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": "Find the value of $x$ such that $\\sqrt{2x + 12} = 8$.",
"role": "user"
}
] | math | {
"ground_truth": "26",
"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": "Calculate the opposite of $-\\frac{1}{2}$.",
"role": "user"
}
] | math | {
"ground_truth": "\\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": "Find the error in each of these examples:\n\na) \\( 225 \\div 25 + 75 = 100 - 16 \\) \\( 25 \\left( \\frac{9}{1+3} \\right) = 84 \\) \\( 25 \\cdot 12 = 84 \\) \\( 25 = 7 \\) (?!)... | math | {
"ground_truth": "29",
"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 point A has coordinates (4, 3), and F is the focus of the parabola $y^2=4x$, if point P moves on the parabola, then when $|PA|+|PF|$ takes the minimum value, the coord... | math | {
"ground_truth": "\\left( \\frac{9}{4}, 3 \\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": "Find the equation of the line passing through the intersection points of the two circles: $x^2 + y^2 + 6x + 4y = 0$ and $x^2 + y^2 + 4x + 2y - 4 = 0$.",
"role": "user"
}
] | math | {
"ground_truth": "x + y - 2 = 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": "Tracy had a bag of candies, and none of the candies could be broken into pieces. She ate $\\frac{1}{4}$ of them and then gave $\\frac{1}{5}$ of what remained to her friend Rachel... | math | {
"ground_truth": "80",
"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": "**Problem 1.**Find all $ (x,y)$ such that:\r\n\\[ \\{\\begin{matrix} \\displaystyle\\dfrac {1}{\\sqrt {1 + 2x^2}} + \\dfrac {1}{\\sqrt {1 + 2y^2}} & = & \\displaystyle\\dfrac {... | math | {
"ground_truth": "\\left(\\frac{81 - \\sqrt{5913}}{324}, \\frac{81 - \\sqrt{5913}}{324}\\right)",
"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 a machine produces $150$ items in one minute, calculate how many items it would produce in $10$ seconds.",
"role": "user"
}
] | math | {
"ground_truth": "25",
"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 set of 6 distinct lattice points is chosen uniformly at random from the set \\(\\{1,2,3,4,5,6\\}^{2}\\). Let \\(A\\) be the expected area of the convex hull of these 6 points. ... | math | {
"ground_truth": "104552",
"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 pressure $(P)$ on a boat sail varies directly with both the area $(A)$ of the sail and the square of the wind's velocity $(V)$. When the area is 2 square feet and the wind ve... | math | {
"ground_truth": "\\textbf{(C)}\\ 20\\sqrt{2}\\text{ mph}",
"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 lemon loaf completely fills a pan measuring $20 \\mathrm{cm}$ by $18 \\mathrm{cm}$ by $5 \\mathrm{cm}$, with a density of $2 \\mathrm{g} / \\mathrm{cm}^3$. Calculate the volume... | math | {
"ground_truth": "144 \\, \\text{g}",
"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": "Two circles are concentric. The area of the ring between them is \\( A \\). In terms of \\( A \\), find the length of the longest chord contained entirely within the ring.",
... | math | {
"ground_truth": "2 \\sqrt{\\frac{A}{\\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": "If Jia releases a 6 yuan \"Lucky Money\" red packet which is grabbed by Yi, Bing, and Ding, and each person receives an integer amount of yuan with each person receiving at least... | math | {
"ground_truth": "\\dfrac{2}{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": "The 6 members of an executive committee each call 6 different people, and these people, in turn, each call 6 other people. If no one is called more than once, calculate the total... | math | {
"ground_truth": "258",
"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 particular classroom test, $15\\%$ of the students scored $60$ points, $20\\%$ scored $75$ points, $30\\%$ scored $85$ points, $25\\%$ scored $90$ points, and the rest score... | math | {
"ground_truth": "\\textbf{(C)}\\ 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": "In the triangle \\( ABC \\) with a given area \\( t \\), draw the midlines \\( BB_1 \\) and \\( CC_1 \\). If \\( D \\) is the midpoint of \\( BB_1 \\) and \\( E \\) is the midpoi... | math | {
