id stringlengths 12 82 | source stringclasses 26
values | question stringlengths 8 1.61k | steps listlengths 1 437 | answer stringlengths 1 608 |
|---|---|---|---|---|
dbb6e346-17d8-5107-804c-31ef3a2b27e6 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following operations is correct?
A: $a^{5}\div a^{2}=a^{3}$
B: $a^{3}+a^{3}=a^{6}$
C: $(a^{3})^{2}=a^{5}$
D: $\sqrt{{a^2}}=a$ | [
"The user asks: Which of the following operations is correct? Options A-D with statements about exponent rules.",
"We need to evaluate each.",
"A: a^5 ÷ a^2 = a^{5-2}=a^3. That's correct, assuming a ≠ 0 (division defined). So A is correct.",
"B: a^3 + a^3 = 2 a^3, not a^6. So incorrect.",
"C: (a^3)^2 = a^{3... | Statement A, \(a^{5}\div a^{2} = a^{3}\) (provided \(a\neq0\)), is the only universally correct operation among the given options. Options B, C, and D are incorrect because \(a^{3}+a^{3} = 2a^{3}\), \((a^{3})^{2} = a^{6}\), and \(\sqrt{a^{2}} = |a|\), respectively. |
73a5fc6f-76bd-5dfc-8127-63a53d41820b | open-r1/OpenR1-Math-220k/cn_k12 | The opposite of $23$ is ( )
A: $-23$
B: $23$
C: $-\frac{1}{23}$
D: $\frac{1}{23}$ | [
"We need interpret \"opposite\" probably means additive inverse, opposite of a number is its negative. So opposite of 23 is -23. So answer A.",
"But note some contexts could be reciprocal? Usually opposite means additive inverse. So answer A.",
"Provide reasoning."
] | The opposite of \(23\) is its additive inverse, which is \(-23\) because \(23 + (-23) = 0\). The answer is A: \(-23\). |
bbe81a48-0158-55fe-8422-0012630deb9e | open-r1/OpenR1-Math-220k/olympiads | 2. Jenny had to add 26 to a certain number. Instead she subtracted 26 and obtained -14 . What number should she have obtained?
A 28
B 32
C 36
D 38
E 42 | [
"We need to parse the problem: \"Jenny had to add 26 to a certain number. Instead she subtracted 26 and obtained -14 . What number should she have obtained?\" So original number = x. She should have added 26: correct result would be x + 26. Instead she subtracted 26: she computed x - 26 = -14. So we can solve for x... | She subtracted 26 from a number \(x\) and got -14, so \(x-26 = -14\), which means \(x=12\). The correct operation is to add 26, so the correct result is \(12+26 = 38\). |
c1521f61-54b9-59ab-a19f-6004c18bfb07 | open-r1/OpenR1-Math-220k/olympiads | ## Task 8
The area of a new playground is square and measures $1600 \mathrm{~m}^{2}$.
How long is one side of the playground?
How many meters of fence are needed for three sides? | [
"The problem states: \"The area of a new playground is square and measures 1600 m^2. How long is one side of the playground? How many meters of fence are needed for three sides?\" So it's a square area 1600, side length sqrt(1600)=40 m. Fence for three sides: 3*40=120 m.",
"Provide answer."
] | The side length of the square playground is 40 m, calculated from its area of 1600 m$^2$. Therefore, 120 m of fence is required to cover three sides. |
e1cc1f33-ea60-585b-9ef2-1cfda7707233 | open-r1/OpenR1-Math-220k/olympiads | ## Task 5
Mr. Müller has manufactured 16 chair legs.
How many chairs can he build? | [
"We need to interpret the problem. \"Mr. Müller has manufactured 16 chair legs. How many chairs can he build?\" Typically a chair has 4 legs. So 16 legs can make 4 chairs. Possibly there may be leftover legs (none). So answer: 4 chairs.",
"But maybe they expect integer division: 16 / 4 = 4. So answer is 4 chairs.... | The calculation $\frac{16\text{ legs}}{4\text{ legs/chair}} = 4\text{ chairs}$ shows that Mr. Müller can build 4 chairs. |
20d46f66-8581-54e1-b6dd-868a9eebd039 | open-r1/OpenR1-Math-220k/olympiads | 29. The numbers $1, 2, 3, 4, 5, 6, 7, 8, 9, 0$ that we use for counting are called Arabic numerals, and they have become the universal symbols for numbers used around the world. Arabic numerals were actually invented by the ancient $\qquad$.
A. Indians
B. China
C. Babylon
D. Arabs | [
"We need answer: Arabic numerals invented by Indians (the Hindu-Arabic numeral system). So answer A."
] | A. Indians. |
9503b700-334e-5379-a645-f4dc5285db6a | open-r1/OpenR1-Math-220k/cn_k12 | Calculate: $(-2m^{3})^{2}$ is equal to ( ).
A: $-2m^{6}$
B: $4m^{6}$
C: $4m^{5}$
D: $-4m^{6}$ | [
"We need compute (-2m^3)^2. Square: (-2)^2 * (m^3)^2 = 4 * m^{6} = 4 m^6. So answer B.",
"Explain exponents: (a^b)^c = a^{bc}. Also sign: negative squared becomes positive.",
"Thus answer B."
] | \((-2m^{3})^{2}=4m^{6}\). The correct choice is **B: \(4m^{6}\)**. |
0d3d603c-8ffe-5a1b-aef2-fc2fa55c74bd | open-r1/OpenR1-Math-220k/cn_k12 | The domain of the function $f\left(x\right)=\sqrt{x+2}+\dfrac{1}{x-1}$ is ( ).
A: $\left(-\infty ,1\right)\cup \left(1,+\infty \right)$
B: $ \left[-2,+\infty \right)$
C: $ \left[-2,1\right)\cup \left(1,+\infty \right)$
D: $ \left(1,+\infty \right)$ | [
"We need domain where expression defined: sqrt(x+2) requires x+2 >=0 => x >= -2. And denominator x-1 !=0 => x !=1. So domain: [ -2, ∞ ) except x=1. That's [-2,1) ∪ (1, ∞). That matches option C.",
"Thus answer C."
] | The square-root term requires $x \ge -2$, and the rational term requires $x \neq 1$. Combining these conditions, the set of admissible $x$ values is $[-2,1) \cup (1, \infty)$, which corresponds to choice C. |
fd26fccd-e9b4-59a5-a1ab-ad21c6c4c1bb | open-r1/OpenR1-Math-220k/cn_k12 | The medicine is on sale everywhere. You can get it at \_\_\_ chemist’s.
A. each B. some C. certain D. any | [
"We need to choose the correct word to fill blank: \"The medicine is on sale everywhere. You can get it at ___ chemist’s.\"",
"Options: A. each, B. some, C. certain, D. any.",
"The sentence: \"The medicine is on sale everywhere. You can get it at ___ chemist’s.\"",
"If something is on sale everywhere, you can... | The medicine is available "everywhere," meaning it can be obtained at **any** chemist's. Options like "each," "some," or "certain" imply restrictions that contradict the unrestricted sense of "everywhere." |
e6f0869a-29ad-546a-a41b-51833a93b4fa | open-r1/OpenR1-Math-220k/cn_k12 | In the process of deriving a contradiction using the method of proof by contradiction, which of the following should be used as conditions? ( )
① The judgment opposite to the conclusion, i.e., the assumption
② The conditions of the original proposition
③ Axioms, theorems, definitions, etc.
④ The original concl... | [
"We need to parse the question: \"In the process of deriving a contradiction using the method of proof by contradiction, which of the following should be used as conditions? ( ) \n① The judgment opposite to the conclusion, i.e., the assumption \n② The conditions of the original proposition \n③ Axioms, theorems,... | In a proof by contradiction, one assumes the negation of the conclusion along with the original hypotheses and established mathematical facts to derive an impossibility. Thus, the conditions that can be used are the opposite judgment (negation of conclusion), the original hypotheses, and axioms/theorems/definitions. |
62a2d7f9-4094-5161-bcf2-026e799de7c6 | open-r1/OpenR1-Math-220k/cn_k12 | Given that $p$ is a true statement, and $q$ is a false statement, then ( )
A: The statement $p \land q$ is true.
B: The statement $p \lor q$ is false.
C: The statement $\lnot p$ is true.
D: The statement $\lnot q$ is true. | [
"We need to answer which statements are true given p true, q false. Evaluate each:",
"A: p ∧ q is true only if both true; q false, so p ∧ q false. So A false.",
"B: p ∨ q is false only if both false; p true, so p ∨ q true. So B false.",
"C: ¬p is true only if p false; p true, so ¬p false. So C false.",
"D: ... | Given \(p\) is true and \(q\) is false, \(\lnot q\) is true because it is the negation of a false statement. Therefore, option D is the only correct statement. |
715a26a6-4b8b-5a6a-b60b-68d743806463 | open-r1/OpenR1-Math-220k/olympiads | 1. Given the set $M$ satisfies $M \subseteq\{0,1,2,3,4\}$ and $M \subseteq\{0,2,4,8\}$, the maximum number of elements in set $M$ is ( ).
A. 1
B. 2
C. 3
D. 6 | [
"We need intersection of two sets: {0,1,2,3,4} and {0,2,4,8}. Intersection = {0,2,4}. So M must be subset of this intersection. Max number of elements = size of intersection = 3. So answer C."
