IB Maths AA Syllabus: What SL and HL Cover

The syllabus is the list of everything the exam can ask. The IB's own guide is long, and it is written for teachers, not for the person sitting the exam. This page gives you the same course in plain words: what each topic covers at SL, what HL adds, and how big the step up really is. Use it to see what is coming, or to check what you have not learned yet.

In my lessons, the part students expect to be easy and then find hard is the unit circle, in trigonometry. There is no calculator on Paper 1, and exact values and trigonometric equations all depend on it.

Is this the syllabus you are on?

Almost certainly yes. The current course was first examined in 2021, and its last exams are in November 2028. Then a new course takes over:

The IB says the new course has less content and adds none. Marks drop too. SL Papers 1 and 2 go from 80 to 75 marks, and HL Papers 1 and 2 from 110 to 100. HL Paper 3 goes from 55 marks to 50, and from 1 hour 15 minutes to 1 hour. The IB launches the new course in February 2027, and I will update this page then.

The five topics, and where HL's extra hours go

These are the teaching hours the IB suggests. Your school may spread them differently, but they show where the weight of the course is.

Three things stand out:

• Three topics roughly double. Number and algebra, geometry and trigonometry, and calculus take 73 of the 90 extra hours.
• Statistics barely grows. It is the second biggest topic at SL and the second smallest at HL.
• HL is SL plus more. Everything below under SL is on the HL course too.

Hours show teaching time. They do not tell you how many marks a topic will get on a paper. The lists below give the main content of each topic, not every line of the IB guide.

Topic 1: Number and algebra

SL: arithmetic and geometric sequences and series, compound interest and depreciation, exponents and logarithms, the binomial theorem, and simple proofs.

HL adds: counting with permutations and combinations, the binomial theorem with fractional and negative powers, partial fractions, complex numbers (including De Moivre's theorem), proof by induction and by contradiction, and systems of up to three linear equations.

The step up: SL asks for the sum to infinity of 12 + 6 + 3 + … (it is 24). HL asks you to work out (1 + i)⁸ with no calculator (it is 16).

Topic 2: Functions

SL: straight lines, domain and range, composite and inverse functions, quadratics, simple rational functions, exponential and logarithmic functions, and transforming graphs.

HL adds: polynomials with the factor and remainder theorems, the sum and product of roots, harder rational functions, odd and even functions, inverses on a restricted domain, modulus and reciprocal graphs, and solving inequalities.

The step up: SL gives you f(x) = 2x + 1 and g(x) = x², and asks for f(g(3)) (it is 19). HL asks for the remainder when x³ − 2x + 5 is divided by x − 2 (it is 9).

Topic 3: Geometry and trigonometry

SL: volume and surface area of 3D solids, the sine and cosine rules, radians, arcs and sectors, the unit circle, the double angle identities for sine and cosine, trigonometric graphs, and trigonometric equations.

HL adds: secant, cosecant and cotangent, inverse trigonometric functions, compound angle identities, and all of vectors: scalar and vector products, lines and planes in 3D, and where they meet.

Vectors are the main reason this topic doubles. In AA they are HL only, so a student who moves from SL to HL has all of them to catch up on.

The step up: SL asks you to solve 2 sin x = 1 for 0 ≤ x ≤ 2π (x = π/6 or 5π/6). HL asks where the line through (1, 2, 3) with direction (1, 1, 1) meets the plane x + y + z = 9 (at (2, 3, 4)).

Topic 4: Statistics and probability

SL: sampling, averages and spread, box plots and cumulative frequency, correlation and regression, Venn and tree diagrams, conditional probability, discrete random variables, and the binomial and normal distributions.

HL adds: Bayes' theorem for up to three events, continuous random variables and their density functions, and the mean and variance of random variables.

This is a small addition, but it depends on calculus. A continuous random variable is handled with integrals, so a weak spot in Topic 5 shows up here too.

The step up: SL gives you X ~ B(10, 0.3) and asks for P(X = 2) (it is 0.233). HL gives you the density f(x) = 3x²/8 for 0 ≤ x ≤ 2 and asks for E(X) (it is 1.5).

Topic 5: Calculus

SL: the idea of a limit, derivatives of powers, sine, cosine, e^x and ln x, the chain, product and quotient rules, tangents and normals, stationary points, optimisation, kinematics, and areas with integrals.

HL adds: differentiating from first principles, implicit differentiation, related rates, more derivatives (including inverse trigonometric functions), L'Hôpital's rule, integration by substitution and by parts, volumes of revolution, first order differential equations (including Euler's method), and Maclaurin series.

The step up: SL expects you to spot that the integral of 2xe^x² from 0 to 1 is e − 1, by reversing the chain rule. HL expects you to integrate x cos x by parts, which gives x sin x + cos x + C.

The part of calculus that costs my students the most marks is the differentiation rules, mainly the chain rule and the quotient rule. They come back in all the exercises, so one weak rule loses marks across the whole topic. For example, the derivative of sin(2x) is 2cos(2x), not cos(2x). Both rules are SL content, so this matters at both levels.

The toolkit and your IA

The last 30 hours are the same at both levels. They are for problem solving, modelling and your exploration, which is the IA. The IA is 20% of your grade at SL and at HL. How the 20 IA marks are split explains how it is marked, and AA IA topic ideas helps you choose a topic.

What is not on the AA syllabus

Not every IB maths topic you find online is on AA. These belong to Maths AI, so you will not need them for your AA exams:

• The Poisson distribution
• Hypothesis tests, such as chi-squared tests and t-tests
• Matrices as a topic of their own
• Graph theory

If you are still choosing between the two courses, read IB Math AA vs AI.

How the syllabus reaches the exam

Any paper can test any topic. Paper 1 has no calculator and Paper 2 needs one. Each lasts 1 hour 30 minutes at SL and 2 hours at HL. HL also has Paper 3, which is two long problem-solving questions in 1 hour 15 minutes, with a calculator.

For how to prepare, see the AA HL study tips and the AA SL common mistakes.

How to use this syllabus

• Before your mocks: go through the five topics and mark each item as secure, shaky or not yet taught. Work on the shaky ones first.
• If you are thinking of dropping to SL: the "HL adds" lists are what you would stop studying. Read should I drop from HL to SL? before you decide.
• If you are applying to Bocconi: its test sits at about SL level. The Bocconi test guide has the official list.

In a first lesson with a new AA student, I do two things. I run an analysis of where they stand, and I have an open conversation about any specific weakness they already know about.

Frequently asked questions

How many topics are in IB Maths AA?

Five, at both SL and HL: number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. There are also 30 hours for the toolkit and the exploration, which is the IA.

What is the difference between AA SL and AA HL?

HL has 240 teaching hours and SL has 150. Everything in SL is also in HL. HL adds content such as complex numbers, vectors, proof by induction and more calculus, and it has a third exam paper.

Are vectors in AA SL?

No. On the current syllabus, vectors in AA are HL only. If you move from SL to HL, you will have all of them to catch up on.

Is the IB Maths AA syllabus changing?

Yes. The current course has its last exams in November 2028. A new course starts in August 2027, with first exams in May 2029. The IB says it has less content and adds none.

Are Poisson and hypothesis testing in IB Maths AA?

No. The Poisson distribution and hypothesis tests belong to Maths AI, not AA.