"ground_truth": "\\frac{5t}{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": "Let $\\triangle P_1P_2P_3$ be an equilateral triangle. For each $n\\ge 4$ , *Mingmingsan* can set $P_n$ as the circumcenter or orthocenter of $\\triangle P_{n-3}P_{n-2}P_{n... | math | {
"ground_truth": "n \\equiv 0 \\pmod{4}",
"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": "Two lines are given by the systems of equations:\n\n$$\n\\frac{x-x_{1}}{m_{1}}=\\frac{y-y_{1}}{n_{1}}=\\frac{z-z_{i}}{p_{1}} \\quad \\text{and} \\quad \\frac{x-x_{2}}{m_{2}}=\\fr... | math | {
"ground_truth": "m_1 m_2 + n_1 n_2 + p_1 p_2 = 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": "Determine the number of ordered quadruples \\((a, b, c, d)\\) of real numbers such that\n\\[\n\\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}^{-1} = \\begin{pmatrix} 2a & 0 \\\\... | math | {
"ground_truth": "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": "Given $(16)^{-2^{-3}}$, calculate the result.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{\\sqrt{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 set \\( A = \\{ z \\mid z^{2n-1} = \\bar{z}, z \\in \\mathbf{C}, n \\in \\mathbf{N}, n \\geqslant 2 \\} \\), how many right-angled triangles can be formed with vertices... | math | {
"ground_truth": "2n^2",
"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": "A driver departed from point A to point B, which are 100 km apart. When the navigator indicated that 30 minutes of travel remained, the driver reduced speed by 10 km/h for the fi... | math | {
"ground_truth": "100 \\text{ km/h}",
"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 primes $p \\geq 3$ with the following property: for any prime $q<p$ , the number\r\n\\[\r\np - \\Big\\lfloor \\frac{p}{q} \\Big\\rfloor q\r\n\\]\r\nis squarefree (i.e... | math | {
"ground_truth": "5, 7, 13",
"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": "Cells of a $n*n$ square are filled with positive integers in the way that in the intersection of the $i-$ th column and $j-$ th row, the number $i+j$ is written. In every s... | math | {
"ground_truth": "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": "Given the ratios, $w$ to $x$ is $5:4$, $y$ to $z$ is $5:3$, and $z$ to $x$ is $1:5$. What is the ratio of $w$ to $y$?\nA) 10:3\nB) 15:4\nC) 3:1\nD) 20:5",
"role": "user"
}
... | math | {
"ground_truth": "B) 15:4",
"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": "Grace is four years younger than Helen. Helen is five years older than Ian. Julia is two years older than Ian. Grace is 20 years old. How many years old is Julia?",
"role": "... | math | {
"ground_truth": "21",
"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": "What is the units digit of the product of the first three even composite numbers?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Let \\( z \\) and \\( w \\) be complex numbers such that \\( |z - 2 - 2i| = 2 \\) and \\( |w + 3 + 5i| = 4 \\). Find the smallest possible value of \\( |z - w| \\).",
"role":... | math | {
"ground_truth": "\\sqrt{74} - 6",
"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 pairs of prime numbers $(p, q)$ such that $pq \\mid \\left(p^{p} + q^{q} + 1\\right)$.",
"role": "user"
}
] | math | {
"ground_truth": "(2, 5) \\text{ or } (5, 2)",
"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": "80 fair six-sided dice are rolled (each side numbered from 1 to 6 with equal probability), and the sum of the numbers rolled is calculated. Which probability is smaller: that the... | math | {
"ground_truth": "\\text{Greater probability is that the sum will not exceed 160.}",
"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": "One day students in school organised a exchange between them such that : $11$ strawberries change for $14$ raspberries, $22$ cherries change for $21$ raspberries, $10$ ... | math | {
"ground_truth": "7 \\ \\text{pears}",
"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 letters A, E, M, O, and U, arranged in alphabetical order, determine the position of the \"word\" MAUOE.",
"role": "user"
}
] | math | {
"ground_truth": "54",
"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 regular octagon, the diagonals also have varying lengths. Calculate the ratio of the length of the diagonal spanning one side to the length of the diagonal spanning three si... | math | {
