id stringlengths 12 82 | source stringclasses 26
values | question stringlengths 8 1.61k | steps listlengths 3 48 | answer stringlengths 1 634 |
|---|---|---|---|---|
b82ef40c-6881-5429-8a9c-836d88b41479 | open-r1/OpenR1-Math-220k/cn_k12 | In the Cartesian coordinate system, if the point $P\left(x,y\right)$ satisfies $x \lt 0$, $y \gt 0$, then the quadrant it lies in is ( )
A: First quadrant
B: Second quadrant
C: Third quadrant
D: Fourth quadrant | [
"Okay, so I need to figure out which quadrant the point P(x, y) is in, given that x is less than 0 and y is greater than 0. Let me start by recalling how the quadrants in the Cartesian coordinate system work.",
"From what I remember, the Cartesian plane is divided into four quadrants by the x-axis and y-axis. The... | Given \( x < 0 \) and \( y > 0 \), the point \( P(x, y) \) lies in the second quadrant, corresponding to option B. |
76a25618-e464-50a2-b961-610a76956531 | open-r1/OpenR1-Math-220k/cn_k12 | Among the four numbers $-1$, $0$, $1$, and $2$, the smallest number is:
A: $0$
B: $-1$
C: $1$
D: $2$ | [
"Okay, so I need to figure out which of the numbers -1, 0, 1, or 2 is the smallest. The options are labeled A through D, with B being -1. Hmm, let's start by recalling how numbers are ordered on the number line. Negative numbers are to the left of zero, and positive numbers are to the right. The further left a numb... | The smallest number among \(-1\), \(0\), \(1\), and \(2\) is \(-1\), corresponding to option B. \boxed{B} |
062cbeef-fd47-5383-87e1-cac047af8215 | open-r1/OpenR1-Math-220k/cn_k12 | If $m \gt n$, which of the following inequalities is correct?
A: $m-2 \lt n-2$
B: $\frac{m}{4} \gt \frac{n}{4}$
C: $6m \lt 6n$
D: $-8m \gt -8n$ | [
"Okay, let's see. The problem is asking which of the given inequalities is correct if m is greater than n. So, m > n. Then there are four options: A, B, C, D. Let me go through each one step by step.",
"Starting with option A: m - 2 < n - 2. Hmm, original inequality is m > n. If we subtract 2 from both sides, doe... | Option B is correct because dividing both sides of \( m > n \) by 4 maintains the inequality direction, resulting in \( \frac{m}{4} > \frac{n}{4} \). The other options are incorrect due to improper inequality handling when subtracting, multiplying by positive numbers, or multiplying by negative numbers. |
2080e976-dad6-596d-b93e-01f04feca5ed | open-r1/OpenR1-Math-220k/olympiads | The value of $\frac{1}{2}+\left(\frac{1}{2} \times \frac{1}{2}\right)$ is
(A) $\frac{3}{8}$
(B) 1
(C) $\frac{1}{6}$
(D) $\frac{1}{4}$
(E) $\frac{3}{4}$ | [
"Okay, let me see. I need to figure out the value of this expression: 1/2 plus (1/2 multiplied by 1/2). The options are given from A to E. Let me break it down step by step.",
"First, I remember that according to the order of operations, I should do the multiplication inside the parentheses first. So the part in ... | The expression \(\frac{1}{2} + \left(\frac{1}{2} \times \frac{1}{2}\right)\) evaluates to \(\frac{3}{4}\), corresponding to option E. |
32b79f80-3dfe-52e2-a360-23688187f029 | open-r1/OpenR1-Math-220k/olympiads | The point with coordinates $(a, 0)$ is on the line with equation $y=x+8$. What is the value of $a$ ? | [
"Okay, let me see. I need to find the value of 'a' for the point (a, 0) that lies on the line y = x + 8. Hmm, so the point is (a, 0), which means the x-coordinate is 'a' and the y-coordinate is 0. Since this point is on the line, its coordinates should satisfy the equation of the line.",
"Alright, so the line equ... | Substituting \( y = 0 \) into the equation \( y = x + 8 \) yields \( a = -8 \), confirming the point \((-8, 0)\) lies on the line. |
70f0da60-2636-5e39-b01c-8c5d7cc7c510 | open-r1/OpenR1-Math-220k/olympiads | 15. One of the biggest mathematical breakthroughs in 2019 was progress on an 82 -year old problem by the renowned mathematician and Fields medalist Terence Tao.
Consider the function
$$
f(n)=\left\{\begin{array}{cl}
\frac{n}{2} & \text { if } n \text { is even } \\
3 n+1 & \text { if } n \text { is odd }
\end{array}\ri... | [
"Okay, so I need to figure out the surname of the German mathematician who proposed the conjecture in 1937 related to the function described. The function f(n) is defined as n/2 if n is even and 3n+1 if n is odd. The conjecture is that no matter what positive integer you start with, applying this function recursive... | The conjecture is known as the Collatz conjecture, named after German mathematician Lothar Collatz who proposed it in 1937. \boxed{Collatz} |
7a2c27c7-3adf-5bed-a067-dd03d8bb91c0 | open-r1/OpenR1-Math-220k/olympiads | ## Task 2
Multiply the numbers 7 and 6. Subtract 5 from the product.
Write the equation and solve. | [
"Okay, let's see. I need to multiply 7 and 6 first. Hmm, 7 times 6. Let me think. 7 times 5 is 35, and then add another 7, so that's 35 + 7 = 42. Right, so 7 multiplied by 6 is 42. Got that part down.",
"Now, the next step is to subtract 5 from that product. So, take 42 and subtract 5. Let me double-check that. 4... | The solution to the equation \( (7 \times 6) - 5 \) is 37, obtained by first multiplying 7 and 6 to get 42, then subtracting 5. |
f89e8df1-f618-5093-8096-1a80a2de96b1 | open-r1/OpenR1-Math-220k/cn_k12 | $-0.9$ does not belong to which of the following sets?
A: Negative numbers
B: Fractions
C: Integers
D: Rational numbers | [
"Okay, let's see. The problem is asking which set the number -0.9 does not belong to. The options are A: Negative numbers, B: Fractions, C: Integers, and D: Rational numbers. Hmm, I need to check each set one by one and see where -0.9 doesn't fit. Let me start by recalling what each of these terms means.",
"First... | -0.9 belongs to the sets of negative numbers, fractions, and rational numbers but not to the set of integers. The correct answer is C. |
d74d8532-97a4-51fc-951f-28406dbccdba | open-r1/OpenR1-Math-220k/cn_k12 | If $\sin \theta + \cos \theta = \frac{1}{5}$, find the value of $\sin 2\theta$. | [
"Okay, so I have this problem here: If sinθ + cosθ = 1/5, find the value of sin2θ. Hmm, let me think. I remember that there's a trigonometric identity that relates sinθ + cosθ to sin2θ. Maybe if I square both sides of the equation, I can use that identity? Let me try that.",
"First, let's start with the given equ... | Squaring both sides of \(\sin \theta + \cos \theta = \frac{1}{5}\) and applying the Pythagorean identity yields \(\sin 2\theta = -\frac{24}{25}\). |
932bbac9-6252-5719-a69f-d3716f17f083 | open-r1/OpenR1-Math-220k/cn_k12 | The coordinates of the point $M(1,2)$ with respect to the $x$-axis are ( ).
A: $(1,-2)$
B: $(-1,2)$
C: $(-1,-2)$
D: $(2,1)$ | [
"Okay, so the problem is asking about the coordinates of point M(1,2) with respect to the x-axis. Hmm, let me think. When they say \"with respect to the x-axis,\" does that mean reflecting the point over the x-axis? Because sometimes in math, when you talk about coordinates with respect to an axis, it could be a re... | Reflecting point \( M(1,2) \) over the \( x \)-axis gives \( (1,-2) \), corresponding to option A. |
edcce4e1-0966-54e0-813d-3e8063e5fee8 | open-r1/OpenR1-Math-220k/cn_k12 | The absolute value of the rational number $-3$ is:
A: $3$
B: $-3$
C: $\pm 3$
D: $\sqrt{3}$ | [
"Okay, so I need to find the absolute value of the rational number -3. Hmm, absolute value... let me remember what that means. I think the absolute value of a number is its distance from zero on the number line, right? So it doesn't matter if the number is positive or negative; the absolute value is always non-nega... | Option A is correct as the absolute value of \(-3\) is \(3\), while options B, C, and D are incorrect for different reasons. The absolute value formula \(|-3| = 3\) confirms this result. |
c526aa46-412e-57cf-ae00-3c7a6b2cf675 | open-r1/OpenR1-Math-220k/cn_k12 | $x^{2}\cdot x^{3}=\left(\ \ \right)$
A: $x^{5}$
B: $x^{6}$
C: $x^{8}$
D: $x^{9}$ | [
"Okay, so I have this math problem here: x squared multiplied by x cubed, and I need to choose the correct answer from the options A to D. Let me think. Hmm, when you multiply variables with exponents, there's a rule for that, right? I remember something about adding the exponents when the bases are the same. Let m... | When multiplying variables with the same base, add the exponents, so \(x^2 \cdot x^3 = x^5\), which is confirmed by substituting \(x = 2\) to get \(32 = 32\). The correct answer is \(\boxed{A}\). |
98e40282-dedb-5975-8109-e8c9bfea79b8 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following calculations is correct?
