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problem_index
int64
is_correct
bool
expected_answer
string
total_attempts
int64
attempts
list
correct_reasoning
string
correct_answer
string
question
string
0
true
0
1
[ { "answer": "0", "attempt_number": 1, "is_correct": true, "reasoning": "I need to evaluate $\\lim_{x \\to \\infty} \\sqrt{x} \\left( \\sqrt[3]{x+1} - \\sqrt[3]{x-1} \\right)$.\n\nLet me rewrite this. Let $f(x) = \\sqrt{x} \\left( \\sqrt[3]{x+1} - \\sqrt[3]{x-1} \\right)$.\n\nAs $x \\to \\infty$, bot...
I need to evaluate $\lim_{x \to \infty} \sqrt{x} \left( \sqrt[3]{x+1} - \sqrt[3]{x-1} \right)$. Let me rewrite this. Let $f(x) = \sqrt{x} \left( \sqrt[3]{x+1} - \sqrt[3]{x-1} \right)$. As $x \to \infty$, both $\sqrt[3]{x+1}$ and $\sqrt[3]{x-1}$ approach $\sqrt[3]{x}$, so their difference approaches 0. And $\sqrt{x} \...
I need to evaluate $\lim_{x \to \infty} \sqrt{x} \left( \sqrt[3]{x+1} - \sqrt[3]{x-1} \right)$. **Step 1: Identify the indeterminate form** As $x \to \infty$: - $\sqrt{x} \to \infty$ - $\sqrt[3]{x+1} - \sqrt[3]{x-1} \to 0$ This is an $\infty \cdot 0$ indeterminate form. **Step 2: Use the difference of cubes identit...
Evaluate the limit: \[ \lim_{x \to \infty} \sqrt{x} \left( \sqrt[3]{x+1} - \sqrt[3]{x-1} \right) \]
1
true
m^2 + 1 = 0
2
[ { "answer": "r^2 + 1 = 0", "attempt_number": 1, "is_correct": false, "reasoning": "We are asked: \"Find the auxiliary equation for the ordinary differential equation with constant coefficients: \\((x^2D^2 + xD + 1)y = \\sin(2\\log x)\\sin(\\log x)\\).\"\n\nInterpretation: The ODE is given as \\((x^2...
We are asked: "Find the auxiliary equation for the ordinary differential equation with constant coefficients: \((x^2D^2 + xD + 1)y = \sin(2\log x)\sin(\log x)\)." Interpretation: We have an ODE: (x^2 D^2 + x D + 1) y = sin(2 log x) sin(log x). Here D = d/dx. This is a Cauchy-Euler (equidimensional) equation because th...
The given differential equation is \((x^2 D^2 + x D + 1)y = \sin(2\log x)\sin(\log x)\). The homogeneous part is \(x^2 y'' + x y' + y = 0\), which is a Cauchy-Euler equation. Assuming a solution of the form \(y = x^m\), we substitute into the homogeneous equation: \[ x^2 \cdot m(m-1)x^{m-2} + x \cdot m x^{m-1} + x^m =...
Find the auxiliary equation for the ordinary differential equation with constant coefficients: \((x^2D^2 + xD + 1)y = \sin(2\log x)\sin(\log x)\).
2
true
-\dfrac{2}{3}
1
[ { "answer": "-\\dfrac{2}{3}", "attempt_number": 1, "is_correct": true, "reasoning": "We need to evaluate the limit: lim_{x->0} (1/(tan^2 x) - 1/x^2). Let's rewrite: tan x = sin x / cos x, so 1/tan^2 x = cot^2 x = cos^2 x / sin^2 x. So expression = cos^2 x / sin^2 x - 1/x^2.\n\nWe need limit as x->0....
We need to evaluate the limit: lim_{x->0} (1/(tan^2 x) - 1/x^2). Let's rewrite: tan x = sin x / cos x, so 1/tan^2 x = cot^2 x = cos^2 x / sin^2 x. So expression = cos^2 x / sin^2 x - 1/x^2. We need limit as x->0. Both terms diverge like 1/x^2? Actually sin x ~ x, cos x ~ 1, so cos^2 x/sin^2 x ~ 1/x^2. So difference is...
