data_source stringclasses 3
values | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict | responses sequencelengths 2 2 |
|---|---|---|---|---|---|
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 0,
"split": "train"
} | [
"To ensure the piecewise function \\( f(x) \\) is continuous, we need to ensure that there are no jumps or breaks at the points where the function definition changes, i.e., at \\( x = 2 \\) and \\( x = -2 \\).\n\nThe function is defined as:\n\\[ f(x) = \\left\\{\n\\begin{array}{cl} \nax+3, & \\text{if } x>2, \\\\\n... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "98",
"style": "rule"
} | {
"index": 1,
"split": "train"
} | [
"To solve this problem, we need to set up a system of equations based on the information given. Let's denote the number of band members by \\( N \\), the number of members in each row by \\( m \\), and the number of rows by \\( r \\). We know the following:\n\n1. When arranged in a rectangular formation, there are ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 2,
"split": "train"
} | [
"To determine the degree of the polynomial \\(4 + 5x^3 + 100 + 2\\pi x^4 + \\sqrt{10}x^4 + 9\\), we need to follow these steps:\n\n1. **Combine like terms**: Identify and combine the constant terms and the terms with the same degree of \\(x\\).\n - The constant terms are \\(4\\), \\(100\\), and \\(9\\). Adding th... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "17",
"style": "rule"
} | {
"index": 3,
"split": "train"
} | [
"To evaluate \\(\\left\\lceil3\\left(6-\\frac{1}{2}\\right)\\right\\rceil\\), we need to follow these steps:\n\n1. **Simplify inside the parentheses:**\n \\[\n 6 - \\frac{1}{2} = \\frac{12}{2} - \\frac{1}{2} = \\frac{11}{2}\n \\]\n\n2. **Multiply by 3:**\n \\[\n 3 \\left( \\frac{11}{2} \\right) = \\frac{3... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 4,
"split": "train"
} | [
"To solve this problem, we need to determine how many days Sam did not work. Let's define the variables and set up the equations based on the information given:\n\n1. Let \\( x \\) be the number of days Sam worked.\n2. Let \\( y \\) be the number of days Sam did not work.\n\nFrom the problem, we know two things:\n1... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "(3, -1)",
"style": "rule"
} | {
"index": 5,
"split": "train"
} | [
"To find the center of the circle given by the equation \\(x^2 - 6x + y^2 + 2y = 9\\), we need to rewrite the equation in the standard form of a circle's equation, which is \\((x - h)^2 + (y - k)^2 = r^2\\). Here, \\((h, k)\\) is the center of the circle and \\(r\\) is the radius.\n\nThe given equation is:\n\\[x^2 ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "[0,3)",
"style": "rule"
} | {
"index": 6,
"split": "train"
} | [
"To solve the inequality \\(\\frac{3(pq^2 + p^2q + 3q^2 + 3pq)}{p+q} > 2p^2q\\) for all \\(q > 0\\), we will first simplify the inequality step by step.\n\n1. **Simplify the numerator:**\n \\[\n 3(pq^2 + p^2q + 3q^2 + 3pq) = 3pq^2 + 3p^2q + 9q^2 + 9pq\n \\]\n So the inequality becomes:\n \\[\n \\frac{3p... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "\\$42409",
"style": "rule"
} | {
"index": 9,
"split": "train"
} | [
"To solve this problem, we need to use the formula for compound interest, which is given by:\n\n\\[ A = P \\left(1 + \\frac{r}{n}\\right)^{nt} \\]\n\nwhere:\n- \\( A \\) is the amount of money accumulated after n years, including interest.\n- \\( P \\) is the principal amount (the amount of money invested).\n- \\( ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 10,
"split": "train"
} | [
