data_source
stringclasses 5
values | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nSuppose the polynomial\n$$f(x) = a_nx^n + a_{n-1}x^{n-1} + \\cdots + a_2x^2 + a_1x + a_0$$has integer coefficients, and its roots are distinct integers.\n\nGiven that $a_n=2$ and $a_0=66$, what is the least possible value of $|a_{n-1}|$?\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 490,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nTom got a Mr. Potato Head for his birthday. It came with 3 hairstyles, 2 sets of eyebrows, 1 pair of googly eyes, 2 sets of ears, and 2 sets of lips, a pair of regular shoes, and a bonus pair of clown shoes. If a complete Mr. Potato Head personality includes eyebrows, eyes, ears, lips, shoes and optionally hair, how many different wacky personalities can Tom come up with? Note that Mr. Potato Head can be bald.\n\nNote: You cannot \"mix and match\". For example, you cannot take the left eyebrow from one pair and the right eyebrow from the other pair.\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "64",
"style": "rule"
} | {
"index": 491,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe set of vectors $\\mathbf{v}$ such that\n\\[\\operatorname{proj}_{\\begin{pmatrix} 2 \\\\ 1 \\end{pmatrix}} \\mathbf{v} = \\begin{pmatrix} 0 \\\\ 0 \\end{pmatrix}\\]lie on a line. Enter the equation of this line in the form \"$y = mx + b$\".\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "y = -2x",
"style": "rule"
} | {
"index": 492,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nThe number $(\\sqrt{2}+\\sqrt{3})^3$ can be written in the form $a\\sqrt{2} + b\\sqrt{3} + c\\sqrt{6}$, where $a$, $b$, and $c$ are integers. What is $a+b+c$?\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 493,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $S$ be the set of points $(a,b)$ with $0 \\le a,$ $b \\le 1$ such that the equation\n\\[x^4 + ax^3 - bx^2 + ax + 1 = 0\\]has at least one real root. Determine the area of the graph of $S.$\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": 494,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nWhat is the domain of the function $f(x) = \\frac{2-x}{\\log(2-\\log(x-2))}$, where $\\log$ is the base $10$ logarithm function? Express your answer in interval notation.\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "(2,12) \\cup (12,102)",
"style": "rule"
} | {
"index": 495,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nLet $z = 1+i$ and $w = \\dfrac{3z+1}{5z+7}$. Find $|w|$.\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "\\frac{5}{13}",
"style": "rule"
} | {
"index": 496,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAn equiangular octagon has four sides of length $1$ and four sides of length $\\frac{\\sqrt{2}}{2}$, arranged so that no two consecutive sides have the same length. What is the area of the octagon?\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "\\frac{7}{2}",
"style": "rule"
} | {
"index": 497,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nA sequence $(a_n)$ is defined as follows:\n\\[a_{i + 1} = \\frac{1}{1 - a_i}\\]for $i \\ge 1.$ If $a_3 = a_1,$ compute $(a_9)^9.$\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "-1",
"style": "rule"
} | {
"index": 498,
"split": "test"
} |
dapo_zero/math500 | [
{
"content": "Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nAltitudes $\\overline{AD}$ and $\\overline{BE}$ of $\\triangle ABC$ intersect at $H$. If $\\angle BAC = 54^\\circ$ and $\\angle ABC = 52^\\circ$, then what is $\\angle AHB$?\n\nRemember to put your answer on its own line after \"Answer:\".",
"role": "user"
}
]
| MATH | {
"ground_truth": "106^\\circ",
"style": "rule"
} | {
"index": 499,
"split": "test"
} |
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