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[
{
"content": "## Task 4 - 240624\n\nRita is experimenting with a balance scale.\n\n(With such a scale, it can be determined whether the content of one pan weighs as much as the content of the other pan or which of the two contents weighs more than the other.)\n\nRita has 17 balls, 6 cubes, and 1 pyramid. She ob... | 1,541 | open-r1/OpenR1-Math-220k |
[
{
"content": "An airplane traces out a regular $n$-sided polygon, and does so at speeds of $v_{1}, v_{2}, \\ldots v_{n}$ along each side. What is the average speed of the airplane?",
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"content": "<think>\nOkay, let's see. The problem is about an airplane tracing out a regular n-si... | 2,091 | open-r1/OpenR1-Math-220k |
[
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"content": "Let $S\\,$ be a set with six elements. In how many different ways can one select two not necessarily distinct subsets of $S\\,$ so that the union of the two subsets is $S\\,$? The order of selection does not matter; for example, the pair of subsets $\\{a, c\\},\\{b, c, d, e, f\\}$ represents the ... | 3,474 | open-r1/OpenR1-Math-220k |
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"content": "146. From a group of 15 people, four participants for the relay race $800+400+200+100$ are selected. In how many ways can the athletes be arranged for the relay stages?",
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"content": "<think>\nOkay, so the problem here is: From a group of 15 people, we need to select... | 1,808 | open-r1/OpenR1-Math-220k |
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"content": "4. The area of the figure enclosed by the curve determined by the equation $|x-1|+|y-1|=1$ is\n(A) 1\n(B) 2\n(C) $\\pi$\n( D ) 4",
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"content": "<think>\nOkay, so I need to find the area enclosed by the curve defined by the equation |x - 1| + |y - 1| = 1. Hmm, let me ... | 2,864 | open-r1/OpenR1-Math-220k |
[
{
"content": "8. Given six points in space $A, B, C, D, E, F$ with no four points being coplanar. Then the maximum number of line segments that can be drawn so that no tetrahedron exists in the graph is $\\qquad$.",
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"content": "<think>\nOkay, so I need to find the maximum number ... | 2,392 | open-r1/OpenR1-Math-220k |
[
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"content": "7.1. The sum of the minuend, subtrahend, and difference is 25. Find the minuend.",
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"content": "<think>\nOkay, so I need to solve this problem where the sum of the minuend, subtrahend, and difference is 25, and I have to find the minuend. Hmm, let me start by recalli... | 2,206 | open-r1/OpenR1-Math-220k |
[
{
"content": "12. A piggy bank contains 24 coins, all nickels, dimes, and quarters. If the total value of the coins is two dollars, what combinations of coins are possible?",
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"content": "<think>\nOkay, so I need to figure out the possible combinations of nickels, dimes, and quart... | 2,407 | open-r1/OpenR1-Math-220k |
[
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"content": "3. Given the complex sequence $\\left\\{a_{n}\\right\\}$ with the general term $a_{n}=(1+\\mathrm{i}) \\cdot\\left(1+\\frac{\\mathrm{i}}{\\sqrt{2}}\\right) \\cdots\\left(1+\\frac{\\mathrm{i}}{\\sqrt{n}}\\right)$, then $\\left|a_{n}-a_{n+1}\\right|=$",
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"content": "<t... | 2,551 | open-r1/OpenR1-Math-220k |
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"content": "7. Given positive real numbers $a, b$ satisfy $a b(a+b)=4$, then the minimum value of $2 a+b$ is $\\qquad$\n\nTranslate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.",
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"content": "<th... | 3,380 | open-r1/OpenR1-Math-220k |
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"content": "Example 6 Let $x y=1$, and $x>y>0$, find the minimum value of $\\frac{x^{2}+y^{2}}{x-y}$.\n\n untranslated text is retained in its original form.",
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"content": "<think>\nOkay, so I need to find the minimum value of the expression (x² + y²)/(x - y) given that xy = 1 a... | 2,354 | open-r1/OpenR1-Math-220k |
[
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"content": "In a bag, there are 8 balls, labeled from 1 to 8. After stirring these 8 balls sufficiently, two balls are drawn from the bag at a time. Let denote $ S$ the sum of the two balls.\r\n\r\n(1) Find the probability such that $ S$ doesn't exceed in eight.\r\n\r\n(2) Let $ f(n)$ be the probability such ... | 3,085 | open-r1/OpenR1-Math-220k |