"To find the center of the circle, we need to determine the midpoint of the diameter. The midpoint of a line segment with endpoints \\((x_1, y_1)\\) and \\((x_2, y_2)\\) is given by the formula:\n\n\\[\n\\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right)\n\\]\n\nHere, the endpoints of the diameter are \\((9... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "k = \\frac{-33}{2}",
"style": "rule"
} | {
"index": 11,
"split": "train"
} | [
"To solve for the value of \\( k \\) in the given functions \\( f(x) = 5x^2 - \\frac{1}{x} + 3 \\) and \\( g(x) = x^2 - k \\), given that \\( f(2) - g(2) = 2 \\), we will follow these steps:\n\n1. **Calculate \\( f(2) \\):**\n \\[\n f(x) = 5x^2 - \\frac{1}{x} + 3\n \\]\n Substitute \\( x = 2 \\):\n \\[\n ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "10\\frac{1}{12}",
"style": "rule"
} | {
"index": 16,
"split": "train"
} | [
"To solve the equation \\( x - \\lfloor x \\rfloor = \\frac{1}{\\lfloor x \\rfloor} \\), let's denote \\( \\lfloor x \\rfloor = n \\), where \\( n \\) is an integer. Then, we can express \\( x \\) as \\( x = n + f \\), where \\( f \\) is the fractional part of \\( x \\) such that \\( 0 \\leq f < 1 \\).\n\nSubstitut... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 17,
"split": "train"
} | [
"To ensure the function \\( f(x) \\) is continuous at \\( x = 2 \\), the left-hand limit as \\( x \\) approaches 2 must equal the right-hand limit as \\( x \\) approaches 2, and both must equal \\( f(2) \\).\n\nThe function \\( f(x) \\) is defined as:\n\\[ f(x) =\n\\begin{cases}\n2x^2 - 3 & \\text{if } x \\le 2, \\... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 18,
"split": "train"
} | [
"To ensure the function \\( f(x) \\) is continuous at \\( x = 3 \\), the left-hand limit as \\( x \\) approaches 3 must equal the right-hand limit as \\( x \\) approaches 3, and both must equal \\( f(3) \\).\n\nThe function \\( f(x) \\) is defined as:\n\\[ f(x) =\n\\begin{cases}\n3x^2 + 2 & \\text{if } x \\le 3, \\... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"index": 19,
"split": "train"
} | [
"To solve this problem, we need to determine the rate at which the faucets fill the tub and then use that rate to find out how long it takes for six faucets to fill a 25-gallon tub.\n\n1. **Determine the rate at which one faucet fills the tub:**\n - Three faucets fill a 100-gallon tub in 6 minutes.\n - Therefor... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "(0,5)",
"style": "rule"
} | {
"index": 20,
"split": "train"
} | [
"To find the point where the line containing the points \\((1, 7)\\) and \\((3, 11)\\) intersects the \\(y\\)-axis, we need to determine the equation of the line first. The equation of a line in slope-intercept form is given by:\n\n\\[ y = mx + b \\]\n\nwhere \\(m\\) is the slope and \\(b\\) is the y-intercept. \n\... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 21,
"split": "train"
} | [
"To find the coefficient of the \\(x^2\\) term in the expansion of the product \\((ax^3 + 3x^2 - 2x)(bx^2 - 7x - 4)\\), we need to identify the terms in the expansion that will result in \\(x^2\\). We do this by considering the product of each term in the first polynomial with each term in the second polynomial and... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "192",
"style": "rule"
} | {
"index": 22,
"split": "train"
} | [
"To solve the problem, we need to determine the function \\( f \\) and then find its inverse \\( f^{-1} \\) such that \\( f^{-1}(64) \\) is found. Let's break it down step by step:\n\n1. **Understanding the given conditions:**\n - We know that \\( f(3) = 1 \\).\n - We also know that \\( f(2x) = 2f(x) \\) for al... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"index": 23,
"split": "train"
} | [
