A2 Core

Core A2 Level Mathematics

Index

• Rational Expressions
• Partial Fractions
• Binomial Expansion II
• Functions
• Modulus 
• Transformations II
• e and natural logarithms
• Numerical Methods
• Trigonometry I - reciprocal and inverse functions
• Trigonometry II - Compound angle formulae
• Coordinate Geometry II - Parametric equations
• Vectors
• Differentiation II
• Integration II
• Differential Equations

Rational expressions

(General Video Links - Link 1 - Link 2)

Introduction

Addition and subtractions of algebraic fractions 
(Video Links - Link 1 - Link 2 - Link 3)

Simplifying fractions

Simplifying algebraic fractions 
( PART ONE | PART TWO)
(Video Links - Link 1 - Link 2 - Link 3)

Multiplication and division of fractions

Multiplication of algebraic fractions
(Video Links - Link 1 - Link 2)

Division of algebraic fractions
(Video Links - Link 1 - Link 2)

Improper fractions and mixed numbers

Improper algebraic fractions to mixed numbers
(Video Links - Link 1)

Mixed numbers to improper algebraic fractions

Partial Fractions

(General Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 -
 
Introduction

Splitting algebraic fractions into products

Splitting an algebraic fraction with one factor in the denominator

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

Using substitution method to solve partial fractions

Splitting an algebraic fraction with three linear factors in the denominator
(Video Links - Link 1 - Link 2 - Link 3 -

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

(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5

Splitting an algebraic fraction with a quadratic and linear factor in the denominator
(Video Links -

Splitting an improper algebraic fraction into partial fractions
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 -

Binomial Expansion

(General Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 -

Expanding binomials with positive whole number powers 
(PART 1 | PART 2)
(Video Links - Link 1 - Link 2 - 

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

(Video Links - Link 1 - Link 2 - Link 3 - 

Expanding binomials with positive fractional powers

(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5
 
Expanding binomials with negative fractional powers

(Video Links - Link 1 - Link 2 - 

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

(Video Links - Link 1 - Link 2 - Link 3 - Link 4 -

Expanding partial fractions using binomial theorem 
(PART 1 | PART 2)
(Video Links - Link 1 - Link 2 - Link 3 -

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

(Video Links - Link 1 - Link 2 - Link 3 -
 
Finding decimal approximations ***Coming soon***
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 -

 

Functions

(General Video Links - Link 1 - Link 2)

Mappings 
(PART ONE | PART TWO)
(Video Links - Link 1)

Types of mappings 
(PART ONE |  PART TWO)

Definition of a function
(Video Links - Link 1 - Link 2 - Link 3 - Link 4)

Domain and range of a function

Sets and notations

Domain and range of functions using set notation 
( PART ONE | PART TWO | PART THREE)
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 )

Finding an element in the range

Finding an element in the domain

Inverse function  
(Introduction | Definition | Method ( PART ONE | PART TWO) | Drawing )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9 - Link 10)

Other types of functions

Composite Functions 
(Method | element in range | element in domain)
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6)

Self inverting functions

General Example

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

Modulus

(General Video Links - Link 1 - Link 2 - Link 3)

Definition and graph of y =|x|
(Video Links - Link 1 - Link 2)

Sketching y = |f(x)| 
( PART ONE | PART TWO ) 
(Video Links - Link 1)

Sketching y = f(|x|)
(Video Links - Link 1 - Link 2 )

Transformations of modulus function

Solving equations with modulus 
( PART ONE | PART TWO ) 
(Video Links - Link 1 - Link 2 - Link 3)

Modulus inequalities 
( PART ONE | PART TWO )
(Video Links - Link 1 - Link 2 - Link 3)

Transformations (combined)

Types ***Coming soon***
y =  x²  | y =  x³ | y =  e^x | 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
(Video Links - Link 1 - Link 2 -
 
Exponential curve and Transformations of f(x) = e^x
(Video Links - Link 1 - Link 2 - Link 3 -

Combined transformation of f(x) = e^x ***Coming soon***

Finding values of e^x

Natural logarithm definition and laws
(Video Links - Link 1 - Link 2 - 


Transformations of f(x) =ln(x)

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

Solving equations with e^x and ln(x) ***Coming soon***
(PART 1 | PART 2 )
(Video Links - Link 1 -

Solving equations with e^x and ln(x) in quadratic form

Exponential Rate of change ***Coming soon***
(Video Links - Link 1 - 

Exponential Growth and decay ***Coming soon***
(Video Links -  

Numerical Methods

Roots of equations

Change of sign 
(PART 1 | PART 2)
(Video Links - Link 1 - Link 2 - Link 3 - 

Fixed point iteration
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 -
 
Interval Bisection ***Coming soon***
(Video Links - Link 1 -
 
Linear interpolation ***Coming soon***

Newton Raphson ***Coming soon***

Numerical Integration

Trapezium rule
(Video Links - Link 1 - Link 2 -
 
Simpsons rule  
(PART 1 | PART 2)
(Video Links -  Link 1

mid ordinate rule  
(PART 1 | PART 2)
(Video Links - Link 1 - link 2 -
 
Errors

Trigonometry I

Reciprocal trigonometric functions
(Video Links - Link 1 - Link 2 - Link 3 )

