AP Mathematics (Calculus & Statistics)

Course Overview 课程介绍

AP 数学实为 Calculus AB/BC 与 Statistics 三门独立考试，本页整合对照。

The AP system has no single "Mathematics" exam; the corresponding courses are AP Calculus AB, AP Calculus BC, and AP Statistics. Calculus AB/BC cover calculus (BC includes all of AB plus parametric/polar/vector functions and series), while Statistics is a dedicated statistics course. All three are core subjects for STEM, economics and data science applicants.

Key Facts 基本信息

Sub-Exam: Calculus AB AP Calculus AB 章节

微积分 AB 含极限、求导、积分、微分方程与积分应用共 8 个单元。

• ABUnit 1. Limits and Continuity
  One-sided limits; asymptotes; squeeze theorem; Intermediate Value Theorem
• ABUnit 2. Differentiation: Definition and Fundamental Properties
  Derivative definition; tangent lines and instantaneous rate of change; basic differentiation rules
• ABUnit 3. Differentiation: Composite, Implicit, and Inverse Functions
  Chain rule for composite functions; implicit and inverse differentiation
• ABUnit 4. Contextual Applications of Differentiation
  Related rates; linear approximation; L'Hôpital's rule
• ABUnit 5. Applying Derivatives to Analyze Functions
  Extrema and monotonicity; concavity and inflection; optimization
• ABUnit 6. Integration and Accumulation of Change
  Riemann sums; Fundamental Theorem of Calculus; integration techniques
• ABUnit 7. Differential Equations
  Slope fields; separable equations; exponential growth and decay models
• ABUnit 8. Applications of Integration
  Area; volumes of revolution; volumes from known cross-sections

Sub-Exam: Calculus BC (all of AB plus the following) AP Calculus BC 章节

BC 在 AB 基础上新增参数/极坐标/向量函数与无穷级数共 2 个单元。

• BCUnit 9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
  Parametric, polar and vector-valued functions; arc length and parametric area
• BCUnit 10. Infinite Sequences and Series
  Convergence tests; Taylor and Maclaurin series; power series; error bounds

Sub-Exam: Statistics AP Statistics 章节

统计学含数据探索、抽样、概率、抽样分布与推断共 9 个单元。

• StatUnit 1. Exploring One-Variable Data
  Distributions and displays; center and spread; normal distribution
• StatUnit 2. Exploring Two-Variable Data
  Scatterplots and correlation; least-squares regression; residual analysis
• StatUnit 3. Collecting Data
  Sampling methods; experimental design; bias and control
• StatUnit 4. Probability, Random Variables, and Probability Distributions
  Discrete and continuous distributions; binomial and geometric distributions
• StatUnit 5. Sampling Distributions
  Central Limit Theorem; sampling distributions for proportions and means
• StatUnit 6. Inference for Categorical Data: Proportions
  Confidence intervals and hypothesis tests for proportions
• StatUnit 7. Inference for Quantitative Data: Means
  Confidence intervals and t-tests for means; paired and two-sample
• StatUnit 8. Inference for Categorical Data: Chi-Square
  Chi-square goodness-of-fit; chi-square tests of independence
• StatUnit 9. Inference for Quantitative Data: Slopes
  Confidence intervals and hypothesis tests for regression slopes

Exam Structure 考试结构

Credit Transfer 学分转换与衔接

4/5 分换算大学学分，BC 5 分常换算微积分 I 与 II。

All three AP math exams use a 1–5 scale; most US colleges grant credit for 4 or 5. Calculus AB typically maps to Calculus I, while a BC score of 4 often earns Calculus I credit and a 5 earns Calculus I + II. Statistics maps to an introductory statistics course. Policies vary by institution.