[
{
"content": "For arbiterary integers $n,$ find the continuous function $f(x)$ which satisfies the following equation. \\[\\lim_{h\\rightarrow 0}\\frac{1}{h}\\int_{x-nh}^{x+nh}f(t) dt=2f(nx).\\] Note that $x$ can range all real numbers and $f(1)=1.$",
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"content": "<think>\nOkay, s... | 2,168 | open-r1/OpenR1-Math-220k |
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"content": "2. If $a^{2}+a+1=0$, determine the value of the expression\n\n$$\na^{1987}+\\frac{1}{a^{1987}}\n$$",
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"content": "<think>\nOkay, let's see. I have this equation a² + a + 1 = 0, and I need to find the value of a¹⁹⁸⁷ + 1/a¹⁹⁸⁷. Hmm, that exponent is really big, 1987. I... | 2,643 | open-r1/OpenR1-Math-220k |
[
{
"content": "976. Find the following limits:\n1) $\\lim _{\\substack{x \\rightarrow 2 \\\\ y \\rightarrow 0}} \\frac{\\tan x y}{y}$\n2) $\\lim _{\\substack{x \\rightarrow 0 \\\\ y \\rightarrow 0}} \\frac{x+y}{x}$.",
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"content": "<think>\nOkay, let's try to solve these two limit p... | 1,501 | open-r1/OpenR1-Math-220k |
[
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"content": "4. If $-\\frac{2}{3}<x<0, y=a x^{3}+a x^{2}+b \\quad(a \\neq 0)$ is a decreasing function, then the range of values for $\\mathrm{a}$ is $\\qquad$ .",
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"content": "<think>\nOkay, let's see. I need to find the range of values for 'a' such that the function y = a x³ + ... | 2,829 | open-r1/OpenR1-Math-220k |
[
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"content": "In a large hospital with several operating rooms, ten people are each waiting for a 45 minute operation. The first operation starts at 8:00 a.m., the second at 8:15 a.m., and each of the other operations starts at 15 minute intervals thereafter. When does the last operation end?\n(A) 10:15 a.m.\n(... | 2,609 | open-r1/OpenR1-Math-220k |
[
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"content": "11.1. For what real values of the parameter a does the graph of the function $f: \\square \\rightarrow \\square$, $f(x)=x^{4}-8 x^{3}+14 x^{2}+$ ax have an axis of symmetry parallel to the line $x=0$?",
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"content": "<think>\nOkay, so I need to find the real values of... | 3,246 | open-r1/OpenR1-Math-220k |
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"content": "2. If $f(x)=\\frac{1}{x}$ has a domain $A$, and $g(x)=f(x+1)-f(x)$ has a domain $B$, then ( ).\n(A) $A \\cup B=\\mathbf{R}$\n(B) $A \\supsetneqq B$\n(C) $A \\subseteq B$\n(D) $A \\cap B=\\varnothing$",
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"content": "<think>\nOkay, let me try to figure out this problem... | 1,883 | open-r1/OpenR1-Math-220k |
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"content": "Example 5 Arrange all powers of 3 and the sums of distinct powers of 3 in an increasing sequence:\n$$\n1,3,4,9,10,12,13, \\cdots \\text {. }\n$$\n\nFind the 100th term of this sequence.",
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"content": "<think>\nOkay, let's see. The problem is to find the 100th term in... | 3,579 | open-r1/OpenR1-Math-220k |
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"content": "Anička has saved 290 coins in her piggy bank, consisting of one-crown and two-crown coins. When she uses a quarter of all the two-crown coins, she collects the same amount as when she uses a third of all the one-crown coins.\n\nWhat is the total amount Anička has saved?\n\n(L. Růžičková)",
"ro... | 1,508 | open-r1/OpenR1-Math-220k |
[
{
"content": "Three balls marked $1,2$ and $3$ are placed in an urn. One ball is drawn, its number is recorded, and then the ball is returned to the urn. This process is repeated and then repeated once more, and each ball is equally likely to be drawn on each occasion. If the sum of the numbers recorded is $6$,... | 3,324 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 9 Let real numbers $s, t$ satisfy the equations $19 s^{2}+99 s+1=0, t^{2}+99 t+19=0$, and $s t \\neq 1$.\nThen $\\frac{s t+4 s+1}{t}=$ $\\qquad$ .",
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"content": "<think>\nOkay, let's see. I need to solve for the expression (st + 4s + 1)/t given that s and t a... | 2,393 | open-r1/OpenR1-Math-220k |
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{
