IB Diploma Programme

Mathematics

Analysis & Approaches

Higher Level

Success in HL Math isn't about finding easy paths, but clear ones. Complete course notes, free to read and download.

Download the notes Answers & teacher pack

Third edition · September 2026 · 658 pages · PDF, 2.5 MB

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Cover of BetterMath: Mathematics, Analysis & Approaches, Higher Level. Third edition, September 2026.

3rd edition

17Chapters

658Pages

83Syllabus points

FreeTo download

The book

Intuitive. Clear. Uncompromising.

These notes skip shortcuts and artificial simplifications to focus on genuine clarity. Mastering AA HL takes dedication and practice; this book is here to support that effort, so you can give your whole attention to the mathematics.

Free

BetterMath — Mathematics: Analysis and Approaches HL

All seventeen chapters: notes, worked examples and practice · 658 pages · PDF, 2.5 MB

Download the notes

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.

What's inside

1Exponents & LogarithmsNumber & Algebra
2Sequences & SeriesNumber & Algebra
3ProofsNumber & Algebra
4Lines & QuadraticsFunctions
5Functions & GraphsFunctions
6PolynomialsFunctions
7Shapes & MeasuresGeometry & Trigonometry
8TrigonometryGeometry & Trigonometry
9VectorsGeometry & Trigonometry
10StatisticsStatistics & Probability
11ProbabilityStatistics & Probability
12Probability DistributionsStatistics & Probability
13Limits & DerivativesCalculus
14Derivative ApplicationsCalculus
15Integral CalculusCalculus
16Differential EquationsCalculus
17Complex NumbersNumber & Algebra

Higher Level content is marked throughout, so a Standard Level reader can see what to skip.

Answers & teacher resources

Check your work, or teach with it

These are free too. Tell me a little about yourself and the downloads open straight away. It helps me see who uses the notes, and where to take them next.

For everyone

Answers

Answers bookletFinal answers to every question in all 17 chapters · 31 pages

For teachers only

Teacher pack · Chapters 1–2

Markschemes, Chapters 1 and 2One PDF, full worked solutions with M and A marks · 39 pages
Formative quizzesA quiz for each chapter, each with its markscheme
Lesson slidesBoard slides, slides with solutions, and teacher cues for each chapter

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About the author

Hasan Khan

Hasan Khan has taught IB Mathematics AA HL for over ten years, is an IB examiner, and has worked as a national curriculum developer. He holds an M.Sc. in Particle Physics from the University of Jyväskylä, Finland, and a Postgraduate Diploma in Education, and has completed teacher training in educational innovation with CERN, ESA and Wolfram.

Found a mistake?

Tell me where it is

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.

Using these

These notes are free to read and download for your own study. For anything else — printing sets for a class, sharing copies, posting them elsewhere, translating them, or any commercial use — please write to me first. I usually say yes, and I like knowing where they end up.
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