Hi Diploma students
These are comprehensive revision notes for Mathematics: Analysis and Approaches, free and open to anyone. Every one of the five syllabus topics is covered at SL, with the additional higher level material flagged inline so you can see at a glance what applies to you.
Please take note that although succinct notes are essential towards your revision, they should not be the only materials you cover — working through practice problems from your textbook and past papers are just as important. Mathematics rewards the pen moving more than the eye scanning.
Happy revising. — Mr. Suta
🧭Start here
There are two DP mathematics subjects and they are genuinely different courses, not an easier one and a harder one. If you are still choosing, or you have picked up notes that turn out to be for the other course, read this page before anything else.
📚Syllabus contents
The syllabus is five topics, all compulsory. Higher level students study everything in the standard level content plus the additional higher level material inside the same five topics — there are no separate HL units and no options. Use the rail on the left, or the cards below, to open any topic.
Number and algebra
Standard form, arithmetic and geometric sequences and series, compound interest, exponents and logarithms, deductive proof and the binomial theorem. At HL: counting principles, partial fractions, complex numbers in three forms, De Moivre’s theorem, proof by induction and by contradiction, and systems of linear equations.
Functions
Straight lines, the language of functions, composite and inverse functions, quadratics in all three forms, the reciprocal and rational functions, exponentials and logarithms, and transformations. At HL: polynomials and the factor and remainder theorems, harder rational functions, odd and even functions, inequalities and the modulus function.
Geometry and trigonometry
Three-dimensional solids, the sine and cosine rules, radians, the unit circle, exact values, identities, the circular functions and trigonometric equations. At HL: reciprocal ratios, inverse trigonometric functions, compound angle identities, and a substantial vectors strand ending in lines and planes in three dimensions.
Statistics and probability
Sampling and bias, summary statistics, correlation and regression, the probability rules, discrete random variables, and the binomial and normal distributions. At HL: Bayes’ theorem and continuous random variables with probability density functions.
Calculus
Limits informally, differentiation and the three rules, tangents and normals, stationary points and optimisation, kinematics, and integration including areas between curves. At HL: differentiation from first principles, l’Hôpital’s rule, implicit differentiation, integration by parts and substitution, volumes of revolution, differential equations and Maclaurin series.
📋Assessment
🧩How to use these pages
Every topic page follows the same shape: what you need to be able to do, then the mathematics broken into the syllabus sub-topics, a worked example, practice questions with full solutions, and a clearly separated list of other people’s resources.
Material that only higher level students need is marked AHL wherever it appears. If you are at standard level you can read straight past those blocks; nothing later depends on them.
Worked examples end by naming the specific mistake that costs marks on that topic. Those paragraphs are the most useful part of the page and the easiest to skip.
🎓Official IB resources
These are the documents that actually govern the course. Most sit behind your school’s IB login on My IB and the Programme Resource Centre, so ask me if you cannot reach one.
- Mathematics: analysis and approaches guide — first assessment 2021. The definitive statement of what is examinable, sub-topic by sub-topic.
- Mathematics formula booklet — you are given a clean copy in every paper. Work with it open from day one.
- Teacher support material — contains annotated sample Explorations, which are the single most useful thing to read before starting your own.
- Specimen papers and markschemes — written for this syllabus, unlike most of what circulates online.
- Subject reports — the examiners telling you, in plain language, what candidates got wrong last session.
📜A note on past papers
I do not link to the unofficial past-paper archives that circulate online. They host IB assessment material without permission, they move domain every few months, and pointing you at them sits badly alongside the academic honesty policy you sign. Ask me for past questions and I will give you properly licensed ones through school.
Bear in mind too that anything from 2020 or earlier was set on the previous mathematics courses — Mathematical Studies, Mathematics SL and Mathematics HL. Those papers contain useful mathematics, but their structure and a fair amount of their content no longer match what you will sit.