"To solve the problem, we need to use the properties of quadratic equations. The given quadratic equation is \\(x^2 + kx + 5 = 0\\). Let's denote the roots of this equation by \\(\\alpha\\) and \\(\\beta\\). According to the problem, the roots differ by \\(\\sqrt{61}\\), so we can write:\n\n\\[\n\\alpha - \\beta = ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "\\frac{20}{3}",
"style": "rule"
} | {
"index": 24,
"split": "train"
} | [
"To solve the equation \\(\\frac{\\sqrt{3x+5}}{\\sqrt{6x+5}} = \\frac{\\sqrt{5}}{3}\\), we will follow these steps:\n\n1. **Square both sides to eliminate the square roots:**\n \\[\n \\left(\\frac{\\sqrt{3x+5}}{\\sqrt{6x+5}}\\right)^2 = \\left(\\frac{\\sqrt{5}}{3}\\right)^2\n \\]\n This simplifies to:\n \... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "58",
"style": "rule"
} | {
"index": 25,
"split": "train"
} | [
"To find the area of the square, we first need to determine the side length of the square. The side length is the distance between the given adjacent vertices \\((-1, 4)\\) and \\((2, -3)\\). The distance \\(d\\) between two points \\((x_1, y_1)\\) and \\((x_2, y_2)\\) in the coordinate plane is given by the distan... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 26,
"split": "train"
} | [
"To solve the inequality \\( n^2 - 11n + 24 \\leq 0 \\), we first need to find the roots of the corresponding equation \\( n^2 - 11n + 24 = 0 \\). This is a quadratic equation, and we can solve it by factoring.\n\nThe quadratic equation \\( n^2 - 11n + 24 = 0 \\) can be factored as:\n\\[ (n - 3)(n - 8) = 0 \\]\n\nS... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 27,
"split": "train"
} | [
"To solve the equation \\( |x + 5| = 20 \\), we need to consider the definition of the absolute value function. The equation \\( |x + 5| = 20 \\) means that \\( x + 5 \\) can be either 20 or -20. Therefore, we have two cases to consider:\n\n1. \\( x + 5 = 20 \\)\n2. \\( x + 5 = -20 \\)\n\nLet's solve each case sepa... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "71",
"style": "rule"
} | {
"index": 28,
"split": "train"
} | [
"To solve for \\( 11 \\# 5 \\) using the given conditions, let's first analyze the conditions provided:\n\n1. \\( r \\# 0 = r \\)\n2. \\( r \\# s = s \\# r \\)\n3. \\( (r + 1) \\# s = (r \\# s) + s + 1 \\)\n\nWe need to find the value of \\( 11 \\# 5 \\). Let's use the third condition to express \\( 11 \\# 5 \\) in... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 29,
"split": "train"
} | [
"To solve the equation \\((x+2)(x-3) = 14\\), we first need to expand and rearrange it into a standard quadratic equation form.\n\n1. Expand the left side of the equation:\n \\[\n (x+2)(x-3) = x^2 - 3x + 2x - 6 = x^2 - x - 6\n \\]\n So the equation becomes:\n \\[\n x^2 - x - 6 = 14\n \\]\n\n2. Move 14... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "\\sqrt{2}+1",
"style": "rule"
} | {
"index": 30,
"split": "train"
} | [
"To rationalize the denominator of the expression \\(\\frac{1}{\\sqrt{2}-1}\\), we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of \\(\\sqrt{2}-1\\) is \\(\\sqrt{2}+1\\).\n\nHere are the ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "103",
"style": "rule"
} | {
"index": 31,
"split": "train"
} | [
"To solve this problem, we need to use the formula for the \\(n\\)-th term of an arithmetic sequence, which is given by:\n\n\\[ a_n = a_1 + (n-1)d \\]\n\nwhere:\n- \\(a_n\\) is the \\(n\\)-th term,\n- \\(a_1\\) is the first term,\n- \\(d\\) is the common difference,\n- \\(n\\) is the term number.\n\nWe are given th... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "-30",
"style": "rule"
} | {
"index": 32,
"split": "train"
} | [