] | The set \(M\) must be a subset of \(\{0,1,2,3,4\}\cap\{0,2,4,8\} = \{0,2,4\}\). The largest \(M\) can be is the intersection itself, which has three elements. |
704b5f6a-7b5f-5a74-908f-803f5dd1d0d8 | open-r1/OpenR1-Math-220k/olympiads | ## Task 1
In every 100 m preliminary race, 8 athletes start. The two best runners will participate in the final. How many athletes participated in the preliminaries if 8 of them competed in the final. | [
"We need to interpret the problem: \"In every 100 m preliminary race, 8 athletes start. The two best runners will participate in the final. How many athletes participated in the preliminaries if 8 of them competed in the final.\"",
"Interpretation: There are preliminary heats, each heat has 8 athletes. From each ... | There are 4 preliminary heats, with 8 athletes per heat, and 2 qualifiers from each heat advance to the final. Therefore, a total of $4 \times 8 = 32$ athletes participated in the preliminary races. |
fad768a4-ba62-5b23-a177-2bcb11b8c4b8 | open-r1/OpenR1-Math-220k/cn_k12 | If ¬(p∧q) is a false proposition, then ( )
A: p is true, q is false
B: p is false, q is false
C: p is true, q is true
D: p is false, q is true | [
"We need to parse problem: If ¬(p∧q) is a false proposition, then ( ...) Choose correct condition.",
"We have ¬(p∧q) is false. That means the negation of (p∧q) is false, i.e., ¬(p∧q) = false. Therefore (p∧q) must be true (since negation false => original true). So p∧q true implies both p true and q true. So answe... | Given \(\lnot(p\land q)\) is false, \(p\land q\) must be true. This occurs only when both \(p\) and \(q\) are true, making **C: \(p\) is true, \(q\) is true** the correct choice. |
185c641b-c732-59d2-b7a1-1b6cbcbea878 | open-r1/OpenR1-Math-220k/olympiads | 3. In the Caribbean, loggerhead turtles lay three million eggs in twenty thousand nests. On average, how many eggs are in each nest?
A 15
B 150
C 1500
D 15000
E 150000 | [
"We need compute: 3,000,000 eggs / 20,000 nests = 150 eggs per nest. So answer B 150."
] | The average number of eggs per nest is calculated by dividing the total number of eggs by the total number of nests: $\frac{3{,}000{,}000\ \text{eggs}}{20{,}000\ \text{nests}} = 150$ eggs per nest. Therefore, each nest contains, on average, 150 eggs (Answer: B). |
d66b5d06-0300-56f9-95a4-fca6c2cb9f0d | open-r1/OpenR1-Math-220k/cn_k12 | To make the fraction $\frac{3}{{x-2}}$ meaningful, the value of $x$ should satisfy ______. | [
"The question: \"To make the fraction $\\frac{3}{{x-2}}$ meaningful, the value of $x$ should satisfy ______.\"",
"Interpretation: They want the condition that denominator is non-zero. So x-2 ≠ 0 => x ≠ 2. So the answer is x ≠ 2 or x ∈ ℝ\\{2}. The blank likely expects \"x ≠ 2\". So respond: $x \\neq 2$."
] | $x \neq 2$. The denominator must not be zero. |
10b6d5a6-4d1e-504c-ab78-f691e9d46e29 | open-r1/OpenR1-Math-220k/olympiads | 77. $\int \frac{\sin 2 x}{\cos x} d x$.
Translate the above text into English, please retain the original text's line breaks and format, and output the translation result directly.
77. $\int \frac{\sin 2 x}{\cos x} d x$. | [
"The user wants translation into English, retaining original line breaks and format. The original text is:",
"\"77. $\\int \\frac{\\sin 2 x}{\\cos x} d x$.\"",
"This is already essentially math expression. Possibly they'd like to translate \"77.\" as \"77.\" perhaps remains. The phrase \"Translate the above tex... | $\displaystyle \int \frac{\sin 2 x}{\cos x}\,dx = \int \frac{2 \sin x \cos x}{\cos x}\,dx = \int 2 \sin x\,dx = -2 \cos x + C$. |
ad0fa471-e751-594e-bc52-00a7ecd2eee3 | open-r1/OpenR1-Math-220k/cn_k12 | Given the set $P = \{x \,|\, x^2 - x - 2 = 0\}$, and the set $T = \{x \,|\, -1 < x \leq 2\}$, find $P \cap T$. | [
"We need to find set P: solutions to x^2 - x - 2 = 0. Solve: x = [1 ± sqrt(1 + 8)]/2 = [1 ± 3]/2. So roots: (1+3)/2 = 2, (1-3)/2 = -1. So P = {2, -1}. T is interval (-1, 2] meaning -1 < x ≤ 2. Intersection of {2, -1} with that interval: -1 is not included because interval is open at -1, so -1 not in T. 2 is include... | The set \(P\) is \(\{-1, 2\}\) and the set \(T\) is the interval \((-1, 2]\). The intersection of \(P\) and \(T\) is \(\{2\}\) because \(-1\) is not in \(T\) while \(2\) is. |
33db7ec2-b91f-59cb-9701-c28cb6058062 | open-r1/OpenR1-Math-220k/cn_k12 | The program obtained by using the bisection method to solve the equation $x^2-2=0$ is ( )
A: Organizational structure diagram
B: Process flow diagram
C: Knowledge structure diagram
D: Program flowchart | [
"The question: \"The program obtained by using the bisection method to solve the equation $x^2-2=0$ is ( ) \nA: Organizational structure diagram \nB: Process flow diagram \nC: Knowledge structure diagram \nD: Program flowchart\"",
"Probably they ask what type of diagram represents the program obtained by usi... | The bisection method for \(x^2-2=0\) is best represented by a **D – Program flowchart**. This flowchart visually outlines the algorithm's steps, including initial interval, midpoint calculation, sign test, interval update, iteration, and termination. |
504f1c8e-ef9d-5fc3-9d6c-6e59fd3a367e | open-r1/OpenR1-Math-220k/cn_k12 | If the fraction $\frac{x}{2-x}$ is meaningful, then the value of $x$ cannot be:
A: $1$
B: $2$
C: $3$
D: $0$ | [
"We need to answer: fraction x/(2 - x) is meaningful means denominator not zero. So 2 - x != 0 => x != 2. Also denominator cannot be undefined or cause other issues? It's just real numbers. So x cannot be 2. So answer choice B.",
"We need to output answer."
] | The fraction $\frac{x}{2-x}$ is defined as long as its denominator $2-x \neq 0$, which means $x \neq 2$. Therefore, the value that makes the fraction undefined is **B: 2**. |
9f181d73-ebb5-5415-8d73-b2fecb2ab994 | open-r1/OpenR1-Math-220k/cn_k12 | Among the following descriptions, the one that can determine a point's location is ______.
① East longitude 118°, north latitude 40°
② Baoji City, Wenhua East Road
③ 60° northeast
④ Oscar Cinema, Hall 1, Row 3. | [
"We have a question: \"Among the following descriptions, the one that can determine a point's location is ______.\"",
"Choices:",
"① East longitude 118°, north latitude 40°\n② Baoji City, Wenhua East Road\n③ 60° northeast\n④ Oscar Cinema, Hall 1, Row 3.",
"We need to choose which description can determine a p... | The Earth's surface can be uniquely fixed by the coordinate pair of East longitude 118° and north latitude 40°. This latitude and longitude combination precisely identifies a single location globally. |
8be917a8-6544-58fc-b0e1-57fef7b5f4f3 | open-r1/OpenR1-Math-220k/cn_k12 | Given that variables $x$ and $y$ are linearly related, and the regression equation is $y = 3 - 2x$, then the relationship between variables $x$ and $y$ is ( )
A: Positive linear correlation
B: Negative linear correlation
C: Linear correlation
D: The positive or negative correlation cannot be determined from the regr... | [
"We need to answer multiple choice: given variables x and y are linearly related, regression equation y = 3 - 2x. The slope is -2, negative. So it's a negative linear correlation. Option B.",
"Thus answer B."
] | The regression line $y = 3 - 2x$ has a slope of $-2$, indicating a negative linear correlation. Therefore, the correct option is **B – Negative linear correlation**. |
364969f4-6c71-5c18-b261-c5052dc7acf9 | open-r1/OpenR1-Math-220k/cn_k12 | Given that a normal vector of plane $\alpha$ is $\overrightarrow{n\_1}=(1,2,-2)$, and a normal vector of plane $\beta$ is $\overrightarrow{n\_2}=(-2,-4,k)$, find the value of $k$ if $\alpha$ is parallel to $\beta$. | [
"We have two planes with normal vectors n1 = (1,2,-2) and n2 = (-2,-4,k). Two planes are parallel if their normal vectors are parallel, i.e., one is a scalar multiple of the other. So there exists λ such that n2 = λ n1. So (-2, -4, k) = λ (1, 2, -2) => -2 = λ*1 => λ = -2. Then we check -4 = λ*2 = -2*2 = -4 OK. Then... | Planes are parallel if their normal vectors are parallel, so $(-2,\,-4,\,k)=\lambda\,(1,\,2,\,-2)$. This yields $\lambda=-2$ from the first component, which is consistent with the second component, and $k=(-2)(-2)=4$ from the third component. |
cd253f38-7cbe-546d-b133-698db2f0e2a1 | open-r1/OpenR1-Math-220k/olympiads | You have exactly $\$ 4.40$ ( 440 ) in quarters ( $25 \phi$ coins), dimes ( $10 \phi$ coins), and nickels ( 5 coins). You have the same number of each type of coin. How many dimes do you have?
(A) 20
(B) 11
(C) 10
(D) 12
(E) 4 | [
"We need to parse problem: \"You have exactly $4.40 ( 440 ) in quarters ( $25 \\phi$ coins), dimes ( $10 \\phi$ coins), and nickels ( 5 coins). You have the same number of each type of coin. How many dimes do you have?\" Not sure about weird symbols φ perhaps stands for cent? Anyway, we have quarters worth 25 cents... | Let \(k\) be the common number of quarters, dimes, and nickels. The total value is \(25k + 10k + 5k = 40k\) cents, which equals \(\$4.40 = 440\) cents, so \(40k = 440\), yielding \(k = 11\); Therefore, the number of dimes is 11 (option B). |
de391b61-b536-5a6a-9c7d-86ceb97a4912 | open-r1/OpenR1-Math-220k/olympiads | $20 \%$ of 20 is equal to
(A) 400
(B) 100
(C) 5
(D) 2
(E) 4 | [
"We need compute 20% of 20. 20% = 0.20. 0.20 * 20 = 4. So answer (E) 4."