"content": "106. Calculate the sum:\n\n$$\nS=\\frac{1}{1 \\cdot 2}+\\frac{1}{2 \\cdot 3}+\\frac{1}{3 \\cdot 4}+\\cdots+\\frac{1}{99 \\cdot 100}\n$$",
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"content": "<think>\nOkay, let's see. I need to calculate the sum S, which is given by 1/(1×2) + 1/(2×3) + 1/(3×4) + ... + 1/(99... | 1,762 | open-r1/OpenR1-Math-220k |
[
{
"content": "On a past Mathematical Olympiad the maximum possible score on a problem was 5. The average score of boys was 4, the average score of girls was 3.25, and the overall average score was 3.60. Find the total number of participants, knowing that it was in the range from 31 to 50.... | 2,284 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 1. A pile of toothpicks 1000 in number, two people take turns to pick any number from it, but the number of toothpicks taken each time must not exceed 7. The one who gets the last toothpick loses. How many toothpicks should the first player take on the first turn to ensure victory? (New Yo... | 2,353 | open-r1/OpenR1-Math-220k |
[
{
"content": "There are functions $f(x)$ with the following properties:\n\n- $f(x)=a x^{2}+b x+c$ for some integers $a, b$ and $c$ with $a>0$, and\n- $f(p)=f(q)=17$ and $f(p+q)=47$ for some prime numbers $p$ and $q$ with $p<q$. For each such function, the value of $f(p q)$ is calculated. The sum of all possible... | 3,418 | open-r1/OpenR1-Math-220k |
[
{
"content": "The center of a circle touching the legs $A C$ and $B C$ of a right triangle $A B C$ lies on the hypotenuse $A B$. Find the radius of the circle, if it is six times smaller than the sum of the legs, and the area of triangle $A B C$ is 27.",
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"content": "<think>\nOkay... | 2,427 | open-r1/OpenR1-Math-220k |
[
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"content": "5. When $1 \\leqslant x \\leqslant 2$, simplify\n$$\n\\sqrt{x+2 \\sqrt{x-1}}+\\sqrt{x-2 \\sqrt{x-1}}=\n$$\n$\\qquad$ .",
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"content": "<think>\nOkay, let me see. So I need to simplify this expression: the square root of (x plus 2 times the square root of (x minus 1)) ... | 3,441 | open-r1/OpenR1-Math-220k |
[
{
"content": "Subject 2. Determine the integer values of $x$ and $y$ such that\n\n$$\nx-3 y+4=0 \\quad \\text { and } \\quad \\sqrt{x^{2}+7 y^{2}+8 x+8 y+4} \\in \\mathbb{Q}\n$$",
"role": "user"
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"content": "<think>\nOkay, let's see. I need to find integer values of x and y that satisfy two cond... | 3,052 | open-r1/OpenR1-Math-220k |
[
{
"content": "In the diagram, the circle has centre $O$. The shaded sector $A O B$ has sector angle $90^{\\circ}$, and $A B$ has arc length $2 \\pi$ units. The area of sector $A O B$ is\n(A) $4 \\pi$\n(D) $24 \\pi$\n(B) $16 \\pi$\n(C) $6 \\pi$\n(E) $8 \\pi$\n\n![](https://cdn.mathpix.com/cropped/2024_04_20_e85e... | 1,452 | open-r1/OpenR1-Math-220k |
[
{
"content": "A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?\n$\\mathrm{(A)}\\ 2\\qquad\\mathrm{(B)}\\ 3\\qquad\\mathrm{(C)}\\ 4\\qquad\\mathrm{(D)}\\ 5\\qquad\\mathrm{(E)}\\ 6$",
... | 2,696 | open-r1/OpenR1-Math-220k |
[
{
"content": "Determine the real polynomials satisfying the relation:\n\n$$\nP\\left(x^{2}\\right)=\\left(x^{2}+1\\right) P(x)\n$$",
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"content": "<think>\nOkay, so I need to figure out all real polynomials P that satisfy the equation P(x²) = (x² + 1) P(x). Hmm, let's start by unde... | 2,482 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. Given the quadratic equation in $x$, $x^{2}-2(p+1)$ - $x+p^{2}+8=0$, the absolute value of the difference of its roots is 2. Then the value of $p$ is ( ).\n(A) 2\n(B) 4\n(C) 6\n(D) 8",
"role": "user"
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"content": "<think>\nOkay, so I have this quadratic equation here: \\(x^{2} - ... | 2,287 | open-r1/OpenR1-Math-220k |
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{
"content": "(solved by Alice Héliou). The sum of twenty consecutive integers is 1030. What is the smallest of these integers?",
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"content": "<think>\nOkay, so the problem is: The sum of twenty consecutive integers is 1030. What is the smallest of these integers? Hmm, let's see. ... | 1,301 | open-r1/OpenR1-Math-220k |
[
{
"content": "(4) Given that $\\vec{a}$ and $\\vec{b}$ are non-zero and non-collinear vectors, let condition $M: \\vec{b} \\perp (\\vec{a}-\\vec{b})$;\ncondition $N$: for all $x \\in \\mathbf{R}$, the inequality $|\\vec{a}-x \\vec{b}| \\geqslant |\\vec{a}-\\vec{b}|$ always holds. Then $M$ is ( ) of $N$.\n(A) a ... | 2,952 | open-r1/OpenR1-Math-220k |
