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[
{
"content": "1. Calculate: $20.15 \\times 2 \\frac{1}{3}+\\frac{7}{20} \\times \\frac{17}{3}+2015=$",
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"content": "<think>\nOkay, so I need to calculate this expression: 20.15 multiplied by 2 and 1/3, plus 7/20 multiplied by 17/3, and then add 2015. Hmm, that looks a bit complica... | 3,278 | open-r1/OpenR1-Math-220k |
[
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"content": "Example 1. The nine-digit number in the form of $1234 \\times \\times \\times \\times \\times$ composed of $1,2,3,4,5,6,7,8,9$, where the ten-thousands place is not 5, the thousands place is not 6, the hundreds place is not 7, the tens place is not 8, and the units place is not 9. How many such ni... | 2,642 | open-r1/OpenR1-Math-220k |
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"content": "2. (5 points) Two different natural numbers end with 5 zeros and have exactly 42 divisors. Find their sum.",
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"content": "<think>\nOkay, let me try to figure out this problem. So, the question is about two different natural numbers that both end with five zeros and h... | 3,511 | open-r1/OpenR1-Math-220k |
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"content": "31. For which values of $n$, is the function $y=n x^{2}$\n$+(n-x) x+n-1$ negative for all $x \\in R$?",
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"content": "<think>\nOkay, so I need to find the values of n for which the function y = n x² + (n - x) x + n - 1 is negative for all real numbers x. Hmm, let me s... | 3,369 | open-r1/OpenR1-Math-220k |
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"content": "449. Find the integrals:\n1) $\\int\\left(3 x^{2}-2 x+5\\right) d x$;\n2) $\\int \\frac{2 x^{2}+x-1}{x^{3}} d x$;\n3) $\\int\\left(1+e^{x}\\right)^{2} d x$\n4) $\\int \\frac{2 x+3}{x^{2}-5} d x$;\n5) $\\int \\frac{x^{2}}{x^{2}+1} d x$;\n6) $\\int \\operatorname{tg}^{2} \\varphi d \\varphi$.",
... | 3,235 | open-r1/OpenR1-Math-220k |
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"content": "13. (15 points) A clothing store purchased 600 pairs of gloves at 12 yuan per pair, and sold 470 pairs at 14 yuan per pair. The remaining pairs were all sold at 11 yuan per pair. Find out how much profit the clothing store made from selling this batch of gloves.\n\n",
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... | 1,225 | open-r1/OpenR1-Math-220k |
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"content": "2. Given $y=|x-2|-\\frac{1}{2}|x|+|x+2|$, and $-1 \\leqslant x \\leqslant 2$. Then the difference between the maximum and minimum values of $y$ is ( ).\n(A) 4\n(B) 3\n(C) 2\n(D) 1",
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"content": "<think>\nOkay, let's see. I need to find the difference between the maxi... | 3,517 | open-r1/OpenR1-Math-220k |
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"content": "Problem 3.3. Several letters A and several letters B were sitting on a pipe. After some A fell and some B disappeared, only three letters remained on the pipe, and the following dialogue occurred between them:\n\nFirst letter: “I am the only one of my kind here.”\n\nSecond letter: “There are defin... | 3,171 | open-r1/OpenR1-Math-220k |
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"content": "Example 8. The random variable $X$ is given by the distribution function\n\n$$\nF(x)=\\left\\{\\begin{array}{lc}\n0 & \\text { if } x \\leq 0 \\\\\nx / 3 & \\text { if } 0 < x \\leq 3 \\\\\n1 & \\text { if } x > 3\n\\end{array}\\right.\n$$\n\nFind the probability that in the result of the trial, t... | 1,322 | open-r1/OpenR1-Math-220k |
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"content": "4. Let $x$ be a number such that $x+\\frac{1}{x}=4$. Find the value of $x^{3}+\\frac{1}{x^{3}}$.\n(A) 48\n(B) 50\n(C) 52\n(D) 54\n(E) None of the above",
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"content": "<think>\nOkay, so I need to find the value of \\( x^3 + \\frac{1}{x^3} \\) given that \\( x + \\frac... | 1,923 | open-r1/OpenR1-Math-220k |
[
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"content": "\\section*{Problem 3 - V11023}\n\nThe quadrilaterals \\(V_{1}, V_{2}, V_{3}\\) agree in the diagonals \\(e\\) and \\(f\\). In \\(V_{1}\\), these diagonals intersect at an angle of \\(30^{\\circ}\\), in \\(V_{2}\\) at \\(45^{\\circ}\\), and in \\(V_{3}\\) at \\(60^{\\circ}\\).\n\nHow do the areas o... | 1,548 | open-r1/OpenR1-Math-220k |
[
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"content": "24. $\\int x^{4} d x$.",