] | \(20\%\) of 20 equals 4. This corresponds to choice **(E)**. |
54f33688-5f6c-509a-bf2a-c64f4734587c | open-r1/OpenR1-Math-220k/cn_k12 | If the set $A=\{x|x^2-2x+m=0\}=\emptyset$, then the range of the real number $m$ is ( )
A: $(-\infty, -1)$
B: $(-\infty, 1)$
C: $(1, +\infty)$
D: $[1, +\infty)$ | [
"The problem: \"If the set A = {x | x^2 - 2x + m = 0} = ∅, then the range of the real number m is ( )\". So A is the set of real solutions x to quadratic equation x^2 - 2x + m = 0. For the set to be empty, equation has no real solutions (i.e., discriminant < 0). So discriminant D = b^2 - 4ac = (-2)^2 - 4*1*m = 4 - ... | The quadratic equation $x^2 - 2x + m = 0$ has no real roots when its discriminant $\Delta = 4 - 4m < 0$, which implies $m > 1$. Therefore, the set of admissible values for the real parameter $m$ is $(1, \infty)$. |
63ddae99-6f6b-5f82-8f74-76993abcaf87 | open-r1/OpenR1-Math-220k/cn_k12 | A school plans to purchase 400 workbooks, with each workbook costing x yuan. The school should pay a total of __ yuan. | [
"We need to fill blank? Probably answer: 400x yuan. The question: \"A school plans to purchase 400 workbooks, with each workbook costing x yuan. The school should pay a total of __ yuan.\" So answer: 400x. Could also be \"400x yuan\". Provide explanation."
] | The total cost is calculated by multiplying the number of workbooks (400) by the price per workbook ($x$), resulting in a total cost of $400x$ yuan. Therefore, the school should pay $400x$ yuan. |
26615747-61e8-5eb8-a076-ed70fc81a8d3 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following real numbers is an irrational number?
A: $0.7$
B: $\frac{1}{2}$
C: $\sqrt{2}$
D: $\sqrt{9}$ | [
"We need to answer which is irrational: 0.7 = 7/10 rational, 1/2 rational, sqrt2 irrational, sqrt9 = 3 rational. So answer C. Provide explanation."
] | The numbers \(0.7\), \(\frac12\), and \(\sqrt{9}\) are rational because they can be expressed as a ratio of two integers. \(\sqrt{2}\) is irrational, as it cannot be written as a fraction of two integers and has a non-repeating, non-terminating decimal expansion. |
42c312d4-855c-5a3a-8558-2701db151124 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following calculations is correct?
A: $a^{2}\cdot a^{6}=a^{8}$
B: $a^{6}\div a^{3}=a^{2}$
C: $2a^{2}+a^{6}=3a^{8}$
D: $(-3a)^{2}=-9a^{2}$ | [
"We need to identify which calculation is correct. Evaluate each.",
"A: a^2 * a^6 = a^(2+6) = a^8 correct.",
"B: a^6 ÷ a^3 = a^(6-3)=a^3, not a^2, so incorrect.",
"C: 2a^2 + a^6 =? cannot combine unlike terms; 2a^2 + a^6 ≠ 3a^8. Incorrect.",
"D: (-3a)^2 = (-3)^2 * a^2 = 9a^2, not -9a^2. So incorrect.",
"T... | Statement A is correct because \(a^{2}\cdot a^{6}=a^{2+6}=a^{8}\) following the law \(a^{m}\,a^{n}=a^{m+n}\). All other options contain errors in exponent rules or term combination. |
c8b7524f-4e39-5aca-8f04-17b68f13b40d | open-r1/OpenR1-Math-220k/olympiads | 5. (3 points) Wang Lei was born on National Day. If three times his age minus 8 is exactly the total number of days in the month he was born, then Wang Lei is $\qquad$ years old this year. | [
"We have a problem: Wang Lei was born on National Day. In many countries, National Day could be Oct 1 (China), July 4 (US), etc. Likely Chinese context: National Day is October 1. So his birthday is October 1. He was born on a certain year; his age this year? The condition: three times his age minus 8 equals exactl... | The equation $3(\text{age})-8 = \text{(days in month)}$ implies that the month must have 31 days for the age to be an integer, resulting in an age of 13. Therefore, Wang Lei is 13 years old. |
0760720c-57b3-55dd-94f4-7032e24d04ec | open-r1/OpenR1-Math-220k/olympiads | ## Task 1
Out of 33 pioneers in a pioneer group, 8 pioneers were able to win medals at the pioneer sports festival because they took first, second, or third place. All other pioneers received certificates for participation.
How many pioneers in this group received certificates? | [
"We need to answer: 33 total, 8 won medals (first, second, third place). The rest got certificates. So 33-8=25. Answer: 25 pioneers received certificates."
] | 25 pioneers did not win a medal. This is found by subtracting the 8 medalists from the 33 total pioneers. |
5f767954-6eab-59bc-a723-5dbf10fa5048 | open-r1/OpenR1-Math-220k/cn_k12 | Variance is a measure of the magnitude of fluctuations in a set of data. For a set of data $x_{1}$, $x_{2}$, $x_{3}$, $\ldots$, $x_{n}$, the variance can be calculated using the following formula: $S^{2}=\frac{1}{n}[(x_{1}-3)^{2}+(x_{2}-3)^{2}+(x_{3}-3)^{2}+\ldots +(x_{n}-3)^{2}]$, where "3" represents the ( ).
A: min... | [
"The question: \"Variance is a measure of the magnitude of fluctuations in a set of data. For a set of data $x_1, x_2, ... x_n$, the variance can be calculated using the formula: $S^2 = \\frac{1}{n} [(x_1 - 3)^2 + (x_2 - 3)^2 + \\dots + (x_n - 3)^2]$, where '3' represents the ( )\". The answer: variance uses the me... | In the variance formula, each observation is subtracted from the **mean** of the data set, squared, summed, and then divided by the number of observations. Options like minimum, mode, and median are not used in the definition of variance. |
cb6f7e20-b7bd-5cd0-ac52-3787e0571332 | open-r1/OpenR1-Math-220k/cn_k12 | Given vectors $\overrightarrow{a}=(1,2)$ and $\overrightarrow{b}=(x,-2)$, if $\overrightarrow{a} \parallel \overrightarrow{b}$, then the real number $x=$ ______. | [
"The problem: vectors a = (1,2) and b = (x, -2). They are parallel (collinear). For 2D vectors, a // b means one is a scalar multiple of the other: (1,2) = k (x, -2) or (x, -2) = k (1,2). Solve for x.",
"Let's set (x, -2) = k (1,2). Then x = k*1 = k, -2 = k*2 => k = -1. So x = k = -1. Check: b = (-1, -2). Is that... | For vectors $\vec a = (1,2)$ and $\vec b = (x,-2)$ to be parallel, $\vec b$ must be a scalar multiple of $\vec a$, so $(x,-2) = k(1,2)$. This implies $x=k$ and $-2=2k$, which yields $k=-1$ and thus $x=-1$. |
025a4e5e-57c4-5c37-a8e5-6922025c8d85 | open-r1/OpenR1-Math-220k/cn_k12 | Translate the graph of the function $y=x^{2}$ up by one unit to obtain the graph of which function?
A: $y=x^{2}-1$
B: $y=\left(x+1\right)^{2}$
C: $y=x^{2}+1$
D: $y=\left(x-1\right)^{2}$ | [
"The problem: \"Translate the graph of the function y = x^2 up by one unit to obtain the graph of which function?\" Upward translation adds 1 to y: y = x^2 + 1. So answer C.",
"Thus need to respond with answer C and maybe explanation."
] | To shift a graph upward by one unit, add 1 to the right-hand side of the equation. Starting with $y = x^{2}$, the upward translation gives $y = x^{2}+1$, which is choice C. |
d0a01921-400f-54cb-b44c-ecb7b4c5aa70 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following equations is correct?
A: $0-\left(-3\right)=3$
B: $(-14)-5=-9$
C: $(-3)-\left(-3\right)=-6$
D: $|5-3|=-\left(5-3\right)$ | [
"The user asks: Which of the following equations is correct? Options A-D.",
"We need to evaluate each.",
"A: 0 - (-3) = 3. Since subtracting negative is adding: 0 - (-3) = 0 + 3 = 3. So true.",
"B: (-14) - 5 = -9. Compute -14 - 5 = -19, not -9. So false.",
"C: (-3) - (-3) = -6. Compute -3 - (-3) = -3 + 3 = ... | Statement A is true because \(0-\left(-3\right)=0+3=3\), while statements B, C, and D are false. Therefore, only statement A is correct. |
b6042d44-599e-5c4c-a29d-f680c498afd2 | open-r1/OpenR1-Math-220k/olympiads | A square garden has an area of 9 square metres. The perimeter of the garden is $N$ metres. What is the value of $N$ ?
## | [
"We have square area 9 m^2, so side length sqrt(9)=3 m. Perimeter = 4*side=12 m. So N=12."
] | The area of the square is $s^2 = 9 \text{ m}^2$, so the side length is $s = \sqrt{9} = 3 \text{ m}$. The perimeter of the square is $N = 4s = 4 \times 3 = 12 \text{ m}$. |
ef699f3b-94a7-533f-be7a-543d56d67b66 | open-r1/OpenR1-Math-220k/olympiads | ## Task 4
From class 1a, 3 Pioneers receive certificates for good performance. An equal number of Pioneers from class 1b also receive certificates.
How many Pioneers will be awarded? | [
"We need to parse the problem: \"From class 1a, 3 Pioneers receive certificates for good performance. An equal number of Pioneers from class 1b also receive certificates. How many Pioneers will be awarded?\" So 3 from class 1a, equal number from class 1b means also 3. So total 3 + 3 = 6. Answer: 6.",
"But maybe t... | Three Pioneers from class 1a and three from class 1b will be awarded certificates. Thus, $3 + 3 = 6$ Pioneers will be awarded. |
4409aeda-7fc0-54a5-b576-8752b01058b6 | open-r1/OpenR1-Math-220k/cn_k12 | Evaluate the integral $$∫_{ 0 }^{ 1 }(e^{x}+2x)dx$$.
Options:
A: 1
B: e-1
C: e+1
D: e | [
"We need compute integral from 0 to1 of (e^x + 2x) dx. Integral of e^x is e^x, evaluate 0 to1 gives e -1. Integral of 2x dx = x^2 from 0 to1 =1. Sum = (e -1)+1 = e. Therefore answer D: e."
] | The integral $\int_{0}^{1}\big(e^{x}+2x\big)\,dx$ splits into $\int_{0}^{1}e^{x}\,dx = e-1$ and $\int_{0}^{1}2x\,dx = 1$, summing to $e$. The value of the integral is $e$, option D. |
2531fe3d-6706-5699-ba3d-52cce81c87aa | open-r1/OpenR1-Math-220k/cn_k12 | From 10 basketballs, one is randomly selected to test its quality. The sampling method that should be used is ____. | [
"We need to answer fill-in-the-blank: For selecting one basketball out of 10 randomly to test quality, the sampling method is \"simple random sampling\". Could also be \"simple random sampling\" as individual selection. No replacement needed because only one selected. So answer: simple random sample (SRS)."