[
{
"content": "22. A rectangular prism with its top and bottom faces as squares is cut into two equal-volume cubes, and the surface area increases by 98 square centimeters. Then the original volume of the rectangular prism is $\\qquad$ cubic centimeters.",
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"content": "<think>\nOka... | 3,486 | open-r1/OpenR1-Math-220k |
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{
"content": "5.6. Find the unit vector collinear with the vector directed along the bisector of angle $B A C$ of triangle $A B C$, if its vertices are given: $A(1 ; 1 ; 1), B(3 ; 0 ; 1), C(0 ; 3 ; 1)$.",
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"content": "<think>\nOkay, so I need to find a unit vector that's collinear... | 2,622 | open-r1/OpenR1-Math-220k |
[
{
"content": "Let $ABC$ be an acute-angled triangle with $AB =4$ and $CD$ be the altitude through $C$ with $CD = 3$. Find the distance between the midpoints of $AD$ and $BC$",
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"content": "<think>\nOkay, let's see. I need to find the distance between the midpoints of AD and BC in ... | 2,540 | open-r1/OpenR1-Math-220k |
[
{
"content": "The expression $\\sqrt{\\frac{4}{3}} - \\sqrt{\\frac{3}{4}}$ is equal to: \n$\\textbf{(A)}\\ \\frac{\\sqrt{3}}{6}\\qquad\\textbf{(B)}\\ \\frac{-\\sqrt{3}}{6}\\qquad\\textbf{(C)}\\ \\frac{\\sqrt{-3}}{6}\\qquad\\textbf{(D)}\\ \\frac{5\\sqrt{3}}{6}\\qquad\\textbf{(E)}\\ 1$",
"role": "user"
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... | 1,575 | open-r1/OpenR1-Math-220k |
[
{
"content": "3) What is the mean (arithmetic) of the numbers 1, 2, 3, . ., 1999, 2000?\n(A) 999\n(B) 999.5\n(C) 1000\n(D) 1000.5\n(E) 1001.",
"role": "user"
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"content": "<think>\nAlright, so I need to find the arithmetic mean of the numbers from 1 all the way up to 2000. The options are given a... | 1,585 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. A school coach decided to reward 12 students who ran the distance in the best time. Each of them must be awarded a \"gold\", \"silver\", or \"bronze\" medal. All three types of medals must be used, and the one who finished earlier cannot be awarded a less valuable medal than the one who finishe... | 2,251 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. Given that $S$ is a set composed of $n(n \\geqslant 3)$ positive numbers. If there exist three distinct elements in $S$ that can form the three sides of a triangle, then $S$ is called a \"triangle number set\". Consider the set of consecutive positive integers $\\{4,5, \\cdots, m\\}$, all of wh... | 3,757 | open-r1/OpenR1-Math-220k |
[
{
"content": "6. Given the set $T=\\{1,2, \\cdots, 2010\\}$, for each non-empty subset of $T$, calculate the reciprocal of the product of all its elements. Then the sum of all such reciprocals is $\\qquad$ .",
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"content": "<think>\nOkay, so I have this problem here: Given the set ... | 3,430 | open-r1/OpenR1-Math-220k |
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"content": "## Task 6\n\nCalculate the numbers.\n\n- A is four times the smallest three-digit number,\n- B is half of the smallest four-digit number,\n- C is the sum of D and E,\n- D is $\\mathrm{B}$ minus $\\mathrm{A}$,\n- E is the sum of B and D.",
"role": "user"
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"content": "<think>\nOkay, ... | 1,137 | open-r1/OpenR1-Math-220k |
[
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"content": "1. If $x=\\frac{a-b}{a+b}$, and $a \\neq 0$, then $\\frac{b}{a}$ equals ( ).\n(A) $\\frac{1-x}{1+x}$\n(B) $\\frac{1+x}{1-x}$\n(C) $\\frac{x-1}{x+1}$\n(D) $\\frac{x+1}{x-1}$",
"role": "user"
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"content": "<think>\nOkay, let's see here. I need to solve for \\(\\frac{b}{a}\\) given tha... | 1,466 | open-r1/OpenR1-Math-220k |
[
{
"content": "9. Suppose $f$ is a function satisfying $f\\left(x+x^{-1}\\right)=x^{6}+x^{-6}$, for all $x \\neq 0$. Determine $f(3)$.",
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"content": "<think>\nOkay, so I need to find f(3) where the function f is defined such that f(x + x⁻¹) equals x⁶ + x⁻⁶ for all x not equal to ze... | 3,675 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 6 Find the unit digit of the sum $1^{2}+2^{2}+3^{2}+4^{2}+\\cdots+1994^{2}$.",
