{"idx": 0, "item": 1, "unique_id": "test/intermediate_algebra/1994.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 627, "hit_cap": false, "gold": "p - q", "pred": "\\frac{1}{2} q (1 + p)", "category": "WM", "category_name": "wrong method or plan", "first_error": "E", "grader_false_negative": false, "note": "hallucinated 'known identity' for double zeta sum"}
{"idx": 1, "item": 4, "unique_id": "test/algebra/1349.json", "subject": "Algebra", "level": 2, "tokens": 436, "hit_cap": false, "gold": "\\text{Evelyn}", "pred": "3.6", "category": "AF", "category_name": "bad final answer (right work, boxed wrong quantity)", "first_error": "L", "grader_false_negative": false, "note": "computed Evelyn is fastest but boxed her speed 3.6"}
{"idx": 2, "item": 9, "unique_id": "test/prealgebra/1139.json", "subject": "Prealgebra", "level": 5, "tokens": 917, "hit_cap": false, "gold": "4", "pred": "2", "category": "CC", "category_name": "counting or casework miss", "first_error": "M", "grader_false_negative": false, "note": "missed parenthesizations; found only 121,144"}
{"idx": 3, "item": 10, "unique_id": "test/number_theory/1032.json", "subject": "Number Theory", "level": 3, "tokens": 441, "hit_cap": false, "gold": "2220", "pred": "222", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "treated digit 0 as ensuring divisibility by 5/10; accepted 222"}
{"idx": 4, "item": 11, "unique_id": "test/intermediate_algebra/1197.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 424, "hit_cap": false, "gold": "\\frac{3}{56}", "pred": "\\frac{8}{63}", "category": "WM", "category_name": "wrong method or plan", "first_error": "E", "grader_false_negative": false, "note": "treated n/(n^2-1) itself as the degree-5 polynomial"}
{"idx": 5, "item": 15, "unique_id": "test/precalculus/990.json", "subject": "Precalculus", "level": 5, "tokens": 842, "hit_cap": false, "gold": "6 - 5i", "pred": "-5i", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "sign slip: -3sqrt2 i * i sqrt2/2 taken as -3 not +3"}
{"idx": 6, "item": 25, "unique_id": "test/intermediate_algebra/1388.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 939, "hit_cap": false, "gold": "1,-2", "pred": "0", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "recurrence f(k+1)=f(k)+k+2 then wrong closed form n^2-1 (inductive step actually failed)"}
{"idx": 7, "item": 26, "unique_id": "test/counting_and_probability/525.json", "subject": "Counting & Probability", "level": 5, "tokens": 434, "hit_cap": false, "gold": "144", "pred": "576", "category": "CC", "category_name": "counting or casework miss", "first_error": "E", "grader_false_negative": false, "note": "subtracted only 'all three together' instead of 'any two adjacent'"}
{"idx": 8, "item": 30, "unique_id": "test/number_theory/864.json", "subject": "Number Theory", "level": 3, "tokens": 244, "hit_cap": false, "gold": "52_8", "pred": "52", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: 52 vs 52_8 (base subscript)"}
{"idx": 9, "item": 33, "unique_id": "test/algebra/1072.json", "subject": "Algebra", "level": 4, "tokens": 962, "hit_cap": false, "gold": "\\frac{243}{625}", "pred": "\\frac{9}{23}", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "simplification slip: model claimed gcd(2187,5625)=243 and wrote 9/23; correct gcd is 9, giving 243/625"}
{"idx": 10, "item": 34, "unique_id": "test/counting_and_probability/119.json", "subject": "Counting & Probability", "level": 4, "tokens": 833, "hit_cap": false, "gold": "-125", "pred": "125", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "dropped (-1)^3 sign"}
{"idx": 11, "item": 41, "unique_id": "test/geometry/627.json", "subject": "Geometry", "level": 4, "tokens": 2048, "hit_cap": true, "gold": "17", "pred": null, "category": "T", "category_name": "truncated / hit 2048 cap", "first_error": "L", "grader_false_negative": false, "note": "loop: same setup repeated; 2048 cap; repeated same parallelogram setup in a loop"}
{"idx": 12, "item": 43, "unique_id": "test/intermediate_algebra/1454.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 993, "hit_cap": false, "gold": "70 \\sqrt{2}", "pred": "50 + 10\\sqrt{41}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "guessed points instead of reflection/geometric argument"}
{"idx": 13, "item": 60, "unique_id": "test/intermediate_algebra/956.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 1831, "hit_cap": false, "gold": "(6,31,-1)", "pred": "(5, 33, 1)", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "linear-system slip giving non-integer c, then rounded"}
