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": "Find the coordinates of the foci of the ellipse $\\dfrac{x^2}{9} + \\dfrac{y^2}{5} = 1$. 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>",
... | math | {
"ground_truth": "(-2, 0), (2, 0)",
"style": "rule"
} | {
"answer": "(-2, 0), (2, 0)",
"index": 200,
"question": "Find the coordinates of the foci of the ellipse $\\dfrac{x^2}{9} + \\dfrac{y^2}{5} = 1$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the constraints \\(3 \\leq p \\leq 10\\) and \\(12 \\leq q \\leq 21\\), calculate the difference between the largest and smallest possible values of \\(\\frac{p}{q}\\). Express your answer as a simplified fraction. Think step by step and then provide the final answer. The reasoning process s... | math | {
"ground_truth": "\\frac{29}{42}",
"style": "rule"
} | {
"answer": "\\frac{29}{42}",
"index": 201,
"question": "Given the constraints \\(3 \\leq p \\leq 10\\) and \\(12 \\leq q \\leq 21\\), calculate the difference between the largest and smallest possible values of \\(\\frac{p}{q}\\). Express your answer as a simplified fraction.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The common difference of the arithmetic sequence $\\{a_n\\}$ is not zero, the first term $a_1=1$, and $a_2$ is the geometric mean of $a_1$ and $a_5$. Calculate the sum of the first 10 terms of the sequence. Express your answer as a single integer. Think step by step and then provide the final answ... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"answer": "100",
"index": 202,
"question": "The common difference of the arithmetic sequence $\\{a_n\\}$ is not zero, the first term $a_1=1$, and $a_2$ is the geometric mean of $a_1$ and $a_5$. Calculate the sum of the first 10 terms of the sequence. Express your answer as a single integer.",
"split": "train"... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In a positive geometric sequence $\\{a_n\\}$, $a_1=1$, and the sum of the first $n$ terms is $S_n$. If $-a_3$, $a_2$, and $a_4$ form an arithmetic sequence, calculate the value of $S_7$. Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning pr... | math | {
"ground_truth": "127",
"style": "rule"
} | {
"answer": "127",
"index": 203,
"question": "In a positive geometric sequence $\\{a_n\\}$, $a_1=1$, and the sum of the first $n$ terms is $S_n$. If $-a_3$, $a_2$, and $a_4$ form an arithmetic sequence, calculate the value of $S_7$. Express your answer as a single integer.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "It is well-known that a quadratic equation has no more than 2 roots. Is it possible for the equation $\\lfloor x^2\\rfloor+px+q=0$ with $p\\neq 0$ to have more than 100 roots? Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> ... | math | {
"ground_truth": "\\text{We have 119 solutions for the equation } \\lfloor x^2 \\rfloor + 60x + 900 = 0 \\text{ : } x_n = -\\frac{n + 900}{60} \\forall n \\in \\{841, 842, \\ldots, 958, 959\\}",
"style": "rule"
} | {
"answer": "\\text{We have 119 solutions for the equation } \\lfloor x^2 \\rfloor + 60x + 900 = 0 \\text{ : } x_n = -\\frac{n + 900}{60} \\forall n \\in \\{841, 842, \\ldots, 958, 959\\}",
"index": 204,
"question": "It is well-known that a quadratic equation has no more than 2 roots. Is it possible for the equat... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a number line on a piece of paper, fold the paper so that the point representing $-3$ coincides with the point representing $1$. Then the point representing $-20$ coincides with the point representing ______. Think step by step and then provide the final answer. The reasoning process should ... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"answer": "18",
"index": 205,
"question": "Given a number line on a piece of paper, fold the paper so that the point representing $-3$ coincides with the point representing $1$. Then the point representing $-20$ coincides with the point representing ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "For natural numbers $m$ greater than $1$, the cube of $m$ can be \"split\" into odd numbers in the following way: ${2}^{3}\\begin{cases}3 \\\\ 5\\end{cases}$, ${3}^{3}\\begin{cases}7 \\\\ \\begin{matrix}9 \\\\ 11\\end{matrix}\\end{cases}$, ${4}^{3}\\begin{cases}13 \\\\ \\begin{matrix}15 \\\\ \\beg... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 206,
"question": "For natural numbers $m$ greater than $1$, the cube of $m$ can be \"split\" into odd numbers in the following way: ${2}^{3}\\begin{cases}3 \\\\ 5\\end{cases}$, ${3}^{3}\\begin{cases}7 \\\\ \\begin{matrix}9 \\\\ 11\\end{matrix}\\end{cases}$, ${4}^{3}\\begin{cases}13 \\\\ ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The distance from point $P$ in the fourth quadrant to the $x$-axis is $5$, and to the $y$-axis is $3$. The coordinates of point $P$ 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 ... | math | {
"ground_truth": "\\left(3,-5\\right)",
"style": "rule"
} | {
"answer": "\\left(3,-5\\right)",
"index": 207,
"question": "The distance from point $P$ in the fourth quadrant to the $x$-axis is $5$, and to the $y$-axis is $3$. The coordinates of point $P$ are ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the sequence $\\{a_n\\}$, where $a_1 = \\\\frac{1}{2}$ and $(n+2)a_{n+1} = na_n$, find the sum of its first 20 terms, denoted as $S_{20}$. Express your answer as a simplified fraction in the format $\\\\boxed{[answer]}$. Think step by step and then provide the final answer. The reasoning pro... | math | {
"ground_truth": "\\\\frac{20}{21}",
"style": "rule"
} | {
"answer": "\\\\frac{20}{21}",
"index": 208,
"question": "Given the sequence $\\{a_n\\}$, where $a_1 = \\\\frac{1}{2}$ and $(n+2)a_{n+1} = na_n$, find the sum of its first 20 terms, denoted as $S_{20}$. Express your answer as a simplified fraction in the format $\\\\boxed{[answer]}$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The six-digit number begins with the digit 2. If this digit is moved from the first place to the last, keeping the order of the other five digits, the resulting number will be three times the original number. Find the original number. Think step by step and then provide the final answer. The reaso... | math | {
"ground_truth": "285714",
"style": "rule"
} | {
"answer": "285714",
"index": 209,
"question": "The six-digit number begins with the digit 2. If this digit is moved from the first place to the last, keeping the order of the other five digits, the resulting number will be three times the original number. Find the original number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the asymptote equation of the hyperbola $x^{2}-\\frac{y^{2}}{2}=1$. Express your answer in the form $y=mx$ or equivalent. 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 <... | math | {
"ground_truth": "y=\\pm\\sqrt{2}x",
"style": "rule"
} | {
"answer": "y=\\pm\\sqrt{2}x",
"index": 210,
"question": "Find the asymptote equation of the hyperbola $x^{2}-\\frac{y^{2}}{2}=1$. Express your answer in the form $y=mx$ or equivalent.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The distance from the focus of the parabola $y^2 = ax$ $(a \\neq 0)$ to its directrix is $(\\quad)$. 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<t... | math | {
"ground_truth": "\\frac{a}{2}",
"style": "rule"
} | {
"answer": "\\frac{a}{2}",
"index": 211,
