国际文凭组织 · IB Diploma
数学：应用与解释 · HL
Papers, samples and curriculum documents for this course. · 本课程的文件、样卷和课程大纲。
Handouts, exercise sheets and slides · 讲义、练习卷与幻灯片
Shared topic documents retain their source course and topic titles. Use your chosen board’s specification for coverage, tier and exam requirements. · 共用专题资料保留原课程与专题名称。请按所选考试局的大纲核对内容、等级及考试要求。
Handouts · 讲义 · A-Level Mathematics · A-Level 数学 (5)
Exercise sheets · 练习页 · A-Level Mathematics · A-Level 数学 (33)
- 1.1 Quadratics · 1.1 二次函数
- 1.2 Functions · 1.2 函数
- 1.3 Coordinate geometry · 1.3 坐标几何
- 1.4 Circular measure · 1.4 弧度制
- 1.5 Trigonometry · 1.5 三角学
- 1.6 Series · 1.6 级数
- 1.7 Differentiation · 1.7 微分
- 1.8 Integration · 1.8 积分
- 2.1 Algebra · 2.1 代数
- 2.2 Logarithmic and exponential functions · 2.2 对数函数与指数函数
- 2.3 Trigonometry · 2.3 三角学
- 2.4 Differentiation · 2.4 微分
- 2.5 Integration · 2.5 积分
- 2.6 Numerical solution of equations · 2.6 方程的数值解
- 3.1 Algebra · 3.1 代数
- 3.2 Logarithmic and exponential functions · 3.2 对数函数与指数函数
- 3.3 Trigonometry · 3.3 三角学
- 3.4 Differentiation · 3.4 微分
- 3.5 Integration · 3.5 积分
- 3.6 Numerical solution of equations · 3.6 方程的数值解
- 3.7 Vectors · 3.7 向量
- 3.8 Differential equations · 3.8 微分方程
- 3.9 Complex numbers · 3.9 复数
- 5.1 Representation of data · 5.1 数据的表示
- 5.2 Permutations and combinations · 5.2 排列与组合
- 5.3 Probability · 5.3 概率
- 5.4 Discrete random variables · 5.4 离散随机变量
- 5.5 The normal distribution · 5.5 正态分布
- 6.1 The Poisson distribution · 6.1 泊松分布
- 6.2 Linear combinations of random variables · 6.2 随机变量的线性组合
- 6.3 Continuous random variables · 6.3 连续随机变量
- 6.4 Sampling and estimation · 6.4 抽样与估计
- 6.5 Hypothesis tests · 6.5 假设检验
Presentation slides · 演示文稿幻灯片 · A-Level Mathematics · A-Level 数学 (5)
Course units and learning goals · 课程单元与学习目标
These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme. · 这些课程教授选定的教学目标。请检查剩余的覆盖缺口；本材料并非完整的备考方案。
1 · Number and algebra
- Exact arithmetic and estimation: A prime number that divides the integer exactly.
- Percentages, ratio and proportional reasoning: A factor that performs a percentage change in one multiplication.
- Sequences, series and recurrence: The constant multiplier between consecutive terms of a geometric sequence.
- Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
- Matrix transformations, inverses and eigenvalues: A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.
- Complex numbers and roots: The number obtained by reversing the sign of the imaginary part.
- prime factor
- A prime number that divides the integer exactly.
- multiplier
- A factor that performs a percentage change in one multiplication.
- common ratio
- The constant multiplier between consecutive terms of a geometric sequence.
- residual
- The observed value minus the value predicted by a fitted model.
- determinant
- A scalar that determines whether a square matrix is invertible and, in two dimensions, its signed area factor.
- complex conjugate
- The number obtained by reversing the sign of the imaginary part.
2 · Functions
- Domains, inverses and composition: The set of allowed inputs to a function.
- Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
- Exponentials, logarithms and modelling: The time for a decaying quantity to fall to half its initial value.
- domain
- The set of allowed inputs to a function.
- residual
- The observed value minus the value predicted by a fitted model.
- half-life
- The time for a decaying quantity to fall to half its initial value.
