data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "(1) Given $\\cos \\alpha =\\frac{\\sqrt{5}}{3}, \\alpha \\in \\left(-\\frac{\\pi }{2},0\\right)$, find $\\sin (\\pi -\\alpha)$;\n\n(2) Given $\\cos \\left(\\theta+ \\frac{\\pi}{4}\\right)= \\frac{4}{5}, \\theta \\in \\left(0, \\frac{\\pi}{2}\\right)$, find $\\cos \\left(\\frac{... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"index": 300,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given $\\cos(15°+\\alpha) = \\frac{15}{17}$, with $\\alpha \\in (0°, 90°)$, find the value of $\\sin(15°-\\alpha)$. \n(2) Given $\\cos\\alpha = \\frac{1}{7}$, $\\cos(\\alpha-\\beta) = \\frac{13}{14}$, and $0 < \\beta < \\alpha < \\frac{\\pi}{2}$, find the value of $\\beta$... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{3}"
} | {
"index": 301,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given $\\frac{\\sin\\alpha + 3\\cos\\alpha}{3\\cos\\alpha - \\sin\\alpha} = 5$, find the value of $\\sin^2\\alpha - \\sin\\alpha\\cos\\alpha$.\n(2) Given a point $P(-4, 3)$ on the terminal side of angle $\\alpha$, determine the value of $\\frac{\\cos\\left(\\frac{\\pi}{2} +... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{4}"
} | {
"index": 302,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given $\\sin \\left( \\frac{\\pi }{3}-\\alpha \\right)=\\frac{1}{2}$, find the value of $\\cos \\left( \\frac{\\pi }{6}+\\alpha \\right)$;\n\n(2) Given $\\cos \\left( \\frac{5\\pi }{12}+\\alpha \\right)=\\frac{1}{3}$ and $-\\pi < \\alpha < -\\frac{\\pi }{2}$, find the value... | math | {
"style": "rule",
"ground_truth": "- \\frac{1}{3}+ \\frac{2 \\sqrt{2}}{3}"
} | {
"index": 303,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given $\\sin\\left( \\alpha +\\frac{\\pi }{4} \\right)=\\frac{\\sqrt{2}}{10}$, with $\\alpha\\in(0,\\pi)$, find the value of $\\cos \\alpha$;\n\n(2) Evaluate: $\\left( \\tan {10^{\\circ} }-\\sqrt{3} \\right)\\sin {40^{\\circ} }$."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 304,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given $\\tan(\\alpha+\\beta)= \\frac{2}{5}$ and $\\tan\\left(\\beta- \\frac{\\pi}{4}\\right)= \\frac{1}{4}$, find the value of $\\frac{\\cos\\alpha+\\sin\\alpha}{\\cos\\alpha-\\sin\\alpha}$; \n(2) Given $\\alpha$ and $\\beta$ are acute angles, and $\\cos(\\alpha+\\beta)= \... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"index": 305,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given a point P(-4, 3) on the terminal side of angle $\\alpha$, calculate the value of $$\\frac {\\cos( \\frac {\\pi}{2}+\\alpha)\\sin(-\\pi-\\alpha)}{\\cos( \\frac {11\\pi}{2}-\\alpha )\\sin( \\frac {9\\pi}{2}+\\alpha )}$$.\n(2) If $\\sin x= \\frac {m-3}{m+5}$ and $\\cos x... | math | {
"style": "rule",
"ground_truth": "-\\frac {5}{12}"
} | {
"index": 306,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given a sequence $\\{a_n\\}$ that satisfies $a_1a_2…a_n=n+1$, find $a_3=$\n\n(2) Let $\\overrightarrow{e_1}, \\overrightarrow{e_2}$ be unit vectors, where $\\overrightarrow{a}=2\\overrightarrow{e_1}+\\overrightarrow{e_2}, \\overrightarrow{b}=\\overrightarrow{e_2}$, and $\\o... | math | {
"style": "rule",
"ground_truth": "6:5:4"
} | {
"index": 307,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given that $0 < x < \\dfrac{4}{3}$, find the maximum value of $x(4-3x)$.\n\n(2) Point $(x,y)$ moves along the line $x+2y=3$. Find the minimum value of $2^{x}+4^{y}$."