"question": "The distance from the focus of the parabola $y^2 = ax$ $(a \\neq 0)$ to its directrix is $(\\quad)$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Consider an ellipse x^2/m + y^2 = 1 (m > 1) and a hyperbola x^2/n - y^2 = 1 (n > 0) that share the same foci F1 and F2. Let P be a point of intersection between the two curves. Calculate the area of the triangle F1PF2. Think step by step and then provide the final answer. The reasoning process sho... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 212,
"question": "Consider an ellipse x^2/m + y^2 = 1 (m > 1) and a hyperbola x^2/n - y^2 = 1 (n > 0) that share the same foci F1 and F2. Let P be a point of intersection between the two curves. Calculate the area of the triangle F1PF2.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a complex number $z = 1 + ai$ (where $a \\in \\mathbb{R}$ and $i$ is the imaginary unit), the point represented by $z$ on the complex plane lies in the fourth quadrant, and $\\overline{z} \\cdot z = 5$, find the value of $a$. Express your answer as a single real number. Think step by step an... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 213,
"question": "Given a complex number $z = 1 + ai$ (where $a \\in \\mathbb{R}$ and $i$ is the imaginary unit), the point represented by $z$ on the complex plane lies in the fourth quadrant, and $\\overline{z} \\cdot z = 5$, find the value of $a$. Express your answer as a single real ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The graph of the function $y=\\sin 2x-\\cos 2x$ can be seen as being obtained by shifting the graph of the function $y=\\sin 2x+\\cos 2x$ to the right. The minimum length of this shift is __________. Think step by step and then provide the final answer. The reasoning process should be enclosed wit... | math | {
"ground_truth": "\\frac{\\pi}{4}",
"style": "rule"
} | {
"answer": "\\frac{\\pi}{4}",
"index": 214,
"question": "The graph of the function $y=\\sin 2x-\\cos 2x$ can be seen as being obtained by shifting the graph of the function $y=\\sin 2x+\\cos 2x$ to the right. The minimum length of this shift is __________.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the equations of two circles, $C_1: (x-1)^2+(y-1)^2=4$ and $C_2: x^2+y^2-8x-10y+m+6=0$, find the value of $m$ such that the circles are externally tangent. Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning process should be enclosed ... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"answer": "26",
"index": 215,
"question": "Given the equations of two circles, $C_1: (x-1)^2+(y-1)^2=4$ and $C_2: x^2+y^2-8x-10y+m+6=0$, find the value of $m$ such that the circles are externally tangent. Express your answer as a single integer.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Factorize: $x^3y - xy$. 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": "xy(x - 1)(x + 1)",
"style": "rule"
} | {
"answer": "xy(x - 1)(x + 1)",
"index": 216,
"question": "Factorize: $x^3y - xy$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In an isosceles triangle, the sides are 3 and 7. Which side is the base? 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": 217,
"question": "In an isosceles triangle, the sides are 3 and 7. Which side is the base?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given \\( f(x) = \\sum_{k=1}^{2017} \\frac{\\cos k x}{\\cos^k x} \\), find \\( f\\left(\\frac{\\pi}{2018}\\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><... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 218,
"question": "Given \\( f(x) = \\sum_{k=1}^{2017} \\frac{\\cos k x}{\\cos^k x} \\), find \\( f\\left(\\frac{\\pi}{2018}\\right) \\).",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Solve the inequality\n\n$$\n12 \\cdot \\frac{|x+10|-|x-20|}{|4 x-25|-|4 x-15|}-\\frac{|x+10|+|x-20|}{|4 x-25|+|4 x-15|} \\geqslant-6\n$$\n\nRecord the sum of its integer solutions that satisfy the condition $|x|<100$. Think step by step and then provide the final answer. The reasoning process shou... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 219,
"question": "Solve the inequality\n\n$$\n12 \\cdot \\frac{|x+10|-|x-20|}{|4 x-25|-|4 x-15|}-\\frac{|x+10|+|x-20|}{|4 x-25|+|4 x-15|} \\geqslant-6\n$$\n\nRecord the sum of its integer solutions that satisfy the condition $|x|<100$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given $x$ and $y$ satisfy $\\left(x-2\\right)^{2}+|y-3|=0$. Simplify and then evaluate the expression: $[\\left(x-2y\\right)\\left(x+2y\\right)-\\left(x-y\\right)^{2}+y\\left(y+2x\\right)]\\div \\left(-2y\\right)$. Think step by step and then provide the final answer. The reasoning process should ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 220,
"question": "Given $x$ and $y$ satisfy $\\left(x-2\\right)^{2}+|y-3|=0$. Simplify and then evaluate the expression: $[\\left(x-2y\\right)\\left(x+2y\\right)-\\left(x-y\\right)^{2}+y\\left(y+2x\\right)]\\div \\left(-2y\\right)$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that the probability is $\\frac{3}{5}$ for a person's daily morning bus to arrive on time, what is the probability that the bus arrives on time for **at least two out of three consecutive days**? Think step by step and then provide the final answer. The reasoning process should be enclosed w... | math | {
"ground_truth": "\\frac{81}{125}",
"style": "rule"
} | {
"answer": "\\frac{81}{125}",
"index": 221,
"question": "Given that the probability is $\\frac{3}{5}$ for a person's daily morning bus to arrive on time, what is the probability that the bus arrives on time for **at least two out of three consecutive days**?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the complex number $z=(2+i)i$, calculate the product of the real part and the imaginary part of the complex number $z$. 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 ... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 222,
"question": "Given the complex number $z=(2+i)i$, calculate the product of the real part and the imaginary part of the complex number $z$. Express your answer as a single integer.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A line passing through the point (1,0) with an inclination angle of 30° intersects the circle (x-2)²+y²=1. Find the length of the chord formed. 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 ... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"answer": "\\sqrt{3}",
"index": 223,
"question": "A line passing through the point (1,0) with an inclination angle of 30° intersects the circle (x-2)²+y²=1. Find the length of the chord formed.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the product of (x+m) and (x+3) does not contain a linear term of x, find the value of m. 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 wit... | math | {
"ground_truth": "-3",
"style": "rule"
} | {
"answer": "-3",
"index": 224,
"question": "If the product of (x+m) and (x+3) does not contain a linear term of x, find the value of m. Express your answer as a single number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In a bag, there are 5 balls of the same size, including 3 black balls and 2 red balls. If two balls are drawn at random, calculate the probability of drawing two balls of the same color. Express your answer as a simplified fraction. Think step by step and then provide the final answer. The reasoni... | math | {
"ground_truth": "\\frac{2}{5}",
"style": "rule"
} | {
"answer": "\\frac{2}{5}",
"index": 225,