] | Simple random sampling is a probability sampling method where each member of a population has an equal chance of being selected. This ensures that every possible sample of a given size has an equal probability of being chosen, minimizing bias. |
5e2e0759-26a8-5dfd-b615-4633c4976216 | open-r1/OpenR1-Math-220k/olympiads | 274. $\int_{0}^{1 / 2} \frac{d x}{\sqrt{1-x^{2}}}$.
Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.
274. $\int_{0}^{1 / 2} \frac{d x}{\sqrt{1-x^{2}}}$.
The above text is already in a mathematical format and does not require transl... | [
"We need to respond with translation keeping line breaks and format, output translation directly. The user text appears to be already English, so probably return the same. They want translation result directly. So output the same lines.",
"Thus produce:",
"274. $\\int_{0}^{1 / 2} \\frac{d x}{\\sqrt{1-x^{2}}}$."... | $\int_{0}^{1 / 2} \frac{d x}{\sqrt{1-x^{2}}} = [\arcsin x]_{0}^{1 / 2} = \arcsin \frac{1}{2} - \arcsin 0 = \frac{\pi}{6}$. |
e3f9ed39-d9e2-5504-921e-790061178992 | open-r1/OpenR1-Math-220k/cn_k12 | Given the set $M=\{-1, 1\}$, the number of sets $N$ that satisfy $N \subseteq M$ is ( )
A: 1
B: 2
C: 3
D: 4 | [
"The problem: Given set M = {-1,1}, the number of sets N that satisfy N ⊆ M (i.e., all subsets of M). How many subsets does a set with two elements have? 2^2 = 4. So answer D: 4. Possibly they're asking number of subsets. So answer D.",
"Thus respond: D."
] | The set \(M\) has two elements, so it has \(2^2=4\) subsets. Thus there are four possible sets \(N\) with \(N\subseteq M\); Answer: D – 4. |
f27b451d-3381-5f04-825b-93a1a9ad696d | open-r1/OpenR1-Math-220k/cn_k12 | Sampling methods include ( )
A: Random sampling, systematic sampling, and stratified sampling
B: Random number method, drawing lots, and stratified sampling method
C: Simple random sampling, stratified sampling, and systematic sampling
D: Systematic sampling, stratified sampling, and random number method | [
"We need to answer multiple-choice question: \"Sampling methods include ( )\". Options list combinations of sampling methods. Probably question from statistics: sampling methods typically include random sampling (simple random), systematic sampling, stratified sampling, cluster sampling, multistage, etc. The option... | Simple random sampling, stratified sampling, and systematic sampling are types of probability sampling methods. These methods ensure that each member of the population has a known, non-zero chance of being selected. |
5fb1f1e4-b69c-56e5-befb-bf906447ae95 | open-r1/OpenR1-Math-220k/olympiads | 2. Xiao Pang and his father played a dart game together, each of them threw 5 times, father scored 48 points, Xiao Pang's score was 8 points less than half of his father's, Xiao Pang scored $\qquad$ points. | [
"We need to parse the problem. It says: \"Xiao Pang and his father played a dart game together, each of them threw 5 times, father scored 48 points, Xiao Pang's score was 8 points less than half of his father's, Xiao Pang scored ___ points.\"",
"Interpretation: father total score = 48 points (over 5 throws). Xiao... | The father's total score was 48 points, with half of this being 24 points. Xiao Pang's score is 8 points less than that, resulting in 16 points. |
83187d2d-3b78-5f60-87fb-0d1189210773 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following calculations is correct?
A: $3a+b=3ab$
B: $a^{2}+a^{2}=a^{4}$
C: $(a-b)^{2}=a^{2}-b^{2}$
D: $(-3a)^{2}=9a^{2}$ | [
"We need to determine which of the given statements is correct (mathematical equality). Let's examine each.",
"A: 3a + b = 3ab. This would only be true for special values, not generally. Unless a,b satisfy something, but as an identity it's false.",
"B: a^2 + a^2 = a^4. Left side = 2 a^2. Right side = a^4. Not ... | The correct identity is D: $ (-3a)^{2}=9a^{2} $, as $ (-3a)^{2}=(-3)^{2}a^{2}=9a^{2} $ for any real or complex number $ a $. The other options are not universally true identities. |
9ff91f9e-ab45-54f4-a382-3be3338e5ca6 | open-r1/OpenR1-Math-220k/cn_k12 | In the Cartesian coordinate system, the coordinates of the point $(-2,3)$ after moving $4$ units to the right are ( ).
A: $(2,3)$
B: $(-6,3)$
C: $(-2,7)$
D: $(-2,-1)$ | [
"The question: point (-2,3) after moving 4 units to the right. Moving to the right increases x-coordinate by 4. So new x = -2 + 4 = 2, y unchanged 3. So answer (2,3). Option A."
] | Moving a point 4 units to the right changes its \(x\)-coordinate from \(-2\) to \(-2+4=2\), resulting in new coordinates of \((2,3)\). The final answer is \(\boxed{A \text{ (2,3)}}\). |
12a96f20-a7ed-5b76-8662-c1916e802d2a | open-r1/OpenR1-Math-220k/cn_k12 | The equation of the circle with center at the point (0,1) and radius 2 is ( )
A: $x^2+(y-1)^2=2$
B: $(x-1)^2+y^2=2$
C: $x^2+(y-1)^2=4$
D: $(x-1)^2+y^2=4$ | [
"We need to answer multiple choice: equation of circle with center (0,1) radius 2. General: (x - h)^2 + (y - k)^2 = r^2. So (x - 0)^2 + (y - 1)^2 = 4. That's x^2 + (y - 1)^2 = 4. Option C."
] | The equation of the circle is $x^2 + (y-1)^2 = 4$. This is choice **C**. |
8cbbddef-f987-5cc5-9ef4-19c3962db9af | open-r1/OpenR1-Math-220k/olympiads | Example 2.25. $\int_{-\infty}^{0} e^{x} d x$.
Translate the text above into English, keeping the original text's line breaks and format, and output the translation result directly.
Example 2.25. $\int_{-\infty}^{0} e^{x} d x$. | [
"The user asks: \"Example 2.25. $\\int_{-\\infty}^{0} e^{x} d x$.\" They want to translate the text above into English, keeping the original text's line breaks and format, and output the translation result directly. The text is already in English? Actually \"Example 2.25. $\\int_{-\\infty}^{0} e^{x} d x$.\" It's al... | The integral $\int_{-\infty}^{0} e^{x} d x$ evaluates to 1. This is found by taking the limit of the definite integral as the lower bound approaches $-\infty$: $\lim_{a \to -\infty} \int_{a}^{0} e^{x} d x = \lim_{a \to -\infty} [e^{x}]_{a}^{0} = \lim_{a \to -\infty} (e^{0} - e^{a}) = 1 - 0 = 1$. |
b6fc1bfd-7272-539b-bcb4-3b2d8d326ebb | open-r1/OpenR1-Math-220k/cn_k12 | Given $\log_{2}3=a$, $\log_{2}5=b$, then $\log_{2} \frac{9}{5}$ equals ( )
A: $a^{2}-b$
B: $2a-b$
C: $\frac{a^{2}}{b}$
D: $\frac{2a}{b}$ | [
"We need to compute log2(9/5) in terms of a=log2 3, b=log2 5.",
"log2(9/5)=log2 9 - log2 5 = log2 (3^2) - b = 2 log2 3 - b = 2a - b. That's option B.",
"Thus answer B.",
"But perhaps they want an expression using a and b. Indeed B.",
"Provide reasoning.",
""
] | Given $\log_{2}\frac{9}{5}= \log_{2}9-\log_{2}5.$ Since $9=3^2,$ $\log_{2}9=2\log_{2}3=2a.$ Also $\log_{2}5=b,$ so $\log_{2}\frac{9}{5}=2a-b.$ The correct choice is **B: \(2a-b\)**. |
3967e9df-3a87-5dcb-9232-718d851c13e2 | open-r1/OpenR1-Math-220k/cn_k12 | What is the sum of the interior angles of a quadrilateral?
A: $180^{\circ}$
B: $360^{\circ}$
C: $540^{\circ}$
D: $720^{\circ}$ | [
"The user asks: \"What is the sum of the interior angles of a quadrilateral?\" Options: 180, 360, 540, 720 degrees. The answer is 360 degrees (since sum = (n-2)*180 = (4-2)*180 = 360). So answer B.",
"Probably they just want the answer. Could explain reasoning."
] | The sum of the interior angles of an \(n\)-sided polygon is given by $(n-2) \times 180^{\circ}$. For a quadrilateral, \(n=4\), resulting in a sum of $360^{\circ}$. |
863bb8e9-f455-5066-8d23-d1a20698a2d6 | open-r1/OpenR1-Math-220k/olympiads | 4. (7 points) A gnome in shoes weighs 2 kg more than a gnome without shoes. If you put five identical gnomes in shoes and five such gnomes without shoes on the scales, the scales will show 330 kg. How much does a gnome in shoes weigh? | [
"We need to parse problem: \"A gnome in shoes weighs 2 kg more than a gnome without shoes. If you put five identical gnomes in shoes and five such gnomes without shoes on the scales, the scales will show 330 kg. How much does a gnome in shoes weigh?\" So we have unknown: weight of a gnome without shoes = x kg. Then... | The equation representing the total weight is $5(w+2) + 5w = 330$ kg, which simplifies to $w = 32$ kg. Therefore, a gnome with shoes weighs $w+2 = 32+2 = 34$ kg. |
f1a5c1b4-a913-5b2d-b2e0-2b092dc4996a | open-r1/OpenR1-Math-220k/cn_k12 | Given that $a$ is a positive integer, point $P(4,2-a)$ lies in the first quadrant, then $a=\_\_\_\_\_\_$. | [
"We need to interpret: point P(4, 2 - a) lies in the first quadrant, given a is positive integer. First quadrant: x>0, y>0. x-coordinate is 4>0 already. y-coordinate is 2 - a > 0 => 2 - a > 0 => a < 2. Since a is positive integer, possible values: 1 only (since a<2, a>0 integer). So a = 1. Answer: 1."
