data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The perimeter of a rectangle is 56. If the length of the rectangle is defined as \\( l = x + 4 \\) and the width is defined as \\( w = x - 2 \\), find the area of the rectangle. Express your answer as a whole number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "187",
"style": "rule"
}
|
{
"answer": "187",
"index": 0,
"question": "The perimeter of a rectangle is 56. If the length of the rectangle is defined as \\( l = x + 4 \\) and the width is defined as \\( w = x - 2 \\), find the area of the rectangle. Express your answer as a whole number.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The negation of the statement \"There exists an $x \\in \\mathbb{R}$ such that $x^2 + 2x + 2 \\leq 0$.\" Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\forall x \\in \\mathbb{R}, x^2 + 2x + 2 > 0",
"style": "rule"
}
|
{
"answer": "\\forall x \\in \\mathbb{R}, x^2 + 2x + 2 > 0",
"index": 1,
"question": "The negation of the statement \"There exists an $x \\in \\mathbb{R}$ such that $x^2 + 2x + 2 \\leq 0$.\"",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that the terminal side of angle $\\alpha$ passes through point $P(4,-3)$, find the value of $2\\sin \\alpha + 3\\cos \\alpha =$ $\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.$ Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{6}{5}",
"style": "rule"
}
|
{
"answer": "\\frac{6}{5}",
"index": 2,
"question": "Given that the terminal side of angle $\\alpha$ passes through point $P(4,-3)$, find the value of $2\\sin \\alpha + 3\\cos \\alpha =$ $\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.$",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In the expression $5 * 4 * 3 * 2 * 1 = 0$, replace the asterisks with the four arithmetic operation signs (using each sign exactly once) so that the equation becomes valid. Other signs, including parentheses, cannot be used. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5 - 4 \\cdot 3 \\div 2 + 1 = 0",
"style": "rule"
}
|
{
"answer": "5 - 4 \\cdot 3 \\div 2 + 1 = 0",
"index": 3,
"question": "In the expression $5 * 4 * 3 * 2 * 1 = 0$, replace the asterisks with the four arithmetic operation signs (using each sign exactly once) so that the equation becomes valid. Other signs, including parentheses, cannot be used.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given $p:|1-\\frac{x-1}{3}|\\leqslant 2$ and $q:x^{2}-2x+(1-m^{2})\\leqslant 0$, if \"$\\lnot p$\" is a necessary but not sufficient condition for \"$\\lnot q$\", find the range of values for the real number $m$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "(-\\infty,-9]\\cup[9,+\\infty)",
"style": "rule"
}
|
{
"answer": "(-\\infty,-9]\\cup[9,+\\infty)",
"index": 4,
"question": "Given $p:|1-\\frac{x-1}{3}|\\leqslant 2$ and $q:x^{2}-2x+(1-m^{2})\\leqslant 0$, if \"$\\lnot p$\" is a necessary but not sufficient condition for \"$\\lnot q$\", find the range of values for the real number $m$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "A group of ten people went to the cinema. They received tickets for 5 adjacent seats in two different rows. Ábel and Bendegúz want to sit next to each other, while Zsuzsi and Anikó want to sit separately. In how many ways can they be seated? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "518400",
"style": "rule"
}
|
{
"answer": "518400",
"index": 5,
"question": "A group of ten people went to the cinema. They received tickets for 5 adjacent seats in two different rows. Ábel and Bendegúz want to sit next to each other, while Zsuzsi and Anikó want to sit separately. In how many ways can they be seated?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the set A = {x | x^2 - 2x + a >= 0} and the condition that 1 is not an element of A, find the range of real number a. Express your answer as an interval or a description of the range. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "(-\\infty, 1)",
"style": "rule"
}
|
{
"answer": "(-\\infty, 1)",
"index": 6,
"question": "Given the set A = {x | x^2 - 2x + a >= 0} and the condition that 1 is not an element of A, find the range of real number a. Express your answer as an interval or a description of the range.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In triangle $ABC$, if $\\sin A > \\sin B$, then the relationship between angles $A$ and $B$ is \\_\\_\\_\\_\\_\\_. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "A > B",
"style": "rule"
}
|
{
"answer": "A > B",
"index": 7,
"question": "In triangle $ABC$, if $\\sin A > \\sin B$, then the relationship between angles $A$ and $B$ is \\_\\_\\_\\_\\_\\_.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "A polygon $\\mathcal{P}$ is drawn on the 2D coordinate plane. Each side of $\\mathcal{P}$ is either parallel to the $x$ axis or the $y$ axis (the vertices of $\\mathcal{P}$ do not have to be lattice points). Given that the interior of $\\mathcal{P}$ includes the interior of the circle \\(x^{2}+y^{2}=2022\\), find the minimum possible perimeter of $\\mathcal{P}$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "8 \\sqrt{2022}",
"style": "rule"
}
|
{
"answer": "8 \\sqrt{2022}",
"index": 8,
"question": "A polygon $\\mathcal{P}$ is drawn on the 2D coordinate plane. Each side of $\\mathcal{P}$ is either parallel to the $x$ axis or the $y$ axis (the vertices of $\\mathcal{P}$ do not have to be lattice points). Given that the interior of $\\mathcal{P}$ includes the interior of the circle \\(x^{2}+y^{2}=2022\\), find the minimum possible perimeter of $\\mathcal{P}$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "$(4a^{3}b-2ab)\\div 2ab=\\_\\_\\_\\_\\_\\_.$ Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "2a^{2} - 1",
"style": "rule"
}
|
{
"answer": "2a^{2} - 1",
"index": 9,
"question": "$(4a^{3}b-2ab)\\div 2ab=\\_\\_\\_\\_\\_\\_.$",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given $\\mathrm{a}, \\mathrm{b}, \\mathrm{c}$ are three natural numbers, and the least common multiple (LCM) of $\\mathrm{a}$ and $\\mathrm{b}$ is $60$, the LCM of $\\mathrm{a}$ and $\\mathrm{c}$ is $270$, find the LCM of $\\mathrm{b}$ and $\\mathrm{c}$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "540",
"style": "rule"
}
|
{
"answer": "540",
"index": 10,
"question": "Given $\\mathrm{a}, \\mathrm{b}, \\mathrm{c}$ are three natural numbers, and the least common multiple (LCM) of $\\mathrm{a}$ and $\\mathrm{b}$ is $60$, the LCM of $\\mathrm{a}$ and $\\mathrm{c}$ is $270$, find the LCM of $\\mathrm{b}$ and $\\mathrm{c}$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "A fair coin is tossed 3 times. What is the probability of at least two consecutive heads? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "$\\frac{3}{8}$",
"style": "rule"
}
|
{
"answer": "$\\frac{3}{8}$",
"index": 11,
