Further Mathematics

Factor theorem, remainder theorem, functions, domain and range, composite and inverse functions

Differentiation from first principles, standard derivatives, tangents, stationary points, integration

Matrix operations, determinants, inverse matrices, transformations using matrices

Equations of circles, tangents to circles, loci, perpendicular bisectors

Arithmetic and geometric progressions, sum formulas, sigma notation

Trigonometric equations, identities, 3D trigonometry in pyramids and prisms

Algebraic proof, direct proof, proof by contradiction, counter-examples

Vector notation, addition and subtraction, position vectors, magnitude

Iteration, solving equations numerically, trapezium rule for integration