Free IB Maths AI HL lessons
One ready-to-teach lesson for each IB Mathematics: Applications and Interpretation 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
- Expanding brackets & factorising · same as AI SL
- Coordinates & straight-line basics · same as AI SL
- Perimeter, area & volume · same as AI SL
- Averages & basic data handling · same as AI SL
- Basic probability · same as AI SL
Unit 1 · Number & Algebra
- Sigma notation & infinite series
- Amortisation & annuities
- Complex numbers — Cartesian form
- Modulus, argument & polar form
- Laws of logarithms & exponential equations
- Writing numbers in standard form · same as AI SL
- Approximation & rounding · same as AI SL
- Arithmetic sequences on the GDC · same as AI SL
- Geometric sequences & sums · same as AI SL
- Simple & compound interest · same as AI SL
Unit 2 · Functions
- Interpreting model roots / vertex in context
- Log-transformed regression
- Logistic model P = L/(1+Ae⁻ᵏᵗ)
- Non-linear regression & residual analysis
- Domain, range, composite & inverse functions
- Straight-line graphs (m and c) · same as AI SL
- Parallel & perpendicular lines · same as AI SL
- Exponential growth models · same as AI SL
- Exponential decay models · same as AI SL
- Sinusoidal models · same as AI SL
Unit 3 · Geometry & Trigonometry
- Graph theory — adjacency & weighted matrices
- Distance & midpoint in 3D · same as AI SL
- Volume & surface area of 3D shapes · same as AI SL
- Right-angle trig applications · same as AI SL
- Cosine rule · same as AI SL
- Area = ½ ab sin C · same as AI SL
- Constructing a Voronoi diagram · same as AI SL
- Arc length & sector area · same as AI SL
Unit 4 · Statistics & Probability
- Binomial distribution
- Poisson distribution
- Normal distribution
- Confidence intervals for a mean (GDC)
- Full hypothesis test — H0/H1, p-value, conclusion
- Linear combinations of random variables & the Central Limit Theorem
- Measures of spread (SD, IQR) · same as AI SL
- Least-squares regression line · same as AI SL
- Chi-squared goodness-of-fit test · same as AI SL
- Combined events & sample-space diagrams · same as AI SL
- Conditional probability · same as AI SL
- Sampling techniques & data collection · same as AI SL
Unit 5 · Calculus
- Optimisation in context
- Indefinite integration (xⁿ, sin, cos, 1/x, eˣ) & by substitution
- Separable first-order DEs
- Coupled differential equations & phase portraits
- Euler's method for numerical solutions to DEs
- Second derivative, concavity & points of inflexion
- Kinematics: displacement, velocity & acceleration
- Local maxima & minima · same as AI SL
- Definite integrals & area under a curve · same as AI SL
- Tangents & normals · same as AI 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.