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math500-0000
[ "\\left( 3, \\frac{\\pi}{2} \\right)" ]
{ "row_pos": 0, "level": 2, "subject": "Precalculus", "unique_id": "test/precalculus/807.json", "solution": "We have that $r = \\sqrt{0^2 + 3^2} = 3.$ Also, if we draw the line connecting the origin and $(0,3),$ this line makes an angle of $\\frac{\\pi}{2}$ with the positive $x$-axis.\n\n[asy]\nunitsize(0.8 ...
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math500-0001
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math500-0002
[ "\\frac{14}{3}" ]
{ "row_pos": 2, "level": 3, "subject": "Algebra", "unique_id": "test/algebra/2584.json", "solution": "$f(-2)+f(-1)+f(0)=\\frac{3(-2)-2}{-2-2}+\\frac{3(-1)-2}{-1-2}+\\frac{3(0)-2}{0-2}=\\frac{-8}{-4}+\\frac{-5}{-3}+\\frac{-2}{-2}=2+\\frac{5}{3}+1=\\boxed{\\frac{14}{3}}$" }
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math500-0003
[ "9" ]
{ "row_pos": 3, "level": 3, "subject": "Number Theory", "unique_id": "test/number_theory/572.json", "solution": "First prime factorize $196=2^2\\cdot7^2$. The prime factorization of any divisor of 196 cannot include any primes other than 2 and 7. We are free to choose either 0, 1, or 2 as the exponent of 2 ...
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math500-0004
[ "\\text{Evelyn}" ]
{ "row_pos": 4, "level": 2, "subject": "Algebra", "unique_id": "test/algebra/1349.json", "solution": "Evelyn covered more distance in less time than Briana, Debra and Angela, so her average speed is greater than any of their average speeds. Evelyn went almost as far as Carla in less than half the time that it...
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math500-0005
[ "42" ]
{ "row_pos": 5, "level": 2, "subject": "Prealgebra", "unique_id": "test/prealgebra/1622.json", "solution": "The side length of the hexagon is equal to the side length of one of the equilateral triangles. Since the hexagon has six sides and the triangle has three sides, the perimeter of the hexagon is twice a...
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math500-0006
[ "27" ]
{ "row_pos": 6, "level": 3, "subject": "Number Theory", "unique_id": "test/number_theory/515.json", "solution": "The sum of three consecutive integers takes the form $(k-1)+(k)+(k+1)=3k$ and hence is a multiple of 3. Conversely, if a number $n$ is a multiple of 3, then $n/3-1$, $n/3$, and $n/3+1$ are three c...
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math500-0007
[ "90^\\circ" ]
{ "row_pos": 7, "level": 4, "subject": "Precalculus", "unique_id": "test/precalculus/927.json", "solution": "For the first line, let $t = 2x = 3y = -z.$ Then\n\\[\\begin{pmatrix} x \\\\ y \\\\ z \\end{pmatrix} = \\begin{pmatrix} t/2 \\\\ t/3 \\\\ -t \\end{pmatrix} = \\frac{t}{6} \\begin{pmatrix} 3 \\\\ 2 \\\...
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math500-0008
[ "3\\sqrt{13}" ]
{ "row_pos": 8, "level": 3, "subject": "Algebra", "unique_id": "test/algebra/2036.json", "solution": "We use the distance formula: \\begin{align*}\n\\sqrt{(2 - (-4))^2 + ((-6) - 3)^2} &= \\sqrt{6^2 + (-9)^2}\\\\\n& = \\sqrt{36 + 81}\\\\\n& = \\sqrt{117} = \\boxed{3\\sqrt{13}}.\n\\end{align*}" }
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math500-0009
[ "4" ]
{ "row_pos": 9, "level": 5, "subject": "Prealgebra", "unique_id": "test/prealgebra/1139.json", "solution": "By the associative property of multiplication, it doesn't help to insert parentheses that specify the order of multiplication. For example, the associative property tells us that $(2\\cdot(3\\cdot 4))\\...
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math500-0010
[ "2220" ]
{ "row_pos": 10, "level": 3, "subject": "Number Theory", "unique_id": "test/number_theory/1032.json", "solution": "Let $M$ be the least positive multiple of 30 that can be written with only the digits 0 and 2. First, $M$ is a multiple of 10, so its units digit must be 0. $M$ is also a multiple of 3, which mea...
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math500-0011
