Complex Numbers

Complex Numbers & Argand Diagrams

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

Exponential Form

de Moivre's Theorem

Applications of de Moivre's Theorem

Roots of Complex Numbers

Matrices

Properties of Matrices

Introduction to Matrices

Determinants of Matrices

Inverses of Matrices

Transformations using Matrices

Transformations using a Matrix

Geometric Transformations with Matrices

Invariant Points & Lines

Further Algebra & Functions

Roots of Polynomials

Roots of Polynomials

Linear Transformations of Roots

Series

Sums of Integers, Squares & Cubes

Method of Differences

Maclaurin Series

Maclaurin Series

Hyperbolic Functions

Hyperbolic Functions

Hyperbolic Functions & Graphs

Logarithmic Forms of Inverse Hyperbolic Functions

Hyperbolic Identities & Equations

Differentiating & Integrating Hyperbolic Functions

Further Calculus

Volumes of Revolution

Volumes of Revolution

Modelling with Volumes of Revolution

Methods in Calculus

Improper Integrals

Mean Value of a Function

Integrating with Partial Fractions

Calculus involving Inverse Trig

Integration by Substitution

Further Vectors

Vector Lines

Equations of Lines in 3D

Pairs of Lines in 3D

Angle between Lines

Shortest Distances - Lines

Vector Planes

Equations of planes

Combinations of Lines & Planes

Combinations of Planes

Shortest Distances - Planes

Polar Coordinates

Polar Coordinates

Polar Coordinates

Calculus with Polar Coordinates

Differential Equations

First Order Differential Equations

Intro to Differential Equations

Solving First Order Differential Equations

Modelling using First Order Differential Equations

Second Order Differential Equations

Solving Second Order Differential Equations

Coupled First Order Linear Equations

Simple Harmonic Motion

Simple Harmonic Motion

Damped or Forced Harmonic Motion

Proof

Proof by Induction

Intro to Proof by Induction

Common Cases of Proof by Induction

Exam boards

• Edexcel A Level Further Maths: Further Statistics 1
• Edexcel A Level Further Maths: Further Mechanics 1
• Edexcel A Level Further Maths: Decision 1

Study tools

• Edexcel A Level Further Maths · Exam Questions
• Edexcel A Level Further Maths · Past Papers

Related links

• A Level Further Maths · Revision Notes
• A Level Further Maths · Exam Questions
• A Level Further Maths · Past Papers
• Edexcel A Level Further Maths: Core Pure · Exam specification