prompt_messages listlengths 4 4 | gt stringlengths 1 44 | first_reward float64 -1 1 |
|---|---|---|
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Square $ABCD$ has side length 2, and $X$ is a point outside the square such that $AX = XB = \\sqrt{2}$. What is the length of the lo... | \sqrt{\sqrt{10}} | -0.5 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "What is the result when the expression $\\dfrac{\\sqrt[5]{11}}{\\sqrt[6]{11}}$ is expressed as 11 raised to what power? Let's think ... | \frac{1}{30} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "What is the result when the expression $\\dfrac{\\sqrt[5]{11}}{\\sqrt[6]{11}}$ is expressed as 11 raised to what power? Let's think ... | \frac{1}{30} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "What is the result when the expression $\\dfrac{\\sqrt[5]{11}}{\\sqrt[6]{11}}$ is expressed as 11 raised to what power? Let's think ... | \frac{1}{30} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "What is the result when the expression $\\dfrac{\\sqrt[5]{11}}{\\sqrt[6]{11}}$ is expressed as 11 raised to what power? Let's think ... | \frac{1}{30} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Let $ S = \\{1, 2, \\cdots, n\\} $. Define $ A $ as a collection of some subsets of $ S $ such that no two elements in $ A $ are mut... | C_n^{\left\lfloor \frac{n}{2} \right\rfloor} | -0.5 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Let $ S = \\{1, 2, \\cdots, n\\} $. Define $ A $ as a collection of some subsets of $ S $ such that no two elements in $ A $ are mut... | C_n^{\left\lfloor \frac{n}{2} \right\rfloor} | -1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Given points $M(0,3)$, $N(-4,0)$, and $P(-2,4)$;\n1. Find the equation of line $l$ that passes through point $P$ and is parallel to ... | S=5 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "A jar is filled with green, blue, red, and yellow jelly beans. The probability of randomly selecting a green jelly bean is 0.25 and ... | 0.40 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "A jar is filled with green, blue, red, and yellow jelly beans. The probability of randomly selecting a green jelly bean is 0.25 and ... | 0.40 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "A jar is filled with green, blue, red, and yellow jelly beans. The probability of randomly selecting a green jelly bean is 0.25 and ... | 0.40 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "A jar is filled with green, blue, red, and yellow jelly beans. The probability of randomly selecting a green jelly bean is 0.25 and ... | 0.40 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Let $ O $ and $ H $ be the circumcenter and orthocenter of triangle $ \\triangle ABC $, respectively. Set $ O $ as the origin of the... | z_{1} + z_{2} + z_{3} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Let $ O $ and $ H $ be the circumcenter and orthocenter of triangle $ \\triangle ABC $, respectively. Set $ O $ as the origin of the... | z_{1} + z_{2} + z_{3} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Let $ O $ and $ H $ be the circumcenter and orthocenter of triangle $ \\triangle ABC $, respectively. Set $ O $ as the origin of the... | z_{1} + z_{2} + z_{3} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "A cylindrical can has a circumference of 18 inches and a height of 8 inches. A spiral strip is painted on it that makes exactly two ... | \sqrt{1552} \text{ inches} | -0.5 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Calculate: $\\left(-2b\\right)^{3}=\\_\\_\\_\\_\\_\\_$. Let's think step by step and output the final answer within $\boxed{}$.",
... | -8b^{3} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Calculate: $\\left(-2b\\right)^{3}=\\_\\_\\_\\_\\_\\_$. Let's think step by step and output the final answer within $\boxed{}$.",
... | -8b^{3} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Calculate: $\\left(-2b\\right)^{3}=\\_\\_\\_\\_\\_\\_$. Let's think step by step and output the final answer within $\boxed{}$.",
... | -8b^{3} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "What is the ratio of $ x $ to $ y $ if: $\\frac{8x - 5y}{11x - 3y} = \\frac{2}{3}$? Express your answer as a common fraction. Let's ... | \frac{9}{2} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "What is the ratio of $ x $ to $ y $ if: $\\frac{8x - 5y}{11x - 3y} = \\frac{2}{3}$? Express your answer as a common fraction. Let's ... | \frac{9}{2} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "The number of sets A that satisfy A ∪ {-1, 1} = {-1, 0, 1} Let's think step by step and output the final answer within $\boxed{}$.",... | 4 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Simplify the expression: $$\\sqrt[3]{1728000}$$ Let's think step by step and output the final answer within $\boxed{}$.",
"role"... | 120 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Simplify the expression: $$\\sqrt[3]{1728000}$$ Let's think step by step and output the final answer within $\boxed{}$.",
"role"... | 120 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Find the number of six-digit palindromes in base 8. Let's think step by step and output the final answer within $\boxed{}$.",
"r... | 3584 | -0.5 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Find the number of six-digit palindromes in base 8. Let's think step by step and output the final answer within $\boxed{}$.",
"r... | 3584 | -0.5 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Consider the expression:\n$\n\\left(\\frac{x^3+1}{x}\\right)\\left(\\frac{y^3+1}{y}\\right) + \\left(\\frac{x^3-1}{y}\\right)\\left(... | 2xy^2 + \frac{2}{xy} | -0.5 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "How many two-digit prime numbers can be formed by choosing two different digits from the set $\\{3, 5, 7, 9\\}$ to be used as the te... | 6 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "How many two-digit prime numbers can be formed by choosing two different digits from the set $\\{3, 5, 7, 9\\}$ to be used as the te... | 6 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "When mailing a letter at the post office, the postage is 0.8 yuan for a letter weighing no more than 20g, 1.6 yuan for a letter weig... | 3.2 | -0.5 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Let $ g(x) = 3x - 2 $. Find the sum of all $ x $ that satisfy the equation $ g^{-1}(x) = g(2x) $. Let's think step by step and outpu... | \frac{8}{17} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Let $ g(x) = 3x - 2 $. Find the sum of all $ x $ that satisfy the equation $ g^{-1}(x) = g(2x) $. Let's think step by step and outpu... | \frac{8}{17} | -1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "Usain runs twice as fast as his mum. His mum runs five times as fast as his pet tortoise, Turbo. They all set off together for a run... | 40 \, \text{m} | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "If one root of the quadratic equation $x^{2}-2x+a=0$ is $3$, find the other root. Let's think step by step and output the final answ... | -1 | 1 |
[
{
"content": "You are a mathematical reasoning assistant. Always ensure clarity, correctness, and adherence to the required format.",
"role": "system"
},
{
"content": "If one root of the quadratic equation $x^{2}-2x+a=0$ is $3$, find the other root. Let's think step by step and output the final answ... | -1 | -1 |
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