[ "\\frac{3}{56}" ]
{ "row_pos": 11, "level": 5, "subject": "Intermediate Algebra", "unique_id": "test/intermediate_algebra/1197.json", "solution": "Let $q(x) = (x^2 - 1) p(x) - x.$ Then $q(x)$ has degree 7, and $q(n) = 0$ for $n = 2$, 3, 4, $\\dots,$ 7, so\n\\[q(x) = (ax + b)(x - 2)(x - 3) \\dotsm (x - 7)\\]for some constants ...
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math500-0012
[ "284" ]
{ "row_pos": 12, "level": 5, "subject": "Number Theory", "unique_id": "test/number_theory/737.json", "solution": "Prime factorize $284=2^2\\cdot71$. The sum of the proper divisors of $284$ is\n\\begin{align*}\n1+2+2^2+71+2 \\cdot 71 &= (1+2+2^2)(1+71)-284 \\\\\n&= 220 \\\\\n&= 2^2\\cdot5\\cdot11.\n\\end{align...
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math500-0013
[ "5" ]
{ "row_pos": 13, "level": 2, "subject": "Geometry", "unique_id": "test/geometry/248.json", "solution": "The volume of the cylinder is $bh=\\pi r^2h$. The radius of the base is $3$ cm, so we have $9\\pi h=45\\pi\\qquad\\Rightarrow h=5$. The height of the cylinder is $\\boxed{5}$ cm." }
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math500-0014
[ "\\sqrt{51}" ]
{ "row_pos": 14, "level": 1, "subject": "Precalculus", "unique_id": "test/precalculus/1303.json", "solution": "The triangle is a right triangle, so $\\sin D = \\frac{EF}{DF}$. Then we have that $\\sin D = 0.7 = \\frac{7}{DF}$, so $DF = 10$.\n\nUsing the Pythagorean Theorem, we find that the length of $DE$ is ...
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math500-0015
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{ "row_pos": 15, "level": 5, "subject": "Precalculus", "unique_id": "test/precalculus/990.json", "solution": "Rotating by $\\frac{\\pi}{4}$ counter-clockwise corresponds to the complex number\n\\[e^{\\pi i/4} = \\frac{1}{\\sqrt{2}} + \\frac{i}{\\sqrt{2}}.\\]Hence,\n\\[w - c = \\left( \\frac{1}{\\sqrt{2}} + \\...
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math500-0016
[ "-50" ]
{ "row_pos": 16, "level": 1, "subject": "Intermediate Algebra", "unique_id": "test/intermediate_algebra/134.json", "solution": "$(1-2)+(3-4)+ \\dots +(97-98)+(99-100) = 50(-1) = \\boxed{-50}.$" }
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math500-0017
[ "\\pi" ]
{ "row_pos": 17, "level": 4, "subject": "Precalculus", "unique_id": "test/precalculus/1199.json", "solution": "We see that the graph reaches its midpoint at $x = 0.$ It is also decreasing at $x = 0.$ The graph of $y = \\sin x$ first reaches its midpoint at $x = \\pi$ for positive values of $x$ (and is decre...
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math500-0018
[ "28" ]
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math500-0019
[ "3" ]
{ "row_pos": 19, "level": 3, "subject": "Intermediate Algebra", "unique_id": "test/intermediate_algebra/1000.json", "solution": "Note that $x = -1$ is always a root of $x^3 + ax^2 + ax + 1 = 0,$ so we can factor out $x + 1,$ to get\n\\[(x + 1) (x^2 + (a - 1) x + 1) = 0.\\]The quadratic factor has real roots i...
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math500-0020
[ "6+9i" ]
{ "row_pos": 20, "level": 3, "subject": "Algebra", "unique_id": "test/algebra/1098.json", "solution": "Distribute the factor of 6 and simplify to obtain $(1+2i)6-3i=6+12i-3i=\\boxed{6+9i}$." }
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math500-0021
[ "13535" ]
{ "row_pos": 21, "level": 3, "subject": "Intermediate Algebra", "unique_id": "test/intermediate_algebra/607.json", "solution": "Let $x = \\sqrt{7} + \\sqrt{5}$ and $y = \\sqrt{7} - \\sqrt{5}.$\n\nFirst, we can square $x = \\sqrt{7} + \\sqrt{5}$ and $y = \\sqrt{7} - \\sqrt{5},$ to get\n\\begin{align*}\nx^2 &= ...
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math500-0022
[ "5" ]
{ "row_pos": 22, "level": 5, "subject": "Algebra", "unique_id": "test/algebra/1837.json", "solution": "Rewriting the sentence \"the ratio of Denali's pay to Nate's pay would be the same if Denali started walking $4x$ more dogs and Nate stayed at $12$ dogs or if $x$ of Nate's dogs were reassigned to Denali\" a...