"To simplify the expression \\((2x - 5)(x + 7) - (x + 5)(2x - 1)\\), we need to expand each term and then combine like terms. Let's do this step by step.\n\nFirst, expand \\((2x - 5)(x + 7)\\):\n\\[\n(2x - 5)(x + 7) = 2x \\cdot x + 2x \\cdot 7 - 5 \\cdot x - 5 \\cdot 7 = 2x^2 + 14x - 5x - 35 = 2x^2 + 9x - 35\n\\]\n... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 34,
"split": "train"
} | [
"To find the value of \\( x \\) that gives the minimum value of the quadratic function \\( f(x) = 2x^2 - 12x + 3 \\), we need to use the vertex formula for a parabola. The vertex form of a quadratic function \\( ax^2 + bx + c \\) gives the \\( x \\)-coordinate of the vertex (which is the minimum or maximum point of... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "8.75",
"style": "rule"
} | {
"index": 35,
"split": "train"
} | [
"To solve the problem \\( x \\cdot \\lfloor x \\rfloor = 70 \\) for a positive \\( x \\), we need to understand the relationship between \\( x \\) and its floor value \\( \\lfloor x \\rfloor \\). Let's denote \\( \\lfloor x \\rfloor \\) by \\( n \\). Since \\( n \\) is the floor of \\( x \\), we know that \\( n \\l... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "2, 3, \\text{ and } 4",
"style": "rule"
} | {
"index": 38,
"split": "train"
} | [
"To determine the possible positive integer values of \\( x \\) such that the triangle with sides \\( 7 \\), \\( 10 \\), and \\( x^2 \\) exists, we need to use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remai... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 39,
"split": "train"
} | [
"To solve the problem, we need to find an integer \\( x \\) such that the square of the integer is 182 greater than the integer itself. This can be expressed with the equation:\n\n\\[ x^2 = x + 182 \\]\n\nFirst, we rearrange the equation to standard quadratic form:\n\n\\[ x^2 - x - 182 = 0 \\]\n\nNext, we solve thi... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "95",
"style": "rule"
} | {
"index": 40,
"split": "train"
} | [
"To find the maximum height of the ball, we need to determine the vertex of the parabolic equation given by the height expression \\( h(t) = -16t^2 + 64t + 31 \\). The equation is in the standard form of a quadratic equation \\( h(t) = at^2 + bt + c \\), where \\( a = -16 \\), \\( b = 64 \\), and \\( c = 31 \\).\n\... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"index": 41,
"split": "train"
} | [
"To determine Karen's average speed, we need to calculate the total time she drove and then use the formula for average speed, which is:\n\n\\[\n\\text{Average Speed} = \\frac{\\text{Total Distance}}{\\text{Total Time}}\n\\]\n\nFirst, we need to find the total time Karen drove. She drove from 9:40 a.m. to 1:20 p.m.... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 42,
"split": "train"
} | [
"To determine the greatest integer value of \\( b \\) for which the expression \\(\\frac{9x^3+4x^2+11x+7}{x^2+bx+8}\\) has a domain of all real numbers, we need to ensure that the denominator \\( x^2 + bx + 8 \\) is never equal to zero. This means the quadratic equation \\( x^2 + bx + 8 = 0 \\) should have no real ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 43,
"split": "train"
} | [
"To solve the problem of expressing \\(\\frac{0.\\overline{666}}{1.\\overline{333}}\\) as a common fraction, we need to first convert the repeating decimals into fractions.\n\n1. **Convert \\(0.\\overline{666}\\) to a fraction:**\n\n Let \\(x = 0.\\overline{666}\\).\n Then, \\(10x = 6.\\overline{666}\\).\n Su... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 45,
"split": "train"
} | [