"ground_truth": "\\frac{1}{\\sqrt{2 + \\sqrt{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": "For how many bases between two and nine inclusive does the representation of $385_{10}$ have a final digit of 1?",
"role": "user"
}
] | math | {
"ground_truth": "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": "For how many integers $n$ between $ 1$ and $2021$ does the infinite nested expression $$ \\sqrt{n + \\sqrt{n +\\sqrt{n + \\sqrt{...}}}} $$ give a rational number?",
... | math | {
"ground_truth": "44",
"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 ratio of boys to girls in Mrs. Taylor's science class is $3:4$. If there are $42$ students in the class, how many more girls than boys are there?\nA) 5 \nB) 6 \nC) 7 \nD) 8 \... | math | {
"ground_truth": "The correct answer given the choices is B) 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": "A polygon made of 4 congruent squares joined edge-to-edge forms a flat arrangement. If one more congruent square is attached to an edge at one of the nine indicated positions, ho... | math | {
"ground_truth": "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": "In the diagram, the area of triangle $ABC$ is 36 square units. What is the area of triangle $BCD$?\n\n[asy]\n\ndraw((0,0)--(40,0)--(12,18)--(0,0));\n\ndot((0,0));\nlabel(\"$A$\",... | math | {
"ground_truth": "144",
"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 the set of $x$-values satisfying the inequality $|\\frac{x^2-5x+4}{3}| < 1$.\n**A)** $x \\in \\left[\\frac{5 - \\sqrt{21}}{2}, \\frac{5 + \\sqrt{21}}{2}\\right]$\n**B)** $x ... | math | {
"ground_truth": "x \\in \\left(\\frac{5 - \\sqrt{21}}{2}, \\frac{5 + \\sqrt{21}}{2}\\right)",
"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 for which value of $k,$ the system\n\\begin{align*}\nx + 2ky + 4z &= 0, \\\\\n4x + ky + z &= 0, \\\\\n3x + 6y + 5z &= 0\n\\end{align*}has a solution where $x,$ $y,$ and... | math | {
"ground_truth": "\\frac{41}{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": "A circle inscribed in triangle \\(ABC\\) touches sides \\(AB\\) and \\(AC\\) at points \\(D\\) and \\(E\\) respectively. Point \\(I_A\\) is the center of the excircle opposite si... | math | {
"ground_truth": "130^\\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": "The areas of projections of a triangle onto the coordinate planes $Oxy$ and $Oyz$ are equal to $\\sqrt{6}$ and $\\sqrt{7}$, respectively, while the area of the projection onto th... | math | {
"ground_truth": "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": "Compute $i^{-101} + i^{-100} + i^{-99} + \\cdots + i^{-1} + i^0 + i^1 + \\cdots + i^{99} + i^{100} + i^{101}$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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": "**(a)** Find the minimal distance between the points of the graph of the function $y=\\ln x$ from the line $y=x$ .**(b)** Find the minimal distance between two points, one of ... | 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": "Find the minimum real $x$ that satisfies $$ \\lfloor x \\rfloor <\\lfloor x^2 \\rfloor <\\lfloor x^3 \\rfloor < \\cdots < \\lfloor x^n \\rfloor < \\lfloor x^{n+1} \\rfloor < \... | math | {
"ground_truth": "\\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 a cube \\( ABCD A_1 B_1 C_1 D_1 \\) with an edge length of 1. A sphere passes through vertices \\( A \\) and \\( C \\) and the midpoints \\( F \\) and \\( E \\) of edges \\... | math | {
"ground_truth": "\\frac{\\sqrt{41}}{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": "Given that $\\cos \\alpha = \\frac{\\sqrt{5}}{5}$, $\\sin (\\alpha - \\beta) = \\frac{\\sqrt{10}}{10}$, and $\\alpha, \\beta \\in (0, \\pi)$,\n\n(I) Find the value of $\\cos (2\\... | math | {
"ground_truth": "\\frac{\\pi}{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": "Every day from day 2, neighboring cubes (cubes with common faces) to red cubes also turn red and are numbered with the day number.",
"role": "user"
}
] | math | {
"ground_truth": "3026",
"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": "Evaluate the product \\[ (a-10) \\cdot (a-9) \\cdot \\dotsm \\cdot (a-1) \\cdot a, \\] where $a=5$.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"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": "Katie and Allie are playing a game. Katie rolls two fair six-sided dice and Allie flips two fair two-sided coins. Katie’s score is equal to the sum of the numbers on the top of t... | math | {
