IB Maths AA topic-by-topic revision means revising one syllabus unit at a time, answering targeted exam-style questions, and then using worked solutions to diagnose the exact step that caused difficulty. Once the individual topics are secure, you should move to mixed questions and timed papers because the final examinations assess the whole syllabus rather than isolated units.
This guide explains what to revise in each of the five official topics, how to use past-paper questions effectively, and when to progress from focused practice to full exam conditions.
Understand the IB Maths AA syllabus structure
The official Mathematics: Analysis and Approaches syllabus contains five topics:
Number and algebra
Functions
Geometry and trigonometry
Statistics and probability
Calculus
These are taught at both Standard Level and Higher Level, although HL includes additional content and greater depth. The IB recommends 150 teaching hours for SL and 240 hours for HL, including 30 hours for investigational, modelling, problem-solving skills, and the mathematical exploration.
The official IB Mathematics AA subject guide provides the detailed syllabus statements. Use it as a checklist rather than assuming that a textbook's chapter order matches the official structure exactly.
How to revise IB Maths AA topic by topic
A productive topic cycle has five stages:
Check the syllabus statement. Identify exactly what is required at your level.
Recall the method. Review definitions, formulae, notation, calculator procedures, and one worked example.
Answer targeted questions. Begin with direct applications, then attempt unfamiliar and multi-part problems.
Review worked solutions. Compare every line, not only the final answer, and identify where your reasoning diverged.
Retest the gap. Complete a similar question without notes several days later.
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This method targets the specific weakness. If you can differentiate a polynomial but repeatedly mishandle the chain rule, revising the whole calculus chapter is inefficient. Instead, practise a focused set such as RevisionDojo's chain, product, and quotient rule questions, review the worked method, and then retest that skill.
The IB Maths AA resource hub brings together syllabus-organized practice and per-question past-paper video solutions. Watching a solution is most useful after making a genuine attempt, because you can then compare the presented reasoning with your own.
Topic-by-topic revision priorities
Official topic
Core revision priorities
Questions that reveal weak understanding
Number and algebra
Sequences and series, indices, logarithms, binomial expansion, proof; complex numbers and further proof at HL
Questions requiring several algebraic transformations or justification
Functions
Domain and range, composite and inverse functions, graph transformations, quadratics, exponentials, logarithms, polynomial and rational functions
Problems connecting algebraic properties to graph features
Geometry and trigonometry
Radians, trigonometric identities and equations, sine and cosine rules, vectors and further HL geometry
Questions involving multiple solutions, intervals, diagrams, or vector reasoning
Statistics and probability
Descriptive statistics, probability rules, distributions, correlation, regression, and hypothesis testing where required
Problems requiring interpretation rather than calculator output alone
Calculus
Limits, differentiation, integration, optimization, kinematics, areas, volumes, and differential equations where required
Extended problems combining functions, algebra, and calculus
Number and algebra
Start by checking whether your manipulation is reliable. Many apparent difficulties in calculus, functions, and probability are actually caused by weak fraction work, exponent laws, logarithms, or rearrangement.
For each subtopic, practise both routine calculations and questions requiring proof or explanation. HL students should give additional attention to complex numbers, induction, contradiction, partial fractions, and systems of equations. The Number and Algebra Questionbank can be used to isolate these skills instead of repeating an entire paper.
Functions
Functions connect much of the course. Revise notation, domain, range, transformations, inverses, composites, intersections, asymptotes, and graphical interpretation before attempting extended problems.
Do not treat graphing technology as a substitute for mathematical explanation. Practise identifying features algebraically and then using technology to check or extend the result. A useful test is whether you can explain why a restriction, asymptote, or number of solutions occurs.
Geometry and trigonometry
Separate this topic into geometric applications, trigonometric graphs and equations, identities, and vectors. Record errors involving radians, exact values, ambiguous cases, restricted intervals, and premature rounding because these often recur.
When reviewing a worked solution, check how the diagram was labelled and how all possible solutions were considered. A correct calculator value can still produce an incomplete answer if another angle lies in the required interval.
Statistics and probability
Learn what each statistic or probability represents, not only the calculator sequence used to obtain it. You should be able to choose an appropriate distribution, state relevant conditions, and interpret an answer in context.
