"
    },
    {
        "sample_index": "779",
        "problem_index": "779",
        "problem_version": "Text Only",
        "question": "In the figure above, line AB, line CD, and line EF intersect at P. If r = 90, s = 50, t = 60, u = 45, and w = 50, what is the value of x?\nChoices:\nA.45\nB.50\nC.65\nD.75\nE.It cannot be determined from the information given",
        "image": "",
        "answer": "C",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, line AB, line CD, and line EF intersect at P. If r = 90, s = 50, t = 60, u = 45, and w = 50, what is the value of x?\nChoices:\nA.45\nB.50\nC.65\nD.75\nE.It cannot be determined from the information given",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, line AB, line CD, and line EF intersect at P. If r = 90, s = 50, t = 60, u = 45, and w = 50, what is the value of x?\nChoices:\nA.45\nB.50\nC.65\nD.75\nE.It cannot be determined from the information given",
        "question_for_eval": "In the figure above, line AB, line CD, and line EF intersect at P. If r = 90, s = 50, t = 60, u = 45, and w = 50, what is the value of x?\nChoices:\nA.45\nB.50\nC.65\nD.75\nE.It cannot be determined from the information given"
    },
    {
        "sample_index": "780",
        "problem_index": "780",
        "problem_version": "Text Only",
        "question": "In triangle ABC above, angle A is 60\u00b0 and triangle ABC is equilateral. The length of AB is 3, and D is the midpoint of AC. What is the length of BC?\nChoices:\nA.3*\\sqrt{3}\nB.4*\\sqrt{2}\nC.4*\\sqrt{3}\nD.6*\\sqrt{2}\nE.5*\\sqrt{3}",
        "image": "",
        "answer": "A",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle ABC above, angle A is 60\u00b0 and triangle ABC is equilateral. The length of AB is 3, and D is the midpoint of AC. What is the length of BC?\nChoices:\nA.3*\\sqrt{3}\nB.4*\\sqrt{2}\nC.4*\\sqrt{3}\nD.6*\\sqrt{2}\nE.5*\\sqrt{3}",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle ABC above, angle A is 60\u00b0 and triangle ABC is equilateral. The length of AB is 3, and D is the midpoint of AC. What is the length of BC?\nChoices:\nA.3*\\sqrt{3}\nB.4*\\sqrt{2}\nC.4*\\sqrt{3}\nD.6*\\sqrt{2}\nE.5*\\sqrt{3}",
        "question_for_eval": "In triangle ABC above, angle A is 60\u00b0 and triangle ABC is equilateral. The length of AB is 3, and D is the midpoint of AC. What is the length of BC?\nChoices:\nA.3*\\sqrt{3}\nB.4*\\sqrt{2}\nC.4*\\sqrt{3}\nD.6*\\sqrt{2}\nE.5*\\sqrt{3}"
    },
    {
        "sample_index": "781",
        "problem_index": "781",
        "problem_version": "Text Only",
        "question": "In the figure above, the figure consists of a quadrilateral and a triangle. CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE?\nChoices:\nA.4\nB.5\nC.6\nD.7\nE.8",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, the figure consists of a quadrilateral and a triangle. CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE?\nChoices:\nA.4\nB.5\nC.6\nD.7\nE.8",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, the figure consists of a quadrilateral and a triangle. CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE?\nChoices:\nA.4\nB.5\nC.6\nD.7\nE.8",
        "question_for_eval": "In the figure above, the figure consists of a quadrilateral and a triangle. CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE?\nChoices:\nA.4\nB.5\nC.6\nD.7\nE.8"
    },
    {
        "sample_index": "782",
        "problem_index": "782",
        "problem_version": "Text Only",
        "question": "In triangle ABC above, AB = AC,point E lies on line AB, point D lies on lien AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC?\nChoices:\nA.6\nB.8\nC.2*x\nD.4*x\nE.4*x^2",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In triangle ABC above, AB = AC,point E lies on line AB, point D lies on lien AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC?\nChoices:\nA.6\nB.8\nC.2*x\nD.4*x\nE.4*x^2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In triangle ABC above, AB = AC,point E lies on line AB, point D lies on lien AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC?\nChoices:\nA.6\nB.8\nC.2*x\nD.4*x\nE.4*x^2",
        "question_for_eval": "In triangle ABC above, AB = AC,point E lies on line AB, point D lies on lien AC, E is the midpoint of line AB, and D is the midpoint of line AC. If AE = x and ED = 4, what is length BC?\nChoices:\nA.6\nB.8\nC.2*x\nD.4*x\nE.4*x^2"
    },
    {
        "sample_index": "783",
        "problem_index": "783",
        "problem_version": "Text Only",
        "question": "The degrees of each angle are shown in the figure, two of the angles are the same and both are x. If x = 20 and y = 30 in the figure above, what is the value of z?\nChoices:\nA.60\nB.70\nC.80\nD.90\nE.100",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Angle"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: The degrees of each angle are shown in the figure, two of the angles are the same and both are x. If x = 20 and y = 30 in the figure above, what is the value of z?\nChoices:\nA.60\nB.70\nC.80\nD.90\nE.100",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: The degrees of each angle are shown in the figure, two of the angles are the same and both are x. If x = 20 and y = 30 in the figure above, what is the value of z?\nChoices:\nA.60\nB.70\nC.80\nD.90\nE.100",
        "question_for_eval": "The degrees of each angle are shown in the figure, two of the angles are the same and both are x. If x = 20 and y = 30 in the figure above, what is the value of z?\nChoices:\nA.60\nB.70\nC.80\nD.90\nE.100"
    },
    {
        "sample_index": "784",
        "problem_index": "784",
        "problem_version": "Text Only",