"ground_truth": "\\frac{25}{72}",
"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": "Evaluate the expression $2^4 + 2^4 + 2^4 + 2^4$.",
"role": "user"
}
] | math | {
"ground_truth": "64",
"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 $\\triangle ABC$, $BC= \\sqrt {5}$, $AC=3$, and $\\sin C=2\\sin A$. \n(Ⅰ) Find the value of $AB$; \n(Ⅱ) Find the value of $\\sin \\left(2A- \\frac {\\pi}{4}\\right)$.",
... | math | {
"ground_truth": "\\frac { \\sqrt {2}}{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": "Given the curve $y=\\frac{1}{3}x^{3}+\\frac{4}{3}$.\n\n(1) Find the equation of the tangent line to the curve at $x=2$;\n\n(2) Find the equation of the tangent line to the curve ... | math | {
"ground_truth": "x-y+2=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": "What is the product of the real roots of the equation\n$$\n\\frac{x^{2}+90 x+2027}{3}=\\sqrt{x^{2}+90 x+2055} ?\n$$",
"role": "user"
}
] | math | {
"ground_truth": "2006",
"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 Ace travels at a constant speed, and when traveling east, Flash runs \\( x \\) times as fast as Ace, and when traveling west, Flash runs \\( x+1 \\) times as fast as A... | math | {
"ground_truth": "\\frac{2xy}{x-1} + \\frac{(x+1)y}{x}",
"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 sum of all the real values of x satisfying $\u0012(x+\\frac{1}{x}-17)^2$ $= x + \\frac{1}{x} + 17.$",
"role": "user"
}
] | math | {
"ground_truth": "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": "How many solutions does the equation: $$ [\\frac{x}{20}]=[\\frac{x}{17}] $$ have over the set of positve integers? $[a]$ denotes the largest integer that is less than or equal... | math | {
"ground_truth": "57",
"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 Cartesian coordinate plane $xOy$, with $O$ being the origin, suppose we have a point $A\\left(-\\frac{1}{2}, \\frac{\\sqrt{3}}{2}\\right)$. If vector $\\overrightarrow{OA}... | math | {
"ground_truth": "\\left(\\frac{\\sqrt{3}}{2}, \\frac{1}{2}\\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": "A four-digit number is split into two two-digit numbers, whose sum equals 42. For example, 2022 is such a four-digit number. Besides 2022, how many other such four-digit numbers ... | math | {
"ground_truth": "2",
"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": "A line passing through point M(2, 1) intersects the X-axis and Y-axis at points P and Q, respectively, and $|MP| = |MQ|$. Find the equation of line L.",
"role": "user"
}
] | math | {
"ground_truth": "x + 2y - 4 = 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": "In the rectangular coordinate system $xoy$, the coordinates of points $A\\left(x_{1}, y_{1}\\right)$ and $B\\left(x_{2}, y_{2}\\right)$ are both positive integers. The angle betw... | math | {
"ground_truth": "(1,5), (9,8)",
"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 the function \\( f(x) \\) be monotonic on \\((-\\infty, +\\infty)\\) and satisfy \\( f(x + y) = f(x) + f(y) \\) with \\( f(1) = -1 \\). If \\( f\\left( k \\log_{2} t \\right)... | math | {
"ground_truth": "(-1 - 2\\sqrt{2}, -1 + 2\\sqrt{2})",
"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": "<u>Round 6</u>**p16.** Let $ABC$ be a triangle with $AB = 3$ , $BC = 4$ , and $CA = 5$ . There exist two possible points $X$ on $CA$ such that if $Y$ and $Z$ are the... | math | {
"ground_truth": "29",
"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 $ABCD$ be a rectangle. Determine the set of all points $P$ from the region between the parallel lines $AB$ and $CD$ such that $\\angle APB=\\angle CPD$ .",
"role... | math | {
"ground_truth": "y = \\frac{b}{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": "$ 2n\\plus{}1$ lines are drawn in the plane, in such a way that every 3 lines define a triangle with no right angles. What is the maximal possible number of acute triangles that... | math | {
"ground_truth": "\\frac{1}{4} \\binom{2n + 2}{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": "If an $n$-vertex graph $G$ does not contain $K_{k}$, then the maximum number of edges in $G$ is:\n$$\nM(n, k)=\\frac{k-2}{k-1} \\cdot \\frac{n^{2}-r^{2}}{2}+C_{r}^{2},\n$$\n\nwhe... | math | {
