Dataset Viewer (First 5GB)
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[{"content":"Find the largest possible value of the expression $$\\frac{\\sqrt{(a-b)^2+(b-c)^2}+\\sq(...TRUNCATED) | "Find the largest possible value of the expression $$\\frac{\\sqrt{(a-b)^2+(b-c)^2}+\\sqrt{(b-c)^2+((...TRUNCATED) | "Find the largest possible value of the expression $$\\frac{\\sqrt{(a-b)^2+(b-c)^2}+\\sqrt{(b-c)^2+((...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given positive real numbers \\( a, b, c > 0 \\) with constraint\n\\[\na + b + c = 1,\n\\]\nwe want (...TRUNCATED) | 1,199 | 11,591 | 74 | ["Okay, so I need to find the largest possible value of this expression:\n\n$$\n\\frac{\\sqrt{(a-b)^(...TRUNCATED) | ["To find the largest possible value of the expression\n\n$$\n\\frac{\\sqrt{(a-b)^2 + (b-c)^2} + \\s(...TRUNCATED) | ["<think>\nOkay, so I need to find the largest possible value of this expression:\n\n$$\n\\frac{\\sq(...TRUNCATED) | ["<think>\nOkay, so I need to find the largest possible value of this expression:\n\n$$\n\\frac{\\sq(...TRUNCATED) | "<think>\nOkay, so I have this problem here where I need to find the largest possible value of a cer(...TRUNCATED) | [{"from":"human","value":"Find the largest possible value of the expression $$\\frac{\\sqrt{(a-b)^2+(...TRUNCATED) |
[{"content":"Find a monic quadratic polynomial $Q(x)$ with integer coefficients such that\n\\[Q(\\sq(...TRUNCATED) | "Find a monic quadratic polynomial $Q(x)$ with integer coefficients such that\n\\[Q(\\sqrt[4]{3} - 2(...TRUNCATED) | "Find a monic quadratic polynomial $Q(x)$ with integer coefficients such that\n\\[Q(\\sqrt[4]{3} - 2(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given the number \\(\\alpha = \\sqrt[4]{3} - 2\\), we want to find a monic quadratic polynomial \\((...TRUNCATED) | 15,423 | 14,304 | 963 | ["Okay, so I need to find a monic quadratic polynomial Q(x) with integer coefficients such that when(...TRUNCATED) | ["Given the problem of finding a monic quadratic polynomial \\( Q(x) \\) with integer coefficients s(...TRUNCATED) | ["<think>\nOkay, so I need to find a monic quadratic polynomial Q(x) with integer coefficients such (...TRUNCATED) | ["<think>\nOkay, so I need to find a monic quadratic polynomial Q(x) with integer coefficients such (...TRUNCATED) | "<think>\nOkay, so I need to find a monic quadratic polynomial Q(x) with integer coefficients such t(...TRUNCATED) | [{"from":"human","value":"Find a monic quadratic polynomial $Q(x)$ with integer coefficients such th(...TRUNCATED) |
[{"content":"Determine the sum of all values of $x$ for which the rational function $$\\frac{x^2+ax+(...TRUNCATED) | "Determine the sum of all values of $x$ for which the rational function $$\\frac{x^2+ax+b}{x^2+cx+d}(...TRUNCATED) | "Determine the sum of all values of $x$ for which the rational function $$\\frac{x^2+ax+b}{x^2+cx+d}(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "We are given a rational function:\n\\[\nf(x) = \\frac{x^2 + a x + b}{x^2 + c x + d}\n\\]\nwhere \\((...TRUNCATED) | 40,193 | 14,216 | 2,512 | ["Okay, so I need to figure out the sum of all values of x where the rational function (x² + a x + (...TRUNCATED) | ["To determine the sum of all values of \\( x \\) for which the rational function \\(\\frac{x^2 + ax(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the sum of all values of x where the rational function (x²(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the sum of all values of x where the rational function (x²(...TRUNCATED) | "<think>\nOkay, so I need to figure out the sum of all values of x where the rational function (x² (...TRUNCATED) | [{"from":"human","value":"Determine the sum of all values of $x$ for which the rational function $$\(...TRUNCATED) |