3 · Geometry and trigonometry
- Angle reasoning, similarity and mensuration: The multiplier that relates corresponding lengths in similar shapes.
- Right triangles and non-right triangles: The side opposite the right angle in a right-angled triangle.
- Vectors and transformation geometry: The vector sum representing the combined displacement or force.
- scale factor
- The multiplier that relates corresponding lengths in similar shapes.
- hypotenuse
- The side opposite the right angle in a right-angled triangle.
- resultant
- The vector sum representing the combined displacement or force.
4 · Statistics and probability
- Data summaries, histograms and interpretation: Frequency divided by class width, used as histogram height.
- Probability, trees and conditional reasoning: The probability of an event after restricting the sample space to a stated condition.
- Binomial, normal and Poisson models: The probability-weighted mean of a random variable.
- Hypothesis testing and contextual conclusions: The chosen probability threshold for rejecting a null hypothesis.
- Confidence intervals, chi-square and regression: An interval calculated by a procedure designed to cover the population parameter at a stated long-run rate.
- frequency density · 频率密度
- Frequency divided by class width, used as histogram height.
- conditional probability
- The probability of an event after restricting the sample space to a stated condition.
- expected value
- The probability-weighted mean of a random variable.
- significance level
- The chosen probability threshold for rejecting a null hypothesis.
- confidence interval
- An interval calculated by a procedure designed to cover the population parameter at a stated long-run rate.
5 · Calculus
- Derivatives and stationary points: The instantaneous rate of change, also the gradient of a tangent.
- Root finding and numerical integration: A repeated update in which each new approximation is calculated from the previous one.
- Chain, product, quotient and implicit differentiation: The rule that multiplies the outer derivative by the inner derivative for a composite function.
- Substitution, parts and partial fractions: An integration method based on the derivative of a product.
- Differential equations and numerical solutions: A specified value that selects a particular solution from a family.
- derivative
- The instantaneous rate of change, also the gradient of a tangent.
- iteration
- A repeated update in which each new approximation is calculated from the previous one.
- chain rule
- The rule that multiplies the outer derivative by the inner derivative for a composite function.
- integration by parts
- An integration method based on the derivative of a product.
- initial condition
- A specified value that selects a particular solution from a family.
IA · School-supervised mathematical exploration
- Planning a mathematical exploration: A condition adopted to make a mathematical model possible and whose effect should be evaluated.
- assumption
- A condition adopted to make a mathematical model possible and whose effect should be evaluated.
Preparing for this qualification · 备考指南
- Current first-assessment-2021 course: AI permits technology on both papers. HL Paper 3 permits technology and tests extended problem solving.
- External examination contributes 80%; the school-supervised mathematical exploration contributes 20%. SL papers are 40% each; HL Papers 1/2 are 30% each and Paper 3 is 20%.
- Public briefs establish structure, not full official learning objectives. School access to the current full guide, formula booklet and calculator policy is required to certify complete parity.
- Do not apply the revised 2029 marks, paper timing or exploration criteria to current cohorts.
Teaching coverage still needed · 仍需教学覆盖内容
- Official question-bank boundaries, scheme alignment and all objective-level teaching coverage require the recorded review; no practice registry promotion.
- The authored diagnostic assessments are not full-length qualification mocks.
- The complete current IB guide, formula booklet, authenticated exploration criteria and full SL/HL objective codes are unavailable in the public archive.
Specifications and sample documents · 课程大纲和样件文件
- 数学：应用与解释 — 样卷 · 2021 ↗
First assessment: 2021
- 数学：应用与解释 — 课程简介 · 2021 ↗
First assessment: 2021
- 计算器使用指南（2020） ↗
- 数学：应用与解释 — 课程简介 · 2029 ↗
First assessment: 2029
Course materials · 课程资料
Course preparation · 课程准备
Documents are available. Board-specific notes, assessments and interactive past-paper practice are not yet available for every course. · 文档已提供。并非所有课程都具备考试局特定的注释、测评及交互式历年真题练习。
Lessons · 课程 →