"ground_truth": "M(n, k) = \\frac{k-2}{k-1} \\cdot \\frac{n^2 - r^2}{2} + \\binom{r}{2}",
"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": "A clock chimes once at every quarter (15 minutes) past each hour and chimes according to the hour in multiples of three (e.g., 3 chimes at 1 PM, 6 chimes at 2 PM, and 36 chimes a... | math | {
"ground_truth": "\\text{March 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": "At the moment, my watch shows a time between 3:20 and 3:25. I observe the exact positions of the hands on my watch and then move the hands so that the minute hand takes the place... | math | {
"ground_truth": "3:21:23",
"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 limit of the function:\n\n\\[\n\\lim _{x \\rightarrow 1} \\frac{1+\\cos \\pi x}{\\operatorname{tg}^{2} \\pi x}\n\\]",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{1}{2}",
"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": "Solve the equation $\\arcsin \\frac{x \\sqrt{11}}{2 \\sqrt{21}}+\\arcsin \\frac{x \\sqrt{11}}{4 \\sqrt{21}}=\\arcsin \\frac{5 x \\sqrt{11}}{8 \\sqrt{21}}$.",
"role": "user"
... | math | {
"ground_truth": "0, \\pm \\frac{21}{10}",
"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": "What is the minimum value of \\((a - 1)^2 + \\left(\\frac{b}{a} - 1\\right)^2 + \\left(\\frac{c}{b} - 1\\right)^2 + \\left(\\frac{4}{c} - 1\\right)^2\\), over all real numbers \\... | math | {
"ground_truth": "12 - 8\\sqrt{2}",
"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 real-valued continuous functions defined on the interval $(-1, 1)$ such that $(1-x^{2}) f(\\frac{2x}{1+x^{2}}) = (1+x^{2})^{2}f(x)$ for all $x$ .",
"role": "use... | math | {
"ground_truth": "f(x) = \\frac{c}{1 - x^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 $(x+3)(x-4) = 20$, find the sum of the possible values of $x$.",
"role": "user"
}
] | math | {
"ground_truth": "1",
"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": "You have a large number of congruent equilateral triangular tiles on a table and you want to fit \\( n \\) of them together to make a convex equiangular hexagon (i.e., one whose ... | math | {
"ground_truth": "\\text{Neither 19 nor 20 is feasible.}",
"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": "\\( p \\) and \\( q \\) are two distinct prime numbers, and \\( n \\) is a positive integer \\( \\geqslant 3 \\). Find all integers \\( a \\) such that the polynomial \\( f(x) = ... | math | {
"ground_truth": "1 + (-1)^n pq \\text{ or } -1 - pq",
"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": "Determine the median number of siblings in the dataset: 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5.",
"role": "user"
}
] | math | {
"ground_truth": "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": "Find $131_4 \\times 21_4 \\div 3_4$. Express your answer in base 4.",
"role": "user"
}
] | math | {
"ground_truth": "1113_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": "Eleven tiles are numbered $1, 2, 3, \\cdots, 11.$ Each of three players randomly selects and keeps three of these tiles, then sums those three values. Determine the probability t... | 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": "What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 55?",
"role": "user"
}
] | math | {
"ground_truth": "3599",
"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": "If $16\\cdot3^x = 7^{y+5}$, then when $y = -5, x =$\n**A)** $\\frac{-3\\ln(2)}{\\ln(3)}$ \n**B)** $\\frac{-4\\ln(2)}{\\ln(3)}$ \n**C)** $-4$ \n**D)** $0$",
"role": "use... | math | {
"ground_truth": "\\frac{-4\\ln(2)}{\\ln(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": "We know $\\mathbb Z_{210} \\cong \\mathbb Z_2 \\times \\mathbb Z_3 \\times \\mathbb Z_5 \\times \\mathbb Z_7$ .\nMoreover,\\begin{align*}\n\t53 & \\equiv 1 \\pmod{2} \n\t53 & \\... | math | {
"ground_truth": "1234",
"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": "Define a sequence recursively by $x_0=7$ and \n\\[x_{n+1}=\\frac{x_n^2 + 6x_n + 5}{x_n+7}\\] \nfor all nonnegative integers $n$. Let $m$ be the least positive integer such that\n... | math | {
"ground_truth": "\\textbf{D) [243, 728]}",
