IBO · DP Math AA SL/HL
IB 数学AA：分析与方法资料
Mathematics: Analysis and Approaches
课程大纲 · 历年试卷与考试样题 · 练习 · 课程目录
单元与课题
选择课题，查看已上线的学习资料。
单元 1 - 数与代数16 个课题
打开此单元 →- 课题 1.1 科学记数法中数的运算Topic 1.1 Operations with Numbers in Standard Form查看资料
- 课题 1.2 等差数列与级数Topic 1.2 Arithmetic Sequences and Series查看资料
- 课题 1.3 等比数列与级数Topic 1.3 Geometric Sequences and Series查看资料
- 课题 1.4 等比数列与级数的财务应用Topic 1.4 Financial Applications of Geometric Sequences and Series查看资料
- 课题 1.5 指数与对数入门Topic 1.5 Exponents and Introduction to Logarithms查看资料
- 课题 1.6 简单演绎证明Topic 1.6 Simple Deductive Proof查看资料
- 课题 1.7 有理数指数与对数法则Topic 1.7 Rational Exponents and Laws of Logarithms查看资料
- 课题 1.8 无穷收敛等比级数Topic 1.8 Infinite Convergent Geometric Series查看资料
- 课题 1.9 二项式定理Topic 1.9 Binomial Theorem查看资料
- 课题 1.10 计数原理与广义二项式定理（仅 HL）Topic 1.10 Counting Principles and Extended Binomial Theorem (HL only)查看资料
- 课题 1.11 部分分式（仅 HL）Topic 1.11 Partial Fractions (HL only)查看资料
- 课题 1.12 复数的直角坐标形式（仅 HL）Topic 1.12 Complex Numbers in Cartesian Form (HL only)查看资料
- 课题 1.13 复数的极坐标形式与欧拉形式（仅 HL）Topic 1.13 Polar and Euler Forms of Complex Numbers (HL only)查看资料
- 课题 1.14 复数根与棣莫弗定理（仅 HL）Topic 1.14 Complex Roots and De Moivre's Theorem (HL only)查看资料
- 课题 1.15 进阶证明（仅 HL）Topic 1.15 Advanced Proof (HL only)查看资料
- 课题 1.16 线性方程组（仅 HL）Topic 1.16 Systems of Linear Equations (HL only)查看资料
单元 2 - 函数16 个课题
打开此单元 →- 课题 2.1 直线Topic 2.1 Straight Lines查看资料
- 课题 2.2 函数、定义域、值域与反函数Topic 2.2 Functions, Domain, Range and Inverse查看资料
- 课题 2.3 绘制函数图像Topic 2.3 Graphing Functions查看资料
- 课题 2.4 图像的关键特征与交点Topic 2.4 Key Features and Intersections of Graphs查看资料
- 课题 2.5 复合函数与反函数Topic 2.5 Composite and Inverse Functions查看资料
- 课题 2.6 二次函数Topic 2.6 Quadratic Functions查看资料
- 课题 2.7 一元二次方程与二次不等式Topic 2.7 Quadratic Equations and Inequalities查看资料
- 课题 2.8 倒数函数与有理函数Topic 2.8 Reciprocal and Rational Functions查看资料
- 课题 2.9 指数函数与对数函数Topic 2.9 Exponential and Logarithmic Functions查看资料
- 课题 2.10 用图像法与解析法解方程Topic 2.10 Solving Equations Graphically and Analytically查看资料
- 课题 2.11 图像变换Topic 2.11 Transformations of Graphs查看资料
- 课题 2.12 多项式函数、图像与方程（仅 HL）Topic 2.12 Polynomial Functions, Graphs, and Equations (HL only)查看资料
- 课题 2.13 进阶有理函数（仅 HL）Topic 2.13 Advanced Rational Functions (HL only)查看资料
- 课题 2.14 奇函数、偶函数与反函数（仅 HL）Topic 2.14 Odd, Even, and Inverse Functions (HL only)查看资料
- 课题 2.15 函数不等式（仅 HL）Topic 2.15 Function Inequalities (HL only)查看资料
- 课题 2.16 进阶图像变换与绝对值方程（仅 HL）Topic 2.16 Advanced Graph Transformations and Modulus Equations (HL only)查看资料
单元 3 - 几何与三角学18 个课题
打开此单元 →- 课题 3.1 三维几何Topic 3.1 Three-Dimensional Geometry查看资料
- 课题 3.2 直角与非直角三角形三角学Topic 3.2 Right and Non-Right Triangle Trigonometry查看资料
- 课题 3.3 三角学的应用Topic 3.3 Applications of Trigonometry查看资料
- 课题 3.4 弧度制、弧长与扇形面积Topic 3.4 Radian Measure, Arc Length, and Sector Area查看资料
- 课题 3.5 单位圆与三角函数精确值Topic 3.5 The Unit Circle and Exact Trigonometric Values查看资料
- 课题 3.6 三角恒等式Topic 3.6 Trigonometric Identities查看资料
- 课题 3.7 圆函数图像Topic 3.7 Graphs of Circular Functions查看资料
- 课题 3.8 三角方程的求解Topic 3.8 Solving Trigonometric Equations查看资料
- 课题 3.9 倒数三角函数与反三角函数（仅 HL）Topic 3.9 Reciprocal and Inverse Trigonometric Functions (HL only)查看资料
