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": "Xiaoming's father needs to ride a mountain bike for 10 minutes and then take the subway for 40 minutes to commute to work every day. One day, the subway was broken, so he rode his bike directly to work, which took a total of 3.5 hours. What is the speed of the subway relative to the mountain bike?... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 100,
"question": "Xiaoming's father needs to ride a mountain bike for 10 minutes and then take the subway for 40 minutes to commute to work every day. One day, the subway was broken, so he rode his bike directly to work, which took a total of 3.5 hours. What is the speed of the subway re... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Let \\\\(α\\\\) and \\\\(β\\\\) be two planes, and \\\\(m\\\\) and \\\\(n\\\\) be two lines. Consider the following four propositions: \n\\\\(①\\\\) If \\\\(m \\perp n\\\\), \\\\(m \\perp α\\\\), and \\\\(n \\parallel β\\\\), then \\\\(α \\perp β\\\\); \n\\\\(②\\\\) If \\\\(m \\perp α\\\\) and \... | math | {
"ground_truth": "②③",
"style": "rule"
} | {
"answer": "②③",
"index": 101,
"question": "Let \\\\(α\\\\) and \\\\(β\\\\) be two planes, and \\\\(m\\\\) and \\\\(n\\\\) be two lines. Consider the following four propositions: \n\\\\(①\\\\) If \\\\(m \\perp n\\\\), \\\\(m \\perp α\\\\), and \\\\(n \\parallel β\\\\), then \\\\(α \\perp β\\\\); \n\\\\(②\\\\) ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A positive integer $n$ is known as an [i]interesting[/i] number if $n$ satisfies\n\\[{\\ \\{\\frac{n}{10^k}} \\} > \\frac{n}{10^{10}} \\] \nfor all $k=1,2,\\ldots 9$.\nFind the number of interesting numbers. Think step by step and then provide the final answer. The reasoning process should be enc... | math | {
"ground_truth": "999989991",
"style": "rule"
} | {
"answer": "999989991",
"index": 102,
"question": "A positive integer $n$ is known as an [i]interesting[/i] number if $n$ satisfies\n\\[{\\ \\{\\frac{n}{10^k}} \\} > \\frac{n}{10^{10}} \\] \nfor all $k=1,2,\\ldots 9$.\nFind the number of interesting numbers.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given $f(x)$ is an even function on $\\mathbb{R}$, and when $x > 0$, $f(x) = \\log_{2}(x+1)$, then find $f(-15)$. 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></answ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 103,
"question": "Given $f(x)$ is an even function on $\\mathbb{R}$, and when $x > 0$, $f(x) = \\log_{2}(x+1)$, then find $f(-15)$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In the arithmetic sequence $\\{a_n\\}$, $a_5=3$, $a_7=7$, then $a_3+a_4+\\ldots+a_9=$ ? 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": "35",
"style": "rule"
} | {
"answer": "35",
"index": 104,
"question": "In the arithmetic sequence $\\{a_n\\}$, $a_5=3$, $a_7=7$, then $a_3+a_4+\\ldots+a_9=$ ?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If real numbers $x$ and $y$ satisfy $\\left(x+i\\right)\\left(3+yi\\right)=2+4i$, then calculate the value of $xy$. 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 answ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"answer": "1",
"index": 105,
"question": "If real numbers $x$ and $y$ satisfy $\\left(x+i\\right)\\left(3+yi\\right)=2+4i$, then calculate the value of $xy$. Express your answer as a single integer.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "There are 3 boys and 3 girls standing in a row. If they are required to stand in an alternating boy-girl pattern, calculate the total number of possible standing arrangements. Express your answer as a whole number. Think step by step and then provide the final answer. The reasoning process should ... | math | {
"ground_truth": "72",
"style": "rule"
} | {
"answer": "72",
"index": 106,
"question": "There are 3 boys and 3 girls standing in a row. If they are required to stand in an alternating boy-girl pattern, calculate the total number of possible standing arrangements. Express your answer as a whole number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The office has just been renovated and adding some plants can help remove the odor. The company offers four types of plants: Pothos, Lucky Bamboo, Jade Plant, and Aloe Vera for employees to choose from. Each employee can choose only one kind of plant. What is the probability that employees A and B... | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"answer": "\\frac{3}{4}",
"index": 107,
"question": "The office has just been renovated and adding some plants can help remove the odor. The company offers four types of plants: Pothos, Lucky Bamboo, Jade Plant, and Aloe Vera for employees to choose from. Each employee can choose only one kind of plant. What is... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the value of $\\tan \\frac{13π}{3}$. Express your answer in simplest form, including any necessary radicals. 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></answ... | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"answer": "\\sqrt{3}",
"index": 108,
"question": "Find the value of $\\tan \\frac{13π}{3}$. Express your answer in simplest form, including any necessary radicals.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "109 apples are distributed among bags. In some bags, there are \\( x \\) apples, and in others, there are three apples.\n\nFind all possible values of \\( x \\) if the total number of bags is 20. Think step by step and then provide the final answer. The reasoning process should be enclosed within ... | math | {
"ground_truth": "10 \\text{ or } 52",
"style": "rule"
} | {
"answer": "10 \\text{ or } 52",
"index": 109,
"question": "109 apples are distributed among bags. In some bags, there are \\( x \\) apples, and in others, there are three apples.\n\nFind all possible values of \\( x \\) if the total number of bags is 20.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given four segments $a$, $2$, $6$, $a+1$ are in proportion, 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"... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 110,
"question": "Given four segments $a$, $2$, $6$, $a+1$ are in proportion, find the value of $a$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Insert a square into an equilateral triangle such that one of its sides rests on the base of the triangle. 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> tag... | math | {
"ground_truth": "a (2 - \\sqrt{3})",
"style": "rule"
} | {
"answer": "a (2 - \\sqrt{3})",
"index": 111,
"question": "Insert a square into an equilateral triangle such that one of its sides rests on the base of the triangle.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Let $ABCD$ be a rectangle in which $AB + BC + CD = 20$ and $AE = 9$ where $E$ is the midpoint of the side $BC$ . Find the area of the rectangle. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final answer ... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"answer": "19",