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math500-0023
[ "x=5" ]
{ "row_pos": 23, "level": 5, "subject": "Algebra", "unique_id": "test/algebra/2193.json", "solution": "We first isolate the square root, so we can then square both sides to get rid of it. Subtracting 4 from both sides gives $x-4 = \\!\\sqrt{11-2x}$. Squaring both sides gives $x^2 - 8x + 16 = 11-2x$, or $x^2...
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math500-0024
[ "10" ]
{ "row_pos": 24, "level": 5, "subject": "Algebra", "unique_id": "test/algebra/2427.json", "solution": "If the interest rate is $r$, it follows that $$20000(1+r)^2 + 20000(1+r) + 20000 \\ge 66200.$$ If we set $x = 1+r$ and divide through the inequality by $200$, it follows that $$100x^2 + 100x - 231 \\ge 0.$$ ...
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math500-0025
[ "1,-2" ]
{ "row_pos": 25, "level": 5, "subject": "Intermediate Algebra", "unique_id": "test/intermediate_algebra/1388.json", "solution": "Setting $x = y = 0,$ we get\n\\[2f(0) = f(0) - 1,\\]so $f(0) = -1.$\n\nSetting $y = 1,$ we get\n\\[f(x) + 1 = f(x + 1) - x - 1,\\]so\n\\[f(x + 1) - f(x) = x + 2.\\]Thus,\n\\begin{al...
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math500-0026
[ "144" ]
{ "row_pos": 26, "level": 5, "subject": "Counting & Probability", "unique_id": "test/counting_and_probability/525.json", "solution": "After Pierre sits, we can place Rosa either two seats from Pierre (that is, with one seat between them) or three seats from Pierre. We tackle these two cases separately:\n\nCas...
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math500-0027
[ "78" ]
{ "row_pos": 27, "level": 2, "subject": "Prealgebra", "unique_id": "test/prealgebra/1840.json", "solution": "To find the profit, we want to find out how much the math club earned from selling the various baked goods and subtract the cost of producing those goods, $\\$15$, from the number we get.\n\nFirst let'...
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math500-0028
[ "-2 + 7i" ]
{ "row_pos": 28, "level": 2, "subject": "Precalculus", "unique_id": "test/precalculus/779.json", "solution": "A $90^\\circ$ rotation around the origin in the counter-clockwise direction corresponds to multiplication by $\\operatorname{cis} 90^\\circ = i.$\n\n[asy]\nunitsize(0.5 cm);\n\ndraw((-3,0)--(8,0));\nd...
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[ { "bucket": "math:-2 + 7i", "label": "-2 + 7i", "count": 100, "match": "exact", "judge": null, "members": [ { "raw": "-2 + 7i", "count": 100 } ] } ]
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true
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false
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[ "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 + 7i", "-2 ...
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math500-0029
[ "225" ]
{ "row_pos": 29, "level": 2, "subject": "Counting & Probability", "unique_id": "test/counting_and_probability/666.json", "solution": "There are $\\binom{5}{4}$ different ways to choose 4 from 5 upper class soldiers. For each of these, there are $\\binom{10}{8}$ ways to choose 8 lower class soldiers. The numbe...
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225
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true
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math500-0030
[ "52_8" ]
{ "row_pos": 30, "level": 3, "subject": "Number Theory", "unique_id": "test/number_theory/864.json", "solution": "Multiplying, we see that $6_8 \\cdot 7_8 = 42_{10} = 52_8.$ Written out, $$\\begin{array}{@{}c@{\\;}c@{}c@{}c} && & 6_8 \\\\ & \\times & & 7_8 \\\\ \\cline{2-4} & & 5 & 2_8 \\\\ \\end{array} $$ Th...
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[ { "bucket": "math:52", "label": "52", "count": 100, "match": "exact", "judge": null, "members": [ { "raw": "52", "count": 96 }, { "raw": "52_8", "count": 4 } ] } ]
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End of preview. Expand in Data Studio

