data_source stringclasses 1
value | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | sub_source stringclasses 6
values |
|---|---|---|---|---|---|
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Tom ordered 5 pairs of black socks and a certain number of pairs of blue socks. The price per pair of black socks was three times that of the blue socks. When the order was fille... | math | {
"ground_truth": "C) 7:19",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the length of side QR in an isosceles triangle PQRS with PQ = PR = 5 inches and the median PM from P to the midpoint M of side QR equal to 4 inches.",
"role": "user... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "On each of the cards written in $2013$ by number, all of these $2013$ numbers are different. The cards are turned down by numbers. In a single move is allowed to point out th... | math | {
"ground_truth": "1986",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given points $A(-3,m)$ and $B(-2,n)$ both lie on the hyperbolic function $y=\\frac{k-1}{x}$, and $m \\gt n$, then the range of $k$ is ______.",
"role": "user"
}
] | math | {
"ground_truth": "k > 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "6 books are lined up on a shelf. How many ways are there to arrange them?",
"role": "user"
}
] | math | {
"ground_truth": "720",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "There are three buckets, X, Y, and Z. The average weight of the watermelons in bucket X is 60 kg, the average weight of the watermelons in bucket Y is 70 kg. The average weight o... | math | {
"ground_truth": "69",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Ankit, Box, and Clark are taking the tiebreakers for the geometry round, consisting of three problems. Problem $k$ takes each $k$ minutes to solve. If for any given problem t... | math | {
"ground_truth": "\\frac{19}{27}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An equilateral triangle of side $x$ has its vertices on the sides of a square side $1$ . What are the possible values of $x$ ?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2\\sqrt{3}}{3}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that circle C passes through points M(0, -2) and N(3, 1), and that the center of circle C lies on the line x + 2y + 1 = 0.\n(Ⅰ) Find the equation of circle C;\n(Ⅱ) Construc... | math | {
"ground_truth": "y = x - 4",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A circular gate features a decorative \"cookie-bite\" cutout that forms part of the design. The gate's overall circular shape has a radius of 2 cm, and the cutout, which is a sec... | math | {
"ground_truth": "3\\pi + 4 \\text{ cm}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the condition under which the equation $\\sqrt{a^2+(kb)^2}=a+kb$ is true, where $a$ and $b$ are real numbers, and $k$ is a positive integer.",
"role": "user"
}
] | math | {
"ground_truth": "(akb = 0) \\land (a + kb \\geq 0)",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "By dividing $2023$ by a natural number $m$ , the remainder is $23$ . How many numbers $m$ are there with this property?",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a triangle \\(ABC\\) with an area of 2. Points \\(P\\), \\(Q\\), and \\(R\\) are taken on the medians \\(AK\\), \\(BL\\), and \\(CN\\) of the triangle \\(ABC\\) respectivel... | math | {
"ground_truth": "\\frac{1}{6}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the complex number $Z=\\log(m^2-2m-2)+(m^2+3m+2)i$. Find the values of $m$ for which \n(1) $Z$ is a real number; \n(2) $Z$ is a pure imaginary number.",
"role": "user"
... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph of \\[\\frac{x^2}{c^2} + \\frac{y^2}{d^2} = 1\\] has its foci at $(0,\\pm 5),$ while the graph of \\[\\frac{x^2}{c^2} - \\frac{y^2}{d^2} = 1\\] has its foci at $(\\pm 8... | math | {
"ground_truth": "\\sqrt{\\frac{39 \\times 89}{4}}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the domain of the function $y = \\sqrt{x^2 - 5x - 6}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Domain}: (-\\infty, -1] \\cup [6, +\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $a,$ $b,$ and $c$ be distinct real numbers such that\n\\[\n\\frac{a^3 + 9}{a} = \\frac{b^3 + 9}{b} = \\frac{c^3 + 9}{c}.\n\\]\nFind $a^3 + b^3 + c^3.$",
"role": "user"
... | math | {
