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.