id stringlengths 15 20 | question stringlengths 20 3.54k | reference_answer stringlengths 1 157 | dataset stringclasses 1
value | meta dict | k int64 8 8 | teacher_reward float64 0 1 | student_reward float64 0 1 | margin float64 -1 1 | delta float64 -1 1 | thinking listlengths 8 8 | no_thinking listlengths 8 8 |
|---|---|---|---|---|---|---|---|---|---|---|---|
sky_work_math_87727 | "A circle is inscribed in a triangle, and the points of tangency with the sides of the triangle are (...TRUNCATED) | 60 | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 0.875 | 0.875 | 0 | 0 | [{"cot":"","answer":"<think>\nOkay, so I need to find the angles of a triangle where, after inscribi(...TRUNCATED) | [{"answer":"We are given a geometric construction involving triangles and inscribed circles, and we (...TRUNCATED) |
sky_work_math_91259 | "1. Petya and Vasya competed in a 60 m race. When Petya finished, Vasya was 9 m behind him. During t(...TRUNCATED) | 1.35 | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 1 | 0 | 1 | 1 | [{"cot":"Okay, let's try to figure out this problem. So, Petya and Vasya had a 60-meter race. When P(...TRUNCATED) | [{"answer":"We are given a race problem involving Petya and Vasya. Let's break it down step by step.(...TRUNCATED) |
sky_work_math_25752 | "Given an arithmetic sequence $\\{a_{n}\\}$ with a common difference of $\\frac{{2π}}{3}$, let $S=\(...TRUNCATED) | -\frac{1}{2} | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 1 | 0 | 1 | 1 | [{"cot":"Okay, so I need to find the value of ab where S is the set {cos a_n | n ∈ N*} and S has o(...TRUNCATED) | [{"answer":"We are given an **arithmetic sequence** $\\{a_n\\}$ with **common difference** $\\frac{2(...TRUNCATED) |
sky_work_math_99026 | "Example 2-35 A unit has 8 male colleagues and 5 female colleagues. It is planned to organize a grou(...TRUNCATED) | 3328 | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 1 | 0.75 | 0.25 | 0.25 | [{"cot":"Okay, so I need to figure out how many different ways there are to form a group from 8 male(...TRUNCATED) | [{"answer":"We are given:\n\n- A unit has **8 male colleagues** and **5 female colleagues**.\n- We n(...TRUNCATED) |
sky_work_math_101652 | "4. Given a moving large circle $\\odot O$ that is externally tangent to a fixed small circle $\\odo(...TRUNCATED) | 36 | synthetic2_math | {
"teacher_avg_reward": 0.8888888888888888
} | 8 | 0.625 | 0 | 0.625 | 0.625 | [{"cot":"Okay, so I need to solve this geometry problem. Let me try to visualize it first. There's a(...TRUNCATED) | [{"answer":"We are given:\n\n- A **fixed small circle** $\\odot O_1$ with **radius 3**, centered at (...TRUNCATED) |
sky_work_math_71239 | Evaluate the expression $\sqrt{7+4\sqrt{3}} - \sqrt{7-4\sqrt{3}}$. | 2\sqrt{3} | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 0 | 0 | 0 | 0 | [{"cot":"Okay, so I need to evaluate the expression √(7 + 4√3) - √(7 - 4√3). Hmm, let me thi(...TRUNCATED) | [{"answer":"We are asked to evaluate the expression:\n\n$$\n\\sqrt{7 + 4\\sqrt{3}} - \\sqrt{7 - 4\\s(...TRUNCATED) |
sky_work_math_62432 | "5. The function $f: \\mathbf{R} \\rightarrow \\mathbf{R}$ satisfies for all $x, y, z \\in \\mathbf{(...TRUNCATED) | 0 | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 0.875 | 0.625 | 0.25 | 0.25 | [{"cot":"Okay, so I need to solve this functional equation problem. The function f: R → R satisfie(...TRUNCATED) | [{"answer":"We are given a functional inequality:\n\n$$\nf(x+y) + f(y+z) + f(z+x) \\geq 3 f(x+2y+z),(...TRUNCATED) |
sky_work_math_85113 | "Let $\\overline{AB}$ be a diameter of circle $\\omega$. Extend $\\overline{AB}$ through $A$ to $C$.(...TRUNCATED) | 432 | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 0.875 | 0 | 0.875 | 0.875 | [{"cot":"Okay, so I need to find the maximum possible length of segment BP, where AB is a diameter o(...TRUNCATED) | [{"answer":"We are given a geometric configuration involving a circle, tangents, and perpendiculars.(...TRUNCATED) |
sky_work_math_42058 | "## Task A-2.2.\n\nInside the circle $k$ with radius 20, there are a circle $k_{1}$ with radius 5 an(...TRUNCATED) | 8+4\sqrt{19} | synthetic2_math | {
"teacher_avg_reward": 0.6
} | 8 | 0.125 | 0 | 0.125 | 0.125 | [{"cot":"","answer":"<think>\nOkay, let's try to tackle this geometry problem. It seems a bit comple(...TRUNCATED) | [{"answer":"We are given a geometric configuration involving a **circle $ k $** with radius 20, a **(...TRUNCATED) |
sky_work_math_74739 | "Example 5. Expand the function\n\n$$\nf(z)=\\frac{z}{z^{2}-2 z-3}\n$$\n\ninto a Taylor series in th(...TRUNCATED) | 1 | synthetic2_math | {
"teacher_avg_reward": 1
} | 8 | 1 | 0.125 | 0.875 | 0.875 | [{"cot":"Okay, so I need to expand the function f(z) = z / (z² - 2z - 3) into a Taylor series aroun(...TRUNCATED) | [{"answer":"We are given the function:\n\n$$\nf(z) = \\frac{z}{z^2 - 2z - 3}\n$$\n\nand asked to exp(...TRUNCATED) |
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