{"idx": 14, "item": 64, "unique_id": "test/precalculus/1146.json", "subject": "Precalculus", "level": 4, "tokens": 435, "hit_cap": false, "gold": "\\frac{35}{64}", "pred": "1", "category": "WM", "category_name": "wrong method or plan", "first_error": "E", "grader_false_negative": false, "note": "claimed coefficient of sin x in sin^7 x is 1 (no expansion)"}
{"idx": 15, "item": 68, "unique_id": "test/precalculus/1313.json", "subject": "Precalculus", "level": 4, "tokens": 843, "hit_cap": false, "gold": "46", "pred": "60", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "numeric guess x=60 'approximately true'"}
{"idx": 16, "item": 71, "unique_id": "test/number_theory/516.json", "subject": "Number Theory", "level": 4, "tokens": 331, "hit_cap": false, "gold": "2516_8", "pred": "2516", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: 2516 vs 2516_8"}
{"idx": 17, "item": 80, "unique_id": "test/intermediate_algebra/1849.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 770, "hit_cap": false, "gold": "501", "pred": "2", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "ignored log domain (k<0 case), only discriminant=0"}
{"idx": 18, "item": 82, "unique_id": "test/algebra/2700.json", "subject": "Algebra", "level": 5, "tokens": 573, "hit_cap": false, "gold": "\\frac{3}{2}", "pred": "\\frac{3}{5}", "category": "MR", "category_name": "misread the problem", "first_error": "E", "grader_false_negative": false, "note": "assumed A and B lie on the squares' diagonals"}
{"idx": 19, "item": 89, "unique_id": "test/number_theory/357.json", "subject": "Number Theory", "level": 4, "tokens": 596, "hit_cap": false, "gold": "21", "pred": "3", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "E", "grader_false_negative": false, "note": "Euclid slip: model wrote 2961 = 378*7 + 291; correct remainder is 315 (2961 = 378*7 + 315)"}
{"idx": 20, "item": 94, "unique_id": "test/prealgebra/1646.json", "subject": "Prealgebra", "level": 5, "tokens": 735, "hit_cap": false, "gold": "80", "pred": "110", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "diagram: angles taken as 110/100 and wrong angle chase"}
{"idx": 21, "item": 96, "unique_id": "test/intermediate_algebra/662.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 713, "hit_cap": false, "gold": "1 \\pm \\sqrt{19}", "pred": "-5", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "false verification: model asserted 32/135+20/99 = 92/585; correct sum is 652/1485, so x=-5 is not a root. Then stopped at one root"}
{"idx": 22, "item": 99, "unique_id": "test/precalculus/1300.json", "subject": "Precalculus", "level": 3, "tokens": 994, "hit_cap": false, "gold": "\\begin{pmatrix} -1/3 \\\\ 2/3 \\\\ 5/3 \\end{pmatrix}", "pred": "\\begin{pmatrix} -\\frac{1}{3} \\\\ \\frac{2}{3} \\\\ \\frac{5}{3} \\end{pmatrix}", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: pmatrix -\\frac{1}{3} vs -1/3"}
{"idx": 23, "item": 100, "unique_id": "test/geometry/183.json", "subject": "Geometry", "level": 5, "tokens": 687, "hit_cap": false, "gold": "145^\\circ", "pred": "75", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "used 'opposite angles supplementary' for cyclic hexagon"}
{"idx": 24, "item": 101, "unique_id": "test/intermediate_algebra/582.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 1160, "hit_cap": false, "gold": "850", "pred": "785", "category": "WM", "category_name": "wrong method or plan", "first_error": "E", "grader_false_negative": false, "note": "took 10th root with a single root of unity, all roots equal modulus"}
{"idx": 25, "item": 103, "unique_id": "test/intermediate_algebra/558.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 949, "hit_cap": false, "gold": "(3,4]", "pred": "2", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "invented period-2 condition, answered lambda=2"}
{"idx": 26, "item": 109, "unique_id": "test/precalculus/44.json", "subject": "Precalculus", "level": 5, "tokens": 1702, "hit_cap": false, "gold": "120^\\circ", "pred": "45", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "product-to-sum slips, then forced tan=1"}
{"idx": 27, "item": 110, "unique_id": "test/intermediate_algebra/345.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 883, "hit_cap": false, "gold": "504", "pred": "\\frac{63}{128}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "assumed whole sequence geometric with ratio 2"}
{"idx": 28, "item": 115, "unique_id": "test/counting_and_probability/1060.json", "subject": "Counting & Probability", "level": 2, "tokens": 522, "hit_cap": false, "gold": "1260", "pred": "420", "category": "MR", "category_name": "misread the problem", "first_error": "E", "grader_false_negative": false, "note": "miscounted letters of ELLIPSE (E x3, dropped I)"}
