messages listlengths 2 2 |
|---|
[
{
"role": "user",
"content": "Let the set $A=\\{1,2,3\\}$, and the set $B=\\{0,1,2\\}$. Then, the number of elements in $A\\cup B$ is $(\\quad)$.\n\nA: $2$\n\nB: $3$\n\nC: $4$\n\nD: $5$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "C",
"test_case": null,
"thin... |
[
{
"role": "user",
"content": "The extreme value points of the function $f(x) = \\frac {1}{3} x^3 - \\frac {1}{4} x^4$ in the interval (0, 3) are __________.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "x = 1",
"test_case": null,
"think_content": null,
"... |
[
{
"role": "user",
"content": "Given the power function $f(x) = x^{9-3m}$ $(m \\in N^*)$ whose graph is symmetric about the origin and is monotonically increasing on $\\mathbb{R}$.\n\n$(1)$ Find the expression for $f(x)$; \n$(2)$ Find the range of values for $a$ that satisfies $f(a+1) + f(3a-4) < 0$.",
... |
[
{
"role": "user",
"content": "A certain school initiated a charity book donation activity called \"A Dream of Reading for Children in Poor Areas\". Within a short week, a large number of books were donated by students. A random survey was conducted on the donation situation of some students, and the collect... |
[
{
"role": "user",
"content": "In an isosceles triangle, one side length is $6$ and the other side length is $14$. What is the perimeter of the triangle?\n\nA: $26$\n\nB: $26$ or $34$\n\nC: $34$\n\nD: $20$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "C",
"test_case"... |
[
{
"role": "user",
"content": "If $a-3b=-3$, then the value of the algebraic expression $5-a+3b$ is ( )\nA: 0\nB: 2\nC: 5\nD: 8",
"info": {
"source": "openR1Math_extended",
"reference_answer": "D",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
... |
[
{
"role": "user",
"content": "Let's consider the following statements:\n- For statement A: The function $f(x) = |x^2 + mx + n|$ has four monotonic intervals.\n- For statement B: The function $g(x) = \\log(x^2 + mx + n)$ has its range as $\\mathbb{R}$.\n\nThen, statement A is to statement B as ( )\n\nA: A su... |
[
{
"role": "user",
"content": "There are 3 girls and 5 boys standing in a row.\n\n(1) If all the girls stand together, how many different arrangements are there?\n\n(2) If no two girls stand next to each other, how many different arrangements are there?",
"info": {
"source": "openR1Math_extended",
... |
[
{
"role": "user",
"content": "6. Which of the following numbers cannot be expressed as the difference of squares of two natural numbers?\nA. 2021\nB. 2020\nC. 2019\nD. 2018\nE. 2017",
"info": {
"source": "openR1Math_extended",
"reference_answer": "D",
"test_case": null,
"think_co... |
[
{
"role": "user",
"content": "Let non-zero vectors $\\vec{a}$ and $\\vec{b}$ satisfy $|\\vec{a}| = |\\vec{b}|$. If $(2\\vec{a} + \\vec{b}) \\cdot \\vec{b} = 0$, then the angle between vectors $\\vec{a}$ and $\\vec{b}$ is $\\_\\_\\_\\_\\_\\_\\_\\_$.",
"info": {
"source": "openR1Math_extended",
... |
[
{
"role": "user",
"content": "Given the function $$f(x)=- \\frac {1}{2}x^{2}+1$$, where $x \\in \\mathbb{R}$.\n1. Find the equation of the tangent line to the function's graph that passes through the point (1,1).\n2. Calculate the area of the closed figure formed by the graph of function $f(x)$ and the line... |
[
{
"role": "user",
"content": "Given that the derivative of the function $f(x)$ is $f'(x)$, and it satisfies $f(x)=2x{{f'}}(1)+\\frac{1}{x}$, then ${f'}\\left(1\\right)=$____.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "1",
"test_case": null,
"think_content":... |
[
{
"role": "user",