"To find the equation of the line in the form \\( y = mx + b \\), we need to use the given slope \\( m = -7 \\) and the point \\( (3, 0) \\). The point-slope form of a line's equation is:\n\n\\[ y - y_1 = m(x - x_1) \\]\n\nwhere \\( (x_1, y_1) \\) is a point on the line and \\( m \\) is the slope. Substituting the ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 46,
"split": "train"
} | [
"To solve the problem, we need to rewrite the equation of the circle in standard form. The given equation is:\n\n\\[ x^2 - 6y - 3 = -y^2 - 4x \\]\n\nFirst, let's rearrange the terms to bring all variables to one side of the equation:\n\n\\[ x^2 + 4x + y^2 - 6y = 3 \\]\n\nNext, we complete the square for the \\(x\\)... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 47,
"split": "train"
} | [
"To solve the problem, we need to evaluate the functions \\( f(x) \\) and \\( g(x) \\) at \\( x = 4 \\) and use the given condition \\( 2f(4) = g(4) \\) to find the value of \\( m \\).\n\nFirst, let's write down the functions:\n\\[ f(x) = x^2 - 2x + m \\]\n\\[ g(x) = x^2 - 2x + 4m \\]\n\nNext, we evaluate \\( f(x) ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "729",
"style": "rule"
} | {
"index": 48,
"split": "train"
} | [
"To solve the problem of finding the product of all constants \\( t \\) such that the quadratic \\( x^2 + tx - 10 \\) can be factored into the form \\( (x+a)(x+b) \\), where \\( a \\) and \\( b \\) are integers, we need to follow these steps:\n\n1. **Understanding the factorization form**:\n The quadratic \\( x^2... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "-29x^5(7x^6-2)",
"style": "rule"
} | {
"index": 49,
"split": "train"
} | [
"To factor the expression \\(58x^5 - 203x^{11}\\), we need to follow these steps:\n\n1. **Identify the greatest common factor (GCF) of the coefficients:**\n The coefficients are 58 and 203. We need to find the GCF of these two numbers.\n - The prime factorization of 58 is \\(2 \\times 29\\).\n - The prime fac... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "66",
"style": "rule"
} | {
"index": 53,
"split": "train"
} | [
"To solve the problem, we start with the given equation:\n\n\\[ m + \\frac{1}{m} = 8 \\]\n\nWe need to find the value of \\( m^2 + \\frac{1}{m^2} + 4 \\). To do this, we first square the given equation:\n\n\\[ \\left( m + \\frac{1}{m} \\right)^2 = 8^2 \\]\n\nExpanding the left side, we get:\n\n\\[ m^2 + 2 \\cdot m ... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"index": 54,
"split": "train"
} | [
"To solve the quadratic equation \\(11x^2 - 44x - 99 = 0\\) by completing the square, we need to follow these steps:\n\n1. **Divide the entire equation by 11** to simplify it:\n \\[\n x^2 - 4x - 9 = 0\n \\]\n\n2. **Move the constant term to the other side of the equation**:\n \\[\n x^2 - 4x = 9\n \\]\n\... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "-\\frac12",
"style": "rule"
} | {
"index": 55,
"split": "train"
} | [
"To evaluate \\(\\log_3 \\frac{1}{\\sqrt{3}}\\), let's break it down step by step:\n\n1. **Simplify the argument of the logarithm:**\n \\[\n \\frac{1}{\\sqrt{3}} = 3^{-\\frac{1}{2}}\n \\]\n This is because \\(\\sqrt{3} = 3^{\\frac{1}{2}}\\) and taking the reciprocal gives us \\(3^{-\\frac{1}{2}}\\).\n\n2. *... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 57,
"split": "train"
} | [
"To solve the equation \\( |x-7| = |x+1| \\), we need to consider the definition of the absolute value function. The absolute value equation \\( |A| = |B| \\) implies that \\( A = B \\) or \\( A = -B \\). Applying this to our equation, we get two cases to consider:\n\n1. \\( x-7 = x+1 \\)\n2. \\( x-7 = -(x+1) \\)\n... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 58,
"split": "train"
} | [