"question": "A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Last month, you borrowed $100 from your friend. If you promise to pay her today, how much will you give to your friend if both of you agreed to return the money with a 10% increase? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "110",
"style": "rule"
}
|
{
"answer": "110",
"index": 12,
"question": "Last month, you borrowed $100 from your friend. If you promise to pay her today, how much will you give to your friend if both of you agreed to return the money with a 10% increase?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given a sequence $\\{a_n\\}$ that is both an arithmetic sequence and a geometric sequence, find the sum of the first $n$ terms of this sequence. Express your answer in terms of $n$ and $a_1$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "na_1",
"style": "rule"
}
|
{
"answer": "na_1",
"index": 13,
"question": "Given a sequence $\\{a_n\\}$ that is both an arithmetic sequence and a geometric sequence, find the sum of the first $n$ terms of this sequence. Express your answer in terms of $n$ and $a_1$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "On the number line, the point representing the rational number $a$ is to the left of the origin, and the point representing the rational number $b$ is to the right of the origin. Simplify the expression $|a-b|+b$. Express your answer as an algebraic expression involving $a$ and $b$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-a+2b",
"style": "rule"
}
|
{
"answer": "-a+2b",
"index": 14,
"question": "On the number line, the point representing the rational number $a$ is to the left of the origin, and the point representing the rational number $b$ is to the right of the origin. Simplify the expression $|a-b|+b$. Express your answer as an algebraic expression involving $a$ and $b$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Calculate the value of the expression $\\sqrt{5^{2}-4^{2}}$. Provide your answer as a single number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "3",
"style": "rule"
}
|
{
"answer": "3",
"index": 15,
"question": "Calculate the value of the expression $\\sqrt{5^{2}-4^{2}}$. Provide your answer as a single number.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "A factory arranges 5 workers to three duty positions, with each worker assigned to only one position. Each position must have at least 1 worker. Calculate the number of ways to assign workers A and B to the same position. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "36",
"style": "rule"
}
|
{
"answer": "36",
"index": 16,
"question": "A factory arranges 5 workers to three duty positions, with each worker assigned to only one position. Each position must have at least 1 worker. Calculate the number of ways to assign workers A and B to the same position.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the sequence $\\{a\\_n\\}$, it satisfies $a\\_1=1, a\\_n+a_{n+1}=( \\frac {1}{4})^{n}(n∈N^{}),, S\\_n=a\\_1+4⋅ a\\_2+4^{2}⋅ a\\_3+…+4^{n-1}a\\_n$. By analogy with the method of deriving the formula for the sum of the first n terms of a geometric sequence in the textbook, find $S\\_n- \\frac {4^{n}}{5}a\\_n=$ ___. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{n}{5}",
"style": "rule"
}
|
{
"answer": "\\frac{n}{5}",
"index": 17,
"question": "Given the sequence $\\{a\\_n\\}$, it satisfies $a\\_1=1, a\\_n+a_{n+1}=( \\frac {1}{4})^{n}(n∈N^{}),, S\\_n=a\\_1+4⋅ a\\_2+4^{2}⋅ a\\_3+…+4^{n-1}a\\_n$. By analogy with the method of deriving the formula for the sum of the first n terms of a geometric sequence in the textbook, find $S\\_n- \\frac {4^{n}}{5}a\\_n=$ ___.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Natural numbers from 1 to 1982 are arranged in some order. A computer examines pairs of adjacent numbers from left to right (the first and second, the second and third, etc. up to the last pair) and swaps the numbers in the examined pair if the larger number is on the left. Then it examines all pairs, moving from the last pair to the first, swapping numbers in the pairs by the same rule. After this examination, the operator received information that the number in the hundredth position did not move both times. Find this number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "100",
"style": "rule"
}
|
{
"answer": "100",
"index": 18,
"question": "Natural numbers from 1 to 1982 are arranged in some order. A computer examines pairs of adjacent numbers from left to right (the first and second, the second and third, etc. up to the last pair) and swaps the numbers in the examined pair if the larger number is on the left. Then it examines all pairs, moving from the last pair to the first, swapping numbers in the pairs by the same rule. After this examination, the operator received information that the number in the hundredth position did not move both times. Find this number.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given a function $f(x)$ on the interval $[a,b]$, if there exists an $x\\_0∈[a,b]$ such that $f(x\\_0)=∫_a^bf(x)dx$, then $x\\_0$ is called an \"integral point\" of the function $f(x)$ on the interval $[a,b]$. Find the \"integral point\" of the function $f(x)=cos(2x+π/6)$ on the interval $[0,π/2]$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "π/4",
"style": "rule"
}
|
{
"answer": "π/4",
"index": 19,
"question": "Given a function $f(x)$ on the interval $[a,b]$, if there exists an $x\\_0∈[a,b]$ such that $f(x\\_0)=∫_a^bf(x)dx$, then $x\\_0$ is called an \"integral point\" of the function $f(x)$ on the interval $[a,b]$. Find the \"integral point\" of the function $f(x)=cos(2x+π/6)$ on the interval $[0,π/2]$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the universal set $U={2,4,a^2-a+1}$, set $A={a+4,4}$, and the complement of $A$ relative to $U$ as ${7}$, find the value of $a$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "a=-2",
"style": "rule"
}
|
{
"answer": "a=-2",
"index": 20,
"question": "Given the universal set $U={2,4,a^2-a+1}$, set $A={a+4,4}$, and the complement of $A$ relative to $U$ as ${7}$, find the value of $a$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that $\\sin\\left(\\frac{\\pi}{2} + \\alpha\\right) = \\frac{1}{3}$, find the value of $\\cos(\\pi + \\alpha)$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-\\frac{1}{3}",
"style": "rule"
}
|
{
"answer": "-\\frac{1}{3}",
"index": 21,
"question": "Given that $\\sin\\left(\\frac{\\pi}{2} + \\alpha\\right) = \\frac{1}{3}$, find the value of $\\cos(\\pi + \\alpha)$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given a set of Pythagorean triples, knowing that two of the numbers are $24$ and $7$, the third number is ____. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "25",
"style": "rule"
}
|
{
"answer": "25",
"index": 22,