}
] | math | {
"style": "rule",
"ground_truth": "4 \\sqrt{2}"
} | {
"index": 308,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given that $\\log_2{2} = a$, express $\\log_8{20} - 2\\log_2{20}$ in terms of $a$.\n(2) Evaluate the expression: $(\\ln{4})^0 + (\\frac{9}{4})^{-0.5} + \\sqrt{(1 - \\sqrt{3})^2} - 2^{\\log_4{3}}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{9}{2} - 2\\sqrt{3}"
} | {
"index": 309,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given that $\\tan \\alpha = -2$, calculate the value of $\\dfrac {3\\sin \\alpha + 2\\cos \\alpha}{5\\cos \\alpha - \\sin \\alpha}$.\n(2) Given that $\\sin \\alpha = \\dfrac {2\\sqrt{5}}{5}$, calculate the value of $\\tan (\\alpha + \\pi) + \\dfrac {\\sin \\left( \\dfrac {5... | math | {
"style": "rule",
"ground_truth": "-\\dfrac{5}{2}"
} | {
"index": 310,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given that $x < 3$, find the maximum value of $f(x) = \\frac{4}{x - 3} + x$;\n(2) Given that $x, y \\in \\mathbb{R}^+$ and $x + y = 4$, find the minimum value of $\\frac{1}{x} + \\frac{3}{y}$."
}
] | math | {
"style": "rule",
"ground_truth": "1 + \\frac{\\sqrt{3}}{2}"
} | {
"index": 311,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given the complex number $z=3+bi$ ($i$ is the imaginary unit, $b$ is a positive real number), and $(z-2)^{2}$ is a pure imaginary number, find the complex number $z$;\n(2) Given that the sum of all binomial coefficients in the expansion of $(3x+ \\frac{1}{ \\sqrt{x}})^{n}$ ... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 312,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Given the hyperbola $C$: $\\dfrac{x^{2}}{a^{2}} - \\dfrac{y^{2}}{b^{2}} = 1$ $(a > 0, b > 0)$, its right vertex is $A$, and a circle $A$ with center $A$ and radius $b$ intersects one of the asymptotes of the hyperbola $C$ at points $M$ and $N$. If $\\angle MAN = 60^{\\circ}... | math | {
"style": "rule",
"ground_truth": "\\dfrac{4}{5}"
} | {
"index": 313,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) How many natural numbers are there that are less than 5000 and have no repeated digits?\n(2) From the digits 1 to 9, five digits are selected each time to form a 5-digit number without repeated digits.\n (i) If only odd digits can be placed in odd positions, how many such... | math | {
"style": "rule",
"ground_truth": "1800"
} | {
"index": 314,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) If $\\cos (\\frac{\\pi}{4}+x) = \\frac{3}{5}$, and $\\frac{17}{12}\\pi < x < \\frac{7}{4}\\pi$, find the value of $\\frac{\\sin 2x + 2\\sin^2 x}{1 - \\tan x}$.\n\n(2) Given the function $f(x) = 2\\sqrt{3}\\sin x\\cos x + 2\\cos^2 x - 1 (x \\in \\mathbb{R})$, if $f(x_0) = \\... | math | {
"style": "rule",
"ground_truth": "\\frac{3 - 4\\sqrt{3}}{10}"
} | {
"index": 315,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) If 7 students stand in a row, and students A and B must stand next to each other, how many different arrangements are there? \n(2) If 7 students stand in a row, and students A, B, and C must not stand next to each other, how many different arrangements are there? \n(3) If... | math | {
"style": "rule",
"ground_truth": "3720"
} | {
"index": 316,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) If the terminal side of angle $\\theta$ passes through $P(-4t, 3t)$ ($t>0$), find the value of $2\\sin\\theta + \\cos\\theta$. \n(2) Given that a point $P$ on the terminal side of angle $\\alpha$ has coordinates $(x, -\\sqrt{3})$ ($x\\neq 0$), and $\\cos\\alpha = \\frac{\\... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"index": 317,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) In $\\triangle ABC$, if $2\\lg \\tan B=\\lg \\tan A+\\lg \\tan C$, then the range of values for $B$ is ______. \n(2) Find the maximum value of the function $y=7-4\\sin x\\cos x+4\\cos ^{2}x-4\\cos ^{4}x$ ______."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 318,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) In an arithmetic sequence $\\{ a_n \\}$, given that $a_1 + a_7 + a_{13} = 6$, find the value of $S_{13}$.\n\n(2) Determine the interval of decrease for the function $y = \\log_{\\frac{1}{2}}(x^2 + 2x - 3)$.\n\n(3) In triangle $ABC$, given $a = \\sqrt{3}$, $b = 1$, and $\\an... | math | {
"style": "rule",
"ground_truth": "10\\pi"
} | {
"index": 319,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) In triangle $ABC$, the sides opposite angles $A$, $B$, $C$ are denoted as $a$, $b$, $c$ respectively. If $2b\\cos B = a\\cos C + c\\cos A$, find $B$.\n\n(2) In an arithmetic sequence $\\{a_n\\}$, if $a_1 + a_7 + a_{13} = 6$, then find $S_{13}$, the sum of the first 13 terms... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{4}"