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"content": "<think>\nOkay, so I need to solve the integral of x to the fourth power with respect to x. Hmm, let me remember how to do integrals of polynomials. I think there's a power rule for integration, right? Let me recall. For a functio... | 2,496 | open-r1/OpenR1-Math-220k |
[
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"content": "## Task 6\n\nAdd the numbers from 1 to 10 !",
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"content": "<think>\nOkay, let me try to figure out how to add the numbers from 1 to 10. Hmm, so I need to sum 1 + 2 + 3 all the way up to 10. I remember there's a formula for the sum of an arithmetic series. Wait, what ... | 629 | open-r1/OpenR1-Math-220k |
[
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"content": "4. (10 points) A school has two classes each in the third and fourth grades. Class 3-1 has 4 more students than Class 3-2, Class 4-1 has 5 fewer students than Class 4-2, and the third grade has 17 fewer students than the fourth grade. Therefore, Class 3-1 has fewer students than Class 4-2 by ____.... | 1,932 | open-r1/OpenR1-Math-220k |
[
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"content": "2. Given complex numbers $z_{1}$ and $z_{2}$, and\n$$\n\\left|z_{1}\\right|=2\\left|z_{2}\\right|=2,\\left|z_{1}+z_{2}\\right|=\\sqrt{7} \\text {. }\n$$\n\nThen $\\left|z_{1}-z_{2}\\right|=(\\quad)$.\n(A) $\\sqrt{5}$\n(B) $\\sqrt{7}$\n(C) 3\n(D) $\\sqrt{3}$",
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"conte... | 2,239 | open-r1/OpenR1-Math-220k |
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"content": "5. Given that $n$ is a two-digit natural number. $n$ divided by 9 leaves a remainder of 1, and $n$ divided by 10 leaves a remainder of 3. Then the remainder when $n$ is divided by 11 is ().\n(A) 0\n(B) 2\n(C) 4\n( D ) 5\n(E) 7",
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"content": "<think>\nOkay, so I have ... | 2,305 | open-r1/OpenR1-Math-220k |
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"content": "3. Let $x, y$, and $z$ be real numbers that satisfy the following system:\n$$\n\\begin{aligned}\nx+3 y+6 z & =1 \\\\\nx y+2 x z+6 y z & =-8 \\\\\nx y z & =2\n\\end{aligned}\n$$\n\nFind the smallest possible value of $x+y+z$.",
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"content": "<think>\nOkay, so I need to... | 3,512 | open-r1/OpenR1-Math-220k |
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"content": "1. Without using a pocket calculator, calculate the value of the expression $2^{3} \\cdot 3^{-9} \\cdot 6^{6} \\cdot 8^{-8} \\cdot 1728$. The result should be written in the form of a power.",
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"content": "<think>\nOkay, let's see. I need to calculate the value of th... | 2,682 | open-r1/OpenR1-Math-220k |
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"content": "10. On a training ride, Laura averages speeds of $12 \\mathrm{~km} / \\mathrm{h}$ for 5 minutes, then $15 \\mathrm{~km} / \\mathrm{h}$ for 10 minutes and finally $18 \\mathrm{~km} / \\mathrm{h}$ for 15 minutes.\nWhat was her average speed over the whole ride?\nA $13 \\mathrm{~km} / \\mathrm{h}$\nB... | 2,133 | open-r1/OpenR1-Math-220k |
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"content": "Example 5 Try to find the maximum value of the following expression $x \\sqrt{1-y^{2}}+y \\sqrt{1-x^{2}}$.\n\n",
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"content": "<think>\nOkay, so I have this problem here where I need to find the maximum value of the expression x times the square root of (1 minus y squ... | 3,881 | open-r1/OpenR1-Math-220k |
[
{
"content": "1. Given $x^{\\frac{1}{2}}+x^{-\\frac{1}{2}}=8$, then $\\frac{x^{2}+1}{x}=$ $\\qquad$ .",
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"content": "<think>\nOkay, so I need to solve this problem where I'm given that x to the power of 1/2 plus x to the power of -1/2 equals 8, and I need to find the value of (x s... | 3,093 | open-r1/OpenR1-Math-220k |
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"content": "B2. Find all real numbers $x$ that satisfy the equation\n\n$$\n\\log _{\\sin x}\\left(\\frac{1}{2} \\sin 2 x\\right)=2\n$$",
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"content": "<think>\nOkay, let's see. I have this logarithmic equation to solve: log base sin x of (1/2 sin 2x) equals 2. Hmm. So, first, I n... | 2,537 | open-r1/OpenR1-Math-220k |
[
{
"content": "1. (8 points) Three people, A, B, and C, participated in a competition, and they placed in the top 3 (no ties).\nA says: “I am first”\nB says: “I am not first”\nC says: “I am not third”\nOnly one of the three is telling the truth.\nIf the ranks of A, B, and C are $A$, $B$, and $C$ respectively, th... | 2,189 | open-r1/OpenR1-Math-220k |
[