{"idx": 29, "item": 120, "unique_id": "test/intermediate_algebra/128.json", "subject": "Intermediate Algebra", "level": 2, "tokens": 709, "hit_cap": false, "gold": "\\text{even}", "pred": "\\text{odd}", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "parity reasoning slip at f(g(f(x))) step"}
{"idx": 30, "item": 123, "unique_id": "test/geometry/283.json", "subject": "Geometry", "level": 4, "tokens": 1003, "hit_cap": false, "gold": "8", "pred": "2", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "shoelace with non-cyclic vertex order / arithmetic"}
{"idx": 31, "item": 126, "unique_id": "test/intermediate_algebra/1063.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 1203, "hit_cap": false, "gold": "1+274i", "pred": "\\frac{1}{137} + i", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "computed F(F(z0)) wrong, 'approximately' z0, fake period 2"}
{"idx": 32, "item": 127, "unique_id": "test/number_theory/847.json", "subject": "Number Theory", "level": 3, "tokens": 321, "hit_cap": false, "gold": "4210_{5}", "pred": "4210_5", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: 4210_5 vs 4210_{5}"}
{"idx": 33, "item": 129, "unique_id": "test/geometry/1140.json", "subject": "Geometry", "level": 5, "tokens": 588, "hit_cap": false, "gold": "\\frac{3840}{289}", "pred": "\\frac{480}{17}", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "used AC as base with altitude to AB"}
{"idx": 34, "item": 138, "unique_id": "test/counting_and_probability/430.json", "subject": "Counting & Probability", "level": 4, "tokens": 435, "hit_cap": false, "gold": "\\frac{1}{3}", "pred": "\\frac{1}{6}", "category": "CC", "category_name": "counting or casework miss", "first_error": "M", "grader_false_negative": false, "note": "missed case where Bob returns same color ball"}
{"idx": 35, "item": 145, "unique_id": "test/intermediate_algebra/1408.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 829, "hit_cap": false, "gold": "-2", "pred": "\\frac{1 + \\sqrt{5}}{2}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "asserted cos(85 theta)=cos(theta) without justification"}
{"idx": 36, "item": 147, "unique_id": "test/intermediate_algebra/966.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 718, "hit_cap": false, "gold": "16", "pred": "12", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "model wrote 3*cbrt(256) = 3*4 = 12; correct value is 12*cbrt(4), about 19.05 (AM-GM weights also unbalanced)"}
{"idx": 37, "item": 150, "unique_id": "test/intermediate_algebra/964.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 999, "hit_cap": false, "gold": "1", "pred": "3", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "table slip, claimed f(3,j)=f(0,j)"}
{"idx": 38, "item": 154, "unique_id": "test/geometry/880.json", "subject": "Geometry", "level": 5, "tokens": 393, "hit_cap": false, "gold": "2\\sqrt{113}", "pred": "2\\sqrt{34}", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "wrong net/unfolding of the room"}
{"idx": 39, "item": 156, "unique_id": "test/precalculus/117.json", "subject": "Precalculus", "level": 3, "tokens": 1033, "hit_cap": false, "gold": "30^\\circ", "pred": "60", "category": "WM", "category_name": "wrong method or plan", "first_error": "L", "grader_false_negative": false, "note": "derivation broken; boxed 60 after computing ~63.4"}
{"idx": 40, "item": 164, "unique_id": "test/precalculus/697.json", "subject": "Precalculus", "level": 2, "tokens": 997, "hit_cap": false, "gold": "-\\sqrt{3}", "pred": "3", "category": "GU", "category_name": "gave up / non-sequitur final answer", "first_error": "L", "grader_false_negative": false, "note": "abandoned simplification; boxed 3 unrelated to work"}
{"idx": 41, "item": 166, "unique_id": "test/prealgebra/1003.json", "subject": "Prealgebra", "level": 5, "tokens": 669, "hit_cap": false, "gold": "\\frac{270}7\\text{ degrees}", "pred": "\\frac{360}{7}", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "wrong angle combination at A"}
{"idx": 42, "item": 168, "unique_id": "test/counting_and_probability/181.json", "subject": "Counting & Probability", "level": 5, "tokens": 585, "hit_cap": false, "gold": "19", "pred": "9", "category": "CC", "category_name": "counting or casework miss", "first_error": "E", "grader_false_negative": false, "note": "miscounted squares per size; ignored tilted squares"}
{"idx": 43, "item": 170, "unique_id": "test/algebra/297.json", "subject": "Algebra", "level": 5, "tokens": 1193, "hit_cap": false, "gold": "1736", "pred": "-1136", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "wrong symmetric-function identity for prod(x_i^2-8)"}
{"idx": 44, "item": 180, "unique_id": "test/prealgebra/1908.json", "subject": "Prealgebra", "level": 3, "tokens": 381, "hit_cap": false, "gold": "3", "pred": "2", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "listed factors of 50 but did not count 50 itself as two-digit"}
