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IB Mathematics AIHL Complete Course Beta

Module 1

Prerequisites & Foundations

Before diving into the AIHL course, it's essential to build a strong foundation. This module covers the prerequisite skills that …

18 lessons
Introduction: Why Foundations Matter 15 min Exponent Laws 20 min Solving Quadratic Equations 20 min Systems of Equations (2x2) 20 min Linear Inequalities 20 min Function Notation & Evaluation 20 min Domain & Range 20 min Inverse Functions 20 min Graph Transformations 20 min Intersections of Graphs 20 min Straight Lines 20 min Distance & Midpoint 20 min Right Triangle Trigonometry (SOH CAH TOA) 20 min Special Triangles & Exact Values 20 min Bearings 20 min Statistics: Central Tendency & Spread 20 min Basic Probability 20 min GDC Skills 20 min
Module 2

12.1 Sequences, Series & TVM

Arithmetic and geometric sequences, sigma notation, financial applications and time value of money.

10 lessons
Arithmetic Sequences 45 min Arithmetic Series 25 min Geometric Sequences 20 min Series & Sigma Notation 30 min Geometric Series 25 min Infinite Convergent Series 30 min Compound Interest & Depreciation 25 min Annuities & Amortization 30 min Logarithmic Scales & Applications 25 min Mixed Practice & Exam Prep 40 min
Module 3

12.2 Functions 1

Introduction to functions, domain and range, inverses, graphing and systems of equations.

10 lessons
Function Notation & Evaluation 20 min Domain & Range 25 min Composite Functions 25 min Inverse Functions 30 min Graphing with Technology 20 min Systems of Linear Equations 25 min Polynomial Equations 25 min Transformations of Graphs 30 min Optimization with Functions 30 min Mixed Practice & Exam Prep 45 min
Module 4

12.3 Models

Linear, quadratic, exponential, cubic and sinusoidal models with GDC applications.

11 lessons
Linear Models 25 min Quadratic Models 30 min Exponential Models 30 min Direct and Inverse Variation 25 min Cubic Models 25 min Sinusoidal Models 30 min Choosing the Right Model 25 min Regression and Correlation 25 min Logistic Models 15 min Piecewise Models 15 min Modelling Exam Practice 40 min
Module 5

12.4 Trigonometry

3D trigonometry, sine and cosine rules, radians, unit circle and sector calculations.

8 lessons
3D Coordinate Geometry 15 min Right-Angled Trigonometry in 3D 20 min Sine Rule, Cosine Rule & Area of Triangle 30 min Bearings & Applications 20 min Radians & The Unit Circle 20 min Arc Length & Sector Area 15 min Volumes & Surface Areas 20 min Trig Exam Practice 25 min
Module 6

12.5 Exponents

Exponential expressions, logarithms, log laws and logarithmic scales.

8 lessons
Exponent Laws 25 min Exponential Equations 25 min Introduction to Logarithms 20 min Logarithm Laws 30 min Solving Logarithmic Equations 25 min Natural Logarithm and e 30 min Semi-Log and Log-Log Graphs 30 min Exponents Exam Practice 40 min
Module 7

12.6 Functions 2

Transformations, curve fitting, linearisation and regression analysis.

7 lessons
Graph Transformations 30 min Curve Fitting & Regression 30 min Transforming a Point 15 min Applications (Scaling Images, Models) 15 min Direct & Inverse Proportion 15 min Logistic Function 15 min Mixed Practice & Exam Prep 45 min
Module 8

12.7 Graph Theory

Graphs, trees, algorithms, adjacency matrices and optimisation problems.

8 lessons
Introduction to Graphs 30 min Adjacency Matrices 25 min Trees & Spanning Trees 30 min Eulerian & Hamiltonian Paths 15 min Kruskal's & Prim's (MST) 15 min Chinese Postman Problem 15 min Travelling Salesman Problem 15 min Mixed Practice & Exam Prep 45 min
Module 9

12.8 Voronoi Diagrams

Voronoi diagrams, perpendicular bisectors, nearest neighbour interpolation.

7 lessons
Voronoi Diagrams 30 min Voronoi Applications 25 min Adding a New Site (Vertex) 15 min Largest Empty Circle 15 min Nearest Neighbour Interpolation 15 min Toxic Waste Problem 15 min Mixed Practice & Exam Prep 45 min
Module 10

12.9 Derivatives

Introduction to differentiation, power rule, tangents, normals and optimisation.

5 lessons
Introduction to Differentiation 30 min Standard Derivatives 20 min Tangents & Normals 25 min Optimisation 30 min Mixed Practice & Exam Prep 45 min
Module 11

12.10 Integration

Anti-derivatives, trapezium rule and integrals as accumulation.

8 lessons
Antiderivatives & Indefinite Integrals 30 min Definite Integrals & Area 30 min Area Between Curves 15 min Area in Reverse (Below x-axis) 15 min Integration With & Without Calculator 15 min Negative Areas & Absolute Value 15 min Area Between Curve and y-axis 15 min Mixed Practice & Exam Prep 45 min
Module 12

12.11 Further Derivatives

Chain rule, product/quotient rules, related rates, concavity and stationary points.