"question": "Given a set of Pythagorean triples, knowing that two of the numbers are $24$ and $7$, the third number is ____.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Assign four intern teachers, named A, B, C, and D, to three different classes, with each class receiving at least one teacher, and with the restriction that teachers A and B cannot be in the same class. Calculate the number of different ways to assign them under these conditions. Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "30",
"style": "rule"
}
|
{
"answer": "30",
"index": 23,
"question": "Assign four intern teachers, named A, B, C, and D, to three different classes, with each class receiving at least one teacher, and with the restriction that teachers A and B cannot be in the same class. Calculate the number of different ways to assign them under these conditions. Express your answer as a single integer.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the function $f\\left(x\\right)=\\left\\{\\begin{array}{l}{ax-1,x＜1,}\\\\{{x^2}-2ax,x≥1}\\end{array}\\right.$ with the range of $R$, the range of the real number $a$ is ____. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "[\\frac{2}{3}, +\\infty)",
"style": "rule"
}
|
{
"answer": "[\\frac{2}{3}, +\\infty)",
"index": 24,
"question": "Given the function $f\\left(x\\right)=\\left\\{\\begin{array}{l}{ax-1,x＜1,}\\\\{{x^2}-2ax,x≥1}\\end{array}\\right.$ with the range of $R$, the range of the real number $a$ is ____.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Define a function $f$ on $\\mathbb{R}$ that satisfies $f(x+1)=2f(x)$. If for $0 \\leqslant x \\leqslant 1$, $f(x)=x(1-x)$, then find $f(x)$ for $-1 \\leqslant x \\leqslant 0$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "- \\dfrac{1}{2}x(x+1)",
"style": "rule"
}
|
{
"answer": "- \\dfrac{1}{2}x(x+1)",
"index": 25,
"question": "Define a function $f$ on $\\mathbb{R}$ that satisfies $f(x+1)=2f(x)$. If for $0 \\leqslant x \\leqslant 1$, $f(x)=x(1-x)$, then find $f(x)$ for $-1 \\leqslant x \\leqslant 0$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "An apple, three pears, and two bananas together weigh 920 grams; two apples, four bananas, and five pears together weigh 1,710 grams. How many grams does a pear weigh? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "130",
"style": "rule"
}
|
{
"answer": "130",
"index": 26,
"question": "An apple, three pears, and two bananas together weigh 920 grams; two apples, four bananas, and five pears together weigh 1,710 grams. How many grams does a pear weigh?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Two congruent 30°-60°-90° triangles are overlapped such that their hypotenuses exactly coincide. If the hypotenuse of each triangle is 12 units, find the area of the overlapping region. Express your answer in simplest radical form. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "6 \\sqrt{3}",
"style": "rule"
}
|
{
"answer": "6 \\sqrt{3}",
"index": 27,
"question": "Two congruent 30°-60°-90° triangles are overlapped such that their hypotenuses exactly coincide. If the hypotenuse of each triangle is 12 units, find the area of the overlapping region. Express your answer in simplest radical form.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The point $A(5,-1)$ is symmetric with respect to the origin to point $B$. The coordinates of point $B$ are ____. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "(-5,1)",
"style": "rule"
}
|
{
"answer": "(-5,1)",
"index": 28,
"question": "The point $A(5,-1)$ is symmetric with respect to the origin to point $B$. The coordinates of point $B$ are ____.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Find the number of integer solutions (x, y) to the equation 1/x + 1/y = 1/7. Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 29,
"question": "Find the number of integer solutions (x, y) to the equation 1/x + 1/y = 1/7. Express your answer as a single integer.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In a granary, there are 3318 stones of grain. A sample of grain is taken, which contains 168 grains, and 22 of them are imperfect. Using this information, calculate the approximate amount of imperfect grains in the granary. Express your answer in stones, rounded to the nearest whole number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "434",
"style": "rule"
}
|
{
"answer": "434",
"index": 30,
"question": "In a granary, there are 3318 stones of grain. A sample of grain is taken, which contains 168 grains, and 22 of them are imperfect. Using this information, calculate the approximate amount of imperfect grains in the granary. Express your answer in stones, rounded to the nearest whole number.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Find the maximum value of the function $f(x)=x\\sin x+\\cos x$ on the interval $\\left[\\dfrac{\\pi}{6},\\pi\\right]$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\dfrac{\\pi}{2}",
"style": "rule"
}
|
{
"answer": "\\dfrac{\\pi}{2}",
"index": 31,
"question": "Find the maximum value of the function $f(x)=x\\sin x+\\cos x$ on the interval $\\left[\\dfrac{\\pi}{6},\\pi\\right]$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "For what value of x is 64^x equal to 512^5? Express your answer as a decimal number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7.5",
"style": "rule"
}
|
{
"answer": "7.5",
"index": 32,
"question": "For what value of x is 64^x equal to 512^5? Express your answer as a decimal number.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Find $n$ such that $n - 76$ and $n + 76$ are both cubes of positive integers. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "140",
"style": "rule"
}
|
{
"answer": "140",
"index": 33,
"question": "Find $n$ such that $n - 76$ and $n + 76$ are both cubes of positive integers.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "If the square root of a number is $\\pm 8$, then the cube root of this number is ______. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"answer": "4",
"index": 34,
"question": "If the square root of a number is $\\pm 8$, then the cube root of this number is ______.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the circle equation $x^{2}+y^{2}+2x-2y-2=0$, find the coordinates of the center and the radius of the circle. Express the center as an ordered pair (x, y) and the radius as a numerical value. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "2",
"style": "rule"
}
|
{
"answer": "2",
"index": 35,
"question": "Given the circle equation $x^{2}+y^{2}+2x-2y-2=0$, find the coordinates of the center and the radius of the circle. Express the center as an ordered pair (x, y) and the radius as a numerical value.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Find the sum: \\( S = 19 \\cdot 20 \\cdot 21 + 20 \\cdot 21 \\cdot 22 + \\cdots + 1999 \\cdot 2000 \\cdot 2001 \\). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "6 \\left( \\binom{2002}{4} - \\binom{21}{4} \\right)",
"style": "rule"
}
|
{
"answer": "6 \\left( \\binom{2002}{4} - \\binom{21}{4} \\right)",
"index": 36,