Graphs of the reciprocal trigonometric functions
(Video Links - Link 1 - Link 2 - Link 3 )

Functions of the reciprocal trigonometric functions 

Proving identities using reciprocal trigonometric functions 
( PART ONE | PART TWO )
(Video Links - Link 1 - Link 2 )

Using Pythagoras' identities  
(PART ONE | PART TWO )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9 - Link 10 - Link 11 )

Inverse trigonometric functions and their graphs
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 ) 

Solving equations with inverse trigonometric functions  
( PART ONE | PART TWO )

Solving trigonometric equations  
( PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE | PART SIX | PART SEVEN | PART EIGHT )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9)

Trigonometry II

Compound Angles 
(General video Links - Link 1 - Link 2 - Link 3 -

Introduction
(PART ONE )
(Video Links - Link 1 -
 
Compound angle (Addition) formula - Introduction and Proofs 
(PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE | PART SIX )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9
 
Compound angle (Addition) formula - Solving Equations 
(PART ONE | PART TWO | PART THREE | PART FOUR )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 -
 
Double angle formula - Introduction and Proofs 
(PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 -
 
Double angle formula - Equations 
(PART ONE )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7

Half Angles and triple angles formula
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 -

acos x + bsin x form - Proofs and uses 
(PART ONE | PART TWO | PART THREE )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - 

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

(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 -

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

(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 -

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 ONE | PART TWO | PART THREE | PART FOUR | PART FIVE | PART SIX   )

Coordinate Geometry problems  
( PART ONE | PART TWO  )

Parametric Differentiation 
(  PART ONE | PART TWO | PART THREE ) 
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5)

Vectors***Coming soon***

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

Geometric Vector addition
Geometric Vector subtraction
Geometric Zero vector
Geometric Scalar multiplication
Vector notation: tail head notation
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

(General video Links - Link 1 - Link 2 - Link 3 - Link 4

Introduction
( PART ONE)

Trigonometric differentiation
( PART ONE )
(Video Links - Link 1 - Link 2 )

Exponetial differentiation
( PART ONE )
(Video Links - Link 1 - Link 2)

Chain rule 
( PART ONE | PART TWO )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8)

Natural logarithm  derivative
( Part ONE) 
(Video Links - Link 1 - Link 2) 

y = a^x derivative
(Video Links - Link 1 - Link 2 - Link 3)

Product rule 
(PART ONE | PART TWO | PART THREE )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4)

Quotient rule 
(PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4) 

Reciprocal of the derivative 
(  PART ONE | PART TWO )
(Video Links - Link 1 - Link 2)

Parametric Differentiation 
(  PART ONE | PART TWO | PART THREE ) 
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5)

Implicit Differentiation 
( PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9)

Rates of Change ***Coming soon***
(Video Links - Link 1 - Link 2 - Link 3 - Link 4)

Integration

(General Video Links - Link 1 - Link 2 -  

AS Level Integration 

(PART ONE )

List of derivatives
(PART ONE ) 
(Video Links - Link 1 - 

Integrals of trigonometric functions 
(PART ONE ) 
(Video Links - Link 1 - Link 2 - Link 3 - 

Integrals of trigonometric functions using identities 
(PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE | PART SIX |
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8

Integrals of exponential and reciprocal functions 
(PART ONE )
 (Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - 

Finding the anti derivative  
(PART ONE | ) 
(Video Links - Link 1

Integration by substitution 
(PART ONE )
(Video Links - Link 1- Link 2 - 

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

(Video Links - Link 1 - Link 2 - Link 3 -

(b) rational functions  
(PART ONE |

(Video Links - Link 1 -

(c) product of functions  
(PART ONE |

(Video Links - Link 1 - Link 2 -

(d) given the substitution 
(PART ONE |

(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9 - Link 10

Integration of partial fractions 
(PART ONE | PART TWO
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 -

Parametric Integration

(Video Links - Link 1 - Link 2 - Link 3 -

Integration by parts 
(PART ONE |
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 -

Mixed examples of Integration
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9 - Link 10 - Link 11 - Link 12 -  Link 13 - 

Definite integration 
(PART ONE | PART TWO |
(Video Links - Link 1 -

Volume of revolution 
(PART ONE | 
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 - Link 9 - Link 10 -

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

(Video Links - Link 1 - 

Numerical integration 

(a) Simpsons rule  
(PART 1 | PART 2)
(Video Links -  Link 1

(b) Mid ordinate rule  
(PART 1 | PART 2)
(Video Links - Link 1  - Link 2 -

(c) Trapezium rule
(Video Links - Link 1 - Link 2 -

Differential equations***NEW***

Introduction (PART ONE )

Forming differential equations ***COMING SOON***

(PART ONE | PART TWO )
(Video Links - Link 1 - Link 2 - Link 3 - Link 4 - Link 5 - Link 6 - Link 7 - Link 8 -

Solving separable variable differential equations ( PART ONE  | PART TWO | PART THREE )
(Video Links - Link 1 - Link 2 - 

Finding the constant (Particular solutions of differential equations)
(PART ONE )
(Video Links - Link 1 - Link 2 - 

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

Topic Maps

***Coming soon***