IB Maths AI HL Course (Early Bird Access; Continuous Updates)

About Course

Note:

IB Math AIHL：全方位大師課（早鳥搶先版）

現在加入，鎖定終身最低價，並參與課程進化！

這不僅僅是一份線上教材，這是一個持續成長的學習生態系。為了回饋首批支持的學生，我們推出了 「早鳥版」。目前課程已具備完整的 AIHL 核心內容，而我們正全力開發「互動測驗」。

現在以優惠價購買的學員，將自動獲得未來所有更新內容，無需支付任何差額。

IB Math AIHL: The Ultimate Masterclass (Early Bird Access)

Join now to lock in the lowest price and shape the future of this course!

This is more than just a static course; it is a “Living Course” that grows with you. We are currently in the Early Bird Phase, offering our comprehensive AIHL core materials at a fraction of the final price while we develop our interactive features and video libraries.

By enrolling today, you secure access to all future updates (including video solutions and quizzes) at no additional cost.

	內容	價格
第一階段 (現在)	核心講義、精選範題、課程架構	早鳥 4 折優惠
第二階段	+ 互動式測驗系統與解析	調漲至 7 折
最終版本	+ 影片解析	恢復原價

	What’s Included	Price Status
Phase 1 (Current)	Core Notes, Example Banks, Full Syllabus Structure	Early Bird (60% OFF)
Phase 2	+ Interactive Quizzes & Mock Exams	Price Increases (30% OFF)
Final Release	+ Video Solutions	Regular Price

Master every topic in the IB Mathematics AI HL syllabus with clear, step-by-step explanations
Build strong skills in functions, statistics, probability, modeling, and HL-level calculus
Learn how to use your calculator effectively for graphing, analysis, and IB-style problem solving
Strengthen real-world modeling skills through data analysis and interpretation
Develop exam-ready techniques for Paper 1, Paper 2, and Paper 3 scenarios
Gain confidence through worked examples, guided practice, and structured revision materials

Course Content

Measurement, Precision, and Spatial Geometry
Learn how to represent quantities precisely and understand the geometric principles that describe two- and three-dimensional space. This chapter introduces exact and approximate numbers, angle relationships, and geometric solids.

Representing Numbers and Accuracy
[Quiz] Representing Numbers and Accuracy
Angles and Triangles
[Quiz] Angles and Triangles
3D Solids, Nets, Surface Area, and Volume
[Quiz] 3D Solids, Nets, Surface Area, and Volume

Describing and Summarizing Data
This chapter develops skills in collecting, organizing, and interpreting data. Students learn measures of central tendency, variability, and graphical methods for data presentation.

Coordinate Geometry and Vector-Based Models
Explore how space can be divided and represented mathematically using coordinates, vectors, and diagrams. The focus is on modeling spatial relationships and lines in 2D and 3D.

Linear Models and Constant Rate of Change
Learn to model relationships with constant rates of change through linear functions, inverse functions, and arithmetic sequences. Regression techniques are introduced for analyzing real data.

Foundations of Probability and Uncertainty
An introduction to the mathematics of chance. Students learn how to calculate, represent, and interpret probabilities using diagrams, formulas, and systematic reasoning.

Polynomial and Power Function Models
Explore how quadratic, cubic, and power functions model different real-world patterns. Emphasis is placed on interpreting graphs, solving equations, and understanding functional relationships.

Exponential, Logarithmic, and Growth Models
Discover how exponential growth, decay, and logarithmic relationships describe processes such as population growth, finance, and natural phenomena.

Trigonometric Models and Complex Numbers
This chapter unites trigonometric and complex number concepts to model periodic behavior and extend the number system beyond the real line.

Matrices for Data, Transformations, and Systems
Learn how matrices can represent and solve systems of equations, model transformations, and analyze steady-state systems in data and applied contexts.

Differential Calculus and Instantaneous Change
Understand how derivatives measure change and describe motion, growth, and optimization. Students master differentiation rules and explore real-world applications.

Integration, Areas, and Introductory Differential Equations
Study the reverse process of differentiation — integration — and its uses in calculating areas, solving differential equations, and modeling change in dynamic systems.

Motion in Two and Three Dimensions
Model motion and change using vectors and calculus. Topics include velocity, acceleration, and systems of coupled differential equations.

Random Variables and Probability Distributions
Examine how random variables model uncertainty. This chapter covers binomial, Poisson, and continuous distributions, along with mean and variance analysis.

Statistical Tests and Validity Measures
Learn how to evaluate hypotheses and test data reliability using Spearman’s correlation, chi-squared tests, and hypothesis testing for various distributions.

Graph Theory and Network Optimization
Discover how graphs represent real-world networks. Students analyze routes, connections, and efficiencies using graph algorithms and optimization methods.