\[ \lim_{x \to 0} \left(\frac{1}{\tan^2 x} - \frac{1}{x^2}\right) = \lim_{x \to 0} \left(\frac{1}{\sin^2 x} - 1 - \frac{1}{x^2}\right) = \lim_{x \to 0} \left(\frac{1}{\sin^2 x} - \frac{1}{x^2}\right) - 1. \] Using the expansion \(\sin x = x - \frac{x^3}{6} + O(x^5)\), we have \[ \sin^2 x = x^2 - \frac{x^4}{3} + O(x^6)...
Evaluate the limit: \[ \lim_{x \to 0} \left(\dfrac{1}{\tan^2 x}-\dfrac{1}{x^2} \right) \]
3
true
34
1
[ { "answer": "34", "attempt_number": 1, "is_correct": true, "reasoning": "We are given: \"Determine the minimum sample size required such that the probability of at least two people being a match at all six genetic markers exceeds 0.001, given that the probability of a match at each individual marker...
We are given: "Determine the minimum sample size required such that the probability of at least two people being a match at all six genetic markers exceeds 0.001, given that the probability of a match at each individual marker is 1/9." Interpretation: We have a population of people. Each person has a genetic profile a...
The probability that two randomly chosen individuals match at a given genetic marker is \( \frac{1}{9} \). Assuming independence across the six markers, the probability that they match at all six markers is \[ p = \left(\frac{1}{9}\right)^6 = \frac{1}{9^6} = \frac{1}{531441}. \] Thus there are effectively \( M = 9^...
Determine the minimum sample size required such that the probability of at least two people being a match at all six genetic markers exceeds 0.001, given that the probability of a match at each individual marker is 1/9.
4
true
\infty
1
[ { "answer": "\\infty", "attempt_number": 1, "is_correct": true, "reasoning": "We need to find limit as x→∞ of (x!)^(1/x). But x is presumably a real variable? Usually factorial is defined for integers. But the limit as x→∞ of (n!)^(1/n) for integer n is known: it's ∞? Actually let's think: n! grows ...
We need to find limit as x→∞ of (x!)^(1/x). But x is presumably a real variable? Usually factorial is defined for integers. But the limit as x→∞ of (n!)^(1/n) for integer n is known: it's ∞? Actually let's think: n! grows super-exponentially? Actually n! ~ (n/e)^n sqrt(2π n). So (n!)^(1/n) ~ ((n/e)^n sqrt(2π n))^(1/n) ...
The limit diverges to infinity. Using Stirling's approximation, \(x! \sim \sqrt{2\pi x}\left(\frac{x}{e}\right)^x\). Then \[ (x!)^{1/x} \sim \left(\sqrt{2\pi x}\right)^{1/x} \cdot \frac{x}{e} = \frac{x}{e} \exp\!\left(\frac{\ln(2\pi x)}{2x}\right) \to \infty \quad \text{as } x\to\infty. \] Thus the limit is \(\infty\...
Find the limit: \[ \lim_{x \to \infty} (x!)^{1/x} \]
5
true
\dfrac{\pi}{2}
1
[ { "answer": "\\frac{\\pi}{2}", "attempt_number": 1, "is_correct": true, "reasoning": "We need to find the length of the polar curve r = sqrt(1 + cos(2θ)) for θ from 0 to π√2/4.\n\nFirst, recall the formula for arc length in polar coordinates: L = ∫_{θ1}^{θ2} sqrt( r^2 + (dr/dθ)^2 ) dθ.\n\nWe have r ...
We need to find the length of the polar curve r = sqrt(1 + cos(2θ)) for θ from 0 to π√2/4. First, recall the formula for arc length in polar coordinates: L = ∫_{θ1}^{θ2} sqrt( r^2 + (dr/dθ)^2 ) dθ. We have r = sqrt(1 + cos(2θ)). Let's simplify. Use identity: cos(2θ) = 2cos^2θ - 1 = 1 - 2 sin^2θ. So 1 + cos(2θ) = 1 + ...