} | {
"index": 320,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Let the function $f(x) = |x - 2| + |x + a|$. If the inequality $f(x) \\geq 3$ always holds for all $x \\in \\mathbb{R}$, find the range of values for the real number $a$.\n(2) Given positive numbers $x, y, z$ that satisfy $x + 2y + 3z = 1$, find the minimum value of $\\frac... | math | {
"style": "rule",
"ground_truth": "16 + 8\\sqrt{3}"
} | {
"index": 321,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Let the function $f(x)=|x+2|+|x-a|$. If the inequality $f(x) \\geqslant 3$ always holds for $x$ in $\\mathbb{R}$, find the range of the real number $a$.\n\n(2) Given positive numbers $x$, $y$, $z$ satisfying $x+2y+3z=1$, find the minimum value of $\\frac{3}{x}+\\frac{2}{y}+... | math | {
"style": "rule",
"ground_truth": "16+8\\sqrt{3}"
} | {
"index": 322,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Point $P$ is any point on the curve $y=x^{2}-\\ln x$. The minimum distance from point $P$ to the line $x-y-4=0$ is ______.\n\n(2) If the tangent line to the curve $y=g(x)$ at the point $(1,g(1))$ is $y=2x+1$, then the equation of the tangent line to the curve $f(x)=g(x)+\\l... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"index": 323,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Simplify: $\\dfrac {\\tan (3\\pi-\\alpha)\\cos (2\\pi-\\alpha)\\sin (-\\alpha+ \\dfrac {3\\pi}{2})}{\\cos (-\\alpha-\\pi)\\sin (-\\pi+\\alpha)\\cos (\\alpha+ \\dfrac {5\\pi}{2})}$; \n(2) Given $\\tan \\alpha= \\dfrac {1}{4}$, find the value of $\\dfrac {1}{2\\cos ^{2}\\alp... | math | {
"style": "rule",
"ground_truth": "\\dfrac {17}{20}"
} | {
"index": 324,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Simplify: $\\dfrac{\\sin(\\pi -\\alpha)\\cos(\\pi +\\alpha)\\sin(\\dfrac{\\pi}{2}+\\alpha)}{\\sin(-\\alpha)\\sin(\\dfrac{3\\pi}{2}+\\alpha)}$.\n\n(2) Given $\\alpha \\in (\\dfrac{\\pi}{2}, \\pi)$, and $\\sin(\\pi -\\alpha) + \\cos \\alpha = \\dfrac{7}{13}$, find $\\tan \\al... | math | {
"style": "rule",
"ground_truth": "-\\dfrac{12}{5}"
} | {
"index": 325,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Simplify: $\\dfrac{\\tan(3\\pi-\\alpha)\\cos(2\\pi-\\alpha)\\sin(-\\alpha+\\dfrac{3\\pi}{2})}{\\cos(-\\alpha-\\pi)\\sin(-\\pi+\\alpha)\\cos(\\alpha+\\dfrac{5\\pi}{2})}$;\n\n(2) Given $\\tan\\alpha=\\dfrac{1}{4}$, find the value of $\\dfrac{1}{2\\cos^{2}\\alpha-3\\sin\\alpha... | math | {
"style": "rule",
"ground_truth": "\\dfrac{17}{20}"
} | {
"index": 326,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Simplify: $f(α)= \\dfrac {\\sin (α+ \\dfrac {3}{2}π)\\sin (-α+π)\\cos (α+ \\dfrac {π}{2})}{\\cos (-α -π )\\cos (α - \\dfrac {π}{2})\\tan (α +π )}$\n(2) Evaluate: $\\tan 675^{\\circ}+\\sin (-330^{\\circ})+\\cos 960^{\\circ}$"
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 327,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Solve the inequality $$\\frac {2x+1}{3-x}≥1$$ \n(2) Given $x>0$, $y>0$, and $x+y=1$, find the minimum value of $$\\frac {4}{x} + \\frac {9}{y}$$."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 328,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Solve the inequality $\\log_{\\frac{1}{2}}(x+2) > -3$\n(2) Calculate: $(\\frac{1}{8})^{\\frac{1}{3}} \\times (-\\frac{7}{6})^{0} + 8^{0.25} \\times \\sqrt[4]{2} + (\\sqrt[3]{2} \\times \\sqrt{3})^{6}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{221}{2}"
} | {
"index": 329,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Solve the inequality $|x+1| + 2|x-1| < 3x + 5$.\n(2) Given $a, b \\in [0, 1]$, find the maximum value of $ab + (1-a-b)(a+b)$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 330,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) The definite integral $\\int_{-1}^{1}(x^{2}+\\sin x)dx=$ ______.\n\n(2) There are 2 red balls, 1 white ball, and 1 blue ball in a box. The probability of drawing two balls with at least one red ball is ______.\n\n(3) Given the function $f(x)=\\begin{cases}1-\\log_{a}(x+2), ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"index": 331,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Two poles are 6m apart with a rope tied between them, and a lamp is hung on the rope. Find the probability that the distance between the lamp and both ends is greater than 2m; \n(2) From the numbers 1, 2, 3, 4, 5, 6, if two numbers are randomly selected and added together,... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"index": 332,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Use the Euclidean algorithm to find the greatest common divisor (GCD) of 117 and 182, and verify it using the method of successive subtraction. \n(2) Use the Horner's method to calculate the value of the polynomial \\\\(f(x)=1-9x+8x^{2}-4x^{4}+5x^{5}+3x^{6}\\\\) at \\\\(x=... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 333,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Use the Euclidean algorithm to find the greatest common divisor (GCD) of 2146 and 1813. \n(2) Use the Horner's method to calculate the value of $v_4$ for the function $f(x) = 2x^5 + 3x^4 + 2x^3 - 4x + 5$ when $x = 2$."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 334,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Use the Euclidean algorithm to find the greatest common divisor of 117 and 182, and verify it using the subtraction method. \n(2) Use the Horner's method to evaluate the polynomial $f(x) = 1 - 9x + 8x^2 - 4x^4 + 5x^5 + 3x^6$ at $x = -1$."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 335,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) Use the Horner's method to calculate the polynomial $f(x) = 3x^6 + 5x^5 + 6x^4 + 79x^3 - 8x^2 + 35x + 12$ when $x = -4$, find the value of $v_3$. \n(2) Convert the hexadecimal number $210_{(6)}$ into a decimal number."
}
] | math | {
"style": "rule",
"ground_truth": "78"
} | {
"index": 336,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1) When $x \\in \\left[\\frac{\\pi}{6}, \\frac{7\\pi}{6}\\right]$, find the maximum value of the function $y = 3 - \\sin x - 2\\cos^2 x$. \n(2) Given that $5\\sin\\beta = \\sin(2\\alpha + \\beta)$ and $\\tan(\\alpha + \\beta) = \\frac{9}{4}$, find $\\tan \\alpha$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"index": 337,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1+11+21+31+41)+(9+19+29+39+49)="
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"index": 338,
"solution": "1. **Identify the terms in each group and their properties**: \n The problem gives us two sums:\n \\[\n (1+11+21+31+41) \\quad \\text{and} \\quad (9+19+29+39+49)\n \\]\n Each group contains five terms, and the terms in each group are increasing by 10.\n\n2. **Rearrange using a... |
DeepScaleR | [
{
"role": "user",
"content": "(12 points in total) 4 students are sitting in a row to watch a movie, and there are 6 seats in the row. \n(1) How many seating arrangements are there such that there is exactly one person between students A and B, and there are no empty seats between them? \n(2) How many sea... | math | {
"style": "rule",
"ground_truth": "240"
} | {
"index": 339,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(12 points) A workshop has a total of 12 workers and needs to equip two types of machines. Each type A machine requires 2 people to operate, consumes 30 kilowatt-hours of electricity per day, and can produce products worth 40,000 yuan; each type B machine requires 3 people to o... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 340,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(12 points) Using the six digits 0, 1, 2, 3, 4, 5, complete the following three questions:\n(1) If digits can be repeated, how many different five-digit even numbers can be formed?\n(2) If digits cannot be repeated, how many different five-digit numbers divisible by 5, with the... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 341,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(13 points) A rental company owns 100 cars. When the monthly rent for each car is set at 3000 yuan, all cars can be rented out. For every 50 yuan increase in the monthly rent per car, there will be one more car that remains unrented. The maintenance cost for each rented car is ... | math | {
"style": "rule",
"ground_truth": "307050"
} | {
"index": 342,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(15) Given the following propositions:\n\n(1) \"If $x > 2$, then $x > 0$\" - the negation of the proposition\n\n(2) \"For all $a \\in (0, +\\infty)$, the function $y = a^x$ is strictly increasing on its domain\" - the negation\n\n(3) \"$π$ is a period of the function $y = \\sin... | math | {
"style": "rule",
"ground_truth": "(2)(3)"
} | {
"index": 343,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(1901 + 1902 + 1903 + \\cdots + 1993) - (101 + 102 + 103 + \\cdots + 193) ="
}
] | math | {
"style": "rule",
"ground_truth": "167400"
} | {
"index": 344,
"solution": "1. **Identify the pattern in the sequences**: \n The problem involves two sums of arithmetic sequences. The first sequence starts at 1901 and ends at 1993, and the second sequence starts at 101 and ends at 193.\n\n2. **Recognize the relationship between the sequences**:\n Each term ... |
DeepScaleR | [
{
"role": "user",
"content": "(2014•Shanghai) In a certain game, the scores are 1, 2, 3, 4, 5. The random variable $\\xi$ represents Xiao Bai's score in this game. If $E(\\xi) = 4.2$, then the probability that Xiao Bai scores 5 points is at least ___."