{"idx": 45, "item": 184, "unique_id": "test/intermediate_algebra/183.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 708, "hit_cap": false, "gold": "(2,\\infty)", "pred": "[2, \\infty)", "category": "WM", "category_name": "wrong method or plan", "first_error": "L", "grader_false_negative": false, "note": "claimed infimum 2 attained (closed bracket)"}
{"idx": 46, "item": 186, "unique_id": "test/number_theory/978.json", "subject": "Number Theory", "level": 4, "tokens": 495, "hit_cap": false, "gold": "7", "pred": "6", "category": "CC", "category_name": "counting or casework miss", "first_error": "M", "grader_false_negative": false, "note": "omitted n=24 from divisor list"}
{"idx": 47, "item": 188, "unique_id": "test/algebra/733.json", "subject": "Algebra", "level": 5, "tokens": 1012, "hit_cap": false, "gold": "6", "pred": "1", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "wrong factorization -(x-1)(x^2-4x+12); true roots 1,-2,6"}
{"idx": 48, "item": 189, "unique_id": "test/geometry/702.json", "subject": "Geometry", "level": 5, "tokens": 893, "hit_cap": false, "gold": "160", "pred": "172", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "wrong coordinate setup for points and ropes"}
{"idx": 49, "item": 194, "unique_id": "test/intermediate_algebra/2196.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 796, "hit_cap": false, "gold": "\\frac{1}{4}", "pred": "\\frac{1}{7}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "tested x=1,y=0 and declared max 1/7"}
{"idx": 50, "item": 204, "unique_id": "test/intermediate_algebra/1510.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 710, "hit_cap": false, "gold": "0", "pred": "16", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "incoherent config; computed 9 then boxed 16"}
{"idx": 51, "item": 213, "unique_id": "test/intermediate_algebra/102.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 903, "hit_cap": false, "gold": "2", "pred": "1", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "partial fractions wrong (should telescope 1/F_n - 1/F_{n+2})"}
{"idx": 52, "item": 214, "unique_id": "test/counting_and_probability/765.json", "subject": "Counting & Probability", "level": 5, "tokens": 643, "hit_cap": false, "gold": "110", "pred": "115", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "model computed -30-75-75+15 as -170; correct value is -165. Then forced 115"}
{"idx": 53, "item": 217, "unique_id": "test/number_theory/417.json", "subject": "Number Theory", "level": 4, "tokens": 1365, "hit_cap": false, "gold": "11,\\! 111,\\! 111,\\! 100", "pred": "11111111111111111100", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "counted 18 ones in a 20-digit string; answer has 18 ones (needs 9)"}
{"idx": 54, "item": 219, "unique_id": "test/counting_and_probability/282.json", "subject": "Counting & Probability", "level": 4, "tokens": 357, "hit_cap": false, "gold": "\\frac{1}{2}", "pred": "\\frac{2}{3}", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "read remainder labels from diagram incorrectly (counted 8 of 12 shaded)"}
{"idx": 55, "item": 222, "unique_id": "test/geometry/547.json", "subject": "Geometry", "level": 4, "tokens": 514, "hit_cap": false, "gold": "54", "pred": "150", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "wrong similarity ratio 1/5 instead of 1/3"}
{"idx": 56, "item": 224, "unique_id": "test/precalculus/190.json", "subject": "Precalculus", "level": 4, "tokens": 842, "hit_cap": false, "gold": "\\frac{9}{256}", "pred": "\\frac{1}{256}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "hallucinated product formula; then asserted 1/16"}
{"idx": 57, "item": 227, "unique_id": "test/precalculus/819.json", "subject": "Precalculus", "level": 3, "tokens": 270, "hit_cap": false, "gold": "\\text{(C)}", "pred": "\\text{C}", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: \\text{C} vs \\text{(C)}"}
{"idx": 58, "item": 228, "unique_id": "test/precalculus/1056.json", "subject": "Precalculus", "level": 4, "tokens": 1475, "hit_cap": false, "gold": "288 \\pi", "pred": "1728\\pi", "category": "WM", "category_name": "wrong method or plan", "first_error": "L", "grader_false_negative": false, "note": "ellipsoid volume formula misapplied (non-orthonormal forms)"}
{"idx": 59, "item": 232, "unique_id": "test/intermediate_algebra/1354.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 1046, "hit_cap": false, "gold": "\\frac{1997}{2}", "pred": "998", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "derivative trick wrong (got 0), then boxed 998 'upon re-evaluating'"}