5 lessons
Chain Rule 30 min Product & Quotient Rules 30 min Related Rates of Change 20 min Second Derivatives & Concavity 20 min Mixed Practice & Exam Prep 45 min
Module 13

12.12 Further Integration

Integration techniques, areas, volumes of revolution and kinematics.

7 lessons
Areas & Volumes 30 min Integration by Substitution 30 min Volumes of Revolution 15 min Integration of Powers, ln, and 1/x 15 min Integration of Exponential Functions 15 min Integration of Trig Functions (sin, cos) 15 min Mixed Practice & Exam Prep 45 min
Module 14

12.13 Statistics

Data types, central tendency, dispersion, histograms and regression.

9 lessons
Measures of Central Tendency 25 min Standard Deviation & Variance 25 min 1 & 2 Variable Statistics on GDC 15 min Frequency Tables & Grouped Data 15 min Linear Transformations of Data 15 min Box & Whisker Diagrams 15 min Cumulative Frequency Graphs 15 min Histograms & Outliers 15 min Mixed Practice & Exam Prep 45 min
Module 15

12.14 Probability

Tree diagrams, Venn diagrams, two-way tables and conditional probability.

6 lessons
Probability Rules 25 min Tree & Venn Diagrams 25 min Conditional Probability 15 min Two-Way Tables 15 min Independent Events 15 min Mixed Practice & Exam Prep 45 min
Module 16

12.15 Probability Distributions

Discrete random variables, binomial and normal distributions.

5 lessons
Binomial Distribution 30 min Normal Distribution 30 min Poisson Distribution 15 min Expected Value & Variance 15 min Mixed Practice & Exam Prep 45 min
Module 17

12.16 Hypothesis Testing

Chi-squared tests, t-tests and Spearman's rank correlation.

11 lessons
Hypothesis Testing Basics 30 min Chi-Squared Tests 30 min Chi-Squared Goodness of Fit 15 min Chi-Squared Independence Test 15 min t-Test for Means 15 min Critical Values & Regions 15 min Type I and Type II Errors 15 min One-Tailed & Two-Tailed Tests 15 min Testing Means (Normal, Binomial, Poisson) 15 min Hypothesis Testing with Normal & Binomial 15 min Mixed Practice & Exam Prep 45 min
Module 18

13.1 Vectors

Vector operations, equations of lines, dot product, kinematics and eigenvalues.

8 lessons
Vector Operations 25 min Scalar (Dot) Product 25 min Vector Equation of a Line 15 min Cross Product & Area of Parallelogram 15 min Shortest Distance (Point to Line) 15 min Vector Kinematics in 2D/3D 15 min Angle Between Vectors & Lines 15 min Mixed Practice & Exam Prep 45 min
Module 19

13.2 Matrices

Matrix operations, determinants, inverses, transformations and eigenvalues.

8 lessons
Matrix Operations 25 min Determinants & Inverses 25 min Eigenvalues & Eigenvectors 15 min Diagonalisation 15 min Matrix Transformations (2D) 15 min Systems of Equations with Matrices 15 min Powers of Matrices 15 min Mixed Practice & Exam Prep 45 min
Module 20

13.3 Complex Numbers

Complex number forms, operations, De Moivre's theorem and geometric representations.

7 lessons
Complex Number Basics 25 min Polar & Exponential Form 30 min Operations with Complex Numbers 15 min Adding Sinusoidal Functions 15 min GDC Methods for Complex Numbers 15 min Geometric Interpretation of Complex Numbers 15 min Mixed Practice & Exam Prep 45 min
Module 21

13.4 Markov Chains & Transition Matrices

Transforming variables, CLT, Poisson distribution and Markov chains.

5 lessons
Markov Chains 30 min Transition Matrices 15 min Steady State & Long-term Probabilities 15 min Powers of Transition Matrices 15 min Mixed Practice & Exam Prep 45 min
Module 22

13.5 Statistics 2

Advanced hypothesis testing, confidence intervals and error analysis.

9 lessons
Linear Regression 30 min Data Collection & Validity 15 min Non-Linear Regression 15 min Spearman's Rank 15 min Confidence Intervals for Mean 15 min Linear Combinations of Random Variables 15 min Central Limit Theorem 15 min Unbiased Estimates 15 min Mixed Practice & Exam Prep 45 min
Module 23

13.6 Differential Equations

Separation of variables, Euler's method, slope fields and coupled systems.

8 lessons
First Order Differential Equations 30 min Euler's Method 25 min Slope Fields & Diagrams 15 min Euler's Method for Coupled Systems 15 min Phase Portraits & Equilibrium Points 15 min Second Order DEs 15 min Qualitative Analysis (Eigenvalue Method) 15 min Mixed Practice & Exam Prep 45 min