A: $a^{3}+a^{3}=a^{6}$
B: $a^{3}\cdot a^{3}=a^{6}$
C: $(a^{2})^{3}=a^{5}$
D: $(ab)^{3}=ab^{3}$ | [
"Okay, so I need to figure out which of these calculations is correct. Let me go through each option one by one. Hmm, let's start with option A: a³ plus a³ equals a⁶. Wait, when you add two terms with the same exponent, you just add the coefficients, right? So if it's like x + x, that's 2x. Similarly, a³ + a³ shoul... | Option B is correct because \(a^3 \cdot a^3 = a^6\), while the other options violate exponent rules. |
b5db9e97-6906-53ba-a994-1ecdc6b3e63a | open-r1/OpenR1-Math-220k/cn_k12 | When solving the system of linear equations $\left\{\begin{array}{l}{2x+y=10}\\{x=2y}\end{array}\right.$, we can eliminate $x$ by substituting the second equation into the first equation to get $4y+y=10$. The mathematical idea reflected in this solution is ( ).
A: Transformational thinking
B: Classification and discu... | [
"Okay, let's see. I need to figure out which mathematical idea is being used here when solving the system of equations by substitution. The problem gives two equations: 2x + y = 10 and x = 2y. They substituted x = 2y into the first equation to get 4y + y = 10. Then I have to choose between these four options: A, B,... | Substituting \(x = 2y\) into the first equation simplifies the system, illustrating transformational thinking (A). Options B, C, and D are less relevant, so the answer is \(\boxed{A}\). |
6befebca-7ac9-56e4-938c-a75ff2db95a0 | open-r1/OpenR1-Math-220k/cn_k12 | The opposite of $-2$ is
A: $2$
B: $-2$
C: $-\frac{1}{2}$
D: $\frac{1}{2}$ | [
"Okay, so the problem is asking for the opposite of -2, and there are four options: A is 2, B is -2, C is -1/2, and D is 1/2. Hmm, let me think.",
"First, what does \"opposite\" mean in math terms? I remember that opposite can have different meanings depending on the context. Sometimes it's the additive inverse, ... | The opposite of \(-2\) is \(2\), as \(-(-2) = 2\) and \(-2 + 2 = 0\), confirming option A is correct. |
954b6032-bdda-5119-9c52-f45f94ce00f1 | open-r1/OpenR1-Math-220k/olympiads | ## Task 4
To become hard-boiled, 3 eggs need to cook for 5 minutes.
How long do you need to cook 6 eggs? | [
"Okay, let's see here. The problem says that to become hard-boiled, 3 eggs need to cook for 5 minutes. Then it's asking how long you need to cook 6 eggs. Hmm, at first glance, I might think, \"Well, if 3 eggs take 5 minutes, then doubling the number of eggs would require doubling the time, so 10 minutes?\" But wait... | The cooking time for 6 eggs is the same as for fewer eggs since boiling water maintains consistent temperature and heat transfer to each egg is independent of quantity. Thus, the answer is \boxed{5} minutes. |
468585ee-0ad7-5932-adc0-598703717d1d | open-r1/OpenR1-Math-220k/cn_k12 | The sum of the interior angles of a dodecagon is ( )
A: 180°
B: 360°
C: 1800°
D: Cannot be calculated | [
"Okay, so I need to figure out the sum of the interior angles of a dodecagon. Hmm, first, what exactly is a dodecagon? Let me recall. I know that a polygon with twelve sides is called a dodecagon. Yeah, \"dodeca\" means twelve in Greek, right? Like a dodecahedron has twelve faces. So a dodecagon must be a 12-sided ... | The sum of the interior angles of a dodecagon (12-sided polygon) is calculated using the formula \((n - 2) \times 180^\circ\), resulting in \(1800^\circ\). The correct answer is option C. |
01775657-adf2-516d-8677-810c2708902e | open-r1/OpenR1-Math-220k/cn_k12 | When negating an existential proposition, the existential quantifier becomes a universal quantifier. ( )
A: Correct
B: Incorrect
C:
D: | [
"Okay, so I need to figure out whether the statement \"When negating an existential proposition, the existential quantifier becomes a universal quantifier\" is correct or incorrect. The options are A: Correct, B: Incorrect, C and D are blank. Let me think about this step by step.",
"First, I remember that in logi... | Negating an existential quantifier (∃) transforms it into a universal quantifier (∀) with the negated predicate, as per De Morgan's laws for quantifiers. The example confirms that "There exists a dog that is brown" becomes "All dogs are not brown" when negated. |
e02f09dd-0080-5251-9b7a-4025a314a807 | open-r1/OpenR1-Math-220k/cn_k12 | Given two vectors $\overrightarrow{a}=(2,m,3)$ and $\overrightarrow{b}=(4,-1,n)$, and $\overrightarrow{a} \parallel \overrightarrow{b}$, then the value of $mn$ is:
A: $1$
B: $-2$
C: $-3$
D: $6$ | [
"Okay, let's see. I need to find the value of mn given that vectors a and b are parallel. The vectors are a = (2, m, 3) and b = (4, -1, n). The options are A:1, B:-2, C:-3, D:6. Hmm, okay.",
"First, I remember that if two vectors are parallel, one must be a scalar multiple of the other. That means there exists so... | Since the vectors are parallel, \(m = -\frac{1}{2}\) and \(n = 6\), so \(mn = -3\). The answer is \(\boxed{C}\). |
7a2e057b-41b1-5e4a-a92e-ba1f5ea79a94 | open-r1/OpenR1-Math-220k/olympiads | ## Task 3
Write down
a) the successor of 19
b) the predecessor of 1
c) all numbers that lie between 8 and 12! | [
"Okay, let's tackle these problems one by one. First, part a) asks for the successor of 19. Hmm, successor means the next number, right? So if I have 19, the next number after that should be 20. Yeah, that makes sense because when you count up from 19, the next one is 20. So I think a) is 20.",
"Moving on to part... | For part a, the successor of 19 is $20$; for part b, the predecessor of 1 is $0$; for part c, the numbers strictly between 8 and 12 are $9,10,11$. |
0fa9955f-b267-5820-b383-2ff74bad2cac | open-r1/OpenR1-Math-220k/cn_k12 | Given the sets $U=\{1,2,3,4,5\}$, $A=\{1,3,5\}$, $B=\{1,2,4,5\}$, then $A$⋂$B=\_\_\_\_\_\_\_\_\_\_$
A: $\{1,3,5\}$
B: $\{1,5\}$
C: $\{1,2,4\}$
D: $\{1,2,4,5\}$ | [
"Okay, let's see. I need to find the intersection of sets A and B. The universal set is U = {1,2,3,4,5}, A is {1,3,5}, and B is {1,2,4,5}. The intersection of two sets, A ∩ B, should be the elements that are common to both A and B. Let me break this down step by step.",
"First, I'll list out the elements of set A... | The intersection of sets \(A = \{1, 3, 5\}\) and \(B = \{1, 2, 4, 5\}\) is \(\{1, 5\}\), corresponding to option \(\boxed{B}\). |
cbd0a1d0-a8a1-56bf-9816-97fcdb714de4 | open-r1/OpenR1-Math-220k/cn_k12 | Given that $y=f(x)$ is an odd function, and $f(3)=7$, then $f(-3)=$ ____. | [
"Okay, let's see. The problem says that y equals f of x is an odd function, and f of 3 is 7. Then they ask for f of -3. Hmm, odd function. I remember that odd functions have some kind of symmetry. Wait, right! Odd functions are symmetric about the origin. So, if you rotate the graph 180 degrees around the origin, i... | Since \( y = f(x) \) is an odd function with \( f(3) = 7 \), it follows that \( f(-3) = -7 \). |
9d335d00-c378-5026-9798-20c357d256c6 | open-r1/OpenR1-Math-220k/cn_k12 | The degree of the monomial $-\frac{1}{4}π\;{x^2}{y^3}$ is ( ).
A: $-\frac{1}{4}$
B: $-\frac{1}{4}π$
C: $5$
D: $6$ | [
"Okay, let's see. The problem is asking for the degree of the monomial -1/4 π x² y³. The options are A: -1/4, B: -1/4 π, C: 5, D: 6. Hmm, I need to remember how to find the degree of a monomial.",
"Wait, right, the degree of a monomial is the sum of the exponents of all the variables in it. So, coefficients and c... | The degree of the monomial \(-\frac{1}{4}\pi x^2 y^3\) is 5, as it is the sum of the exponents of the variables \(x\) and \(y\). The correct answer is \(\boxed{C}\). |
e5ccb96b-a3d8-59d1-a29e-3b2a875e8b36 | open-r1/OpenR1-Math-220k/olympiads | ## Task 2
At the ABC Mathematics Olympiad, 45 students from Erich-Weinert-Oberschule received a certificate. At the Juri-Gagarin-Oberschule, 17 fewer students received a certificate.