"index": 112,
"question": "Let $ABCD$ be a rectangle in which $AB + BC + CD = 20$ and $AE = 9$ where $E$ is the midpoint of the side $BC$ . Find the area of the rectangle.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "How many solutions are there in the set of positive integers for the equation \\( x^7 + y^8 = z^9 \\)? 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": "There are infinitely many solutions in positive integers.",
"style": "rule"
} | {
"answer": "There are infinitely many solutions in positive integers.",
"index": 113,
"question": "How many solutions are there in the set of positive integers for the equation \\( x^7 + y^8 = z^9 \\)?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the equation \\\\(\\\\frac{x-y}{z-y}=-10\\\\), find the value of \\\\(\\\\frac{x-z}{y-z}\\\\). 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 enc... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 114,
"question": "Given the equation \\\\(\\\\frac{x-y}{z-y}=-10\\\\), find the value of \\\\(\\\\frac{x-z}{y-z}\\\\). Express your answer as a single number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that $\\alpha$ is an angle in the third quadrant, and $3\\cos 2\\alpha +\\sin \\alpha =2$, find $\\tan \\alpha$. 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><... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{4}",
"style": "rule"
} | {
"answer": "\\frac{\\sqrt{2}}{4}",
"index": 115,
"question": "Given that $\\alpha$ is an angle in the third quadrant, and $3\\cos 2\\alpha +\\sin \\alpha =2$, find $\\tan \\alpha$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Within the elastic limit, when an object is hung on a spring, the length $y$ (in cm) of the spring is related to the mass $x$ (in kg) of the object as shown in the table below:\n\n|x (kg)|0|1|2|3|4|5|...|\n|-|-|-|-|-|-|-|-|\n|y (cm)|10|10.5|11|11.5|12|12.5|...|\n\nUsing the data provided, establis... | math | {
"ground_truth": "14.5 \\text{ cm}",
"style": "rule"
} | {
"answer": "14.5 \\text{ cm}",
"index": 116,
"question": "Within the elastic limit, when an object is hung on a spring, the length $y$ (in cm) of the spring is related to the mass $x$ (in kg) of the object as shown in the table below:\n\n|x (kg)|0|1|2|3|4|5|...|\n|-|-|-|-|-|-|-|-|\n|y (cm)|10|10.5|11|11.5|12|12.... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the difference between the maximum and minimum values of the function $y=\\log_a x$ ($0<a<1$) on the interval $[2,4]$ is 2, 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 shou... | math | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"answer": "\\frac{\\sqrt{2}}{2}",
"index": 117,
"question": "If the difference between the maximum and minimum values of the function $y=\\log_a x$ ($0<a<1$) on the interval $[2,4]$ is 2, find the value of $a$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The set of angles that share the same terminal side as the angle $-100^\\circ$ 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": "\\{\\alpha | \\alpha = k \\cdot 360^\\circ - 100^\\circ, k \\in \\mathbb{Z}\\}",
"style": "rule"
} | {
"answer": "\\{\\alpha | \\alpha = k \\cdot 360^\\circ - 100^\\circ, k \\in \\mathbb{Z}\\}",
"index": 118,
"question": "The set of angles that share the same terminal side as the angle $-100^\\circ$ is ____.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In a class that includes Petya and Vanya, there are 31 students. In how many ways can a football team be selected from the class? 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 withi... | math | {
"ground_truth": "2 \\binom{29}{10} + \\binom{29}{9}",
"style": "rule"
} | {
"answer": "2 \\binom{29}{10} + \\binom{29}{9}",
"index": 119,
"question": "In a class that includes Petya and Vanya, there are 31 students. In how many ways can a football team be selected from the class?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the sum of all the angles except one of a convex polygon is 2190 degrees, calculate the number of sides of the polygon. 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... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"answer": "15",
"index": 120,
"question": "If the sum of all the angles except one of a convex polygon is 2190 degrees, calculate the number of sides of the polygon. Express your answer as a whole number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the function $y=ax^{2}+b$, the slope of the tangent line at point $(1,3)$ is $2$. Find $\\frac{a}{b}$____. 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></answe... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"answer": "\\frac{1}{2}",
"index": 121,
"question": "Given the function $y=ax^{2}+b$, the slope of the tangent line at point $(1,3)$ is $2$. Find $\\frac{a}{b}$____.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Convert 3 x 10^10 nanometers to meters, given that one nanometer equals one millionth of a millimeter and 1000 millimeters equal 1 meter. Express your answer in meters, rounded to the nearest whole number if necessary. Think step by step and then provide the final answer. The reasoning process sho... | math | {
"ground_truth": "30 \\text{ meters}",
"style": "rule"
} | {
"answer": "30 \\text{ meters}",
"index": 122,
"question": "Convert 3 x 10^10 nanometers to meters, given that one nanometer equals one millionth of a millimeter and 1000 millimeters equal 1 meter. Express your answer in meters, rounded to the nearest whole number if necessary.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The zeros of the function $f(x) = x^2-ax+2a$ are integers. What is the sum of the possible values 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... | math | {
"ground_truth": "$16$",
"style": "rule"
} | {
"answer": "$16$",
"index": 123,
"question": "The zeros of the function $f(x) = x^2-ax+2a$ are integers. What is the sum of the possible values of $a$?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If $θ∈[0,π)$ and $\\cos θ(\\sin θ+\\cos θ)=1$, then $θ=$ ______. 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: } 0 \text{ or } \frac {π}{4}",
"style": "rule"
} | {
"answer": "\text{Answer: } 0 \text{ or } \frac {π}{4}",
"index": 124,
"question": "If $θ∈[0,π)$ and $\\cos θ(\\sin θ+\\cos θ)=1$, then $θ=$ ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Simplify: $\\dfrac{\\sqrt{1+2\\sin 610^{\\circ}\\cos 430^{\\circ}}}{\\sin 250^{\\circ}+\\cos 790^{\\circ}}=$\\_\\_\\_\\_\\_\\_\\_. 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 with... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 125,