math500

100 instances, evaluated from connections-dev/create-interpret-task-general-x100 (commit 8485bb7), eval code at git 87dd0ea. Files: data/math500.jsonl (one row per instance), metrics/math500.json, audit/math500.jsonl (answer groups that string match called wrong, next to the gold answer, to see what it misses).

Results

Metric Value
Instances 100
Samples (successful / total) 9950 / 10000
Mean accuracy (pass@1) 0.959
pass@5 0.985
pass@10 0.988
pass@100 0.989
Majority vote 0.970
Truncated (hit the token limit) 0.0%
No answer 0.0%
Answer taken from \boxed{} (no tags) 99.7%
Answered without <answer> tags or a box 0.0%
Answer taken from the first bold span 0.0%
Confidently wrong (top wrong answer >= 50.0% of samples) 2.0%
Modal answer correct 97.0%
Neither (modal wrong, no dominant wrong answer) 1.0%
Distinct answers per instance (mean) 1.33
Answer entropy, bits (mean) 0.10

By level

level Instances Mean accuracy Any sample correct
1 11 0.951 1.000
2 25 0.960 0.960
3 19 0.999 1.000
4 22 0.994 1.000
5 23 0.896 1.000

By subject

subject Instances Mean accuracy Any sample correct
Algebra 25 1.000 1.000
Counting & Probability 6 0.973 1.000
Geometry 7 0.923 1.000
Intermediate Algebra 19 0.863 0.947
Number Theory 11 1.000 1.000
Prealgebra 18 0.958 1.000
Precalculus 14 0.999 1.000

How answers are scored

  • Answer: the text after the last </think>. The last <answer>...</answer> wins (answer_source = tag). If the tags are missing, the last \boxed{...} is used (boxed; Qwen3's habit on math). Failing that, if the model wrote just the answer (one line, at most 3 tokens, generation finished normally), that is used and marked bare; failing that, the first **bold** span (at most 12 tokens) is used and marked bold (answers written as a sentence with the answer in bold). Anything else is no answer, which counts as wrong.
  • Bucket: answers that mean the same thing are grouped: lowercase, strip accents/articles/punctuation, U.S. = United States, numbers (50,000, 50k, 8.3 million) and dates are canonicalised (a currency stays part of the number), and for SimpleQA an answer whose words are all inside exactly one longer answer is merged into it ("Coast Guard" into "United States Coast Guard"). Answers over 12 tokens are never merged. RAT is not merged.
  • Match (correct): the bucket equals a gold answer (exact), or for SimpleQA is contained in it or contains it without hedging words (contains). Failed requests are null; no answer is false.
  • Metrics: acc is the fraction of successful samples that are correct (= pass@1); pass@k is the unbiased estimator; majority vote takes the top bucket and splits ties as fractional credit; entropy is in bits over the answered buckets. Failed requests are excluded from every rate.
  • Judge (SimpleQA only, optional): the simple-evals SimpleQA grader on each distinct bucket; per-sample verdicts are in the judge column.

