Free topical revision checklist for IB DP Mathematics: Analysis and Approaches (AA) SL & HL. Track confidence (1–5), last reviewed and next review. Aligned to 2026 IB DP subject guide expectations. Rate your confidence (1–5), track review dates, then export as CSV or print.
| Topic | Sub-topic | Resources | Confidence (1–5) | Last reviewed | Next review |
|---|---|---|---|---|---|
| 1. Number & algebra (core) | Sets and set notation (union, intersection, complement) | Topic resources | |||
| 1. Number & algebra (core) | Intervals on the real line; inequality notation | Topic resources | |||
| 1. Number & algebra (core) | Number systems (integers, rationals, irrationals, reals) and approximations | Topic resources | |||
| 1. Number & algebra (core) | Surds: simplification, rationalising denominators | Topic resources | |||
| 1. Number & algebra (core) | Indices and laws of exponents; scientific notation | Topic resources | |||
| 1. Number & algebra (core) | Logarithms: laws, solving log/exponential equations, change of base | Topic resources | |||
| 1. Number & algebra (core) | Arithmetic sequences: nth term, sums | Topic resources | |||
| 1. Number & algebra (core) | Geometric sequences: nth term, sums, infinite geometric series (where applicable) | Topic resources | |||
| 1. Number & algebra (core) | The binomial theorem (expansion; simple applications/approximations) | Topic resources | |||
| 1. Number & algebra (core) | Proof: direct proof and counterexamples | Topic resources | |||
| 1. Number & algebra (core) | Proof by contradiction — (HL emphasis) | Topic resources | |||
| 1. Number & algebra (core) | Mathematical induction — (HL) | Topic resources | |||
| 1. Number & algebra (core) | Complex numbers: arithmetic, modulus-argument form — (HL) | Topic resources | |||
| 2. Functions (core) | Function concept; domain, range and restrictions | Topic resources | |||
| 2. Functions (core) | Composite and inverse functions (existence and graph interpretation) | Topic resources | |||
| 2. Functions (core) | Graph transformations: translations, stretches, reflections | Topic resources | |||
| 2. Functions (core) | Polynomial functions: roots, factor theorem (HL), multiplicity and turning points | Topic resources | |||
| 2. Functions (core) | Rational functions: asymptotes, holes, end behaviour | Topic resources | |||
| 2. Functions (core) | Exponential and logarithmic functions: growth/decay, linearisation | Topic resources | |||
| 2. Functions (core) | Trigonometric functions (sin, cos, tan): graphs, period, amplitude | Topic resources | |||
| 2. Functions (core) | Trigonometric identities (incl. double-angle where applicable) — (HL depth) | Topic resources | |||
| 2. Functions (core) | Solving equations: algebraic, numerical and graphical methods | Topic resources | |||
| 2. Functions (core) | Solving inequalities; solution sets and sign diagrams | Topic resources | |||
| 2. Functions (core) | Modelling with functions: choosing model, parameter meaning, validity | Topic resources | |||
| 2. Functions (core) | Technology use: graphing/solver outputs and interpretation | Topic resources | |||
| 3. Geometry & trigonometry (core) | Angle measure: degrees and radians; arc length and sector area | Topic resources | |||
| 3. Geometry & trigonometry (core) | Trigonometric ratios and the unit circle | Topic resources | |||
| 3. Geometry & trigonometry (core) | Sine rule, cosine rule, triangle area formula | Topic resources | |||
| 3. Geometry & trigonometry (core) | Trigonometric equations in a given interval | Topic resources | |||
| 3. Geometry & trigonometry (core) | Vectors in 2D/3D: components, magnitude, unit vectors | Topic resources | |||
| 3. Geometry & trigonometry (core) | Vector operations: addition, scalar multiplication | Topic resources | |||
| 3. Geometry & trigonometry (core) | Scalar (dot) product and angle between vectors | Topic resources | |||
| 3. Geometry & trigonometry (core) | Vector/coordinate geometry: lines, intersections, distance, midpoint | Topic resources | |||
| 3. Geometry & trigonometry (core) | Geometry of circles (equations, tangents) — (HL focus where applicable) | Topic resources | |||
| 3. Geometry & trigonometry (core) | 3D geometry: lines and planes, angles between lines/planes — (HL) | Topic resources | |||
| 3. Geometry & trigonometry (core) | Geometric reasoning and proof (congruence/similarity where needed) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Limit concept and continuity (graphical and algebraic) — (HL emphasis) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Differentiation from first principles (as required) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Differentiation rules (product/quotient/chain) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Implicit differentiation — (HL) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Related rates problems | Topic resources | |||
| 4. Calculus (core + HL extensions) | Tangent and normal; interpreting derivative as rate of change | Topic resources | |||
| 4. Calculus (core + HL extensions) | Optimisation (max/min); modelling constraints | Topic resources | |||
| 4. Calculus (core + HL extensions) | Integration as anti-derivative; definite integrals | Topic resources | |||
| 4. Calculus (core + HL extensions) | Area between curves; interpreting signed area | Topic resources | |||
| 4. Calculus (core + HL extensions) | Techniques: substitution and integration by parts — (HL) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Partial fractions — (HL where applicable) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Kinematics via calculus (s, v, a relationships) — (HL depth) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Differential equations (separable) and modelling — (HL) | Topic resources | |||
