Number and Algebra

Complex numbers in Cartesian form and matrix algebra — HL extensions covering complex number operations, modulus-argument representation, powers and roots of complex numbers, matrix multiplication, determinants, inverses, and systems of equations solved by row reduction. These HL-only topics appear in AI HL Paper 1 and Paper 2, and complex number skills are also applicable in Paper 3 investigations.

Functions

Advanced modelling extending AI SL into logarithmic, power, and sinusoidal regression models using technology, and the interpretation of model parameters in sophisticated real-world contexts. AI HL Functions develops a deeper understanding of when and how to select the best mathematical model for a dataset — a critical skill for the Internal Assessment and the Paper 3 extended investigation.

Geometry and Trigonometry

Voronoi diagrams and discrete graph theory — Hamiltonian paths, Eulerian circuits, minimum spanning trees, and the Chinese postman and travelling salesman problems. Unique to AI HL, these discrete mathematics topics are directly relevant to computer science, logistics, and operations research, and are a frequent focus of the AI HL Paper 3 extended problem-solving investigation.

Statistics and Probability

Advanced hypothesis testing and probability distributions extending AI SL — covering the Poisson distribution, t-tests for means, non-parametric tests including Spearman’s rank correlation, Type I and Type II errors, and the power of a statistical test. These skills are central to AI HL Paper 2 and Paper 3 and directly applicable to the Internal Assessment investigation and analysis.

Calculus

Differential equations, Euler’s method for numerical solutions, and slope fields — extending AI SL into separable differential equations and their solutions in applied population, decay, and growth models. These techniques are assessed in Paper 2 and are a common focus of the AI HL Paper 3 extended investigation, which rewards clear mathematical modelling and communication of results.

Get Number and Algebra, Functions, Geometry and Trigonometry, Statistics and Probability, and Calculus — including all HL extensions in a single enrolment — and build complete coverage of the Applications & Interpretation HL syllabus without paying for each topic separately.

Enrol — All 5 Topics →