"content": "Given that $S_n$ is the sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$, if $S_3+S_7=37$, then $19a_3+a_{11}=$ ()\nA: $47$\nB: $73$\nC: $37$\nD: $74$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "D",
"test_case": null,... |
[
{
"role": "user",
"content": "The number of hyperbolas with asymptotes \\\\(2x \\pm 3y = 0\\\\) is \\\\((\\quad)\\)\nA: \\\\(1\\\\)\nB: \\\\(2\\\\)\nC: \\\\(3\\\\)\nD: Infinite",
"info": {
"source": "openR1Math_extended",
"reference_answer": "D",
"test_case": null,
"think_content... |
[
{
"role": "user",
"content": "If the complex number $(m^{2}+i)(1-mi)$ is a real number, then the real number $m=$ \nA: $- \\sqrt {2}$\nB: $ \\sqrt {2}$\nC: $-1$\nD: $1$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "D",
"test_case": null,
"think_content": null,... |
[
{
"role": "user",
"content": "(2014 Jiangxi Province Key High Schools Alliance Second Mock Exam for Senior High School Students) 21. To us all in China, \\_\\_\\_\\_\\_\\_\\_ experience of taking the college entrance examination seems an important way to judge whether one’s life is \\_\\_\\_\\_\\_\\_ comple... |
[
{
"role": "user",
"content": "Given the universal set $U = [0, 2]$ and the set $M = \\{x \\mid x^2 - x \\leq 0\\}$, find the complement of $M$ with respect to $U$, denoted as $\\complement_U M$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "(1, 2]",
"test_case": nul... |
[
{
"role": "user",
"content": "Which of the following calculations is correct?\n\nA: $\\left(a^{3}\\right)^{2}=a^{5}$\n\nB: $ a^{2}+a^{5}=a^{7}$\n\nC: $ \\left(ab\\right)^{3}=ab^{3}$\n\nD: $ a^{2}\\cdot a^{5}=a^{7}$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "D",
"... |
[
{
"role": "user",
"content": "Let $\\{a_n\\}$ be a geometric sequence with a common ratio not equal to 1, and $a_4=16$. The sum of the first $n$ terms is denoted as $S_n$, and $5S_1$, $2S_2$, $S_3$ form an arithmetic sequence. \n(1) Find the general formula for the sequence $\\{a_n\\}$. \n(2) Let $b_n = \... |
[
{
"role": "user",
"content": "Simplify first, then evaluate: $4xy+\\left(2x-y\\right)\\left(2x+y\\right)-\\left(2x+y\\right)^{2}$, where $x=2022$ and $y=-\\sqrt{2}$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "-4",
"test_case": null,
"think_content": null,
... |
[
{
"role": "user",
"content": "Given the function $y=(m-1)x^{m^{2}}+1$ is a linear function, then $m=$ $\\boxed{\\text{\\_\\_\\_\\_\\_\\_}}$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "-1",
"test_case": null,
"think_content": null,
"answer_content": nu... |
[
{
"role": "user",
"content": "1-2+3-4+5-6+7-8+…+4999-5000= ．",
"info": {
"source": "openR1Math_extended",
"reference_answer": "-2500",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assistant",
"content": "<think>\nOkay, ... |
[
{
"role": "user",
"content": "In $\\triangle ABC$, the sides $a$, $b$, and $c$ opposite to the angles $A$, $B$, and $C$ respectively form a geometric sequence. Given that $\\sin B= \\frac {5}{13}$ and $\\cos B= \\frac {12}{ac}$, find the value of $a+c$.",
"info": {
"source": "openR1Math_extended",... |
[
{
"role": "user",
"content": "Given $a+b=8$ and $ab=c^2+16$, find the value of $a+2b+3c$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "12",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assistant",
"con... |
[
{
"role": "user",
"content": "When a red die and a blue die are thrown at the same time, observe the numbers facing up. Let event A be \"the number facing up on the red die is a multiple of 3\", and event B be \"the sum of the numbers on the two dice is greater than 8\". Then, $P(B|A) = \\_\\_\\_\\_\\_\\_$.... |
[
{
"role": "user",
