#### 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

#### 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

Defining a vector between 2 points

Finding direction of a vector

Force Vector Diagrams

Resolving Force Vectors

Resolving forces into their components

Resolving Forces into components part 2

Vector Revision part 1

Vector midpoints

Vectors in linear combinations

Vectors in component form recap

Vectors in polar form

The scalar product or dot product of a vector revisited

What's a vector projection

Calculating vector projections

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

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

#### Geometry

Direct proof

Proof by contrapositive

Proof by contradiction

Equivalent statements

Disproving statements

Geometric Proofs using Vectors part 1

Geometric proofs using vectors Part 2

#### Trigonometry

Trigonometry: Unit circle revision done fast

Solving trig equations of the form sin(ax+b) = c

Pythagorean identity

Pythagorean identity rearrangement

Using Pythagorean Identities Part 1

The general solution of trigonometric equations

Sketching Tan Functions

Reciprocals of Trigonometric Functions

Transformations of the reciprocal Trigonometric functions

Complementary Trigonometric Relationships

Exact values of reciprocal trigonometric functions

Solving reciprocal trig functions

The pythagorean Identity and reciprocal trigonometric functions

Proving Trigonometric identities

2 more pythagorean identities

Angle sum and difference indentities

Angle sum and difference identities part 2

Double angle identity proofs and an example

More proofs of trig identities

Express the sum of trigonometric functions as a single function

Express the sum of trigonometric functions as a single function part 2

Product Sum Trigonometric Identities

#### Matrix Arithmetic

What is a matrix

Matrix Equality

Storing Information in Matrices

Adding and subtracting matrices

Multiplying matrices by a scalar

Multiplying Matrices the better way

An Application of Matrix Multiplication

Powers of Matrices

The Identity Matrix

Matrices Recap

Solving Matrix equations using the multiplicative inverse

Simultaneous equations using matrices

Matrix Calculations on the Casio FX-CG50AU

#### Transformations in the Plane

Transformations in one dimensional space A different to think about mathematical operations

Linear Transformations Introduction

Transforming a figure using Matrix Transformations

What is actually happening in a linear transformation

Dilation transformations Using Matrices

Shear Transformations Using Matrices

Reflections in the x and y axis using Matrix Transformations

Projections of an image onto the x axis or y axis using Matrix Transformations

Rotations about the Origin Using Matrices

Reflect an object in y= x and y = -x using Matrix Transformations

Reflecting in the line y = mx with Matrix Transformations

Composition of Matrix Transformations

Inverse Matrix Transformation

Transforming multiple points using a single matrix transformation

Transforming relations using matrices part 1

Transforming relations using matrices part 2

Transforming relations no shortcuts

Transforming relations using matrices part 3

Finding an unknown matrix of transformation

Equation of ellipses crash course

Finding area of a transformation using the determinant

General Transformations part 1

General Transformations part 2

#### Real & Complex Numbers

Intro to complex numbers

Working with imaginary and complex numbers

Powers of i

Simplifying with powers of i

Adding and subtracting complex numbers

Multiplying complex numbers by a constant

Multiplying complex numbers by each other

Equality of complex numbers

Complex Numbers The Recap

Complex number conjugates

The multiplicative inverse of a complex number

Argand Diagrams What complex numbers and Vectors have in common

Solving equations with complex numbers

Completing the square with complex numbers

Polar Form of a complex number

Polar form Multiplication and division of complex numbers

De Moivres theorem raising complex numbers to a power