"To solve the equation \\( |y-6| + 2y = 9 \\), we need to consider the definition of the absolute value function. The absolute value \\( |y-6| \\) can be broken down into two cases: when \\( y-6 \\geq 0 \\) and when \\( y-6 < 0 \\).\n\n**Case 1: \\( y-6 \\geq 0 \\) which simplifies to \\( y \\geq 6 \\)**\n\nIn this... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "\\frac{9}{2}",
"style": "rule"
} | {
"index": 59,
"split": "train"
} | [
"To solve the problem, we need to use the properties of quadratic equations and their roots. Let's start by identifying the roots and using the given information step by step.\n\n1. **Identify the roots of the first quadratic equation:**\n The equation \\(x^2 - mx + 2 = 0\\) has roots \\(a\\) and \\(b\\). By Viet... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "-80\\leq g(x)\\leq 82",
"style": "rule"
} | {
"index": 60,
"split": "train"
} | [
"To solve the problem, we need to understand the function \\( g(x) = f(f(f(f(x)))) \\) where \\( f(x) = 3x - 2 \\). We will compute the expression for \\( g(x) \\) step by step.\n\n1. **Compute \\( f(f(x)) \\):**\n \\[\n f(f(x)) = f(3x - 2) = 3(3x - 2) - 2 = 9x - 6 - 2 = 9x - 8\n \\]\n\n2. **Compute \\( f(f(f... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"index": 61,
"split": "train"
} | [
"To find the center of the circle given by the equation \\(x^2 + y^2 = -2x - 10y - 16\\), we need to rewrite the equation in the standard form of a circle's equation, which is \\((x - h)^2 + (y - k)^2 = r^2\\). Here, \\((h, k)\\) is the center of the circle and \\(r\\) is the radius.\n\nStarting with the given equa... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "5-12i",
"style": "rule"
} | {
"index": 63,
"split": "train"
} | [
"To simplify \\((3-2i)^2\\), we need to use the formula for the square of a binomial, which is \\((a-b)^2 = a^2 - 2ab + b^2\\). Here, \\(a = 3\\) and \\(b = 2i\\).\n\nSo, we have:\n\\[\n(3-2i)^2 = 3^2 - 2 \\cdot 3 \\cdot 2i + (2i)^2\n\\]\n\nNow, let's calculate each term separately:\n1. \\(3^2 = 9\\)\n2. \\(-2 \\cd... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 65,
"split": "train"
} | [
"To solve this problem, we need to understand the relationship between the terms of the sequence. Since each term (after the first) is inversely proportional to the term preceding it, we can express this relationship as:\n\n\\[ a_{n} \\cdot a_{n-1} = k \\]\n\nwhere \\( a_{n} \\) is the \\( n \\)-th term, \\( a_{n-1... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "169",
"style": "rule"
} | {
"index": 66,
"split": "train"
} | [
"To solve this problem, we need to maximize the sum of the four products \\(fg + gh + hj + fj\\). We know the values of \\(f\\), \\(g\\), \\(h\\), and \\(j\\) are 5, 6, 7, and 8, but not necessarily in that order. Let's denote the sum by \\(S\\):\n\n\\[ S = fg + gh + hj + fj \\]\n\nTo maximize \\(S\\), we should tr... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "-112",
"style": "rule"
} | {
"index": 67,
"split": "train"
} | [
"To solve the problem, we first need to find the solutions \\( p \\) and \\( q \\) to the equation \\((x-5)(2x+9) = x^2 - 13x + 40\\).\n\n1. **Expand and simplify the equation:**\n \\[\n (x-5)(2x+9) = 2x^2 + 9x - 10x - 45 = 2x^2 - x - 45\n \\]\n So the equation becomes:\n \\[\n 2x^2 - x - 45 = x^2 - 13x... |
DigitalLearningGmbH/MATH-lighteval-r1 | [
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 68,
"split": "train"
} | [
"To solve the problem of finding how many integers \\( n \\) satisfy the inequality \\(\\sqrt{n} \\le \\sqrt{4n - 6} < \\sqrt{2n + 5}\\), we need to break it down into two parts and solve each part step by step.\n\n### Part 1: \\(\\sqrt{n} \\le \\sqrt{4n - 6}\\)\n\nFirst, we square both sides of the inequality to e... |
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