"content": "In response to the municipal government's call for \"green commuting,\" Xiao Zhang changed his mode of transportation from driving to work to riding a public bicycle. It is known that Xiao Zhang's home is 10 kilometers away from his workplace. The average hourly distance he tra... |
[
{
"role": "user",
"content": "Which of the following transformations is correct?\n\nA: From $2+x=3$, we get $x=3+2$\n\nB: From $2x=3x+4$, we get $2x-3x=4$\n\nC: From $3x=2$, we get $x=\\frac{3}{2}$\n\nD: From $x=0$, we get $3x=3$",
"info": {
"source": "openR1Math_extended",
"reference_answer... |
[
{
"role": "user",
"content": "The distance from the point (0, b) to the line $x+y-2=0$ is $\\sqrt{2}$. Then, $b$ equals ( )\n\nA: 0 or 4 \nB: 4 \nC: 0 \nD: $\\sqrt{2}$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\text{A}",
"test_case": null,
"think_cont... |
[
{
"role": "user",
"content": "Given $m$ and $n$ satisfy $m+n-1=0$, the line $mx+y+n=0$ passes through the fixed point ( )\nA: $(1,-1)$\nB: $(0,-n)$\nC: $(0,0)$\nD: $(-1,1)$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "A",
"test_case": null,
"think_content": ... |
[
{
"role": "user",
"content": "Calculate: $4\\sin 60^{\\circ}-|1-\\sqrt{3}|+(\\frac{1}{3})^{-1}+\\sqrt[3]{{-27}}$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\sqrt{3} + 1",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
... |
[
{
"role": "user",
"content": "11.142. In a regular triangular prism, a plane is drawn through the side of the lower base and the opposite vertex of the upper base, forming an angle of $45^{\\circ}$ with the plane of the lower base. The area of the section is $S$. Find the volume of the prism.",
"info": ... |
[
{
"role": "user",
"content": "Calculate: $(-2023)^{0}-4\\sin45°+|-\\sqrt{8}|=\\_\\_\\_\\_\\_\\_$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "1",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assistant",
... |
[
{
"role": "user",
"content": "Which of the following objects can determine a set? ( )\nA: All points in the first quadrant\nB: All students with good grades in a class\nC: All difficult problems in the high school grade one math textbook\nD: All numbers close to 1",
"info": {
"source": "openR1Mat... |
[
{
"role": "user",
"content": "In $\\triangle ABC$, the sides opposite to $\\angle A$, $\\angle B$, and $\\angle C$ are $a$, $b$, and $c$, respectively. If $a$, $b$, and $c$ form an arithmetic sequence, $\\sin B = \\frac{4}{5}$, and the area of $\\triangle ABC$ is $\\frac{3}{2}$, then $b =$ $\\_\\_\\_\\_\\_\... |
[
{
"role": "user",
"content": "10. (1990 American Mathematical Invitational) A fair coin is tossed 10 times, let $\\frac{i}{j}$ be the probability that no two heads appear consecutively, where $i$ and $j$ are relatively prime, find $i+j$.\n\n",
"info": {
"source": "openR1Math_extended",
"refe... |
[
{
"role": "user",
"content": "Which of the following functions is both a decreasing function and an odd function?\n\nA: $f(x)=(\\frac{1}{2})^x-1$\n\nB: $f(x)=\\frac{1}{x}$\n\nC: $f\\left(x\\right)=-x$\n\nD: $f\\left(x\\right)=-e^{|x|}$",
"info": {
"source": "openR1Math_extended",
"reference_... |
[
{
"role": "user",
"content": "If the even function $f(x)$ is monotonically decreasing on $(-\\infty, 0]$, and $a=f(\\log_{2}3)$, $b=f(\\log_{4}5)$, $c=f(2^{\\frac{3}{2}})$, then which of the following is true?\nA: $a < b < c$\nB: $b < a < c$\nC: $c < a < b$\nD: $c < b < a$",
"info": {
"source": "o... |
[
{
"role": "user",
"content": "Given the vector $\\overrightarrow{a}=(-1,2,2)$, then $|2\\overrightarrow{a}|$ is equal to:\n\nA: $9$\n\nB: $3$\n\nC: $6$\n\nD: $2\\sqrt{3}$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "C",
