IB Maths AA Notes (SL & HL)

IB Maths AA rewards method, not just answers. These notes follow the Analysis and Approaches syllabus topic by topic, with SL and HL in one note and HL-only content clearly tagged. Every worked example shows where the M1 and A1 marks come from, every formula says whether it is in the formula booklet, and every Paper 2 skill comes with the GDC steps. The notes are written for students sitting the new syllabus (first exams May 2029) and still work for exams up to November 2028.

What every note gives you

• SL and HL in one note. HL-only parts carry an HL ONLY tag, so SL students can skip them.
• Formula booklet tags. You see at a glance what is given in the exam and what you must learn.
• Marked like the markscheme. Worked examples show the M1, A1 and R1 marks, so you know what to write.
• Paper 1 and Paper 2 skills. Non-calculator methods, plus GDC steps for Paper 2.
• 2029 syllabus status. Each topic says whether anything changes for May 2029 exams.
• Exam-style questions with answers, and free practice papers in the Paper Generator.

Notes ready now

1. 1Sequences, series and the binomial theoremArithmetic and geometric sequences and series, sigma notation, sums to infinity, the binomial theorem with Pascal's triangle and ⁿCᵣ, and (HL) the binomial series for negative and fractional powers.~8 min read · SL + HL
2. 1Exponents and logarithmsLaws of exponents, logarithms as inverses of exponentials, natural logs and e, the laws of logarithms and change of base, solving exponential and log equations, and exponential and logarithmic functions and models.~7 min read · SL
3. 1Proof, counting and partial fractionsDeductive proof and identities, and for HL: proof by induction and by contradiction, counting principles with permutations and combinations, partial fractions, and solving systems of linear equations.~8 min read · SL + HL
4. 1Complex numbersCartesian form and arithmetic with complex numbers, the Argand diagram, modulus and argument, polar and Euler forms, conjugate roots of polynomials, De Moivre's theorem, nth roots and trig identities.~6 min read · HL
5. 2Functions, inverses and compositesStraight lines and their equations, what a function is, domain and range, key features of graphs, composite functions, inverse functions and their graphs, and (HL) odd and even functions, self-inverse functions and restricting domains.~6 min read · SL + HL
6. 2Quadratics and the discriminantThe three forms of a quadratic, completing the square, the vertex and axis of symmetry, solving by factorising and the formula, the discriminant and the number of roots, quadratic inequalities and hidden quadratics.~6 min read · SL
7. 2Transformations of graphsTranslations, reflections and stretches of y = f(x), combining transformations in the right order, mapping points, and (HL) the graphs of |f(x)|, f(|x|), 1/f(x), f(ax + b) and [f(x)]².~6 min read · SL + HL
8. 2Polynomials, rational functions and inequalitiesReciprocal and rational functions with their asymptotes, and for HL: the factor and remainder theorems, polynomial graphs, sum and product of roots, oblique asymptotes, and solving polynomial and rational inequalities.~6 min read · SL + HL
9. 3Trigonometry: triangles, radians, arcs and sectorsDistance and midpoint in 3D, volume and surface area of solids, angles in 3D, right-angled trig, the sine rule (including the ambiguous case), the cosine rule, area ½ab sin C, bearings, radians, arc length and sector area.~7 min read · SL
10. 3Trig identities, equations and graphsThe unit circle and exact values, the Pythagorean and double angle identities, graphs of sin, cos and tan with transformations, modelling with trig functions, solving trig equations in an interval, and for HL: sec, cosec, cot, inverse trig functions and compound angle identities.~9 min read · SL + HL
11. 3Vectors, lines and planesHL vectors in full: column and i, j, k notation, magnitude and unit vectors, the scalar product and angles, vector equations of lines, intersecting, parallel and skew lines, the vector product, equations of planes, and intersections and angles between lines and planes.~10 min read · HL
12. 4Statistics and probabilitySampling and data, mean, median, mode, quartiles, standard deviation, outliers, box plots and cumulative frequency, the effect of transforming data, probability rules, Venn and tree diagrams, conditional probability and independence, and Bayes’ theorem for HL.~9 min read · SL + HL
13. 4Random variables, binomial and normal distributionsDiscrete random variables and expected value, fair games, the binomial distribution with its mean and variance, the normal distribution, standardising with z-scores and inverse normal problems, and for HL: variance of discrete variables, E(aX + b), Var(aX + b) and continuous random variables with probability density functions.~8 min read · SL + HL
14. 5DifferentiationWhat a derivative really is, every rule you need (power, chain, product, quotient), tangents and normals, stationary points, concavity, optimisation, and the HL extras: first principles, implicit differentiation, related rates and l'Hôpital's rule.~20 min read · SL + HL
15. 5Integration and kinematicsAntiderivatives and the constant of integration, definite integrals and areas, area between curves, integrating eˣ, 1/x, sin and cos, reverse chain rule, kinematics with displacement and distance, and for HL: substitution, integration by parts, arctan and arcsin integrals, and volumes of revolution.~9 min read · SL + HL
16. 5Differential equations and Maclaurin seriesHL first-order differential equations: separating variables, slope fields, homogeneous equations with y = vx, integrating factors and modelling growth and cooling, plus Maclaurin series from the formula booklet, building new series by substitution, multiplication and differentiation, series from a differential equation, and limits using series.~9 min read · HL

Exam special notes

Built from the IB examiners' subject reports: where students actually lose marks, and how to stop it.

1. ★IB Maths AA Grade Boundaries (May 2025 & Nov 2024)Every grade boundary for IB Maths AA from the IB subject reports: May 2025 time zones 1–3 and November 2024, SL and HL, overall and paper by paper, and what it takes to get a 7.~6 min read · Grade boundaries
2. ★IB Maths AA Exam Traps: 57 Mistakes Examiners Flagged57 mistakes IB examiners flagged in the November 2024 and May 2025 Maths AA subject reports, grouped by topic, each with the fix, plus a last-week checklist.~12 min read · Exam traps
3. ★IB Maths IA Guide: How to Score Highly on the Exploration (AA & AI)A practical guide to the IB Maths exploration for AA and AI, SL and HL: what each criterion rewards, how to choose a topic with enough mathematics, a structure that works and the mistakes moderators flagged in the 2024–25 reports.~8 min read · IA guide
4. ★IB Maths Command Terms and Markscheme Codes (M1, A1, R1, AG, FT)What every IB Maths command term asks for, and how examiners award marks: M1, A1, R1, AG, FT, implied marks, misreads, "hence" vs "hence or otherwise", accuracy and the presentation rules that cost students marks.~9 min read · Command terms & marks
5. ★IB Maths AA HL Paper 3: Strategy for the Problem-Solving PaperHow to approach the IB Maths AA HL Paper 3 investigations: the structure of the paper, timing, a step-by-step method for unfamiliar problems, a worked mini-investigation, and what the 2024–25 examiners said.~8 min read · Paper 3 strategy
6. ★IB Maths AA Paper 1: Non-Calculator Skills and Exact ValuesThe skills IB Maths AA Paper 1 tests without a calculator: exact trig values and the unit circle, logs, surds and indices, arithmetic shortcuts, sketching by hand, solving trig equations and the slips examiners see every session.~8 min read · Paper 1 guide
7. ★IB Maths AA Formula Booklet: What Is Given and What to MemoriseWhat the IB Maths AA formula booklet (SL and HL) contains, topic by topic, and the formulas, values and facts it leaves out that you must memorise, plus how to use the booklet quickly in the exam.~8 min read · Formula booklet guide

Full syllabus map

Practise any topic with full mark schemes in the free IB Paper Generator.

Frequently asked questions