IB Math HL

The Additional Higher Level syllabus of Analysis & Approaches, taught code by code — every lesson is one official AHL subtopic (AHL 1.10, AHL 1.11, …), pitched at genuine HL depth: proof by induction and contradiction, complex numbers to De Moivre and roots, and worked examples marked the way HL examiners mark — method, accuracy, and reasoning.

HL = SL + these extension codes. The shared foundation is the complete SL course — an HL student works both. English-only, like the real exam. Topics open in syllabus order.

1. 01Number & Algebra (AHL)Permutations and the extended binomial theorem, partial fractions, complex numbers from Cartesian to Euler form, De Moivre with powers and roots, proof by induction and contradiction, and 3×3 systems — AHL 1.10 to 1.16.Start
2. Premium02Functions (AHL)Factor and remainder theorems, sums and products of roots, rational functions with oblique asymptotes, self-inverse and even/odd structure, modulus equations and inequalities, and the |f|, 1/f, f(|x|) graph family — AHL 2.12 to 2.16.Start
3. Premium03Geometry & Trigonometry (AHL)Reciprocal and inverse trig, compound angles, and the whole vector toolkit: scalar and vector products, lines and planes in space, intersections and angles — AHL 3.9 to 3.18.Start
4. Premium04Statistics & Probability (AHL)Bayes' theorem, and continuous random variables with probability density functions — mode, median, mean and variance from integrals — AHL 4.13 to 4.14.Start
5. Premium05Calculus (AHL)First principles and l'Hôpital, implicit differentiation and related rates, the full derivative library, integration by substitution and parts, volumes of revolution, differential equations, and Maclaurin series — AHL 5.12 to 5.19.Start