"question": "In a bag, there are 5 balls of the same size, including 3 black balls and 2 red balls. If two balls are drawn at random, calculate the probability of drawing two balls of the same color. Express your answer as a simplified fraction.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The equation of the line passing through point $P(2,3)$ and having equal intercepts on the two coordinate axes 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>... | math | {
"ground_truth": "x+y-5=0 \\text{ or } 3x-2y=0",
"style": "rule"
} | {
"answer": "x+y-5=0 \\text{ or } 3x-2y=0",
"index": 226,
"question": "The equation of the line passing through point $P(2,3)$ and having equal intercepts on the two coordinate axes is ____.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that in triangle $\\triangle ABC$, the sides opposite to the internal angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Angle $B$ is obtuse. Let the area of $\\triangle ABC$ be $S$. If $4bS=a(b^{2}+c^{2}-a^{2})$, then the maximum value of $\\sin A + \\sin C$ is ____. Think step by... | math | {
"ground_truth": "\\frac{9}{8}",
"style": "rule"
} | {
"answer": "\\frac{9}{8}",
"index": 227,
"question": "Given that in triangle $\\triangle ABC$, the sides opposite to the internal angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Angle $B$ is obtuse. Let the area of $\\triangle ABC$ be $S$. If $4bS=a(b^{2}+c^{2}-a^{2})$, then the maximum value of $\\... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In a survey, the reading amounts of four students A, B, C, and D have the following relationships: the sum of the reading amounts of A and C is equal to the sum of the reading amounts of B and D; the sum of the reading amounts of A and B is greater than the sum of the reading amounts of C and D; t... | math | {
"ground_truth": "\\text{A, D, B, C}",
"style": "rule"
} | {
"answer": "\\text{A, D, B, C}",
"index": 228,
"question": "In a survey, the reading amounts of four students A, B, C, and D have the following relationships: the sum of the reading amounts of A and C is equal to the sum of the reading amounts of B and D; the sum of the reading amounts of A and B is greater than... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A subset \\( S \\) of the set \\(\\{1,2, \\ldots, 10\\}\\) is chosen randomly, with all possible subsets being equally likely. Compute the expected number of positive integers which divide the product of the elements of \\( S \\). (By convention, the product of the elements of the empty set is 1.)... | math | {
"ground_truth": "\\frac{375}{8}",
"style": "rule"
} | {
"answer": "\\frac{375}{8}",
"index": 229,
"question": "A subset \\( S \\) of the set \\(\\{1,2, \\ldots, 10\\}\\) is chosen randomly, with all possible subsets being equally likely. Compute the expected number of positive integers which divide the product of the elements of \\( S \\). (By convention, the produc... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In $\\triangle ABC$, the sides opposite to $\\angle A$, $\\angle B$, and $\\angle C$ are $a$, $b$, and $c$ respectively. $M$ is the midpoint of $BC$ with $BM=MC=2$, and $AM=b-c$. Find the maximum area of $\\triangle ABC$. Think step by step and then provide the final answer. The reasoning process ... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"answer": "2\\sqrt{3}",
"index": 230,
"question": "In $\\triangle ABC$, the sides opposite to $\\angle A$, $\\angle B$, and $\\angle C$ are $a$, $b$, and $c$ respectively. $M$ is the midpoint of $BC$ with $BM=MC=2$, and $AM=b-c$. Find the maximum area of $\\triangle ABC$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In $\\triangle ABC$, $AB=3$, $AC=2$, and $\\angle A=60^{\\circ}$. Find the area of $\\triangle ABC$, $S_{\\triangle ABC}=$ ______. 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 with... | math | {
"ground_truth": "\\frac {3}{2} \\sqrt {3}",
"style": "rule"
} | {
"answer": "\\frac {3}{2} \\sqrt {3}",
"index": 231,
"question": "In $\\triangle ABC$, $AB=3$, $AC=2$, and $\\angle A=60^{\\circ}$. Find the area of $\\triangle ABC$, $S_{\\triangle ABC}=$ ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Five people are seated around a circular table. Let f represent the number of people sitting next to at least one female and m represent the number of people sitting next to at least one male, where f and m are non-negative integers. Calculate the number of unique ordered pairs (f, m). Think step ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 232,
"question": "Five people are seated around a circular table. Let f represent the number of people sitting next to at least one female and m represent the number of people sitting next to at least one male, where f and m are non-negative integers. Calculate the number of unique order... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the equation $x^{4}=a_{0}+a_{1}(x-2)+a_{2}(x-2)^{2}+a_{3}(x-2)^{3}+a_{4}(x-2)^{4}$, use the binomial theorem to calculate the value of $a_{2}$. Express your answer as a single integer. Think step by step and then provide the final answer. The reasoning process should be enclosed within <thin... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"answer": "24",
"index": 233,
"question": "Given the equation $x^{4}=a_{0}+a_{1}(x-2)+a_{2}(x-2)^{2}+a_{3}(x-2)^{3}+a_{4}(x-2)^{4}$, use the binomial theorem to calculate the value of $a_{2}$. Express your answer as a single integer.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In the sequence $\\{a_n\\}$, $a_{n+1} - a_n - n = 0$, then $a_{2017} - a_{2016} =$ ______. 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>",
... | math | {
"ground_truth": "2016",
"style": "rule"
} | {
"answer": "2016",
"index": 234,
"question": "In the sequence $\\{a_n\\}$, $a_{n+1} - a_n - n = 0$, then $a_{2017} - a_{2016} =$ ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In three different polygons, we have drawn all the diagonals. The second polygon has 3 more sides and 3 times as many diagonals as the first one. The third polygon has 7 times as many diagonals as the second one. How many more sides does the third polygon have than the second one? Think step by st... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 235,
"question": "In three different polygons, we have drawn all the diagonals. The second polygon has 3 more sides and 3 times as many diagonals as the first one. The third polygon has 7 times as many diagonals as the second one. How many more sides does the third polygon have than the... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given two arithmetic sequences $\\{a_n\\}$ and $\\{b_n\\}$, where $a_1=25$ and $b_1=125$, and $a_2+b_2=150$, find the value of the 2006th term of the sequence $\\{a_n+b_n\\}$. Express your answer as a single numerical value. Think step by step and then provide the final answer. The reasoning proce... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"answer": "150",
"index": 236,
"question": "Given two arithmetic sequences $\\{a_n\\}$ and $\\{b_n\\}$, where $a_1=25$ and $b_1=125$, and $a_2+b_2=150$, find the value of the 2006th term of the sequence $\\{a_n+b_n\\}$. Express your answer as a single numerical value.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The domain of the function $y=\\log(2x-x^2)$ 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": "(0, 2)",
"style": "rule"
} | {
"answer": "(0, 2)",