Columns

Column Description
instance_id instance id (same ids as the generations repo)
gold list of accepted gold answers
meta dataset metadata for the instance (RAT: difficulty, cues; SimpleQA: topic, answer_type, ...)
n_samples / n_success / n_answered / n_bare / n_boxed samples seen / requests that succeeded / samples with an answer / bare answers without tags / answers from \boxed{}
n_bold answers taken from the first bold span of an untagged sentence
n_correct / n_truncated / n_no_answer string-match correct / finish_reason=length / no answer
answer_counts the distribution: list of {bucket, label, count, match, judge, members}, most common first
n_distinct / modal_answer / modal_frac / entropy distinct buckets, top bucket, its share of successes, entropy in bits
modal_is_correct / top_wrong_frac / collapsed_wrong top bucket correct; share of samples in the most common wrong bucket; that share >= 0.5 (confidently wrong)
acc / pass_any / majority_correct fraction correct, any correct, majority vote (ties split)
judge_acc / judge_pass_any / judge_majority_correct / judge_counts same, from the LLM judge (judge runs only)
sample_idx, ok, answer, answer_source, bucket, truncated, correct, judge per-sample lists aligned by position: the judgment for every sample
Full metrics JSON
{
  "n_instances": 100,
  "n_instances_with_samples": 100,
  "n_samples": 10000,
  "n_success": 9950,
  "n_failed": 50,
  "acc_mean": 0.9592382820638425,
  "pass_any_mean": 0.99,
  "majority_correct_mean": 0.97,
  "truncation_rate": 0.00030150753768844223,
  "no_answer_rate": 0.00030150753768844223,
  "bare_rate": 0.0,
  "boxed_rate": 0.9968844221105527,
  "bold_rate": 0.0,
  "entropy_mean": 0.09660363697596018,
  "n_distinct_mean": 1.33,
  "collapse": {
    "threshold": 0.5,
    "collapsed_wrong_frac": 0.02,
    "modal_correct_frac": 0.97,
    "other_frac": 0.01,
    "top_wrong_frac_mean": 0.031058113226814156
  },
  "pass_at_k": {
    "1": {
      "value": 0.9592382820638425,
      "n_instances": 100
    },
    "5": {
      "value": 0.9846545271250211,
      "n_instances": 100
    },
    "10": {
      "value": 0.9883641964917858,
      "n_instances": 100
    },
    "100": {
      "value": 0.9893617021276596,
      "n_instances": 94
    }
  },
  "breakdowns": {
    "level": {
      "1": {
        "n_instances": 11,
        "acc_mean": 0.950909090909091,
        "pass_any_mean": 1.0
      },
      "2": {
        "n_instances": 25,
        "acc_mean": 0.96,
        "pass_any_mean": 0.96
      },
      "3": {
        "n_instances": 19,
        "acc_mean": 0.9994736842105262,
        "pass_any_mean": 1.0
      },
      "4": {
        "n_instances": 22,
        "acc_mean": 0.9936363636363637,
        "pass_any_mean": 1.0
      },
      "5": {
        "n_instances": 23,
        "acc_mean": 0.8962534002775766,
        "pass_any_mean": 1.0
      }
    },
    "subject": {
      "Algebra": {
        "n_instances": 25,
        "acc_mean": 0.9995999999999999,
        "pass_any_mean": 1.0
      },
      "Counting & Probability": {
        "n_instances": 6,
        "acc_mean": 0.9731786941580757,
        "pass_any_mean": 1.0
      },
      "Geometry": {
        "n_instances": 7,
        "acc_mean": 0.9228571428571428,
        "pass_any_mean": 1.0
      },
      "Intermediate Algebra": {
        "n_instances": 19,
        "acc_mean": 0.8629186166239164,
        "pass_any_mean": 0.9473684210526315
      },
      "Number Theory": {
        "n_instances": 11,
        "acc_mean": 1.0,
        "pass_any_mean": 1.0
      },
      "Prealgebra": {
        "n_instances": 18,
        "acc_mean": 0.958294573643411,
        "pass_any_mean": 1.0
      },
      "Precalculus": {
        "n_instances": 14,
        "acc_mean": 0.9992857142857143,
        "pass_any_mean": 1.0
      }
    }
  },
  "subset": "math500",
  "n_requested": "all",
  "input": {
    "repo": "connections-dev/create-interpret-task-general-x100",
    "sha": "8485bb7b97b7b1fa1474c31ea397b8aee0e9f5f7",
    "subset": "math500"
  },
  "enable_thinking": true,
  "answer_prefill": "",
  "judge_model": null,
  "judge_settings": null,
  "eval_git": {
    "sha": "87dd0ea592e6ef65a8bb3e5fa11fa92985654613",
    "dirty": false
  }
}
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