"test_case": null,
"think_content": nul... |
[
{
"role": "user",
"content": "In triangle $\\triangle ABC$, it is known that $AB=6$, $AC=BC=4$. $P$ is the intersection point of the angle bisector of $\\angle ACB$ with side $AB$, and $M$ is a point on $PC$ such that $\\overrightarrow {BM} = \\overrightarrow {BA} + \\lambda \\left( \\frac { \\overrightarro... |
[
{
"role": "user",
"content": "A batch of equipment is worth $a$ ten thousand yuan. Due to wear and tear from use, its value decreases by $b\\%$ every year. The value of this batch of equipment after $n$ years is ( ).\n\nA: $na(1-b\\%)$\n\nB: $a(1-nb\\%)$\n\nC: $a(1-b\\%)^{n}$\n\nD: $a[1-(b\\%)^{n}]$",
"... |
[
{
"role": "user",
"content": "Given the equation $(2a+b)x-1=0$ has no solution with respect to $x$, then the value of $ab$ is ( )\nA: Negative\nB: Positive\nC: Non-negative\nD: Non-positive",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\text{D}",
"test_case": null... |
[
{
"role": "user",
"content": "The solution set of the inequality $\\dfrac{x}{x+1} < 0$ is .",
"info": {
"source": "openR1Math_extended",
"reference_answer": "(-1,0)",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assistant",
... |
[
{
"role": "user",
"content": "Given $x \\gt 0$, $y \\gt 0$, and $x+4y-2xy=0$. Find:$(1)$ the minimum value of $xy$;$(2)$ the minimum value of $x+y$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\frac{9}{2}",
"test_case": null,
"think_content": null,
"a... |
[
{
"role": "user",
"content": "Given a linear regression equation $y = 2 - x$, when the variable $x$ increases by one unit, ( )\n\nA: $y$ increases by an average of 1 unit \nB: $y$ increases by an average of 2 units \nC: $y$ decreases by an average of 1 unit \nD: $y$ decreases by an average of 2 units",
... |
[
{
"role": "user",
"content": "A senior high school student participated in the level tests for Physics, Chemistry, and Politics. It is known that the probabilities of this student achieving an A+ in Physics, Chemistry, and Politics are $\\dfrac{7}{8}$, $\\dfrac{3}{4}$, and $\\dfrac{5}{12}$ respectively. The... |
[
{
"role": "user",
"content": "Given the equation of a circle is $x^2+y^2-2x-9=0$, and the equation of a line is $mx+y+m-2=0$, then the positional relationship between the line and the circle is ( ) \nA: Intersect \nB: Separate \nC: Tangent \nD: Uncertain",
"info": {
"source": "openR1Math_exte... |
[
{
"role": "user",
"content": "To enhance security awareness, a shopping mall plans to randomly select 3 days for emergency evacuation drills in the next consecutive 10 days. The probability that the selected 3 days are consecutive is ___ (express the answer as a simplest fraction).",
"info": {
"so... |
[
{
"role": "user",
"content": "Given that in $\\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $\\frac{a-c}{a-b} = \\frac{\\sin A + \\sin B}{\\sin (A+B)}$.\n(I) Find the value of angle $B$;\n(II) If the circumradius of $\\triangle ABC$ is $1$, find the maximum v... |
[
{
"role": "user",
"content": "The base radius of a cylinder is 3, and its lateral area is $12\\pi$. The volume of the cylinder is \\_\\_\\_\\_\\_\\_.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "18\\pi",
"test_case": null,
"think_content": null,
"answer... |
[
{
"role": "user",
"content": "The point P lies on the curve $y = x^2 - \\ln x$. Find the minimum distance from point P to the straight line $y=x-2$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\sqrt{2}",
"test_case": null,
"think_content": null,
"answ... |
[
{
"role": "user",
