Edexcel A Level Further Maths: Core Pure
Exam Questions

Introduction to Complex Numbers, Solving Equations with Complex Roots, Modulus & Argument, Modulus-Argument Form, Loci in Argand Diagrams, Regions in Argand Diagrams

Exponential Form, de Moivre's Theorem, Applications of de Moivre's Theorem, Roots of Complex Numbers

Introduction to Matrices, Determinants of Matrices, Inverses of Matrices

Transformations using a Matrix, Geometric Transformations with Matrices, Invariant Points & Lines

Roots of Polynomials, Linear Transformations of Roots

Sums of Integers, Squares & Cubes, Method of Differences

Maclaurin Series

Hyperbolic Functions & Graphs, Logarithmic Forms of Inverse Hyperbolic Functions, Hyperbolic Identities & Equations, Differentiating & Integrating Hyperbolic Functions

Volumes of Revolution, Modelling with Volumes of Revolution

Improper Integrals, Mean Value of a Function, Integrating with Partial Fractions, Calculus involving Inverse Trig, Integration by Substitution

Equations of Lines in 3D, Pairs of Lines in 3D, Angle between Lines, Shortest Distances - Lines

Equations of planes, Combinations of Lines & Planes, Combinations of Planes, Shortest Distances - Planes

Polar Coordinates, Calculus with Polar Coordinates

Intro to Differential Equations, Solving First Order Differential Equations, Modelling using First Order Differential Equations

Solving Second Order Differential Equations, Coupled First Order Linear Equations

Simple Harmonic Motion, Damped or Forced Harmonic Motion

Intro to Proof by Induction, Common Cases of Proof by Induction