"question": "Simplify: $\\dfrac{\\sqrt{1+2\\sin 610^{\\circ}\\cos 430^{\\circ}}}{\\sin 250^{\\circ}+\\cos 790^{\\circ}}=$\\_\\_\\_\\_\\_\\_\\_.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In an arithmetic sequence {a_n}, we have a_9 = 1/2*a_12 + 6 and a_2 = 4. Let the sum of the first n terms of {a_n} be S_n. Calculate the sum of the first 10 terms of the sequence {1/S_n}. Express your answer as a simplified fraction. Think step by step and then provide the final answer. The reason... | math | {
"ground_truth": "\\frac{10}{11}",
"style": "rule"
} | {
"answer": "\\frac{10}{11}",
"index": 126,
"question": "In an arithmetic sequence {a_n}, we have a_9 = 1/2*a_12 + 6 and a_2 = 4. Let the sum of the first n terms of {a_n} be S_n. Calculate the sum of the first 10 terms of the sequence {1/S_n}. Express your answer as a simplified fraction.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The longer base of a trapezoid has a length of 24 cm. Find the length of the shorter base, given that the distance between the midpoints of the diagonals of the trapezoid is 4 cm. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> ... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 127,
"question": "The longer base of a trapezoid has a length of 24 cm. Find the length of the shorter base, given that the distance between the midpoints of the diagonals of the trapezoid is 4 cm.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "What is the time 45 minutes after 10:20? Express your answer in 12-hour clock format (HH:MM). 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": "11:05",
"style": "rule"
} | {
"answer": "11:05",
"index": 128,
"question": "What is the time 45 minutes after 10:20? Express your answer in 12-hour clock format (HH:MM).",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that $e_1$ and $e_2$ are the eccentricities of an ellipse and a hyperbola with common foci $F_1$ and $F_2$, and $P$ is a common point of the two curves such that $\\overrightarrow{PF_1} \\cdot \\overrightarrow{PF_2} = 0$, find the value of $\\frac{e_1^2 + e_2^2}{(e_1 e_2)^2}$. Think step by ... | math | {
"ground_truth": "\\frac{e_1^2 + e_2^2}{(e_1 e_2)^2} = 2",
"style": "rule"
} | {
"answer": "\\frac{e_1^2 + e_2^2}{(e_1 e_2)^2} = 2",
"index": 129,
"question": "Given that $e_1$ and $e_2$ are the eccentricities of an ellipse and a hyperbola with common foci $F_1$ and $F_2$, and $P$ is a common point of the two curves such that $\\overrightarrow{PF_1} \\cdot \\overrightarrow{PF_2} = 0$, find ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In the polar coordinate system, find the polar equation of the line that passes through the center of the circle $\\rho = 6\\cos\\theta$ and is perpendicular to the polar axis. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tag... | math | {
"ground_truth": "\\rho\\cos\\theta = 3",
"style": "rule"
} | {
"answer": "\\rho\\cos\\theta = 3",
"index": 130,
"question": "In the polar coordinate system, find the polar equation of the line that passes through the center of the circle $\\rho = 6\\cos\\theta$ and is perpendicular to the polar axis.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given \\( a > 0 \\), find the solution set for the inequality \\( \\left|\\frac{2x - 3 - 2a}{x - a}\\right| \\leq 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... | math | {
"ground_truth": "\\{x \\mid a + 1 \\leq x \\leq a + 3\\}",
"style": "rule"
} | {
"answer": "\\{x \\mid a + 1 \\leq x \\leq a + 3\\}",
"index": 131,
"question": "Given \\( a > 0 \\), find the solution set for the inequality \\( \\left|\\frac{2x - 3 - 2a}{x - a}\\right| \\leq 1 \\).",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find all triples $ (x,y,z)$ of real numbers which satisfy the simultaneous equations\n\n\\[ x \\equal{} y^3 \\plus{} y \\minus{} 8\\]\n\n\\[y \\equal{} z^3 \\plus{} z \\minus{} 8\\]\n\n\\[ z \\equal{} x^3 \\plus{} x \\minus{} 8.\\] Think step by step and then provide the final answer. The reason... | math | {
"ground_truth": " (x, y, z) = (2, 2, 2) ",
"style": "rule"
} | {
"answer": " (x, y, z) = (2, 2, 2) ",
"index": 132,
"question": "Find all triples $ (x,y,z)$ of real numbers which satisfy the simultaneous equations\n\n\\[ x \\equal{} y^3 \\plus{} y \\minus{} 8\\]\n\n\\[y \\equal{} z^3 \\plus{} z \\minus{} 8\\]\n\n\\[ z \\equal{} x^3 \\plus{} x \\minus{} 8.\\]",
"split": "... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given an arithmetic sequence {a_n}, the sum of the first n terms is denoted as S_n. If a_2 + a_8 + a_11 = 30, find the value of S_13. 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></thin... | math | {
"ground_truth": "130",
"style": "rule"
} | {
"answer": "130",
"index": 133,
"question": "Given an arithmetic sequence {a_n}, the sum of the first n terms is denoted as S_n. If a_2 + a_8 + a_11 = 30, find the value of S_13. Express your answer as a single numerical value.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Three balls labeled $A$, $B$, and $C$ are randomly placed into four boxes numbered $1$, $2$, $3$, and $4$. If box $1$ has no balls, find the total number of different ways to place the balls in boxes $2$, $3$, and $4$. Express your answer as a single integer. Think step by step and then provide th... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 134,
"question": "Three balls labeled $A$, $B$, and $C$ are randomly placed into four boxes numbered $1$, $2$, $3$, and $4$. If box $1$ has no balls, find the total number of different ways to place the balls in boxes $2$, $3$, and $4$. Express your answer as a single integer.",
"spli... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that vertices $B$ and $C$ of $\\triangle ABC$ are on the ellipse $2x^{2}+3y^{2}=1$, vertex $A$ is a focus of the ellipse, and the other focus is on line segment $BC$. Find the perimeter of $\\triangle ABC$. Think step by step and then provide the final answer. The reasoning process should be... | math | {
"ground_truth": "2\\sqrt{2}",
"style": "rule"
} | {
"answer": "2\\sqrt{2}",
"index": 135,
"question": "Given that vertices $B$ and $C$ of $\\triangle ABC$ are on the ellipse $2x^{2}+3y^{2}=1$, vertex $A$ is a focus of the ellipse, and the other focus is on line segment $BC$. Find the perimeter of $\\triangle ABC$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "For the ellipse $\\frac{{x}^{2}}{m}+{y}^{2}=1$ with eccentricity $e=\\frac{\\sqrt{3}}{2}$, the value of $m$ 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": "4 \\text{ or } \\frac{1}{4}",
"style": "rule"
} | {
"answer": "4 \\text{ or } \\frac{1}{4}",
"index": 136,
"question": "For the ellipse $\\frac{{x}^{2}}{m}+{y}^{2}=1$ with eccentricity $e=\\frac{\\sqrt{3}}{2}$, the value of $m$ is ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "There are a certain number of red balls, green balls, and blue balls in a bag. Of the balls in the bag, $\\frac{1}{3}$ are red and $\\frac{2}{7}$ are blue. The number of green balls in the bag is 8 less than twice the number of blue balls. Find the number of green balls in the bag. Express your an... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"answer": "16",