"index": 237,
"question": "The domain of the function $y=\\log(2x-x^2)$ is.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Trapezoid $ABCD^{}_{}$ has sides $AB=92^{}_{}$, $BC=50^{}_{}$, $CD=19^{}_{}$, and $AD=70^{}_{}$, with $AB^{}_{}$ parallel to $CD^{}_{}$. A circle with center $P^{}_{}$ on $AB^{}_{}$ is drawn tangent to $BC^{}_{}$ and $AD^{}_{}$. Given that $AP^{}_{}=\\frac mn$, where $m^{}_{}$ and $n^{}_{}$ are re... | math | {
"ground_truth": "$164$",
"style": "rule"
} | {
"answer": "$164$",
"index": 238,
"question": "Trapezoid $ABCD^{}_{}$ has sides $AB=92^{}_{}$, $BC=50^{}_{}$, $CD=19^{}_{}$, and $AD=70^{}_{}$, with $AB^{}_{}$ parallel to $CD^{}_{}$. A circle with center $P^{}_{}$ on $AB^{}_{}$ is drawn tangent to $BC^{}_{}$ and $AD^{}_{}$. Given that $AP^{}_{}=\\frac mn$, wher... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given eight small squares, in how many different ways can six of these squares be shaded so that the shaded squares form the net of a cube? 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>... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"answer": "6",
"index": 239,
"question": "Given eight small squares, in how many different ways can six of these squares be shaded so that the shaded squares form the net of a cube? Express your answer as a single integer.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given vectors $\\overrightarrow{a}=(\\sin x,1)$ and $\\overrightarrow{b}=( \\frac{1}{2},\\cos x)$, and assuming $\\overrightarrow{a} \\parallel \\overrightarrow{b}$, find the acute angle $x$ in radians. Express your answer as a fraction of $\\pi$. Think step by step and then provide the final answ... | math | {
"ground_truth": "\\frac {\\pi}{4}",
"style": "rule"
} | {
"answer": "\\frac {\\pi}{4}",
"index": 240,
"question": "Given vectors $\\overrightarrow{a}=(\\sin x,1)$ and $\\overrightarrow{b}=( \\frac{1}{2},\\cos x)$, and assuming $\\overrightarrow{a} \\parallel \\overrightarrow{b}$, find the acute angle $x$ in radians. Express your answer as a fraction of $\\pi$.",
"sp... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The sum of the interior angles of a convex polygon minus the measure of one interior angle is 2570 degrees. Find the measure of this interior angle. Express your answer in degrees as a whole number. Think step by step and then provide the final answer. The reasoning process should be enclosed with... | math | {
"ground_truth": "130",
"style": "rule"
} | {
"answer": "130",
"index": 241,
"question": "The sum of the interior angles of a convex polygon minus the measure of one interior angle is 2570 degrees. Find the measure of this interior angle. Express your answer in degrees as a whole number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The equation of a circle is given as (x+2)^2 + y^2 = 5. Find the equation of the circle that is symmetrical to this circle with respect to the origin (0,0). Express your answer in the standard form of a circle equation, (x-h)^2 + (y-k)^2 = r^2. Think step by step and then provide the final answer.... | math | {
"ground_truth": "(x-2)^2 + y^2 = 5",
"style": "rule"
} | {
"answer": "(x-2)^2 + y^2 = 5",
"index": 242,
"question": "The equation of a circle is given as (x+2)^2 + y^2 = 5. Find the equation of the circle that is symmetrical to this circle with respect to the origin (0,0). Express your answer in the standard form of a circle equation, (x-h)^2 + (y-k)^2 = r^2.",
"spli... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In a cube, the centers of the bases are connected to the centers of the lateral faces. Calculate the surface area of the resulting octahedron if the edge of the cube is equal to \\( a \\). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think>... | math | {
"ground_truth": "a^2 \\sqrt{3}",
"style": "rule"
} | {
"answer": "a^2 \\sqrt{3}",
"index": 243,
"question": "In a cube, the centers of the bases are connected to the centers of the lateral faces. Calculate the surface area of the resulting octahedron if the edge of the cube is equal to \\( a \\).",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Two lines with slopes \\(\\frac{1}{4}\\) and \\(\\frac{5}{4}\\) intersect at \\((1,1)\\). What is the area of the triangle formed by these two lines and the vertical line \\(x=5\\)? Express your answer as a single number. Think step by step and then provide the final answer. The reasoning process ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"answer": "8",
"index": 244,
"question": "Two lines with slopes \\(\\frac{1}{4}\\) and \\(\\frac{5}{4}\\) intersect at \\((1,1)\\). What is the area of the triangle formed by these two lines and the vertical line \\(x=5\\)? Express your answer as a single number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ is $S_n$. If $a_1$, $a_3$, and $a_4$ form a geometric sequence, then the value of $$\\frac {S_{3}-S_{2}}{S_{5}-S_{3}}$$ is \\_\\_\\_\\_\\_. Think step by step and then provide the final answer. The reasoning process should be enc... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 245,
"question": "The sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ is $S_n$. If $a_1$, $a_3$, and $a_4$ form a geometric sequence, then the value of $$\\frac {S_{3}-S_{2}}{S_{5}-S_{3}}$$ is \\_\\_\\_\\_\\_.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the complex number $z$ satisfies $i \\cdot z = -\\frac{1}{2}(1+i)$, then the imaginary part of the conjugate of $z$ 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... | math | {
"ground_truth": "Imaginary part of \\bar{z} = -\\frac{1}{2}",
"style": "rule"
} | {
"answer": "Imaginary part of \\bar{z} = -\\frac{1}{2}",
"index": 246,
"question": "If the complex number $z$ satisfies $i \\cdot z = -\\frac{1}{2}(1+i)$, then the imaginary part of the conjugate of $z$ is \\_\\_\\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given an arithmetic sequence $\\{a_n\\}$ with a non-zero common difference, $a_1 + a_2 + a_5 > 13$, and $a_1, a_2, a_5$ form a geometric sequence, then the range of values for $a_1$ is ______. Think step by step and then provide the final answer. The reasoning process should be enclosed within <th... | math | {
"ground_truth": "(1, +\\infty)",
"style": "rule"
} | {
"answer": "(1, +\\infty)",
"index": 247,
"question": "Given an arithmetic sequence $\\{a_n\\}$ with a non-zero common difference, $a_1 + a_2 + a_5 > 13$, and $a_1, a_2, a_5$ form a geometric sequence, then the range of values for $a_1$ is ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If $\\frac{xy}{x+y}= a,\\frac{xz}{x+z}= b,\\frac{yz}{y+z}= c$, where $a, b, c$ are other than zero, then $x$ equals: 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></a... | math | {
"ground_truth": "$\\frac{2abc}{ac+bc-ab}$",
"style": "rule"
} | {
"answer": "$\\frac{2abc}{ac+bc-ab}$",
"index": 248,
"question": "If $\\frac{xy}{x+y}= a,\\frac{xz}{x+z}= b,\\frac{yz}{y+z}= c$, where $a, b, c$ are other than zero, then $x$ equals:",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The sequences \\(\\left(x_{n}\\right)\\) and \\(\\left(y_{n}\\right)\\) are given by the formulas \\(x_{n}=2n-1\\) and \\(y_{n}=n^{2}\\). If we list all the common terms of these sequences in increasing order, we obtain the sequence \\(\\left(c_{n}\\right)\\). Write the formula for the \\(n\\)-th ... | math | {
"ground_truth": "(2n-1)^2",
"style": "rule"
} | {
"answer": "(2n-1)^2",
