IB Mathematics:
Analysis & Approaches HL

Number and Algebra in IB Mathematics AA HL extends the SL content with complex numbers in Cartesian, polar, and exponential (Euler) form — including De Moivre’s theorem, nth roots of complex numbers, and conjugate roots of polynomial equations. Students also study proof by mathematical induction for sums, divisibility, and inequalities, and work with the binomial theorem for rational exponents. Partial fractions and the solution of systems of linear equations using matrices are also covered. This HL content is assessed in Paper 1, Paper 2, and the extended Paper 3.

Functions in IB Mathematics AA HL extends the SL course with rational functions including reciprocal and quotient forms, oblique asymptotes, and the behaviour of functions near discontinuities. Students work with the factor and remainder theorems for polynomials, sum and product of roots, and the fundamental theorem of algebra. Odd and even functions, self-inverse functions, and more advanced transformation work are also covered. AA HL Functions content appears across Paper 1 and Paper 2, and may feature in the extended Paper 3.

Geometry and Trigonometry in IB Mathematics AA HL extends the SL content with 3D vectors — including the dot product, cross product, vector equations of lines and planes, and the angles and distances between geometric objects in three dimensions. Students also work with more advanced trigonometric identities including compound angle, double angle, and sum-to-product formulae, and prove trigonometric results formally. The 3D vector geometry content is one of the most substantial HL-only areas and is examined across Paper 1 and Paper 2.

Statistics and Probability in IB Mathematics AA HL extends the SL content with Bayes’ theorem for conditional probability, the Poisson distribution, and a deeper treatment of continuous random variables including probability density functions and the calculation of mean, variance, and standard deviation analytically. Students also work with more formal hypothesis testing and confidence intervals. The HL-only statistical content is assessed in Paper 2 and may also appear in the extended Paper 3 examination.

Calculus in IB Mathematics AA HL is the most demanding topic in the course — extending AA SL into L’Hôpital’s rule for limits, Maclaurin series for standard functions and their applications, implicit differentiation, related rates, and integration by parts, by substitution, and using partial fractions. Students also study first- and second-order differential equations including separable equations and homogeneous equations. Calculus is the primary focus of the extended Paper 3 examination unique to AA HL, and is examined heavily across Paper 1 and Paper 2.