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": "For the protection of an oil platform located at sea, it is necessary to place 5 radars around it, each covering a circle with a radius of $r=25$ km. Determine the maximum distan... | math | {
"ground_truth": "\\frac{672 \\pi}{\\tan 36^\\circ}",
"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 unit cube \\( ABCD-A_1B_1C_1D_1 \\), point \\( E \\) is on edge \\( AA_1 \\) such that \\( AE = \\frac{3 - \\sqrt{6}}{3} \\). A plane \\(\\alpha\\) is formed through points ... | math | {
"ground_truth": "60^\\circ",
"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 vectors $\\overrightarrow{a}=(\\cos \\theta, \\sin \\theta)$ and $\\overrightarrow{b}=(\\sqrt {3},-1)$, calculate the maximum value of $|2 \\overrightarrow{a} - \\overright... | math | {
"ground_truth": "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 number $N$ is in base 10, $503$ in base $b$ and $305$ in base $b+2$ find product of digits of $N$",
"role": "user"
}
] | math | {
"ground_truth": "64",
"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 $p$ be an odd prime. Determine the positive integers $x$ and $y$ with $x\\leq y$ for which the number $\\sqrt{2p}-\\sqrt{x}-\\sqrt{y}$ is non-negative and as small ... | math | {
"ground_truth": "x = \\frac{p-1}{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": "There are 294 distinct cards with numbers \\(7, 11, 7^{2}, 11^{2}, \\ldots, 7^{147}, 11^{147}\\) (each card has exactly one number, and each number appears exactly once). How man... | math | {
"ground_truth": "15987",
"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 many positive three-digit integers with each digit being either prime or even are divisible by 5?",
"role": "user"
}
] | math | {
"ground_truth": "16",
"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": "On a 9 cm ruler without any markings, place three intermediate markings so that it can measure distances from 1 to 9 cm with an accuracy of 1 cm.",
"role": "user"
}
] | math | {
"ground_truth": "\\text{Solution Confirmed: Three marks at 1 cm, 4 cm, and 7 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": "Let $L_1$ and $L_2$ be perpendicular lines, and let $F$ be a point at a distance $18$ from line $L_1$ and a distance $25$ from line $L_2$ . There are two distinct po... | math | {
"ground_truth": "210",
"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 sequence $\\{a_{n}\\}$ where $a_{1}=1$, $a_{n+1}=\\ln a_{n}+2$, and let $T_{n}=\\sum_{i=1}^{n}[a_{i}]$ (where $\\left[x\\right]$ represents the greatest integer not excee... | math | {
"ground_truth": "6064",
"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 sum of all the odd integers between $200$ and $400$?",
"role": "user"
}
] | math | {
"ground_truth": "30000",
"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": "Find all functions $f$ defined on the integers greater than or equal to $1$ that satisfy:\n(a) for all $n,f(n)$ is a positive integer.\n(b) $f(n + m) =f(n)f(m)$ for all ... | math | {
"ground_truth": "f(n) = 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": "What is the smallest positive integer $n$ such that $2^n - 1$ is a multiple of $2015$ ?",
"role": "user"
}
] | math | {
"ground_truth": "60",
"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 $z$ be a nonreal complex number such that $|z| = 2.$ Find the real part of $\\frac{1}{1 - z}.$",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1-x}{5-2x}",
"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": "Consider the natural implementation of computing Fibonacci numbers:\n\n\\begin{tabular}{l}\n1: \\textbf{FUNCTION} $\\text{FIB}(n)$ : \n2: $\\qquad$ \\textbf{IF} $n = 0$ \\tex... | math | {
"ground_truth": "176",
"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 how many ways can you place two knights - one white and one black - on a $16 \\times 16$ chessboard so that they threaten each other? (A knight moves in an \"L\" shape, i.e., ... | math | {
"ground_truth": "1680",
"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": "It is known that $\\frac{7}{13} + \\sin \\phi = \\cos \\phi$ for some real $\\phi$ . What is sin $2\\phi$ ?",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{120}{169}",