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"content": "$A B$ and $A C$ are equal chords, $M A N$ is a tangent, the angular measure of arc $B C$, not containing point $A$, is $200^{\\circ}$. Find the angles $M A B$ and $N A C$.",
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"content": "<think>\nOkay, so I have this geometry problem here. Let me try to visualize it ... | 3,589 | open-r1/OpenR1-Math-220k |
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"content": "Wesley is 15 and his sister Breenah is 7 . The sum of their ages is 22 . In how many years will the sum of their ages be double what it is now?\n(A) 7\n(B) 8\n(C) 15\n(D) 14\n(E) 11",
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"content": "<think>\nOkay, let's see. The problem says Wesley is 15 and his sister... | 1,797 | open-r1/OpenR1-Math-220k |
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"content": "13.318. The price of one product was reduced twice, each time by $15 \\%$. For another product, which initially had the same price as the first, the price was reduced once by $x \\%$. What should the number $x$ be so that after all the specified reductions, both products have the same price again?... | 2,211 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. If $x, y \\geqslant 0$, and $x+y=1$, then the range of $\\sqrt[3]{7 x+1}+$ $\\sqrt[3]{7 y+1}$ is $\\qquad$ .",
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"content": "<think>\nOkay, let's see. The problem is: If x and y are non-negative numbers such that x + y = 1, then find the range of the expression ∛(7... | 3,844 | open-r1/OpenR1-Math-220k |
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"content": "10.090. The distance from the center of the circle to a chord of length 16 cm is 15 cm. Find the area of the triangle circumscribed around the circle, if the perimeter of the triangle is $200 \\mathrm{~cm}$.",
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"content": "<think>\nAlright, let's tackle this problem ... | 2,733 | open-r1/OpenR1-Math-220k |
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"content": "4-7. Along a straight alley, 100 lamps are placed at equal intervals, numbered sequentially from 1 to 100. At the same time, from different ends of the alley, Petya and Vasya started walking towards each other at different constant speeds (Petya from the first lamp, Vasya from the hundredth). When... | 2,981 | open-r1/OpenR1-Math-220k |
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{
"content": "Lynnelle and Moor love toy cars, and together, they have $27$ red cars, $27$ purple cars, and $27$ green cars. The number of red cars Lynnelle has individually is the same as the number of green cars Moor has individually. In addition, Lynnelle has $17$ more cars of any color than Moor has of any ... | 2,067 | open-r1/OpenR1-Math-220k |
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"content": "52. Divide the number 10 into two parts, the difference between which is 5.",
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"content": "<think>\nOkay, let's see. The problem is to divide the number 10 into two parts such that the difference between them is 5. Hmm. Alright, so I need to find two numbers that add... | 1,911 | open-r1/OpenR1-Math-220k |
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"content": "A1. In a circle with diameter 4, we inscribe a square, in the resulting square we inscribe a circle, and in this one again a square, and we repeat the process. What is the diameter of the fourth circle?\n(A) $\\frac{1}{\\sqrt{2}}$\n(B) $\\frac{1}{2}$\n(C) 1\n(D) $\\sqrt{2}$\n(E) $2 \\sqrt{2}$",
... | 2,470 | open-r1/OpenR1-Math-220k |
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"content": "68. Find two numbers, the ratio of which is 3, and the ratio of the sum of their squares to their sum is 5.",
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"content": "<think>\nOkay, let's see. I need to find two numbers where their ratio is 3, and the ratio of the sum of their squares to their sum is 5. Hmm, l... | 1,734 | open-r1/OpenR1-Math-220k |
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{
"content": "2. Lily pours 296 litres of water into the top of the pipework shown in the diagram. Each time a pipe forks, half the water flows to one side and half to the other. How many litres of water will reach container $\\mathrm{Y}$ ?\nA 210\nB 213\nC 222\nD 225\nE 231",
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"c... | 3,491 | open-r1/OpenR1-Math-220k |
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"content": "## Problem Statement\n\nFind the distance from point $M_{0}$ to the plane passing through three points $M_{1}, M_{2}, M_{3}$.\n\n$M_{1}(1 ; 2 ;-3)$\n\n$M_{2}(1 ; 0 ; 1)$\n\n$M_{3}(-2 ;-1 ; 6)$\n\n$M_{0}(3 ;-2 ;-9)$",