}
] | math | {
"style": "rule",
"ground_truth": "0.2"
} | {
"index": 345,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(6?3) + 4 - (2 - 1) = 5. To make this statement true, the question mark between the 6 and the 3 should be replaced by"
}
] | math | {
"style": "rule",
"ground_truth": "\\div"
} | {
"index": 346,
"solution": "We start by simplifying the expression on the right side of the equation:\n\\[ (6?3) + 4 - (2 - 1) = 5. \\]\n\nFirst, simplify the parentheses on the right:\n\\[ 2 - 1 = 1. \\]\n\nNow, substitute this back into the equation:\n\\[ (6?3) + 4 - 1 = 5. \\]\n\nSimplify further:\n\\[ (6?3) + ... |
DeepScaleR | [
{
"role": "user",
"content": "(Answer in numbers) \nFrom 5 different storybooks and 4 different math books, 4 books are to be selected and given to 4 students, one book per student. How many different ways are there to: \n(1) Select 2 storybooks and 2 math books? \n(2) Ensure one specific storybook and o... | math | {
"style": "rule",
"ground_truth": "1080"
} | {
"index": 347,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Caos) A cao [sic] has 6 legs, 3 on each side. A walking pattern for the cao is defined as an ordered sequence of raising and lowering each of the legs exactly once (altogether 12 actions), starting and ending with all legs on the ground. The pattern is safe if at any point, he... | math | {
"style": "rule",
"ground_truth": "1416528"
} | {
"index": 348,
"solution": "```\nAnswer: 1416528\n# 1 = on ground, 0 = raised, 2 = back on ground\ncache = {}\ndef pangzi(legs):\n if legs == (2,2,2,2,2,2): return 1\n elif legs.count(0) > 3: return 0\n elif legs[0] + legs[1] + legs[2] == 0: return 0\n elif legs[3] + legs[4] + legs[5] == 0: return 0\n ... |
DeepScaleR | [
{
"role": "user",
"content": "(Convert the following binary number to decimal: 101111011<sub>(2)</sub>)"
}
] | math | {
"style": "rule",
"ground_truth": "379"
} | {
"index": 349,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Elective 4-4: Coordinate Systems and Parametric Equations)\n\nIn the rectangular coordinate system $xOy$, a pole coordinate system is established with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar coordinate equation ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}+2"
} | {
"index": 350,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Experimental Class Question) Given that $\\cos \\alpha = \\frac{1}{7}$ and $\\cos (\\alpha - \\beta) = \\frac{13}{14}$, with $0 < \\beta < \\alpha < \\pi$.\n\n1. Find the value of $\\sin (2\\alpha - \\frac{\\pi}{6})$;\n2. Find the value of $\\beta$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{3}"
} | {
"index": 351,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Exploring with a counter) Write any multiple of 3, cube each of its digits and add them together, then cube each digit of the new number obtained and add them together to get another new number, and keep repeating this process... \n(1) Write out the calculation formulas; \n(... | math | {
"style": "rule",
"ground_truth": "153"
} | {
"index": 352,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(For science students) In the expansion of $(x^2 - 3x + 2)^4$, the coefficient of the $x^2$ term is __________ (Answer with a number)."