] | Since point \(P\) is in the first quadrant, its coordinates must both be positive, which implies \(2-a>0\). Given that \(a\) is a positive integer, the only value satisfying \(0<a<2\) is \(a=1\). |
5a9452cd-25fc-5dee-8a07-98d04f035760 | open-r1/OpenR1-Math-220k/olympiads | The value of $\left(2^{3}\right)^{2}-4^{3}$ is
(A) 0
(B) -8
(C) 4
(D) 10
(E) 12 | [
"We need calculate (2^3)^2 - 4^3. 2^3 =8. (8)^2 =64. 4^3 =64. 64 -64 =0. Answer A."
] | \[(2^{3})^{2} = 64\] and \[4^{3} = 64\], so the difference is \[64 - 64 = 0\]. The value is (A) 0. |
2f83637b-0b92-5845-877c-7c664bc06bd1 | open-r1/OpenR1-Math-220k/olympiads | 5. A small rabbit eats 2 pieces of cabbage a day, a large rabbit eats 4 pieces of cabbage a day, now raising two large rabbits, one small rabbit, every day $\qquad$ pieces of cabbage need to be prepared. | [
"The user says: \"5. A small rabbit eats 2 pieces of cabbage a day, a large rabbit eats 4 pieces of cabbage a day, now raising two large rabbits, one small rabbit, every day pieces of cabbage need to be prepared.\"",
"Looks like a Chinese math problem: We need to fill in the blank (how many pieces of cabbage nee... | Two large rabbits require $2 \times 4 = 8$ pieces of cabbage, and one small rabbit needs $1 \times 2 = 2$ pieces. Therefore, $8 + 2 = 10$ pieces of cabbage must be prepared each day. |
f8133c6b-179c-5282-aab1-b8b4804caa82 | open-r1/OpenR1-Math-220k/cn_k12 | The three logical structures of an algorithm are ( )
A: Sequential structure; Flow structure; Loop structure
B: Sequential structure; Conditional structure; Nested structure
C: Sequential structure; Conditional structure; Loop structure
D: Flow structure; Conditional structure; Loop structure | [
"We need to answer the multiple choice question: \"The three logical structures of an algorithm are ( )\". Options given. The correct answer: typical three basic control structures in algorithms: sequence, selection (conditional), and iteration (loop). So answer is C: Sequential structure; Conditional structure; ... | The three fundamental logical structures for algorithms are sequential, conditional, and loop structures. Thus, the correct choice is C: Sequential structure; Conditional structure; Loop structure. |
1802e9e8-879a-5fc3-a0da-f2376cf7ca12 | open-r1/OpenR1-Math-220k/olympiads | Task 15. (8 points)
Announcement: "Have free time and want to earn money? Write now and earn up to 2500 rubles a day working as a courier with the service 'Food.There-Here!'. Delivery of food from stores, cafes, and restaurants.
How much will a school student working as a courier with the service 'Food.There-Here!' e... | [
"We need to parse the problem.",
"The announcement says earn up to 2500 rubles a day working as a courier. Minimum load is 1250 rubles a day after income tax deduction. The question: \"How much will a school student working as a courier with the service 'Food.There-Here!' earn in a month (4 weeks), working 4 days... | The calculation results in 20000. This is the final numerical value. |
daff7435-c585-5ad5-b552-6758d384c63e | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following calculations is correct?
A: $3x+2x=5x^{2}$
B: $\sqrt{9}=±3$
C: $(2x)^{2}=2x^{2}$
D: $2^{-1}=\frac{1}{2}$ | [
"We need to answer which of the following calculations is correct. Evaluate each.",
"A: 3x+2x = (3+2)x =5x. Not 5x^2. So incorrect.",
"B: sqrt(9) = ±3? By definition principal square root of a nonnegative real is nonnegative, sqrt(9)=3, not ±3. So incorrect.",
"C: (2x)^2 = (2x)*(2x) =4x^2. Not 2x^2. So incorr... | Statements A, B, and C are incorrect because \(3x+2x=5x\), \(\sqrt{9}=3\), and \((2x)^2=4x^2\), respectively. Statement D, \(2^{-1}=\frac{1}{2}\), is correct. |
28b893a9-8de7-52d6-8c14-ad7a6c593a7a | open-r1/OpenR1-Math-220k/cn_k12 | $\sqrt{9}=\left(\ \ \right)$
A: $\pm 3$
B: $3$
C: $±\sqrt{3}$
D: $\sqrt{3}$ | [
"The user provides a question: \"$\\sqrt{9}=\\left(\\ \\ \\right)$\". Multiple choice answers: A: ±3, B: 3, C: ±√3, D: √3.",
"We need to select the correct answer. The principal square root of 9 is 3. So answer B: 3. But some might think it's ±3? However the sqrt symbol denotes principal (non-negative) root. So a... | The principal square root of 9 is 3, as \(3^2=9\). Therefore, the correct choice is B: 3. |
68bc9859-60f3-5fa8-80c5-202473ae041b | open-r1/OpenR1-Math-220k/cn_k12 | If the variance of a set of data $a_1, a_2, a_3, a_4, a_5, a_6$ is 2, then the variance of another set of data $2a_1, 2a_2, 2a_3, 2a_4, 2a_5, 2a_6$ is ( )
A: 2
B: 6
C: 8
D: -2 | [
"We need to answer: If variance of a set of data a_i is 2, then variance of scaled data 2 a_i is what? Usually variance scales by factor squared of scaling: var(cX) = c^2 var(X). So var(2a_i) = 4 * 2 = 8. Answer: C.",
"But note that there is possibility of sample vs population variance. Regardless, scaling multip... | The variance of the transformed data is \(\operatorname{Var}(c a_i) = c^2 \operatorname{Var}(a_i)\). Given \(c=2\) and \(\operatorname{Var}(a_i)=2\), the new variance is \(2^2 \times 2 = 8\). |
670ee4a3-e86a-5e52-ab7d-eca643189df4 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following statements about a pyramid is correct? ( )
A: A quadrilateral pyramid has four edges.
B: A pentagonal pyramid has five faces.
C: A hexagonal pyramid has six vertices.
D: Any pyramid has only one base. | [
"We need to identify correct statement about a pyramid (geometric polyhedron). Let's recall definitions: A pyramid is a polyhedron formed by connecting a polygonal base to a point called the apex. The base is an n-gon, pyramid has n triangular lateral faces plus the base. So total faces: n+1. Number of vertices: n+... | Statement D is true because, by definition, a pyramid has only one base. Statements A, B, and C are false as a quadrilateral pyramid has 8 edges, a pentagonal pyramid has 6 faces, and a hexagonal pyramid has 7 vertices. |
c35d37e5-6b9c-57af-b04e-0777f7906f97 | open-r1/OpenR1-Math-220k/olympiads | [Mathematical logic (miscellaneous).] [ Arithmetic. Mental arithmetic, etc. ]
Rabbits are sawing a log. They made 10 cuts. How many chunks did they get?
# | [
"We need to interpret problem: \"Rabbits are sawing a log. They made 10 cuts. How many pieces/chunks did they get?\" Classic puzzle: With n cuts, maximum number of pieces is n+1 if cuts are done sequentially, but if you can rearrange pieces and cut multiple at once, could be more. For a log (a straight line segment... | Each cut increases the number of pieces by one, so $n$ cuts result in $n+1$ pieces. With 10 cuts, there are $10+1 = \boxed{11}$ pieces. |
0eb46b5a-8fc6-5f2f-9eb9-41a6b87831bd | open-r1/OpenR1-Math-220k/cn_k12 | Among the following propositions, the correct one is\\((\\) \\()\\)
A: If two vectors are equal, then their starting points and endpoints coincide respectively.
B: Two parallel vectors with equal magnitudes are equal vectors.
C: If _\\(a\\)_ and _\\(b\\)_ are both unit vectors, then _\\(a\\)_\\(=\\) _\\(b\\)_.
D: Two ... | [
"The question: \"Among the following propositions, the correct one is ( )\". Likely a multiple-choice question. Options A, B, C, D.",
"We need identify which statements are correct.",
"Interpretation:",
"A: If two vectors are equal, then their starting points and endpoints coincide respectively. Usually a vec... | Two equal vectors have equal magnitudes by definition because equality requires both the same magnitude and direction. Therefore, statement D is always true. |
94b38e61-32fd-5415-9ec2-7b4293594420 | open-r1/OpenR1-Math-220k/olympiads | 7. In 1981, the United States developed the world's first space shuttle, the “$\qquad$”号, which successfully completed its first manned space flight test.
A. Houston
B. New York
C. Columbia
D. Apollo
Note: The Chinese character "号" in the blank should be replaced with the corresponding English name, which is "Columbia... | [
"The user just gave a question and answer: \"7. In 1981, the United States developed the world's first space shuttle, the “____号”, which successfully completed its first manned space flight test. A. Houston B. New York C. Columbia D. Apollo ... Note: The Chinese character '号' in the blank should be replaced with th... | The first operational Space Shuttle, **Columbia** (STS-1), completed its first manned flight on April 12-13, 1981. Thus, **Columbia** fills the blank, making option **C** correct. |
2daf2651-6280-560b-939f-d3853a91d0fe | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following phenomena is impossible? ( )
A: A conductor heats up when conducting electricity
B: Three non-collinear points determine a plane
C: Seeds germinate without water
D: Someone wins the lottery for two consecutive weeks | [
"We need to answer which phenomenon is impossible among options. Let's analyze each:",
"A: A conductor heats up when conducting electricity – that's Joule heating, possible.",
"B: Three non-collinear points determine a plane – geometric theorem, true.",
"C: Seeds germinate without water – germination requires... | Seeds germinate without water is impossible because water is a fundamental requirement for initiating enzymatic activity and metabolic reactions necessary for sprouting. Therefore, C is the impossible phenomenon. |
86feba0f-073d-5068-aa17-2a2580506314 | open-r1/OpenR1-Math-220k/cn_k12 | When $x=-1$, the value of the function $y=-2x$ is equal to:
A: $2$
B: $-2$
C: $\frac{1}{2}$
D: $-\frac{1}{2}$ | [
"We just evaluate y = -2x at x = -1: -2 * (-1) = 2. Answer A."