{"idx": 60, "item": 239, "unique_id": "test/geometry/229.json", "subject": "Geometry", "level": 5, "tokens": 1215, "hit_cap": false, "gold": "16", "pred": "30", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "substitution slip 2c^2=18*2k (should be 9*2k)"}
{"idx": 61, "item": 240, "unique_id": "test/prealgebra/874.json", "subject": "Prealgebra", "level": 4, "tokens": 422, "hit_cap": false, "gold": "116", "pred": "128", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "misread diagram labels; restated 128 as given"}
{"idx": 62, "item": 248, "unique_id": "test/precalculus/920.json", "subject": "Precalculus", "level": 4, "tokens": 1321, "hit_cap": false, "gold": "\\begin{pmatrix} -1 & 0 \\\\ 0 & -1 \\end{pmatrix}", "pred": "\\begin{pmatrix} 7 & 14 \\\\ -2 & -3 \\end{pmatrix}", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "eigenvalues are primitive 6th roots, treated as cube roots"}
{"idx": 63, "item": 249, "unique_id": "test/number_theory/1065.json", "subject": "Number Theory", "level": 4, "tokens": 937, "hit_cap": false, "gold": "17", "pred": "9", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "model claimed 10^2 = 2 (mod 23); correct value is 10^2 = 100 = 8 (mod 23)"}
{"idx": 64, "item": 255, "unique_id": "test/precalculus/452.json", "subject": "Precalculus", "level": 2, "tokens": 538, "hit_cap": false, "gold": "\\text{(E)}", "pred": "E", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: E vs \\text{(E)}"}
{"idx": 65, "item": 257, "unique_id": "test/geometry/473.json", "subject": "Geometry", "level": 4, "tokens": 386, "hit_cap": false, "gold": "864 \\mbox{ inches}^2", "pred": "864", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: 864 vs 864 inches^2 (units)"}
{"idx": 66, "item": 264, "unique_id": "test/geometry/826.json", "subject": "Geometry", "level": 5, "tokens": 572, "hit_cap": false, "gold": "1\\frac{4}{5}", "pred": "5 \\frac{5}{6}", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "wrong placement of points from diagram"}
{"idx": 67, "item": 274, "unique_id": "test/geometry/686.json", "subject": "Geometry", "level": 5, "tokens": 316, "hit_cap": false, "gold": "18+2\\pi", "pred": "36", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "rounded corners ignored; offset nonagon perimeter"}
{"idx": 68, "item": 284, "unique_id": "test/precalculus/768.json", "subject": "Precalculus", "level": 5, "tokens": 608, "hit_cap": false, "gold": "3 \\pm 2 \\sqrt{2}", "pred": "3 + 2\\sqrt{2}, 3 - 2\\sqrt{2}", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: '3+2sqrt2, 3-2sqrt2' vs 3 \\pm 2\\sqrt2"}
{"idx": 69, "item": 285, "unique_id": "test/intermediate_algebra/1411.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 2048, "hit_cap": true, "gold": "440", "pred": null, "category": "T", "category_name": "truncated / hit 2048 cap", "first_error": "L", "grader_false_negative": false, "note": "loop: enumerating triples"}
{"idx": 70, "item": 286, "unique_id": "test/intermediate_algebra/960.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 862, "hit_cap": false, "gold": "\\frac{17}{21}", "pred": "\\frac{25}{2}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "invented generating function product"}
{"idx": 71, "item": 292, "unique_id": "test/intermediate_algebra/90.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 1030, "hit_cap": false, "gold": "898", "pred": "1260", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "sequence values/period wrong (true period 10)"}
{"idx": 72, "item": 295, "unique_id": "test/precalculus/1201.json", "subject": "Precalculus", "level": 3, "tokens": 827, "hit_cap": false, "gold": "11", "pred": "5", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "E", "grader_false_negative": false, "note": "wrong factorization (z^2+2zi-1)^2-1"}
{"idx": 73, "item": 296, "unique_id": "test/intermediate_algebra/754.json", "subject": "Intermediate Algebra", "level": 2, "tokens": 410, "hit_cap": false, "gold": "\\text{(B)}", "pred": "B", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: B vs \\text{(B)}"}
{"idx": 74, "item": 301, "unique_id": "test/prealgebra/1044.json", "subject": "Prealgebra", "level": 5, "tokens": 462, "hit_cap": false, "gold": "5.4 \\text{ cents}", "pred": "5.2", "category": "MR", "category_name": "misread the problem", "first_error": "E", "grader_false_negative": false, "note": "read wrong counts from the table"}
{"idx": 75, "item": 302, "unique_id": "test/prealgebra/465.json", "subject": "Prealgebra", "level": 4, "tokens": 368, "hit_cap": false, "gold": "5", "pred": "3", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "fake 'calculator' result 0.00279279..."}
