To prepare for IB Math Analysis and Approaches, start from whether you are sitting SL or HL. The two levels are one syllabus: items numbered SL are studied by everyone, items numbered AHL only by Higher Level students, and that line decides what is worth your time. Build the syllabus topic by topic alongside your class, work past papers with their mark schemes for command terms and timing, and plan the exploration separately.
Brilliant covers most of the functions, trigonometry, statistics and probability on the Standard Level syllabus, and a good share of the calculus. Higher Level adds a second body of content on top, and Brilliant meets that in patches: strong on complex numbers and vectors, absent on the integration techniques and the proof methods. What it never does is rehearse the assessment — no papers, no mark schemes, no exploration.
One thing to settle first: Analysis and Approaches is one of the IB’s two Diploma Programme mathematics courses. Applications and Interpretation is the other, and it is not mapped here — if your subject line says AI rather than AA, this page is not about your course.
SL or HL — which half applies to you?
The two levels are one syllabus, not two. HL students study every Standard Level item and then further higher level content in each of the five topics — number and algebra, functions, geometry and trigonometry, statistics and probability, calculus. The syllabus makes the line visible: items numbered SL are studied by everyone, items numbered AHL only by HL students. That line decides which Brilliant courses are worth your time.
Item by item, the maps are on two pages: IB Math AA SL coverage for the shared syllabus, and IB Math AA HL coverage, which repeats those items and lists the higher level ones separately.
A concrete instance of the line, from the calculus topic: the derivative from first principles — f′(x) as the limit of a difference quotient — is AHL content. An SL student meets the derivative as a gradient function and as a rate of change and stops there. So the whole limit-definition run in Derivatives, from Difference Quotients to The Limit Definition of Derivative, is HL work, and nothing the SL syllabus asks for.
What Brilliant teaches from the shared syllabus
Functions is the strongest topic. Domain, range, notation and composition are in Introduction to Functions, with inverses at Inverting a Function. The quadratic in all three forms — factored, vertex, and the formula with its discriminant — runs through Quadratics. Rational functions and asymptotes are in Equations and Curves at Reciprocal Power Functions, and the exponential and logarithmic pair across Exponential Functions and Logarithms, log laws and change of base included, at Taking Logs of Both Sides.
Trigonometry is nearly as complete. Trigonometric Functions builds radians and the unit circle from arc length, covers The Pythagorean Identity, amplitude and period in The Sine Graph, and analytic solving in Equations in cos(θ) and sin(θ). Polar Coordinate Plane adds Arcs and Arc Length for sectors.
Statistics and probability is spread across four courses: centre, spread and outliers in Everyday Statistics; sample spaces, Venn Diagrams and expected value in Probability and Chance; conditional probability and independence in Probability in Data; correlation and regression in Regression and Exploring Data Visually.
Calculus and number are partial but real. Calculus covers the derivative as a rate of change, the power, chain, product and quotient rules, optimisation, and definite integrals as area, and reaches the sum of an infinite convergent geometric series in Sequences and Limits. Two newer courses now sit alongside it. Derivatives builds average rate of change into the instantaneous one at Local Linearity, writes the equation of a tangent at The Tangent Line, and reads increasing and decreasing behaviour off the sign of the derivative at Net Change. Limits opens on sequences, which is where the syllabus’s arithmetic and geometric sequences get their first real home, at Arithmetic Sequences. Both courses are still being written — Limits has three of fourteen levels built and Derivatives four of eleven — so what the coverage pages show is the whole of what they currently teach. Scientific notation and the exponent laws are in Exponents and Radicals; the forms of a straight line are in Linear Relationships.
What HL adds, and where Brilliant meets it
Complex Numbers is an HL course and only an HL course. Every syllabus item its 50 lessons reach is higher level content — Cartesian form, modulus and argument in The Square Root of -1, polar and Euler form in Transforming Points, De Moivre’s theorem and roots in Raising to any Power. An SL student can skip it entirely; an HL student gets one of the best matches in the catalog.
Vectors covers the vector groundwork: components and addition in Vector Components, and the scalar product with the angle between two vectors in General Dot Products.
The rest sits in courses you are already using — the factor and remainder theorems in Polynomials at Roots from Factored Form, odd and even functions in Even and Odd Powers, the reciprocal and inverse trigonometric ratios at Inverse Cosine, continuity in Function Limits and the derivative from first principles in Derivatives at The Limit Definition of Derivative, Maclaurin series in Sine and Cosine. And Bayes’ theorem, which HL states as a topic of its own and few other syllabi name at all: it is taught in Combining Probabilities.
What you will have to get elsewhere
Both levels. Sequences and series are still thin, but no longer a hole: Limits opens on arithmetic and geometric sequences and on getting from a recursive rule to an nth term formula, and the sum of an infinite geometric series is in Calculus. What is missing is the sum of the first n terms for either kind of sequence, and sigma notation. Also the binomial theorem, Pascal’s triangle and nCr; deductive proof; three-dimensional geometry, meaning distance in space and the volume and surface area of pyramids, cones and spheres; the sine and cosine rules for non-right triangles, with angles of elevation and depression; the binomial and normal distributions, z-values and inverse normal calculations; kinematics; and indefinite integrals beyond powers of x, including substitution.