"ground_truth": "-27",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An equilateral triangle $ABC$ shares a common side $BC$ with a regular hexagon $BCDEFG,$ as pictured. What is the number of degrees in $\\angle FAG$ (not pictured)? [asy]\npair p... | math | {
"ground_truth": "0^\\circ.",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "We call a positive integer balanced if\n- it has six digits,\n- each of its six digits is non-zero, and\n- the product of its first three digits is equal to the product of its la... | math | {
"ground_truth": "4, 5 and 8",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $ABCDE$ be an equilateral and equiangular convex pentagon of perimeter $2$. Each side of the pentagon is extended to form a five-pointed star. Compute the perimeter of this s... | math | {
"ground_truth": "6.472",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The fourth and seventh terms of a geometric sequence of real numbers are $6!$ and $7!$ respectively. What is the first term?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{720}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a square of side length 4, a point on the interior of the square is randomly chosen and a circle of radius 1 is drawn centered at the point. What is the probability that the c... | math | {
"ground_truth": "\\frac{\\pi + 8}{16}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "1. Find the standard equation of an ellipse with a major axis length of 20 and an eccentricity of $\\frac{3}{5}$.\n2. Given that point P is on the ellipse $\\frac{x^2}{5} + \\fra... | math | {
"ground_truth": "\\left(\\frac{\\sqrt{15}}{2}, -1\\right)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a sequence $\\{a_{n}\\}$ where $a_{1}=3$, $a_{2}=46$, and ${a_{n+2}}=\\sqrt{{a_{n+1}}{a_n}-\\frac{π}{{{a_{n+1}}}}}$, $\\left(\\pi \\approx 3.14\\right)$, find the maximum n... | math | {
"ground_truth": "2022",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The first term of a given sequence is 3, and each successive term is the sum of all the previous terms of the sequence. What is the value of the first term which exceeds 10,000?"... | math | {
"ground_truth": "6144",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $A(-4,0)$, and $B$ is a moving point on the circle $F: (x-4)^2 + y^2 = 4$ (with $F$ as the center of the circle), the perpendicular bisector of segment $AB$ intersects line... | math | {
"ground_truth": "x^2 - \\frac{y^2}{15} = 1 \\ (x \\neq 0)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jordan has $\\frac{60}{7}$ pounds of chocolate and wants to create 5 equal piles. After keeping one pile for himself, he divides the remaining chocolate equally among 3 friends. ... | math | {
"ground_truth": "\\frac{16}{7}",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the quadratic function $y=x^{2}-2x+3$ is factored into the form $y=\\left(x-h\\right)^{2}+k$, then $y=$____.",
"role": "user"
}
] | math | {
"ground_truth": "(x - 1)^2 + 2",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\\\(A\\\\) be a moving point on the circle \\\\(x^{2}+y^{2}-4x-4y+7=0\\\\), then the maximum distance from \\\\(A\\\\) to the line \\\\(x-y-5=0\\\\) is \\_\\_\\_\\_\\_\\_.",... | math | {
"ground_truth": "\\dfrac {5 \\sqrt {2}}{2}+1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Among the following four propositions, the number of correct propositions is ______.\n$(1)$ The negation of the proposition \"If $f(x)$ is a periodic function, then $f(x)$ is a t... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "What is the remainder when $x^3 + 7x^2 + 4$ divides $2x^5 + 11x^4 - 48x^3 - 60x^2 + 20x + 50$?",
"role": "user"
}
] | math | {
"ground_truth": "-27x^3 - 68x^2 + 32x + 50",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given $|\\overrightarrow{a}|=2$, $|\\overrightarrow{b}|=1$, $|\\overrightarrow{a}+\\overrightarrow{b}|=\\sqrt{3}$, find $|\\overrightarrow{a}-\\overrightarrow{b}|$.",
"role":... | math | {
"ground_truth": "\\sqrt{7}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that $\\alpha = 1690^\\circ$, find the value of $\\theta$ in the interval $0^\\circ < \\theta < 360^\\circ$, where $\\theta$ has the same terminal side as $\\alpha$.",
... | math | {
"ground_truth": "250^\\circ",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $n$ points $A_1, A_2, \\ldots, A_n$ , ( $n>2$ ), be considered in the space, where no four points are coplanar. Each pair of points $A_i, A_j$ are connected by an edge. ... | math | {