How many students from the Juri-Gagarin-Oberschule received a certificate? | [
"Okay, let's see. The problem is about two schools participating in the ABC Mathematics Olympiad. The first school, Erich-Weinert-Oberschule, had 45 students who received certificates. The second school, Juri-Gagarin-Oberschule, had 17 fewer students receiving certificates. The question is asking how many students ... | 28 students from Juri-Gagarin-Oberschule received a certificate, calculated by subtracting 17 from the 45 students at Erich-Weinert-Oberschule. |
3a4befaa-5c74-50af-b681-ab55fcfb160d | open-r1/OpenR1-Math-220k/olympiads | The missing number in the geometric sequence $2,6,18,54$, , 486 is
(A) 72
(B) 90
(C) 108
(D) 162
(E) 216 | [
"Okay, so I need to find the missing number in this geometric sequence: 2, 6, 18, 54, _, 486. The options are A) 72, B) 90, C) 108, D) 162, E) 216. Let me think step by step.",
"First, what is a geometric sequence? It's a sequence where each term after the first is found by multiplying the previous term by a cons... | The common ratio is 3, so the missing term is 54 × 3 = 162, which corresponds to option D. |
d63ab07c-5916-5031-a1ba-cf49493e1d1c | open-r1/OpenR1-Math-220k/olympiads | ## Task 7
An animal has two right and two left legs, two legs in front and two at the back.
How many legs does it have? | [
"Okay, let's see. The problem says an animal has two right and two left legs, two legs in front and two at the back. The question is, how many legs does it have? Hmm, this seems a bit tricky. Let me break it down step by step.",
"First, the animal has two right legs and two left legs. So if I add those together, ... | The animal has four legs, categorized by front/back and right/left positions. Each leg belongs to one front/back and one right/left pair. |
2e541bae-35fc-5f8f-8c8a-0ab36f7bf081 | open-r1/OpenR1-Math-220k/cn_k12 | In a certain place, the slogan "Save water, protect the environment" is promoted. If saving $30cm^{3}$ of water is denoted as $+30cm^{3}$, then wasting $10cm^{3}$ of water is denoted as ( )
A: $+10cm^{3}$
B: $-10cm^{3}$
C: $+0cm^{3}$
D: $-20cm^{3}$ | [
"Okay, let me try to figure this out. So the problem says that saving 30 cm³ of water is denoted as +30 cm³. Then they're asking what wasting 10 cm³ of water would be denoted as, with the options given.",
"First, I need to understand the context here. They're using positive numbers to represent saving water. So s... | The correct answer is B: $-10 \text{ cm}^3$, as wasting water is represented by a negative value while saving water is positive. |
cf1e934f-18ee-504c-9ddb-17cdd57b5b3b | open-r1/OpenR1-Math-220k/olympiads | 10. Write the number $a_{0}=9.3 \pm 0.5$ using a double inequality. | [
"Okay, so I need to write the number a₀ = 9.3 ± 0.5 using a double inequality. Hmm, let me think. I remember that when a number is given with a plus-minus error, like x ± y, it means the actual value lies somewhere between x - y and x + y. So in this case, the value is 9.3, and the error is 0.5. Therefore, the lowe... | The value \( a_0 = 9.3 \pm 0.5 \) is represented by the double inequality \( 8.8 \leq a_0 \leq 9.8 \). |
e3d21e94-35d9-5d7d-9641-7e0e98d49a07 | open-r1/OpenR1-Math-220k/cn_k12 | Athletes A, B, C, and D participated in the shooting pre-qualifying competition. The average scores and variances of their shooting results are shown in the table below. To select an athlete with good and stable performance to participate in the competition, which athlete should be chosen?
| Statistical | A | B | ... | [
"Okay, so I need to figure out which athlete to choose based on their average scores and variances. The question says they want someone with good and stable performance. Good probably means high average score, and stable means low variance, right? Because variance measures how spread out the scores are. Lower varia... | Athlete C has the highest average score of 8 points and the lowest variance of 0.9, making them the best choice for both high performance and consistency. |
a01e1c9a-c367-5436-a0d4-3d9624666287 | open-r1/OpenR1-Math-220k/cn_k12 | Given that $A(-1,4)$ and point $B(a,2)$ lie on the same inverse proportion function graph, the value of $a$ is ( )
A: $-2$
B: $-1$
C: $-\frac{1}{2}$
D: $1$ | [
"Okay, let me try to figure out this problem. So, we have points A(-1,4) and B(a,2) lying on the same inverse proportion function graph, and we need to find the value of 'a' from the given options. Hmm, inverse proportion function... right, that's like y = k/x or something similar, right? Let me recall. In an inver... | The constant \( k \) is \(-4\) since \((-1) \times 4 = -4\), so \( a \times 2 = -4 \) gives \( a = -2 \). |
f84a2cec-97c2-5568-a184-d25f92635586 | open-r1/OpenR1-Math-220k/cn_k12 | The fraction $\frac{1}{x+1}$ is meaningful when ______. | [
"Okay, let's see. The problem is asking: The fraction 1/(x+1) is meaningful when ______. Hmm. So I need to figure out for what values of x this fraction is defined or meaningful. Alright, fractions are defined as long as the denominator isn't zero, right? Because division by zero is undefined. So that must mean tha... | The fraction \(\frac{1}{x+1}\) is undefined when \(x = -1\) and meaningful for all other real numbers, so \(x \neq -1\). |
bf5621ee-a8b4-571f-9907-298217923278 | open-r1/OpenR1-Math-220k/olympiads | ## Task 4
Note the largest four-digit and the smallest three-digit number that can be written with different digits. Calculate their sum. | [
"Okay, so I need to figure out the largest four-digit number and the smallest three-digit number that can be written with different digits. Then, I have to add them together. Let me start by tackling each part one by one.",
"First, the largest four-digit number with different digits. The largest four-digit number... | The sum of the largest four-digit number with different digits (9876) and the smallest three-digit number with different digits (102) is 9978. |
5a57b9d2-d2aa-591f-87ea-c112dbb6d2e0 | open-r1/OpenR1-Math-220k/cn_k12 | In residual analysis, what is the vertical axis of the residual plot? | [
"Okay, so I need to figure out what the vertical axis of a residual plot represents in residual analysis. Let me start by recalling what I know about residual plots.",
"First, residuals themselves are the differences between the observed values of the dependent variable and the predicted values from a regression ... | The vertical axis of a residual plot displays the residuals, which are the differences between observed values (\(y_i\)) and predicted values (\(\hat{y}_i\)) from a regression model. This plot helps assess the model's appropriateness by examining the distribution and patterns of these residuals. |
34ae469d-16b6-5a4c-b06e-27f3ab8f8081 | open-r1/OpenR1-Math-220k/cn_k12 | If an increase in temperature of $3^{\circ}\mathrm{C}$ is denoted as $+3^{\circ}\mathrm{C}$, then a decrease in temperature of $2^{\circ}\mathrm{C}$ is denoted as:
A: $-3^{\circ}\mathrm{C}$
B: $+3^{\circ}\mathrm{C}$
C: $-2^{\circ}\mathrm{C}$
D: $+2^{\circ}\mathrm{C}$ | [
"Okay, so I need to figure out this temperature problem. Let me read it again. It says that if an increase in temperature of 3 degrees Celsius is denoted as +3°C, then a decrease in temperature of 2 degrees Celsius should be denoted as which option: A, B, C, or D.",
"Hmm, let's start by understanding the question... | A decrease of \(2^{\circ}\mathrm{C}\) is represented as \(-2^{\circ}\mathrm{C}\), making option C correct. |
22029c22-1e3e-5ae9-886a-c8547ca457ab | open-r1/OpenR1-Math-220k/cn_k12 | What is the value of $\sqrt{16}$?