"question": "Find the sum: \\( S = 19 \\cdot 20 \\cdot 21 + 20 \\cdot 21 \\cdot 22 + \\cdots + 1999 \\cdot 2000 \\cdot 2001 \\).",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the function f(x) = x^5 - ax^3 + bx + 2, and f(-5) = 3, calculate the value of f(5) + f(-5). Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"answer": "4",
"index": 37,
"question": "Given the function f(x) = x^5 - ax^3 + bx + 2, and f(-5) = 3, calculate the value of f(5) + f(-5). Express your answer as a single integer.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that \\( x \\) and \\( y \\) are acute angles and \\( x + y = 60^\\circ \\), find the maximum value of \\( \\sin x + \\sin y \\). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 38,
"question": "Given that \\( x \\) and \\( y \\) are acute angles and \\( x + y = 60^\\circ \\), find the maximum value of \\( \\sin x + \\sin y \\).",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "If the inequality $mx^{2}+mx+1 > 0$ holds for any $x$, determine the range of $m$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "[0, 4)",
"style": "rule"
}
|
{
"answer": "[0, 4)",
"index": 39,
"question": "If the inequality $mx^{2}+mx+1 > 0$ holds for any $x$, determine the range of $m$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Let $y=(x-a)^2+(x-b)^2, a, b$ constants. For what value of $x$ is $y$ a minimum? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "$\\frac{a+b}{2}$",
"style": "rule"
}
|
{
"answer": "$\\frac{a+b}{2}$",
"index": 40,
"question": "Let $y=(x-a)^2+(x-b)^2, a, b$ constants. For what value of $x$ is $y$ a minimum?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Three males and two females write their names on sheets of paper and randomly arrange them in order from left to right. What is the probability that all of the female names appear to the right of all the male names? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{1}{10}",
"style": "rule"
}
|
{
"answer": "\\frac{1}{10}",
"index": 41,
"question": "Three males and two females write their names on sheets of paper and randomly arrange them in order from left to right. What is the probability that all of the female names appear to the right of all the male names?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the function f(x) = x ln x, find the value of x_0 such that f'(x_0) = 2. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "e",
"style": "rule"
}
|
{
"answer": "e",
"index": 42,
"question": "Given the function f(x) = x ln x, find the value of x_0 such that f'(x_0) = 2.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that $i$ is the imaginary unit, find the distance from the origin to the point that corresponds to the complex number $\\frac{3}{(2-i)^2}$ on the complex plane. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{3}{5}",
"style": "rule"
}
|
{
"answer": "\\frac{3}{5}",
"index": 43,
"question": "Given that $i$ is the imaginary unit, find the distance from the origin to the point that corresponds to the complex number $\\frac{3}{(2-i)^2}$ on the complex plane.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Determine the integer $k$ such that the zero $x_0$ of the function $f(x) = \\ln x + 2x - 6$ lies in the interval $[k, k+1)$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "k=2",
"style": "rule"
}
|
{
"answer": "k=2",
"index": 44,
"question": "Determine the integer $k$ such that the zero $x_0$ of the function $f(x) = \\ln x + 2x - 6$ lies in the interval $[k, k+1)$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "How many different ways can 7 identical balls be placed into four different boxes, with each box containing at least one ball? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "20",
"style": "rule"
}
|
{
"answer": "20",
"index": 45,
"question": "How many different ways can 7 identical balls be placed into four different boxes, with each box containing at least one ball?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Find the exact value of $\\tan 45^{\\circ}$. Express your answer as a single number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 46,
"question": "Find the exact value of $\\tan 45^{\\circ}$. Express your answer as a single number.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In a seven-pointed star (heptagram), how many convex quadrilaterals are there? Express your answer as a whole number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"answer": "7",
"index": 47,
"question": "In a seven-pointed star (heptagram), how many convex quadrilaterals are there? Express your answer as a whole number.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given an arithmetic sequence $\\{a_n\\}$ with a common difference $d \\neq 0$, and $a_1$, $a_3$, $a_{13}$ form a geometric sequence. If $a_1 = 1$, and $S_n$ is the sum of the first $n$ terms of the sequence $\\{a_n\\}$, then the minimum value of $$\\frac {2S_{n}+16}{a_{n}+3}$$ is \\_\\_\\_\\_\\_\\_. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"answer": "4",
"index": 48,
"question": "Given an arithmetic sequence $\\{a_n\\}$ with a common difference $d \\neq 0$, and $a_1$, $a_3$, $a_{13}$ form a geometric sequence. If $a_1 = 1$, and $S_n$ is the sum of the first $n$ terms of the sequence $\\{a_n\\}$, then the minimum value of $$\\frac {2S_{n}+16}{a_{n}+3}$$ is \\_\\_\\_\\_\\_\\_.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The range of the function $y=\\sin ^{2}x-2\\sin x$ is $y\\in $____. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "y \\in [-1, 3]",
"style": "rule"
}
|
{
"answer": "y \\in [-1, 3]",
"index": 49,
"question": "The range of the function $y=\\sin ^{2}x-2\\sin x$ is $y\\in $____.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Suppose that \\( x \\) and \\( y \\) are real numbers with \\( -4 \\leq x \\leq -2 \\) and \\( 2 \\leq y \\leq 4 \\). Find the greatest possible value of \\( \\frac{x+y}{x} \\). Express your answer as a single numerical value. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 50,
"question": "Suppose that \\( x \\) and \\( y \\) are real numbers with \\( -4 \\leq x \\leq -2 \\) and \\( 2 \\leq y \\leq 4 \\). Find the greatest possible value of \\( \\frac{x+y}{x} \\). Express your answer as a single numerical value.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "There is a thin rod with a non-uniform mass distribution, known to have a linear density of $\\rho(x) = x^3$ (taking the line where the rod is located as the x-axis, and one end of the rod as the origin). The length of the rod is 1. Try to express the mass $M$ of the rod using a definite integral. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{1}{4}",
"style": "rule"
}
|
{
"answer": "\\frac{1}{4}",
"index": 51,
