question_text stringclasses 3
values | retrieval_text stringclasses 3
values | evidence_quality float64 0.93 0.95 | source_knowledge stringclasses 3
values | solution_relation dict | knowledge_evidence dict | structured_conditions dict |
|---|---|---|---|---|---|---|
A town has a population of 5,000. If its population increases by 6 percent each year, what will the population be after 2 years, assuming the growth rate remains constant? | 题目给出初始人口 5,000、固定年增长率 6% 和时间 2 年。固定百分比增长对应指数模型 P=P₀(1+r)^t。代入 P₀=5000、r=0.06、t=2，得到 P=5000(1.06)^2=5618，所以正确答案为 5,618。关键适用条件是每个年度的增长比例相同；若增长的是固定人数，模型将改为线性增长。 | 0.94 | 指数增长知识材料：当一个量以固定百分比增长时，每个时间周期都乘以同一个增长因子。若初始量为 P₀，周期增长率为 r，经过 t 个周期后的量为 P=P₀(1+r)^t。这里的增长率必须用小数表示。 | {
"relation_type": "直接应用",
"linked_concepts": [
"百分比增长",
"增长因子",
"指数函数",
"指数增长模型"
],
"reasoning_link": "题目说明人口每年增加固定的 6%，因此不能将每年增加的数量固定为 300，而应在每一年将当前人口乘以 1.06。初始人口对应 P₀，2 年对应 t=2。",
"answer_derivation": "代入指数增长公式：P=5000(1+0.06)^2=5000(1.06)^2=5000×1.1236=5618。因此 2 年后的模型预计人口为 5,618，对应选项 5,618。... | {
"concept_name": "指数增长模型",
"concept_definition": "若某个量在每个相同时间周期内都按固定百分比增长，则该量形成指数增长。每个周期的增长因子为 1+r，其中 r 是以小数表示的正增长率。",
"formula_or_theorem": "P=P₀(1+r)^t，其中 P₀ 为初始量，r 为每个周期的增长率，t 为周期数。",
"applicability_conditions": [
"每个周期的百分比增长率保持不变。",
"增长率 r 应以小数代入公式，例如 6% 应写为 0.06。",
"t 表示完整的相同时间周期数。",
"该模型给... | {
"question_type": "问题解决与数据分析：指数增长模型",
"given_conditions": [
"初始人口为 5,000。",
"每年增长率为 6%，即 r=0.06。",
"增长率每年保持不变。",
"计算时间为 2 年。"
],
"target_quantity": "求 2 年后的预计人口。",
"answer_choices": [
"5,300",
"5,600",
"5,618",
"5,636"
]
} |
A line passes through the points (2, 5) and (8, 17). What is the x-coordinate of the point where the line intersects the x-axis? | 题目给定直线经过 (2,5) 和 (8,17)，要求求其 x 轴截距。根据斜率公式 m=(17−5)/(8−2)=2，点斜式给出 y−5=2(x−2)，即 y=2x+1。x 轴上的点满足 y=0，因此 0=2x+1，x=−1/2。该题直接应用两点斜率、点斜式和截距定义；适用前提是两点横坐标不同且确实位于同一直线上。 | 0.95 | 线性函数知识材料：非竖直直线的斜率等于两点纵坐标差与横坐标差之比。直线通常可写成斜截式 y=mx+b，其中 m 为斜率，b 为 y 轴截距。与 x 轴的交点满足 y=0。 | {
"relation_type": "直接应用",
"linked_concepts": [
"两点式斜率",
"点斜式",
"斜截式",
"x 轴截距"
],
"reasoning_link": "题目给出的两个点直接提供了计算斜率所需的坐标。将 (2,5) 和 (8,17) 代入斜率公式得到 m=2，再用点斜式建立直线方程，最后利用 x 轴上 y=0 的条件求截距。",
"answer_derivation": "m=(17−5)/(8−2)=2。使用点斜式：y−5=2(x−2)，化简得 y=2x+1。令 y=0，得到 0=2x+1，因此 x=−1/2，对应选项 −1/2。"... | {
"concept_name": "斜率、斜截式与 x 轴截距",
"concept_definition": "给定两个横坐标不同的点，直线斜率为 m=(y₂−y₁)/(x₂−x₁)。直线的斜截式为 y=mx+b；令 y=0 即可求出其与 x 轴交点的横坐标。",
"formula_or_theorem": "m=(y₂−y₁)/(x₂−x₁)；y−y₁=m(x−x₁)；x 轴截距由 y=0 求得。",
"applicability_conditions": [
"两点的横坐标必须不同，否则斜率公式的分母为零。",
"两点必须确定同一条直线。",
"求 x 轴截距时必须将 y 设为 0。"... | {
"question_type": "代数：线性方程与直线模型",
"given_conditions": [
"直线经过点 (2, 5)。",
"直线经过点 (8, 17)。",
"x 轴上的点满足 y=0。"
],
"target_quantity": "求该直线与 x 轴交点的横坐标。",
"answer_choices": [
"−1/2",
"1/2",
"2",
"−2"
]
} |
In a circle, AB is a diameter and C is a point on the circle. If AC=9 and BC=12, what is the area of the circle? | 在圆中，AB 是直径，C 在圆上，AC=9、BC=12。根据直径所对圆周角为直角，三角形 ABC 是以 AB 为斜边的直角三角形。由勾股定理，AB²=9²+12²=225，所以直径 AB=15，半径 r=15/2。圆面积为 A=πr²=π(15/2)²=225π/4。该题是圆周角定理、勾股定理和圆面积公式的组合应用。 | 0.93 | 圆与直角三角形知识材料：以圆的直径为一边、圆周上另一点为顶点的圆周角为直角。因此，当 AB 是直径且 C 在圆上时，三角形 ABC 在 C 处为直角三角形。直径 AB 是该直角三角形的斜边，可用勾股定理求出，再将直径除以 2 得半径，最后使用圆面积公式。 | {
"relation_type": "组合应用",