A: $\pm 4$
B: $-4$
C: $4$
D: None of the above | [
"Okay, let's see. The question is asking for the value of √16. The options are A: ±4, B: -4, C: 4, D: None of the above. Hmm, I need to remember what the square root symbol means.",
"Wait, in math class, they taught us that the principal square root is the non-negative one. So even though both 4 and -4 squared gi... | The square root symbol denotes the principal (non-negative) root, so \(\sqrt{16} = 4\), making Option C correct. |
9955a48c-afcd-56c4-9ead-5fa6fbde5d2e | open-r1/OpenR1-Math-220k/cn_k12 | Let $A = B = \{a, b, c, d, \ldots, x, y, z\}$ be sets containing the 26 letters of the English alphabet. Define a mapping $f: A \rightarrow B$ such that each letter in A is mapped to the subsequent letter in B, that is $a \rightarrow b$, $b \rightarrow c$, $c \rightarrow d$, $\ldots$, $z \rightarrow a$. A word composed... | [
"Okay, let's see. I need to decrypt the ciphertext \"nbui\". The problem says that each letter in set A is mapped to the subsequent letter in B. So, for example, a becomes b, b becomes c, ..., and z wraps around to a. That sounds like a Caesar cipher with a shift of +1. But since we're decrypting, we need to revers... | The ciphertext "nbui" decrypted with a shift of -1 yields the plaintext "math". |
72be6ed5-7dd4-5a87-975c-8f065ec64113 | open-r1/OpenR1-Math-220k/cn_k12 | Given \\(|x+2|+(y-3)^{2}=0\\), then \\(x^{y}=\\)
A: \\(-8\\)
B: \\(-6\\)
C: \\(6\\)
D: \\(8\\) | [
"Okay, so I need to solve this equation: |x + 2| + (y - 3)² = 0. Then find x^y and choose between options A to D. Hmm, let me think. Alright, absolute value and a square term. Both of these are non-negative, right? Because absolute values are always zero or positive, and squares are also always zero or positive. So... | Solving \(|x + 2| + (y - 3)^2 = 0\) gives \(x = -2\) and \(y = 3\), so \(x^y = (-2)^3 = -8\), corresponding to option A. |
e6975ec4-94bf-585b-bc41-24e3e7b4a381 | open-r1/OpenR1-Math-220k/cn_k12 | If a line passes through $(1,2)$ and $(4,2+\sqrt{3})$, then the slope of this line is:
A: $\frac{\sqrt{3}}{3}$
B: $1$
C: $\sqrt{3}$
D: Does not exist | [
"Okay, let's see. The problem is asking for the slope of a line that passes through two points: (1, 2) and (4, 2 + √3). The options are given as A: √3/3, B: 1, C: √3, D: Does not exist. Hmm, slope... right, the formula for slope between two points (x1, y1) and (x2, y2) is (y2 - y1)/(x2 - x1). Let me make sure I rem... | The slope of the line passing through \((1, 2)\) and \((4, 2 + \sqrt{3})\) is \(\frac{\sqrt{3}}{3}\), corresponding to option \(\boxed{A}\). |
80e25f07-4953-5cf7-9508-4c7bf1f7ac1e | open-r1/OpenR1-Math-220k/cn_k12 | Given a function $f\left(x\right)=\left\{\begin{array}{l}x+5,x≥4,\\ x-2,x＜4,\end{array}\right.$, then the value of $f\left(3\right)$ is ( )
A: $1$
B: $2$
C: $8$
D: $9$ | [
"Okay, let me try to figure out the value of f(3) for this piecewise function. Hmm, the function f(x) is defined differently depending on whether x is greater than or equal to 4 or less than 4. So, first, I need to check which condition the input x=3 satisfies.",
"Alright, since 3 is the input here, and 3 is defi... | Since \( 3 < 4 \), we use \( f(3) = 3 - 2 = 1 \), so the answer is \(\boxed{A}\). |
72e072bd-b033-57cb-b8bf-0bce0ed61502 | open-r1/OpenR1-Math-220k/cn_k12 | A certain kindergarten conducted a survey among all the children to find out which type of zongzi they like to decide which flavor of zongzi to buy. The most important data to pay attention to in the survey results is:
A: Variance
B: Mean
C: Median
D: Mode | [
"Okay, so I need to figure out which statistical measure is the most important for the kindergarten's survey on zongzi preferences. The options are variance, mean, median, or mode. Let me start by recalling what each of these terms means.",
"First, variance measures how spread out the data is. Like, if most kids ... | The mode (D) is the most appropriate statistical measure for determining the most preferred zongzi flavor among children, as it identifies the most frequently occurring category in categorical data. |
6aeb66cb-0753-5859-99ce-06f64207d663 | open-r1/OpenR1-Math-220k/cn_k12 | Given the set $A=\{x|x^2-4=0\}$, which of the following statements is incorrect? ( )
A: $2 \in A$
B: $-2 \notin A$
C: $A=\{-2, 2\}$
D: $\emptyset \subseteq A$ | [
"Okay, let's tackle this problem step by step. The question is asking which of the given statements about the set A is incorrect. The set A is defined as {x | x² - 4 = 0}. Let me first understand what this set actually is.",
"So, the set A consists of all real numbers x such that when you square them and subtract... | The incorrect statement is option B, which claims -2 is not in set A, despite solving \( x^2 - 4 = 0 \) showing that A = {-2, 2}. |
707b72c7-dba4-5c81-bbfe-0f6c46cc6a31 | open-r1/OpenR1-Math-220k/cn_k12 | Given sets $M=\{0,1\}$ and $N=\{-1,0\}$, then $M\cap N=$
A: $\{-1,0,1\}$
B: $\{-1,1\}$
C: $\{0\}$
D: $\varnothing$ | [
"Okay, let's see. I need to find the intersection of sets M and N. The intersection, M ∩ N, should be the set of elements that are common to both M and N. Right? So, first, I need to recall what the sets M and N are.",
"The problem states that M is {0, 1} and N is {-1, 0}. So, set M has the elements 0 and 1, and ... | The intersection of sets \( M = \{0, 1\} \) and \( N = \{-1, 0\} \) is \( \{0\} \), corresponding to option C. |
8506656c-cef0-5f07-b6db-202e305bc41d | open-r1/OpenR1-Math-220k/cn_k12 | In a meeting room, there are not enough chairs. Someone asks, "Do you still need any?" The reply is, "Yes, I think four chairs are needed for the lecture this afternoon." Which option correctly completes the sentence: "I need a ______ chairs"?
- A. dozen
- B. dozens
- C. dozen of
- D. dozens of | [
"Okay, let me think about this question. The problem is about choosing the correct option to complete the sentence: \"I need a ______ chairs\". The options are dozen, dozens, dozen of, and dozens of.",
"First, I remember that \"dozen\" can be used as a noun or an adjective. When we use it with a specific number, ... | The correct answer is A. dozen, as "a dozen chairs" is grammatically correct with the singular noun following the article "a." |
8f8df84c-1e31-55e7-ba9e-c388c540c50a | open-r1/OpenR1-Math-220k/cn_k12 | When $x$ is ______, the fraction $\frac{3x-1}{x+3}$ is undefined. | [
"Okay, so I need to figure out when the fraction (3x - 1)/(x + 3) is undefined. Hmm, let's start by remembering when a fraction is undefined. I think it's when the denominator is zero because you can't divide by zero. Right, so if the denominator x + 3 equals zero, then the whole fraction would be undefined.",
"S... | The fraction \(\frac{3x - 1}{x + 3}\) is undefined when \(x = -3\) because the denominator equals zero at this value. |
eb58e5f5-4dbc-54e2-9e1f-45727331d62d | open-r1/OpenR1-Math-220k/cn_k12 | Given propositions $p$ and $q$, if the proposition "$\neg p$" and the proposition "$p \lor q$" are both true, then the correct conclusion is ( )
A: Both $p$ and $q$ are true propositions.
B: Both $p$ and $q$ are false propositions.
C: $p$ is a true proposition, and $q$ is a false proposition.
D: $p$ is a false proposit... | [
"Alright, so I have this logic problem here. Let me read it again carefully. It says: Given propositions p and q, if the proposition \"¬p\" (which means not p) and the proposition \"p ∨ q\" (which means p or q) are both true, then the correct conclusion is one of the options A to D. The options are about whether p ... | Since ¬p is true, p is false, and for p ∨ q to be true, q must be true, making option D correct. |
25bdaea4-b915-5c77-9e97-3969ff28b2e9 | open-r1/OpenR1-Math-220k/cn_k12 | Among the following functions, the one where $y$ is inversely proportional to $x$ is:
A: $y=\frac{x}{6}$
B: $y=6x$
C: $x+y=6$
D: $y=\frac{6}{x}$ | [
"Okay, let's see. The question is asking which of the given functions has y inversely proportional to x. The options are A through D. Hmm, inversely proportional... I remember that inverse proportionality means that as one quantity increases, the other decreases in such a way that their product is a constant. So if... | Option D (\( y = \frac{6}{x} \)) is the function where \( y \) is inversely proportional to \( x \), as it follows the form \( y = \frac{k}{x} \) with \( k = 6 \). |
78bf1404-9288-52b6-939a-b781d872153f | open-r1/OpenR1-Math-220k/cn_k12 | The table below records the average and variance of the recent selection competition results of four high jump athletes A, B, C, and D:
| | A | B | C | D |
|----------|------|------|------|------|
| Average ($cm$) | $185$ | $180$ | $185$ | $180$ |
| Variance | $3.6$ | $3.6$ | $7.4$ | $8.1$ |
Acco... | [
"Okay, so I need to figure out which athlete to choose based on their average performance and the variance of their results. The problem states that we want someone with good performance and stable results. Let me break this down step by step.",
"First, looking at the averages. The average tells us the typical pe... | Athlete A has the highest average (185 cm) and the lowest variance (3.6) among all athletes, making them the optimal choice for both performance and consistency. |
e6a68879-47cd-5267-b4a5-d8fb2d2681f8 | open-r1/OpenR1-Math-220k/olympiads | [ Arithmetic. Mental calculation, etc.]
The kids brought a full basket of mushrooms from the forest. In total, 289 mushrooms were collected, and each basket had the same number of mushrooms. How many kids were there?
