prompt listlengths 1 1 | reward_model dict | data_source stringclasses 1
value | ability stringclasses 1
value | extra_info dict |
|---|---|---|---|---|
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\left(\\dfrac{1}{\\tan^2 x}-\\dfrac{1}{x^2} \\right) \\]",
"role": "user"
}
] | {
"ground_truth": "-\\dfrac{2}{3}",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "0",
"problem": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\left(\\dfrac{1}{\\tan^2 x}-\\dfrac{1}{x^2} \\right) \\]",
"solution": "Okay, so I need to evaluate the limit as x approaches 0 of (1/tan²x - 1/x²). Hmm, let me think. First, I remember that tanx is sinx/cosx, so tan²x would be sin²x/cos²x. The... |
[
{
"content": "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.",
"role": "user"
}
] | {
"ground_truth": "34",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "1",
"problem": "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.",
"solution": "Okay, so I need to figure out the minimum sample si... |
[
{
"content": "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 $A$?",
"role": "user"
}
] | {
"ground_truth": "|A|",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "2",
"problem": "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 $A$?",
"solution": "Okay, let's try to figure out the cardinality... |
[
{
"content": "Find the longest geometric progression with a common ratio greater than 1 that can be formed from the set \\( \\{100, 101, 102, \\ldots, 1000\\} \\). What is the length of this progression?",
"role": "user"
}
] | {
"ground_truth": "6",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "3",
"problem": "Find the longest geometric progression with a common ratio greater than 1 that can be formed from the set \\( \\{100, 101, 102, \\ldots, 1000\\} \\). What is the length of this progression?",
"solution": "Okay, so I need to find the longest geometric progression (GP) with a common rati... |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{\\sum_{k=1}^n k^p}{n^{p+1}} \\]",
"role": "user"
}
] | {
"ground_truth": "\\dfrac{1}{p+1}",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "4",
"problem": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{\\sum_{k=1}^n k^p}{n^{p+1}} \\]",
"solution": "Okay, so I need to find the limit as n approaches infinity of the sum from k=1 to n of k^p divided by n^(p+1). Hmm. Let me think. I remember that when dealing with sums involving powers... |
[
{
"content": "Evaluate the limit: \\[ \\lim_{t\\to 0}\\left(\\frac{1}{\\ln(1 + t)}+\\frac{1}{\\ln(1-t)}\\right). \\]",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "5",
"problem": "Evaluate the limit: \\[ \\lim_{t\\to 0}\\left(\\frac{1}{\\ln(1 + t)}+\\frac{1}{\\ln(1-t)}\\right). \\]",
"solution": "Okay, so I need to find the limit as t approaches 0 of the expression (1 / ln(1 + t)) + (1 / ln(1 - t)). Hmm, let me think about how to approach this. First, I remember... |
[
{
"content": "Determine the radius of convergence for the function \\( \\frac{1}{z^2 + 2z + 2} \\).",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{2}",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "6",
"problem": "Determine the radius of convergence for the function \\( \\frac{1}{z^2 + 2z + 2} \\).",
"solution": "Okay, so I need to find the radius of convergence for the function \\( \\frac{1}{z^2 + 2z + 2} \\). Hmm, let me think. I remember that the radius of convergence is related to power seri... |
[
{
"content": "A cube is to be colored using 6 distinct colors such that no two adjacent faces share the same color. How many distinct ways can this be done?",
"role": "user"
}
] | {
"ground_truth": "30",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "7",
"problem": "A cube is to be colored using 6 distinct colors such that no two adjacent faces share the same color. How many distinct ways can this be done?",
"solution": "Okay, so I need to figure out how many distinct ways there are to color a cube using 6 distinct colors, with the condition that ... |
[
{
"content": "In a group of 10 chickens, 9 are real and each weighs 2kg, while 1 is a false chicken that weighs either 1kg or 3kg, each with a probability of \\(\\frac{1}{2}\\). A machine randomly selects each chicken with a probability of \\(\\frac{1}{2}\\) for weighing, and after weighing, all chickens are re... | {
"ground_truth": "\\dfrac{3}{5}",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "8",