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"content": "<think>\nOkay, so I need to find the ... | 2,567 | open-r1/OpenR1-Math-220k |
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{
"content": "|Rabbits sawed several logs. They made 10 cuts and got 16 chunks. How many logs did they saw\n\n#",
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"content": "<think>\nOkay, let's see. The problem says that rabbits sawed several logs. They made 10 cuts and got 16 chunks. The question is, how many logs did they s... | 1,668 | open-r1/OpenR1-Math-220k |
[
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"content": "8. Function\n$$\nf(x)=\\left\\{\\begin{array}{ll}\n\\sin \\pi x^{2}, & -1<x<0 ; \\\\\n\\mathrm{e}^{x-1}, & x \\geqslant 0\n\\end{array}\\right.\n$$\n\nsatisfies $f(1)+f(a)=2$. Then the possible values of $a$ are ( ).\n(A) 1 or $-\\frac{\\sqrt{2}}{2}$\n(B) $-\\frac{\\sqrt{2}}{2}$\n(C) 1\n(D) 1 or $... | 2,212 | open-r1/OpenR1-Math-220k |
[
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"content": "## Task 5 - 010615\n\nHow many different types of second-class passenger train tickets are needed for a route with 15 stations, if there should be a ticket for every possible connection?\n\nHow did you determine the number?\n\n",
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"content": "<think>\nOkay, so I need... | 1,414 | open-r1/OpenR1-Math-220k |
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"content": "Exercise 2. Find all pairs of digits $(a, b)$ such that the integer whose four digits are $a b 32$ is divisible by 99.",
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"content": "<think>\nOkay, let's try to solve this problem where we need to find all pairs of digits (a, b) such that the four-digit number ab32 ... | 2,947 | open-r1/OpenR1-Math-220k |
[
{
"content": "In the diagram, $\\triangle A B C$ has an area of 84 and $A C=12$. Point $D$ is on $A C$ so that $B D$ is perpendicular to $A C$. What is the length of $B D$ ?\n\n",
"... | 1,082 | open-r1/OpenR1-Math-220k |
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"content": "7. As shown in the figure, construct the inscribed circle $\\odot O$ inside the square $A B C D$, tangent to $A B$ at point $Q$ and to $C D$ at point $P$. Connect $P A, P B$ to form isosceles $\\triangle P A B$. Rotating these three figures (the square, the circle, and the isosceles triangle) arou... | 3,105 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. Find all functions $f: \\mathbb{Z} \\rightarrow \\mathbb{R}$ such that $f(1)=\\frac{5}{2}$ and\n\n$$\nf(x) f(y)=f(x+y)+f(x-y), \\text { for all } x, y \\in \\mathbb{Z}\n$$",
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"content": "<think>\nOkay, so I need to find all functions f from the integers to the rea... | 3,475 | open-r1/OpenR1-Math-220k |
[
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"content": "The value of $(4-3) \\times 2$ is\n(A) -2\n(B) 2\n(C) 1\n(D) 3\n(E) 5",
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"content": "<think>\nOkay, let's see. The problem is (4 - 3) × 2, and I need to figure out which of the options A to E is the correct answer. Alright, first, I remember that in math problems, es... | 760 | open-r1/OpenR1-Math-220k |
[
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"content": "$4 \\cdot 42$ If $a$ and $b$ represent two unequal positive numbers, then\n(A) $\\frac{2 a b}{a+b}>\\sqrt{a b}>\\frac{a+b}{2}$.\n(B) $\\sqrt{a b}>\\frac{2 a b}{a+b}>\\frac{a+b}{2}$.\n(C) $\\frac{2 a b}{a+b}>\\frac{a+b}{2}>\\sqrt{a b}$.\n(D) $\\frac{a+b}{2}>\\frac{2 a b}{a+b}>\\sqrt{a b}$.\n(E) $\\... | 2,041 | open-r1/OpenR1-Math-220k |
[
{
"content": "A positive integer $N$ with three digits in its base ten representation is chosen at random, \nwith each three digit number having an equal chance of being chosen. The probability that $\\log_2 N$ is an integer is \n$\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ 3/899 \\qquad \\textbf{(C)}\\ 1/225 \... | 2,156 | open-r1/OpenR1-Math-220k |
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"content": "3. The telephone numbers in a certain city consist of 5 digits, each of which can be any one of the ten digits $0-9$. If a telephone number is chosen at random, the probability that it consists of 5 different digits is ( ).\n\n",
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"content": "<think>\nOkay, so I need... | 3,419 | open-r1/OpenR1-Math-220k |
