IB Mathematics
Topic-based preparation for IB Math AA and AI at SL and HL levels. AA-exclusive and AI-exclusive topics are clearly marked.
Sequences & Series
Arithmetic and geometric sequences, sigma notation, and applications.
Exponents & Logarithms
Laws of exponents, log rules, and solving exponential equations.
Binomial Theorem
Expanding binomials, Pascal's triangle, and binomial coefficients.
Complex Numbers AA HL
Cartesian, polar form, De Moivre's theorem, and roots of unity.
Proof AA HL
Mathematical induction, proof by contradiction, and direct proof.
Functions & Graphs
Domain, range, inverse, composite, and transformations.
Quadratic Functions
Vertex form, discriminant, and solving quadratic equations.
Rational & Other Functions
Polynomial, rational, and piecewise functions with asymptotes.
Trigonometric Functions
Unit circle, radian measure, sine/cosine/tangent graphs.
Trigonometric Identities & Equations
Pythagorean identities, double angle, and solving trig equations.
3D Geometry
Volume, surface area, and applications with non-right triangles.
Vectors AA HL
Vector equations of lines/planes, dot and cross products.
Graph Theory AI HL
Vertices, edges, adjacency matrices, and network algorithms.
Descriptive Statistics
Mean, median, standard deviation, and data display.
Probability
Conditional probability, independence, and Bayes' theorem.
Probability Distributions
Binomial and normal distributions, expected value.
Hypothesis Testing
Chi-squared test, t-test, and p-values.
Further Statistics AI HL
Confidence intervals, regression analysis, and non-parametric tests.
Differentiation
Derivatives, chain rule, and applications to curve sketching.
Integration
Definite and indefinite integrals, area under curves, and kinematics.
Further Calculus AA HL
L'Hôpital's rule, improper integrals, and Maclaurin series.
Further Applications AI HL
Euler's method, coupled differential equations, and phase portraits.