"index": 249,
"question": "The sequences \\(\\left(x_{n}\\right)\\) and \\(\\left(y_{n}\\right)\\) are given by the formulas \\(x_{n}=2n-1\\) and \\(y_{n}=n^{2}\\). If we list all the common terms of these sequences in increasing order, we obtain the sequence \\(\\left(c_{n}\\right)\\). Wr... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a parabola $y^{2}=4x$ with a focus $F$, and points $A$ and $B$ on the parabola such that $\\angle{AFB}=90^{\\circ}$. The midpoint $M$ of chord $AB$ has a projection $M_{1}$ on the directrix $l$. Find the maximum value of $\\frac{|MM_{1}|}{|AB|}$. Think step by step and then provide the final... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"answer": "\\frac{\\sqrt{2}}{2}",
"index": 250,
"question": "Given a parabola $y^{2}=4x$ with a focus $F$, and points $A$ and $B$ on the parabola such that $\\angle{AFB}=90^{\\circ}$. The midpoint $M$ of chord $AB$ has a projection $M_{1}$ on the directrix $l$. Find the maximum value of $\\frac{|MM_{1}|}{|AB|}$... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given $f(x) = a\\sin{2x} + b\\tan{x} + 1$, and $f(-2) = 4$, then $f(\\pi + 2) = \\ ?$ 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>",
"ro... | math | {
"ground_truth": "-2",
"style": "rule"
} | {
"answer": "-2",
"index": 251,
"question": "Given $f(x) = a\\sin{2x} + b\\tan{x} + 1$, and $f(-2) = 4$, then $f(\\pi + 2) = \\ ?$",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the recursive sequence $\\left\\{ a_n \\right\\}$ defined by $a_1=-\\frac{1}{4}$ and $a_n=1-\\frac{1}{a_{n-1}}$ for $n > 1$, find the value of $a_{2018}$. Express your answer as a single number. Think step by step and then provide the final answer. The reasoning process should be enclosed wi... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 252,
"question": "Given the recursive sequence $\\left\\{ a_n \\right\\}$ defined by $a_1=-\\frac{1}{4}$ and $a_n=1-\\frac{1}{a_{n-1}}$ for $n > 1$, find the value of $a_{2018}$. Express your answer as a single number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The sum of the exterior angles of a regular decagon 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": "360^{\\circ}",
"style": "rule"
} | {
"answer": "360^{\\circ}",
"index": 253,
"question": "The sum of the exterior angles of a regular decagon is ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The line $l$ passes through the point $P(1, 2)$ with a slope of $\\sqrt{3}$. The equation of line $l$ 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></a... | math | {
"ground_truth": "\\sqrt{3}x - y + 2 - \\sqrt{3} = 0",
"style": "rule"
} | {
"answer": "\\sqrt{3}x - y + 2 - \\sqrt{3} = 0",
"index": 254,
"question": "The line $l$ passes through the point $P(1, 2)$ with a slope of $\\sqrt{3}$. The equation of line $l$ is __________.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that $ab > 0$ and $2a + b = 5$, find the minimum value of $\\frac{2}{a + 1} + \\frac{1}{b + 1}$. 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... | math | {
"ground_truth": "\\frac{9}{8}",
"style": "rule"
} | {
"answer": "\\frac{9}{8}",
"index": 255,
"question": "Given that $ab > 0$ and $2a + b = 5$, find the minimum value of $\\frac{2}{a + 1} + \\frac{1}{b + 1}$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that $z=1+i$ (where $i$ is the imaginary unit), calculate the value of $\\frac{2}{z}$. Express your answer as a complex number in the form $a+bi$, where $a$ and $b$ are real numbers. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think>... | math | {
"ground_truth": "1-i",
"style": "rule"
} | {
"answer": "1-i",
"index": 256,
"question": "Given that $z=1+i$ (where $i$ is the imaginary unit), calculate the value of $\\frac{2}{z}$. Express your answer as a complex number in the form $a+bi$, where $a$ and $b$ are real numbers.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that $\\overrightarrow{e\\_1} = (1, 0)$, $\\overrightarrow{e\\_2} = (0, 1)$, $\\overrightarrow{a} = \\overrightarrow{e\\_1} - 2\\overrightarrow{e\\_2}$, and $\\overrightarrow{b} = k\\overrightarrow{e\\_1} + \\overrightarrow{e\\_2}$, if $\\overrightarrow{a} \\parallel \\overrightarrow{b}$, ca... | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"answer": "-\\frac{1}{2}",
"index": 257,
"question": "Given that $\\overrightarrow{e\\_1} = (1, 0)$, $\\overrightarrow{e\\_2} = (0, 1)$, $\\overrightarrow{a} = \\overrightarrow{e\\_1} - 2\\overrightarrow{e\\_2}$, and $\\overrightarrow{b} = k\\overrightarrow{e\\_1} + \\overrightarrow{e\\_2}$, if $\\overrightarro... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given an arithmetic sequence $\\{a_n\\}$ with the sum of the first $n$ terms denoted as $S_n$ and the common difference $d < 0$, it is known that $S_7=21$ and $a_2 \\cdot a_6 = 5$. Find the value of $a_{19}$. Think step by step and then provide the final answer. The reasoning process should be enc... | math | {
"ground_truth": "-12",
"style": "rule"
} | {
"answer": "-12",
"index": 258,
"question": "Given an arithmetic sequence $\\{a_n\\}$ with the sum of the first $n$ terms denoted as $S_n$ and the common difference $d < 0$, it is known that $S_7=21$ and $a_2 \\cdot a_6 = 5$. Find the value of $a_{19}$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Calculate the simplified result of the expression $\\left(-a\\right)^{2}\\cdot a^{4}$. Express your answer as a simplified algebraic expression. 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... | math | {
"ground_truth": "a^{6}",
"style": "rule"
} | {
"answer": "a^{6}",
"index": 259,
"question": "Calculate the simplified result of the expression $\\left(-a\\right)^{2}\\cdot a^{4}$. Express your answer as a simplified algebraic expression.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "What is the largest \\( x \\) such that \\( x^2 \\) divides \\( 24 \\cdot 35 \\cdot 46 \\cdot 57 \\)? 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<... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"answer": "12",
"index": 260,
"question": "What is the largest \\( x \\) such that \\( x^2 \\) divides \\( 24 \\cdot 35 \\cdot 46 \\cdot 57 \\)?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In order to beautify the environment, we select any two types of flowers from four colors: red, yellow, white, and purple, to plant in one flower bed, and the remaining two types in another flower bed. Find the probability that the red and purple flowers are not in the same flower bed. Think step ... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"answer": "\\frac{2}{3}",
"index": 261,
"question": "In order to beautify the environment, we select any two types of flowers from four colors: red, yellow, white, and purple, to plant in one flower bed, and the remaining two types in another flower bed. Find the probability that the red and purple flowers are ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the function f(x) = 4 + log_a(x+1), find the coordinates of the fixed point that the graph of the function always passes through, regardless of the value of 'a'. Express your answer as an ordered pair (x, y). Think step by step and then provide the final answer. The reasoning process should ... | math | {
"ground_truth": "(0, 4)",
"style": "rule"
} | {
"answer": "(0, 4)",
"index": 262,
