## Core A2 Level Mathematics

### Rational expressions

Introduction

Simplifying algebraic fractions
( PART ONE | PART TWO)

### Partial Fractions

Introduction

Splitting an algebraic fraction with two linear factors in the denominator (PART 1 | PART 2)

Splitting an algebraic fraction with repeated linear factor in the denominator
(PART 1 | PART 2)

### Binomial Expansion

Expanding binomials with positive whole number powers
(PART 1 | PART 2)
Expanding binomials with negative whole number powers
(PART 1 | PART 2)

Expanding combinations of binomial expansions
(PART 1 | PART 2)

Expanding partial fractions using binomial theorem
(PART 1 | PART 2)

Finding the validity of binomial expansions
(PART 1 | PART 2)

Finding decimal approximations ***Coming soon***

### Functions

Mappings
(PART ONE | PART TWO)

Types of mappings
(PART ONEPART TWO)

Domain and range of functions using set notation
( PART ONE | PART TWO | PART THREE)

Inverse function
(Introduction | Definition | Method ( PART ONE | PART TWO) | Drawing )

Composite Functions
(Method | element in range | element in domain)

Self inverting functions

General Example

Odd, even and periodic functions ***Coming soon***

### Modulus

Definition and graph of y =|x|

Sketching y = |f(x)|
( PART ONE | PART TWO

Sketching y = f(|x|)

Transformations of modulus function

Solving equations with modulus
( PART ONE | PART TWO

Modulus inequalities
( PART ONE | PART TWO )

### Transformations (combined)

Types ***Coming soon***
y =  x | y =  x3 | y =  ex | y = ln x | y = sin x | y = cos x | y = tan x |

y = cosec x | y = sec x | y = cot x | y =  sin-1 x | y =  cos-1 x| y =  tan-1 x |

y = 1/x | Drawn curves

### e and Natural Logarithm

Definition of e and laws

Exponential curve and Transformations of f(x) = ex

Combined transformation of f(x) = ex ***Coming soon***

Finding values of ex

Natural logarithm definition and laws

Transformations of f(x) =ln(x)

Combined transformation of f(x) =ln(x) ***Coming soon***

Solving equations with ex and ln(x) ***Coming soon***
(PART 1 | PART 2 )

Solving equations with ex and ln(x) in quadratic form

Exponential Rate of change ***Coming soon***

Exponential Growth and decay ***Coming soon***

### Numerical Methods

#### Roots of equations

Change of sign
(PART 1 | PART 2)

Fixed point iteration

Interval Bisection ***Coming soon***

Linear interpolation ***Coming soon***

Newton Raphson ***Coming soon***

#### Numerical Integration

Trapezium rule

Simpsons rule
(PART 1 | PART 2)

mid ordinate rule
(PART 1 | PART 2)

Errors

### Trigonometry I

Reciprocal trigonometric functions

Graphs of the reciprocal trigonometric functions

Functions of the reciprocal trigonometric functions

Proving identities using reciprocal trigonometric functions
( PART ONE | PART TWO )

Using Pythagoras' identities

Inverse trigonometric functions and their graphs

Solving equations with inverse trigonometric functions

Solving trigonometric equations

### Trigonometry II

Compound Angles

Introduction
(PART ONE )

Compound angle (Addition) formula - Introduction and Proofs

Compound angle (Addition) formula - Solving Equations

Double angle formula - Introduction and Proofs

Double angle formula - Equations
(PART ONE )

Half Angles and triple angles formula

acos x + bsin x form - Proofs and uses

acos x + bsin x form -Equations
(PART ONE )

Factor formula - Proofs and uses
( PART ONE | PART TWO |

Factor formula Equations
( PART ONE )

### Coordinate Geometry - Parametric equation***NEW***

Introduction
( PART ONE )

Plotting parametric equations
( PART ONE | PART TWO )

Convert parametric to Cartesian form
| PART FOUR | PART FIVE | PART SIX   )

Coordinate Geometry problems
( PART ONE | PART TWO  )

Parametric Differentiation
PART ONE | PART TWO | PART THREE )

### Vectors***Coming soon***

Introduction
Definitions and notations used (representations, equal vectors, opposite vectors)
Geometric properties of vectors

Geometric Vector subtraction
Geometric Zero vector
Geometric Scalar multiplication
General problems
Column form vectors: Notation
Column form vectors: Addition and Subtraction

Column form vectors: Scalar Mulitplication
Column form vectors: Mixed addition and mulitplication
Vectors as translations
3 Dimenisonal vectors: Coordinates
3 Dimenisonal vectors: Length between two points
3 Dimenisonal vectors: Mid point between two points
3 Dimenisonal vectors: Column vectors and arithmetic
ijk vector notation: Converting between ijk and column form
ijk vector notation: What are they?
ijk vector notation: Geometric view
ijk vector notation: Arithmetic
Modulus of a vector
Unit vectors
Position vectors
Position vectors: Finding coordinates and position vectors
Position vectors: Modulus and mid point
1 Dimensional vectors:
Change between column vectors and magnitude/direction form
General vector problems
Vector equation of a straight line: Introduction and using
Vector equation of a straight line: point and vector parallel to line
Vector equation of a straight line: 2 points in line
Vector equation of a straight line: Converting between vector and Cartesian form
Vector equation of a straight line: Geometry of straight lines in 2 Dimensions
Vector equation of a straight line: Geometry of straight lines in 3 Dimensions

Scalar product: Introduction and vector multiplication
Scalar product: Scalar product formula
Scalar product:How are angles involved and proof of formula
Scalar product: Angle between two vectors
Scalar product: Perpendicular vectors
Scalar product: Parallel vectors
Scalar product: General problems involving straight lines
Coordinate geometry with vectors: Intersection between two lines or vectors
Coordinate geometry with vectors: Distance between a point and line
Coordinate geometry with vectors: General problems and examples

### Differentiation

Introduction
( PART ONE)

Trigonometric differentiation
( PART ONE )

Exponetial differentiation
( PART ONE )

Chain rule
( PART ONE | PART TWO )

Natural logarithm  derivative
( Part ONE

y = a^x derivative

Product rule
(PART ONE | PART TWO | PART THREE )

Quotient rule
(PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE )

Reciprocal of the derivative
PART ONE | PART TWO )

Parametric Differentiation
PART ONE | PART TWO | PART THREE )

Implicit Differentiation
( PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE )

Rates of Change ***Coming soon***

### Integration

AS Level Integration
(PART ONE )

List of derivatives
(PART ONE )
Integrals of trigonometric functions
(PART ONE )

Integrals of trigonometric functions using identities

Integrals of exponential and reciprocal functions
(PART ONE )

Finding the anti derivative
(PART ONE | )

Integration by substitution
(PART ONE )

(a) function of a linear function
(PART ONE | PART TWO

(b) rational functions
(PART ONE |

(c) product of functions
(PART ONE |

(d) given the substitution
(PART ONE |

Integration of partial fractions

Parametric Integration

Integration by parts
(PART ONE |

Mixed examples of Integration

Definite integration

Volume of revolution
(PART ONE

Finding the area from a function in parametric form
(PART ONE |

Numerical integration

(a) Simpsons rule
(PART 1 | PART 2)

(b) Mid ordinate rule
(PART 1 | PART 2)

(c) Trapezium rule

### Differential equations***NEW***

Introduction (PART ONE )

Forming differential equations ***COMING SOON***

(PART ONE | PART TWO )

Solving separable variable differential equations

Finding the constant (Particular solutions of differential equations)
(PART ONE )

General problems  ***COMING SOON***
(PART ONE )

### ***Coming soon***

1. 2. 3. 