{"idx": 76, "item": 303, "unique_id": "test/geometry/965.json", "subject": "Geometry", "level": 5, "tokens": 762, "hit_cap": false, "gold": "28", "pred": "21", "category": "WM", "category_name": "wrong method or plan", "first_error": "L", "grader_false_negative": false, "note": "asserted triangles ACD and ABC have equal area"}
{"idx": 77, "item": 305, "unique_id": "test/algebra/2257.json", "subject": "Algebra", "level": 4, "tokens": 514, "hit_cap": false, "gold": "\\frac9{19}", "pred": "\\frac{9}{19}", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: \\frac{9}{19} vs \\frac9{19}"}
{"idx": 78, "item": 306, "unique_id": "test/intermediate_algebra/1544.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 1048, "hit_cap": false, "gold": "6", "pred": "4", "category": "CC", "category_name": "counting or casework miss", "first_error": "L", "grader_false_negative": false, "note": "missed double-root (c=d) cases"}
{"idx": 79, "item": 308, "unique_id": "test/geometry/711.json", "subject": "Geometry", "level": 5, "tokens": 546, "hit_cap": false, "gold": "1+2\\sqrt{3}", "pred": "\\frac{13\\sqrt{3}}{4}", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "wrong shape of the cut pieces"}
{"idx": 80, "item": 317, "unique_id": "test/intermediate_algebra/2152.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 535, "hit_cap": false, "gold": "0", "pred": "2", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "summed leading coefficients as x^2 each; ignored interpolation=1"}
{"idx": 81, "item": 327, "unique_id": "test/intermediate_algebra/117.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 2048, "hit_cap": true, "gold": "15", "pred": null, "category": "T", "category_name": "truncated / hit 2048 cap", "first_error": "L", "grader_false_negative": false, "note": "degenerate repetition of one equation"}
{"idx": 82, "item": 332, "unique_id": "test/intermediate_algebra/190.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 446, "hit_cap": false, "gold": "2", "pred": "\\frac{4\\sqrt{3}}{3}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "assumed x=y=z is optimal without checking"}
{"idx": 83, "item": 339, "unique_id": "test/intermediate_algebra/1566.json", "subject": "Intermediate Algebra", "level": 3, "tokens": 674, "hit_cap": false, "gold": "2k", "pred": "4k", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "claimed 4ah cancels"}
{"idx": 84, "item": 340, "unique_id": "test/precalculus/801.json", "subject": "Precalculus", "level": 3, "tokens": 1480, "hit_cap": false, "gold": "55^\\circ", "pred": "96^\\circ", "category": "WM", "category_name": "wrong method or plan", "first_error": "L", "grader_false_negative": false, "note": "unjustified jump to 96 degrees"}
{"idx": 85, "item": 351, "unique_id": "test/precalculus/826.json", "subject": "Precalculus", "level": 3, "tokens": 889, "hit_cap": false, "gold": "\\frac{1}{16}", "pred": "\\frac{1}{8}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "hallucinated partial product 1/2^3"}
{"idx": 86, "item": 352, "unique_id": "test/precalculus/1281.json", "subject": "Precalculus", "level": 4, "tokens": 740, "hit_cap": false, "gold": "11 \\sqrt{5} + 11", "pred": "40", "category": "GU", "category_name": "gave up / non-sequitur final answer", "first_error": "L", "grader_false_negative": false, "note": "derived 2sqrt157+12 then boxed 40"}
{"idx": 87, "item": 355, "unique_id": "test/intermediate_algebra/1166.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 393, "hit_cap": false, "gold": "100", "pred": "120", "category": "WM", "category_name": "wrong method or plan", "first_error": "E", "grader_false_negative": false, "note": "assumed a=b=c optimal"}
{"idx": 88, "item": 358, "unique_id": "test/intermediate_algebra/860.json", "subject": "Intermediate Algebra", "level": 2, "tokens": 493, "hit_cap": false, "gold": "\\text{ellipse}", "pred": "\\text{circle}", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "ignored x/2 scaling; called it a circle"}
{"idx": 89, "item": 369, "unique_id": "test/prealgebra/1187.json", "subject": "Prealgebra", "level": 2, "tokens": 560, "hit_cap": false, "gold": "21", "pred": "45", "category": "GE", "category_name": "geometry or diagram", "first_error": "E", "grader_false_negative": false, "note": "misread diagram (height 3 vs 5 swap)"}
{"idx": 90, "item": 371, "unique_id": "test/intermediate_algebra/955.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 780, "hit_cap": false, "gold": "17", "pred": "7", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "checked only 3 points; constructed non-extremal example"}
