Core Pure Mathematics
- Complex numbers — Cartesian and modulus-argument form, Argand diagrams, De Moivre's theorem, roots of unity, loci in the complex plane
- Matrices — matrix algebra, determinants, inverse matrices, transformations, eigenvalues and eigenvectors
- Further algebra — proof by induction, roots of polynomials (Vieta's formulas), method of differences, partial fractions with repeated factors
- Further calculus — volumes of revolution, improper integrals, reduction formulas, Maclaurin and Taylor series
- Polar coordinates — polar curves, area enclosed by polar curves, converting between polar and Cartesian
- Hyperbolic functions — definitions, identities, inverse hyperbolic functions, integration involving hyperbolic functions
- Differential equations — first and second order ODEs, complementary function and particular integral, systems of differential equations
- Further vectors — vector equations of planes, intersection of lines and planes, distances