# | [
"Okay, let's see. The problem says that some kids brought a full basket of mushrooms from the forest. In total, there are 289 mushrooms collected, and each basket had the same number of mushrooms. The question is asking how many kids there were.",
"Hmm, so each kid has a basket, right? And all the baskets have th... | Since 289 is 17² and its only reasonable factors are 1, 17, and 289, the number of kids must be **17**. |
b58f016c-b8c2-5684-8e48-6dc80ed74a6b | open-r1/OpenR1-Math-220k/olympiads | Rosie is saving money. She has $\$ 120$ in her account today and will begin saving by making $\$ 30$ deposits into her account. If she makes $m$ such deposits, the expression that best represents the number of dollars in her account is
(A) $120+m$
(B) $30 \mathrm{~m}$
(C) $30+120 \mathrm{~m}$
(D) $150 \mathrm{~m}$
(E) ... | [
"Okay, let's see. Rosie has $120 in her account today. She starts saving by making $30 deposits. If she makes m such deposits, we need to figure out the expression that represents the total amount in her account. The options are A through E, and I need to pick the correct one.",
"First, let's break down the probl... | Option E (\(120 + 30m\)) is correct as it accounts for the initial $120 and the total deposits of $30m, verified by examples. The other options incorrectly combine the initial amount and deposits. |
ac1cf476-b8b2-56be-b96f-f0a63ff7966a | open-r1/OpenR1-Math-220k/cn_k12 | The slope of the line $y+3x-1=0$ is ( )
A: $k=3$
B: $k= \frac {1}{3}$
C: $k=-3$
D: $k=- \frac {1}{3}$ | [
"Okay, so I need to find the slope of the line given by the equation y + 3x - 1 = 0. Hmm, let me recall how to do this. I think the slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So maybe I should rearrange the given equation into that form.",
"Let me start with the o... | The slope of the line \( y + 3x - 1 = 0 \) is \(-3\), which corresponds to option C. |
83863fae-a51e-5f63-9edf-0b257ed4da75 | open-r1/OpenR1-Math-220k/cn_k12 | Compare the following numbers: $-2$ and $-3$. | [
"Okay, let's see. I need to compare -2 and -3. Hmm, comparing negative numbers can be a bit tricky sometimes. Let me think. So, negative numbers are on the left side of zero on the number line. The more left you go, the smaller the number becomes. Right? So, like -1 is greater than -2 because it's closer to zero. W... | On a number line, \(-2\) is to the right of \(-3\), making \(-2\) greater than \(-3\). This is confirmed by the mathematical rule that for negative numbers, the one with the smaller absolute value is greater. |
ef98119d-cf5e-5b7f-a5f2-e0df7aa29f6c | open-r1/OpenR1-Math-220k/olympiads | 41. The quality of gold is indicated by $\mathrm{K}$, pure gold is $\qquad$ , and jewelry with $50 \%$ gold content is $\qquad$ _.
A. $12 \mathrm{~K} 、 6 \mathrm{~K}$
B. $48 \mathrm{~K} 、 24 \mathrm{~K}$
C. $36 \mathrm{~K} 、 18 \mathrm{~K}$
D. $24 \mathrm{~K}, 12 \mathrm{~K}$ | [
"Okay, so I need to figure out this question about gold quality indicated by K, which I think stands for karats. The question says that pure gold is something, and jewelry with 50% gold content is something else. The options are A, B, C, D. Let me recall what I know about gold purity.",
"First, I remember that ka... | Pure gold is 24K (100% gold), and jewelry with 50% gold content is 12K. The correct answer is D. |
9f235268-63aa-50ec-8bf9-910bf03aac69 | open-r1/OpenR1-Math-220k/olympiads | Problem 6. (8 points)
Anna Ivanovna bought a car from her neighbor last November for 300,000 rubles with an engine power of 250 hp, and in May she purchased a used rowing catamaran for 6 rubles. The transport tax rate is set at 75 rubles per 1 hp. How much transport tax should Anna Ivanovna pay? (Provide the answer as... | [
"Okay, let's see. Anna bought a car and a catamaran. The problem is asking for the transport tax she needs to pay. Hmm, I remember that transport tax in Russia is usually based on the engine power of vehicles. The catamaran is a rowing one, so maybe it doesn't have an engine? Let me think.",
"First, the car: it's... | Anna owned the car for 2 months, resulting in a prorated tax of 3,125 ₽, while the rowing catamaran incurred no tax due to having no engine. |
e6d0f049-80f4-544e-8df5-5bea731426bb | open-r1/OpenR1-Math-220k/olympiads | ## Task 4
Add the numbers 1 to 10. | [
"Okay, let's see. I need to add all the numbers from 1 to 10. Hmm, how do I do that? Well, I could just start adding them one by one. Let me try that first.",
"Starting with 1 plus 2, that's 3. Then add 3, which makes 6. Next, add 4 to get 10. Then 5 added to 10 is 15. Wait, let me check that again. 1+2 is 3, +3 ... | The sum of numbers from 1 to 10 is calculated using the arithmetic series formula \( \frac{n(n+1)}{2} \), yielding 55 when \( n = 10 \). |
35784293-5a9c-5cd0-9516-a8e7100e7b91 | open-r1/OpenR1-Math-220k/cn_k12 | Vector $\overrightarrow{a}=(t,1)$, $\overrightarrow{b}=(2,4)$. If $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$, then the value of the real number $t$ is:
A: $1$
B: $-1$
C: $2$
D: $-2$ | [
"Okay, so I need to find the value of t such that vector a, which is (t, 1), is perpendicular to vector b, which is (2, 4). The options are A: 1, B: -1, C: 2, D: -2. Hmm, perpendicular vectors... I remember that when two vectors are perpendicular, their dot product is zero. Let me recall: the dot product of two vec... | For vectors \(\overrightarrow{a} = (t, 1)\) and \(\overrightarrow{b} = (2, 4)\) to be perpendicular, their dot product must be zero, giving \(2t + 4 = 0\) and \(t = -2\), which corresponds to option D. |
444b9488-a644-5881-ad32-7a7c8a8ad100 | open-r1/OpenR1-Math-220k/cn_k12 | If $f(x) = 2x^{3} + x^{2} - 5$, then $f'(1) =$
A: $3$
B: $8$
C: $-8$
D: $-3$ | [
"Okay, so I need to find f'(1) for the function f(x) = 2x³ + x² - 5. Hmm, let me remember how to take derivatives. I think the basic rule is that the derivative of x^n is n*x^(n-1). So I need to apply that to each term in the function.",
"First, let's break down the function term by term. The first term is 2x³. T... | The derivative of \( f(x) = 2x^3 + x^2 - 5 \) is \( f'(x) = 6x^2 + 2x \), and evaluating at \( x = 1 \) gives \( f'(1) = 8 \), corresponding to option B. |
d2a3d13c-27b5-562c-9be1-7836380695ea | open-r1/OpenR1-Math-220k/cn_k12 | Among the following set of numbers: -8, 0, -32, -(-5.7), the number of negative numbers is ( )
A: 1
B: 2
C: 3
D: 4 | [
"Okay, let's see. I need to figure out how many negative numbers are in the set: -8, 0, -32, -(-5.7). The options are A:1, B:2, C:3, D:4. Hmm, let me go through each number one by one.",
"First number is -8. That's definitely negative because of the minus sign in front. So that's one negative number.",
"Second ... | The set contains two negative numbers: -8 and -32, while 0 and -(-5.7) are not negative. The answer is B. |
2e842348-4226-5b39-a991-1e4192d0cba6 | open-r1/OpenR1-Math-220k/cn_k12 | The leadership relationship among members of a comprehensive governance leadership group in a unit can be represented by a diagram, which is usually called ( )
A: Program Flowchart
B: Process Flowchart
C: Knowledge Structure Diagram
D: Organizational Structure Diagram | [
"Okay, so I need to figure out which diagram represents the leadership relationships in a governance leadership group. The options are Program Flowchart, Process Flowchart, Knowledge Structure Diagram, or Organizational Structure Diagram.",
"First, let me recall what each of these diagrams typically shows. A Prog... | The correct answer is **D: Organizational Structure Diagram**, as it maps leadership relationships and hierarchies, unlike other options that focus on program flow, process flow, or knowledge structure. |
b9e429fd-dc62-5ec4-9de5-476b9cb9afd4 | open-r1/OpenR1-Math-220k/cn_k12 | In deductive reasoning, as long as it conforms to the form of deductive reasoning, the conclusion is always correct. ( )
A: Correct
B: Incorrect
C:
D: | [
"Okay, so I need to figure out whether the statement about deductive reasoning is correct. The question says, \"In deductive reasoning, as long as it conforms to the form of deductive reasoning, the conclusion is always correct. ( )\" The options are A: Correct, B: Incorrect, C and D are empty. Let me think thro... | The statement is incorrect because deductive reasoning requires both valid structure and true premises to guarantee a true conclusion. Validity alone does not ensure correctness if the premises are false. |
810cecac-43c0-5f15-98c7-7ee1842b760f | open-r1/OpenR1-Math-220k/olympiads | ## Task 2
In a competition, 26 athletes started from East Germany. Exactly half of them managed to win a medal.
How many athletes from East Germany won a medal? | [
"Okay, let's see. The problem says there are 26 athletes from East Germany, and exactly half of them won a medal. The question is asking how many athletes from East Germany won a medal. Hmm, this seems straightforward, but I should take it step by step to make sure I don't make a mistake.",
"First, let me parse t... | Half of the 26 athletes from East Germany won a medal, resulting in \boxed{13} medal winners. |
b880d54e-1405-55fd-a187-b94cbcfc8ea3 | open-r1/OpenR1-Math-220k/olympiads | The equation that best represents "a number increased by five equals 15 " is
(A) $n-5=15$
(D) $n+15=5$
(B) $n \div 5=15$
(E) $n \times 5=15$
(C) $n+5=15$ | [
"Okay, let's see. The problem is asking which equation represents \"a number increased by five equals 15.\" The options are labeled A to E, with different equations. Hmm, I need to figure out which one is correct.",
"First, let me break down the sentence: \"a number increased by five equals 15.\" The phrase \"a n... | The equation representing "a number increased by five equals 15" is \( n + 5 = 15 \), which corresponds to option C. |
5e4372c8-281e-51a9-82a0-98f1d53c7cab | open-r1/OpenR1-Math-220k/olympiads | Cayli must choose one activity from each of the following groups: art, sports, and music. If there are 2 art choices, 3 sports choices, and 4 music choices, how many possible combinations of art, sports, and music choices can Cayli make?