"problem": "In a group of 10 chickens, 9 are real and each weighs 2kg, while 1 is a false chicken that weighs either 1kg or 3kg, each with a probability of \\(\\frac{1}{2}\\). A machine randomly selects each chicken with a probability of \\(\\frac{1}{2}\\) for weighing, and after weighing, all chick... |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^0 xe^{-4x} \\, dx \\).",
"role": "user"
}
] | {
"ground_truth": "-\\infty",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "9",
"problem": "Evaluate the integral \\( \\int_{-\\infty}^0 xe^{-4x} \\, dx \\).",
"solution": "Okay, so I need to evaluate the integral from negative infinity to 0 of x times e to the power of -4x dx. Hmm, let's see. I remember that integrals involving infinity are improper integrals, so I probably ... |
[
{
"content": "If a function $f(x)$ is differentiable at $x = a$, is it necessarily differentiable in an open interval including $x = a$?",
"role": "user"
}
] | {
"ground_truth": "No",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "10",
"problem": "If a function $f(x)$ is differentiable at $x = a$, is it necessarily differentiable in an open interval including $x = a$?",
"solution": "Okay, so I need to figure out if a function f(x) being differentiable at a single point x = a necessarily means it's differentiable in some open in... |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} x \\left( \\left(1 + \\frac{1}{x}\\right)^{1 + \\frac{1}{x}} - 1 \\right) \\]",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "11",
"problem": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} x \\left( \\left(1 + \\frac{1}{x}\\right)^{1 + \\frac{1}{x}} - 1 \\right) \\]",
"solution": "Okay, so I need to evaluate the limit as x approaches infinity of x times the quantity ((1 + 1/x)^(1 + 1/x) minus 1). Hmm, that looks a bit intim... |
[
{
"content": "Determine the number of distinct terms in the expansion of \\((x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8)^4\\).",
"role": "user"
}
] | {
"ground_truth": "25",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "12",
"problem": "Determine the number of distinct terms in the expansion of \\((x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8)^4\\).",
"solution": "Okay, so I need to find the number of distinct terms in the expansion of \\((x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8)^4\\). Hmm, let's see. When you expand a po... |
[
{
"content": "Let $A$ be a $3 \\times 3$ matrix and $\\vec{x}, \\vec{y}, \\vec{z}$ be vectors in $\\mathbb{R}^3$. Given the equations:\n\\[ A\\vec{x} = \\begin{pmatrix} 1 \\\\ 0 \\\\ 1 \\end{pmatrix}, \\quad A\\vec{y} = \\begin{pmatrix} 0 \\\\ 1 \\\\ 0 \\end{pmatrix}, \\quad A\\vec{z} = \\begin{pmatrix} 1 \\\\ ... | {
"ground_truth": "0",
"style": "rule-lighteval/MATH_v2"
} | deepmath | MATH | {
"index": "13",
"problem": "Let $A$ be a $3 \\times 3$ matrix and $\\vec{x}, \\vec{y}, \\vec{z}$ be vectors in $\\mathbb{R}^3$. Given the equations:\n\\[ A\\vec{x} = \\begin{pmatrix} 1 \\\\ 0 \\\\ 1 \\end{pmatrix}, \\quad A\\vec{y} = \\begin{pmatrix} 0 \\\\ 1 \\\\ 0 \\end{pmatrix}, \\quad A\\vec{z} = \\begin{pmatr... |
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DeepMath RLCSD-format difficulty splits
This dataset is derived from zwhe99/DeepMath-103K
at revision 5cf055d1fe3d7a2eb19719ac020211469736ae44 and uses the nested parquet schema released by
Leyiii/RLCSD.
Files
| Path | Rows | Difficulty |
|---|---|---|
deepmath_full/train.parquet |
103,022 | Full upstream dataset |
deepmath_easy_10k/train.parquet |
10,000 | 1.0 <= difficulty < 5.0 |
deepmath_medium_10k/train.parquet |
10,000 | 5.0 <= difficulty < 7.0 |
deepmath_hard_10k/train.parquet |
10,000 | 7.0 <= difficulty <= 10.0 |
The three subsets are pairwise disjoint by difficulty. Rows with missing required
fields and every occurrence of a duplicated normalized question are excluded from
the three sampling pools. Within each difficulty band, samples are selected
proportionally by exact half-step difficulty and then by topic.
Selection is deterministic (seed 42) and uses a SHA-256
ordering over the normalized question, source index, and pinned source revision.
Schema
Each parquet has exactly the RLCSD-style fields prompt, reward_model,
data_source, ability, and extra_info. extra_info.solution is selected uniformly from DeepMath's three R1 solutions
with Python's random.seed(42) behavior; reward_model.ground_truth comes from
final_answer.
License and attribution
The upstream DeepMath-103K dataset is released under the MIT license. Please also follow its citation and attribution requirements.
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