}
] | math | {
"style": "rule",
"ground_truth": "248"
} | {
"index": 353,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Full score for this problem is 12 points) Given $f(x) = e^x - ax - 1$.\n\n(1) Find the intervals where $f(x)$ is monotonically increasing.\n(2) If $f(x)$ is monotonically increasing on the domain $\\mathbb{R}$, find the range of possible values for $a$.\n(3) Does there exist a... | math | {
"style": "rule",
"ground_truth": "a = 1"
} | {
"index": 354,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Full score: 8 points) \nDuring the 2010 Shanghai World Expo, there were as many as 11 types of admission tickets. Among them, the price for a \"specified day regular ticket\" was 200 yuan per ticket, and the price for a \"specified day concession ticket\" was 120 yuan per tic... | math | {
"style": "rule",
"ground_truth": "300"
} | {
"index": 355,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Geometry Proof Exercise) From a point A outside a circle ⊙O with radius 2, draw a line intersecting ⊙O at points C and D. A line segment AB is tangent to ⊙O at B. Given that AC=4 and AB=$4 \\sqrt {2}$, find $tan∠DAB$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac { \\sqrt {2}}{4}"
} | {
"index": 356,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(In the 15th Jiangsu Grade 7 First Trial) On a straight street, there are 5 buildings numbered from left to right as 1, 2, 3, 4, 5. The building numbered $k$ has exactly $k$ (where $k=1, 2, 3, 4, 5$) workers from Factory A. The distance between two adjacent buildings is 50 mete... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"index": 357,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(In the coordinate system and parametric equations optional question) In the polar coordinate system, it is known that the line $l: p(\\sin\\theta - \\cos\\theta) = a$ divides the region enclosed by the curve $C: p = 2\\cos\\theta$ into two parts with equal area. Find the value... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 358,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(In the preliminaries of optimal method and experimental design) When using the 0.618 method to find the optimal amount to add in an experiment, if the current range of excellence is $[628, 774]$ and the good point is 718, then the value of the addition point for the current ex... | math | {
"style": "rule",
"ground_truth": "684"
} | {
"index": 359,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(In this question, 12 points) During a shooting training session, the probabilities of a shooter hitting the 10, 9, 8, and 7 rings are 0.21, 0.23, 0.25, and 0.28, respectively. Calculate the probability that the shooter in a single shot:\n(1) Hits either the 10 or 7 ring; \n(2... | math | {
"style": "rule",
"ground_truth": "0.03"
} | {
"index": 360,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Lucas Numbers) The Lucas numbers are defined by $L_{0}=2, L_{1}=1$, and $L_{n+2}=L_{n+1}+L_{n}$ for every $n \\geq 0$. There are $N$ integers $1 \\leq n \\leq 2016$ such that $L_{n}$ contains the digit 1 . Estimate $N$."
}
] | math | {
"style": "rule",
"ground_truth": "1984"
} | {
"index": 361,
"solution": "```\nAnswer: 1984\nlucas_ones n = length . filter (elem '1') $ take (n + 1) lucas_strs\n where\n lucas = 2 : 1 : zipWith (+) lucas (tail lucas)\n lucas_strs = map show lucas\nmain = putStrLn . show $ lucas_ones 2016\n```"
} |
DeepScaleR | [
{
"role": "user",
"content": "(Self-Isogonal Cubics) Let $A B C$ be a triangle with $A B=2, A C=3, B C=4$. The isogonal conjugate of a point $P$, denoted $P^{*}$, is the point obtained by intersecting the reflection of lines $P A$, $P B, P C$ across the angle bisectors of $\\angle A, \\angle B$, and $\\angl... | math | {
"style": "rule",
"ground_truth": "49"
} | {
"index": 362,
"solution": "The first main insight is that all the cubics pass through the points $A, B, C, H$ (orthocenter), $O$, and the incenter and three excenters. Since two cubics intersect in at most nine points, this is all the intersections of a cubic with a cubic. On the other hand, it is easy to see tha... |
DeepScaleR | [
{
"role": "user",
"content": "(The 2018 Anqing City, Anhui Province, China, High School Second Mock Exam) Given that the focus of the parabola $x^{2}=4y$ is $F$, points $A$ and $B$ are on the parabola, and satisfy $\\overrightarrow{AF}=λ\\overrightarrow{FB}$. If $|\\overrightarrow{AF}|=\\frac{3}{2}$, then t... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 363,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(The full score for this question is 12 points) Given $f(x+1)=x^2-1$, \n(1) Find $f(x)$ \n(2) Find the maximum and minimum values of $f(x)$, and specify the corresponding values of $x$"
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 364,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(The full score for this question is 8 points) Arrange 3 male students and 2 female students in a row, \n (1) The number of all different arrangements; \n(2) The number of arrangements where exactly two male students are adjacent; \n(3) The number of arrangements where male... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 365,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(The full score for this question is 8 points) There are 4 red cards labeled with the numbers 1, 2, 3, 4, and 2 blue cards labeled with the numbers 1, 2. Four different cards are drawn from these 6 cards. \n(1) If it is required that at least one blue card is drawn, how many d... | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 366,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(The full score of this question is 12 points) In a box, there are three cards labeled 1, 2, and 3, respectively. Now, two cards are drawn from this box with replacement in succession, and their labels are denoted as $x$ and $y$, respectively. Let $\\xi = |x-2| + |y-x|$. \n(1)... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{9}"
} | {
"index": 367,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(The full score of this question is 14 points) It is known that A and B are two fixed points on a plane, and the moving point P satisfies $|PA| + |PB| = 2$.\n(1) Find the equation of the trajectory of point P;\n(2) Suppose the line $l: y = k (k > 0)$ intersects the trajectory o... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 368,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(This question has a total of 10 points)\nFrom a group consisting of 5 male doctors and 4 female doctors, select 3 doctors to form a medical team. The requirement is that the team must include both male and female doctors. How many different team formation plans are there?"