        "question": "Point O is the center of both circles in the figure above. If the circumference of the large circle is 36 and the radius of the small circle is half of the radius of the large circle, what is the length of the darkened arc?\nChoices:\nA.10\nB.8\nC.6\nD.4\nE.2",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: Point O is the center of both circles in the figure above. If the circumference of the large circle is 36 and the radius of the small circle is half of the radius of the large circle, what is the length of the darkened arc?\nChoices:\nA.10\nB.8\nC.6\nD.4\nE.2",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: Point O is the center of both circles in the figure above. If the circumference of the large circle is 36 and the radius of the small circle is half of the radius of the large circle, what is the length of the darkened arc?\nChoices:\nA.10\nB.8\nC.6\nD.4\nE.2",
        "question_for_eval": "Point O is the center of both circles in the figure above. If the circumference of the large circle is 36 and the radius of the small circle is half of the radius of the large circle, what is the length of the darkened arc?\nChoices:\nA.10\nB.8\nC.6\nD.4\nE.2"
    },
    {
        "sample_index": "785",
        "problem_index": "785",
        "problem_version": "Text Only",
        "question": "In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper, only one quadrilateral is showing. If x + y = 80, how many sides does the polygon have?\nChoices:\nA.Ten\nB.Nine\nC.Eight\nD.Seven\nE.Six",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Applied"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper, only one quadrilateral is showing. If x + y = 80, how many sides does the polygon have?\nChoices:\nA.Ten\nB.Nine\nC.Eight\nD.Seven\nE.Six",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper, only one quadrilateral is showing. If x + y = 80, how many sides does the polygon have?\nChoices:\nA.Ten\nB.Nine\nC.Eight\nD.Seven\nE.Six",
        "question_for_eval": "In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper, only one quadrilateral is showing. If x + y = 80, how many sides does the polygon have?\nChoices:\nA.Ten\nB.Nine\nC.Eight\nD.Seven\nE.Six"
    },
    {
        "sample_index": "786",
        "problem_index": "786",
        "problem_version": "Text Only",
        "question": "In the figure above, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4, what is the radius of the smaller circle?\nChoices:\nA.1\nB.2\nC.4\nD.8\nE.16",
        "image": "",
        "answer": "B",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4, what is the radius of the smaller circle?\nChoices:\nA.1\nB.2\nC.4\nD.8\nE.16",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4, what is the radius of the smaller circle?\nChoices:\nA.1\nB.2\nC.4\nD.8\nE.16",
        "question_for_eval": "In the figure above, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4, what is the radius of the smaller circle?\nChoices:\nA.1\nB.2\nC.4\nD.8\nE.16"
    },
    {
        "sample_index": "787",
        "problem_index": "787",
        "problem_version": "Text Only",
        "question": "In the figure above, the smaller circles each have radius 3. They are tangent to the larger circle at points A and C, and are tangent to each other at point B, which is the center of the larger circle. What is the perimeter of the shaded region?\nChoices:\nA.6*\\pi\nB.8*\\pi\nC.9*\\pi\nD.12*\\pi\nE.15*\\pi",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Length"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the figure above, the smaller circles each have radius 3. They are tangent to the larger circle at points A and C, and are tangent to each other at point B, which is the center of the larger circle. What is the perimeter of the shaded region?\nChoices:\nA.6*\\pi\nB.8*\\pi\nC.9*\\pi\nD.12*\\pi\nE.15*\\pi",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the figure above, the smaller circles each have radius 3. They are tangent to the larger circle at points A and C, and are tangent to each other at point B, which is the center of the larger circle. What is the perimeter of the shaded region?\nChoices:\nA.6*\\pi\nB.8*\\pi\nC.9*\\pi\nD.12*\\pi\nE.15*\\pi",
        "question_for_eval": "In the figure above, the smaller circles each have radius 3. They are tangent to the larger circle at points A and C, and are tangent to each other at point B, which is the center of the larger circle. What is the perimeter of the shaded region?\nChoices:\nA.6*\\pi\nB.8*\\pi\nC.9*\\pi\nD.12*\\pi\nE.15*\\pi"
    },
    {
        "sample_index": "788",
        "problem_index": "788",
        "problem_version": "Text Only",
        "question": "In the diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?\nChoices:\nA.5*a^2 + 10\nB.25*a^2 + 50\nC.25*a^2 + 100\nD.125*a^2 + 250\nE.cannot be determined",
        "image": "",
        "answer": "D",
        "question_type": "multi-choice",
        "metadata": {
            "split": "testmini",
            "source": "GEOS",
            "subject": "Plane Geometry",
            "subfield": "Area"
        },
        "query_wo": "Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.\nQuestion: In the diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?\nChoices:\nA.5*a^2 + 10\nB.25*a^2 + 50\nC.25*a^2 + 100\nD.125*a^2 + 250\nE.cannot be determined",
        "query_cot": "Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.\nQuestion: In the diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?\nChoices:\nA.5*a^2 + 10\nB.25*a^2 + 50\nC.25*a^2 + 100\nD.125*a^2 + 250\nE.cannot be determined",
        "question_for_eval": "In the diagram above, There are two triangles ABC an BDE, where BE is on AB. Angle A is congruent to angle BED, and angle C is congruent to angle D. If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?\nChoices:\nA.5*a^2 + 10\nB.25*a^2 + 50\nC.25*a^2 + 100\nD.125*a^2 + 250\nE.cannot be determined"
    }
]