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"content": "Tamika selects two different numbers at random from the set $\\{ 8,9,10 \\}$ and adds them. Carlos takes two different numbers at random from the set $\\{3, 5, 6\\}$ and multiplies them. What is the probability that Tamika's result is greater than Carlos' result?\n$\\text{(A)}\\ \\dfrac{4}{9} \\... | 3,705 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Problem Statement\n\nCalculate the volumes of solids formed by rotating the figures bounded by the graphs of the functions. The axis of rotation is $O x$.\n\n$$\ny=x e^{x}, y=0, x=1\n$$",
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"content": "<think>\nOkay, so I need to find the volume of the solid formed... | 2,672 | open-r1/OpenR1-Math-220k |
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"content": "7.3. If the first digit of a two-digit natural number $N$ is multiplied by 4, and the second digit is multiplied by 2, then the sum of the numbers obtained after the multiplication will give $\\frac{N}{2}$. Find $N$ (list all solutions).",
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"content": "<think>\nOkay,... | 1,973 | open-r1/OpenR1-Math-220k |
[
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"content": "## Task Condition\n\nDerive the equation of the normal to the given curve at the point with abscissa $x_{0}$.\n\n$y=x+\\sqrt{x^{3}}, x_{0}=1$",
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"content": "<think>\nOkay, so I need to find the equation of the normal to the curve y = x + √(x³) at the point where x₀ =... | 3,227 | open-r1/OpenR1-Math-220k |
[
{
"content": "2.222. $\\left(\\frac{2-n}{n-1}+4 \\cdot \\frac{m-1}{m-2}\\right):\\left(n^{2} \\cdot \\frac{m-1}{n-1}+m^{2} \\cdot \\frac{2-n}{m-2}\\right) ; m=\\sqrt[4]{400}, n=\\sqrt{5}$.",
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"content": "<think>\nOkay, so I need to simplify this big expression here. Let me first w... | 3,218 | open-r1/OpenR1-Math-220k |
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{
"content": "Example 4. Given the quadratic function $\\mathrm{y}=3 \\mathrm{p} \\mathrm{x}^{2}-6 \\mathrm{px} +3 p-2$, for what value of $p$ will the distance between the two intersection points of this parabola with the $x$-axis be $\\frac{\\sqrt{6}}{3}$.\n\n---\n\nThe translation maintains the original text... | 2,938 | open-r1/OpenR1-Math-220k |
[
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"content": "Let $S$ be the set of all real values of $x$ with $0 < x < \\pi/2$ such that $\\sin x$, $\\cos x$, and $\\tan x$ form the side lengths (in some order) of a right triangle. Compute the sum of $\\tan^2 x$ over all $x$ in $S$.",
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"content": "<think>\nOkay, so I have th... | 3,509 | open-r1/OpenR1-Math-220k |
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"content": "Task A-1.2. (4 points)\n\nDetermine the natural number whose 9-fold is between 1100 and 1200, and whose 13-fold is between 1500 and 1600.\n\nFor a natural number $n$, the $n$-fold of a number is the number that is $n$ times larger than that number.",
"role": "user"
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"content": "<th... | 2,337 | open-r1/OpenR1-Math-220k |
[
{
"content": "Exercise 1. Find $a$ such that $\\frac{1}{\\sqrt{a+7}}+\\frac{1}{7}=\\frac{19}{84}$.",
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"content": "<think>\nAlright, let's tackle this problem. So, I need to find the value of 'a' that satisfies the equation: 1 divided by the square root of (a + 7) plus 1/7 equals 1... | 1,774 | open-r1/OpenR1-Math-220k |
[
{
"content": "[ Arithmetic. Mental calculation, etc.]\n\nWhat angle do the hour and minute hands form at 4:12?\n\n#",
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"content": "<think>\nOkay, so I need to figure out the angle between the hour and minute hands at 4:12. Hmm, let's see. I remember that clocks can be a bit tricky... | 1,323 | open-r1/OpenR1-Math-220k |
[
{
"content": "1. (10 points) If $\\frac{2013 \\times 2013}{2014 \\times 2014+2012}=\\frac{\\mathrm{n}}{\\mathrm{m}}$ (where $m$ and $n$ are coprime natural numbers), then the value of $m+n$ is ( )\nA. 1243\nB. 1343\nC. 4025\nD. 4029",
"role": "user"
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"content": "<think>\nOkay, so I need to solve... | 2,196 | open-r1/OpenR1-Math-220k |
[
{
"content": "Square $A B C D$ has sides of length 2. The midpoint of $B C$ is $E$. Point $F$ is on $A E$ so that $D F$ is perpendicular to $A E$. Determine the length of $D F$.\n\n",
... | 2,329 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Example 5. Given the function\n\n$$\nf(x)= \\begin{cases}0 & \\text { if } x \\leq 0 \\\\ c e^{-\\alpha x} & \\text { if } x>0 \\quad(\\alpha>0)\\end{cases}\n$$\n\nFor what value of the constant $c$ is the function $f(x)$ a probability density function of some random variable $X$?",
"role":... | 1,481 | open-r1/OpenR1-Math-220k |
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{