"content": "Which of the following equations is a quadratic equation?\n\nA: $2x^{2}=5x-1$\n\nB: $x+\\frac{1}{x}=2$\n\nC: $(x-3)\\left(x+1\\right)=x^{2}-5$\n\nD: $3x-y=5$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "A",
"test_case": null,
"th... |
[
{
"role": "user",
"content": "Calculate:$(1)\\sqrt{10} \\times \\sqrt{2} + \\sqrt{15} \\div \\sqrt{3}$;$(2)\\sqrt{27} - (\\sqrt{12} - \\sqrt{\\frac{1}{3}})$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\frac{4}{3}\\sqrt{3}",
"test_case": null,
"think_conten... |
[
{
"role": "user",
"content": "After running the following program, the output value is ( )\n\n$$\\boxed{\\begin{matrix}i=0 \\\\ DO \\\\ \\quad i=i+1 \\\\ LOOP UNTIL\\quad 2^i > 2 000 \\\\ \\quad i=i-1 \\\\ PRINT\\quad i \\\\ END\\end{matrix}}$$\nA: $8$\nB: $9$\nC: $10$\nD: $11$",
"info": {
"sou... |
[
{
"role": "user",
"content": "11. (5 points)\nXiao Huhu encountered a problem: Compare the sizes of $\\frac{99}{100}, \\frac{100}{101}, \\frac{199}{201}$. He is very confused, please help him find the correct answer.\nA. $\\frac{99}{100}>\\frac{100}{101}>\\frac{199}{201}$\nB. $\\frac{199}{201}>\\frac{100}{1... |
[
{
"role": "user",
"content": "Find all positive integers $n$ such that $n^4 - n^3 + 3n^2 + 5$ is a perfect square.",
"info": {
"source": "openR1Math_extended",
"reference_answer": " n = 2 ",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
... |
[
{
"role": "user",
"content": "Given the set A={2, 0, 1, 9}, and B={x|x=2a, a∈A}, find the sum of all elements in A∪B.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "34",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"... |
[
{
"role": "user",
"content": "If $$\\int_{1}^{a} (2x + \\frac{1}{x})dx = 3 + \\ln 2$$ (where $a > 1$), then the value of $a$ is \\_\\_\\_\\_\\_\\_.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "2",
"test_case": null,
"think_content": null,
"answer_conten... |
[
{
"role": "user",
"content": "(Full score: 10 points) Given a complex number $z$ that satisfies $z + |z| = 2 + 8i$, find the complex number $z$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "z = -15 + 8i",
"test_case": null,
"think_content": null,
"answe... |
[
{
"role": "user",
"content": "A math teacher is 176 cm tall. The heights of his grandfather, father, and son are 173 cm, 170 cm, and 182 cm, respectively. Since the son's height is related to the father's height, the teacher uses the method of linear regression analysis to predict his grandson's height as _... |
[
{
"role": "user",
"content": "In the right triangular prism $ABC-A_1B_1C_1$, if $\\overrightarrow{CA} = \\overrightarrow{a}$, $\\overrightarrow{CB} = \\overrightarrow{b}$, and $\\overrightarrow{CC_1} = \\overrightarrow{c}$, then find $\\overrightarrow{A_1B}$.",
"info": {
"source": "openR1Math_exte... |
[
{
"role": "user",
"content": "Given the functions $f(x)=e^{x}$ ($e$ is the base of the natural logarithm) and $g(x)=\\frac{a}{2}x+b$ ($a,b \\in \\mathbb{R}$).\n\n(1) If $h(x)=f(x)g(x)$, $b=1-\\frac{a}{2}$, and $a=-4$, find the maximum value of $h(x)$ on $[0,1]$.\n\n(2) If $a=4$, find the range of the real n... |
[
{
"role": "user",
"content": "Let P and Q be two sets. The \"difference set\" of P and Q is defined as P - Q = {x | x ∈ P, x ∉ Q}. Given that $$P = \\{x | 1 - \\frac{2}{x} < 0\\}$$ and Q = {x ||x - 2| < 1}, find Q - P.\n\nA: {x | 0 < x < 1}\nB: {x | 0 < x ≤ 1}\nC: {x | 1 ≤ x < 2}\nD: {x | 2 ≤ x < 3}",
"... |
[
{
"role": "user",
"content": "Xiao Ming is practicing shooting. In the first stage, he shot $4$ bullets with scores of $8$, $9$, $9$, and $10$ respectively. What is the median of the data $8$, $9$, $9$, $10$?\n\nA: $8$\n\nB: $9$\n\nC: $9.5$\n\nD: $10$",
