## Topic 1: Combinatorics

Addition and Multiplication principles

Factorials!

Permutations

Arrangements in a circle

Arrangements from like objects

Addition and multiplication principles revision

Factorials and permutations revision

Permutations of like objects

Permutations with restrictions

Combinations

Combinations with restrictions

Pascals triangle and subsets of a set

Pigeonhole principle

Basic Set Theory

The inclusion exclusion principle for 2 and 3 sets

## Topic 2: Vectors in the Plane

Vectors Introduction

Adding Vectors Graphically

Vectors Multiplying by a scalar

Vectors in 2D and 3D Shapes

Vectors in component form

Adding Vectors in component form

Vectors multiplying by a scalar in component form

Vectors finding the magnitude

Vectors finding the unit vector

Finding direction of a vector

Defining a vector between 2 points

Vector Revision part 1

The dot product part 1

The dot product part 2

The dot product part 3

The scalar product or dot product of a vector revisited

Force Vector Diagrams

Resolving Force Vectors

Resolving forces into their components

Resolving Forces into components part 2

Vector midpoints

Vectors in linear combinations

Vectors in component form recap

Vectors in polar form

What's a vector projection

Calculating vector projections

Resolving a vector into components parallel and perpendicular to a second vector

Applications of vectors displacement and velocity

Applications of vectors displacement and velocity collisions

Applications of vectors relative velocity

Triangle of forces

Inclined plane recap part 1

Solving equilibrium questions using resolution of forces

## Topic 3: Introduction to Proof

Direct proof

Proof by contrapositive

Proof by contradiction

Equivalent statements

Disproving statements

Geometric proofs from the ground up

Proving the angle in a semi-circle is a right angle

Prove the angle at the centre theorem

The angle on the same arc theorem

Proving Chord of Circle Theorem

Proving Tangent to a circle and the radius are perpendicular Using Proof by Contradiction

Proving the tangents from an external point theorem

Proving the cyclic quadrilateral theorem

Geometric Proofs using Vectors part 1

Geometric proofs using vectors Part 2