] | When \(x = -1\), \(y = -2(-1) = 2\). The correct choice is **A: \(2\)**. |
65f54d25-90ff-5f45-b7a9-8ef6a890edce | open-r1/OpenR1-Math-220k/cn_k12 | Calculate: $-3 + 2 = \quad$; $\quad (-3) \times 2 = \quad$. | [
"The user asks: \"Calculate: $-3 + 2 = \\quad$; $\\quad (-3) \\times 2 = \\quad$.\"",
"We need to provide the results: -3 + 2 = -1; (-3) * 2 = -6.",
"Probably just answer both. Provide explanation maybe."
] | $-3 + 2 = -1$ and $(-3)\times 2 = -6$. |
1ceb5a84-d56f-51a3-a633-0209d8d7870b | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following calculations is correct?
A: $a^{8}\div a^{2}=a^{4}$
B: $5ab-2ab=3$
C: $(a-b)^{2}=a^{2}-b^{2}$
D: $(-ab^{3})^{2}=a^{2}b^{6}$ | [
"We need to identify which of the given calculations is correct. Let's examine each.",
"A: a^8 ÷ a^2 = a^(8-2) = a^6, not a^4. So A is wrong.",
"B: 5ab - 2ab = (5-2)ab = 3ab, not 3. So B is wrong.",
"C: (a-b)^2 = a^2 -2ab + b^2, not a^2 - b^2. So wrong.",
"D: (-ab^3)^2: square the whole expression. (-1)^2=1... | Option D, \((-ab^{3})^{2}=a^{2}b^{6}\), is the only correct calculation because squaring a product squares each factor, and \((-1)^{2}=1\). The other options contain errors in exponent subtraction, factoring, or binomial expansion. |
cff69271-6f6f-5ac0-a30a-65e3c59e5421 | open-r1/OpenR1-Math-220k/cn_k12 | Given that variables $x$ and $y$ are linearly related, and the sample means obtained from observational data are $\overset{.}{x}=2$ and $\overset{.}{y}=3$, the linear regression equation obtained from this observational data cannot be
A: $y=3x-3$
B: $y=2x+1$
C: $y=x+1$
D: $y=0.5x+2$ | [
"We need to parse the question. It says \"Given that variables x and y are linearly related, and the sample means obtained from observational data are x̄ = 2 and ȳ = 3, the linear regression equation obtained from this observational data cannot be [options].\"",
"So which regression line cannot have that mean po... | The fitted line for simple linear regression must pass through the sample means \((\bar x, \bar y)\), which are \((2,3)\). Only option B, \(y = 2x + 1\), fails to satisfy the condition \(3 = a(2)+b\) because \(2(2)+1 = 5 \neq 3\). |
d6ebdf98-162d-51f3-8b32-29ccc6eb9be7 | open-r1/OpenR1-Math-220k/cn_k12 | Given a regression equation $$\hat y = 2 + 3x$$, when the variable $x$ increases by one unit, then ( )
A: $y$ increases by an average of 2 units
B: $y$ increases by an average of 3 units
C: $y$ decreases by an average of 2 units
D: $y$ decreases by an average of 3 units | [
"We need to answer the multiple choice. Regression equation ŷ = 2 + 3x. The coefficient of x is 3, meaning that for each one unit increase in x, predicted y increases by 3 units on average. So answer B. Provide explanation."
] | The slope \(\beta_1 = 3\) indicates that for a one-unit increase in \(x\), the predicted value of \(y\) increases by 3 units. Therefore, \(y\) increases by an average of 3 units. |
0fb952fa-22d5-5c60-97ee-782a8e3c9160 | open-r1/OpenR1-Math-220k/cn_contest | Example 3. Simplify: $\sqrt{(a-5)^{2}}$ | [
"We need to answer: Simplify sqrt((a-5)^2). Typically sqrt(x^2) = |x|. So sqrt((a-5)^2) = |a-5|. Could also be expressed as |5 - a| (same). If we assume a≥5 then equals a-5 else 5-a. So answer: |a-5|. Provide reasoning."
] | The expression simplifies to $|a-5|$. This can be written piece-wise as $a-5$ if $a \ge 5$, and $5-a$ if $a < 5$. |
40ffdb61-40c0-5af2-9f82-589affdc464d | open-r1/OpenR1-Math-220k/cn_k12 | Let the function $y = f(x)$. When the independent variable $x$ changes from $x_0$ to $x_0 + \Delta x$, the change in the function $\Delta y$ is ( )
A: $f(x_0 + \Delta x)$
B: $f(x_0) + \Delta x$
C: $f(x_0) \cdot \Delta x$
D: $f(x_0 + \Delta x) - f(x_0)$ | [
"We need to answer the multiple choice: the change in function Δy when x changes from x0 to x0+Δx. Δy = f(x0+Δx) - f(x0). So answer D.",
"Provide explanation."
] | The change in the function, denoted $\Delta y$, is the difference between the function's values at $x_{0}+\Delta x$ and $x_{0}$, so $\Delta y = f(x_{0}+\Delta x) - f(x_{0})$. Therefore, the correct choice is D: $f(x_{0}+\Delta x) - f(x_{0})$. |
ddda4fed-0fd1-58ac-b1d9-b516694baf1d | open-r1/OpenR1-Math-220k/olympiads | 23. In the canteen for lunch, 4 first-course dishes, 5 second-course dishes, and 3 desserts are prepared for selection. In how many ways can one lunch be composed? | [
"We need to parse the problem: There are 4 first-course dishes, 5 second-course dishes, and 3 desserts. We want number of ways to compose one lunch. Typically a lunch consists of one first-course, one second-course, and one dessert? The problem states \"In the canteen for lunch, 4 first-course dishes, 5 second-cour... | The total number of different lunch combinations is found by multiplying the number of possibilities for each course: $4 \times 5 \times 3 = 60$. Therefore, there are 60 possible lunch options. |
8771cf2b-06c4-53ff-9a46-56253ecfe9ca | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following calculations is correct?
A: $\sqrt{2}×\sqrt{3}=\sqrt{6}$
B: $\sqrt{2}+\sqrt{3}=\sqrt{5}$
C: $(\sqrt{2})^{2}=2\sqrt{2}$
D: $2+\sqrt{2}=2\sqrt{2}$ | [
"We need to answer: Which of the following calculations is correct? Options A through D. Evaluate each statement.",
"A: sqrt(2)*sqrt(3) = sqrt(6). Indeed property sqrt(a)*sqrt(b) = sqrt(ab) for non-negative a,b. So true.",
"B: sqrt(2)+sqrt(3) = sqrt(5). Not true: sqrt2+sqrt3 ≈1.414+1.732=3.146, sqrt5≈2.236. So ... | Only statement A is correct, as \(\sqrt{2}\times\sqrt{3}=\sqrt{2\cdot 3}=\sqrt{6}\). The other statements B, C, and D are incorrect due to misconceptions about adding square roots, squaring square roots, and combining rational and irrational numbers. |
8a70fade-64ea-554f-bf40-b3de41ea4148 | open-r1/OpenR1-Math-220k/olympiads | A six-sided die has the numbers one to six on its sides. What is the probability of rolling a five?
(A) $\frac{2}{6}$
(B) $\frac{1}{6}$
(C) $\frac{5}{6}$
(D) $\frac{3}{6}$
(E) $\frac{4}{6}$ | [
"The user asks a simple probability question: A six-sided die with numbers 1-6, probability of rolling a five. It's 1 favorable outcome out of 6 possible equally likely outcomes: 1/6. So answer (B) 1/6. Provide explanation."
] | The probability of rolling a five on a six-sided die is $\frac{1}{6}$. This is calculated by dividing the number of favorable outcomes (1, rolling a five) by the total number of possible outcomes (6). |
c5ee5ead-f602-5a8f-8c98-1319d2fbe3ca | open-r1/OpenR1-Math-220k/cn_k12 | During a class meeting, it was decided to vote on whether to add a new class committee member. The voting method that best reflects the true will of all students is ( ).
A: By a show of hands of those who agree to add the new member.
B: By a show of hands of those who disagree to add the new member.
C: By secret ballot... | [
"We need to answer which voting method best reflects true will of all students. Options: show of hands for agree, show of hands for disagree, secret ballot, recorded vote. The best reflect true will is secret ballot (C) because it ensures anonymity and reduces pressure. Recorded vote (public) might influence. Show ... | A secret ballot ensures anonymity, preventing peer pressure or fear of retaliation from influencing votes and thus accurately reflecting students' genuine preferences. Unlike public voting methods, a secret ballot guarantees that the true will of the group is captured without distortion. |
74ce85a9-21ad-5fb3-9929-cce17d65cb4c | open-r1/OpenR1-Math-220k/olympiads | 22. China has currently built 9 tidal power stations, the $\qquad$ tidal power station, completed in 1980, is China's first bidirectional tidal power station, and it is also one of the largest bidirectional tidal power stations in the world.
A. Xiamen
B. Jiangxia
C. Humen
D. Sanya | [
"The question: \"22. China has currently built 9 tidal power stations, the ____ tidal power station, completed in 1980, is China's first bidirectional tidal power station, and it is also one of the largest bidirectional tidal power stations in the world.\"",
"Options: A. Xiamen, B. Jiangxia, C. Humen, D. Sanya.",... | The original answer is not provided, so I cannot shorten it. Please provide the mathematical answer you would like me to shorten. |
bfd95ff7-d334-5855-9951-fba4246ce0a1 | open-r1/OpenR1-Math-220k/olympiads | 4. The "=" sign was invented by the British person
A. De Morgan
B. Recorde
C. Oughtred | [
"We need respond to a quiz type question: \"The \"=\" sign was invented by the British person: A. De Morgan, B. Recorde, C. Oughtred\". The correct answer: The equals sign was invented by Robert Recorde, a Welsh mathematician (British). So answer B. Provide explanation."
] | The equals sign "=" was introduced by Welsh mathematician Robert Recorde in his 1557 work *The Whetstone of Wealth*, chosen because "no two things can be more equal than parallel lines." |
445a0438-ba7e-514a-958c-3f1f6b3323c7 | open-r1/OpenR1-Math-220k/olympiads | ## Task 18
$a=9, b=628 ; \quad$ To the sixfold of $a$, add half of $b$. | [
"The user asks: \"Task 18: a=9, b=628 ; To the sixfold of a, add half of b.\" So we need to compute 6*a + b/2.",
"a=9 => sixfold = 6*9=54. b=628 => half = 314.",
"Sum = 54 + 314 = 368.",
"We need probably give answer. Might also show steps. Provide answer: 368.",
"Consider whether they want expression: 6a +... | The expression $6a+\frac{b}{2}$ evaluates to $368$ when $a=9$ and $b=628$. This is calculated by first finding $6a = 6 \cdot 9 = 54$ and $\frac{b}{2} = \frac{628}{2} = 314$, then summing these results: $54 + 314 = 368$. |
a58e4f17-b5eb-53b3-9dcb-abd377ff8532 | open-r1/OpenR1-Math-220k/olympiads | ## Task 1
In 5 windows of a residential building, there are a total of 40 glass panes.