"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": "Compute $\\arccos (\\sin 3).$ All functions are in radians.",
"role": "user"
}
] | math | {
"ground_truth": "3 - \\frac{\\pi}{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": "Draw a line through the point \\(P(3,0)\\) such that it is bisected by the point \\(P\\) and lies between the two lines \\(2x - y - 2 = 0\\) and \\(x + y + 3 = 0\\). What is the ... | math | {
"ground_truth": "8x - y - 24 = 0",
"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 quadratic polynomial \\( f(x) = ax^2 + bx + c \\) such that\n\n\\[ f\\left( \\frac{a - b - c}{2a} \\right) = f\\left( \\frac{c - a - b}{2a} \\right) = 0 \\]\n\nfind the v... | math | {
"ground_truth": "0",
"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 \\\\(t < 0\\\\), let the function \\\\(f(x) = x^{3} + \\dfrac{3(t-1)}{2}x^{2} - 3tx\\\\).\n\\\\((1)\\\\) If \\\\(f(x)\\\\) has no extremum in \\\\((0,2)\\\\), find the valu... | math | {
"ground_truth": "0 > t \\geqslant -\\dfrac{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": "Solve the Riccati equation\n\n$$\ny^{\\prime} - y^{2} + 2 e^{x} y = e^{2 x} + e^{x}\n$$\n\ngiven its particular solution \\( y_{1} = e^{x} \\).",
"role": "user"
}
] | math | {
"ground_truth": "y = e^x + \\frac{1}{C - x}",
"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 the acute-angled triangle $ABC$ the angle $ \\angle B = 30^o$ , point $H$ is the intersection point of its altitudes. Denote by $O_1, O_2$ the centers of circles inscrib... | math | {
"ground_truth": "45^\\circ",
"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 $n$ be a positive integer. Each cell of an $n \\times n$ table is coloured in one of $k$ colours where every colour is used at least once. Two different colours $A$ a... | math | {
"ground_truth": "k \\leq 2n-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 quadrilateral ABCD have sides AB = 5, BC = 6, and CD = 25. Both vertex angles B and C are obtuse, and sin C = -cos B = 4/5. Calculate the length of side AD.",
"role": "... | math | {
"ground_truth": "26.85",
"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 a table with $25$ columns and $300$ rows, Kostya painted all its cells in three colors. Then, Lesha, looking at the table, for each row names one of the three colors and m... | math | {
"ground_truth": "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": "In a regular octagon $A_1A_2A_3\\cdots A_7A_8$ centered at the origin, let $\\overrightarrow{a_{0}}=\\overrightarrow{A_{8}A_{1}}, \\ \\vec{a}_{i}=\\overrightarrow{A_{i}A_{i+1}} \... | math | {
"ground_truth": "\\vec{b}_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": "Given that \\(\\tan \\alpha = -\\frac{1}{2}\\), if \\(c = \\frac{2 \\cos \\alpha - \\sin \\alpha}{\\sin \\alpha + \\cos \\alpha}\\), find the value of \\(c\\).",
"role": "use... | math | {
"ground_truth": "5",
"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": "Find all triplets $(x,y,p)$ of positive integers such that $p$ be a prime number and $\\frac{xy^3}{x+y}=p$",
"role": "user"
}
] | math | {
"ground_truth": "(x, y, p) = (14, 2, 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": "A pair of sneakers and a pair of socks together cost $\\$101$. The pair of sneakers costs $\\$100$ more than the pair of socks. What is the cost of the sneakers in dollars?",
... | math | {
"ground_truth": "\\$100.5",
"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 $\\frac{4}{7}=\\frac{M}{77}=\\frac{98}{N^2}$, find the value of $M+N$.",
"role": "user"
}
] | math | {
"ground_truth": "57.1",
"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": "Chandra now has five bowls of different colors (red, blue, yellow, green, purple) and four glasses that match the colors of the first four bowls (red, blue, yellow, green). If sh... | math | {
"ground_truth": "19",
"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 \\( z = 5 + 2i \\), find \\( z^2 \\) and then determine the magnitude of \\( z^2 \\).",
"role": "user"
}
] | math | {
"ground_truth": "29",