[{"content":"What is the largest positive integer that has exactly six distinct positive divisors, a(...TRUNCATED) | "What is the largest positive integer that has exactly six distinct positive divisors, and can be ex(...TRUNCATED) | "What is the largest positive integer that has exactly six distinct positive divisors, and can be ex(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "**Problem restatement:** \nFind the largest positive integer \\( n \\) such that: \n1. \\( n \\) (...TRUNCATED) | 11,384 | 11,405 | 711 | ["Okay, so I need to find the largest positive integer that has exactly six distinct positive diviso(...TRUNCATED) | ["To find the largest positive integer that has exactly six distinct positive divisors and can be ex(...TRUNCATED) | ["<think>\nOkay, so I need to find the largest positive integer that has exactly six distinct positi(...TRUNCATED) | ["<think>\nOkay, so I need to find the largest positive integer that has exactly six distinct positi(...TRUNCATED) | "<think>\nOkay, so I need to find the largest positive integer that has exactly six distinct positiv(...TRUNCATED) | [{"from":"human","value":"What is the largest positive integer that has exactly six distinct positiv(...TRUNCATED) |
[{"content":"Let $f(x)$ and $g(x)$ be functions defined on the real numbers with ranges $[-a,a]$ and(...TRUNCATED) | "Let $f(x)$ and $g(x)$ be functions defined on the real numbers with ranges $[-a,a]$ and $[-b,b]$ re(...TRUNCATED) | "Let $f(x)$ and $g(x)$ be functions defined on the real numbers with ranges $[-a,a]$ and $[-b,b]$ re(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given:\n\n- \\(f(x)\\) has range \\([-a, a]\\)\n- \\(g(x)\\) has range \\([-b, b]\\)\n- The range o(...TRUNCATED) | 34,634 | 12,651 | 2,164 | ["Okay, so I have this problem where there are two functions, f(x) and g(x). Their ranges are given (...TRUNCATED) | ["Given two functions \\( f(x) \\) and \\( g(x) \\) defined on the real numbers with ranges \\([-a, (...TRUNCATED) | ["<think>\nOkay, so I have this problem where there are two functions, f(x) and g(x). Their ranges a(...TRUNCATED) | ["<think>\nOkay, let's try to figure out this problem. So we have two functions, f(x) and g(x), with(...TRUNCATED) | "<think>\nOkay, let's try to figure out this problem. So we have two functions, f(x) and g(x), with (...TRUNCATED) | [{"from":"human","value":"Let $f(x)$ and $g(x)$ be functions defined on the real numbers with ranges(...TRUNCATED) |
[{"content":"Let $p(x)$ be a polynomial with integer coefficients such that $p(1) = p(3) = p(5) = p((...TRUNCATED) | "Let $p(x)$ be a polynomial with integer coefficients such that $p(1) = p(3) = p(5) = p(7) = p(9) = (...TRUNCATED) | "Let $p(x)$ be a polynomial with integer coefficients such that $p(1) = p(3) = p(5) = p(7) = p(9) = (...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given:\n- \\( p(x) \\) is a polynomial with integer coefficients,\n- \\( p(1) = p(3) = p(5) = p(7) (...TRUNCATED) | 26,514 | 16,443 | 1,657 | ["Okay, so I have this problem here: There's a polynomial p(x) with integer coefficients. It has roo(...TRUNCATED) | ["Given a polynomial \\( p(x) \\) with integer coefficients such that \\( p(1) = p(3) = p(5) = p(7) (...TRUNCATED) | ["<think>\nOkay, so I have this problem here: There's a polynomial p(x) with integer coefficients. I(...TRUNCATED) | ["<think>\nOkay, so I have this problem here: There's a polynomial p(x) with integer coefficients. I(...TRUNCATED) | "<think>\nOkay, so I need to find the smallest possible value of p(2) given that p(x) is a polynomia(...TRUNCATED) | [{"from":"human","value":"Let $p(x)$ be a polynomial with integer coefficients such that $p(1) = p(3(...TRUNCATED) |
[{"content":"In a triangle, the length of the hypotenuse is 15 units, and the length of one leg is 3(...TRUNCATED) | "In a triangle, the length of the hypotenuse is 15 units, and the length of one leg is 3 units. The (...TRUNCATED) | "In a triangle, the length of the hypotenuse is 15 units, and the length of one leg is 3 units. The (...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Let's analyze the problem step by step.\n\n---\n\n### Given:\n- Right triangle with hypotenuse \\( (...TRUNCATED) | 48,848 | 11,633 | 3,053 | ["Okay, so I need to find the length of the other leg in a right triangle where the hypotenuse is 15(...TRUNCATED) | ["Given a triangle with a hypotenuse of 15 units and one leg of 3 units, we need to find the length (...TRUNCATED) | ["<think>\nOkay, so I need to find the length of the other leg in a right triangle where the hypoten(...TRUNCATED) | ["<think>\nOkay, let's see. I need to find the length of the other leg in a right triangle where the(...TRUNCATED) | "<think>\nOkay, so I need to find the length of the other leg in a right triangle where the hypotenu(...TRUNCATED) | [{"from":"human","value":"In a triangle, the length of the hypotenuse is 15 units, and the length of(...TRUNCATED) |