How many panes are in 3 windows? | [
"We need to interpret the problem. \"In 5 windows of a residential building, there are a total of 40 glass panes. How many panes are in 3 windows?\" Assuming uniform distribution. So 40 panes /5 windows = 8 panes per window. Then 3 windows have 3*8 = 24 panes. Provide answer."
] | There are 8 panes per window, so 3 windows contain 24 panes. |
aa86f0cf-4d35-5a6a-81cb-6f28e3817314 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following propositions is true?
A: If $a+b \lt 0$, then $ab \lt 0$
B: Corresponding angles are equal
C: The sum of interior angles of a triangle is $180^{\circ}$
D: Equal angles are vertical angles | [
"We need to answer which proposition is true among options A-D. Probably multiple could be true or false. Let's analyze each.",
"A: If a+b < 0 then ab < 0. Not necessarily. Counterexample: a = -2, b = -1, sum = -3 <0, product = 2 >0. So false.",
"B: \"Corresponding angles are equal.\" In geometry, corresponding... | Propositions B and C are true, with B being true under the hypothesis of parallel lines and C being true in Euclidean plane geometry. Propositions A and D are false. |
52fa3c7e-8b2e-5de1-8b8b-6a1064fdc767 | open-r1/OpenR1-Math-220k/olympiads | When two numbers are added, the result is -26 . If one of the numbers is 11 , what is the other number?
(A) -37
(B) 37
(C) -15
(D) 15
(E) -48 | [
"We need to solve: x + 11 = -26 => x = -37. So answer (A) -37.",
"We need to respond with answer."
] | The unknown number \(x\) satisfies \(x + 11 = -26\), which simplifies to \(x = -26 - 11 = -37\). Thus, the other number is \(-37\), which is answer option (A). |
4bc59358-1e94-5947-ac8a-57b27df45c84 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following statements is correct? ( )
A: A quadrilateral with a pair of adjacent equal sides is a rhombus.
B: A parallelogram with one right angle is a rectangle.
C: A parallelogram with perpendicular diagonals is a square.
D: A quadrilateral with one pair of parallel sides is a parallelogram. | [
"We need to evaluate each statement's correctness.",
"A: \"A quadrilateral with a pair of adjacent equal sides is a rhombus.\" Not necessarily. A kite has a pair of adjacent equal sides but not all sides equal, not a rhombus. So false.",
"B: \"A parallelogram with one right angle is a rectangle.\" In a parallel... | Statement B is correct because a parallelogram with one right angle is a rectangle. Statements A, C, and D are false as kites are not necessarily rhombuses, perpendicular diagonals do not guarantee squares, and only one pair of parallel sides defines a trapezoid, not a parallelogram. |
03b5e322-6957-5b72-8664-b66107e963a3 | open-r1/OpenR1-Math-220k/olympiads | 140. An example of multiplication. One morning at breakfast, the Crackhams were discussing high matters, when suddenly George asked his sister Dora to quickly multiply
$$
1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 0
$$
How long will it take the reader to find this product? | [
"We need to answer: \"How long will it take the reader to find this product?\" The product given includes a factor 0, so product is 0. The answer likely: immediate, essentially zero time. But maybe they want a comedic answer: It's the product of numbers 1 through 10, which includes 0, so product is 0; the answer is... | The product is **0** because the expression includes a factor of **0**. The time required to determine this is virtually none, as it is evident from the final factor. |
54c8d808-f0dd-56ef-b2a0-ed5f65df4823 | open-r1/OpenR1-Math-220k/cn_k12 | The opposite of $-6$ is ____,The absolute value of $-8$ is ____,The reciprocal of $-3$ is ____. | [
"The user asks: \"The opposite of $-6$ is ____,The absolute value of $-8$ is ____,The reciprocal of $-3$ is ____.\"",
"They likely want fill-in-the-blank answers: opposite of -6 is 6 (since opposite means additive inverse). Absolute value of -8 is 8. Reciprocal of -3 is -1/3.",
"So answer: 6, 8, -1/3.",
"Need... | The opposite of \(-6\) is \(6\), the absolute value of \(-8\) is \(8\), and the reciprocal of \(-3\) is \(-\frac13\). |
e61c020a-094e-58be-998b-4f26d43bc267 | open-r1/OpenR1-Math-220k/cn_k12 | Variance is a measure of the degree of data fluctuation. For a set of data $x_{1}$, $x_{2}$, $x_{3}$, $\ldots$, $x_{n}$, the variance can be calculated using the following formula: $s^{2}=\frac{1}{n}[(x_{1}-5)^{2}+(x_{2}-5)^{2}+(x_{3}-5)^{2}+\ldots +(x_{n}-5)^{2}]$, where "5" represents the ( ).
A: minimum value
B: m... | [
"We need to answer: In variance formula, the term subtracted is the mean. The formula given uses 5, implying the mean is 5. So answer B. Provide explanation."
] | The number "5" represents the mean of the data set, as it is the value subtracted from each observation within the squared terms in the variance calculation. Therefore, the correct option is B – mean. |
5a00726b-717c-5875-98bc-26048b0a7cfd | open-r1/OpenR1-Math-220k/cn_k12 | The absolute value of $-\frac{3}{2}$ is ( ).
A: $-\frac{2}{3}$
B: $-\frac{3}{2}$
C: $\frac{2}{3}$
D: $\frac{3}{2}$ | [
"We need to answer absolute value of -3/2 is 3/2. So option D. Provide answer."
] | The absolute value of $-\frac{3}{2}$ is $\frac{3}{2}$. The correct choice is D: $\displaystyle \frac{3}{2}$. |
118d20e8-b6c9-536b-a802-54e6313d0940 | open-r1/OpenR1-Math-220k/olympiads | The integer 42 is
(A) an odd number
(D) divisible by 7
(B) a prime number
(C) a perfect cube | [
"We need to answer which statements about integer 42 are true. Options A-E? The problem lists (A) an odd number, (D) divisible by 7, (B) a prime number, (C) a perfect cube. We need choose correct statements. 42 is even, not odd. So A false. Divisible by 7? 42/7=6, yes true, D true. 42 is not prime (divisible by 2,3... | 42 is an even, composite number, and not a perfect cube. Since \(42 \div 7 = 6\), 42 is divisible by 7, making statement (D) true. |
a0d08422-fb1c-580d-8aa4-25ba98932b17 | open-r1/OpenR1-Math-220k/cn_k12 | Given a regression equation $y = 3 - 5x$, when the variable $x$ increases by one unit,
A. $y$ decreases by an average of 5 units.
B. $y$ increases by an average of 3 units.
C. $y$ decreases by an average of 3 units.
D. $y$ increases by an average of 5 units. | [
"We need to interpret regression equation y = 3 - 5x. This is a linear relationship: slope = -5. For each increase of x by 1 unit, y changes by slope * Δx = -5 * 1 = -5. So y decreases by 5 units. So answer A.",
"But need to ensure wording: \"average\" maybe implying average change. So yes.",
"Return answer A. ... | The regression equation $y = 3 - 5x$ has a slope of \(-5\), meaning for a one-unit increase in \(x\), \(y\) decreases by 5 units on average. Therefore, when \(x\) increases by one unit, \(y\) **decreases by 5 units**. |
3c075cb4-c664-5ae4-8a47-fe13d57719db | open-r1/OpenR1-Math-220k/olympiads | 18. (6 points) Two ribbons, A and B, were originally the same length. If ribbon A is cut by 18 meters and ribbon B is cut by 12 meters, the length of ribbon B is then twice the length of ribbon A. What was the original length of ribbons A and B? | [
"We need to solve: Let original length = L (same for both). After cutting: A length = L - 18. B length = L - 12. Given B length = 2 * A length. So L - 12 = 2(L - 18). Solve: L - 12 = 2L - 36 => bring terms: -12 + 36 = 2L - L => 24 = L. So original length = 24 meters.",
"Check: A after cut = 24 - 18 = 6. B after c... | The original length of each ribbon was \(L\) meters, and after cutting, ribbon B is twice as long as ribbon A, so \(L-12 = 2(L-18)\). Solving this equation yields \(L = 24\) meters. |
f6b1628b-b3fb-5592-b5fe-e47fe02e381e | open-r1/OpenR1-Math-220k/olympiads | 2. If $x+2 y=14$ and $y=3$, what is the value of $2 x+3 y$ ? | [
"We need to solve: x + 2y = 14, y = 3. Then x = 14 - 2y = 14 - 6 = 8. Compute 2x + 3y = 2*8 + 3*3 = 16 + 9 = 25. Answer: 25."
] | Given \(x+2y = 14\) and \(y = 3\), we find \(x = 14 - 2(3) = 8\). Then \(2x + 3y = 2(8) + 3(3) = 16 + 9 = 25\). |
cef2c88d-0c60-5e13-b67b-28dc7f5eb589 | open-r1/OpenR1-Math-220k/cn_k12 | Given $p$: $x=2$, $q$: $0 < x < 3$, then $p$ is the $(\quad)$ of $q$.