"index": 137,
"question": "There are a certain number of red balls, green balls, and blue balls in a bag. Of the balls in the bag, $\\frac{1}{3}$ are red and $\\frac{2}{7}$ are blue. The number of green balls in the bag is 8 less than twice the number of blue balls. Find the number of green ball... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Determine the number of points on the circle $x^{2}+y^{2}-2x+4y-3=0$ that are at a distance of $\\frac{\\sqrt{2}}{2}$ from the line $x+y+3=0$. 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... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"answer": "4",
"index": 138,
"question": "Determine the number of points on the circle $x^{2}+y^{2}-2x+4y-3=0$ that are at a distance of $\\frac{\\sqrt{2}}{2}$ from the line $x+y+3=0$. Express your answer as a whole number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the interval where the function f(x) = x^2 * e^x is monotonically decreasing. Express your answer as an interval in the format (a, b) 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></think> tags and ... | math | {
"ground_truth": "(-2, 0)",
"style": "rule"
} | {
"answer": "(-2, 0)",
"index": 139,
"question": "Find the interval where the function f(x) = x^2 * e^x is monotonically decreasing. Express your answer as an interval in the format (a, b) where a and b are real numbers.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the variance of the sample $a_1, a_2, \\ldots, a_n$ is 3, then the variance of the sample $3a_1+1, 3a_2+2, \\ldots, 3a_n+1$ 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... | math | {
"ground_truth": "27",
"style": "rule"
} | {
"answer": "27",
"index": 140,
"question": "If the variance of the sample $a_1, a_2, \\ldots, a_n$ is 3, then the variance of the sample $3a_1+1, 3a_2+2, \\ldots, 3a_n+1$ is ____.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "What is the perimeter of $\\triangle UVZ$ if $UVWX$ is a rectangle that lies flat on a horizontal floor, a vertical semi-circular wall with diameter $XW$ is constructed, point $Z$ is the highest point on this wall, and $UV=20$ and $VW=30$? Think step by step and then provide the final answer. The ... | math | {
"ground_truth": "86",
"style": "rule"
} | {
"answer": "86",
"index": 141,
"question": "What is the perimeter of $\\triangle UVZ$ if $UVWX$ is a rectangle that lies flat on a horizontal floor, a vertical semi-circular wall with diameter $XW$ is constructed, point $Z$ is the highest point on this wall, and $UV=20$ and $VW=30$?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The angles $\\alpha$ that satisfy the condition $|\\sin\\alpha| = -\\sin\\alpha$ 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>",
"ro... | math | {
"ground_truth": "[2k\\pi-\\pi, 2k\\pi], k \\in \\mathbb{Z}",
"style": "rule"
} | {
"answer": "[2k\\pi-\\pi, 2k\\pi], k \\in \\mathbb{Z}",
"index": 142,
"question": "The angles $\\alpha$ that satisfy the condition $|\\sin\\alpha| = -\\sin\\alpha$ are.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the value of the algebraic expression $x^2 + 3x - 5$ is 2, then the value of the algebraic expression $2x^2 + 6x - 3$ 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 <an... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"answer": "11",
"index": 143,
"question": "If the value of the algebraic expression $x^2 + 3x - 5$ is 2, then the value of the algebraic expression $2x^2 + 6x - 3$ is.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Observe the following equations:\n$$\nC_5^1 + C_5^5 = 6,\n$$\n$$\nC_9^1 + C_9^5 + C_9^9 = 2^7 + 2^3,\n$$\n$$\nC_{13}^1 + C_{13}^5 + C_{13}^9 + C_{13}^{13} = 2^{11} - 2^5,\n$$\n$$\nC_{17}^1 + C_{17}^5 + C_{17}^9 + C_{17}^{13} + C_{17}^{17} = 2^{15} + 2^7,\n$$\n$$\n…\n$$\nFrom the given equations, i... | math | {
"ground_truth": "2^{4n-1} + (-1)^n \\cdot 2^{2n-1}",
"style": "rule"
} | {
"answer": "2^{4n-1} + (-1)^n \\cdot 2^{2n-1}",
"index": 144,
"question": "Observe the following equations:\n$$\nC_5^1 + C_5^5 = 6,\n$$\n$$\nC_9^1 + C_9^5 + C_9^9 = 2^7 + 2^3,\n$$\n$$\nC_{13}^1 + C_{13}^5 + C_{13}^9 + C_{13}^{13} = 2^{11} - 2^5,\n$$\n$$\nC_{17}^1 + C_{17}^5 + C_{17}^9 + C_{17}^{13} + C_{17}^{17}... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "180 grams of 920 purity gold was alloyed with 100 grams of 752 purity gold. What is the purity of the resulting alloy? 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": "860",
"style": "rule"
} | {
"answer": "860",
"index": 145,
"question": "180 grams of 920 purity gold was alloyed with 100 grams of 752 purity gold. What is the purity of the resulting alloy?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A square lies at the base of a pyramid. The angles formed by the lateral faces with the base are in the ratio 1:2:4:2. Find these angles. 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 enclos... | math | {
"ground_truth": "\\frac{\\pi}{6}, \\frac{\\pi}{3}, \\frac{2\\pi}{3}, \\frac{\\pi}{3}",
"style": "rule"
} | {
"answer": "\\frac{\\pi}{6}, \\frac{\\pi}{3}, \\frac{2\\pi}{3}, \\frac{\\pi}{3}",
"index": 146,
"question": "A square lies at the base of a pyramid. The angles formed by the lateral faces with the base are in the ratio 1:2:4:2. Find these angles.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In a geometric sequence $\\{a_n\\}$ where all terms are positive, if $\\log_{2}a_{2} + \\log_{2}a_{8} = 1$, then $a_{3} \\cdot a_{7} =$ ? 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 enclos... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"answer": "2",
"index": 147,
"question": "In a geometric sequence $\\{a_n\\}$ where all terms are positive, if $\\log_{2}a_{2} + \\log_{2}a_{8} = 1$, then $a_{3} \\cdot a_{7} =$ ?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In triangle $\\triangle ABC$, $\\sin A = \\frac{3}{5}$, $\\tan B = 2$. Find the value of $\\tan 2\\left(A+B\\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": "\\frac{44}{117}",
"style": "rule"
} | {
"answer": "\\frac{44}{117}",
"index": 148,
"question": "In triangle $\\triangle ABC$, $\\sin A = \\frac{3}{5}$, $\\tan B = 2$. Find the value of $\\tan 2\\left(A+B\\right)$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the minimum value of the function f(x) = 2cos^2 x + sin x. 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.\... | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"answer": "-1",
"index": 149,
"question": "Find the minimum value of the function f(x) = 2cos^2 x + sin x. Express your answer as a single number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The algebraic expression $1 + \\frac{1}{1 + \\frac{1}{1 + \\cdots}}$ where the ellipsis \"...\" indicates the pattern repeats indefinitely, represents a fixed value that can be determined as follows: Let the original expression be $t$, then we have $1 + \\frac{1}{t} = t$, which leads to $t^2 - t -... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 150,