The polar curve is given by \( r = \sqrt{1 + \cos(2\theta)} \) for \( 0 \le \theta \le \frac{\pi\sqrt{2}}{4} \). First simplify \( r \). Using the identity \( 1 + \cos(2\theta) = 2\cos^2\theta \), we have \[ r = \sqrt{2\cos^2\theta} = \sqrt{2}\,|\cos\theta|. \] On the interval \( 0 \le \theta \le \frac{\pi\sqrt{2...
Find the length of the polar curve given by \( r = \sqrt{1 + \cos(2\theta)} \) for \( 0 \leq \theta \leq \frac{\pi\sqrt{2}}{4} \).
6
true
|A|
1
[ { "answer": "|A|", "attempt_number": 1, "is_correct": true, "reasoning": "We are asked: \"Let $A$ be a proper infinite subset of a set $X$. If $x$ and $y$ are two distinct elements of $X$ that are not in $A$, and we define $B = \\{x, y\\} \\cup A$, what is the cardinality of $B$ in terms of the card...
We are asked: "Let $A$ be a proper infinite subset of a set $X$. If $x$ and $y$ are two distinct elements of $X$ that are not in $A$, and we define $B = \{x, y\} \cup A$, what is the cardinality of $B$ in terms of the cardinality of $A$?" Interpretation: A is a proper infinite subset of X. So A is infinite, and A ⊂ X,...
The set \(A\) is infinite. Adding a finite number of elements to an infinite set does not change its cardinality. Since \(x\) and \(y\) are distinct and not in \(A\), the set \(B = A \cup \{x, y\}\) is the union of \(A\) with a two-element set. Therefore, \(|B| = |A|\). \boxed{|A|}
Let $A$ be a proper infinite subset of a set $X$. If $x$ and $y$ are two distinct elements of $X$ that are not in $A$, and we define $B = \{x, y\} \cup A$, what is the cardinality of $B$ in terms of the cardinality of $A$?
7
true
\phi^4
1
[{"answer":"\\phi^4","attempt_number":1,"is_correct":true,"reasoning":"We need to find the ratio of (...TRUNCATED)
"We need to find the ratio of the area of the original regular pentagon (circumscribed in a circle) (...TRUNCATED)
"The regular pentagon \\(ABCDE\\) is inscribed in a circle. Draw all its diagonals, which intersect (...TRUNCATED)
"Consider a regular pentagon circumscribed in a circle. Connect each vertex of this pentagon to ever(...TRUNCATED)
8
true
6
1
[{"answer":"6","attempt_number":1,"is_correct":true,"reasoning":"We need to find the longest geometr(...TRUNCATED)
"We need to find the longest geometric progression (GP) with common ratio > 1 that can be formed fro(...TRUNCATED)
"The longest geometric progression with common ratio greater than 1 that can be formed from the set (...TRUNCATED)
"Find the longest geometric progression with a common ratio greater than 1 that can be formed from t(...TRUNCATED)
9
true
0
1
[{"answer":"0","attempt_number":1,"is_correct":true,"reasoning":"We need to find the expectation E[s(...TRUNCATED)
"We need to find the expectation E[sin(B_t)] where B_t is a standard Brownian motion. B_t ~ N(0, t).(...TRUNCATED)
"The expectation \\(\\mathbb{E}[\\sin(B_t)]\\) is computed directly using the distribution of \\(B_t(...TRUNCATED)
"Find the expectation \\( \\mathbb{E}[X_t] \\) where \\( X_t = \\sin(B_t) \\) and \\( B_t \\) is a s(...TRUNCATED)
End of preview. Expand in Data Studio