A: Sufficient but not necessary condition
B: Necessary but not sufficient condition
C: Necessary and sufficient condition
D: Neither necessary nor sufficient condition | [
"We need to interpret: Given p: x = 2 , q: 0 < x < 3 . Then p is the ______ of q.",
"We consider logical relationship between statements p and q.",
"p: \"x = 2\". q: \"0 < x < 3\". For any real x, p implies q? If x=2 then indeed 0<2<3, so p => q. Does q imply p? No, q includes many values (e.g., x=1). So p is s... | The statement \(p\) guarantees \(q\), but \(q\) can be true without \(p\) being true, so \(p\) is a sufficient but not necessary condition for \(q\). **Answer: A**. |
b8d229ee-96ed-508d-8475-9168f59c7992 | open-r1/OpenR1-Math-220k/cn_k12 | If $p: x > 2$, and $q: x > 3$, then $p$ is a condition of $q$. (Choose the appropriate one from "sufficient but not necessary", "necessary but not sufficient", "necessary and sufficient", and "neither sufficient nor necessary" to fill in the blank) | [
"We need to interpret statement: \"If p: x > 2, and q: x > 3, then p is a condition of q.\" We need to fill blank: p is a condition of q. Determine relationship: Is p sufficient or necessary for q? Let's think: p: x > 2. q: x > 3.",
"If x > 3, then automatically x > 2. So q implies p. Therefore p is necessary for... | \(p\) is necessary for \(q\) because \(q \implies p\), but \(p\) is not sufficient for \(q\) because \(p \not\implies q\). |
e6398af4-6148-5fe5-83e3-ed68e2765c8b | open-r1/OpenR1-Math-220k/amc_aime | Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned $6$ years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is $30$ years. How many years older than Bella is Anna?
$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qqu... | [
"We need to parse problem: Anna and Bella birthdays together. Five years ago, Bella turned 6 years old, and she received a newborn kitten as a birthday present. That implies five years ago Bella's age was 6. So currently Bella's age = 6 + 5 = 11. The kitten was newborn then, so age of kitten now = 5 years.",
"Sum... | Bella is currently 11 years old and the kitten is 5 years old. The sum of their ages and Anna's age is 30, so Anna is 14 years old, making the age difference 3 years. |
081f3194-8944-5871-a81f-7c02c9164b4e | open-r1/OpenR1-Math-220k/cn_k12 | From a bag containing 3 red balls and 2 white balls, if you draw 3 balls at random, and event A is defined as "at least one of the three drawn balls is white," then what is the complementary event to A?
A: 1 white ball and 2 red balls
B: 2 white balls and 1 red ball
C: 3 red balls
D: At least one red ball | [
"The user asks: \"From a bag containing 3 red balls and 2 white balls, if you draw 3 balls at random, and event A is defined as 'at least one of the three drawn balls is white,' then what is the complementary event to A?",
"Options: A: 1 white ball and 2 red balls, B: 2 white balls and 1 red ball, C: 3 red balls,... | The event "at least one of the three drawn balls is white" has the complement "no white ball is drawn," meaning all three balls are red. This corresponds to option C: 3 red balls. |
976abd33-6c17-5d9a-a43a-c53695c77a1b | open-r1/OpenR1-Math-220k/olympiads | 2. Find the pattern and fill in the number:
$$
100,81,64,49 \text {, }
$$
$\qquad$ $, 25,16,9,4,1$ . | [
"We need to identify pattern: Sequence: 100,81,64,49, ?, 25,16,9,4,1. Likely squares descending: 10^2=100, 9^2=81, 8^2=64, 7^2=49, 6^2=36, 5^2=25, 4^2=16, 3^2=9, 2^2=4, 1^2=1. So missing number is 36. Provide explanation. Could also be reversed order? But given pattern suggests squares descending. So answer: 36. Pr... | The given sequence consists of consecutive perfect squares in decreasing order: $10^2, 9^2, \dots, 1^2$. The missing number in the sequence $100, 81, 64, 49, \dots, 1$ is $6^2$, which equals 36. |
f02c5e8e-6277-5943-951d-a1fdd72247f8 | open-r1/OpenR1-Math-220k/olympiads | Emil and Olivia ran a race. Their race times totalled 1 hour 52 minutes. If Emil's time was 4 minutes less than Olivia's time, how many minutes did it take Olivia to run the race?
(A) 78
(B) 56
(C) 58
(D) 74
(E) 55 | [
"We need to solve: total time = 1 hour 52 minutes = 60+52=112 minutes. Let O = Olivia's time, E = Emil's time = O - 4. Then O + (O - 4) = 112 → 2O - 4 =112 → 2O = 116 → O = 58 minutes. Answer C 58.",
"Check options: C=58.",
"Thus answer is 58."
] | Olivia's time is \(O\) minutes and Emil's is \(O-4\) minutes, totaling \(O + (O-4) = 112\) minutes. Solving for \(O\), we get \(2O - 4 = 112\), which yields \(O = 58\) minutes for Olivia. |
cefdfba5-c792-5be7-a9e2-066f93e3dacc | open-r1/OpenR1-Math-220k/cn_k12 | The reciprocal of $5$ is ( ).
A: $-5$
B: $-\frac{1}{5}$
C: $\frac{1}{5}$
D: $\pm 5$ | [
"We need to answer: The reciprocal of 5 is ?. Reciprocal of a number is 1 over that number: 1/5. So answer C. Should output C maybe with explanation.",
"Thus final answer: C: 1/5."
] | The reciprocal of \(a\) is \(\frac{1}{a}\). For \(a=5\), the reciprocal is \(\frac{1}{5}\), corresponding to option C. |
2e17e848-138f-51c0-a0ca-f8fd74585c0a | open-r1/OpenR1-Math-220k/cn_k12 | To prove "In the angles of a triangle, there is at least one angle that is greater than or equal to 60°" using the method of contradiction, one should first assume ( )
A: Every angle of the triangle is less than 60°
B: There is an angle in the triangle that is greater than 60°
C: Every angle of the triangle is greater... | [
"We need to answer a multiple-choice question: \"To prove 'In the angles of a triangle, there is at least one angle that is greater than or equal to 60°' using the method of contradiction, one should first assume ( )\" Options: A: Every angle of the triangle is less than 60°, B: There is an angle in the triangle t... | Assuming every angle is less than 60° leads to a total sum less than 180°, contradicting the triangle angle sum theorem. Therefore, at least one angle must be greater than or equal to 60°. |
183f7dad-cd2b-5e05-858d-32534a7812fe | open-r1/OpenR1-Math-220k/cn_k12 | Given sets $A=\{x|x^{2}-3x \lt 0\}$ and $B=\{x|y=\ln (x-2)\}$, then $A\cap B=$
A: $(2,+\infty)$
B: $(2,3)$
C: $(3,+\infty)$
D: $(-\infty ,2)$ | [
"We need to interpret sets A and B.",
"Set A = { x | x^2 - 3x < 0 }. Solve inequality: x(x-3) < 0. This is satisfied when x is between 0 and 3 (since product of two factors is negative when they have opposite signs). So A = (0,3).",
"Set B = { x | y = ln(x-2)}? Wait B is defined as {x| y = ln(x-2) }. That seems... | Set A is $(0,3)$ and Set B is $(2,\infty)$, so their intersection $A \cap B$ is $(2,3)$. The correct choice is B: $(2,3)$. |
48bb4dac-4648-5043-8cbf-52a2b252fe49 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following idioms describes a random event?
A: Fishing for the moon in the water
B: Castles in the air
C: Waiting by a stump for a hare
D: Catching a turtle in a jar | [
"We need to answer which idiom describes a random event. We have four idioms (likely from some language - maybe Russian?). \"Fishing for the moon in the water\" is a phrase meaning doing something impossible, chasing an illusion. \"Castles in the air\" means unrealistic plans, fantasies. \"Waiting by a stump for a ... | This idiom signifies waiting for a chance occurrence, embodying the concept of a random and unpredictable event. It's like waiting by a stump for a hare, hoping for luck. |
c5a7c5df-db45-57ea-bac1-3f35ce7bed22 | open-r1/OpenR1-Math-220k/olympiads | 4. (5 points) In the third grade, there are two classes, Class A and Class B. If 4 students are transferred from Class A to Class B, the number of students in both classes will be equal. Class A has $\qquad$ more students than Class B. | [
"We need to parse the problem.",
"It says: In the third grade, there are two classes, Class A and Class B. If 4 students are transferred from Class A to Class B, the number of students in both classes will be equal. Class A has ___ more students than Class B.",
"We need to find the difference between the origin... | The original difference in the number of students between Class A and Class B is 8. This is found by setting the new class sizes equal after 4 students moved from A to B, resulting in the equation $A - 4 = B + 4$, which simplifies to $A - B = 8$. |
End of preview. Expand in Data Studio
Math Think SFT Mini — GPT-OSS Short Answers
352,199 train rows derived from cs-giung/math-think-sft-mini-oss.
Only answer is replaced. id, source, question, steps, row order and feature types
are unchanged. The source reasoning remains GPT-OSS-generated.
Format
id: string, source: string, question: string, steps: list[string], answer: string.
The final answer is a shortened rewrite, not necessarily just a boxed value. steps
retain the parent's exact strings, including empty entries and whitespace.
Shortening
- All API calls use Gemini 2.5 Flash Lite Batch (
gemini-2.5-flash-lite); no other-provider fallback. - 874 answers have audited local assistant repairs, with no additional API calls.
These consolidate complete candidate sentences or rewrite persistent/truncated cases from
the original answer. See
manual_repairs.jsonwhen present for per-row provenance. maxOutputTokens=256,thinkingBudget=0. This limit uses Gemini tokens, not the GPT-OSS tokenizer. A truncated API response is rejected, never silently published.- Input: original answer only; no question or reasoning steps supplied.
- Prompt: preserve conclusion, important mathematical values, equations, units, option letters, notation and essential conditions; at most two concise sentences. Do not re-solve, correct the answer or introduce new claims.
- Sentence/format validation rejects empty output, reasoning tags, code fences and more than two sentences (LaTeX-aware heuristic). Successful output is stripped only at its outer whitespace, as in the earlier SA workflow.
- Every row must succeed before export. Original answers and the retry/usage ledger remain in the immutable local source/SQLite archive, not in extra dataset columns.
Verification
All non-answer values and row order are checked against the parent. Source ordered-row
SHA-256: 8d347504b26a4faff2df373efbcc6a942c4a61e7a92fce1a748839a7f845739b. Full saved-Parquet and remote row validation
is required before making a newly created repository public. See validation.json
and provenance.json for hashes, prompts, model counts and usage summaries.
This is structural/format verification, not mathematical or semantic verification. Shortening can omit nuance or preserve source mistakes; review outputs separately. The parent's source attribution, licenses and decontamination limitations still apply. No new decontamination was performed and no zero-contamination claim is made. This aggregate grants no additional rights to upstream content.
Load
from datasets import load_dataset
dataset = load_dataset("cs-giung/math-think-sft-mini-oss-sa", split="train")
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