"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 that $3 \\in \\{x+2, x^2+2x\\}$, find the value of $x$.",
"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": "For which integer pairs \\((x, y)\\) does the following system of inequalities hold?\n\n$$\n\\begin{gathered}\ny + \\frac{1}{2} > \\left| x^2 - 2x \\right| \\\\\ny \\leq 2 - \\le... | math | {
"ground_truth": "(0, 0), (0, 1), (1, 1), (1, 2), (2, 0), (2, 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": "If the one-variable quadratic equation $x^{2}-2x+m=0$ has two equal real roots with respect to $x$, calculate the value of $m$.",
"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": "Point \\( Q \\) is located outside circle \\( D \\) in a plane. Define circle \\( D \\) with radius \\( 5 \\) cm. A second circle with radius \\( 8 \\) cm is centered at \\( Q \\... | math | {
"ground_truth": "\\textbf{(B)} \\ 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": "Given the function $y = \\cos x - \\sin x$, translate it graphically to the right by $φ$ ($φ > 0$) units, and then stretch the horizontal coordinates of each point on the obtaine... | math | {
"ground_truth": "\\frac{π}{2},\\frac{1}{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": "The Lions defeated the Eagles 3 out of 5 times they played initially. They then played $N$ more times, and the Eagles ended up winning at least 90% of all the games played. What ... | math | {
"ground_truth": "25",
"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 $x \\gt 0$, $y \\gt 0$, and $x+y=1$, find the minimum value of $\\frac{1}{x}+\\frac{4}{y}$.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"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 that $p$ and $q$ are positive numbers for which $\\operatorname{log}_{9}(p) = \\operatorname{log}_{12}(q) = \\operatorname{log}_{16}(p+q)$. Find the value of $\\frac{q}{p... | math | {
"ground_truth": "\\frac{1 + \\sqrt{5}}{2}",
"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": "Let $\\{a_n\\}$ be a sequence where $a_1 = 1$ and $a_{n+1} = (-1)^n (a_n + 1)$. Let $S_n$ denote the sum of the first $n$ terms of $\\{a_n\\}$. Find $S_{2013}$.",
"role": "us... | math | {
"ground_truth": "-1005",
"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": "Joe and Gracie are at positions $3+4i$ and $-2+3i$ respectively on the complex plane. A third point, $1+i$, is also marked on the plane. Calculate the total distance Joe travels ... | math | {
"ground_truth": "2\\sqrt{13}",
"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": "[b]Problem Section #4\n\nb) Let $A$ be a unit square. What is the largest area of a triangle whose vertices lie on the perimeter of $A$ ? Justify your answer.",
"role": "us... | 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": "If the ratio of the lengths of the medians on the right-angled sides of a right-angled triangle is $m$, then the range of $m$ is.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2} < m < 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": "What multiple of 18 is closest to 2021?",
"role": "user"
}
] | math | {
"ground_truth": "2016",
"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 $\\tan \\left(x+ \\frac {\\pi}{4}\\right)=2$, find the value of $\\frac {\\tan x}{\\tan 2x}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac {4}{9}",
"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 focal length of the ellipse $\\dfrac {x^{2}}{2} + \\dfrac {y^{2}}{4} = 2$.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given the function $f(x)=2\\sqrt{3}\\sin\\frac{\\omega x}{2}\\cos\\frac{\\omega x}{2}+6\\cos^2\\frac{\\omega x}{2}-3$ ($\\omega>0$) \n(1) If $y=f(x+\\theta)$ ($0<\\theta<\\frac{... | math | {
"ground_truth": "\\frac{1}{6}",
"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 \\(a, b, c, d\\) are equal to \\(2, 3, 5, 6\\), in some order. Find the largest possible value of\n\\[ab + bc + cd + da.\\]",
"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": "Points $P$, $Q$, $R$, and $S$ lie in the plane of square $EFGH$ such that triangles $EPF$, $FQG$, $GRH$, and $HSE$ are all equilateral. If $EFGH$ has an area of 36, find the area... | math | {