"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 $\\triangle ABC$ with right angle at $C$, altitude $CH$ and median $CM$ bisect the right angle. If the area of $\\triangle CHA$ is $K$, calculate the area of $\\triangle ABC$.... | math | {
"ground_truth": "2K",
"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 is an integer $k\\geq 2$ . Determine the smallest positive integer $n$ , such that, among any $n$ points in the plane, there exist $k$ points among them, such that al... | math | {
"ground_truth": "n = (k-1)^2 + 1 = k^2 - 2k + 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": "Given that point P is any point on the graph of the function $f(x) = 2\\sqrt{2x}$, and a tangent line is drawn from point P to circle D: $x^2 + y^2 - 4x + 3 = 0$, with the points... | math | {
"ground_truth": "\\sqrt{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 DeBose family has two boys with ages $8$ each, a girl aged $16$, and a boy aged $18$. What is the mean (average) age of the children?",
"role": "user"
}
] | math | {
"ground_truth": "12.5",
"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 $x$ and $y$ are positive integers, and $2^{x+1} \\cdot 4^y = 128$, then $x+2y=$ ?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Find all numbers of the form \\( 22 \\ldots 2 \\) that can be expressed as the sum of two perfect squares.",
"role": "user"
}
] | math | {
"ground_truth": "2",
"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": "A triple of positive integers \\((a, b, c)\\) is considered tasty if \\(\\operatorname{lcm}(a, b, c) \\mid a + b + c - 1\\) and \\(a < b < c\\). Find the sum of \\(a + b + c\\) a... | math | {
"ground_truth": "44",
"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 value of $x^2-6x+13$ can never be less than.",
"role": "user"
}
] | math | {
"ground_truth": "4",
"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 value of $k$ such that the quadratic equation $3x^2 - 7x + k = 0$ has exactly one solution for $x$.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{49}{12}",
"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 the plane, if the slopes of the lines $PA$ and $PB$ connecting the moving point $P$ and the fixed points $A(-4,0)$, $B(4,0)$ are multiplied to give a constant value ($-\\frac{... | math | {
"ground_truth": "\\frac{x^2}{64} + \\frac{y^2}{\\frac{64}{9}} = 1 \\quad (x \\neq \\pm 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 laser is placed at the point $(2,3)$. The laser beam travels in a straight line. Larry wants the beam to hit and bounce off the $y$-axis, then hit and bounce off the $x$-axis, ... | 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": "What is the minimum value of the expression $2x^2 + 3y^2 - 12x + 6y + 25$ for real $x$ and $y$?",
"role": "user"
}
] | math | {
"ground_truth": "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": "Given circle $C_{1}$: $x^{2}+\\left(y-a\\right)^{2}=a^{2}(a \\gt 0)$, the distance from the center of the circle to the line $x-y-2=0$ is $2\\sqrt{2}$. Find the number of common ... | 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": "Compute the sum of the arithmetic series $24 + 24.2 + 24.4 + \\cdots + 48$.",
"role": "user"
}
] | math | {
"ground_truth": "4356",
"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 two integers have a sum of 29. When two more integers are added to the first two, the sum becomes 47. Finally, when three more integers are added to the sum of the previous... | 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": "Let $x_1, x_2,... , x_{84}$ be the roots of the equation $x^{84} + 7x - 6 = 0$ . Compute $\\sum_{k=1}^{84} \\frac{x_k}{x_k-1}$ .",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{77}{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": "Given point P(2, 2) is on the curve $y=ax^3+bx$, if the slope of the tangent line at point P is 9, then: \n(i) $ab= \\boxed{-3}$; \n(ii) The range of the function $f(x)=ax^3+bx... | math | {
"ground_truth": "[-2, 18]",
"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 triangle \\( ABC \\), the altitude \\( AH \\) is equal to the median \\( BM \\). Find the angle \\( MBC \\).",
"role": "user"
}
] | math | {
"ground_truth": "30^\\circ",
"style": "rule"
} | {
"id": "numina_olympiads-0",
"rating": null,
"split": "confidence_train",
"sub_source": "olympiads"
} | olympiads |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.