"ground_truth": "n = 15",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Five people are doing some work. The first, second, and third, working together, complete the work in an hour, just like the second, fourth, and fifth do the work in an hour. The... | math | {
"ground_truth": "\\frac{2}{3} \\text{ hours (40 minutes)}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given plane vectors $\\overrightarrow{a}$, $\\overrightarrow{b}$, $\\overrightarrow{c}$, satisfying $|\\overrightarrow{b}|=2$, $|\\overrightarrow{a}+\\overrightarrow{b}|=1$, $\\o... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Suppose $a$ , $b$ and $c$ are integers such that the greatest common divisor of $x^2+ax+b$ and $x^2+bx+c$ is $x+1$ (in the set of polynomials in $x$ with integer coe... | math | {
"ground_truth": "-6",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the roots of the equation $\\frac{18}{x^2 - 9} - \\frac{3}{x - 3} = 2$.",
"role": "user"
}
] | math | {
"ground_truth": "-4.5",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $M$ be the greatest five-digit number whose digits have a product of $180$. Find the sum of the digits of $M$.",
"role": "user"
}
] | math | {
"ground_truth": "20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $y=f(x)$ that satisfies $f(-x)=-f(x)$ and $f(1+x)=f(1-x)$ for $x \\in [-1,1]$ with $f(x)=x^{3}$, find the value of $f(2015)$.",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest whole number that is larger than the sum\n\\[3\\dfrac{1}{3} + 4\\dfrac{1}{2} + 5\\dfrac{1}{5} + 6\\dfrac{1}{6}.\\]\nA) 19\nB) 20\nC) 21\nD) 22\nE) 23",
"rol... | math | {
"ground_truth": "B) 20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How many positive integers $A$ are there such that if we append $3$ digits to the rightmost of decimal representation of $A$ , we will get a number equal to $1+2+\\cdots + ... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a truncated cone with the top base radius \\( r_1 = 5 \\) cm, bottom base radius \\( r_2 = 10 \\) cm, and slant height \\( A_1A_2 = 20 \\) cm. A string is tied at the midpo... | math | {
"ground_truth": "4 \\, \\text{cm}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The sum of three numbers is $125$. The ratio of the first to the second is $\\frac{3}{4}$, and the ratio of the second to the third is $\\frac{7}{6}$. Find the second number.",
... | math | {
"ground_truth": "\\frac{3500}{73}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x)=\\cos{2\\omega x}-\\sin{(2\\omega x+\\frac{\\pi}{6})}$ where $\\omega>0$, determine the range of values for $\\omega$ such that the function has exactly ... | math | {
"ground_truth": "[\\frac{7}{12},\\frac{13}{12})",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the sum of the first $n$ terms of the sequence ${ a_{n} }$ is $S_{n}=n^{2}-2n-1$, find the value of $a_{1}+a_{17}$.",
"role": "user"
}
] | math | {
"ground_truth": "29",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The coefficient of $x^5y^2$ in the expansion of $(x^2+x+y)^5$ is what?",
"role": "user"
}
] | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let ($a_1$, $a_2$, ... $a_{12}$) be a list of the first 12 positive integers such that for each $2 \\leq i \\leq 12$, exactly one of either $a_i + 1$ or $a_i-1$ (but not both) mu... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of paths from $A$ to $B$ on the picture that go along gridlines only, do not pass through any point twice, and never go upwards?\n![Image](https://cdn.ar... | math | {
"ground_truth": "924",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Add the following binary numbers: $1101_2$, $1010_2$, $111_2$, and $-1011_2$. Express your answer in base $2$.",
"role": "user"
}
] | math | {
"ground_truth": "100011_2",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given Aria, Bella, and Clara each will randomly be assigned a whole number from $1$ to $15$, inclusive, with no two of them getting the same number, calculate the probability tha... | math | {
"ground_truth": "\\textbf{(C) } \\frac{8}{546}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find the smallest integer $k\\ge3$ with the property that it is possible to choose two of the number $1,2,...,k$ in such a way that their product is equal to the sum of the r... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If 1 pint of paint is needed to paint a statue 12 ft. high, how many pints of paint will it take to paint 720 statues, each 2 ft. high, given that the statues are similar in shap... | math | {