| 4. Calculus (core + HL extensions) | Maclaurin/Taylor series; approximation and error — (HL) | Topic resources | |||
| 5. Statistics & probability (core) | Data types; sampling methods and bias | Topic resources | |||
| 5. Statistics & probability (core) | Descriptive statistics: mean/median/mode; variance/SD; IQR/outliers | Topic resources | |||
| 5. Statistics & probability (core) | Bivariate data: correlation, regression basics, residuals | Topic resources | |||
| 5. Statistics & probability (core) | Probability rules; Venn diagrams and counting (as required) | Topic resources | |||
| 5. Statistics & probability (core) | Conditional probability and independence; tree diagrams | Topic resources | |||
| 5. Statistics & probability (core) | Discrete random variables; expected value and variance | Topic resources | |||
| 5. Statistics & probability (core) | Binomial distribution (conditions, calculations) — (where applicable) | Topic resources | |||
| 5. Statistics & probability (core) | Continuous distributions overview; normal distribution | Topic resources | |||
| 5. Statistics & probability (core) | Normal standardisation (z-scores) and applications | Topic resources | |||
| 5. Statistics & probability (core) | Confidence intervals (interpretation) — (HL emphasis) | Topic resources | |||
| 5. Statistics & probability (core) | Hypothesis testing (p-value/critical region) — (HL emphasis) | Topic resources | |||
| 6. Internal Assessment (IA) readiness | Choose a focused question that requires mathematics beyond trivial computation | Topic resources | |||
| 6. Internal Assessment (IA) readiness | Use technology appropriately (GDC/graphing/statistics tools) and explain outputs | Topic resources | |||
| 6. Internal Assessment (IA) readiness | Show mathematical communication: definitions, notation, and clear structure | Topic resources | |||
| 6. Internal Assessment (IA) readiness | Interpret results, validate model, discuss limitations and improvements | Topic resources | |||
| 6. Internal Assessment (IA) readiness | Academic honesty: cite sources, include original work and reasoning | Topic resources |
Tip: Pair this checklist with past paper practice and spaced repetition. Always confirm exact assessment components (SL/HL, options) with your school’s IB DP route for the 2026 exam session.
Quick answers about this free revision checklist, how to use it for exam prep, and how it relates to the official syllabus.
This revision checklist mirrors the official IB DP Mathematics: Analysis and Approaches (AA) syllabus for the 2026 examination series. Every topic and sub-topic on the page is taken from the published syllabus document, so working through the list in order gives you full coverage of what your exam can assess. It covers both Standard Level (SL) and Higher Level (HL) topic expectations. For the authoritative version, always cross-check with the latest syllabus PDF on your exam board's website before your final revision push.
The number of top-level topic groups varies by subject, but you can see the exact count on this page — each major heading in the checklist corresponds to one syllabus topic group, and each row below it is a syllabus-level sub-topic. Use the confidence column (1–5) to flag which sub-topics need more work, and re-score yourself weekly to track real progress instead of guessing.
16–20 weeks of consistent revision is realistic for IB DP — work through one topic per week alongside ongoing past-paper practice and Internal Assessment polish. Use this checklist to plan your weeks: filter by topics you have rated 1–3 and spend your first revision block there. Subjects with heavy practical or extended-writing components (e.g. sciences, English) need more past-paper time in the final block than the topic-by-topic phase.
Revise in roughly the order the syllabus lists the topics — exam boards build later topics on earlier ones, so taking them in syllabus order avoids gaps. Once you have rated every topic, switch to weakest-first: filter the checklist by confidence ≤ 2 and prioritise those topics in your next study block. This is more effective than re-revising topics you already score 4–5 on.
You can find past papers and mark schemes via Tutopiya's Past Paper Finder and on your exam board's official site. Once you have rated each sub-topic on this checklist, attempt past-paper questions on your weakest topics first — practising under timed conditions is the single best predictor of exam performance, more so than re-reading notes.
Use the Download CSV or Print PDF button at the bottom of the checklist. CSV opens in Excel, Numbers or Google Sheets so you can sort by confidence and re-arrange revision order. The PDF is print-ready for offline use. A free Tutopiya account is required for download — this also unlocks the matching topic resources, notes and worked examples on the Learning Portal.
Yes, the checklist itself is free — you can view, score and re-score every topic on this page without an account. The CSV / PDF downloads and access to matching Tutopiya Learning Portal resources require a free account. There is no payment required at any point; teachers and parents can also use this checklist freely with their students.
Yes. The topics and sub-topics on this page are drawn from the current 2026 IB DP Mathematics: Analysis and Approaches (AA) specification published by your exam board. Exam boards occasionally tweak weighting or assessment structure mid-cycle, so do a quick sanity-check against the official syllabus PDF when you start your revision and again 4 weeks before the exam.