"question": "The algebraic expression $1 + \\frac{1}{1 + \\frac{1}{1 + \\cdots}}$ where the ellipsis \"...\" indicates the pattern repeats indefinitely, represents a fixed value that can be determined as follows: Let the original expression be $t$, then we have $1 + \\frac{1}{t} = t... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A pagoda has 7 layers, and the number of red lamps on each layer doubles the number from the layer below, with a total of 381 lamps. Calculate the number of lamps at the top layer. Express your answer as a whole number. Think step by step and then provide the final answer. The reasoning process sh... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 151,
"question": "A pagoda has 7 layers, and the number of red lamps on each layer doubles the number from the layer below, with a total of 381 lamps. Calculate the number of lamps at the top layer. Express your answer as a whole number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Processing a batch of parts, it takes $a$ hours for both A and B to complete the work together, and it takes $b$ hours for A to complete the work alone. Then, it takes B alone hours to complete the work. Think step by step and then provide the final answer. The reasoning process should be encl... | math | {
"ground_truth": "\\frac{ab}{b - a}",
"style": "rule"
} | {
"answer": "\\frac{ab}{b - a}",
"index": 152,
"question": "Processing a batch of parts, it takes $a$ hours for both A and B to complete the work together, and it takes $b$ hours for A to complete the work alone. Then, it takes B alone hours to complete the work.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that \\(\\{a_n\\}\\) is an arithmetic sequence and \\(S_n\\) represents the sum of the first \\(n\\) terms, if \\(a_1=6\\), \\(a_4+a_6=4\\), find \\(S_5\\). Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the fina... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"answer": "20",
"index": 153,
"question": "Given that \\(\\{a_n\\}\\) is an arithmetic sequence and \\(S_n\\) represents the sum of the first \\(n\\) terms, if \\(a_1=6\\), \\(a_4+a_6=4\\), find \\(S_5\\).",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the function $f(x) = \\begin{cases} f(x+2), & x\\leq-1 \\\\ 2x+2, & -1<x<1 \\\\ 2^{x}-4, & x\\geq1\\end{cases}$, then $f[f(-2016)] = \\_\\_\\_\\_\\_\\_$. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final a... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"answer": "0",
"index": 154,
"question": "Given the function $f(x) = \\begin{cases} f(x+2), & x\\leq-1 \\\\ 2x+2, & -1<x<1 \\\\ 2^{x}-4, & x\\geq1\\end{cases}$, then $f[f(-2016)] = \\_\\_\\_\\_\\_\\_$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given triangle ABC with sides a, b, and c opposite to angles A, B, and C respectively, if $$\\frac {c}{a+b}+ \\frac {a}{b+c}$$ equals 1, calculate the measure of angle B in degrees, given that B is within the range (0°, 180°). Express your answer in degrees, rounding to the nearest whole number if... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"answer": "60",
"index": 155,
"question": "Given triangle ABC with sides a, b, and c opposite to angles A, B, and C respectively, if $$\\frac {c}{a+b}+ \\frac {a}{b+c}$$ equals 1, calculate the measure of angle B in degrees, given that B is within the range (0°, 180°). Express your answer in degrees, rounding t... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "How many integers are greater than \\( \\frac{5}{7} \\) and less than \\( \\frac{28}{3} \\)? 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 wit... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"answer": "9",
"index": 156,
"question": "How many integers are greater than \\( \\frac{5}{7} \\) and less than \\( \\frac{28}{3} \\)? Express your answer as a whole number.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The greatest common divisor (GCD) of the three numbers 638, 522, and 406 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": "2",
"style": "rule"
} | {
"answer": "2",
"index": 157,
"question": "The greatest common divisor (GCD) of the three numbers 638, 522, and 406 is _____",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Alice and Bob take turns writing numbers on a blackboard. Alice starts by writing an integer \\(a\\) between -100 and 100 inclusive on the board. On each of Bob's turns, he writes twice the number Alice wrote last. On each of Alice's subsequent turns, she writes the number 45 less than the number ... | math | {
"ground_truth": "0, 30, 42, 45",
"style": "rule"
} | {
"answer": "0, 30, 42, 45",
"index": 158,
"question": "Alice and Bob take turns writing numbers on a blackboard. Alice starts by writing an integer \\(a\\) between -100 and 100 inclusive on the board. On each of Bob's turns, he writes twice the number Alice wrote last. On each of Alice's subsequent turns, she wr... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the locus of all points in the plane from which two flagpoles appear equally tall. The poles have heights \\( h \\) and \\( k \\) and are a distance \\( 2a \\) apart. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and... | math | {
"ground_truth": "The locus is the circle with diameter AB.",
"style": "rule"
} | {
"answer": "The locus is the circle with diameter AB.",
"index": 159,
"question": "Find the locus of all points in the plane from which two flagpoles appear equally tall. The poles have heights \\( h \\) and \\( k \\) and are a distance \\( 2a \\) apart.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that the function $y=(m-1)x^{m^{2}}+1$ is a linear function, 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 answer should be enclosed within <answer></answer> tags.\n<think>",
... | math | {
"ground_truth": "m = -1",
"style": "rule"
} | {
"answer": "m = -1",
"index": 160,
"question": "Given that the function $y=(m-1)x^{m^{2}}+1$ is a linear function, find the value of $m$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The diameter of a spherical cell is $5\\times 10^{2}$ nanometers. Find the length of a cell chain formed by $2\\times 10^{3}$ such cells. Express your answer in nanometers, using scientific notation. Think step by step and then provide the final answer. The reasoning process should be enclosed wit... | math | {
"ground_truth": "1\\times 10^{6}",
"style": "rule"
} | {
"answer": "1\\times 10^{6}",
"index": 161,
"question": "The diameter of a spherical cell is $5\\times 10^{2}$ nanometers. Find the length of a cell chain formed by $2\\times 10^{3}$ such cells. Express your answer in nanometers, using scientific notation.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Suppose there are $n$ points in a plane no three of which are collinear with the property that if we label these points as $A_1,A_2,\\ldots,A_n$ in any way whatsoever, the broken line $A_1A_2\\ldots A_n$ does not intersect itself. Find the maximum value of $n$ . Think step by step and then ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 162,