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"content": "<think>\nOkay, let's see. I need to find the unit digit of the sum of squares from 1 squared up to 1994 squared. Hmm, so the question is asking for the last digit of t... | 2,558 | open-r1/OpenR1-Math-220k |
[
{
"content": "A bag of popping corn contains $\\frac{2}{3}$ white kernels and $\\frac{1}{3}$ yellow kernels. Only $\\frac{1}{2}$ of the white kernels will pop, whereas $\\frac{2}{3}$ of the yellow ones will pop. A kernel is selected at random from the bag, and pops when placed in the popper. What is the probabi... | 2,052 | open-r1/OpenR1-Math-220k |
[
{
"content": "3.1.1. (12 points) Calculate $\\sin (\\alpha+\\beta)$, if $\\sin \\alpha+\\cos \\beta=\\frac{1}{4}$ and $\\cos \\alpha+\\sin \\beta=-\\frac{8}{5}$. Answer: $\\frac{249}{800} \\approx 0.31$.",
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"content": "<think>\nAlright, so I need to find sin(α + β) given that sinα... | 2,017 | open-r1/OpenR1-Math-220k |
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"content": "4. Let's write the natural number $a$ in its canonical form:\n\n$$\na=p_{1}^{s_{1}} \\cdot p_{2}^{s_{2}} \\cdot \\ldots \\cdot p_{n}^{s_{n}}\n$$\n\nwhere $p_{1}, p_{2}, \\ldots, p_{n}$ are distinct prime numbers, and $s_{1}, s_{2}, \\ldots, s_{n}$ are natural numbers.\n\nIt is known that the numbe... | 2,820 | open-r1/OpenR1-Math-220k |
[
{
"content": "16. Chloe chose a three-digit integer with all its digits different and wrote it on lots of pieces of paper. Peter picked some of the pieces of paper and added the three-digit integers on them. His answer was 2331. How many pieces of paper did Peter pick?\nA 2331\nB 21\nC 9\nD 7\nE 3",
"role":... | 2,044 | open-r1/OpenR1-Math-220k |
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"content": "4.017. Find four numbers that form a geometric progression, where the third term is 9 more than the first, and the second term is 18 more than the fourth.",
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"content": "<think>\nOkay, so I need to find four numbers that form a geometric progression. Let's remember t... | 1,860 | open-r1/OpenR1-Math-220k |
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{
"content": "## Problem Statement\n\nCalculate the area of the figure bounded by the graphs of the functions:\n\n$$\nx=\\frac{1}{y \\sqrt{1+\\ln y}}, x=0, y=1, y=e^{3}\n$$",
"role": "user"
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"content": "<think>\nOkay, let me try to figure out how to calculate the area of the figure bounded by th... | 1,398 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. In the right prism $A B C-A_{1} B_{1} C_{1}$, the side length of the square $A A_{1} C_{1} C$ is 4, the plane $A B C \\perp$ plane $A A_{1} C_{1} C, A B=$ $3, B C=5$. If there is a point $D$ on the line segment $B C_{1}$ such that $A D \\perp A_{1} B$, then the value of $\\frac{B D}{B C_{1}}$ i... | 3,434 | open-r1/OpenR1-Math-220k |
[
{
"content": "7. $[7]$ A student at Harvard named Kevin\nWas counting his stones by 11\nHe messed up $n$ times\nAnd instead counted $9 \\mathrm{~s}$\nAnd wound up at 2007.\nHow many values of $n$ could make this limerick true?",
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"content": "<think>\nOkay, so I need to solve this ... | 3,116 | open-r1/OpenR1-Math-220k |
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{
"content": "$1 \\cdot 73$ The value of the algebraic expression $\\sqrt{11+6 \\sqrt{2}}+\\sqrt{11-6 \\sqrt{2}}$ is\n(A) a natural number.\n(B) an irrational number.\n(C) a fraction.\n(D) none of the above conclusions is correct.\n(2nd China Tianjin \"Chinese Youth Cup\" Mathematics Invitational, 1988)",
"... | 3,857 | open-r1/OpenR1-Math-220k |
[
{
"content": "$17 \\cdot 135$ In an isosceles triangle, the altitude to the base is 8, and the perimeter is 32. Then the area of the triangle is\n(A) 56.\n(B) 48.\n(C) 40.\n(D) 32.\n(E) 24.\n(9th American High School Mathematics Examination, 1958)",
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"content": "<think>\nOkay, so ... | 1,960 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. [5] Given right triangle $A B C$, with $A B=4, B C=3$, and $C A=5$. Circle $\\omega$ passes through $A$ and is tangent to $B C$ at $C$. What is the radius of $\\omega$ ?",
"role": "user"
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{
"content": "<think>\nAlright, so I have this geometry problem here. Let me try to visualize... | 2,342 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 1 The graph of the function $y=f(x)$ is symmetric to the graph of the function $g(x)=\\log _{2} x(x>0)$ with respect to the origin, then the expression for $f(x)$ is ().\n(A) $f(x)=\\frac{1}{\\log _{2} x}(x>0)$\n(B) $f(x)=\\log _{2}(-x)(x>0)$\n(C) $f(x)=-\\log _{2} x(x<0)$\n(D) $f(x)=-\\lo... | 1,871 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 1. Find $\\int e^{x^{2}} \\cdot x d x$.",