"question": "There is a thin rod with a non-uniform mass distribution, known to have a linear density of $\\rho(x) = x^3$ (taking the line where the rod is located as the x-axis, and one end of the rod as the origin). The length of the rod is 1. Try to express the mass $M$ of the rod using a definite integral.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Two ships depart from the same port in opposite directions at the same time. Ship A sails with the current while ship B sails against the current. The speed of both ships in still water is $50$ kilometers per hour. The speed of the water current is $a$ kilometers per hour. After $2$ hours, ship A sails ______ kilometers farther than ship B. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "4a",
"style": "rule"
}
|
{
"answer": "4a",
"index": 52,
"question": "Two ships depart from the same port in opposite directions at the same time. Ship A sails with the current while ship B sails against the current. The speed of both ships in still water is $50$ kilometers per hour. The speed of the water current is $a$ kilometers per hour. After $2$ hours, ship A sails ______ kilometers farther than ship B.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that line segments AB and CD are parallel, and angle D is twice angle B, and AD = a and CD = b, find the length of AB. Express your answer as an algebraic expression in terms of a and b. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "a+b",
"style": "rule"
}
|
{
"answer": "a+b",
"index": 53,
"question": "Given that line segments AB and CD are parallel, and angle D is twice angle B, and AD = a and CD = b, find the length of AB. Express your answer as an algebraic expression in terms of a and b.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Find all triples $ \\left(p,x,y\\right)$ such that $ p^x\\equal{}y^4\\plus{}4$ , where $ p$ is a prime and $ x$ and $ y$ are natural numbers. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "(5, 1, 1)",
"style": "rule"
}
|
{
"answer": "(5, 1, 1)",
"index": 54,
"question": "Find all triples $ \\left(p,x,y\\right)$ such that $ p^x\\equal{}y^4\\plus{}4$ , where $ p$ is a prime and $ x$ and $ y$ are natural numbers.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "\nHermann and Chekalinsky laid out 13 different cards on the table. Each card can be in one of two positions: face up or face down. The players take turns flipping one card. The player who, after making a move, causes the situation to repeat itself (including the initial situation) loses. Chekalinsky made the first move. Who can guarantee a win regardless of how the opponent plays? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "Chekalinsky",
"style": "rule"
}
|
{
"answer": "Chekalinsky",
"index": 55,
"question": "\nHermann and Chekalinsky laid out 13 different cards on the table. Each card can be in one of two positions: face up or face down. The players take turns flipping one card. The player who, after making a move, causes the situation to repeat itself (including the initial situation) loses. Chekalinsky made the first move. Who can guarantee a win regardless of how the opponent plays?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given an equilateral triangle with perimeter p, find the area of its circumscribed circle. Express your answer as a simplified formula involving pi and p. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{\\pi p^2}{27}",
"style": "rule"
}
|
{
"answer": "\\frac{\\pi p^2}{27}",
"index": 56,
"question": "Given an equilateral triangle with perimeter p, find the area of its circumscribed circle. Express your answer as a simplified formula involving pi and p.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The NIMO problem writers have invented a new chess piece called the *Oriented Knight*. This new chess piece has a limited number of moves: it can either move two squares to the right and one square upward or two squares upward and one square to the right. How many ways can the knight move from the bottom-left square to the top-right square of a $16\\times 16$ chess board? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "252",
"style": "rule"
}
|
{
"answer": "252",
"index": 57,
"question": "The NIMO problem writers have invented a new chess piece called the *Oriented Knight*. This new chess piece has a limited number of moves: it can either move two squares to the right and one square upward or two squares upward and one square to the right. How many ways can the knight move from the bottom-left square to the top-right square of a $16\\times 16$ chess board?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The sum of the two roots of the quadratic equation $x^{2}+2x-1=0$ with respect to $x$ is ______. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-2",
"style": "rule"
}
|
{
"answer": "-2",
"index": 58,
"question": "The sum of the two roots of the quadratic equation $x^{2}+2x-1=0$ with respect to $x$ is ______.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. If $a + b + c = 20$, the area of the triangle is $10\\sqrt{3}$, and $A = 60^{\\circ}$, then $a =$ _____. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "7",
"style": "rule"
}
|
{
"answer": "7",
"index": 59,
"question": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. If $a + b + c = 20$, the area of the triangle is $10\\sqrt{3}$, and $A = 60^{\\circ}$, then $a =$ _____.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that $\\sin (\\pi - \\alpha) = -\\frac{2}{3}$ and $\\alpha \\in (-\\frac{\\pi}{2}, 0)$, find the value of $\\tan \\alpha$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-\\frac{2\\sqrt{5}}{5}",
"style": "rule"
}
|
{
"answer": "-\\frac{2\\sqrt{5}}{5}",
"index": 60,
"question": "Given that $\\sin (\\pi - \\alpha) = -\\frac{2}{3}$ and $\\alpha \\in (-\\frac{\\pi}{2}, 0)$, find the value of $\\tan \\alpha$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Solve the following equation:\n\n$$\n2^{-\\sin ^{2} x}+2^{-\\cos ^{2} x}=\\sin y+\\cos y .\n$$ Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "x = \\frac{\\pi}{4} + k \\frac{\\pi}{2}, \\quad y = \\frac{\\pi}{4} + 2l\\pi",
"style": "rule"
}
|
{
"answer": "x = \\frac{\\pi}{4} + k \\frac{\\pi}{2}, \\quad y = \\frac{\\pi}{4} + 2l\\pi",
"index": 61,
"question": "Solve the following equation:\n\n$$\n2^{-\\sin ^{2} x}+2^{-\\cos ^{2} x}=\\sin y+\\cos y .\n$$",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Archimedes' \"Sphere within a Cylinder\" states that the ratio of the surface area (and volume) of a sphere to its circumscribed cylinder is __________. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{2}{3}",
"style": "rule"
}
|
{
"answer": "\\frac{2}{3}",
"index": 62,
"question": "Archimedes' \"Sphere within a Cylinder\" states that the ratio of the surface area (and volume) of a sphere to its circumscribed cylinder is __________.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given a sequence $\\{a_n\\}$ where $a_1=2,$ and $na_{n+1}=2(n+1)a_n,$ find the value of $a_5.$ Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "160",
"style": "rule"
}
|
{
"answer": "160",
"index": 63,