"content": "[Area and Volume (Extremum Problems).]\n\nConsider all possible rectangular parallelepipeds whose bases are squares and each of whose lateral faces has a perimeter of 6. Find among them the parallelepiped with the greatest volume and calculate this volume.",
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"conten... | 1,993 | open-r1/OpenR1-Math-220k |
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"content": "Condition of the problem\n\nCalculate the limit of the function:\n\n$\\lim _{x \\rightarrow 0} \\frac{1-\\cos 2 x}{\\cos 7 x-\\cos 3 x}$",
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"content": "<think>\nOkay, so I need to find the limit as x approaches 0 of (1 - cos2x)/(cos7x - cos3x). Hmm, let's see. I reme... | 2,483 | open-r1/OpenR1-Math-220k |
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{
"content": "45. Find the scalar product of vectors $\\vec{a}=(3 ; 5)$ and $\\vec{b}=(-2 ; 7)$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the scalar product of two vectors, right? The vectors given are \\(\\vec{a} = (3; 5)\\) and \\(\\vec{b} = (-2; 7)\\). Hmm, scalar produc... | 2,923 | open-r1/OpenR1-Math-220k |
[
{
"content": "3B. A tower made of cards requires 2 cards for one level, 7 cards for two levels, and 15 cards for a tower of three levels (see diagram). How many cards are needed for a tower of $n$ levels?",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how many cards are nee... | 2,244 | open-r1/OpenR1-Math-220k |
[
{
"content": "Mr. Stein is ordering a two-course dessert at a restaurant. For each course, he can choose to eat pie, cake, rødgrød, and crème brûlée, but he doesn't want to have the same dessert twice. In how many ways can Mr. Stein order his meal? (Order matters.)",
"role": "user"
},
{
"content": "... | 1,355 | open-r1/OpenR1-Math-220k |
[
{
"content": "62*. Given two points: $A_{1}\\left(x_{1}, y_{1}, z_{1}\\right)$ and $A_{2}\\left(x_{2}, y_{2}, z_{2}\\right)$. Point $P$ defines two vectors: $\\overrightarrow{P A}_{1}=\\vec{q}_{1}$ and $\\overrightarrow{P A}_{2}=\\vec{q}_{2}$. What does the set of points $P$ represent, for which the condition $... | 3,125 | open-r1/OpenR1-Math-220k |
[
{
"content": "Is there a 6-digit number that becomes 6 times larger when its last three digits are moved to the beginning of the number, keeping the order of the digits?",
"role": "user"
},
{
"content": "<think>\nAlright, let's tackle this problem step by step. So, the question is asking if there's ... | 2,933 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Task 1 - 280731\n\nThe volume of a cube $w_{1}$ is eight times as large as the volume of a cube $w_{2}$.\n\nIf the volume of $w_{2}$ were exactly $9 \\mathrm{~cm}^{3}$ smaller, it would be equal to one twelfth of the volume of $w_{1}$.\n\nDetermine from these data the edge lengths $a_{1}$ and $... | 1,818 | open-r1/OpenR1-Math-220k |
[
{
"content": "28. Define a new operation “ $\\oplus$ ” : $a \\oplus b=\\left\\{\\begin{array}{ll}a, & (\\text { if } a \\geq b) \\\\ b, & \\text { (if } a<b)\\end{array}\\right.$, for example: $6.5 \\oplus 2=6.5,1 \\oplus 7=7$. Then $\\frac{2.3 \\oplus \\frac{7}{3}+\\frac{1}{9} \\oplus 0.1}{\\frac{4}{9} \\oplus... | 3,085 | open-r1/OpenR1-Math-220k |
[
{
"content": "Find the value of $ c$ such that $ \\sum_{n \\equal{} 1}^{11} (n \\minus{} c)(2n \\minus{} c)$ is minimal and find the minimum value $ m$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the value of c that minimizes the sum from n=1 to 11 of (n - c)(2n - c). Hmm, le... | 2,345 | open-r1/OpenR1-Math-220k |
[
{
"content": "$10 \\cdot 61$ The algebraic expression $\\frac{1}{\\log _{2} 100!}+\\frac{1}{\\log _{3} 100!}+\\frac{1}{\\log _{4} 100!}+\\cdots+\\frac{1}{\\log _{100} 100!}$ has the value\n(A) 0.01 .\n(B) 0.1 .\n(C) 1 .\n(D) 2 .\n(E) 0 .\n(49th American High School Mathematics Examination, 1998)",
"role": "... | 2,014 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. (10 points) Xiaohua needs to arrive at the Youth Palace for an activity at 2 PM, but his watch is 4 minutes fast every hour. He deliberately set his watch correctly at 10 AM. When Xiaohua arrives at the Youth Palace at 2 PM according to his watch, he actually arrives ( ) minutes early.\nA. 14\n... | 3,129 | open-r1/OpenR1-Math-220k |
[
{
"content": "11. Given the complex number $z$ satisfies $z \\cdot \\bar{z}-z-\\bar{z}=3$, and $\\arg (z-1)$ $=\\frac{\\pi}{3}$. Then $z=$ $\\qquad$ .",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. The problem is about a complex number z that satisfies two conditions: first, the equatio... | 2,337 | open-r1/OpenR1-Math-220k |
[
{
