The four IB Maths courses: SL AA, SL AI, HL AA and HL AI
IB Diploma maths comes in two courses, Analysis and Approaches (AA) and Applications and Interpretation (AI), and each is offered at Standard Level (SL) and Higher Level (HL). This page sets out what each one covers, how it is examined, and where to start revising it on this site. Every course has its own topic list, practice questions, notes and mock papers here.
AA or AI, SL or HL: the short version
- AA leans on algebra, proof and calculus by hand. One of its papers (Paper 1) is taken without a calculator.
- AI leans on modelling, statistics and using technology well. Every AI paper needs a graphic display calculator (GDC).
- SL is 150 teaching hours and two exam papers. HL is 240 hours, more topics and a third paper.
- Every course has the same internal assessment: the mathematical exploration, worth 20% of the grade.
Unsure which suits you? IB Maths AI vs AA compares the two courses topic by topic, and IB Maths HL vs SL covers the jump in level. Universities set their own entry requirements, so check the course pages of the places you are thinking of.
Standard Level: Applications and Interpretation
Maths for describing real situations: sequences and financial maths, linear, quadratic, exponential and sinusoidal models, right-angled and non-right-angled trigonometry, Voronoi diagrams, statistics from sampling to the chi-squared test, and an introduction to differential and integral calculus.
- Paper 1 (short questions) and Paper 2 (longer questions): 1 hour 30 minutes each, 40% each, GDC on both
- Typical question: fit a model to data on the GDC, then interpret what it predicts and where it breaks down
Standard Level: Analysis and Approaches
Maths built on algebra: sequences and the binomial theorem, functions and their graphs, quadratics, exponentials and logarithms, trigonometry in radians, probability and the normal distribution, and calculus, including kinematics and areas under curves.
- Paper 1 without a calculator and Paper 2 with a GDC: 1 hour 30 minutes each, 40% each
- Typical question: differentiate by hand, find a stationary point exactly, then show it is a maximum
Higher Level: Applications and Interpretation
Everything in SL AI, plus matrices and eigenvalues, Markov chains, complex numbers, vectors and kinematics, graph theory (spanning trees, the Chinese postman and travelling salesman problems), more statistical tests, and differential equations with slope fields, Euler's method and phase portraits.
- Papers 1 and 2: 2 hours each, 30% each; Paper 3: 1 hour 15 minutes, 20%, two extended problems; GDC on every paper
- Typical Paper 3 problem: build a model step by step from a context, then test and improve it
Higher Level: Analysis and Approaches
Everything in SL AA, plus proof by induction and contradiction, complex numbers and De Moivre's theorem, vectors, lines and planes in 3D, further functions and inequalities, Bayes' theorem and continuous random variables, and further calculus: integration by parts, differential equations and Maclaurin series.
- Paper 1 without a calculator; Papers 2 and 3 with a GDC. Papers 1 and 2: 2 hours each, 30% each; Paper 3: 1 hour 15 minutes, 20%
- Typical Paper 3 problem: a long, guided investigation of one idea, with the earlier parts leading to a general result
Where to go next
- Starting the course: the PreIB bridging programme takes you from IGCSE or MYP maths to the start of your Diploma course.
- Revising a topic: open your course page above and pick the topic. Each topic has notes, worked examples and practice questions.
- Before a mock or the final exam: the free practice exams and IB Maths past papers (the official specimens, the IB store and our own practice papers).
- The exploration: the IA guide takes you from choosing a topic to the five marking criteria.
Parents: the Parent Playbook explains the courses and the exams in plain English. Choosing a course before the Diploma? See the PreIB course review.