(A) 9
(B) 24
(C) 12
(D) 14
(E) 20 | [
"Okay, so Cayli has to choose one activity from each of three categories: art, sports, and music. The question is asking how many possible combinations she can make. Let me think about how to approach this.",
"First, let me recall if there's a specific principle in combinatorics that applies here. Hmm, when you h... | The total number of possible combinations is found by multiplying the choices from each group: 2 (art) × 3 (sports) × 4 (music) = 24, corresponding to option B. |
f1c62e7f-9e81-5cc6-8a86-eabd348f6fd4 | open-r1/OpenR1-Math-220k/olympiads | The value of $0.3+0.03$ is
(A) 0.303
(B) 0.6
(C) 3.3
(D) 0.33
(E) 0.06 | [
"Okay, let's see. The problem is asking for the value of 0.3 plus 0.03, and there are five options to choose from. Hmm, I need to add these two decimal numbers. Let me think about how to approach this.",
"First, I remember that when adding decimals, it's important to line up the decimal points to make sure the pl... | The sum of \(0.3\) and \(0.03\) is \(0.33\), confirmed by both decimal addition and fraction conversion, making option D correct. |
e3e45296-9bb8-5e16-84f8-e9630e9b6038 | open-r1/OpenR1-Math-220k/olympiads | The expression $\sqrt{5^{2}-4^{2}}$ is equal to
(A) 1
(B) 2
(C) 3
(D) 4
(E) 9 | [
"Okay, let's see. I have this problem here: the square root of (5 squared minus 4 squared). And I need to figure out which of the options A through E it corresponds to. The options are 1, 2, 3, 4, or 9. Hmm, let me break this down step by step.",
"First, I should remember the order of operations, right? Parenthes... | Evaluating \(5^2 - 4^2 = 25 - 16 = 9\), the square root is \(\sqrt{9} = 3\), corresponding to option \(\boxed{C}\). |
eee98dc2-aecc-56f3-94fe-15001426ba08 | open-r1/OpenR1-Math-220k/olympiads | The radius of the circle is 13, the chord is 10. Find its distance from the center.
# | [
"Okay, so I need to find the distance from the center of a circle to a chord, given that the radius of the circle is 13 and the chord length is 10. Hmm, let me think about how chords relate to the radius and distances from the center.",
"I remember that in a circle, the perpendicular distance from the center to a... | Using the Pythagorean theorem with radius 13 and half chord length 5, the distance from the center to the chord is 12. |
f904d8da-1328-5fff-8306-fdd152bf6be8 | open-r1/OpenR1-Math-220k/olympiads | 10. “ $\qquad$ ” was launched from China's Xichang Satellite Launch Center on December 2, 2013, entered the lunar orbit on December 6, and the "Yutu" (Jade Rabbit) lunar rover successfully soft-landed in the Sinus Iridum (Bay of Rainbows) landing area on December 14. This marks the first time a Chinese probe has landed... | [
"Okay, let's see. The question is about a Chinese space probe that was launched in 2013, entered lunar orbit a few days later, and then landed a rover called Yutu on the moon. The options are Chang'e-3, Chang'e-2, Chang'e-1, and Tiangong-2.",
"First, I need to recall the different Chang'e missions. From what I re... | The correct answer is A. Chang'e-3, which was China's first lunar lander and rover mission launched in December 2013. The other options were either orbiters or a space lab, making Chang'e-3 the only correct choice for a soft landing on the Moon with the "Yutu" rover. |
3cfcbf2b-79bd-59aa-937f-9eb35afd4259 | open-r1/OpenR1-Math-220k/cn_k12 | The derivative of the function $f(x)=x+e^{x}$ is __( ).
A: $e^{x}$
B: $1+ \frac{1}{x}$
C: $1+xe^{x-1}$
D: $1+e^{x}$ | [
"Okay, so I need to find the derivative of the function f(x) = x + e^x. Hmm, let's start by recalling some basic rules of differentiation. I remember that when you take the derivative of a sum, you can take the derivatives of each term separately and then add them together. So, the derivative of x plus the derivati... | The derivative of \( f(x) = x + e^x \) is \( f'(x) = 1 + e^x \), corresponding to option **D**. |
ec6d3c64-ba68-5556-9925-808fb74dc7d9 | open-r1/OpenR1-Math-220k/olympiads | 662. Point $A$ was moved 13 units to the right and resulted in a point with a coordinate of 8. What was the coordinate of point $A$? | [
"Okay, let's see here. The problem says that point A was moved 13 units to the right and resulted in a point with a coordinate of 8. We need to find the original coordinate of point A. Hmm, moving to the right on a coordinate line usually means increasing the coordinate value, right? So if moving to the right by 13... | The original coordinate of point \( A \) was \(-5\), as moving it 13 units to the right results in the new coordinate of 8. |
38fadadd-96af-5c39-bcc9-d03873308c65 | open-r1/OpenR1-Math-220k/olympiads | ## Task 6
A ride on the Pioneer Railway in Küchwald covers a distance of $2.3 \mathrm{~km}$. Normally, there are 5 trips per day.
How many kilometers does the Pioneer Railway travel in 8 days? | [
"Okay, let's see. The problem is about calculating the total kilometers the Pioneer Railway travels in 8 days. Hmm. Let me break it down step by step.",
"First, the railway covers 2.3 km per ride. Normally, there are 5 trips per day. So, each day they do 5 trips, and each trip is 2.3 km. So, to find out the daily... | The Pioneer Railway travels 11.5 km daily, covering a total of 92 km over 8 days. |
69f69b4c-fafc-5c00-b1b0-e679f9285127 | open-r1/OpenR1-Math-220k/olympiads | Exercise 2. In a deck of cards consisting only of red cards and black cards, there are 2 times as many black cards as red cards. If 4 black cards are added, there are then 3 times as many black cards as red cards. How many cards did the deck have before adding the 4 black cards?
Only a numerical answer is expected her... | [
"Okay, let's see. So there's this deck of cards, right? It only has red cards and black cards. The problem says that initially, there are 2 times as many black cards as red cards. Then, if we add 4 black cards, the number of black cards becomes 3 times the number of red cards. We need to find out how many cards wer... | Initially, there are 4 red cards and 8 black cards, making a total of 12 cards. |
1ce0d58c-d705-52a0-ad6e-d724dbb88be8 | open-r1/OpenR1-Math-220k/cn_k12 | The monotonic increasing interval of the function $f(x)=e^{x}-x$ is $(\quad)$
A: $(-\infty,1)$
B: $(1,+\infty)$
C: $(-\infty,0)$
D: $(0,+\infty)$ | [
"Okay, so I need to find the monotonic increasing interval for the function f(x) = e^x - x. The options are given as A, B, C, D with different intervals. Let me recall how to determine where a function is increasing or decreasing.",
"I remember that a function is increasing on an interval if its derivative is pos... | The function \( f(x) = e^x - x \) is increasing on \( (0, +\infty) \) and decreasing on \( (-\infty, 0) \), so the correct answer is \( \boxed{D} \). |
c9d42267-6b43-5a72-8a39-46248961a3c5 | open-r1/OpenR1-Math-220k/olympiads | 81. A crab has 2 claws and 8 legs. Some crabs were boiled in a pot, and their legs are 30 more than their claws. So, there are $\qquad$ crabs in the pot. | [
"Alright, let's see here. The problem is about crabs in a pot. Each crab has 2 claws and 8 legs. After boiling them, the total number of legs is 30 more than the total number of claws. We need to find out how many crabs are in the pot.",
"Okay, let me break this down. First, each crab contributes 2 claws and 8 le... | The number of crabs is 5, as determined by solving the equation \(8x - 2x = 30\), which simplifies to \(6x = 30\) and yields \(x = 5\). |
c125b2c0-9538-5069-b5b3-627f96f39ad5 | open-r1/OpenR1-Math-220k/cn_k12 | $x^{15}\div x^{3}$ is equal to:
A: $x^{5}$
B: $x^{45}$
C: $x^{12}$
D: $x^{18}$ | [
"Okay, so I need to solve this problem: x raised to the 15th power divided by x cubed. The options are A through D, and I need to pick the right one. Let me think.",
"First, I remember that when you divide exponents with the same base, you subtract the exponents. Wait, is that right? Let me recall. Yeah, like x^a... | Using the exponent division rule \( \frac{x^a}{x^b} = x^{a-b} \), we find \( x^{15} \div x^{3} = x^{12} \), which is option C. |
b24a04a6-57a2-5139-bf74-906e25537d77 | open-r1/OpenR1-Math-220k/olympiads | Hannah scored 312 points during the basketball season. If her average (mean) was 13 points per game, how many games did she play?
(A) 24
(B) 41
(C) 17
(D) 13
(E) 30 | [
"Okay, let's see. The problem says Hannah scored 312 points during the basketball season, and her average was 13 points per game. The question is asking how many games she played. The options are A through E, with numbers 24, 41, 17, 13, and 30. Hmm, right.",
"Alright, so average points per game is total points d... | Hannah played 24 games, calculated by dividing her total points (312) by her average points per game (13). The answer is \(\boxed{A}\). |
797417a3-3487-50e3-8034-e7e4190cf5d2 | open-r1/OpenR1-Math-220k/olympiads | ## Task 3
Now Hans comes with his two siblings. All 3 want to ride the carousel once. A ride costs 10 Pfennig.