"linked_concepts": [
"直径所对圆周角为直角",
"勾股定理",
"圆的半径",
"圆面积"
],
"reasoning_link": "因为 AB 是直径且 C 在圆上，所以 ∠ACB 为直角，AC 和 BC 是两条直角边，AB 是斜边。先用勾股定理求直径，再将其转换为半径并计算圆面积。",
"answer_derivation": "AB²=9²+12²=81+144=225，所以 AB=15。半径 r=15/2。圆面积 A=π(15/2)²=225π/4，因此正确答案为 225π/4。",
"lim... | {
"concept_name": "圆周角定理、勾股定理与圆面积",
"concept_definition": "若一个三角形的三个顶点都在同一圆上，且其中一边是圆的直径，则该直径所对的圆周角为直角。因此，直径是该直角三角形的斜边。直角三角形的边长满足勾股定理，圆的面积等于 π 乘以半径的平方。",
"formula_or_theorem": "∠ACB=90°；AB²=AC²+BC²；A=πr²，且 r=AB/2。",
"applicability_conditions": [
"AB 必须确实是圆的直径，且 A、B、C 都位于同一个圆上。",
"勾股定理只能用于直角三角形。",
"圆的... | {
"question_type": "几何：圆、直角三角形与勾股定理",
"given_conditions": [
"AB 是圆的直径。",
"点 C 在该圆上。",
"AC=9。",
"BC=12。",
"圆面积公式为 A=πr²。"
],
"target_quantity": "求该圆的面积。",
"answer_choices": [
"225π/16",
"225π/4",
"225π/2",
"450π"
]
} |
SAT Math Concepts and Formula Evidence Retrieval Dataset
Designed for SAT math questions, this dataset pairs original question text and structured conditions with relevant concept definitions, formulas or theorems, applicability conditions, solution links, and source materials. Its JSON records include consolidated retrieval text and an evidence quality score ranging from 0 to 1, supporting workflows that retrieve reliable mathematical grounds for each question. Typical uses include RAG knowledge retrieval, evidence-backed explanations, and retrieval system development and evaluation.
Technical Specifications
| Field | Type | Description |
|---|---|---|
| question_text | string | The complete original SAT math question, including its prompt, requested task, and mathematical expressions. |
| retrieval_text | string | Evidence text combining question conditions, concepts, formulas or theorems, applicability conditions, and solution links for RAG retrieval and generation. |
| evidence_quality | number | A composite score from 0 to 1 assessing mathematical evidence accuracy, source traceability, and relevance to solving the question. |
| source_knowledge | string | Original materials used to extract or verify mathematical concepts, definitions, formulas, theorems, and their sources. May include textbooks, official resources, or curated knowledge excerpts. |
| solution_relation | object | Annotations describing how the question conditions and mathematical evidence correspond to the solution process. |
| knowledge_evidence | object | Concept definitions, formulas or theorems, applicability conditions, and reliable source evidence relevant to solving the question. |
| structured_conditions | object | Structured information extracted from the question text, such as question type, given conditions, objective, and answer choices. |
Compliance Statement
| Authorization Type | CC-BY-NC-SA 4.0 (Attribution–NonCommercial–ShareAlike) |
| Commercial Use | Requires exclusive subscription or authorization contract (monthly or per-invocation charging) |
| Privacy and Anonymization | No PII, no real company names, simulated scenarios follow industry standards |
| Compliance System | Compliant with China's Data Security Law / EU GDPR / supports enterprise data access logs |
Source & Contact
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