Topic module: Further Pure 2 A-Level Edexcel

Isomorphism of groups

Identity and inverse elements

Binary operations

Definition

Lagrange’s theorem

Subgroups

Order of a group

Commutative groups

Different types of groups

What defines a group

The Cayley-Hamilton theorem

Area of surface of revolution about the x-axis

Deriving and using reduction formulae

Length of an arc

Reducing a symmetrical matrix to diagonal form

Eigenvalues and eigenvectors

Combining combinations

Combinations of n different items

Permutations with restrictions : items must not be together

Permutations with restrictions : items at the ends

Permutations with restrictions: letters / items together

Permutations of repeated letters in a word

Permutations of r items from n different items

Permutations of n different items

Exam Questions – Transformations of the complex plane

Exam Questions – Loci in the complex plane

Exam Questions – Recurrence relations

Exam Questions – Divisibility and multiple tests

Exam Questions – Recurrence relationships

Further transformations

Transformations of the complex plane

Using complex numbers to represent regions on an Argand diagram

The locus of a point moving on the arc of a circle

The locus of a point moving along a half-line

The locus of a point moving along a perpendicular bisector

The locus of a point moving in a circle

Recurrence relationship proofs

Divisibility and multiple test proofs

Definition and finding the nth term

Recurrence relationships