IB Maths AA HL revision notes: Complete course, PDF

Version 2.0, 17 October 2026 · 322 pages · PDF · CC BY-NC-ND 4.0

Chapters

1. 1.Sequences and series: arithmetic, geometric and financial applicationsSL 1.2, 1.3, 1.4, 1.8
2. 2.Exponents and logarithmsSL 1.1, 1.5, 1.7
3. 3.Proof: direct, by contradiction, by counterexample and by inductionSL 1.6, AHL 1.15
4. 4.Binomial theorem, counting principles and partial fractionsSL 1.9, AHL 1.10, 1.11
5. 5.Complex numbers: Cartesian, polar and Euler formsAHL 1.12, 1.13
6. 6.De Moivre's theorem, roots of complex numbers and polynomial equationsAHL 1.14
7. 7.Systems of linear equationsAHL 1.16
8. 8.Functions: domain, range, composite and inverse functionsSL 2.2, 2.5, AHL 2.14
9. 9.Straight lines, quadratic functions and the discriminantSL 2.1, 2.6, 2.7
10. 10.Graphs: key features, transformations and solving equations graphicallySL 2.3, 2.4, 2.10, 2.11
11. 11.Rational, exponential and logarithmic functionsSL 2.8, 2.9, AHL 2.13
12. 12.Polynomials: factor and remainder theorems, roots and their sums and productsAHL 2.12
13. 13.Inequalities and the modulus functionAHL 2.15, 2.16
14. 14.Triangles, three-dimensional geometry and applicationsSL 3.1, 3.2, 3.3
15. 15.Radians, the unit circle and trigonometric identitiesSL 3.4, 3.5, 3.6, AHL 3.9, 3.10, 3.11
16. 16.Trigonometric functions and equationsSL 3.7, 3.8
17. 17.Vectors: components, magnitude and the scalar productAHL 3.12, 3.13
18. 18.Lines in three dimensions: vector equations, intersections and skew linesAHL 3.14-3.15
19. 19.The vector product, planes and intersectionsAHL 3.16, 3.17, 3.18
20. 20.Data: sampling, presentation, centre and spreadSL 4.1, 4.2, 4.3
21. 21.Correlation and linear regressionSL 4.4, 4.10
22. 22.Probability: rules, conditional probability, independence and Bayes' theoremSL 4.5-4.6, AHL 4.13
23. 23.Discrete random variables and the binomial distributionSL 4.7, 4.8, AHL 4.14 (discrete)
24. 24.The normal distribution and standardisationSL 4.9, 4.12
25. 25.Continuous random variables and probability density functionsAHL 4.14 (continuous)
26. 26.Limits, continuity and the derivative from first principlesSL 5.1, AHL 5.12-5.13
27. 27.Differentiation rules and standard derivativesSL 5.3, 5.6, 5.7, AHL 5.15
28. 28.Tangents, normals, curve analysis and optimisationSL 5.2, 5.4, 5.7, 5.8
29. 29.Integration: antiderivatives and standard integralsSL 5.5, 5.10, AHL 5.15
30. 30.Definite integrals, areas, volumes of revolution and kinematicsSL 5.9, 5.11, AHL 5.17
31. 31.Implicit differentiation, related rates and optimisationAHL 5.14
32. 32.Integration by substitution and by partsAHL 5.16
33. 33.Differential equations and Maclaurin seriesAHL 5.18, 5.19