"question": "Given the function f(x) = 4 + log_a(x+1), find the coordinates of the fixed point that the graph of the function always passes through, regardless of the value of 'a'. Express your answer as an ordered pair (x, y).",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given $f(x)=ax+2a+1$, when $x\\in[-1,1]$, the value of $f(x)$ is both positive and negative. 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 sho... | math | {
"ground_truth": "\\left(-1,- \\dfrac {1}{3}\\right)",
"style": "rule"
} | {
"answer": "\\left(-1,- \\dfrac {1}{3}\\right)",
"index": 263,
"question": "Given $f(x)=ax+2a+1$, when $x\\in[-1,1]$, the value of $f(x)$ is both positive and negative. The range of the real number $a$ is $\\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a triangular prism $ABC$($A\\_1B\\_1C\\_1$), where the side edges and base edges are all equal, the projection of $A\\_1$ on the base $ABC$ is the midpoint of $BC$. The cosine value of the angle formed by the skew lines $AB$ and $CC\\_1$ is to be found. Think step by step and then provide th... | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"answer": "\\frac{3}{4}",
"index": 264,
"question": "Given a triangular prism $ABC$($A\\_1B\\_1C\\_1$), where the side edges and base edges are all equal, the projection of $A\\_1$ on the base $ABC$ is the midpoint of $BC$. The cosine value of the angle formed by the skew lines $AB$ and $CC\\_1$ is to be found.... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "\nWith a monthly income of 30,000 rubles, obligatory monthly expenses are as follows: 15,000 rubles for food, 5,000 rubles for utilities, and 2,500 rubles for phone, Internet, and transport expenses. With current savings of 10,000 rubles, you plan to buy a new TV for 25,000 rubles. In how many mon... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 265,
"question": "\nWith a monthly income of 30,000 rubles, obligatory monthly expenses are as follows: 15,000 rubles for food, 5,000 rubles for utilities, and 2,500 rubles for phone, Internet, and transport expenses. With current savings of 10,000 rubles, you plan to buy a new TV for 25... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In the obtuse triangle $\\triangle ABC$, with side lengths $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively, given $a \\lt c \\lt b$, then in triangle $ABC$, ______ is the obtuse angle. Think step by step and then provide the final answer. The reasoning process should be enclose... | math | {
"ground_truth": "B",
"style": "rule"
} | {
"answer": "B",
"index": 266,
"question": "In the obtuse triangle $\\triangle ABC$, with side lengths $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$ respectively, given $a \\lt c \\lt b$, then in triangle $ABC$, ______ is the obtuse angle.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a triangle $ABC$, let $a, b, c$ be the lengths of the sides opposite to angles $A, B, C$ respectively. If $a^{2}=b^{2}+c^{2}-bc$, find the measure of angle $A$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the ... | math | {
"ground_truth": "60^{\\circ}",
"style": "rule"
} | {
"answer": "60^{\\circ}",
"index": 267,
"question": "Given a triangle $ABC$, let $a, b, c$ be the lengths of the sides opposite to angles $A, B, C$ respectively. If $a^{2}=b^{2}+c^{2}-bc$, find the measure of angle $A$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Postman Pechkin is riding a bicycle down the road. He noticed that every 4.5 kilometers, a suburban bus overtakes him, and every 9 minutes, a suburban bus traveling in the opposite direction passes him. The interval between bus movements in both directions is 12 minutes. At what speed is Pechkin t... | math | {
"ground_truth": "15 \\text{ km/h}",
"style": "rule"
} | {
"answer": "15 \\text{ km/h}",
"index": 268,
"question": "Postman Pechkin is riding a bicycle down the road. He noticed that every 4.5 kilometers, a suburban bus overtakes him, and every 9 minutes, a suburban bus traveling in the opposite direction passes him. The interval between bus movements in both direction... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a regular 18-gon \\( M \\), find the number of sets of four vertices of this 18-gon that form the vertices of trapezoids. 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 ... | math | {
"ground_truth": "504",
"style": "rule"
} | {
"answer": "504",
"index": 269,
"question": "Given a regular 18-gon \\( M \\), find the number of sets of four vertices of this 18-gon that form the vertices of trapezoids.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the circles $(x-3)^2+y^2=16$ and $(x+1)^2+(y-m)^2=1$ are tangent, find 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></... | math | {
"ground_truth": "3 \text{ or } -3",
"style": "rule"
} | {
"answer": "3 \text{ or } -3",
"index": 270,
"question": "Given the circles $(x-3)^2+y^2=16$ and $(x+1)^2+(y-m)^2=1$ are tangent, find the real number $m= \\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In $\\triangle ABC$, the sides opposite to $\\angle A$, $\\angle B$, and $\\angle C$ are denoted as $a$, $b$, and $c$ respectively. Given that $a=\\frac{\\sqrt{5}}{2}b$ and $\\angle A=2\\angle B$, calculate the value of $\\cos B$. Express your answer as a single fraction. Think step by step and th... | math | {
"ground_truth": "\\frac{\\sqrt{5}}{4}",
"style": "rule"
} | {
"answer": "\\frac{\\sqrt{5}}{4}",
"index": 271,
"question": "In $\\triangle ABC$, the sides opposite to $\\angle A$, $\\angle B$, and $\\angle C$ are denoted as $a$, $b$, and $c$ respectively. Given that $a=\\frac{\\sqrt{5}}{2}b$ and $\\angle A=2\\angle B$, calculate the value of $\\cos B$. Express your answer ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A line oblique to plane $\\alpha$ can form __________ plane(s) perpendicular to plane $\\alpha$. 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... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 272,
"question": "A line oblique to plane $\\alpha$ can form __________ plane(s) perpendicular to plane $\\alpha$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that $O$ is the circumcenter of acute $\\triangle ABC$, $\\angle BAC = 60^{\\circ}$, extend $CO$ to intersect $AB$ at point $D$, and extend $BO$ to intersect $AC$ at point $E$. Find $\\frac{BD}{CE}=$ ______. Think step by step and then provide the final answer. The reasoning process should b... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 273,
"question": "Given that $O$ is the circumcenter of acute $\\triangle ABC$, $\\angle BAC = 60^{\\circ}$, extend $CO$ to intersect $AB$ at point $D$, and extend $BO$ to intersect $AC$ at point $E$. Find $\\frac{BD}{CE}=$ ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A body moves from $x=0$ to $x=4$ (unit: $m$) under the influence of a force $F(x)$, given by\n$$\nF(x) = \n\\begin{cases}\n5, & 0 \\leq x \\leq 2,\\\\\n3x + 4, & x > 2 \n\\end{cases}\n$$\n(unit: $N$), in the direction of the force $F$. Calculate the work done by the force $F(x)$. Think step by ste... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 274,
"question": "A body moves from $x=0$ to $x=4$ (unit: $m$) under the influence of a force $F(x)$, given by\n$$\nF(x) = \n\\begin{cases}\n5, & 0 \\leq x \\leq 2,\\\\\n3x + 4, & x > 2 \n\\end{cases}\n$$\n(unit: $N$), in the direction of the force $F$. Calculate the work done by the fo... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the sum of the binomial coefficients in the binomial expansion of $$(x^{2}- \\frac {2}{x})^{n}$$ is 64, then the constant term in this expansion is \\_\\_\\_\\_\\_\\_ (answer with a number). Think step by step and then provide the final answer. The reasoning process should be enclosed within <t... | math | {