He has 50 Pfennig in his pocket.
How much money will he have left? | [
"Okay, let me try to figure this out. So, Hans has two siblings, right? That means there are three of them in total: Hans plus two siblings. They all want to ride the carousel once. Each ride costs 10 Pfennig. Hans has 50 Pfennig with him. The question is, how much money will he have left after paying for all three... | Hans has 50 Pfennig and needs to pay 30 Pfennig for three rides, leaving him with 20 Pfennig. |
e13dcde5-6dd9-57c5-bbbb-506b9a5b75c6 | open-r1/OpenR1-Math-220k/olympiads | What is the smallest prime number that is greater than 50 ? | [
"Okay, let's see. The question is asking for the smallest prime number greater than 50. Hmm, primes are numbers greater than 1 that have no divisors other than 1 and themselves. So first, I know that 50 is not a prime number because it's divisible by 2 and 5. The next number after 50 is 51. Is 51 prime?",
"Wait, ... | The smallest prime number greater than 50 is 53, as it is not divisible by any prime numbers less than or equal to its square root (approximately 7.28). |
6f4565d3-37ed-5971-9a36-cbd816bdb239 | open-r1/OpenR1-Math-220k/cn_k12 | The axis of symmetry of the parabola $y=(x-5)^2+4$ is ( )
A: Line $x=4$
B: Line $x=-4$
C: Line $x=-5$
D: Line $x=5$ | [
"Okay, let's see. The problem is asking about the axis of symmetry of the parabola given by the equation y = (x - 5)^2 + 4. The options are lines x = 4, x = -4, x = -5, and x = 5. Hmm, I need to remember how to find the axis of symmetry for a parabola in this form.",
"Wait, the equation is written in vertex form,... | The axis of symmetry is the vertical line \( x = 5 \), corresponding to option D. |
81334cd4-c2bb-5e42-994b-583c840559c6 | open-r1/OpenR1-Math-220k/cn_k12 | The variance of a set of data is 5. If each data point in this set is multiplied by 2 and then increased by 3, the variance of the resulting set of data is ______. | [
"Okay, let's see. The problem is about finding the new variance after transforming each data point. The original variance is 5. Each data point is multiplied by 2 and then increased by 3. I need to figure out what happens to the variance after these transformations. Hmm.",
"First, I remember that variance is affe... | Multiplying each data point by 2 increases the variance to 20, and adding 3 to each data point leaves the variance unchanged. The final variance is 20. |
94b0a43f-dced-5248-9044-c5d63aa31bff | open-r1/OpenR1-Math-220k/olympiads | There are 15 girls in a class of 27 students. The ratio of boys to girls in this class is
(A) $4: 5$
(B) $5: 3$
(C) $3: 4$
(D) $4: 9$
(E) $9: 5$ | [
"Okay, let's see. The problem says there are 15 girls in a class of 27 students. We need to find the ratio of boys to girls. The options are given from A to E. Hmm, ratios can sometimes trip me up, but I think I can handle this.",
"First, let's figure out how many boys there are. If the total number of students i... | The ratio of boys to girls is 4:5, as there are 12 boys and 15 girls in a class of 27 students. The correct answer is A. |
2f990b28-2078-5595-ad85-a6d934eb4142 | open-r1/OpenR1-Math-220k/olympiads | 89. $\int \sin \frac{x}{2} d x$.
Translate the text above into English, keeping the original text's line breaks and format, and output the translation result directly.
89. $\int \sin \frac{x}{2} d x$. | [
"Okay, so I need to solve the integral of sin(x/2) dx. Hmm, let's see. Integrals of trigonometric functions usually involve some substitution. The standard integral of sin(ax) dx is -1/a cos(ax) + C, right? Wait, let me make sure.",
"If I remember correctly, when integrating sin(ax) with respect to x, the integra... | The integral of $\sin \frac{x}{2}$ is $-2 \cos \frac{x}{2} + C$, found by substituting $u = \frac{x}{2}$ and integrating. |
c929de6b-57bf-5172-bec3-b95e0d03fa1f | open-r1/OpenR1-Math-220k/cn_k12 | Determine the smallest positive period of the function $y=\cos (2x- \frac {π}{3})$.
A: $\frac {π}{2}$
B: $π$
C: $2π$
D: $4π$ | [
"Okay, so I need to find the smallest positive period of the function y = cos(2x - π/3). Hmm, let's see. I remember that the period of a cosine function is normally 2π, right? But when there's a coefficient inside the cosine, like cos(Bx - C), that affects the period. Wait, how does that work again?",
"Oh yeah, t... | The smallest positive period of \( y = \cos(2x - \frac{\pi}{3}) \) is \( \pi \), as determined by the coefficient \( B = 2 \) in the general cosine function form \( \cos(Bx - C) \), where the period is \( \frac{2\pi}{|B|} \). The phase shift does not affect the period. |
421cdac9-2831-5be6-a1f1-b543d2dd39da | open-r1/OpenR1-Math-220k/cn_k12 | In the same plane, two non-overlapping lines can only have two positional relationships: intersecting and ______. | [
"Okay, so I need to figure out the two positional relationships that two non-overlapping lines can have in the same plane. The question states that they can either intersect or something else. Let me think.",
"First, I remember that in geometry, when two lines are in the same plane, they are called coplanar. For ... | In a plane, two non-overlapping lines can either intersect or be parallel, as confirmed by Euclidean geometry where skew lines do not exist. |
2b816b1d-488b-5708-ac28-40dfa153c11c | open-r1/OpenR1-Math-220k/olympiads | ## Task 3
Multiply 8 by 4, then subtract the number 15 from the product. | [
"Okay, let's see. I need to multiply 8 by 4 first. Hmm, 8 times 4. Let me think. 8 multiplied by 4 is like adding 8 four times: 8 + 8 + 8 + 8. Let me add them up. 8 plus 8 is 16, then another 8 makes 24, and one more 8 brings it to 32. So, 8 times 4 is 32. Got that part down.",
"Now, the next step is to subtract ... | Multiplying 8 by 4 gives 32, and subtracting 15 from this product results in 17. |
03560f1f-2f40-5a40-b8b6-ee9f45f8e067 | open-r1/OpenR1-Math-220k/olympiads | Example 6.1. A ball is randomly drawn from an urn containing 4 white, 9 black, and 7 red balls. What is the probability of drawing a white ball? | [
"Okay, let's see. The problem is about calculating the probability of drawing a white ball from an urn. The urn has 4 white balls, 9 black balls, and 7 red balls. Hmm, probability problems can sometimes be tricky, but I think this one is straightforward. Let me break it down step by step.",
"First, I need to reme... | The probability of drawing a white ball is \(\frac{4}{20} = \frac{1}{5}\), calculated by dividing the 4 white balls by the total of 20 balls. The final answer is \(\boxed{\dfrac{1}{5}}\). |
75f68d1b-5322-5560-a294-a9e18fb1e63c | open-r1/OpenR1-Math-220k/cn_k12 | Given $x, y \in \mathbb{R}$, then "$x=y$" is ( ) "$|x|=|y|$".
A: Sufficient but not necessary condition
B: Necessary but not sufficient condition
C: Necessary and sufficient condition
D: Neither sufficient nor necessary condition | [
"Okay, so I need to figure out whether \"x = y\" is a sufficient condition, necessary condition, both, or neither for \"|x| = |y|\". Let me start by recalling what these terms mean.",
"A sufficient condition means that if the condition is met, then the statement must be true. So if \"x = y\" is a sufficient condi... | $x = y$ is sufficient but not necessary for $|x| = |y|$, as equal numbers have equal absolute values, but equal absolute values don't guarantee the numbers themselves are equal. \boxed{A} |
cc7fd39c-657e-5103-b146-24be79090ee3 | open-r1/OpenR1-Math-220k/olympiads | 500. Find the area of a rectangle with sides 3 and 5. | [
"Okay, so I need to find the area of a rectangle with sides 3 and 5. Hmm, let me remember how to calculate the area of a rectangle. I think it's something like multiplying the length by the width. Yeah, that sounds right. Let me visualize a rectangle. It has two pairs of equal sides. So if one side is 3 units long ... | The area of a rectangle with sides 3 and 5 is calculated by multiplying the length and width, resulting in 15. |
1f8ad51d-b604-5409-a224-67aca0cbdc25 | open-r1/OpenR1-Math-220k/cn_k12 | If \\(p\\) is a true statement, and \\(q\\) is a false statement, then ( )
A: \\(p\\) and \\(q\\) is a true statement
B: \\(p\\) or \\(q\\) is a false statement
C: Not \\(p\\) is a true statement
D: Not \\(q\\) is a true statement | [
"Okay, let's see. I need to figure out which of the options A, B, C, or D is correct given that p is true and q is false. Hmm. Let's start by recalling some basic logic concepts.",
"First, let me remember what the logical operators mean. \"And\", \"or\", and \"not\" are the basic ones here.",
"Starting with opt... | Given \( p \) true and \( q \) false, option D (\(\lnot q\)) is true, while A, B, and C are false. Thus, the correct answer is \(\boxed{D}\). |
ccc418e7-85da-5e6d-bdb4-689dabf5f66a | open-r1/OpenR1-Math-220k/olympiads | ## Task 1
The new residential building on the outskirts of the city has 5 floors. On each floor, there are 8 living rooms. In addition, the building has a club room, 6 basement rooms, and a laundry room.