"question": "Suppose there are $n$ points in a plane no three of which are collinear with the property that if we label these points as $A_1,A_2,\\ldots,A_n$ in any way whatsoever, the broken line $A_1A_2\\ldots A_n$ does not intersect itself. Find the maximum value of $n$ ."... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that the points (3, 1) and (-4, 6) are on opposite sides of the line $3x-2y+a=0$, find the range of values for $a$. Express your answer as an inequality. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the final a... | math | {
"ground_truth": "-7<a<24",
"style": "rule"
} | {
"answer": "-7<a<24",
"index": 163,
"question": "Given that the points (3, 1) and (-4, 6) are on opposite sides of the line $3x-2y+a=0$, find the range of values for $a$. Express your answer as an inequality.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the complex number $z=\\frac{1+3i}{1-i}$ ($i$ is the imaginary unit), 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<t... | math | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"answer": "\\sqrt{5}",
"index": 164,
"question": "Given the complex number $z=\\frac{1+3i}{1-i}$ ($i$ is the imaginary unit), find the value of $|z|$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the function $f(x)=\\sin^{2}ωx+\\sqrt{3}\\sin ωx\\cos ωx$, where $x\\in R$, $f(α)=-\\frac{1}{2}$, $f(β)=\\frac{1}{2}$, and the minimum value of $|α-β|$ is $\\frac{3}{4}π$, calculate the value of the positive number $ω$. Express your answer as a single value. Think step by step and then provi... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"answer": "\\frac{1}{3}",
"index": 165,
"question": "Given the function $f(x)=\\sin^{2}ωx+\\sqrt{3}\\sin ωx\\cos ωx$, where $x\\in R$, $f(α)=-\\frac{1}{2}$, $f(β)=\\frac{1}{2}$, and the minimum value of $|α-β|$ is $\\frac{3}{4}π$, calculate the value of the positive number $ω$. Express your answer as a single v... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Among $-1$, $0$, $0.2$, $\\frac{1}{7}$, and $3$, there are ____ positive 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":... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"answer": "3",
"index": 166,
"question": "Among $-1$, $0$, $0.2$, $\\frac{1}{7}$, and $3$, there are ____ positive numbers.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "ABCD is a parallelogram with an area of 120. K is the midpoint of side AD, and L is the midpoint of side CD. Find the area of triangle BKL. 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 encl... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"answer": "45",
"index": 167,
"question": "ABCD is a parallelogram with an area of 120. K is the midpoint of side AD, and L is the midpoint of side CD. Find the area of triangle BKL.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The sides of a triangle are 3 and 6, and the angle between them is $60^{\\circ}$. Find the length of the angle bisector of the triangle drawn from the vertex of this angle. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags an... | math | {
"ground_truth": "2\\sqrt{3}",
"style": "rule"
} | {
"answer": "2\\sqrt{3}",
"index": 168,
"question": "The sides of a triangle are 3 and 6, and the angle between them is $60^{\\circ}$. Find the length of the angle bisector of the triangle drawn from the vertex of this angle.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The original price of a new model of mobile phone is $a$ yuan. In the next $m$ months, the price decreases by $p\\%$ on average every month. The function expression of the price $y$ yuan as a function of the number of months $x$ is: \\_\\_\\_\\_\\_\\_. Think step by step and then provide the final... | math | {
"ground_truth": "y=a(1-p\\%)^x \\ (0\\leq x\\leq m)",
"style": "rule"
} | {
"answer": "y=a(1-p\\%)^x \\ (0\\leq x\\leq m)",
"index": 169,
"question": "The original price of a new model of mobile phone is $a$ yuan. In the next $m$ months, the price decreases by $p\\%$ on average every month. The function expression of the price $y$ yuan as a function of the number of months $x$ is: \\_\... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Compute the value of $({(\\dfrac{2}{3})}^{0}+3\\times {{(\\dfrac{9}{4})}^{-\\frac{1}{2}}}+(\\log 4+\\log 25))$. 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... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"answer": "5",
"index": 170,
"question": "Compute the value of $({(\\dfrac{2}{3})}^{0}+3\\times {{(\\dfrac{9}{4})}^{-\\frac{1}{2}}}+(\\log 4+\\log 25))$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given that the common ratio of a geometric sequence is 2, and the sum of the first four terms equals 1, find the sum of the first eight terms. 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": "17",
"style": "rule"
} | {
"answer": "17",
"index": 171,
"question": "Given that the common ratio of a geometric sequence is 2, and the sum of the first four terms equals 1, find the sum of the first eight terms.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Factorization: $2{a^2}-2a+\\frac{1}{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": "2(a - \\frac{1}{2})^2",
"style": "rule"
} | {
"answer": "2(a - \\frac{1}{2})^2",
"index": 172,
"question": "Factorization: $2{a^2}-2a+\\frac{1}{2}=\\_\\_\\_\\_\\_\\_.$",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given: $a > 0$ and $a \\neq 1$\n\nProposition $p$: The function $y = \\log_{a}(x+3)$ is decreasing in the interval $(0,+\\infty)$;\n\nProposition $q$: The curve $y = x^{2}+(2a-3)x+1$ intersects the $x$-axis at two distinct points.\n\nIf $p \\lor q$ is true, and $p \\land q$ is false, find the rang... | math | {
"ground_truth": "\\left[ \\frac{1}{2},1\\right) \\cup \\left( \\frac{5}{2},+\\infty\\right)",
"style": "rule"
} | {
"answer": "\\left[ \\frac{1}{2},1\\right) \\cup \\left( \\frac{5}{2},+\\infty\\right)",
"index": 173,
"question": "Given: $a > 0$ and $a \\neq 1$\n\nProposition $p$: The function $y = \\log_{a}(x+3)$ is decreasing in the interval $(0,+\\infty)$;\n\nProposition $q$: The curve $y = x^{2}+(2a-3)x+1$ intersects the... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the remainder when \\( 20^{16} + 201^{6} \\) is divided by 9. 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": 174,
"question": "Find the remainder when \\( 20^{16} + 201^{6} \\) is divided by 9.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the arithmetic sequence $\\{a\\_n\\}$, where $a\\_1=35$, $d=-2$, and $S\\_n=0$, find the 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> t... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"answer": "36",
"index": 175,