- 课题 3.10 和差角与倍角恒等式（仅 HL）Topic 3.10 Compound Angle and Double Angle Identities (HL only)查看资料
- 课题 3.11 三角函数图像的对称性（仅 HL）Topic 3.11 Symmetry of Trigonometric Graphs (HL only)查看资料
- 课题 3.12 二维与三维向量（仅 HL）Topic 3.12 Vectors in Two and Three Dimensions (HL only)查看资料
- 课题 3.13 向量的数量积（仅 HL）Topic 3.13 Scalar Product of Vectors (HL only)查看资料
- 课题 3.14 直线的向量方程（仅 HL）Topic 3.14 Vector Equations of Lines (HL only)查看资料
- 课题 3.15 三维空间中直线的位置关系（仅 HL）Topic 3.15 Relationships Between Lines in 3D (HL only)查看资料
- 课题 3.16 向量的向量积（仅 HL）Topic 3.16 Vector Product of Vectors (HL only)查看资料
- 课题 3.17 平面的向量方程（仅 HL）Topic 3.17 Vector Equations of Planes (HL only)查看资料
- 课题 3.18 与平面的相交和夹角（仅 HL）Topic 3.18 Intersections and Angles with Planes (HL only)查看资料
单元 4 - 统计与概率14 个课题
打开此单元 →- 课题 4.1 抽样、数据类型、偏差与离群值Topic 4.1 Sampling, Data Types, Bias, and Outliers查看资料
- 课题 4.2 数据展示与箱线图Topic 4.2 Data Presentation and Box Plots查看资料
- 课题 4.3 集中趋势与离散程度的度量Topic 4.3 Measures of Central Tendency and Dispersion查看资料
- 课题 4.4 相关与线性回归Topic 4.4 Correlation and Linear Regression查看资料
- 课题 4.5 概率的基本概念Topic 4.5 Basic Probability Concepts查看资料
- 课题 4.6 复合、条件与独立事件Topic 4.6 Combined, Conditional, and Independent Events查看资料
- 课题 4.7 离散随机变量Topic 4.7 Discrete Random Variables查看资料
- 课题 4.8 二项分布Topic 4.8 Binomial Distribution查看资料
- 课题 4.9 正态分布Topic 4.9 Normal Distribution查看资料
- 课题 4.10 x 对 y 的回归直线Topic 4.10 Regression Line of x on y查看资料
- 课题 4.11 条件概率与独立性的形式化表达Topic 4.11 Formal Conditional Probability and Independence查看资料
- 课题 4.12 标准化正态变量Topic 4.12 Standardized Normal Variables查看资料
- 课题 4.13 贝叶斯定理（仅 HL）Topic 4.13 Bayes' Theorem (HL only)查看资料
- 课题 4.14 随机变量与概率密度函数（仅 HL）Topic 4.14 Random Variables and Probability Density Functions (HL only)查看资料
单元 5 - 微积分19 个课题
打开此单元 →- 课题 5.1 极限与导数Topic 5.1 Limits and the Derivative查看资料
- 课题 5.2 增函数与减函数Topic 5.2 Increasing and Decreasing Functions查看资料
- 课题 5.3 基本求导法则Topic 5.3 Basic Differentiation Rules查看资料
- 课题 5.4 切线与法线Topic 5.4 Tangents and Normals查看资料
- 课题 5.5 积分入门Topic 5.5 Introduction to Integration查看资料
- 课题 5.6 求导技巧Topic 5.6 Differentiation Techniques查看资料
- 课题 5.7 二阶导数与图像性质Topic 5.7 Second Derivative and Graph Behaviour查看资料
- 课题 5.8 极值、优化与拐点Topic 5.8 Extrema, Optimization, and Points of Inflexion查看资料
- 课题 5.9 微积分运动学Topic 5.9 Kinematics with Calculus查看资料
- 课题 5.10 进阶不定积分Topic 5.10 Advanced Indefinite Integration查看资料
- 课题 5.11 定积分与面积Topic 5.11 Definite Integrals and Areas查看资料
- 课题 5.12 连续性、可微性、导数定义与高阶导数（仅 HL）Topic 5.12 Continuity, Differentiability, First Principles, and Higher Derivatives (HL only)查看资料
- 课题 5.13 洛必达法则与麦克劳林极限（仅 HL）Topic 5.13 L'Hopital's Rule and Maclaurin Limits (HL only)查看资料
- 课题 5.14 隐函数求导、相关变化率与优化（仅 HL）Topic 5.14 Implicit Differentiation, Related Rates, and Optimization (HL only)查看资料
- 课题 5.15 进阶导数与积分（仅 HL）Topic 5.15 Further Derivatives and Integrals (HL only)查看资料
- 课题 5.16 换元积分法与分部积分法（仅 HL）Topic 5.16 Integration by Substitution and Parts (HL only)查看资料
- 课题 5.17 与 y 轴围成的面积及旋转体体积（仅 HL）Topic 5.17 Areas with y-axis and Volumes of Revolution (HL only)查看资料
- 课题 5.18 一阶微分方程（仅 HL）Topic 5.18 First Order Differential Equations (HL only)查看资料
- 课题 5.19 麦克劳林级数（仅 HL）Topic 5.19 Maclaurin Series (HL only)查看资料
历年试卷与考试样题
以下为已上架文件的快捷入口；完整年份和试卷选项请打开课程中的真题选择器。