"content": "11.55 Simplify the fraction $\\frac{n!}{(n+1)!-n!}$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to simplify the fraction \\(\\frac{n!}{(n+1)! - n!}\\). Hmm, factorials can sometimes be tricky, but let me think step by step. \n\nFirst, I know that \\(n!\\) means the prod... | 865 | open-r1/OpenR1-Math-220k |
[
{
"content": "If the integers $-7,10,9,0,-9$ are ordered from least to greatest, what is the third integer in the list?\n(A) -7\n(B) 10\n(C) 9\n(D) 0\n(E) -9",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem here where I need to order the integers -7, 10, 9, 0, -9 from least to... | 1,182 | open-r1/OpenR1-Math-220k |
[
{
"content": "5. If $\\theta \\in\\left(0, \\frac{\\pi}{2}\\right), f(\\theta)=\\cos \\theta+\\theta \\sin \\theta$, then among the following judgments\n(1) $f(\\theta)>1$,(2) $f(\\theta)1$; there also exists $\\theta$, such that $f(\\theta)<1$, the correct sequence number is $\\qquad$ .",
"role": "user"
... | 3,087 | open-r1/OpenR1-Math-220k |
[
{
"content": "1A. a) Let $f$ be a real function defined on $\\mathbb{R}$. Find the real function $g(x)$, if $f(x)=3x+2$ and $f\\left(x^{2}+x g(x)\\right)=3 x^{2}+6 x+5$, for every $x \\in \\mathbb{R} \\backslash\\{0\\}$.\n\nb) Let $f(x)=x+2$, for every $x \\in \\mathbb{R}$. Find the function $g(x)$ such that $f... | 2,556 | open-r1/OpenR1-Math-220k |
[
{
"content": "The locus of the centers of all circles of given radius $a$, in the same plane, passing through a fixed point, is:\n$\\textbf{(A) }\\text{a point}\\qquad \\textbf{(B) }\\text{a straight line}\\qquad \\textbf{(C) }\\text{two straight lines}\\qquad \\textbf{(D) }\\text{a circle}\\qquad \\textbf{(E)... | 1,305 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Task Condition\n\nFind the angle between the planes:\n\n$x-3 y+5=0$\n\n$2 x-y+5 z-16=0$",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the angle between two planes given by the equations x - 3y + 5 = 0 and 2x - y + 5z - 16 = 0. Hmm, I remember that the angle betw... | 3,142 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 1 Let $m, n$ be positive integers, find the minimum value of $\\left|12^{m}-5^{m}\\right|$.\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.",
"role": "user"
},
{
"content": "<think>\nO... | 2,739 | open-r1/OpenR1-Math-220k |
[
{
"content": "Problem 2. Misha, Anton, Katya, and Natasha organized a table tennis tournament. When asked who took which place, they answered:\n\nMisha: - I was neither first nor last.\n\nAnton: - I was not last.\n\nKatya: - I was first.\n\nNatasha: - I was last.\n\nIt is known that one of the kids lied, while ... | 2,566 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. Vasya constructed a robot, but he messed up the program, so the robot makes random moves that somehow always lead it to the right point.\n\nA move is a one-kilometer displacement either north (N), east (E), south (S), or west (W).\n\nThe robot reached its goal in 22 moves:\n\n# EENENNWNENESEEEE... | 1,541 | open-r1/OpenR1-Math-220k |
[
{
"content": "6. A box contains $m$ red balls, 9 white balls, and $n$ black balls, all of which are identical except for their color. If at least 17 balls must be drawn to ensure that there are 5 red balls, and at least 17 balls must be drawn to ensure that there are 8 balls of the same color. Then the value of... | 3,207 | open-r1/OpenR1-Math-220k |
[
{
"content": "8. In the diagram, the area of the large square is $16 \\mathrm{~cm}^{2}$ and the area of each small corner square is $1 \\mathrm{~cm}^{2}$. What is the shaded area?\nA $3 \\mathrm{~cm}^{2}$\nB $\\frac{7}{2} \\mathrm{~cm}^{2}$\nC $4 \\mathrm{~cm}^{2}$\nD $\\frac{11}{2} \\mathrm{~cm}^{2}$\nE $6 \\m... | 2,587 | open-r1/OpenR1-Math-220k |
[
{
"content": "12. Given the sequence $\\left\\{a_{n}\\right\\}$, where $a_{1}=1, a_{2}=2, a_{n} a_{n+1} a_{n+2}=a_{n}+a_{n+1}+a_{n-2}$, and $a_{n+1} a_{n+2} \\neq 1$, then $a_{1}+a_{2}+\\cdots+a_{2004}=$ $\\qquad$",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this sequence problem here.... | 2,813 | open-r1/OpenR1-Math-220k |
[
{
"content": "A5. What is the perimeter of a right triangle if one interior angle is $60^{\\circ}$ and the lengths of the legs differ by 2 units?\n(A) $4 \\sqrt{3}+6$\n(B) $4 \\sqrt{3}-6$\n(C) $4 \\sqrt{3}+2$\n(D) $4 \\sqrt{3}+4$\n(E) 6",
"role": "user"
},
{
"content": "<think>\nOkay, let me see. So... | 2,524 | open-r1/OpenR1-Math-220k |
[
{
"content": "28. Consider a sequence of real numbers $\\left\\{a_{n}\\right\\}$ defined by $a_{1}=1$ and $a_{n+1}=\\frac{a_{n}}{1+n a_{n}}$ for $n \\geq 1$.\nFind the value of $\\frac{1}{a_{2005}}-2000000$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the value of 1/a_{2005} m... | 2,613 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. Teacher Wang decorated the classroom with stickers, arranging them in a row. She first stuck 15 Bing Dwen Dwen stickers, and then inserted 2 Shuey Rhon Rhon stickers between each adjacent pair of Bing Dwen Dwen stickers. Teacher Wang stuck a total of $\\qquad$ stickers.",
