Free IB Maths AA HL lessons
One ready-to-teach lesson for each IB Mathematics: Analysis and Approaches HL topic: editable slides and teacher notes with timings, free to download with a teacher account. School plans and the teacher trial add a levelled worksheet with answers.
Topics HL shares with SL use the SL lesson: they are marked “same as SL”.
Unit 0 · Prior knowledge
- Number operations & order of operations (BIDMAS) · same as AA SL
- Rounding, estimation & standard form · same as AA SL
- Laws of indices (integer powers) · same as AA SL
- Expanding brackets & factorising · same as AA SL
- Solving linear equations & inequalities · same as AA SL
- Coordinates & straight-line basics · same as AA SL
- Perimeter, area & volume · same as AA SL
- Pythagoras & right-angle trig (SOH-CAH-TOA) · same as AA SL
- Averages & basic data handling · same as AA SL
- Basic probability · same as AA SL
Unit 1 · Number & Algebra
- Solving exponential & log equations
- Binomial theorem for positive integer n
- Binomial theorem for rational / negative n
- Complex numbers — Cartesian form
- Modulus, argument & polar form
- De Moivre & Euler form (roots of unity)
- 3×3 linear systems (GDC + elimination)
- Consistent, inconsistent & dependent systems
- Partial fractions (linear & repeated factors)
- Counting principles: permutations & combinations
- Arithmetic sequences & series · same as AA SL
- Geometric sequences & series · same as AA SL
- Natural logs & change of base · same as AA SL
Unit 2 · Functions
- Discriminant & the number of real roots
- Rational functions & vertical/horizontal asymptotes
- Reciprocal & modulus graphs
- Factor theorem & remainder theorem
- Composite & inverse functions
- Odd & even functions, self-inverse functions
- Gradient & intercepts of a line · same as AA SL
- Parallel & perpendicular lines · same as AA SL
- Quadratic graphs & vertex · same as AA SL
- Solving quadratics (factor, formula, complete square) · same as AA SL
- Combined transformations · same as AA SL
- Logarithmic graphs & solving log equations · same as AA SL
Unit 3 · Geometry & Trigonometry
- Compound-angle & double-angle identities
- Vector algebra (add, scale, dot product)
- Reciprocal & inverse trigonometric functions
- Equations of planes; angles & intersections of planes
- Right-angle trig (SOH CAH TOA) · same as AA SL
- Sine rule · same as AA SL
- Cosine rule · same as AA SL
- Arc length & sector area · same as AA SL
- Solving trig equations · same as AA SL
Unit 4 · Statistics & Probability
- Binomial distribution
- Continuous random variables (pdf, cdf)
- Measures of spread (SD, IQR) · same as AA SL
- Least-squares regression line · same as AA SL
- Conditional probability · same as AA SL
- Independent & mutually exclusive events · same as AA SL
- Discrete random variables & E(X) · same as AA SL
- Normal distribution (probability lookups) · same as AA SL
- Inverse normal (finding cut-off values) · same as AA SL
Unit 5 · Calculus
- Implicit differentiation
- Definite integrals & area between curves
- Separable first-order DEs
- Maclaurin series
- L'Hôpital's rule
- Derivatives of trig, inverse trig, exponential & log functions
- Product & quotient rules · same as AA SL
- Tangents & normals at a point · same as AA SL
- Optimisation in context · same as AA SL
- Antiderivatives (integration) · same as AA SL
- Kinematics: displacement, velocity, acceleration · same as AA SL
Teaching the whole course?
The scheme of work puts these topics in teaching order, week by week. With a school plan, Create lesson builds each lesson for your class from the full question bank and sets the practice as homework marked by AI.