"ground_truth": "240",
"style": "rule"
} | {
"answer": "240",
"index": 275,
"question": "If the sum of the binomial coefficients in the binomial expansion of $$(x^{2}- \\frac {2}{x})^{n}$$ is 64, then the constant term in this expansion is \\_\\_\\_\\_\\_\\_ (answer with a number).",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Let $S$ be the total number of subsets of a set containing 10 elements, and let $T$ be the number of subsets consisting of 3 elements. Find the value of $\\frac {T}{S}$. Express your answer as a simplified fraction. Think step by step and then provide the final answer. The reasoning process should... | math | {
"ground_truth": "\\frac {15}{128}",
"style": "rule"
} | {
"answer": "\\frac {15}{128}",
"index": 276,
"question": "Let $S$ be the total number of subsets of a set containing 10 elements, and let $T$ be the number of subsets consisting of 3 elements. Find the value of $\\frac {T}{S}$. Express your answer as a simplified fraction.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Use the digits 0, 1, and 2 to form natural numbers without repeating any digits. What is the total number of such 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 with... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 277,
"question": "Use the digits 0, 1, and 2 to form natural numbers without repeating any digits. What is the total number of such natural numbers?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "For which values of \\( n \\) can an \\( n \\times n \\) checkered board be divided into one \\( 3 \\times 3 \\) square and some number of strips each consisting of seven cells, such that the square is adjacent to the side of the board? Think step by step and then provide the final answer. The rea... | math | {
"ground_truth": "n \\equiv 3 \\pmod{7}",
"style": "rule"
} | {
"answer": "n \\equiv 3 \\pmod{7}",
"index": 278,
"question": "For which values of \\( n \\) can an \\( n \\times n \\) checkered board be divided into one \\( 3 \\times 3 \\) square and some number of strips each consisting of seven cells, such that the square is adjacent to the side of the board?",
"split": ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The line y=x+n intersects with the line y=mx+3n (where m is a constant, m ≠ 0, and m ≠ 1) at point A. When the value of n changes, the distance from point A to the line y=3/4x-3 is always a constant. Calculate the value of m that satisfies this condition. Express your answer as a fraction or decim... | math | {
"ground_truth": "3/2",
"style": "rule"
} | {
"answer": "3/2",
"index": 279,
"question": "The line y=x+n intersects with the line y=mx+3n (where m is a constant, m ≠ 0, and m ≠ 1) at point A. When the value of n changes, the distance from point A to the line y=3/4x-3 is always a constant. Calculate the value of m that satisfies this condition. Express your... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Three bags of flour are labeled with the masses (25±0.1) kg, (25±0.2) kg, and (25±0.3) kg, respectively. When any two bags are randomly selected, what is the maximum possible difference in their masses? Express your answer in kilograms. Think step by step and then provide the final answer. The rea... | math | {
"ground_truth": "0.6",
"style": "rule"
} | {
"answer": "0.6",
"index": 280,
"question": "Three bags of flour are labeled with the masses (25±0.1) kg, (25±0.2) kg, and (25±0.3) kg, respectively. When any two bags are randomly selected, what is the maximum possible difference in their masses? Express your answer in kilograms.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Yulia thought of a number. Dasha added 1 to Yulia's number, and Anya added 13 to Yulia's number. It turned out that the number obtained by Anya is 4 times the number obtained by Dasha. What number did Yulia think of? Think step by step and then provide the final answer. The reasoning process shoul... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 281,
"question": "Yulia thought of a number. Dasha added 1 to Yulia's number, and Anya added 13 to Yulia's number. It turned out that the number obtained by Anya is 4 times the number obtained by Dasha. What number did Yulia think of?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a set of data $\\{x\\_1\\}$, $\\{x\\_2\\}$, $\\{...\\}$, $\\{x\\_n\\}$ with a variance of $\\frac{1}{2}$, find the variance of the data $\\{2x\\_1-5\\}$, $\\{2x\\_2-5\\}$, $\\{...\\}$, $\\{2x\\_n-5\\}$. Think step by step and then provide the final answer. The reasoning process should be enc... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 282,
"question": "Given a set of data $\\{x\\_1\\}$, $\\{x\\_2\\}$, $\\{...\\}$, $\\{x\\_n\\}$ with a variance of $\\frac{1}{2}$, find the variance of the data $\\{2x\\_1-5\\}$, $\\{2x\\_2-5\\}$, $\\{...\\}$, $\\{2x\\_n-5\\}$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A student scored $110$, $114$, $121$, $119$, and $126$ in five stage exams during his/her senior year. Calculate the variance of these scores. 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 e... | math | {
"ground_truth": "30.8",
"style": "rule"
} | {
"answer": "30.8",
"index": 283,
"question": "A student scored $110$, $114$, $121$, $119$, and $126$ in five stage exams during his/her senior year. Calculate the variance of these scores.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the left focus of the hyperbola $\\frac{x^{2}}{m} - \\frac{y^{2}}{m-2} = 1$ coincides with the focus of the parabola $y^{2} = -8x$, find the value 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 ans... | math | {
"ground_truth": "m = 3",
"style": "rule"
} | {
"answer": "m = 3",
"index": 284,
"question": "If the left focus of the hyperbola $\\frac{x^{2}}{m} - \\frac{y^{2}}{m-2} = 1$ coincides with the focus of the parabola $y^{2} = -8x$, find the value of $m$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Among all six-digit numbers, how many have digits that sum up to 52? Provide your answer as a single integer count. 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></an... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"answer": "21",
"index": 285,
"question": "Among all six-digit numbers, how many have digits that sum up to 52? Provide your answer as a single integer count.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that i is the imaginary unit, find the value of a (a ∈ R) such that the expression z = (a+i)/(1+i) represents a pure imaginary number. Express your answer as a single real number. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></t... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 286,
"question": "Given that i is the imaginary unit, find the value of a (a ∈ R) such that the expression z = (a+i)/(1+i) represents a pure imaginary number. Express your answer as a single real number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the proposition p: The exponential function f(x) = (2a - 6)^x is strictly decreasing on R, and the proposition q: Both real roots of the equation x^2 - 3ax + 2a^2 + 1 = 0 are greater than 3. If p or q is true, and p and q are both false, find the range of values for the real number a. Think ... | math | {