}... | math | {
"style": "rule",
"ground_truth": "70"
} | {
"index": 369,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(This question is worth 14 points.)\n\nA newspaper stand in a city buys the \"Evening News\" from the newspaper office at a price of 0.20 yuan per copy and sells it at 0.30 yuan per copy. The unsold newspapers can be returned to the newspaper office at a price of 0.05 yuan per ... | math | {
"style": "rule",
"ground_truth": "825"
} | {
"index": 370,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(a) A natural number $n$ is less than 120. What is the largest remainder that the number 209 can give when divided by $n$?\n\n(b) A natural number $n$ is less than 90. What is the largest remainder that the number 209 can give when divided by $n$?"
}
] | math | {
"style": "rule",
"ground_truth": "69"
} | {
"index": 371,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(a) A natural number \\( n \\) is less than 120. What is the maximum remainder that the number 209 can leave when divided by \\( n \\)?\n\n(b) A natural number \\( n \\) is less than 90. What is the maximum remainder that the number 209 can leave when divided by \\( n \\)?"
}... | math | {
"style": "rule",
"ground_truth": "69"
} | {
"index": 372,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(a) In a tennis tournament with 64 players, how many matches are played?\n\n(b) In a tournament with 2011 players, how many matches are played?"
}
] | math | {
"style": "rule",
"ground_truth": "113"
} | {
"index": 373,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(a) In the diagram, $\\triangle PQR$ is right-angled at $R$. If $PQ = 25$ and $RQ = 24$, determine the perimeter and area of $\\triangle PQR$.\n\n(b) In the diagram, $\\triangle ABC$ is right-angled at $C$ with $AB = c$, $AC = b$, and $BC = a$. Also, $\\triangle ABC$ has a peri... | math | {
"style": "rule",
"ground_truth": "65"
} | {
"index": 374,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(a) The natural number \\( n \\) is less than 150. What is the largest remainder that the number 269 can give when divided by \\( n \\)?\n\n(b) The natural number \\( n \\) is less than 110. What is the largest remainder that the number 269 can give when divided by \\( n \\)?"
... | math | {
"style": "rule",
"ground_truth": "109"
} | {
"index": 375,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(from The Good Soldier Svejk) Senior military doctor Bautze exposed $abccc$ malingerers among $aabbb$ draftees who claimed not to be fit for the military service. He managed to expose all but one draftees. (He would for sure expose this one too, if the lucky guy was not tak... | math | {
"style": "rule",
"ground_truth": "10999"
} | {
"index": 376,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(x^2+1)(2x+1)^9=a_0+a_1(x+2)+a_2(x+2)^2+\\ldots+a_{11}(x+2)^{11}, calculate the sum of the coefficients a_0 through a_11."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"index": 377,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "(Ⅰ) Find the equation of the line that passes through the intersection point of the two lines $2x-3y-3=0$ and $x+y+2=0$, and is perpendicular to the line $3x+y-1=0$. \n(Ⅱ) Given the equation of line $l$ in terms of $x$ and $y$ as $mx+y-2(m+1)=0$, find the maximum distance from... | math | {
"style": "rule",
"ground_truth": "2 \\sqrt {2}"
} | {
"index": 378,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**\nConsider a set of numbers $\\{1, 2, 3, 4, 5, 6, 7\\}$. Two different natural numbers are selected at random from this set. What is the probability that the greatest common divisor (gcd) of these two numbers is one? Express your answer as a common fraction.\n\n**"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{17}{21}"
} | {
"index": 379,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**\nEvaluate \n\\[\n\\frac{3}{\\log_8{3000^4}} + \\frac{4}{\\log_9{3000^4}},\n\\]\ngiving your answer as a fraction in lowest terms.\n\n**"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 380,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**\nHow many non-similar regular 500-pointed stars are there?\n\n**"
}
] | math | {
"style": "rule",
"ground_truth": "99"
} | {
"index": 381,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**\nLet \\( P \\) be a point on the parabola \\( y = x^2 - 6x + 15 \\), and let \\( Q \\) be a point on the line \\( y = 2x - 7 \\). Find the shortest possible distance \\( PQ \\).\n\n**"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{6 \\sqrt{5}}{5}"
} | {
"index": 382,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**A person rolls seven standard, six-sided dice. What is the probability that there is at least one pair but no three dice show the same value?**"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{315}{972}"
} | {
"index": 383,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**Circle $T$ has a circumference of $12\\pi$ inches, and segment $XY$ is a diameter. If the measure of angle $TXZ$ is $45^{\\circ}$, what is the length, in inches, of segment $XZ$?**"
}
] | math | {
"style": "rule",
"ground_truth": "6\\sqrt{2}"
} | {