"info": {
"source": "openR1Math_extended",
... |
[
{
"role": "user",
"content": "Given that the maximum value of $x$ that satisfies the inequality $(x^2 - 4x + a) + |x - 3| \\leq 5$ is 3, find the value of $a$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "8",
"test_case": null,
"think_content": null,
"a... |
[
{
"role": "user",
"content": "Given real numbers $x$ and $y$ that satisfy the equation $x^{2}+y^{2}-4x+6y+12=0$, find the minimum value of $|2x-y-2|$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "5-\\sqrt{5}",
"test_case": null,
"think_content": null,
"... |
[
{
"role": "user",
"content": "A certain project requires 24 days for Team A to complete on their own, and 18 days for Team B to complete on their own. Now, if 6 people from Team B are transferred to Team A, then Team A alone would need 18 days to complete the project, and Team B alone would need 24 days. If... |
[
{
"role": "user",
"content": "Given that the line $l: ax-y+3=0$ is the axis of symmetry of the circle $C: x^{2}+y^{2}+2x-4y-4=0$, a tangent line to circle $C$ passes through point $P(a,-2)$ and touches the circle at point $Q$. Find the length of $|PQ|$.",
"info": {
"source": "openR1Math_extended",... |
[
{
"role": "user",
"content": "A straight line $l$, whose parametric equations are \n$$\n\\begin{cases}\nx = x_{0} + t\\cos\\theta \\\\\ny = t\\sin\\theta\n\\end{cases}\n$$\n($t$ is the parameter), passes through the left focus $F_1$ of the ellipse $\\frac{x^2}{3} + y^2 = 1$ and intersects the positive y-axi... |
[
{
"role": "user",
"content": "Use mathematical induction to prove that when \\\\((n+1)(n+2)\\cdots (n+n) = {{2}^{n}}\\cdot 1\\cdot 3\\cdots (2n-1), (n \\in {{N}_{+}})\\\\), from \\\\(n=k\\\\) to \\\\(n=k+1\\\\), the term that should be added to the left side is \\\\((\\quad)\\\\)\nA: \\\\(2k+1\\\\)\nB: \\\\... |
[
{
"role": "user",
"content": "Given sets $A=(-\\infty, 4]$, $B=\\{1,3,5,7\\}$, find $A$ ⋂ $B$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\{1,3\\}",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assistan... |
[
{
"role": "user",
"content": "The real number $x$ satisfies $\\log_{2}x = 3 - 2\\cos^{2}\\theta$. The value of $|x - 2| + |x - 8|$ is ( )\n\nA: 6 \nB: 6 or -6 \nC: 10 \nD: Uncertain",
"info": {
"source": "openR1Math_extended",
"reference_answer": "A",
"test_case": null,
"thin... |
[
{
"role": "user",
"content": "Given that $\\{a_n\\}$ is a geometric sequence with the sum of the first $n$ terms denoted as $S_n (n\\in\\mathbb{N^*})$, and $\\frac{1}{a_1}-\\frac{1}{a_2}=\\frac{2}{a_3}$, $(S_6=63)$.\n\n(1) Find the general term formula for $\\{a_n\\}$;\n(2) If for any $n\\in\\mathbb{N^*}$, ... |
[
{
"role": "user",
"content": "The radius and the coordinates of the center of the circle $x^2+y^2-4x+2y+4=0$ are ( )\nA: $r=1$; $(﹣2,1)$\nB: $r=2$; $(﹣2,1)$\nC: $r=1$; $(2,﹣1)$\nD: $r=2$; $(2,﹣1)$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\text{C}",
"test_cas... |
[
{
"role": "user",
"content": "The first term of the sequence ${a_n}$ is $a_1=2$, and $a_{n+1}=3a_{n}+2 (n∈N^{*})$. Let $b_n=\\log_{3}(a_n+1)$, then the sum of the first 2019 terms of the sequence $\\{ \\frac {1}{b_{2n-1}b_{2n+1}}\\}$ is $S_{2019}=\\_\\_\\_\\_\\_\\_.$",
"info": {
"source": "openR1M... |
[
{
"role": "user",
"content": "Given that the vertex of the parabola is at the origin, and the focus is on the y-axis, for a point M(m, -3) on the parabola, the distance from point M to the focus of the parabola is 5,\n(1) Find the value of m;\n(2) Determine the equation of the parabola and the equation of i... |
[
{
"role": "user",