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About Course

Note:

IB Math AIHL：全方位大師課（早鳥搶先版）

IB Math AIHL: The Ultimate Masterclass (Early Bird Access)

What Will You Learn?

Course Content

Measurement, Precision, and Spatial Geometry Learn how to represent quantities precisely and understand the geometric principles that describe two- and three-dimensional space. This chapter introduces exact and approximate numbers, angle relationships, and geometric solids.

Representing Numbers and Accuracy

[Quiz] Representing Numbers and Accuracy

Angles and Triangles

[Quiz] Angles and Triangles

3D Solids, Nets, Surface Area, and Volume

[Quiz] 3D Solids, Nets, Surface Area, and Volume

Describing and Summarizing Data This chapter develops skills in collecting, organizing, and interpreting data. Students learn measures of central tendency, variability, and graphical methods for data presentation.

How to Collect, Organize, and Classify Data

[Quiz] How to Collect, Organize, and Classify Data

Measures of Center and Spread (Mean, Median, SD)

[Quiz] Measures of Center and Spread (Mean, Median, SD)

Graphs and Visual Representations of Data

[Quiz] Graphs and Visual Representations of Data

Correlation and Two-Variable Relationships

[Quiz] Correlation and Two-Variable Relationships

Coordinate Geometry and Vector-Based Models Explore how space can be divided and represented mathematically using coordinates, vectors, and diagrams. The focus is on modeling spatial relationships and lines in 2D and 3D.

Coordinates, Distance, and 3D Geometry Essentials

Equations of Lines and Geometric Interpretation

Voronoi Diagrams

Displacement Vectors

Scalar and Vector Products

Lines in Vector Form and Applications

Linear Models and Constant Rate of Change Learn to model relationships with constant rates of change through linear functions, inverse functions, and arithmetic sequences. Regression techniques are introduced for analyzing real data.

Function Concepts and Notation

Linear Equations and Real-World Modelling

Inverse Functions

Arithmetic Sequences and Series

Linear Regression: Fitting a Line to Data and Making Predictions

Foundations of Probability and Uncertainty An introduction to the mathematics of chance. Students learn how to calculate, represent, and interpret probabilities using diagrams, formulas, and systematic reasoning.

The Concept of Probability

Tree Diagrams and Outcome Structures

Combined Events in Probability – Diagrams, Notation, and Core Laws

Polynomial and Power Function Models Explore how quadratic, cubic, and power functions model different real-world patterns. Emphasis is placed on interpreting graphs, solving equations, and understanding functional relationships.

Quadratic Functions and Their Graphs

Quadratic Applications and Equations

Cubic Behavior and Contextual Modelling

Direct, Inverse, and General Power Models

Exponential, Logarithmic, and Growth Models Discover how exponential growth, decay, and logarithmic relationships describe processes such as population growth, finance, and natural phenomena.

Geometric Sequences and Series

Financial Applications of Geometric Sequences

Growth, Decay, and Exponential Curves

Algebra with Exponents and Logarithms

Logistic Models

Trigonometric Models and Complex Numbers This chapter unites trigonometric and complex number concepts to model periodic behavior and extend the number system beyond the real line.

Radians and Angular Measure

Sinusoidal Models

Complex Numbers

Complex Numbers on the Plane

Complex Numbers as Tools for Oscillations

Matrices for Data, Transformations, and Systems Learn how matrices can represent and solve systems of equations, model transformations, and analyze steady-state systems in data and applied contexts.

Introduction to Matrices and Operations

Multiplying Matrices and What It Means

Using Matrices to Solve Systems of Equations

Matrix Transformations: Rotations, Reflections, Stretches

Representing Systems and Steady States

Eigenvalues and Eigenvectors

Differential Calculus and Instantaneous Change Understand how derivatives measure change and describe motion, growth, and optimization. Students master differentiation rules and explore real-world applications.

Limit Concepts and Derivative Definitions

Chain Rule, Product/Quotient, and Beyond

Optimization, Motion, and Curvature

Integration, Areas, and Introductory Differential Equations Study the reverse process of differentiation — integration — and its uses in calculating areas, solving differential equations, and modeling change in dynamic systems.

Approximate Areas and Integration Concepts

Techniques of Integration

Applications of Integration

Introduction to Differential Equations

Slope Fields and Solution Methods

Motion in Two and Three Dimensions Model motion and change using vectors and calculus. Topics include velocity, acceleration, and systems of coupled differential equations.

Vector Quantities and Components

Using Calculus to Describe Changing Motion

Exact and Approximate Solutions of Coupled Equations

Random Variables and Probability Distributions Examine how random variables model uncertainty. This chapter covers binomial, Poisson, and continuous distributions, along with mean and variance analysis.

Random Variables and Basic Probability Models

Number of Successes in Fixed Trials or Intervals