Reasoning Traces Collection

Reasoning traces generated by LLMs on math datasets (Deepmath-103k, AIME), collected for SFT training.

Configs

Config Model Dataset Problems Pass@1 Pass@2
qwen_step-deepmath Qwen3.5-397B-A17B DeepMath-103K (0-14K) 13,982 82.9% 86.0%
qwen_logic-deepmath Qwen3.5-397B-A17B DeepMath-103K (0-14K) 13,989 82.5% 85.4%
qwen-aime Qwen3.5-397B-A17B AIME 1983–2024 933 97.0% 98.8% (Pass@2) / 99.6% (Pass@8)
minimax-deepmath MiniMax-M2.5 DeepMath-103K (0-14K) 13,990 80.1% 86.0%
glm-deepmath GLM-5-FP8 DeepMath-103K (0-14K, 200 skipped) 13,800 79.9% 83.9% (Pass@8)
kimi-deepmath Kimi-K2.5 DeepMath-103K (0-14K) 14,000 74.3% 79.0% (Pass@8)

Fields

  • problem_index — index in the source dataset
  • is_correct — whether any attempt solved the problem correctly
  • expected_answer — ground truth answer
  • total_attempts — number of attempts made (max 2 for DeepMath, max 8 for AIME)
  • attempts — all attempts with full details (reasoning, solution, answer, is_correct)
  • correct_reasoning — reasoning from the first correct attempt (null if unsolved)
  • correct_answer — solution from the first correct attempt (null if unsolved)
  • question — problem text from the source dataset (DeepMath configs only)

qwen_step-deepmath

Model: Qwen3.5-397B-A17B
Source dataset: zwhe99/DeepMath-103K (indices 0–13,999)
Max attempts: 2

Prompt:

You are a helpful math expert. Solve the problem step-by-step. End your response exactly with: \boxed{<answer>}

Statistics:

Metric Value
Total problems 13,982
Pass@1 82.9% (11,596 / 13,982)
Pass@2 86.0% (12,021 / 13,982)
Unsolved 1,961
Mean reasoning length 22,857 chars
Mean solution length 1,978 chars

qwen_logic-deepmath

Model: Qwen3.5-397B-A17B
Source dataset: zwhe99/DeepMath-103K (indices 0–13,999)
Max attempts: 2

Prompt:

You are a careful math solver.

Focus on the core logic and avoid unnecessary complexity.
Address all important details, but avoid over-explaining or repeating the same reasoning.
Cover all required cases, but avoid over-elaboration on less important ones.
Verify the solution step-by-step, ensuring the conclusion follows directly from the reasoning.
Keep the solution focused and concise.
The final answer must be stated as: \boxed{<answer>}

Statistics:

Metric Value
Total problems 13,989
Pass@1 82.5% (11,540 / 13,989)
Pass@2 85.4% (11,940 / 13,989)
Unsolved 2,049
Mean reasoning length 20,368 chars
Mean solution length 1,773 chars

minimax-deepmath

Model: MiniMaxAI/MiniMax-M2.5
Source dataset: zwhe99/DeepMath-103K (indices 0–13,999)
Max attempts: 2

Prompt:

You are a helpful math expert. Solve the problem step by step.
Give enough justification to support the answer, but do not over-explore alternatives.
The final line must be exactly: \boxed{<answer>}

Statistics:

Metric Value
Total problems 13,990
Pass@1 80.1% (11,201 / 13,990)
Pass@2 86.0% (12,029 / 13,990)
Unsolved 1,961
Mean reasoning length 14,694 chars
Mean solution length 840 chars


glm-deepmath

Model: zai-org/GLM-5
Source dataset: zwhe99/DeepMath-103K (indices 0–13,999)
Max attempts: 8

Prompt:

You are solving math problems under strict correctness requirements.

Work toward the answer with explicit logical checks.
Do not rely on intuition alone.
When a solution depends on considering multiple possibilities, make sure the cases are complete.
When counting, verify that nothing is missed and nothing is counted twice.
When using a known theorem or standard fact, apply it carefully to the exact setting.