"ground_truth": "144 + 72\\sqrt{3}",
"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": "How many of the fractions $\\frac{1}{2023}, \\frac{2}{2023}, \\frac{3}{2023}, \\cdots, \\frac{2022}{2023}$ simplify to a fraction whose denominator is prime?",
"role": "user"... | math | {
"ground_truth": "22",
"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 parabola $y = x^2 - 8x + c$, determine the value of $c$ for which the vertex of the parabola will be a point on the $x$-axis.",
"role": "user"
}
] | math | {
"ground_truth": "16",
"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": "The integers \\(1, 2, \\ldots, 64\\) are written in the squares of an \\(8 \\times 8\\) chess board, such that for each \\(1 \\leq i < 64\\), the numbers \\(i\\) and \\(i+1\\) ar... | math | {
"ground_truth": "432",
"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 $S$ be the set of 81 points $(x, y)$ such that $x$ and $y$ are integers from $-4$ through $4$ . Let $A$ , $B$ , and $C$ be random points chosen independently ... | math | {
"ground_truth": "\\frac{200}{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": "Determine all positive integer numbers $n$ satisfying the following condition:\n the sum of the squares of any $n$ prime numbers greater than $3$ is divisible by $n$ .",
... | math | {
"ground_truth": "1, 2, 3, 4, 6, 8, 12, 24",
"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 units digit of \\(31^{2020}\\).\n- Find the units digit of \\(37^{2020}\\).",
"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": "Given two sets $A=\\{0, a\\}$ and $B=\\{3^a, 1\\}$. If the intersection of $A$ and $B$ is $A \\cap B = \\{1\\}$, then what is the union of $A$ and $B$, $A \\cup B$?",
"role":... | math | {
"ground_truth": "\\{0, 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": "In a triangle $ABC$ , let $I$ denote the incenter. Let the lines $AI,BI$ and $CI$ intersect the incircle at $P,Q$ and $R$ , respectively. If $\\angle BAC = 40^o$ , wha... | math | {
"ground_truth": "20^\\circ",
"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": "The arithmetic mean of twelve numbers is 40. If three numbers $x$, $y$ and $z$ are added to the list, where $z = x + 10$, the mean of the fifteen-member list becomes 50. What is ... | math | {
"ground_truth": "90",
"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": "Consider the sets $P=\\\\{ x | x > 1 \\\\}$ and $Q=\\\\{ x | f(x)=\\\\ln (2-x) \\\\}$. Find the intersection $P \\cap Q$.",
"role": "user"
}
] | math | {
"ground_truth": "(1, 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": "Given that seven consecutive integers beginning with $c$ have an average of $d$, determine the average of seven consecutive integers beginning with $d+1$.",
"role": "user"
... | math | {
"ground_truth": "c+7",
"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": "What is the sum of the last two digits of this portion of the Fibonacci Factorial Series: $1!+1!+2!+3!+5!+8!+13!+21!+34!+55!+89!+144!$?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Let \\( \\triangle ABC \\) be a triangle inscribed in a unit circle with center \\( O \\). Let \\( I \\) be the incenter of \\( \\triangle ABC \\), and let \\( D \\) be the inter... | math | {
"ground_truth": "\\frac{15}{169}",
"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 sum of the squares of the roots for the quadratic equation \\(2x^2 - 9x + 7\\).",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{53}{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": "If the growth rate each month is $x$, derive the equation based on the information that the revenue in January was 4 million yuan and the revenue in the first quarter was a total... | math | {
"ground_truth": "400+400(1+x)+400(1+x)^{2}=2000",
"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 graph of the function \\( y = \\log_{\\frac{1}{2}} |x + a| \\), determine the range of values for \\( a \\) such that the graph does not pass through the second quadran... | math | {