"question": "Given the arithmetic sequence $\\{a\\_n\\}$, where $a\\_1=35$, $d=-2$, and $S\\_n=0$, find the value of $n$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "For which positive numbers \\(x, y, u, v\\) does the following system of equations hold?\n\n\\[\n\\begin{cases}\nx + y = u \\\\\nv \\cdot x \\cdot y = u + v \\\\\nx \\cdot y \\cdot u \\cdot v = 16\n\\end{cases}\n\\] Think step by step and then provide the final answer. The reasoning process should... | math | {
"ground_truth": "x = 2, y = 2, u = 2, v = 2",
"style": "rule"
} | {
"answer": "x = 2, y = 2, u = 2, v = 2",
"index": 176,
"question": "For which positive numbers \\(x, y, u, v\\) does the following system of equations hold?\n\n\\[\n\\begin{cases}\nx + y = u \\\\\nv \\cdot x \\cdot y = u + v \\\\\nx \\cdot y \\cdot u \\cdot v = 16\n\\end{cases}\n\\]",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "An isosceles triangle has one side that is 2 cm and another side that is 9 cm. What is the perimeter of this triangle? 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": "20 \\text{ cm}",
"style": "rule"
} | {
"answer": "20 \\text{ cm}",
"index": 177,
"question": "An isosceles triangle has one side that is 2 cm and another side that is 9 cm. What is the perimeter of this triangle?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A middle school has a total of 1800 students, including 1200 junior high school students and 600 senior high school students. To understand the students' participation in the \"Reading Day\" activity, it was decided to use stratified sampling to extract a sample of 180 students from the entire stu... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"answer": "60",
"index": 178,
"question": "A middle school has a total of 1800 students, including 1200 junior high school students and 600 senior high school students. To understand the students' participation in the \"Reading Day\" activity, it was decided to use stratified sampling to extract a sample of 180... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "There are two four-digit numbers A and B. The common logarithm of A is \\(a + \\lg b\\), where \\(a\\) and \\(b\\) are non-zero digits. The sum of the thousand's place digit and the unit's place digit of B is \\(\\frac{5}{2} b\\), and B is \\(5b + 1\\) less than half of A. Find these two four-digi... | math | {
"ground_truth": "4000 \\text{ and } 1979",
"style": "rule"
} | {
"answer": "4000 \\text{ and } 1979",
"index": 179,
"question": "There are two four-digit numbers A and B. The common logarithm of A is \\(a + \\lg b\\), where \\(a\\) and \\(b\\) are non-zero digits. The sum of the thousand's place digit and the unit's place digit of B is \\(\\frac{5}{2} b\\), and B is \\(5b + ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A cube, whose surface is entirely painted red, is evenly cut into $512$ smaller cubes. These small cubes are then mixed and placed into a bag. Now, if one cube is randomly taken out from the bag, the probability that exactly two faces are painted red is ______. Think step by step and then provide ... | math | {
"ground_truth": "\\dfrac{9}{64}",
"style": "rule"
} | {
"answer": "\\dfrac{9}{64}",
"index": 180,
"question": "A cube, whose surface is entirely painted red, is evenly cut into $512$ smaller cubes. These small cubes are then mixed and placed into a bag. Now, if one cube is randomly taken out from the bag, the probability that exactly two faces are painted red is ___... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The distance between the two parallel lines $3x-\\sqrt{7}y+2=0$ and $6x-2\\sqrt{7}y+3=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<th... | math | {
"ground_truth": "\\frac{1}{8}",
"style": "rule"
} | {
"answer": "\\frac{1}{8}",
"index": 181,
"question": "The distance between the two parallel lines $3x-\\sqrt{7}y+2=0$ and $6x-2\\sqrt{7}y+3=0$ is ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Determine the angle of inclination $\\alpha$ of the straight line $x + \\sqrt{3}y - 1 = 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>",
... | math | {
"ground_truth": "\\frac{5\\pi}{6}",
"style": "rule"
} | {
"answer": "\\frac{5\\pi}{6}",
"index": 182,
"question": "Determine the angle of inclination $\\alpha$ of the straight line $x + \\sqrt{3}y - 1 = 0$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If the angle between the vectors $\\mathbf{a}$ and $\\mathbf{b}$ is $43^\\circ,$ what is the angle between the vectors $-\\mathbf{a}$ and $\\mathbf{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 s... | math | {
"ground_truth": "137",
"style": "rule"
} | {
"answer": "137",
"index": 183,
"question": "If the angle between the vectors $\\mathbf{a}$ and $\\mathbf{b}$ is $43^\\circ,$ what is the angle between the vectors $-\\mathbf{a}$ and $\\mathbf{b}$?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the minimum value of the function $y=xe^{x}$. Express your answer as a single value, including the negative sign if the value is negative. 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": "-\\dfrac{1}{e}",
"style": "rule"
} | {
"answer": "-\\dfrac{1}{e}",
"index": 184,
"question": "Find the minimum value of the function $y=xe^{x}$. Express your answer as a single value, including the negative sign if the value is negative.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given the set of numbers { -3, -2, -1, 4, 5 }, find the largest possible product when three different numbers are multiplied. 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 ... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"answer": "30",
"index": 185,
"question": "Given the set of numbers { -3, -2, -1, 4, 5 }, find the largest possible product when three different numbers are multiplied. Express your answer as a single numerical value.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given $\\sin \\alpha + 2\\sin^2 \\frac{\\alpha}{2} = 2 (0 < \\alpha < \\pi)$, find the value of $\tan \\alpha$. If the value does not exist, indicate that it is undefined. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and... | math | {
"ground_truth": "undefined",
"style": "rule"
} | {
"answer": "undefined",
"index": 186,
"question": "Given $\\sin \\alpha + 2\\sin^2 \\frac{\\alpha}{2} = 2 (0 < \\alpha < \\pi)$, find the value of $\tan \\alpha$. If the value does not exist, indicate that it is undefined.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Find the equation of the tangent line to the curve $y=e^{x}+x$ at the point $(0,1)$. 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>",
"rol... | math | {
"ground_truth": "y=2x+1",
"style": "rule"
} | {
"answer": "y=2x+1",
"index": 187,