Keep the solution focused.
The final line must be exactly: \boxed{<answer>}

Statistics:

Metric Value
Total problems 13,800
Pass@1 79.9% (11,030 / 13,800)
Pass@8 83.9% (11,576 / 13,800)
Unsolved 2,224
Mean reasoning length 24,854 chars
Mean solution length 1,370 chars

Note: 200 of the 14,000 problems (indices 0–13,999) are missing from this config. These are tail problems whose expected solutions are very long; with the prompt above, generation hit the effective context limit before completing, and they were skipped rather than re-run with a higher token budget.

qwen-aime

Model: Qwen3.5-397B-A17B
Source dataset: gneubig/aime-1983-2024 (all 933 problems)
Max attempts: 8

Prompt:

You are a careful math solver.        
Focus on the core logic and avoid unnecessary complexity.
Address all important details, but avoid over-explaining or repeating the same reasoning.
Cover all required cases, but avoid over-elaboration on less important ones.
Verify the solution step-by-step, ensuring the conclusion follows directly from the reasoning.
Keep the solution focused and concise.                                                    
The final line must be exactly: ### \<answer\>. Example: ### 40.

Statistics:

Metric Value
Total problems 933
Pass@1 97.0% (905 / 933)
Pass@2 98.8% (922 / 933)
Pass@8 99.6% (929 / 933)
Unsolved 4
Mean reasoning length 26,773 chars
Mean solution length 1,882 chars

Unsolved problem indices: 138, 153, 294, 882

kimi-deepmath

Model: moonshotai/Kimi-K2.5
Source dataset: zwhe99/DeepMath-103K (indices 0–13,999)
Max attempts: 8

Prompt:

You are a helpful math expert. Solve the problem step-by-step. End your response exactly with: \boxed{<answer>}

Statistics:

Metric Value
Total problems 14,000
Pass@1 74.3% (10,397 / 14,000)
Pass@8 79.0% (11,061 / 14,000)
Unsolved 2,939
Mean reasoning length 17,757 chars
Mean solution length 1,947 chars

*-add_steps variants

glm-deepmath-add_steps and minimax-deepmath-add_steps take each model's correct solution and add latent thoughts between visible steps — an adaptation of the latent thoughts idea.

Prompt:

You are given a math problem and a teacher solution split into logical steps.

Your task is to add concise latent thoughts that explain the hidden reasoning needed to
go from one visible step to the next.

The latent thoughts should include only:
- missing background knowledge,
- the key idea behind the step,
- the short reasoning bridge that justifies the step,
- any hidden assumption needed for the transition.

Requirements:
- Keep the latent thoughts concise.
- Do not add alternative solution paths.
- Do not add unnecessary self-correction or long verification.
- Do not introduce new facts or methods not supported by the original solution.
- Make the result easier for a weak student to learn from.
- Preserve the original mathematical meaning.
- The final line must be exactly: \boxed{<answer>}

Output format:
For each step: first write one short hidden idea, then write the original visible step.

Problem:
{problem}

Teacher solution steps:
{solution_steps}

*-student_aware variants

glm-deepmath-student_aware and minimax-deepmath-student_aware rewrite each correct solution into a student-teachable format, inserting latent thoughts only where a weak student would struggle.

Prompt:

You are given a math problem and a teacher solution.

Your task is to rewrite the solution into a student-teachable format by adding latent thoughts.

The student is weak and tends to fail on long, overly compressed, or repetitive reasoning.
So only add latent thoughts that help explain difficult transitions.

Include:
1. a short latent plan before the solution,
2. short latent thoughts only before steps that require a non-obvious reasoning jump.

Requirements:
- Be concise.
- Prefer short local reasoning bridges over long hidden monologue.
- Do not add alternative methods.
- Do not add unnecessary verification.
- Preserve the original mathematical meaning.
- Make the final result easy for a weak student to imitate.
- The final line must be exactly: \boxed{<answer>}

Problem:
{problem}

Teacher solution:
{teacher_solution}

Student-teachable solution with latent thoughts:
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