How many rooms does the residential building have? | [
"Okay, let's see. I need to figure out the total number of rooms in this residential building. Let me start by breaking down the information given.",
"First, the building has 5 floors. Each of these floors has 8 living rooms. So, to find the total number of living rooms, I should multiply the number of floors by ... | The residential building has 40 living rooms across 5 floors with 8 rooms each, plus 8 additional rooms (1 club, 6 basement, and 1 laundry), totaling 48 rooms. |
2dae0f52-efb1-5c83-a6b3-ce8e01f94eaa | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following operations is correct?
A: $a^{2}+a^{3}=a^{5}$
B: $a^{2}\cdot a^{3}=a^{6}$
C: $(a^{3})^{4}=a^{7}$
D: $(3a)^{2}=9a^{2}$ | [
"Okay, so I need to figure out which of these operations is correct. Let me take each option one by one and check them. Hmm, let's start with option A: a squared plus a cubed equals a to the fifth power. Wait, when you add exponents, do you add the exponents or something? No, wait, exponent rules. When you multiply... | Option D is correct as \((3a)^2 = 9a^2\), while the other options incorrectly apply exponent rules. |
301c14c6-ad4c-5adb-bdce-6358570eeb82 | open-r1/OpenR1-Math-220k/cn_k12 | The value of $(-2023)^{0}$ is:
A: $0$
B: $1$
C: $-1$
D: $-\frac{1}{2023}$ | [
"Okay, so the question is asking for the value of (-2023) raised to the power of 0. The options are A: 0, B: 1, C: -1, D: -1/2023. Hmm, let me think.",
"First, I remember that any non-zero number raised to the power of 0 is 1. Is that right? Let me confirm. The exponent rule states that a^0 = 1 for any a ≠ 0. So,... | Since \(-2023\) is a non-zero number, \((-2023)^0 = 1\). The answer is option B. |
fac03368-3bd6-59d7-ace3-1ab88b4bf6f9 | open-r1/OpenR1-Math-220k/olympiads | What is the value of $\frac{1}{1}+\frac{2}{2}+\frac{3}{3}$ ?
(A) 1
(B) 0
(C) 3
(D) 9
(E) 10 | [
"Okay, let me try to figure out this problem. So, the question is asking for the value of 1/1 + 2/2 + 3/3, and then choose the correct answer from the options given. The options are A) 1, B) 0, C) 3, D) 9, E) 10. Hmm, let me break this down step by step.",
"First, I need to compute each fraction individually and ... | The value of \(\frac{1}{1} + \frac{2}{2} + \frac{3}{3}\) simplifies to \(1 + 1 + 1 = 3\), corresponding to option (C). |
075e4603-38a1-5b65-9f09-0bc161d7a0d6 | open-r1/OpenR1-Math-220k/olympiads | ## Task 2
Rainer, Horst, and Klaus help their neighbors carry coal. Rainer carries 40 buckets of coal into the basement, Horst carries only a quarter of that. Klaus brings 15 more buckets of coal than Horst into the basement.
a) How many buckets of coal does Horst carry into the basement and how many does Klaus carry... | [
"Okay, let's see. I need to solve part a) first. The problem says Rainer carries 40 buckets of coal. Horst carries only a quarter of that. So first, I need to find out how much Horst carried. A quarter of Rainer's amount. Rainer has 40 buckets, so a quarter would be 40 divided by 4, right? Let me check. 40 divided ... | Horst carries 10 buckets and Klaus carries 25 buckets. Together, they carry 75 buckets. |
ee5e9bce-3e65-5e6b-9ce4-e2a85e2ab5ef | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following equations is true?
A: $\sqrt{{{(-2)}^2}}=-2$
B: $-{(\sqrt{5})^2}=5$
C: $\sqrt{x^2}=x$
D: $\sqrt{{{(-6)}^2}}=6$ | [
"Okay, so I need to figure out which of these equations A, B, C, or D is true. Let me go through each option one by one and check their validity.",
"Starting with option A: √((-2)^2) = -2. Hmm, let's compute the left side first. The expression inside the square root is (-2)^2. When you square a negative number, t... | Option D is true because \(\sqrt{(-6)^2} = \sqrt{36} = 6\), while the other options are false due to incorrect evaluations or lack of universal validity. |
453ef6a8-0f15-5b7c-9a9d-620017b25841 | open-r1/OpenR1-Math-220k/cn_k12 | The cube root of $-27$ is
A: $-\frac{1}{3}$
B: $-3$
C: $+3$
D: $\frac{1}{3}$ | [
"Okay, so I need to find the cube root of -27. Hmm, cube roots. Let me remember. The cube root of a number is a value that, when multiplied by itself three times, gives the original number. Since we're dealing with -27, which is negative, the cube root should also be negative because a negative number times itself ... | The cube root of \(-27\) is \(-3\) because \((-3)^3 = -27\). \boxed{B} |
85e89558-1679-53f5-8bf6-2794bc9cd972 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following equations is a linear equation in two variables?
A: $4x-y=3$
B: $2x=5$
C: $x-y+1$
D: $x^{2}-1=0$ | [
"Okay, so I need to figure out which of the given options is a linear equation in two variables. Let's see, the options are A, B, C, and D. Let me start by recalling what a linear equation in two variables is. From what I remember, a linear equation in two variables should have two variables, usually x and y, and b... | Option A (\(4x - y = 3\)) is a linear equation in two variables as it has two variables to the first power in the form \(Ax + By = C\), while the other options either have fewer variables, are not equations, or involve higher powers. |
8d7b8838-1e33-5941-ac76-e2f370f9a670 | open-r1/OpenR1-Math-220k/cn_k12 | Which of the following calculations is correct?
A: $-3x-3x=0$
B: $x^{4}-x^{3}=x$
C: $x^{2}+x^{2}=2x^{4}$
D: $-4xy+3xy=-xy$ | [
"Alright, let's tackle this problem step by step. The question asks which of the given calculations is correct among options A to D. I need to check each one individually to see if they simplify correctly. Let me go through each option one by one.",
"Starting with option A: -3x - 3x = 0. Hmm, okay. So, combining ... | Option D is correct as \(-4xy + 3xy = -xy\), while the other options contain errors in combining like terms or simplifying expressions. |
7ec65a80-9103-5aa7-972d-307235479a6b | open-r1/OpenR1-Math-220k/cn_k12 | Given that the probability of a normally distributed population falling in the interval $(0.2, +\infty)$ is $0.5$, then the corresponding normal curve $f(x)$ reaches its highest point at $x=$ ______. | [
"Okay, let's see. The problem says that in a normally distributed population, the probability of falling into the interval (0.2, +∞) is 0.5. We need to find the x-value where the normal curve f(x) reaches its highest point, which is the mean of the distribution.",
"Hmm, right, the normal distribution is symmetric... | The normal curve reaches its highest point at the mean, which is 0.2 since the probability of the interval \((0.2, +\infty)\) being 0.5 indicates it is the median, and in a normal distribution, the mean, median, and mode are equal. |
3e1e5a5b-6821-5f04-a54a-7f71a113a932 | open-r1/OpenR1-Math-220k/cn_k12 | The value of $\cos 43^{\circ}\cos 13^{\circ}+\sin 43^{\circ}\sin 13^{\circ}$ is equal to \_\_\_\_\_\_. | [
"Okay, so I need to find the value of cos 43 degrees multiplied by cos 13 degrees plus sin 43 degrees multiplied by sin 13 degrees. Hmm, let me think. I remember there are some trigonometric identities that involve products of cosines and sines. Maybe the cosine addition or subtraction formulas?",
"Wait, the expr... | The expression \(\cos 43^{\circ}\cos 13^{\circ} + \sin 43^{\circ}\sin 13^{\circ}\) simplifies to \(\cos(30^{\circ}) = \frac{\sqrt{3}}{2}\). |
8eb6986b-1e88-5b2b-89b1-6c65ca43f85b | open-r1/OpenR1-Math-220k/olympiads | 1. (8 points) The calculation result of the expression $2015-20 \times 15$ is $\qquad$ | [
"Okay, let me try to figure out this math problem. The expression is 2015 minus 20 multiplied by 15. Hmm, I need to remember the order of operations here. Wait, right, PEMDAS—Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. So multiplication comes before subtraction. That means I shoul... | Following the order of operations, we first calculate \(20 \times 15 = 300\), then subtract this from 2015 to get \(\boxed{1715}\). |
c9c26d0c-2904-560e-8cfd-227a34163920 | open-r1/OpenR1-Math-220k/cn_k12 | The imaginary part of the complex number $2-3i$ is ( )
A: $-3$
B: $3$
C: $3i$
D: $-3i$ | [
"Okay, so I need to figure out the imaginary part of the complex number 2 - 3i. Let me start by recalling what a complex number is. A complex number is usually written in the form a + bi, where 'a' is the real part and 'b' is the imaginary part. The 'i' here represents the imaginary unit, which is the square root o... | The imaginary part of \(2 - 3i\) is \(-3\), corresponding to option A. |
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