"question": "Find the equation of the tangent line to the curve $y=e^{x}+x$ at the point $(0,1)$.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "A courier named Zhang Hai delivered packages in the third week of June with the following distribution: 1 day with 41 packages, 2 days with 35 packages, and 4 days with 37 packages. Calculate Zhang Hai's average daily delivery package count for that week. Express your answer in packages. Think ste... | math | {
"ground_truth": "37",
"style": "rule"
} | {
"answer": "37",
"index": 188,
"question": "A courier named Zhang Hai delivered packages in the third week of June with the following distribution: 1 day with 41 packages, 2 days with 35 packages, and 4 days with 37 packages. Calculate Zhang Hai's average daily delivery package count for that week. Express your ... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "One cup contains 5 spoons of tea, and another contains 5 spoons of milk. A spoon of milk is transferred from the second cup to the first, and then a spoon of the mixture (tea with milk) is transferred back from the first cup to the second. Which quantity is greater: tea in the milk or milk in the ... | math | {
"ground_truth": "They\\ are\\ equal",
"style": "rule"
} | {
"answer": "They\\ are\\ equal",
"index": 189,
"question": "One cup contains 5 spoons of tea, and another contains 5 spoons of milk. A spoon of milk is transferred from the second cup to the first, and then a spoon of the mixture (tea with milk) is transferred back from the first cup to the second. Which quantit... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Given a sphere O with radius R, there are two points A and B on its surface, and $$\\angle AOB= \\frac {\\pi }{6}$$. The spherical distance between points A and B is __________. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> ta... | math | {
"ground_truth": "\\frac {\\pi }{6}R",
"style": "rule"
} | {
"answer": "\\frac {\\pi }{6}R",
"index": 190,
"question": "Given a sphere O with radius R, there are two points A and B on its surface, and $$\\angle AOB= \\frac {\\pi }{6}$$. The spherical distance between points A and B is __________.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "What shape must a plug have so that it can fit into three types of holes: triangular, square, and circular? 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> ta... | math | {
"ground_truth": "Reuleaux Triangle",
"style": "rule"
} | {
"answer": "Reuleaux Triangle",
"index": 191,
"question": "What shape must a plug have so that it can fit into three types of holes: triangular, square, and circular?",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "It is known that $O$ is the origin of the coordinate system, $\\overrightarrow{OA} = (-3, 1)$, $\\overrightarrow{OB} = (0, 5)$, and $\\overrightarrow{AC} \\parallel \\overrightarrow{OA}$, $\\overrightarrow{BC} \\perp \\overrightarrow{AB}$. Find the coordinates of point $C$. Think step by step and ... | math | {
"ground_truth": "(12, -4)",
"style": "rule"
} | {
"answer": "(12, -4)",
"index": 192,
"question": "It is known that $O$ is the origin of the coordinate system, $\\overrightarrow{OA} = (-3, 1)$, $\\overrightarrow{OB} = (0, 5)$, and $\\overrightarrow{AC} \\parallel \\overrightarrow{OA}$, $\\overrightarrow{BC} \\perp \\overrightarrow{AB}$. Find the coordinates of... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "In the Cartesian coordinate system, let the vertices of triangle $ABC$ be $A(0,a)$, $B(b,0)$, $C(c,0)$, and point $P(0,p)$ lies on segment $AO$ (other than the endpoints), where $a$, $b$, $c$, and $p$ are all non-zero real numbers. Lines $BP$ and $CP$ intersect $AC$ and $AB$ at points $E$ and $F$,... | math | {
"ground_truth": "\\left(\\frac{1}{b}-\\frac{1}{c}\\right)x - \\left(\\frac{1}{p}-\\frac{1}{a}\\right)y = 0",
"style": "rule"
} | {
"answer": "\\left(\\frac{1}{b}-\\frac{1}{c}\\right)x - \\left(\\frac{1}{p}-\\frac{1}{a}\\right)y = 0",
"index": 193,
"question": "In the Cartesian coordinate system, let the vertices of triangle $ABC$ be $A(0,a)$, $B(b,0)$, $C(c,0)$, and point $P(0,p)$ lies on segment $AO$ (other than the endpoints), where $a$,... |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Solve the inequality system $\\left\\{\\begin{array}{l}{2(x-1)<x+1}\\\\{1-\\frac{2x+5}{3}\\leq x}\\end{array}\\right.$, and write down its positive integer solutions. 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": "1 \\text{ and } 2",
"style": "rule"
} | {
"answer": "1 \\text{ and } 2",
"index": 194,
"question": "Solve the inequality system $\\left\\{\\begin{array}{l}{2(x-1)<x+1}\\\\{1-\\frac{2x+5}{3}\\leq x}\\end{array}\\right.$, and write down its positive integer solutions.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "If $S_n$ is the sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$, and $S_9=-36$, $S_{13}=-104$, then the geometric mean of $a_5$ and $a_7$ is ______. Think step by step and then provide the final answer. The reasoning process should be enclosed within <think></think> tags and the f... | math | {
"ground_truth": "±4\\sqrt{2}",
"style": "rule"
} | {
"answer": "±4\\sqrt{2}",
"index": 195,
"question": "If $S_n$ is the sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$, and $S_9=-36$, $S_{13}=-104$, then the geometric mean of $a_5$ and $a_7$ is ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Solve the inequality system: $\\left\\{\\begin{array}{}2x+5\\leqslant 3\\left(x+2\\right) \\\\ 2x-\\dfrac{1+3x}{2} \\lt 1\\end{array}\\right.$, and write down its non-negative integer solutions. Think step by step and then provide the final answer. The reasoning process should be enclosed within <... | math | {
"ground_truth": "0, 1, 2, 3",
"style": "rule"
} | {
"answer": "0, 1, 2, 3",
"index": 196,
"question": "Solve the inequality system: $\\left\\{\\begin{array}{}2x+5\\leqslant 3\\left(x+2\\right) \\\\ 2x-\\dfrac{1+3x}{2} \\lt 1\\end{array}\\right.$, and write down its non-negative integer solutions.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "When $x=3$, $px^{3}+qx+1=2018$. Then when $x=-3$, the value of $px^{3}+qx+1$ 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": "-2016",
"style": "rule"
} | {
"answer": "-2016",
"index": 197,
"question": "When $x=3$, $px^{3}+qx+1=2018$. Then when $x=-3$, the value of $px^{3}+qx+1$ is ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "The coordinates of the focus of the parabola $x=- \\frac {1}{4}y^{2}$ 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":... | math | {
"ground_truth": "(-1,0)",
"style": "rule"
} | {
"answer": "(-1,0)",
"index": 198,
"question": "The coordinates of the focus of the parabola $x=- \\frac {1}{4}y^{2}$ are ______.",
"split": "train"
} |
SynthLabsAI/Big-Math-RL-Verified | [
{
"content": "Calculate: $(2x^{-1}y^{3})^{2}\\div (x^{-3}y^{6})$. 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": "4x",
"style": "rule"
} | {
"answer": "4x",
"index": 199,
"question": "Calculate: $(2x^{-1}y^{3})^{2}\\div (x^{-3}y^{6})$.",
"split": "train"
} |
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