"index": 384,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**Compute the sum of all four-digit numbers where every digit is distinct and then find the remainder when this sum is divided by 1000.**"
}
] | math | {
"style": "rule",
"ground_truth": "720"
} | {
"index": 385,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**How many different positive integers can be represented as a difference of two distinct members of the set $\\{1, 3, 6, \\ldots, 45\\}$, where the numbers form an arithmetic sequence? Already given that the common difference between successive elements is 3.**"
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 386,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**How many positive factors does 72 have, and what is their sum?**"
}
] | math | {
"style": "rule",
"ground_truth": "195"
} | {
"index": 387,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**Problem Statement**: Let $r$ and $k$ be integers such that $-5 < r < 8$ and $0 < k < 10$. What is the probability that the division $r \\div k$ results in an integer value? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{33}{108}"
} | {
"index": 388,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**Q13.** Determine the greatest value of the sum $M=11xy+3x+2012yz$ , where $x,y,z$ are non negative integers satisfying condition $x+y+z=1000.$"
}
] | math | {
"style": "rule",
"ground_truth": "503000000"
} | {
"index": 389,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**Q14.** Let be given a trinagle $ABC$ with $\\angle A=90^o$ and the bisectrices of angles $B$ and $C$ meet at $I$ . Suppose that $IH$ is perpendicular to $BC$ ( $H$ belongs to $BC$ ). If $HB=5 \\text{cm}, \\; HC=8 \\text{cm}$ , compute the area of $\\triangle ... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 390,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**Q8.** Given a triangle $ABC$ and $2$ point $K \\in AB, \\; N \\in BC$ such that $BK=2AK, \\; CN=2BN$ and $Q$ is the common point of $AN$ and $CK$ . Compute $\\dfrac{ S_{ \\triangle ABC}}{S_{\\triangle BCQ}}.$"
}
] | math | {
"style": "rule",
"ground_truth": "7/4"
} | {
"index": 391,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**Sarah has misplaced her friend Layla's phone number. Sarah recalls that the first four digits are either 3086, 3089, or 3098. The remaining digits are 0, 1, 2, and 5, but she is not sure about their order. If Sarah randomly calls a seven-digit number based on these criteria, ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{72}"
} | {
"index": 392,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**The first term of a sequence is $2089$. Each succeeding term is the sum of the squares of the digits of the previous term. What is the $2089^{\\text{th}}$ term of the sequence?**"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 393,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**p1.** Is it possible to place six points in the plane and connect them by nonintersecting segments so that each point will be connected with exactly\na) Three other points?\nb) Four other points?**p2.** Martian bank notes can have denomination of $1, 3, 5, 25$ marts. Is it ... | math | {
"style": "rule",
"ground_truth": "1376"
} | {
"index": 394,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**p1.** The Evergreen School booked buses for a field trip. Altogether, $138$ people went to West Lake, while $115$ people went to East Lake. The buses all had the same number of seats and every bus has more than one seat. All seats were occupied and everybody had a seat. H... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 395,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**p1.** Triangle $ABC$ has side lengths $AB = 3^2$ and $BC = 4^2$ . Given that $\\angle ABC$ is a right angle, determine the length of $AC$ .**p2.** Suppose $m$ and $n$ are integers such that $m^2+n^2 = 65$ . Find the largest possible value of $m-n$ .**p3.** Six m... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 396,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**p22.** Consider the series $\\{A_n\\}^{\\infty}_{n=0}$ , where $A_0 = 1$ and for every $n > 0$ , $$ A_n = A_{\\left[ \\frac{n}{2023}\\right]} + A_{\\left[ \\frac{n}{2023^2}\\right]}+A_{\\left[ \\frac{n}{2023^3}\\right]}, $$ where $[x]$ denotes the largest integer v... | math | {
"style": "rule",
"ground_truth": "653"
} | {
"index": 397,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**p4.** What is gcd $(2^6 - 1, 2^9 - 1)$ ?**p5.** Sarah is walking along a sidewalk at a leisurely speed of $\\frac12$ m/s. Annie is some distance behind her, walking in the same direction at a faster speed of $s$ m/s. What is the minimum value of $s$ such that Sarah and... | math | {
"style": "rule",
"ground_truth": "\\frac{21}{16}"
} | {
"index": 398,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "**polyhedral**\n\nwe call a $12$ -gon in plane good whenever:\nfirst, it should be regular, second, it's inner plane must be filled!!, third, it's center must be the origin of the coordinates, forth, it's vertices must have points $(0,1)$ , $(1,0)$ , $(-1,0)$ and $(0,-1)$ .... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 399,
"solution": ""
} |
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