"question": "Given a sequence $\\{a_n\\}$ where $a_1=2,$ and $na_{n+1}=2(n+1)a_n,$ find the value of $a_5.$ Express your answer as a single integer.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that vectors $\\overrightarrow{e\\_1}$ and $\\overrightarrow{e\\_2}$ form an angle of $\\dfrac {2π}{3}$, and $\\overrightarrow{a} = \\overrightarrow{e\\_1} + 2\\overrightarrow{e\\_2}$, find the magnitude of $\\overrightarrow{a}$ (denoted as $|\\overrightarrow{a}|$). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\sqrt{3}",
"style": "rule"
}
|
{
"answer": "\\sqrt{3}",
"index": 64,
"question": "Given that vectors $\\overrightarrow{e\\_1}$ and $\\overrightarrow{e\\_2}$ form an angle of $\\dfrac {2π}{3}$, and $\\overrightarrow{a} = \\overrightarrow{e\\_1} + 2\\overrightarrow{e\\_2}$, find the magnitude of $\\overrightarrow{a}$ (denoted as $|\\overrightarrow{a}|$).",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Determine the sign of the number\n\n$$\nA = \\frac{1}{1} - \\frac{1}{2} - \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} - \\frac{1}{6} - \\frac{1}{7} + \\ldots + \\frac{1}{2012} + \\frac{1}{2013} - \\frac{1}{2014} - \\frac{1}{2015} + \\frac{1}{2016}\n$$\n\nThe signs are assigned as follows: \"+\" before the first fraction, then two \"-\", and two \"+\" alternately. The last fraction has a \"+\". Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "A > 0",
"style": "rule"
}
|
{
"answer": "A > 0",
"index": 65,
"question": "Determine the sign of the number\n\n$$\nA = \\frac{1}{1} - \\frac{1}{2} - \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} - \\frac{1}{6} - \\frac{1}{7} + \\ldots + \\frac{1}{2012} + \\frac{1}{2013} - \\frac{1}{2014} - \\frac{1}{2015} + \\frac{1}{2016}\n$$\n\nThe signs are assigned as follows: \"+\" before the first fraction, then two \"-\", and two \"+\" alternately. The last fraction has a \"+\".",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The diagonals of a rhombus are 10 and 24. Find the radius of the circle inscribed in the rhombus. Express your answer as a fraction. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{60}{13}",
"style": "rule"
}
|
{
"answer": "\\frac{60}{13}",
"index": 66,
"question": "The diagonals of a rhombus are 10 and 24. Find the radius of the circle inscribed in the rhombus. Express your answer as a fraction.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Let \\( S = \\{r_1, r_2, \\cdots, r_n\\} \\subseteq \\{1, 2, 3, \\cdots, 50\\} \\), and let any two numbers in \\( S \\) not be divisible by 7 when summed. Find the maximum value of \\( n \\). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "23",
"style": "rule"
}
|
{
"answer": "23",
"index": 67,
"question": "Let \\( S = \\{r_1, r_2, \\cdots, r_n\\} \\subseteq \\{1, 2, 3, \\cdots, 50\\} \\), and let any two numbers in \\( S \\) not be divisible by 7 when summed. Find the maximum value of \\( n \\).",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "An inscribed circle with radius \\( R \\) is placed in a certain angle, and the length of the chord connecting the tangent points is \\( a \\). Two tangents are drawn parallel to this chord, forming a trapezoid. Find the area of this trapezoid. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{8R^3}{a}",
"style": "rule"
}
|
{
"answer": "\\frac{8R^3}{a}",
"index": 68,
"question": "An inscribed circle with radius \\( R \\) is placed in a certain angle, and the length of the chord connecting the tangent points is \\( a \\). Two tangents are drawn parallel to this chord, forming a trapezoid. Find the area of this trapezoid.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In the expansion of $$(3 \\sqrt {x}-2 3x )^{11}$$, randomly select one term. Suppose the probability that the selected term is a rational term is $$\\alpha$$. Then, $$\\int_{ 0 }^{ 1 }x^{\\alpha} \\, dx= \\_\\_\\_\\_\\_\\_ ． Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac {6}{7}",
"style": "rule"
}
|
{
"answer": "\\frac {6}{7}",
"index": 69,
"question": "In the expansion of $$(3 \\sqrt {x}-2 3x )^{11}$$, randomly select one term. Suppose the probability that the selected term is a rational term is $$\\alpha$$. Then, $$\\int_{ 0 }^{ 1 }x^{\\alpha} \\, dx= \\_\\_\\_\\_\\_\\_ ．",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In the arithmetic sequence $\\{a\\_n\\}$, $a\\_1+a\\_9=10$, the value of $a\\_5$ is $\\_\\_\\_\\_\\_\\_$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 70,
"question": "In the arithmetic sequence $\\{a\\_n\\}$, $a\\_1+a\\_9=10$, the value of $a\\_5$ is $\\_\\_\\_\\_\\_\\_$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given an isosceles triangle $\\triangle ABC$, the exterior angle adjacent to $\\angle A$ is $130^{\\circ}$. Find the possible measures of the vertex angle of this triangle. Express your answer(s) in degrees. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "50^{\\circ} \\text{ or } 80^{\\circ}",
"style": "rule"
}
|
{
"answer": "50^{\\circ} \\text{ or } 80^{\\circ}",
"index": 71,
"question": "Given an isosceles triangle $\\triangle ABC$, the exterior angle adjacent to $\\angle A$ is $130^{\\circ}$. Find the possible measures of the vertex angle of this triangle. Express your answer(s) in degrees.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "A small regular tetrahedron is placed inside a paper box shaped as a regular tetrahedron with an edge length of 5. If the small tetrahedron can rotate freely inside the box, the maximum edge length of the small tetrahedron is ______. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{5}{3}",
"style": "rule"
}
|
{
"answer": "\\frac{5}{3}",
"index": 72,
"question": "A small regular tetrahedron is placed inside a paper box shaped as a regular tetrahedron with an edge length of 5. If the small tetrahedron can rotate freely inside the box, the maximum edge length of the small tetrahedron is ______.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In Class 8a, there are 33 students. At the beginning of the school year, two clubs were organized in the class. According to school rules, a club can be formed if at least 70% of all the students in the class sign up for it. What is the minimum number of students that could have signed up for both clubs simultaneously? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "15",
"style": "rule"
}
|
{
"answer": "15",
"index": 73,
"question": "In Class 8a, there are 33 students. At the beginning of the school year, two clubs were organized in the class. According to school rules, a club can be formed if at least 70% of all the students in the class sign up for it. What is the minimum number of students that could have signed up for both clubs simultaneously?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that $i$ is the imaginary unit, and the complex number $z$ satisfies the equation $z(2-i) = 10 + 5i$, find the value of $z$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "z = 3 + 4i",
"style": "rule"
}
|
{
"answer": "z = 3 + 4i",
"index": 74,
