BetterMath Notes

The notes

Complete course notes for IB Mathematics: Analysis and Approaches HL, to read, download and use in class.

3rd edition
BetterMath — Mathematics: Analysis and Approaches HL
All seventeen chapters: notes, worked examples and practice · Third edition · September 2026 · 668 pages · PDF, 2.6 MB
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Notes that explain why

Each chapter builds the topic in order, starting from the reason it exists. Formulas from the IB booklet are marked, and every idea comes with a fully worked example.

Your Turn, every section

A practice block closes each section, so you check an idea while it is fresh rather than at the end of the chapter.

Exam-style problems

Chapters end with Paper 1 and Paper 2 style questions, then challenge investigations for anyone who wants to go further.

Look inside

The first pages of Chapter 2

The chapter opens with why the topic matters, then builds each idea with definitions, worked examples and a Your Turn block. Click a page to read the whole chapter.

Chapters

One chapter at a time

Each chapter is its own PDF, with the syllabus points it covers. Higher Level content is marked throughout, so a Standard Level reader can see what to skip.

Syllabus map
1Exponents & LogarithmsNumber & Algebra · 1.1, 1.5, 1.7 · 32 ppPDF
2Sequences & SeriesNumber & Algebra · 1.2–1.4, 1.8–1.10 · 46 ppPDF
3ProofsNumber & Algebra · 1.6, 1.15 · 29 ppPDF
4Lines & QuadraticsFunctions · 1.16, 2.1–2.4, 2.6, 2.7 · 39 ppPDF
5Functions & GraphsFunctions · 2.5, 2.8–2.11, 2.13–2.16 · 56 ppPDF
6PolynomialsFunctions · 1.11, 2.12 · 34 ppPDF
7Shapes & MeasuresGeometry & Trigonometry · 3.1–3.4 · 32 ppPDF
8TrigonometryGeometry & Trigonometry · 3.5–3.11 · 40 ppPDF
9VectorsGeometry & Trigonometry · 3.12–3.18 · 41 ppPDF
10StatisticsStatistics & Probability · 4.1–4.4, 4.10 · 42 ppPDF
11ProbabilityStatistics & Probability · 4.5, 4.6, 4.11, 4.13 · 38 ppPDF
12Probability DistributionsStatistics & Probability · 4.7–4.9, 4.12, 4.14 · 35 ppPDF
13Limits & DerivativesCalculus · 5.1–5.4, 5.6–5.8, 5.12, 5.13, 5.15 · 39 ppPDF
14Derivative ApplicationsCalculus · 5.8, 5.9, 5.14 · 36 ppPDF
15Integral CalculusCalculus · 5.5, 5.9–5.11, 5.15–5.17 · 45 ppPDF
16Differential EquationsCalculus · 5.18, 5.19 · 32 ppPDF
17Complex NumbersNumber & Algebra · 1.12–1.14 · 31 ppPDF

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Notes this size will contain errors, and the ones a reader finds are worth more than the ones I go looking for. If a line does not follow, an answer looks wrong, or a passage is hard to read, please say so and I will fix it in the next release.

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