IB Maths syllabus topics: all 94 sub-topic guides
Deep-dive revision pages for every syllabus sub-topic across all four DP maths courses. Skim the list to find what you're stuck on.
Exam-style questions by topic: IB Maths AA SLIB Maths AI SLIB Maths AA HLIB Maths AI HL
SL AI
Number and Algebra
- Scientific notation and estimation
- Arithmetic sequences and series
- Geometric sequences and compound interest
- Financial maths — loans, mortgages and CG50
- Exponents and logarithms in real-world models
Functions
- Linear functions and modelling
- Quadratic functions — vertex, roots, and applications
- Exponential growth and decay models
- Sinusoidal models for periodic data
- Piecewise functions and modelling
Geometry and Trigonometry
- 3D geometry — volume, surface area, and packaging
- Sine rule vs cosine rule — the decision tree
- Voronoi diagrams — nearest-neighbour problems
- 3D trigonometry — angle of elevation and depression
- Bearings and navigation problems
Statistics and Probability
- Chi-squared test — goodness of fit and independence
- Correlation, regression, and Pearson's r
- Normal distribution — CG50 and TI-Nspire keystrokes
- Conditional probability with tree diagrams
- Expected value and fair games
Calculus
SL AA
Number and Algebra
- Arithmetic and geometric sequences
- Binomial expansion for positive integer n
- Exponent and logarithm laws
- Surds, rationalising, and exact answers
- Quadratics, discriminant, and the nature of roots
Functions
- Domain, range, and function composition
- Function transformations — translations, stretches, reflections
- Inverse functions and one-to-one mappings
- Exponential and logarithmic functions
- Rational functions and asymptotes
Geometry and Trigonometry
- The unit circle — exact values and identities
- Trigonometric identities — Pythagorean and double-angle
- Solving trigonometric equations in a given interval
- Sine rule, cosine rule, and area of a triangle
Statistics and Probability
- Mean, median, mode, and IQR
- Probability — Venn diagrams and independence
- Binomial distribution — B(n,p)
- Normal distribution and z-scores
Calculus
HL AI
Number and Algebra
- Matrices — multiplication, inverse, and determinant
- Systems of linear equations and Gaussian elimination
- Complex numbers in Cartesian and polar form
- Sequences, series, and the sum to infinity
- Exponential models for real-world decay
Functions
- Modelling with functions — piecewise, exponential, logistic
- Graph theory — adjacency matrices and walks
- Eulerian and Hamiltonian circuits
- Minimum spanning trees — Kruskal and Prim
- The Chinese Postman problem
Geometry and Trigonometry
- Voronoi diagrams — construction and applications
- 3D vectors — dot product and cross product
- Vector equations of lines in 2D and 3D
- Sinusoidal modelling with seasonal data
Statistics and Probability
- Chi-squared test and confidence intervals
- Linear regression and residual analysis
- Normal and Poisson distributions
- Hypothesis testing — t-test and chi-squared
- Markov chains and transition matrices
Calculus
HL AA
Number and Algebra
- Proof by induction — the 3-step method
- Binomial theorem for rational and negative exponents
- Complex numbers — Cartesian, polar, and Euler forms
- De Moivre's theorem and roots of unity
- Systems of equations and partial fractions
Functions
- Rational functions — asymptotes, holes, and sketches
- Inequalities — rational and modulus
- Polynomial division and the factor theorem
- Logarithm laws and change of base
- Sequences, series, and induction proofs
Geometry and Trigonometry
- Compound and double-angle formulas
- Trigonometric equations — HL identities in a finite interval
- 3D vectors — dot product, cross product, and applications
- Lines and planes in 3D — intersections and distances
- Vector proofs and geometric arguments
Statistics and Probability
- Conditional probability and Bayes' theorem
- Discrete probability distributions — expectation and variance
- Normal distribution and standardisation
- Binomial distribution — mean, variance and unknown parameters