{"idx": 91, "item": 372, "unique_id": "test/geometry/846.json", "subject": "Geometry", "level": 2, "tokens": 652, "hit_cap": false, "gold": "90^\\circ", "pred": "50^\\circ", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "treated D as circumcenter with wrong angle facts"}
{"idx": 92, "item": 379, "unique_id": "test/prealgebra/1865.json", "subject": "Prealgebra", "level": 4, "tokens": 1094, "hit_cap": false, "gold": "12", "pred": "12^{\\mathrm{th}}", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: 12^{th} vs 12"}
{"idx": 93, "item": 381, "unique_id": "test/counting_and_probability/188.json", "subject": "Counting & Probability", "level": 5, "tokens": 930, "hit_cap": false, "gold": "\\frac{1}{2}", "pred": "\\frac{1}{9}", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "wrong region vertices and shoelace arithmetic"}
{"idx": 94, "item": 383, "unique_id": "test/algebra/101.json", "subject": "Algebra", "level": 4, "tokens": 718, "hit_cap": false, "gold": "x \\in [-2,7]", "pred": "[-2, 7]", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: [-2,7] vs x \\in [-2,7]"}
{"idx": 95, "item": 392, "unique_id": "test/precalculus/902.json", "subject": "Precalculus", "level": 5, "tokens": 2048, "hit_cap": true, "gold": "\\sqrt{66}", "pred": null, "category": "T", "category_name": "truncated / hit 2048 cap", "first_error": "L", "grader_false_negative": false, "note": "degenerate repetition '324 - 324 + d_6^2'"}
{"idx": 96, "item": 398, "unique_id": "test/prealgebra/1991.json", "subject": "Prealgebra", "level": 4, "tokens": 557, "hit_cap": false, "gold": "\\text{Navin}", "pred": "39.52", "category": "AF", "category_name": "bad final answer (right work, boxed wrong quantity)", "first_error": "L", "grader_false_negative": false, "note": "computed Navin earns most but boxed his pay 39.52"}
{"idx": 97, "item": 400, "unique_id": "test/geometry/817.json", "subject": "Geometry", "level": 5, "tokens": 609, "hit_cap": false, "gold": "\\frac{14}{3}", "pred": "7", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "wrong tangency configuration"}
{"idx": 98, "item": 401, "unique_id": "test/intermediate_algebra/1806.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 1229, "hit_cap": false, "gold": "\\frac{13}{4}", "pred": "4", "category": "GU", "category_name": "gave up / non-sequitur final answer", "first_error": "L", "grader_false_negative": false, "note": "algebra collapsed to '=2'; boxed 4 without derivation"}
{"idx": 99, "item": 408, "unique_id": "test/precalculus/398.json", "subject": "Precalculus", "level": 5, "tokens": 1178, "hit_cap": false, "gold": "\\begin{pmatrix} 1/5 \\\\ -18/5 \\end{pmatrix}", "pred": "\\begin{pmatrix} 0.2 \\\\ -3.6 \\end{pmatrix}", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: 0.2,-3.6 vs 1/5,-18/5"}
{"idx": 100, "item": 412, "unique_id": "test/intermediate_algebra/2146.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 1016, "hit_cap": false, "gold": "406", "pred": "421", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "chose a=2 outside its own derived interval [19/11,20/11]"}
{"idx": 101, "item": 419, "unique_id": "test/precalculus/145.json", "subject": "Precalculus", "level": 4, "tokens": 952, "hit_cap": false, "gold": "\\begin{pmatrix} -7 \\\\ 16 \\\\ 5 \\end{pmatrix}", "pred": "\\begin{pmatrix} 0 \\\\ 30 \\\\ -30 \\end{pmatrix}", "category": "WM", "category_name": "wrong method or plan", "first_error": "L", "grader_false_negative": false, "note": "chose v1=0 without minimizing |v|"}
{"idx": 102, "item": 420, "unique_id": "test/precalculus/625.json", "subject": "Precalculus", "level": 3, "tokens": 548, "hit_cap": false, "gold": "\\begin{pmatrix} 16/49 \\\\ 48/49 \\\\ 24/49 \\end{pmatrix}", "pred": "\\begin{pmatrix} \\frac{16}{49} \\\\ \\frac{48}{49} \\\\ \\frac{24}{49} \\end{pmatrix}", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: pmatrix \\frac{16}{49} vs 16/49"}
{"idx": 103, "item": 422, "unique_id": "test/intermediate_algebra/2015.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 1063, "hit_cap": false, "gold": "\\{1\\pm\\sqrt{5},-2\\}", "pred": "\\{-2, 1, 1\\}", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "wrong Vieta product ABC and sum; then forced {-2,1,1}"}
{"idx": 104, "item": 425, "unique_id": "test/precalculus/1133.json", "subject": "Precalculus", "level": 5, "tokens": 427, "hit_cap": false, "gold": "3R^2", "pred": "a^2 + b^2 + c^2 - 9R^2", "category": "WM", "category_name": "wrong method or plan", "first_error": "E", "grader_false_negative": false, "note": "hallucinated formula for AF^2"}
{"idx": 105, "item": 428, "unique_id": "test/intermediate_algebra/121.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 1000, "hit_cap": false, "gold": "64", "pred": "32", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "'balancing' guesswork, infeasible point"}
