IB Mathematics

Course Overview 课程介绍

IB 数学分为 AA（偏纯数）与 AI（偏应用统计）两门，各设 HL/SL，IA 占 20%。

Since 2019, IB Mathematics is split into two separate courses, each at HL and SL. Mathematics: Analysis and Approaches (AA) is more abstract and proof-oriented, suited for STEM, mathematics, physics, and theoretical economics. Mathematics: Applications and Interpretation (AI) emphasizes statistics, modeling and real-world applications, suited for social science, biology, business and psychology. Both cover five core topics (number and algebra, functions, geometry and trigonometry, statistics and probability, calculus) with different depth and emphasis. Math AA HL absorbs content from the former Further Mathematics HL.

Key Facts 基本信息

SL Syllabus SL 阶段章节（AA / AI 共 5 大主题）

• SL1. Number and algebra
  AA: sequences, logarithms, binomial expansion, introduction to proof · AI: sequences, logarithms, financial mathematics, compound interest and annuities
• SL2. Functions
  AA: function properties, transformations, composite functions, quadratics · AI: function modeling, regression models, linearization with logarithms
• SL3. Geometry and trigonometry
  AA: trigonometric identities, solving triangles, coordinate geometry · AI: trig applications, 3D geometry, introduction to Voronoi diagrams
• SL4. Statistics and probability
  AA: probability, discrete distributions, binomial and normal · AI: descriptive statistics, correlation and regression, introduction to hypothesis testing
• SL5. Calculus
  AA: limits, differentiation, integration and applications, rigorous proof · AI: differentiation, integration applications, numerical methods, modeling

HL Additional Topics HL 额外章节

• HL6. Number and algebra (HL)
  AA: complex numbers, matrices, introduction to group theory, mathematical induction · AI: matrix operations, graph theory, recurrence relations
• HL7. Functions (HL)
  AA: polynomial functions (in depth), rational functions, absolute value functions · AI: model selection and fitting, log-transform modeling
• HL8. Geometry and trigonometry (HL)
  AA: vectors, vector equations, complex plane geometry, conic sections · AI: vector applications, graph algorithms, extended Voronoi diagrams
• HL9. Statistics and probability (HL)
  AA: continuous random variables, probability density, confidence intervals · AI: hypothesis testing, chi-square tests, confidence intervals, power distributions
• HL10. Calculus (HL)
  AA: differential equations, series convergence, Maclaurin series · AI: differential equation modeling, numerical integration, Euler's method
• HL11. Paper 3 investigation
  HL-only Paper 3: two extended questions emphasizing inquiry and synthesis (AA leans pure math, AI leans modeling)

Internal Assessment 内部评估 IA

IA 是数学探究报告，占 20%，AA 偏纯数推演，AI 偏真实数据建模。

The IB Mathematics IA (shared framework for AA and AI) is an individual mathematical exploration worth 20% of the final grade. Students choose a topic or problem and produce a 12-20 page report covering question formulation, mathematical derivation or modeling, analysis and conclusion. AA favors rigorous pure-math exploration; AI favors real-data modeling and interpretation. Assessment criteria: communication, mathematical presentation, reflection, personal engagement.

Exam Structure 考试结构（AA / AI 结构相同）