"question": "Given that $i$ is the imaginary unit, and the complex number $z$ satisfies the equation $z(2-i) = 10 + 5i$, find the value of $z$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the equation 4^x - 4^(x-1) = 24, find the value of (2x)^x. Express your answer as a numerical value, including any necessary mathematical notation. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "25\\sqrt{5}",
"style": "rule"
}
|
{
"answer": "25\\sqrt{5}",
"index": 75,
"question": "Given the equation 4^x - 4^(x-1) = 24, find the value of (2x)^x. Express your answer as a numerical value, including any necessary mathematical notation.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "For a given natural number \\( n (n > 5) \\), find all real numbers \\( a \\) such that there exist non-negative real numbers \\( x_{1}, x_{2}, \\cdots, x_{n} \\) satisfying the conditions:\n\n\\[\n\\sum_{k=1}^{n} k x_{k} = a, \\quad\n\\sum_{k=1}^{n} k^{3} x_{k} = a^{2}, \\quad\n\\sum_{k=1}^{n} k^{5} x_{k} = a^{3}.\n\\] Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\{1^2, 2^2, 3^2, \\ldots, n^2\\}",
"style": "rule"
}
|
{
"answer": "\\{1^2, 2^2, 3^2, \\ldots, n^2\\}",
"index": 76,
"question": "For a given natural number \\( n (n > 5) \\), find all real numbers \\( a \\) such that there exist non-negative real numbers \\( x_{1}, x_{2}, \\cdots, x_{n} \\) satisfying the conditions:\n\n\\[\n\\sum_{k=1}^{n} k x_{k} = a, \\quad\n\\sum_{k=1}^{n} k^{3} x_{k} = a^{2}, \\quad\n\\sum_{k=1}^{n} k^{5} x_{k} = a^{3}.\n\\]",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Determine the range of values for $a$ such that the inequality concerning $x$, $(a-1)x^2 - 2(a-1)x - 2 < 0$, always holds true. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-1 < a \\leq 1",
"style": "rule"
}
|
{
"answer": "-1 < a \\leq 1",
"index": 77,
"question": "Determine the range of values for $a$ such that the inequality concerning $x$, $(a-1)x^2 - 2(a-1)x - 2 < 0$, always holds true.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given $A=\\{x|\\lg x > 0\\}$, then $C_{R}A=$ ? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\{x|x \\leq 1\\}",
"style": "rule"
}
|
{
"answer": "\\{x|x \\leq 1\\}",
"index": 78,
"question": "Given $A=\\{x|\\lg x > 0\\}$, then $C_{R}A=$ ?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The regular price for a T-shirt is $25 and the regular price for a pair of jeans is $75. If the T-shirt is sold at a 30% discount and the jeans are sold at a 10% discount, calculate the total discount. Express your answer in dollars, rounded to two decimal places. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "15.00",
"style": "rule"
}
|
{
"answer": "15.00",
"index": 79,
"question": "The regular price for a T-shirt is $25 and the regular price for a pair of jeans is $75. If the T-shirt is sold at a 30% discount and the jeans are sold at a 10% discount, calculate the total discount. Express your answer in dollars, rounded to two decimal places.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The solution of the equation $\\dfrac{1+2^{x}}{1+x^{-x}}= \\dfrac{1}{4}$ is $x=$ . Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "-2",
"style": "rule"
}
|
{
"answer": "-2",
"index": 80,
"question": "The solution of the equation $\\dfrac{1+2^{x}}{1+x^{-x}}= \\dfrac{1}{4}$ is $x=$ .",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The equation of the line that passes through the point (-1, 3) and is perpendicular to the line $x-2y+1=0$ is ________. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "y+2x-1=0",
"style": "rule"
}
|
{
"answer": "y+2x-1=0",
"index": 81,
"question": "The equation of the line that passes through the point (-1, 3) and is perpendicular to the line $x-2y+1=0$ is ________.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given a set of data arranged in ascending order: 23, 28, 30, x, 34, 39, and the median is 31, then $x= \\_\\_\\_\\_\\_\\_$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\text{answer}",
"style": "rule"
}
|
{
"answer": "\text{answer}",
"index": 82,
"question": "Given a set of data arranged in ascending order: 23, 28, 30, x, 34, 39, and the median is 31, then $x= \\_\\_\\_\\_\\_\\_$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Three \"mryak\" are 10 rubles more expensive than five \"bryak\". Six \"mryak\" are 31 rubles more expensive than eight \"bryak\". By how many rubles are seven \"mryak\" more expensive than nine \"bryak\"? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "38",
"style": "rule"
}
|
{
"answer": "38",
"index": 83,
"question": "Three \"mryak\" are 10 rubles more expensive than five \"bryak\". Six \"mryak\" are 31 rubles more expensive than eight \"bryak\". By how many rubles are seven \"mryak\" more expensive than nine \"bryak\"?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "For some positive integers \\( m \\) and \\( n \\), \\( 2^{m} - 2^{n} = 1792 \\). Determine the value of \\( m^{2} + n^{2} \\). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "185",
"style": "rule"
}
|
{
"answer": "185",
"index": 84,
"question": "For some positive integers \\( m \\) and \\( n \\), \\( 2^{m} - 2^{n} = 1792 \\). Determine the value of \\( m^{2} + n^{2} \\).",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "\\[\\frac{\\tan 96^{\\circ} - \\tan 12^{\\circ} \\left( 1 + \\frac{1}{\\sin 6^{\\circ}} \\right)}{1 + \\tan 96^{\\circ} \\tan 12^{\\circ} \\left( 1 + \\frac{1}{\\sin 6^{\\circ}} \\right)} =\\] Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{\\sqrt{3}}{3}",
"style": "rule"
}
|
{
"answer": "\\frac{\\sqrt{3}}{3}",
"index": 85,
"question": "\\[\\frac{\\tan 96^{\\circ} - \\tan 12^{\\circ} \\left( 1 + \\frac{1}{\\sin 6^{\\circ}} \\right)}{1 + \\tan 96^{\\circ} \\tan 12^{\\circ} \\left( 1 + \\frac{1}{\\sin 6^{\\circ}} \\right)} =\\]",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Steve has a bank account that earns 10% interest every year. He puts $100 in it, and then 10 each year. How much money is in it after two years? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "142",
"style": "rule"
}
|
{
"answer": "142",
"index": 86,
"question": "Steve has a bank account that earns 10% interest every year. He puts $100 in it, and then 10 each year. How much money is in it after two years?",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "The hyperbola with its foci on the x-axis, given by x^2/16 - y^2/m = 1, has a focal length of 4√5. Find the value of m. Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "4",
"style": "rule"
}
|
{
"answer": "4",
"index": 87,
"question": "The hyperbola with its foci on the x-axis, given by x^2/16 - y^2/m = 1, has a focal length of 4√5. Find the value of m. Express your answer as a single integer.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In square $ABCD$ with side length $2$ , let $P$ and $Q$ both be on side $AB$ such that $AP=BQ=\\frac{1}{2}$ . Let $E$ be a point on the edge of the square that maximizes the angle $PEQ$ . Find the area of triangle $PEQ$ . Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "1",