"ground_truth": "(-\\infty, -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": "Find the greatest common divisor (gcd) and least common multiple (lcm) of 18 and 24.",
"role": "user"
}
] | math | {
"ground_truth": "72",
"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 $x = 3$ and $y = 2,$ what is the value of $3x^2 - 4y + 5?$",
"role": "user"
}
] | math | {
"ground_truth": "24",
"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 first three terms of an arithmetic sequence are 3, 8, and 13. What is the value of the 15th term?",
"role": "user"
}
] | math | {
"ground_truth": "73",
"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 $AB$ be a segment of length $2$ . The locus of points $P$ such that the $P$ -median of triangle $ABP$ and its reflection over the $P$ -angle bisector of triangle $... | math | {
"ground_truth": "2\\pi",
"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 Jo and Blair take turns counting numbers by incrementally adding 2 to the last number the other person said, starting with 1, determine the 23rd number said in this se... | math | {
"ground_truth": "45",
"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 acute triangle $ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $\\frac{b^2 - a^2 - c^2}{ac} = \\frac{\\cos(A + C)}{\\sin A \\cos ... | math | {
"ground_truth": "(-2\\sqrt{2}, 2\\sqrt{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": "**p1.**What is the ratio of the area of an equilateral triangle to the area of the largest rectangle that can be inscribed inside the triangle?**p2.** Define $$ P(x) = x^{12} +... | math | {
"ground_truth": "\\frac{105}{512}",
"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": "Determine all functions $f : \\mathbb R \\to \\mathbb R$ satisfying the following two conditions:\n\n(a) $f(x + y) + f(x - y) = 2f(x)f(y)$ for all $x, y \\in \\mathbb R$ , a... | math | {
"ground_truth": "f(x) = 0",
"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 $PROBLEMZ$ be a regular octagon inscribed in a circle of unit radius. Diagonals $MR$ , $OZ$ meet at $I$ . Compute $LI$ .",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{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 vectors $\\overrightarrow{a}=(1,1)$ and $\\overrightarrow{b}=(-1,2)$, then the dot product $\\overrightarrow{a}\\cdot \\overrightarrow{b}$ equals ______.",
"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": "Given the function $f(x)=2\\sin(\\omega x+\\phi)(\\omega > 0)$ whose graph is symmetric about the line $x=\\frac{\\pi}{3}$, and $f\\left(\\frac{\\pi}{12}\\right)=0$, find the min... | math | {
"ground_truth": "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": "There are 5 people standing in a row, and the positions of A and B cannot be adjacent to C, find the number of different arrangements.",
"role": "user"
}
] | math | {
"ground_truth": "36",
"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": "Squares $ABCD$, $EFGH$, and $GHIJ$ are identical in area. Point $C$ divides side $IH$ of square $GHIJ$ in the ratio 1:3, starting from $I$ towards $H$, and point $D$ divides side... | math | {
"ground_truth": "\\frac{3}{8}",
"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 highest temperature of $26^{\\circ}\\mathrm{C}$ and the lowest temperature of $12^{\\circ}\\mathrm{C}$, determine the range of temperature change $t\\left(^{\\circ}\\ma... | math | {
"ground_truth": "12 \\leqslant t \\leqslant 26",
"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 finite sets of positive integers with at least two elements such that for any two numbers $ a$ , $ b$ ( $ a > b$ ) belonging to the set, the number $ \\frac {b^2}{a ... | math | {
"ground_truth": "\\{x, 2x\\}",
"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 $T_1$ be an isosceles triangle with sides of length 8, 11, and 11. Let $T_2$ be an isosceles triangle with sides of length $b$ , 1, and 1. Suppose that the radius of t... | math | {
"ground_truth": "\\frac{14}{11}",
"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": "Determine the sum of the possible values of $a$ if the zeroes of the function $f(x) = x^2 - ax + 3a$ are integers.",
"role": "user"
}
] | math | {
"ground_truth": "53",