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{
"content": "<think>\nOkay, so I need to find the integral of e^(x²) multiplied by x with respect to x. Hmm, let me think. The integral is ∫e^{x²} · x dx. Alright, first, I remember that integrating e to the power of ... | 1,469 | open-r1/OpenR1-Math-220k |
[
{
"content": "[Coordinate method on the plane] $\\left[\\begin{array}{l}\\text { [ Chords and secants (other) ] }\\end{array}\\right]$\n\nFind the length of the chord that the line $y=3 x$ cuts from the circle $(x+1)^{2}+(y-2)^{2}=25$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to fi... | 2,684 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Task 3\n\nCalculate in writing: $438+8006+98+728$",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. I need to add these four numbers: 438, 8006, 98, and 728. Hmm, adding them all together. Alright, let me start by writing them down one by one to make sure I have them right... | 1,996 | open-r1/OpenR1-Math-220k |
[
{
"content": "In trapezoid $A B C D, A D$ is parallel to $B C$ and $B C: A D=5: 7$. Point $F$ lies on $A D$ and point $E$ lies on $D C$ so that $A F: F D=4: 3$ and $C E: E D=2: 3$. If the area of quadrilateral $A B E F$ is 123 , determine the area of trapezoid $A B C D$.\n\n![](https://cdn.mathpix.com/cropped/2... | 3,794 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Task 5\n\n$50-24+36$;\n\n$$\n24+36+32\n$$\n\n$$\n45+26-11 ; \\quad 100-27-42\n$$",
"role": "user"
},
{
"content": "<think>\nOkay, let me tackle these math problems one by one. Hmm, starting with the first one: 50 minus 24 plus 36. Alright, so I need to remember the order of operatio... | 1,054 | open-r1/OpenR1-Math-220k |
[
{
"content": "(a) Show that for every $n\\in\\mathbb{N}$ there is exactly one $x\\in\\mathbb{R}^+$ so that $x^n+x^{n+1}=1$. Call this $x_n$.\r\n(b) Find $\\lim\\limits_{n\\rightarrow+\\infty}x_n$.",
"role": "user"
},
{
"content": "<think>\nAlright, let's tackle part (a) first. The problem states tha... | 3,451 | open-r1/OpenR1-Math-220k |
[
{
"content": "On the plane, nine parallel lines intersect with $n$ other parallel lines, all of which are perpendicular to the first nine. The lines together form a total of 756 rectangles. What is the value of $n$?",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem here where t... | 2,080 | open-r1/OpenR1-Math-220k |
[
{
"content": "5. Use square tiles of the same size to pave a square floor, with white tiles around the edges and black tiles in the middle (as shown in Fig. 1 and Fig. 2). When 80 white tiles are used around the square floor, the number of black tiles needed is $\\qquad$.\n\n保留源文本的换行和格式，直接输出翻译结果如下：\n\n5. Use sq... | 1,387 | open-r1/OpenR1-Math-220k |
[
{
"content": "[ Coordinate method on the plane ] $\\left[\\begin{array}{l}\\text { [Properties and characteristics of the tangent] }\\end{array}\\right.$\n\nCompose the equation of the circle with the center at point $M(3 ; 2)$, touching the line $y=2 x+6$.",
"role": "user"
},
{
"content": "<think>\... | 2,134 | open-r1/OpenR1-Math-220k |
[
{
"content": "Problem 4. If an octopus has an even number of legs, it always tells the truth. If it has an odd number, it always lies. One day, a green octopus said to a dark blue one:\n\n- I have 8 legs. And you only have 6.\n- I have 8 legs, - the dark blue one was offended. - And you only have 7.\n\n- The da... | 3,570 | open-r1/OpenR1-Math-220k |
[
{
"content": "## 1. Aljmez\n\nOn the planet Aljmez, a day is called NAD, an hour is called TAS, a minute is called NIM, and a second is called KES. One NAD lasts ten TAS, one TAS lasts ten NIM, and one NIM lasts eight KES. How many Earth seconds does one Aljmezian KES last, if one NAD lasts as long as one day?\... | 1,748 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. Given the quadratic trinomial in $x$ with integer coefficients $a x^{2}+b x+c$, when $x$ takes the values $1, 3, 6, 8$, a student recorded the values of this quadratic trinomial as $1, 5, 25, 50$. Upon checking, only one of these results is incorrect. The incorrect result is ( ).\n(A) When $x=1... | 3,489 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. The numbers 1 and 2 are written on the board. It is allowed to add new numbers in the following way: If the numbers $a$ and $b$ are written on the board, then the number $a b+a+b$ can be written. Can the following numbers be obtained in this way:\na) 13121,\nb) 12131.",
"role": "user"
},