"ground_truth": "C) 20",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a certain class, with any distribution of 200 candies, there will be at least two students who receive the same number of candies (possibly none). What is the minimum number o... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The graph below shows the total accumulated dollars (in millions) spent by the Coastal City government during $1990$. For example, about $1.2$ million had been spent by the begin... | math | {
"ground_truth": "\\text{(C)}\\ 3.3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The diagram shows a square with sides of length \\(4 \\text{ cm}\\). Four identical semicircles are drawn with their centers at the midpoints of the square’s sides. Each semicirc... | math | {
"ground_truth": "8 - 2\\pi",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let the function $f(x)=|x+2|-|x-3|-a$ \n(I) When $a=1$, find the maximum value of the function $f(x)$; \n(II) If $f(x) \\leqslant \\frac{4}{a}$ holds for any $x \\in \\mathbb{R... | math | {
"ground_truth": "(0,1] \\cup [4,+\\infty)",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function $f(x) = \\sin 2\\omega x + 2\\cos^2 \\omega x$ where $\\omega > 0$ and the smallest positive period of the function is $\\pi$. \n$(Ⅰ)$ Find the value of $\\om... | math | {
"ground_truth": "[2k\\pi - \\frac{5\\pi}{12}, 2k\\pi + \\frac{7\\pi}{12}], \\quad k \\in \\mathbb{Z}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A unit circle is centered at $(0, 0)$ on the $(x, y)$ plane. A regular hexagon passing through $(1, 0)$ is inscribed in the circle. Two points are randomly selected from th... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that the vertex of angle $\\theta$ is at the origin of the coordinates, the initial side is the non-negative semi-axis of $x$, and $P(-\\frac{3}{5}, \\frac{4}{5})$ is the i... | math | {
"ground_truth": "-\\frac{3}{5}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Alex has an $20 \\times 16$ grid of lightbulbs, initially all off. He has $36$ switches, one for each row and column. Flipping the switch for the $i$ th row will toggle the ... | math | {
"ground_truth": "2^{35}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the sequence of numbers with only even digits in their decimal representation, determine the $2014^\\text{th}$ number in the sequence.",
"role": "user"
}
] | math | {
"ground_truth": "62048",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Janabel sold one widget on the first day. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she ... | math | {
"ground_truth": "400",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the value of the expression $x^2 + y^2 + z^2$ , \n\nif $x + y + z = 13$ , $xyz= 72$ and $\\frac1x + \\frac1y + \\frac1z = \\frac34$ .",
"role": "user"
}
] | math | {
"ground_truth": "61",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In the expansion of $(x+y)^{2}(x-2y)^{4}$, find the coefficient of $x^{2}y^{4}$.",
"role": "user"
}
] | math | {
"ground_truth": "-24",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Determine the number of distinct pairs \\((x, y)\\) of real numbers satisfying both of the equations:\n\\[ x = 3x^2 + y^2 \\]\n\\[ y = 3xy \\]\nA) 0 \nB) 1 \nC) 2 \nD) 3 \nE)... | math | {
"ground_truth": "C) 2",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "A tangent to the circle \\(x^2 + y^2 = 9\\) is drawn from the left focus \\(F\\) of the hyperbola \\(\\frac{x^2}{9} - \\frac{y^2}{16} = 1\\), with the point of tangency being \\(... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "How to cross a desert? A traveler needs to cross 80 km of desert. Each day he can travel 20 km and carry food and water supplies for 3 days. Therefore, he must establish intermed... | math | {
"ground_truth": "\\text{Yes, he can cross the desert in 6 days.}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Simplify the expression $\\dfrac{cx(b^2x^3 + 3b^2y^3 + c^3y^3) + dy(b^2x^3 + 3c^3x^3 + c^3y^3)}{cx + dy}$.",
"role": "user"
}
] | math | {