[{"content":"Let $S$ be the set of all real values of $x$ with $0 < x < \\frac{\\pi}{4}$ such that $(...TRUNCATED) | "Let $S$ be the set of all real values of $x$ with $0 < x < \\frac{\\pi}{4}$ such that $\\sin x$, $\(...TRUNCATED) | "Let $S$ be the set of all real values of $x$ with $0 < x < \\frac{\\pi}{4}$ such that $\\sin x$, $\(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "**Problem:** \nLet \\( S \\) be the set of all real numbers \\( x \\) with \\( 0 < x < \\frac{\\pi(...TRUNCATED) | 29,029 | 21,363 | 1,814 | ["Okay, so I need to solve this problem where I have to find all real numbers x between 0 and π/4 s(...TRUNCATED) | ["Given the problem, we need to find all real values \\( x \\) with \\( 0 < x < \\frac{\\pi}{4} \\) (...TRUNCATED) | ["<think>\nOkay, so I need to solve this problem where I have to find all real numbers x between 0 a(...TRUNCATED) | ["<think>\nOkay, so I need to solve this problem where I have to find all real numbers x between 0 a(...TRUNCATED) | "<think>\nOkay, so I need to solve this problem where I have to find all real numbers x between 0 an(...TRUNCATED) | [{"from":"human","value":"Let $S$ be the set of all real values of $x$ with $0 < x < \\frac{\\pi}{4}(...TRUNCATED) |
[{"content":"A regular tetrahedron has a volume of 12. Find the length of the segment connecting the(...TRUNCATED) | "A regular tetrahedron has a volume of 12. Find the length of the segment connecting the center of a(...TRUNCATED) | "A regular tetrahedron has a volume of 12. Find the length of the segment connecting the center of a(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "**Given:**\n- A regular tetrahedron with volume \\(V = 12\\).\n- Need to find the length of the seg(...TRUNCATED) | 58,740 | 12,185 | 3,671 | ["Okay, so I need to find the length of a segment in a regular tetrahedron. The tetrahedron has a vo(...TRUNCATED) | ["To find the length of the segment connecting the center of a face of a regular tetrahedron to the (...TRUNCATED) | ["<think>\nOkay, so I need to find the length of a segment in a regular tetrahedron. The tetrahedron(...TRUNCATED) | ["<think>\nOkay, so I need to find the length of a segment in a regular tetrahedron. The tetrahedron(...TRUNCATED) | "<think>\nOkay, let me try to figure out this problem. So we have a regular tetrahedron with a volum(...TRUNCATED) | [{"from":"human","value":"A regular tetrahedron has a volume of 12. Find the length of the segment c(...TRUNCATED) |
[{"content":"Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} + \\frac{b}{x(...TRUNCATED) | "Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} + \\frac{b}{x^2+1} = \\fr(...TRUNCATED) | "Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} + \\frac{b}{x^2+1} = \\fr(...TRUNCATED) |
ai2-adapt-dev/openmath-2-math
| "Given the equation:\n\\[\n\\frac{a}{x-1} + \\frac{b}{x^2+1} = \\frac{x^3 - 2x^2 + 5x - 3}{x^3 + x^2(...TRUNCATED) | 23,040 | 14,699 | 1,440 | ["Okay, so I need to find the values of a and b such that the equation (a)/(x - 1) + (b)/(x² + 1) e(...TRUNCATED) | ["To find the values of \\(a\\) and \\(b\\) such that the equation\n\n\\[\n\\frac{a}{x-1} + \\frac{b(...TRUNCATED) | ["<think>\nOkay, so I need to find the values of a and b such that the equation (a)/(x - 1) + (b)/(x(...TRUNCATED) | ["<think>\nOkay, so I need to find the values of a and b such that the equation (a)/(x - 1) + (b)/(x(...TRUNCATED) | "<think>\nOkay, so I need to find the values of a and b such that the equation (a)/(x - 1) + (b)/(x(...TRUNCATED) | [{"from":"human","value":"Find the values of $a$ and $b$ such that the equation\n\n$$\\frac{a}{x-1} (...TRUNCATED) |
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