Online Textbooks for Analysis & Approaches and Applications & Interpretation
Concepts, proofs, and analytical thinking. Ideal for students pursuing mathematics, physics, or engineering.
Sequences, series, binomial theorem, proof by induction
Domain/range, transformations, inverse, composite, modelling
Radians, unit circle, identities, sine/cosine rules, 3D trig
Descriptive stats, distributions, regression, hypothesis testing
Differentiation, integration, areas, optimization, kinematics
Cartesian & polar form, de Moivre, roots of unity
Partial fractions, proof, systems of equations, row reduction
Scalar/vector products, lines & planes, intersections
Inverse trig, compound/double angle, general solutions
Combinations/permutations, conditional, discrete distributions
Limits, L'Hôpital, implicit diff, Maclaurin series, DEs
Real-world applications and technology-integrated approaches. Ideal for social sciences, business, and life sciences.
Number systems, finance, loans/annuities, sequences, GDC use
Linear, quadratic, exponential, logistic, piecewise modelling
2D/3D measurement, sine/cosine rules, Voronoi diagrams
Bivariate data, regression, normal/binomial distributions
Differentiation, optimisation, integration, trapezoidal rule
Graph theory, adjacency matrices, minimum spanning trees
Fourier series (intro), smoothing, transformation of curves
Markov chains, transition matrices, steady-state, χ² test
Related rates, implicit differentiation, slope fields, Euler's method
Complete guide to writing an IB Mathematics Extended Essay — from research question to final submission.
Research question selection, investigation methodology, assessment criteria, writing structure, common mistakes
Pure mathematics, statistics, applied modelling, number theory, geometry — with example research questions
Criteria A–E explained with examples, scoring strategies, common mistakes to avoid
MathHub's IB textbooks are organized to follow the official IB Mathematics curriculum guide. AA students should focus on the Number & Algebra, Functions, Geometry & Trigonometry, and Calculus chapters, with HL-only topics (complex numbers, further calculus, proof by induction) clearly marked. AI students will find the Statistics & Probability and modelling chapters most relevant, alongside the applied calculus sections.
Each chapter covers the full depth required for IB exams, including Paper 1 (no calculator) and Paper 2 (calculator allowed) techniques. We include exam-style worked examples at the difficulty level of actual IB papers, with step-by-step solutions that mirror the mark scheme approach examiners expect.
For the Internal Assessment (IA), our blog features guides on choosing topics, structuring your exploration, and meeting the assessment criteria. For the Extended Essay (EE) in mathematics, we provide topic suggestions with links to relevant mathematical theory covered in our textbooks.
Study guides, IA tips & YouTube picks for AA and AI
IB-style problems with instant feedback in our Question Bank.
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