"content": "The opposite number of \\\\(-2016\\\\) is \\_\\_\\_\\_\\_\\_ .",
"info": {
"source": "openR1Math_extended",
"reference_answer": "2016",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assistant",
... |
[
{
"role": "user",
"content": "In order to estimate the number of fish in a pond, initially 2,000 fish were caught, marked (without affecting their survival), and then released back into the pond. After some time, 500 fish were caught again, of which 40 were marked. Based on the data provided, estimate the t... |
[
{
"role": "user",
"content": "Factorize the following expressions: \n(1) $3ax^2+6axy+3ay^2$ \n(2) $a^2(x-y)-b^2(x-y)$ \n(3) $a^4+3a^2-4$; \n(4) $4x^2-y^2-2y-1$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "(2x+y+1)(2x-y-1)",
"test_case": null,
"think_cont... |
[
{
"role": "user",
"content": "A four-digit number is divisible by 9, and the three-digit number obtained by removing the last digit is exactly a multiple of 4. What is the last digit of the largest such four-digit number?",
"info": {
"source": "openR1Math_extended",
"reference_answer": "3",
... |
[
{
"role": "user",
"content": "Given $A=\\{1, 2, a^2-3a-1\\}$, $B=\\{1, 3\\}$, and $A \\cap B = \\{3, 1\\}$, then $a=$ ______.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "-1 \\text{ or } 4",
"test_case": null,
"think_content": null,
"answer_content": nu... |
[
{
"role": "user",
"content": "Given proposition $p$: $\\forall x \\in \\mathbb{N}^{*}$, $\\left( \\frac{1}{2} \\right)^{x} \\geqslant \\left( \\frac{1}{3} \\right)^{x}$, and proposition $q$: $\\exists x \\in \\mathbb{N}^{*}$, $2^{x} + 2^{1-x} = 2 \\sqrt{2}$, then among the following propositions, the true o... |
[
{
"role": "user",
"content": "If the hyperbola $C_{1}$ has the same focal length as the hyperbola ${C_2}:\\frac{{{x^2}}}{7}-{y^2}=1$, and $C_{1}$ passes through the point $\\left(3,1\\right)$, then the standard equation of the hyperbola $C_{1}$ is ( )\n\nA: $\\frac{{{x^2}}}{6}-\\frac{{{y^2}}}{2}=1$\n\nB: $\... |
[
{
"role": "user",
"content": "If the eccentricity of the hyperbola $x^{2}+ky^{2}=1$ is $2$, then the value of the real number $k$ is ______.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "-\\frac{1}{3}",
"test_case": null,
"think_content": null,
"answer_c... |
[
{
"role": "user",
"content": "Given that $\\theta$ is an internal angle of a triangle, and $\\sin \\theta + \\cos \\theta = \\frac{1}{2}$, then the equation $x^{2}\\sin \\theta - y^{2}\\cos \\theta = 1$ represents\nA: An ellipse with foci on the $x$-axis\nB: An ellipse with foci on the $y$-axis\nC: A hyperb... |
[
{
"role": "user",
"content": "A certain craft factory plans to produce 2100 handicrafts in a week, with an average daily production of 300. However, the actual daily production deviates from the plan. The table below shows the production situation for a week (positive for overproduction and negative for und... |
[
{
"role": "user",
"content": "In the geometric sequence $\\{a_n\\}$, $a_2$ and $a_6$ are the two roots of the equation $x^2 - 34x + 64 = 0$. What is the value of $a_4$?",
"info": {
"source": "openR1Math_extended",
"reference_answer": "8",
"test_case": null,
"think_content": null,... |
[
{
"role": "user",
"content": "Given the function $y=mx^{2}+x+5$, find the range of values for $m$ that makes the function increasing on the interval $[-2,+\\infty)$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "[0, \\frac{1}{4}]",
"test_case": null,
"think_co... |
[
{
"role": "user",
"content": "In the rectangular coordinate system $Oxy$, the straight line $\\frac {x}{2}- \\frac {y}{4}=1$ intersects the coordinate axes at points A and B. Determine the standard equation of the circle passing through points O, A, and B.",