"ground_truth": "a > \\frac{7}{2}",
"style": "rule"
} | {
"answer": "a > \\frac{7}{2}",
"index": 287,
"question": "Given the proposition p: The exponential function f(x) = (2a - 6)^x is strictly decreasing on R, and the proposition q: Both real roots of the equation x^2 - 3ax + 2a^2 + 1 = 0 are greater than 3. If p or q is true, and p and q are both false, find the ra... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Five boys and four girls are to sit on chairs numbered from the first to the ninth, with boys sitting on chairs with odd numbers and girls on chairs with even numbers. In how many ways can this be done? Think step by step and then provide the final answer. The reasoning process should be enclosed ... | math | {
"ground_truth": "2880",
"style": "rule"
} | {
"answer": "2880",
"index": 288,
"question": "Five boys and four girls are to sit on chairs numbered from the first to the ninth, with boys sitting on chairs with odd numbers and girls on chairs with even numbers. In how many ways can this be done?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find all the integer solutions $(x,y,z)$ of the equation $(x + y + z)^5 = 80xyz(x^2 + y^2 + z^2)$ , 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... | math | {
"ground_truth": "(a, -a, 0) and its permutations, where a is an integer.",
"style": "rule"
} | {
"answer": "(a, -a, 0) and its permutations, where a is an integer.",
"index": 289,
"question": "Find all the integer solutions $(x,y,z)$ of the equation $(x + y + z)^5 = 80xyz(x^2 + y^2 + z^2)$ ,",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\\begin{cases} x= \\frac { \\sqrt {2}}{2}t- \\sqrt {2} \\\\ y= \\frac { \\sqrt {2}}{4}t\\end{cases}$ (where $t$ is the parameter), and the parametric equation of ellipse $C$ is $\\begin{cases} x=\\cos \\theta \\\\ y=... | math | {
"ground_truth": "\\left(- \\frac { \\sqrt {2}}{2}, \\frac { \\sqrt {2}}{4}\\right)",
"style": "rule"
} | {
"answer": "\\left(- \\frac { \\sqrt {2}}{2}, \\frac { \\sqrt {2}}{4}\\right)",
"index": 290,
"question": "In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\\begin{cases} x= \\frac { \\sqrt {2}}{2}t- \\sqrt {2} \\\\ y= \\frac { \\sqrt {2}}{4}t\\end{cases}$ (where $t$ is the param... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "To estimate the number of fish in the lake, $100$ fish were caught and marked, then released back into the lake. After a while, when the marked fish had mixed with the rest of the fish, a second catch was made of $200$ fish, of which $25$ were found to be marked. We can estimate that there are $\\... | math | {
"ground_truth": "800",
"style": "rule"
} | {
"answer": "800",
"index": 291,
"question": "To estimate the number of fish in the lake, $100$ fish were caught and marked, then released back into the lake. After a while, when the marked fish had mixed with the rest of the fish, a second catch was made of $200$ fish, of which $25$ were found to be marked. We c... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Simplify: $$\\sqrt {y+2+3 \\sqrt {2y-5}}- \\sqrt {y-2+ \\sqrt {2y-5}}$$. 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 {2}",
"style": "rule"
} | {
"answer": "\\sqrt {2}",
"index": 292,
"question": "Simplify: $$\\sqrt {y+2+3 \\sqrt {2y-5}}- \\sqrt {y-2+ \\sqrt {2y-5}}$$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A company is to choose 3 graduates from 5 candidates, A, B, C, D, and E, each having equal chances of being selected. Calculate the probability that both A and B are hired at the same time. Express your answer as a simplified fraction. Think step by step and then provide the final answer. The reas... | math | {
"ground_truth": "\\frac{3}{10}",
"style": "rule"
} | {
"answer": "\\frac{3}{10}",
"index": 293,
"question": "A company is to choose 3 graduates from 5 candidates, A, B, C, D, and E, each having equal chances of being selected. Calculate the probability that both A and B are hired at the same time. Express your answer as a simplified fraction.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If $x$ and $y$ satisfy ${(x+2)^2}+\\sqrt{y-18}=0$, then the value of $\\sqrt{x+y}$ 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>",... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 294,
"question": "If $x$ and $y$ satisfy ${(x+2)^2}+\\sqrt{y-18}=0$, then the value of $\\sqrt{x+y}$ is ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In the newly built school dormitory, there are some double rooms, and the rest are triple rooms. Overall, the dormitory can accommodate more than 30 but less than 70 places. When $\\frac{1}{5}$ of the available places were filled, the number of unfilled places turned out to be the total number of ... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"answer": "50",
"index": 295,
"question": "In the newly built school dormitory, there are some double rooms, and the rest are triple rooms. Overall, the dormitory can accommodate more than 30 but less than 70 places. When $\\frac{1}{5}$ of the available places were filled, the number of unfilled places turned o... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Compute the following expression: $75 \\times \\left(-\\frac{1}{5}\\right)^2 - 24 \\div (-2)^3 - |-8|$ 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... | math | {
"ground_truth": " -2 ",
"style": "rule"
} | {
"answer": " -2 ",
"index": 296,
"question": "Compute the following expression: $75 \\times \\left(-\\frac{1}{5}\\right)^2 - 24 \\div (-2)^3 - |-8|$",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If $\\triangle A_{1} A_{2} A_{3}$ is an equilateral triangle and $A_{n+3}$ is the midpoint of segment $A_{n} A_{n+1}$ for all positive integers $n$, then find the degree measure of $\\angle A_{44} A_{45} A_{43}$. Express your answer in degrees as a numerical value. Think step by step and then prov... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"answer": "120",
"index": 297,
"question": "If $\\triangle A_{1} A_{2} A_{3}$ is an equilateral triangle and $A_{n+3}$ is the midpoint of segment $A_{n} A_{n+1}$ for all positive integers $n$, then find the degree measure of $\\angle A_{44} A_{45} A_{43}$. Express your answer in degrees as a numerical value.",
... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The maximum value of the function \\( f(x) = 2 \\sin^2 x - \\tan^2 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": "... | math | {
"ground_truth": "3 - 2 \\sqrt{2}",
"style": "rule"
} | {
"answer": "3 - 2 \\sqrt{2}",
"index": 298,
"question": "The maximum value of the function \\( f(x) = 2 \\sin^2 x - \\tan^2 x \\) is ___",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The hyperbola $\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1$ has a right focus at $F$ and an eccentricity of $e$. A line passing through point $F$ with a slope angle of $\\frac{\\pi}{3}$ intersects this hyperbola at points $A$ and $B$. If the midpoint of $A B$ is $M$ and the distance $|FM|$ equals ... | math | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"answer": "\\sqrt{2}",
"index": 299,
"question": "The hyperbola $\\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1$ has a right focus at $F$ and an eccentricity of $e$. A line passing through point $F$ with a slope angle of $\\frac{\\pi}{3}$ intersects this hyperbola at points $A$ and $B$. If the midpoint of $A B$ is... |
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