HL only, on top of that. Vector equations of lines and planes, skew lines and the vector product. Integration by substitution and by parts, volumes of revolution, differential equations. Implicit differentiation and related rates. L’Hôpital’s rule. Proof by induction and by contradiction. Partial fractions, permutations and combinations, modulus graphs, compound angle identities.
Your textbook covers all of these — bring it to the topics above rather than replacing your course with Brilliant.
Which courses, and in what order?
| Course | Level | What it gets you | Start here |
|---|---|---|---|
| Introduction to Functions (68 lessons) | SL & HL | Domain, range, notation, composition, inverses, transformations | Inverting a Function |
| Quadratics (69) | SL & HL | Factored and vertex form, completing the square, the discriminant | Completing Any Square |
| Equations and Curves (61) | SL & HL | Rational functions, asymptotes, multi-step transformations | Domain and Range of Hyperbolas |
| Exponential Functions (34) | SL & HL | Exponential models, growth and decay, exponential against linear growth | Finding the Base and Coefficient |
| Logarithms (29) | SL & HL | e^x and ln x, the log laws, solving exponential equations | The Product Rule |
| Trigonometric Functions (62) | SL & HL | Radians, the unit circle, identities, amplitude and period | The Unit Circle |
| Polynomials (52) | SL & HL | Roots, sign regions, and the HL factor and remainder theorems | Roots from Factored Form |
| Calculus (42) | SL & HL | Limits, the derivative as a rate of change, the rules, optimisation | Rate Of Change |
| Limits (20) | SL & HL | Arithmetic and geometric sequences, convergence, the limit idea | Arithmetic Sequences |
| Derivatives (23) | SL & HL | Rate of change into the derivative, tangents, first principles at HL | The Tangent Line |
| Complex Numbers (50) | HL | Cartesian, polar and Euler form, conjugates, De Moivre, roots | Both Square Roots |
| Vectors (39) | HL | Components, addition, the scalar product, the angle between vectors | General Dot Products |
Work the statistics topic alongside, in Everyday Statistics at Quartiles and Probability and Chance at Probability and Value; both sit well below Diploma level and go quickly.
Following a class? Ignore the order and open the course matching this week’s topic — lessons are short and stand alone. Revising? Work the topics your past papers keep flagging. Short on time in HL? Complex Numbers repays the hours fastest.
Two things no amount of Brilliant covers
The exploration. The internal assessment is an individual piece of mathematical writing worth 20% of your final grade at both levels, judged on criteria — presentation, mathematical communication, personal engagement, reflection, use of mathematics — that no problem set touches. Choosing a topic and structuring the write-up are a conversation with your teacher.
The graphic display calculator. Several syllabus items are written around it: sketching a graph from screen to paper, finding key features with graphing technology, solving equations that have no analytic approach, normal probability calculations. Paper 2 assumes you know your model; Paper 1 assumes you can work without one. Brilliant’s interactives are not a calculator and teach neither habit.
What should you use from the IB?
Your school has the subject guide, the specimen papers, and past papers with mark schemes — ask your teacher, since the IB sells them rather than publishing them free. Papers are where you learn command terms and how marks split between method and answer. A workable rhythm: sit a paper section under time, separate the misses into mathematics you could not do and marks you lost to presentation, and bring the first group back to the lessons above. Brilliant cannot tell you either thing.
Is Brilliant a complete IB Math AA course?
No. Brilliant is not an IB course, is not affiliated with or endorsed by the International Baccalaureate, and includes no past papers, no mark schemes, no exploration support and no timing practice. It is the understanding layer, and works best beside a class rather than instead of one. Use Brilliant for the mathematics and IB materials for the assessment.
How this mapping was made
Brilliant’s curriculum team maps each skill to the single syllabus item it fits most closely, using the IB’s Mathematics: Analysis and Approaches guide for first assessment 2021 as the authority on what each item requires. The data was pulled on September 15, 2026 against the live course catalog.
Frequently asked questions
I am choosing between SL and HL. Does this page help?
Partly. Read the higher level half of the HL coverage page — complex numbers, vectors in three dimensions, series, a much longer calculus — and decide whether that is a year you want. Brilliant’s coverage should not drive the choice; your teacher’s advice and your other subjects should.
I am doing Applications and Interpretation. Is any of this useful?
Some of it — the two courses share statistics, probability and function basics — but AI is not mapped here. Start from What math does Brilliant cover? instead.
Related resources
- IB Math AA SL coverage: syllabus-by-syllabus Brilliant lesson mapping
- IB Math AA HL coverage: syllabus-by-syllabus Brilliant lesson mapping
- Does Brilliant cover Calculus?
- What math does Brilliant cover?
- Explore Brilliant’s courses
Sources
[1] International Baccalaureate, Mathematics: Analysis and Approaches Guide, first assessment 2021 — SL and AHL syllabus content, internal assessment criteria and weighting.
[2] Brilliant, standards alignment database, pulled on September 15, 2026.
[3] Brilliant, “IB Math AA SL coverage: syllabus-by-syllabus Brilliant lesson mapping”, accessed September 2026.
[4] Brilliant, “Courses”, accessed September 2026.