... | 2,938 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. If $x_{1}, x_{2}$ are two distinct real roots of the equation $x^{2}+2 x-k=0$, then $x_{1}^{2}+x_{2}^{2}-2$ is ( ).\n(A) Positive\n(B) Zero\n(C) Negative\n(D) Not greater than zero\n\nTranslate the text above into English, please keep the original text's line breaks and format, and output the t... | 1,414 | open-r1/OpenR1-Math-220k |
[
{
"content": "1) Two nonnegative real numbers $x, y$ have constant sum $a$. Find the minimum value of $x^m + y^m$, where m is a given positive integer.\n2) Let $m, n$ be positive integers and $k$ a positive real number. Consider nonnegative real numbers $x_1, x_2, . . . , x_n$ having constant sum $k$. Prove tha... | 3,101 | open-r1/OpenR1-Math-220k |
[
{
"content": "If $\\frac{1}{2 n}+\\frac{1}{4 n}=\\frac{3}{12}$, then $n$ equals\n(A) 6\n(B) $\\frac{1}{2}$\n(C) $\\frac{1}{3}$\n(D) 2\n(E) 3",
"role": "user"
},
{
"content": "<think>\nOkay, let's see here. I need to solve for n in the equation (1/(2n)) + (1/(4n)) = 3/12. Hmm, okay. Let me start by u... | 2,020 | open-r1/OpenR1-Math-220k |
[
{
"content": "15. In a live military exercise, the Red side has set up 20 positions along a straight line. To test 5 different new weapons, it is planned to equip 5 positions with these new weapons, with the requirement that the first and last positions are not equipped with new weapons, and that among every 5 ... | 296 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 12. What is the minimum number of trials that need to be conducted so that with a probability of at least $\\alpha(0<\\alpha<1)$, one can expect the event $A$ to occur at least once, if the probability of event $A$ in one trial is $p$?",
"role": "user"
},
{
"content": "<think>\... | 1,980 | open-r1/OpenR1-Math-220k |
[
{
"content": "In the figure, the outer equilateral triangle has area $16$, the inner equilateral triangle has area $1$, and the three trapezoids are congruent. What is the area of one of the trapezoids?\n[asy] size((70)); draw((0,0)--(7.5,13)--(15,0)--(0,0)); draw((1.88,3.25)--(9.45,3.25)); draw((11.2,0)--(7.5,... | 3,869 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Task 5 - 210835\n\nSomeone withdraws a certain amount of money from their savings account. They receive this amount paid out in a total of 29 banknotes, exclusively in 10-mark notes, 20-mark notes, and 50-mark notes. The number of 10-mark notes is 1 less than the number of 20-mark notes. The nu... | 2,181 | open-r1/OpenR1-Math-220k |
[
{
"content": "[ Fermat's Little Theorem ]\n\nFind the remainder when $2^{100}$ is divided by 101.\n\n#",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the remainder when 2^100 is divided by 101. Hmm, the problem mentions Fermat's Little Theorem. Let me try to remember what that th... | 2,630 | open-r1/OpenR1-Math-220k |
[
{
"content": "1. It is known that the equation $x^{4}-8 x^{3}+a x^{2}+b x+16=0$ has (taking into account multiplicity) four positive roots. Find $a-b$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this equation: \\(x^{4} - 8x^{3} + a x^{2} + b x + 16 = 0\\), and it's given that all fou... | 2,389 | open-r1/OpenR1-Math-220k |
[
{
"content": "Before starting to paint, Bill had $130$ ounces of blue paint, $164$ ounces of red paint, and $188$ ounces of white paint. Bill painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and white, not necessarily i... | 2,640 | open-r1/OpenR1-Math-220k |
[
{
"content": "1. Given the complex number $z$ satisfies $|z|-z=3-\\mathrm{i}$. Then $z=$\n$\\qquad$ .",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. The problem is about a complex number z that satisfies the equation |z| - z = 3 - i. I need to find z. Hmm, complex numbers can sometimes ... | 1,974 | open-r1/OpenR1-Math-220k |
[
{
"content": "7.293. $\\left\\{\\begin{array}{l}(x+y)^{x}=(x-y)^{y}, \\\\ \\log _{2} x-\\log _{2} y=1\\end{array}\\right.$\n\nThe system of equations is:\n\\[\n\\left\\{\\begin{array}{l}\n(x+y)^{x}=(x-y)^{y}, \\\\\n\\log _{2} x-\\log _{2} y=1\n\\end{array}\\right.\n\\]",
"role": "user"
},
{
"content... | 2,432 | open-r1/OpenR1-Math-220k |
[
{
"content": "For a right-angled triangle with acute angles $\\alpha$ and $\\beta$:\n\n$$\n\\operatorname{tg} \\alpha+\\operatorname{tg} \\beta+\\operatorname{tg}^{2} \\alpha+\\operatorname{tg}^{2} \\beta+\\operatorname{tg}^{3} \\alpha+\\operatorname{tg}^{3} \\beta=70\n$$\n\nDetermine the angles.",