"style": "rule"
}
|
{
"answer": "1",
"index": 88,
"question": "In square $ABCD$ with side length $2$ , let $P$ and $Q$ both be on side $AB$ such that $AP=BQ=\\frac{1}{2}$ . Let $E$ be a point on the edge of the square that maximizes the angle $PEQ$ . Find the area of triangle $PEQ$ .",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Volume $A$ equals one fourth of the sum of the volumes $B$ and $C$ , while volume $B$ equals one sixth of the sum of the volumes $A$ and $C$ . There are relatively prime positive integers $m$ and $n$ so that the ratio of volume $C$ to the sum of the other two volumes is $\\frac{m}{n}$ . Find $m+n$ . Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "35",
"style": "rule"
}
|
{
"answer": "35",
"index": 89,
"question": "Volume $A$ equals one fourth of the sum of the volumes $B$ and $C$ , while volume $B$ equals one sixth of the sum of the volumes $A$ and $C$ . There are relatively prime positive integers $m$ and $n$ so that the ratio of volume $C$ to the sum of the other two volumes is $\\frac{m}{n}$ . Find $m+n$ .",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Let \\(a\\) and \\(b\\) be two integers. Suppose that \\(\\sqrt{7-4 \\sqrt{3}}\\) is a root of the equation \\(x^{2} + ax + b = 0\\). Find the value of \\(b - a\\). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "5",
"style": "rule"
}
|
{
"answer": "5",
"index": 90,
"question": "Let \\(a\\) and \\(b\\) be two integers. Suppose that \\(\\sqrt{7-4 \\sqrt{3}}\\) is a root of the equation \\(x^{2} + ax + b = 0\\). Find the value of \\(b - a\\).",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given a variable $x$, write a computer program that inputs the value of $x$ and outputs the value of the piecewise function $f(x) = \\begin{cases} x+2, & \\text{if } x \\geq 0, \\\\ x^2, & \\text{if } x < 0. \\end{cases}$ Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\begin{matrix} \\text{INPUT } ``x=\"; x \\\\ \\text{IF } x \\geq 0 \\text{ THEN } \\\\ \\quad y = x + 2 \\\\ \\text{ELSE } \\\\ \\quad y = x^2 \\\\ \\text{END IF } \\\\ \\text{PRINT } ``y=\"; y \\\\ \\text{END} \\end{matrix}",
"style": "rule"
}
|
{
"answer": "\\begin{matrix} \\text{INPUT } ``x=\"; x \\\\ \\text{IF } x \\geq 0 \\text{ THEN } \\\\ \\quad y = x + 2 \\\\ \\text{ELSE } \\\\ \\quad y = x^2 \\\\ \\text{END IF } \\\\ \\text{PRINT } ``y=\"; y \\\\ \\text{END} \\end{matrix}",
"index": 91,
"question": "Given a variable $x$, write a computer program that inputs the value of $x$ and outputs the value of the piecewise function $f(x) = \\begin{cases} x+2, & \\text{if } x \\geq 0, \\\\ x^2, & \\text{if } x < 0. \\end{cases}$",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Place the numbers 1, 2, 3, ..., 25 into the table below, filling each small square with a number such that each number is used exactly once and some numbers are already filled in. Each number in a small square must be equal to the average of its adjacent numbers (those sharing a common edge with four adjacent squares). Determine the number to place in the square marked with \\(*\\).\n\n(Note: The table and already filled numbers are implied but not provided here.) Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "14",
"style": "rule"
}
|
{
"answer": "14",
"index": 92,
"question": "Place the numbers 1, 2, 3, ..., 25 into the table below, filling each small square with a number such that each number is used exactly once and some numbers are already filled in. Each number in a small square must be equal to the average of its adjacent numbers (those sharing a common edge with four adjacent squares). Determine the number to place in the square marked with \\(*\\).\n\n(Note: The table and already filled numbers are implied but not provided here.)",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given the function $y=x^{2}-4px-2$, its graph passes through points $A(\\tan α,1)$ and $B(\\tan β,1)$. Find $\\sin 2(α+β)$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac {2p}{p^{2}+1}",
"style": "rule"
}
|
{
"answer": "\\frac {2p}{p^{2}+1}",
"index": 93,
"question": "Given the function $y=x^{2}-4px-2$, its graph passes through points $A(\\tan α,1)$ and $B(\\tan β,1)$. Find $\\sin 2(α+β)$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Find the number of pairs of integer solutions (x, y) that satisfy the equation (x-8)(x-10) = 2^y. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "0",
"style": "rule"
}
|
{
"answer": "0",
"index": 94,
"question": "Find the number of pairs of integer solutions (x, y) that satisfy the equation (x-8)(x-10) = 2^y.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Calculate $\\cos(-75^{\\circ})$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{\\sqrt{6} - \\sqrt{2}}{4}",
"style": "rule"
}
|
{
"answer": "\\frac{\\sqrt{6} - \\sqrt{2}}{4}",
"index": 95,
"question": "Calculate $\\cos(-75^{\\circ})$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Solve the inequality system: $\\left\\{\\begin{array}{l}{3(x-1)<5x+11}\\\\{2x>\\frac{9-x}{4}}\\end{array}\\right.$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "x > 1",
"style": "rule"
}
|
{
"answer": "x > 1",
"index": 96,
"question": "Solve the inequality system: $\\left\\{\\begin{array}{l}{3(x-1)<5x+11}\\\\{2x>\\frac{9-x}{4}}\\end{array}\\right.$.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "If an angle is $57^{\\circ}13'$, then its complement is ____. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "32^{\\circ}47'",
"style": "rule"
}
|
{
"answer": "32^{\\circ}47'",
"index": 97,
"question": "If an angle is $57^{\\circ}13'$, then its complement is ____.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "In an opaque box, there are 2 white ping-pong balls of the same texture and size, and 3 yellow ping-pong balls. What is the probability of randomly drawing a yellow ping-pong ball? Express your answer as a fraction. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\frac{3}{5}",
"style": "rule"
}
|
{
"answer": "\\frac{3}{5}",
"index": 98,
"question": "In an opaque box, there are 2 white ping-pong balls of the same texture and size, and 3 yellow ping-pong balls. What is the probability of randomly drawing a yellow ping-pong ball? Express your answer as a fraction.",
"split": "train"
}
|
SynthLabsAI/Big-Math-RL-Verified
|
[
{
"content": "Given that the lateral surface of a cone unfolds into a semicircle with a radius of 2, the height of this cone is ______ . Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer should be enclosed within <answer></answer> tags.\n<think>",
"role": "user"
}
] |
math
|
{
"ground_truth": "\\sqrt{3}",
"style": "rule"
}
|
{
"answer": "\\sqrt{3}",
"index": 99,
"question": "Given that the lateral surface of a cone unfolds into a semicircle with a radius of 2, the height of this cone is ______ .",
"split": "train"
}
|
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 6