"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": "Adventurers A and B went on an expedition in the desert. One morning at 7:00, A set off first, walking east at a speed of 6 kilometers per hour. One hour later, B set off, moving... | math | {
"ground_truth": "424",
"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 parabola $y^2=4x$ with focus $F$, and the distance from a point $A$ on the parabola to the y-axis is 3, then $|AF|=$ ___.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Chris and Dana each roll a sheet of 10-inch by 12-inch paper to form a cylindrical tube. Chris tapes the two 12-inch sides together without overlap. Dana tapes the two 10-inch si... | math | {
"ground_truth": "60",
"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 $f(x)=1+\\frac{a}{{{e^{2x}}-1}}$ is an odd function, then the real number $a=$____.",
"role": "user"
}
] | math | {
"ground_truth": "a = 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 \\( m \\) be a fixed integer greater than 1. The sequence \\( x_0, x_1, x_2, \\ldots \\) is defined as follows:\n\\[ x_i = \\left\\{ \\begin{array}{ll}\n2^i, & \\text{if } 0 ... | math | {
"ground_truth": "m-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": "Sasha marked several cells of an $8 \\times 13$ table such that in any $2 \\times 2$ square there was an odd number of marked cells. Then he marked several more cells so that in ... | math | {
"ground_truth": "48",
"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": "Find the largest $k$ for which there exists a permutation $(a_1, a_2, \\ldots, a_{2022})$ of integers from $1$ to $2022$ such that for at least $k$ distinct $i$ with ... | math | {
"ground_truth": "1011",
"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": "A group of ten people went to the cinema. They received tickets for 5 adjacent seats in two different rows. Ábel and Bendegúz want to sit next to each other, while Zsuzsi and Ani... | math | {
"ground_truth": "518400",
"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 how many integer values of $n$ between 1 and 392 inclusive does the decimal representation of $\\frac{n}{392}$ terminate?",
"role": "user"
}
] | math | {
"ground_truth": "8",
"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 the parabola $y^2=4x$, a line passing through the focus $F$ intersects the parabola at points $A$ and $B$ (point $A$ is below the x-axis). Point $A_1$ is symmetric to point... | math | {
"ground_truth": "\\frac {\\sqrt {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": "Cagney can frost a cupcake every 15 seconds and Lacey can frost a cupcake every 25 seconds. However, both take a 30-second break after every 3 minutes of continuous work. Calcula... | math | {
"ground_truth": "76",
"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": "What is the sum of the whole-number factors of 30?",
"role": "user"
}
] | math | {
"ground_truth": "72",
"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": "Verify that the invertible elements modulo 8 are 1, 3, 5, 7 and that they are equal to their inverses.",
"role": "user"
}
] | math | {
"ground_truth": "1, 3, 5, 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": "Consider a sequence of eleven squares that have side lengths $3, 6, 9, 12,\\ldots, 33$ . Eleven copies of a single square each with area $A$ have the same total area as the to... | math | {
"ground_truth": "414",
"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": "Factor the polynomial $x^{15} - x$ as completely as possible into polynomials and monomials with integral coefficients and determine the number of factors in the complete factori... | math | {
"ground_truth": "4",
"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 $F$ be the set of all $n-tuples$ $(A_1,A_2,…,A_n)$ such that each $A_i$ is a subset of ${1,2,…,2019}$ . Let $\\mid{A}\\mid$ denote the number of elements o the set... | math | {
"ground_truth": "2019(2^{2019n} - 2^{2018n})",
"style": "rule"
} | {
"id": "numina_aops_forum-0",
"rating": null,
"split": "confidence_train",
"sub_source": "aops_forum"
} | aops_forum |
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