"ground_truth": "b^2x^3 + 3c^2xy^3 + c^3y^3",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\(a\\) and \\(b\\) be positive real numbers such that \\(a + b = 2.\\) Find the set of all possible values of \\(\\frac{1}{a} + \\frac{1}{b}.\\)",
"role": "user"
}
] | math | {
"ground_truth": "[2, \\infty)",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If \\( b-6, b-5, b-4 \\) are three roots of the equation \\( x^{4} + r x^{2} + s x + t = 0 \\), find the value of \\( c = r + t \\).",
"role": "user"
}
] | math | {
"ground_truth": "-61",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The probability of getting rain on any given day in July in Coastal Town is $\\frac{1}{20}$. What is the probability that it rains on at most 1 day in July? Express your answer a... | math | {
"ground_truth": "0.271",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( a \\) and \\( b \\) be distinct real numbers such that\n\\[\n\\begin{vmatrix} 2 & 5 & 10 \\\\ 4 & a & b \\\\ 4 & b & a \\end{vmatrix} = 0.\n\\]\nFind \\( a + b \\).",
... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given 6 digits: \\(0, 1, 2, 3, 4, 5\\). Find the sum of all four-digit even numbers that can be written using these digits (the same digit can be repeated in a number).",
"ro... | math | {
"ground_truth": "1769580",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "For real positive numbers $x,$ the set $A(x)$ is defined by \r\n\\[A(x)=\\{[nx]\\ | \\ n\\in{ \\mathbb{N}}\\},\\] where $[r]$ denotes the greatest integer not exceeding rea... | math | {
"ground_truth": "\\alpha > 2",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If $\\log_{M^2} N = \\log_N M$ where $M \\neq N$, $MN > 0$, $M \\neq 1$, $N \\neq 1$, determine the value of $MN$.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{a number greater than 1 and less than 2}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Construct a square on one side of an equilateral triangle. On one non-adjacent side of the square, construct a regular pentagon, as shown. On a non-adjacent side of the pentagon,... | math | {
"ground_truth": "23",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a block wall that is 100 feet long and 7 feet high, where blocks are 1 foot high and either 2 feet long or 1 foot long and the vertical joins are staggered, calculate the m... | math | {
"ground_truth": "353",
"style": "rule"
} | {
"id": "numina_amc_aime-0",
"rating": null,
"split": "confidence_train",
"sub_source": "amc_aime"
} | amc_aime |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given that Geely Company produces \"Emgrand\", \"King Kong\", and \"Freedom Ship\" cars with production volumes of 1600, 6000, and 2000 units respectively, and that 48 cars are s... | math | {
"ground_truth": "8, 30, 10",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The function $y=f(x)$ is an even function with the smallest positive period of 4, and when $x \\in [-2, 0]$, $f(x) = 2x + 1$. If there exist $x_1, x_2, \\ldots, x_n$ satisfying $... | math | {
"ground_truth": "1513",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The numbers $p,$ $q,$ $r,$ $s$ are equal to 1, 3, 5, 7, in some order. Find the largest possible value of\n\\[pq + qr + rs + sp.\\]",
"role": "user"
}
] | math | {
"ground_truth": "64",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The ratio of the volume of a rectangular parallelepiped to the volume of a sphere inscribed in it is equal to \\( k \\). Find the angles at the base of the parallelepiped and the... | math | {
"ground_truth": "\\arcsin \\frac{6}{\\pi k} ; \\pi - \\arcsin \\frac{6}{\\pi k} ; k \\geq \\frac{6}{\\pi}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Participants A and B are taking part in a legal knowledge quiz, which consists of 10 different questions, including 6 multiple-choice questions and 4 true/false questions. A and ... | math | {
"ground_truth": "\\frac {13}{15}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "An ice ballerina rotates at a constant angular velocity at one particular point with her arms initially extended. Her moment of inertia is $I$. When she pulls her arms in, her ne... | math | {
"ground_truth": "\\frac{10}{7}",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $A=\\{x | -1 \\lt x \\lt 2\\}$, $B=\\{x | x\\in Z\\}$, then $A\\cap B=\\_\\_\\_\\_\\_\\_$.",
"role": "user"
}
] | math | {
