Version 1.0, 17 October 2026 · 329 pages · PDF · CC BY-NC-ND 4.0
Chapters
- 1.Standard form, rounding, bounds and percentage errorSL 1.1, 1.6
- 2.Arithmetic and geometric sequences and seriesSL 1.2, 1.3, AHL 1.11
- 3.Financial mathematics: compound interest, depreciation, loans and annuitiesSL 1.4, 1.7
- 4.Exponents, logarithms and solving equations with technologySL 1.5, 1.8, AHL 1.9, 1.10
- 5.Complex numbers: Cartesian, polar and Euler forms and applicationsAHL 1.12, 1.13
- 6.Matrices: operations, determinants, inverses and systems of equationsAHL 1.14
- 7.Eigenvalues, eigenvectors and powers of matricesAHL 1.15
- 8.Functions, straight lines, domain, range and graphsSL 2.1, 2.2, 2.3, 2.4
- 9.Modelling with functions: linear, quadratic, exponential, variation, cubic and sinusoidalSL 2.5, 2.6
- 10.Composite and inverse functions and transformations of graphsAHL 2.7, 2.8
- 11.Models at HL: exponential, logarithmic, logistic and piecewise models; log-log and semi-log graphsAHL 2.9, 2.10
- 12.Triangles, three-dimensional geometry and applicationsSL 3.1, 3.2, 3.3
- 13.Circles, perpendicular bisectors and Voronoi diagramsSL 3.4, 3.5, 3.6
- 14.Radians, the unit circle, trigonometric identities and equationsAHL 3.7, 3.8
- 15.Matrices as geometric transformationsAHL 3.9
- 16.Vectors: components, lines, kinematics, scalar and vector productsAHL 3.10, 3.11, 3.12, 3.13
- 17.Graph theory: graphs, adjacency matrices and walksAHL 3.14
- 18.Trees and cycles: Eulerian and Hamiltonian graphs, minimum spanning treesAHL 3.15
- 19.The Chinese postman and travelling salesman problemsAHL 3.16
- 20.Data: sampling, presentation, centre and spreadSL 4.1, 4.2, 4.3
- 21.Correlation and regression: Pearson, Spearman and non-linear modelsSL 4.4, 4.10, AHL 4.13
- 22.Probability: rules, diagrams, conditional probability and independenceSL 4.5, 4.6
- 23.Discrete random variables: binomial and Poisson distributionsSL 4.7, 4.8, AHL 4.17
- 24.The normal distributionSL 4.9
- 25.Hypothesis tests: chi-squared and t-tests; designing a studySL 4.11, AHL 4.12
- 26.Linear combinations of random variables, estimators, the central limit theorem and confidence intervalsAHL 4.14, 4.15, 4.16
- 27.Hypothesis tests at HL: means, proportions, Poisson means, correlation, and type I and II errorsAHL 4.18
- 28.Markov chains and transition matricesAHL 4.19
- 29.Derivatives: gradients, polynomials, tangents and normalsSL 5.1, 5.2, 5.3, 5.4
- 30.Integration of polynomials, areas and the trapezoidal ruleSL 5.5, 5.8
- 31.Local maxima and minima and optimisationSL 5.6, 5.7
- 32.Differentiation at HL: standard derivatives, chain, product and quotient rules, related rates and the second derivativeAHL 5.9, 5.10
- 33.Integration at HL: standard integrals, areas, volumes of revolution and kinematicsAHL 5.11, 5.12, 5.13
- 34.Differential equations: setting up, separating variables, slope fields and Euler's methodAHL 5.14, 5.15, 5.16
- 35.Coupled linear systems, phase portraits and second-order differential equationsAHL 5.17, 5.18
Versions and corrections
Version 1.0, 17 October 2026: first edition, the complete course in 35 chapters with figures and a one-page summary per chapter. Every chapter checked blind by a second reader and reviewed line by line before release.
Found a mistake, however small? Write to pietro@pietromeloni.com. It gets fixed in the next version, and this page says what changed.
How to use them
Read a chapter before the worksheet on the same syllabus points, then do the worksheet without the notes. In the last week before the exam, use only the one-page summaries at the end of each chapter.
The formulas table in every chapter says what is in the formula booklet and what is not: in the exam you have the booklet, so the time goes into the second column.
Frequently asked questions
Which version is current?
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Version 1.0, published 17 October 2026. The version is printed on the cover and on page 2 of the PDF. If yours is older, download this one: corrections are listed below.
Can I share it with my class?
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Yes, that is what it is for. The licence is CC BY-NC-ND 4.0: share it unchanged and not for sale. Teachers may print it and give it to their classes. Please keep the file name and page 2, which carry the version.
Does it cover the SL course too?
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The HL volume contains the SL content as well; the sections that are HL only are marked AHL in the chapter headings. A separate SL edition, with those sections removed, follows once the HL volume is complete.
Is it an official IB document?
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No. It is written by Pietro Meloni and is not endorsed by or affiliated with the International Baccalaureate Organization. No IB examination material is reproduced: every example is original.