{"idx": 106, "item": 431, "unique_id": "test/precalculus/499.json", "subject": "Precalculus", "level": 4, "tokens": 822, "hit_cap": false, "gold": "\\left[ \\frac{\\pi^2}{8}, \\frac{5 \\pi^2}{4} \\right]", "pred": "\\left[\\frac{\\pi^2}{8}, \\frac{\\pi^2}{4}\\right]", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "used theta range [0,pi/2] instead of [0,pi] for arccos"}
{"idx": 107, "item": 432, "unique_id": "test/intermediate_algebra/1462.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 1560, "hit_cap": false, "gold": "331", "pred": "-\\frac{1985}{3}", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "L", "grader_false_negative": false, "note": "sum of a_n claimed -1985/2 without derivation"}
{"idx": 108, "item": 445, "unique_id": "test/intermediate_algebra/1779.json", "subject": "Intermediate Algebra", "level": 4, "tokens": 1114, "hit_cap": false, "gold": "15", "pred": "4", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "tangency points computed wrong, degenerate quadrilateral"}
{"idx": 109, "item": 454, "unique_id": "test/precalculus/323.json", "subject": "Precalculus", "level": 5, "tokens": 1654, "hit_cap": false, "gold": "y = 2x + 3", "pred": "y = -\\frac{1}{22}x - \\frac{15}{22}", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "solved for M incorrectly"}
{"idx": 110, "item": 456, "unique_id": "test/intermediate_algebra/1102.json", "subject": "Intermediate Algebra", "level": 1, "tokens": 1009, "hit_cap": false, "gold": "-2,1", "pred": "1, -2", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: '1, -2' vs '-2,1' (order)"}
{"idx": 111, "item": 460, "unique_id": "test/prealgebra/914.json", "subject": "Prealgebra", "level": 4, "tokens": 328, "hit_cap": false, "gold": "75^\\circ", "pred": "105", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "wrong angle correspondence in diagram"}
{"idx": 112, "item": 467, "unique_id": "test/prealgebra/1114.json", "subject": "Prealgebra", "level": 2, "tokens": 257, "hit_cap": false, "gold": "15\\mbox{ cm}^2", "pred": "15", "category": "FN", "category_name": "grader false negative (correct answer, format)", "first_error": "L", "grader_false_negative": true, "note": "correct answer, grader rejected: 15 vs 15 cm^2 (units)"}
{"idx": 113, "item": 468, "unique_id": "test/algebra/224.json", "subject": "Algebra", "level": 4, "tokens": 327, "hit_cap": false, "gold": "8", "pred": "7", "category": "CC", "category_name": "counting or casework miss", "first_error": "L", "grader_false_negative": false, "note": "excluded t=12 although 12<12.25"}
{"idx": 114, "item": 475, "unique_id": "test/counting_and_probability/1003.json", "subject": "Counting & Probability", "level": 5, "tokens": 1281, "hit_cap": false, "gold": "29", "pred": "127", "category": "SL", "category_name": "algebra or arithmetic slip", "first_error": "M", "grader_false_negative": false, "note": "sign slip 47/288-48/288 then flipped; wrong probability model"}
{"idx": 115, "item": 478, "unique_id": "test/intermediate_algebra/1279.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 529, "hit_cap": false, "gold": "\\frac{2}{1005}", "pred": "0", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "bogus degree argument; contradicts itself"}
{"idx": 116, "item": 481, "unique_id": "test/intermediate_algebra/1467.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 2048, "hit_cap": true, "gold": "8n^2 + 4n + 1", "pred": null, "category": "T", "category_name": "truncated / hit 2048 cap", "first_error": "L", "grader_false_negative": false, "note": "degenerate repetition of one expression"}
{"idx": 117, "item": 483, "unique_id": "test/precalculus/1082.json", "subject": "Precalculus", "level": 3, "tokens": 962, "hit_cap": false, "gold": "\\frac{8}{15}", "pred": "1", "category": "GU", "category_name": "gave up / non-sequitur final answer", "first_error": "L", "grader_false_negative": false, "note": "abandoned algebra; assumed right triangle, boxed 1"}
{"idx": 118, "item": 494, "unique_id": "test/intermediate_algebra/1930.json", "subject": "Intermediate Algebra", "level": 5, "tokens": 991, "hit_cap": false, "gold": "\\frac{1}{4}", "pred": "0", "category": "WM", "category_name": "wrong method or plan", "first_error": "M", "grader_false_negative": false, "note": "assumed reciprocal real-root pairs; region collapses"}
{"idx": 119, "item": 497, "unique_id": "test/geometry/561.json", "subject": "Geometry", "level": 5, "tokens": 733, "hit_cap": false, "gold": "\\frac{7}{2}", "pred": "2", "category": "GE", "category_name": "geometry or diagram", "first_error": "M", "grader_false_negative": false, "note": "wrong decomposition of octagon; boxed 2 unrelated to sqrt2-1/2"}