Free IB Maths lessons

A ready-to-teach lesson for each topic of the IB Diploma maths courses. Every lesson has editable PowerPoint slides and teacher notes with timings and common mistakes, free with a teacher account; school plans and the teacher trial add a printable worksheet in three levels with its answers.

Every free lesson

IB Maths AA SL

Number operations & order of operations (BIDMAS) · Rounding, estimation & standard form · Laws of indices (integer powers) · Expanding brackets & factorising · Solving linear equations & inequalities · Coordinates & straight-line basics · Perimeter, area & volume · Pythagoras & right-angle trig (SOH-CAH-TOA) · Averages & basic data handling · Basic probability · Arithmetic sequences & series · Geometric sequences & series · Natural logs & change of base · Exponential equations · Binomial expansion (positive integer n) · Specific coefficients & terms · Applications: compound interest & depreciation · Gradient & intercepts of a line · Parallel & perpendicular lines · Quadratic graphs & vertex · Discriminant & roots · Solving quadratics (factor, formula, complete square) · Combined transformations · Rational functions & asymptotes · Logarithmic graphs & solving log equations · Composite functions (f∘g) · Inverse functions & their graphs · Right-angle trig (SOH CAH TOA) · Sine rule · Cosine rule · Arc length & sector area · Trig identities (Pythagorean, double-angle) · Solving trig equations · Modelling with sinusoidal functions · Measures of spread (SD, IQR) · Least-squares regression line · Conditional probability · Independent & mutually exclusive events · Discrete random variables & E(X) · Normal distribution (probability lookups) · Inverse normal (finding cut-off values) · Product & quotient rules · Tangents & normals at a point · Optimisation in context · Antiderivatives (integration) · Definite integrals & area under a curve · Kinematics: displacement, velocity, acceleration

IB Maths AI SL

Expanding brackets & factorising · Coordinates & straight-line basics · Perimeter, area & volume · Averages & basic data handling · Basic probability · Writing numbers in standard form · Approximation & rounding · Arithmetic sequences on the GDC · Geometric sequences & sums · Simple & compound interest · Amortisation & annuities on the GDC · Logarithms & exponential equations · Straight-line graphs (m and c) · Parallel & perpendicular lines · Interpreting quadratic vertex + roots in context · Exponential growth models · Exponential decay models · Domain, range & inverse functions · Sinusoidal models · Direct & inverse variation, cubic models · Distance & midpoint in 3D · Volume & surface area of 3D shapes · Right-angle trig applications · Cosine rule · Area = ½ ab sin C · Constructing a Voronoi diagram · Arc length & sector area · Measures of spread (SD, IQR) · Least-squares regression line · Chi-squared goodness-of-fit test · Combined events & sample-space diagrams · Conditional probability · Discrete distributions & E(X) · Continuous distributions (normal on GDC) · Two-sample t-test · Sampling techniques & data collection · Power-rule differentiation · Local maxima & minima · Optimisation problems · Definite integrals & area under a curve · Tangents & normals

IB Maths AA HL

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 · 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 · Compound-angle & double-angle identities · Vector algebra (add, scale, dot product) · Reciprocal & inverse trigonometric functions · Equations of planes; angles & intersections of planes · Binomial distribution · Continuous random variables (pdf, cdf) · 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

IB Maths AI HL

Sigma notation & infinite series · Amortisation & annuities · Complex numbers — Cartesian form · Modulus, argument & polar form · Laws of logarithms & exponential equations · 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 · Graph theory — adjacency & weighted matrices · 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 · 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

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See also the IB Maths scheme of work, starter questions and in-class tools.