"ground_truth": "\\{0,1\\}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "If the ratio of the legs of a right triangle is $1:3$, and a perpendicular is drawn from the vertex of the right angle to the hypotenuse, what is the ratio of the corresponding s... | math | {
"ground_truth": "\\textbf{(B)}\\ 1:9",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let $z_1,z_2,z_3,\\dots,z_{12}$ be the 12 zeroes of the polynomial $z^{12}-2^{36}$ . For each $j$ , let $w_j$ be one of $z_j$ or $i z_j$ . Then the maximum possible valu... | math | {
"ground_truth": "784",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Let \\( f(x) = x^3 + 3x - 1 \\) have roots \\( a, b, c \\). Given that\n\\[\n\\frac{1}{a^3 + b^3} + \\frac{1}{b^3 + c^3} + \\frac{1}{c^3 + a^3}\n\\]\ncan be written as \\( \\frac... | math | {
"ground_truth": "3989",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Calculate the value of the expression $\\sqrt{25\\sqrt{25\\sqrt{25}}}$.\nA) $5 \\sqrt{5}$\nB) $5 \\sqrt[4]{125}$\nC) $25 \\sqrt[4]{5}$\nD) $5 \\cdot 5^{0.75}$\nE) $5 \\cdot \\sqr... | math | {
"ground_truth": "5 \\sqrt[4]{125}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The necessary and sufficient condition for the function $f(x) = a\\ln x - b\\sin x + 3$ to have an inverse function is $a=0$ and $b\\neq0$.",
"role": "user"
}
] | math | {
"ground_truth": "b=0\\text{ and }a\\neq0",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The area of the enclosed shape formed by the curves $y=x^2$ and $y=x^3$ is __________.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{12}",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "<u>Round 1</u>**p1.** The fractal T-shirt for this year's Duke Math Meet is so complicated that the printer broke trying to print it. Thus, we devised a method for manually assem... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Solve the equation\n\n$$\n2x + 2 + \\operatorname{arctg} (x) \\cdot \\sqrt{x^{2}+1} + \\operatorname{arctg}(x+2) \\cdot \\sqrt{x^{2}+4x+5} = 0\n$$",
"role": "user"
}
] | math | {
"ground_truth": "-1",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In a college basketball game between Team Alpha and Team Beta, the game was tied at the end of the first quarter. The number of points scored by Team Alpha in the four quarters f... | math | {
"ground_truth": "\\textbf{(C)}\\ 30",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "In triangle \\( \\triangle ABC \\), the sides opposite to angles \\( A \\), \\( B \\), and \\( C \\) are \\( a \\), \\( b \\), and \\( c \\) respectively. If the angles \\( A \\)... | math | {
"ground_truth": "\\frac{2\\pi}{7}",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given a mathematics contest with 15 problems, a student gains 6 points for a correct answer and loses 3 points for an incorrect answer. If Nathan answered every problem and his s... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Given the function f(x) = x² + ax - e^x, g(x) = ln(x).\n(1) When a = e - 1, find the equation of the tangent line to the curve y = f(x) at the point x = 1.\n(2) If the function F... | math | {
"ground_truth": "a ≤ e - 1",
"style": "rule"
} | {
"id": "numina_cn_k12-0",
"rating": null,
"split": "confidence_train",
"sub_source": "cn_k12"
} | cn_k12 |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Find all values of $x$ with $0 \\le x < 2 \\pi$ that satisfy $\\sin x - \\cos x = 1.$ Enter all solutions, separated by commas.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{\\pi}{2}, \\pi",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "The point $D$ $(5,3)$ is reflected over the $y$-axis to point $E$. Then $E$ is reflected over the line $y=-x$ to $F$. What is the area of triangle $DEF$?",
"role": "user"
}... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"id": "numina_synthetic_math-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_math"
} | synthetic_math |
math_box | [
{
"content": "Please reason step by step, and put your final answer within \\boxed{}.",
"role": "system"
},
{
"content": "Jerry starts at the origin of a two-dimensional grid. He tosses a fair coin $10$ times. With each heads, he moves one unit up, and with each tails, he moves one unit down. Determ... | math | {
"ground_truth": "\\text{A) } \\frac{15}{64}",
"style": "rule"
} | {
"id": "numina_synthetic_amc-0",
"rating": null,
"split": "confidence_train",
"sub_source": "synthetic_amc"
} | synthetic_amc |
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