"role": ... | 3,567 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. Given the function $y=a \\cos x+b$ has a maximum value of 1 and a minimum value of $-7$, the maximum value of $a \\cos x+b \\sin x$ is ( ).\nA. 1\nB. 3\nC. 5\nD. 7",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to solve this problem where I'm given a function y = a cos x... | 2,129 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 2.65. Calculate the volume of the body formed by the rotation around the $O Y$ axis of the curvilinear trapezoid bounded by the hyperbola $x y=2$ and the lines $y_{1}=1, y_{2}=4$ and $y_{3}=0$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to calculate the volume o... | 3,688 | open-r1/OpenR1-Math-220k |
[
{
"content": "In this problem, the symbol $0$ represents the number zero, the symbol $1$ represents the number seven, the symbol $2$ represents the number five, the symbol $3$ represents the number three, the symbol $4$ represents the number four, the symbol $5$ represents the number two, the symbol $6$ represe... | 2,527 | open-r1/OpenR1-Math-220k |
[
{
"content": "1(!). The perimeter of a triangle is \\(12 \\mathrm{~cm}\\), and the length of one of its sides is 5 cm. Find the relationship between the lengths of the other two sides and plot the graph of this relationship.",
"role": "user"
},
{
"content": "<think>\nOkay, let me try to figure out t... | 1,895 | open-r1/OpenR1-Math-220k |
[
{
"content": "7. (Average/Difficult) A geometric sequence has a nonzero first term, distinct terms, and a positive common ratio. If the second, fourth, and fifth terms form an arithmetic sequence, find the common ratio of the geometric sequence.",
"role": "user"
},
{
"content": "<think>\nOkay, so I ... | 2,011 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. Thirty students from five classes came up with 40 tasks, and students from one class came up with the same number of tasks, while students from different classes came up with a different number. How many students came up with one task?",
"role": "user"
},
{
"content": "<think>\nOkay... | 3,652 | open-r1/OpenR1-Math-220k |
[
{
"content": "Example 6. Expand the function in powers of the difference $z-3$\n\n$$\nf(z)=\\frac{1}{3-2 z}\n$$",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to expand the function f(z) = 1/(3 - 2z) in powers of (z - 3). Hmm, expanding a function into a power series... I remember that T... | 3,257 | open-r1/OpenR1-Math-220k |
[
{
"content": "2. The students went to see an exhibition and had to pay 120 EUR for the bus fare. Since three students fell ill, each of the remaining students had to pay an additional 2 EUR for the transport. How many students signed up for the exhibition?",
"role": "user"
},
{
"content": "<think>\n... | 1,607 | open-r1/OpenR1-Math-220k |
[
{
"content": "3. Substituting the natural number $n$ into $n^{3}-n$, the following result can be obtained ( ).\nA. 678927\nB. 695644\nC. 728910\nD. 874231\nE. 934508",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. The problem is asking which of the given options is a possible result when... | 2,789 | open-r1/OpenR1-Math-220k |
[
{
"content": "## Task 3 - 241213\n\nDetermine all real numbers $x$ for which $2 x-3,5 x-14$ and $\\frac{2 x-3}{5 x-14}$ are integers.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find all real numbers x such that 2x - 3, 5x - 14, and (2x - 3)/(5x - 14) are all integers. Hmm, let me ... | 3,574 | open-r1/OpenR1-Math-220k |
[
{
"content": "377. The density function $f(x)$ of a random variable $X$, whose possible values are contained in the interval $(a, b)$, is given. Find the density function of the random variable $Y=3X$.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem where I need to find the d... | 3,107 | open-r1/OpenR1-Math-220k |
[
{
"content": "[Isosceles, inscribed and circumscribed trapezoids]\n\nThe perimeter of a trapezoid circumscribed about a circle is 40. Find the midline of the trapezoid.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the midline of a trapezoid that's circumscribed about a circle. ... | 3,636 | open-r1/OpenR1-Math-220k |
[
{
"content": "4. In triangle $ABC$, it holds that $\\frac{h_{a} h_{b}}{h_{c}}=c$, where $h_{a}, h_{b}, h_{c}$ are the lengths of the altitudes, and $c$ is the length of one side of the triangle. Determine one of the angles of this triangle.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have ... | 1,506 | open-r1/OpenR1-Math-220k |
[
{
"content": "The number $\\sqrt {2}$ is equal to: \n$\\textbf{(A)}\\ \\text{a rational fraction} \\qquad \\textbf{(B)}\\ \\text{a finite decimal} \\qquad \\textbf{(C)}\\ 1.41421 \\\\ \\textbf{(D)}\\ \\text{an infinite repeating decimal} \\qquad \\textbf{(E)}\\ \\text{an infinite non - repeating decimal}$",
... | 1,593 | open-r1/OpenR1-Math-220k |
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