Use the Statistics and Probability topic resources to alternate between calculations and interpretation. When correcting mistakes, classify whether you selected the wrong model, entered data incorrectly, confused conditional probability, or failed to communicate the conclusion.
Calculus
Calculus depends heavily on functions and algebra, so repair those foundations when errors persist. Revise differentiation and integration techniques separately before combining them in optimization, motion, area, volume, and differential-equation problems.
For each extended question, annotate the worked solution with the purpose of every step: forming a derivative, locating a stationary point, checking its nature, applying a boundary, or interpreting the result. This develops method recognition rather than superficial memorization.
Use worked solutions actively
A worked solution should answer three questions:
Where did my method first become invalid?
Which mathematical idea should I have recognized?
What evidence will show that I can now apply it independently?
Pause a video before each major step and predict what should happen next. Then close the solution and redo the question from a blank page. Jojo AI can help explain an unfamiliar step, but the final test of understanding is whether you can reproduce the reasoning without assistance.
Keep an error log with four columns: topic, exact error, corrected principle, and retest date. RevisionDojo's guide to targeted Questionbank revision provides a practical framework for organizing these short, focused sessions.
Move from isolated topics to exam readiness
Topic revision is the first phase, not the final phase. IB questions can combine functions, trigonometry, probability, algebra, and calculus, so students must eventually identify methods without being told which chapter is being tested.
Use this progression:
Phase 1: Single-subtopic questions with notes available
Phase 2: Topic-wide questions without notes
Phase 3: Mixed-topic sets under moderate time pressure
Phase 4: Complete papers under official conditions
Phase 5: Targeted repair based on the paper analysis
The official IB Mathematics AA subject brief confirms that Paper 1 does not permit technology, while Paper 2 permits technology. At HL, Paper 3 also permits technology and contains two compulsory extended-response problem-solving questions. The exploration is compulsory at both levels and contributes 20% of the final grade.
Therefore, include both non-calculator and calculator practice. SL students sit Papers 1 and 2, each worth 40%, while HL students sit Papers 1 and 2, each worth 30%, and Paper 3, worth 20%. These are official assessment rules; the order and frequency of your revision sessions are personal study recommendations.
Common topic-revision mistakes
Avoid these patterns:
Reading notes repeatedly without solving questions
Watching a worked solution before attempting the problem
Marking an answer as understood because the final number looks familiar
Ignoring notation, reasoning, units, exact values, or contextual conclusions
Practising only comfortable topics
Remaining in topic mode until the examination without attempting mixed papers
Memorizing calculator commands without understanding the underlying mathematics
A stronger routine spends most of the session solving, correcting, and retesting. Revision notes and flashcards are useful for recall, but mathematical performance develops through written problem-solving.
A practical weekly plan
A balanced week might contain three focused sessions and one mixed review:
Session
Main task
1
Learn or review one subtopic, then answer direct questions
2
Complete harder exam-style questions from the same subtopic
3
Reattempt errors and use worked video solutions for unresolved gaps
4
Complete a mixed, timed set and update the error log
HL students will normally need more time because of the additional syllabus content and Paper 3 demands. The RevisionDojo guide to scoring well in Maths AA HL explains how topic practice can be combined with mixed problem-solving and paper simulation.
Conclusion
Effective IB Maths AA topic-by-topic revision follows a simple principle: finish a unit, solve targeted questions, review worked solutions for anything shaky, and then retest the exact gap. Cover all five official topics, but do not stop at isolated practice because the examinations require you to connect ideas and select methods independently.
RevisionDojo's Maths AA Questionbank, Jojo AI explanations, and per-question past-paper video solutions can support this process. Use them first for focused topic repair, then progress to mixed sets and Mock Exams under realistic conditions.
Emma holds an MMath from the University of Oxford and has taught IB Mathematics for over 20 years, including every year since Analysis & Approaches replaced the old Higher and Standard Level syllabus in 2019. Her focus is IB Mathematics: Analysis & Approaches at SL and HL, developing genuine mathematical intuition from foundational algebra through to the toughest HL topics.