"role": "user"
}... | 1,305 | open-r1/OpenR1-Math-220k |
[
{
"content": "1. A vessel with a capacity of 10 liters is filled with air containing $24\\%$ oxygen. A certain volume of air was pumped out of the vessel and the same volume of argon was added. Then, the same volume of the mixture as the first time was pumped out and again the same volume of argon was added. In... | 2,709 | open-r1/OpenR1-Math-220k |
[
{
"content": "1. (16 points) Fresh mushrooms contain $80 \\%$ water by mass, while dried mushrooms contain $20 \\%$ water. How many kg of dried mushrooms can be obtained from 20 kg of fresh mushrooms?",
"role": "user"
},
{
"content": "<think>\nAlright, so here's this problem about mushrooms. Let me ... | 2,005 | open-r1/OpenR1-Math-220k |
[
{
"content": "Ana and Luíza train every day for the Big Race that will take place at the end of the year at school, each always at the same speed. The training starts at point $A$ and ends at point $B$, which are $3000 \\mathrm{~m}$ apart. They start at the same time, but when Luíza finishes the race, Ana still... | 3,309 | open-r1/OpenR1-Math-220k |
[
{
"content": "In one American company, every employee is either a Democrat or a Republican. After one Republican decided to become a Democrat, the number of each became equal. Then, three more Republicans decided to become Democrats, and the number of Democrats became twice the number of Republicans. How many e... | 1,469 | open-r1/OpenR1-Math-220k |
[
{
"content": "3. Let the function $f: \\mathbf{R} \\rightarrow \\mathbf{R}$, for any $x, y \\in \\mathbf{R}$, we have $f(x+y)=f(x)+f(y)$, and when $x<0$, $f(x)<0$. If the graph of $y=f(x)$ intersects or is tangent to the line $2007 x + 2008 y = 2009$, then the number of intersection or tangent points is ( ).\n(... | 2,866 | open-r1/OpenR1-Math-220k |
[
{
"content": "464. A number consists of three digits; the sum of these digits is 11; the digit in the units place is twice the digit in the hundreds place. If you add 297 to the desired number, you get a number written with the same digits as the desired number, but in reverse order. What number has these prope... | 1,893 | open-r1/OpenR1-Math-220k |
[
{
"content": "69. Faulty Locomotive. We set off by railway from Angchester to Clinkerton. But an hour after the train started, a locomotive malfunction was discovered. We had to continue the journey at a speed that was $\\frac{3}{5}$ of the original. As a result, we arrived in Clinkerton 2 hours late, and the d... | 3,102 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. In $\\triangle A B C$, it is known that $A B=A C=8 \\sqrt{3}$, and the altitude $A D$ $=8$. Then the radius of the circumcircle of $\\triangle A B C$ is $(\\quad$.\n(A) 8\n(B) 9\n(C) 10\n(D) 12",
"role": "user"
},
{
"content": "<think>\nOkay, let's try to solve this problem step by ... | 3,618 | open-r1/OpenR1-Math-220k |
[
{
"content": "33. For $n=1,2,3, \\ldots$, let $a_{n}=n^{2}+100$, and let $d_{n}$ denote the greatest common divisor of $a_{n}$ and $a_{n+1}$. Find the maximum value of $d_{n}$ as $n$ ranges over all positive integers.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the maximum val... | 3,535 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Task 1\n\nThe school garden is getting a new wire fence. There is always 1 meter between one post and the next. 8 meters have already been completed.\n\nHow many posts have been used so far?",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. The school garden is putting up ... | 939 | open-r1/OpenR1-Math-220k |
[
{
"content": "3. If Peter walks along a moving escalator at his normal speed, it takes 40 seconds to finish riding on the escalator. If Peter walks at twice his normal speed, it takes 30 seconds to finish riding on the escalator. How many seconds does it take for Peter to finish riding on the escalator if he st... | 1,583 | open-r1/OpenR1-Math-220k |
[
{
"content": "Let's determine the sum of the following series:\n\n$$\n\\binom{n}{0}+\\binom{n+1}{1}+\\binom{n+2}{2}+\\ldots+\\binom{n+k}{k}\n$$\n\nwhere $n$ and $k$ are natural numbers. (The symbol $\\binom{n}{k}$ represents the number of ways to choose $k$ elements from a set of $n$ elements, disregarding the ... | 1,819 | open-r1/OpenR1-Math-220k |
[
{
"content": "1) The integers have a mean of 6 and a sum of 18. How many integers are there? (A) 3 (B) 6\n\n(C) 12\n\n(D) 108\n\n(E) cannot be determined.",
"role": "user"
},
{
"content": "<think>\nAlright, so I've got this problem here. Let me read it again. It says, \"The integers have a mean of 6... | 1,203 | open-r1/OpenR1-Math-220k |
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