"info": {
"source": "openR1Math_extende... |
[
{
"role": "user",
"content": "$\\sqrt{12}+\\sqrt{\\frac{1}{3}}=$____.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "\\frac{7\\sqrt{3}}{3}",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assistant",
"cont... |
[
{
"role": "user",
"content": "If the graph of the function $y=kx^{2}-2x-1$ intersects the $x$-axis, then the range of values for $k$ is ( ).\n\nA: $k\\geqslant -1$\n\nB: $k \\gt -1$\n\nC: $k \\gt -1$ and $k\\neq 0$\n\nD: $k\\geqslant -1$ and $k\\neq 0$",
"info": {
"source": "openR1Math_extended",
... |
[
{
"role": "user",
"content": "If $x$ and $y$ are positive numbers, and $\\frac{1}{x} + \\frac{4}{y} = 1$, then $x+y$ has ( ).\n\nA: Minimum value $9$\n\nB: Maximum value $9$\n\nC: Minimum value $5+2\\sqrt{2}$\n\nD: Maximum value $5+2\\sqrt{2}$",
"info": {
"source": "openR1Math_extended",
"re... |
[
{
"role": "user",
"content": "Given that the sum of two monomials $-2a^2b^{m+1}$ and $na^2b^4$ is 0, find the value of $m+n$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "5",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
... |
[
{
"role": "user",
"content": "In the ancient Chinese mathematical classic \"The Nine Chapters on the Mathematical Art,\" there is a description: \"Now there are good horses and donkeys traveling from Chang'an to Qi. Qi is 1,125 miles away from Chang'an. The good horse travels 103 miles on the first day and ... |
[
{
"role": "user",
"content": "Given the sequence $\\{a\\_n\\}$ that satisfies $a\\_n= \\frac{a_{n-1}}{a_{n-2}}\\ (n \\in \\mathbb{N}^*, n\\geqslant 3)$, with $a\\_1=2$ and $a\\_5= \\frac{1}{3}$, find the value of $a\\_{2016}$.",
"info": {
"source": "openR1Math_extended",
"reference_answer": ... |
[
{
"role": "user",
"content": "1. In triangle $ABC$, the median $BD$ is drawn, and the centroid $G$ is marked on it. A line parallel to $BC$ and passing through point $G$ intersects $AB$ at point $E$. It turns out that $\\angle AEC = \\angle DGC$. Prove that $\\angle ACB = 90^{\\circ}$.",
"info": {
... |
[
{
"role": "user",
"content": "A certain food retail store has recently introduced a new cold beverage product, with a cost of $8$ dollars per unit. During the sales process, the daily sales quantity $y$ (units) is related to the selling price $x$ (dollars per unit) by the equation $y=-x+30$. If the profit o... |
[
{
"role": "user",
"content": "Show that $M=\\sqrt[3]{\\sqrt{5}+2}-\\sqrt[3]{\\sqrt{5}-2}$ is an integer.",
"info": {
"source": "openR1Math_extended",
"reference_answer": "1",
"test_case": null,
"think_content": null,
"answer_content": null
}
},
{
"role": "assist... |
[
{
"role": "user",
"content": "If $\\lim_{{\\Delta x}\\to0}\\frac{{f({-2+\\Delta x})-f({-2-\\Delta x})}}{{\\Delta x}}=-2$, then ${f'}\\left(-2\\right)=\\left(\\ \\ \\right)$\n\nA: $1$\n\nB: $-1$\n\nC: $2$\n\nD: $-2$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "B",
"... |
[
{
"role": "user",
"content": "Given that point $P(m,2)$ lies on the $y$-axis, the value of $m$ is ( )\n\nA: $2$\n\nB: $0$\n\nC: $-2$\n\nD: $1$",
"info": {
"source": "openR1Math_extended",
"reference_answer": "B",
"test_case": null,
"think_content": null,
"answer_content": n... |
[
{
"role": "user",
"content": "Given the sets $M=\\{x|\\lg x^2 = 0\\}$, and $N=\\{x|2^{-1} < 2^{x+1} < 2^2, x \\in \\mathbb{Z}\\}$, then $M \\cap N =$ ( )\n\nA: $\\{-1, 1\\}$\n\nB: $\\{-1\\}$\n\nC: $\\{0\\}$\n\nD: $\\{-1, 0\\}$",
"info": {
"source": "openR1Math_extended",
"reference_answer": ... |
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