AS Core

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Core AS Level Mathematics


Contents


AS LEVEL CORE NOTES

 


Numbers (Under construction)


Whole numbers 

Ordering whole numbers 

Adding whole numbers

Subtracting whole numbers

Multiplying whole numbers

Dividing whole numbers

Whole number properties (Number theory)

Number Theory Introduction

Factors and Highest Common Factors (HCF)

Multiples and Lowest Common Multiples (LCM)

Prime numbers

Prime number decomposition

Odd and even numbers

 Square, cube and triangle numbers

Positive Fractions 

Equivalent fractions and simplifying fractions

 Ordering fractions

Top heavy fractions and mixed numbers

Adding and subtracting fractions

Multiplication of fractions

Dividing of fractions

Adding, subtracting, multiplication and division of mixed numbers 

Use of calculator 

Positive decimals 

Ordering Positive decimals

Adding positive decimals

Subtracting positive decimals

Multiplying positive decimals

Dividing positive decimals

Directed (negative) numbers 

Rational Decimal (positive and negative) Numbers (including fractions and decimals) 

Converting decimals to fractions

Converting fractions to decimals 

 Arithmetic with negative fractions

 Arithmetic with negative decimals



Order of operations 

Non calculator

Use of calculator

Units of measures

Time

Distance

Angles

Rounding


Rounding numbers to decimal places

 Rounding numbers to significant figures

 Rounding numbers to powers of 10

Surds and indices  


Surds: Introduction
(Video Links - LINK 1 - LINK 2 -  )

Real numbers  and irrational numbers
(PART ONE)

Why are surds irrational numbers? (Under construction)


 Ordering real numbers (Under construction)
 
Properties of real numbers (Under construction)

Addition and subtraction of real (surd) numbers
(PART ONE | PART TWO )

Problem with using decimal form of real numbers (Under construction)

Simplifying surds (factorising surds)
(PART ONE | PART TWO | PART THREE | PART FOUR)

(Video Links - LINK 1 - LINK 2 -  )
 
Multiplication of real (surd) numbers 
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  )


Division (rationalising the denominator) of real numbers
(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 - )

 
Adding and subtracting surd fractions 
(PART ONE | PART TWO )

 Mulitplying surd fractions
(PART ONE )
 
Dividing surd fractions (Under construction)

General problems with surds (Under construction)

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - )

Finding decimal approximations of real numbers (Under construction)

Solving equations with surds (Under construction)

Indices: Introduction
(PART ONE )

(Video Links - LINK 1 - LINK 2 -  )

Indices: positive whole number powers
(PART ONE | PART TWO | PART THREE)
 
Indices: negative whole number powers
(PART ONE )
 
Indices: positive fractional powers
(PART ONE )

(Video Links - LINK 1 - LINK 2 -  )
 
Indices: negative fractional powers
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  )
 
Indices: Rules of indices
(PART ONE) 

(Video Links - LINK 1 - LINK 2 -  )

Indices: Mixed Number Examples
(PART ONE )

(Video Links - LINK 1 - LINK 2 -  LINK 3 - ) 

Indices: Mixed Algebra Examples
(PART ONE | PART TWO | PART THREE | PART FOUR )

(Video Links - LINK 1 - LINK 2 -  ) 

Solving equations with unknown base
(PART ONE | PART TWO)
 
Solving equations with unknown powers
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  )
 

Algebra (Under Construction)

Introduction, definition and notations

(Video Links - LINK 1 - LINK 2 -  ) 

Simplifying expressions: Collecting like terms

Simplifying expressions: Multiplication

Simplifying expressions: Division

Expanding single bracket

(Video Links - LINK 1 - LINK 2 -  )

Expanding several brackets

(Video Links - LINK 1 - LINK 2 -  )

Factorising expressions

(Video Links - LINK 1 - LINK 2 -  )

Solving linear equations: Balance method and algebraic tiles approach

Solving linear equations: one and two step equations

(Video Links - LINK 1 - LINK 2 -  )


Solving linear equations: Unknowns on both sides

(Video Links - LINK 1 - LINK 2 -  )

Solving linear equations: brackets

(Video Links - LINK 1 - LINK 2 -  )
Solving linear equations: Mixed (including basic fractions)

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - LINK 5 -)

Creating equations: Linear

Creating equations: Proportional

Creating equations: Inversely proportional    
 
Substitution: Expressions

Substitution: Formulae

Rearranging Formulae - Changing the subject
(PART ONE | PART TWO | PART THREE )

Methods as formula


Quadratic functions

Introduction and types of quadratics
(PART ONE)

(Video Links - LINK 1 - LINK 2 -  )
 
Plotting quadratic functions (Under construction)
(PART ONE)

Sketching quadratic functions 
(PART ONE | PART TWO | PART THREE | PART FOUR) 

(Video Links - LINK 1 - LINK 2 -  )

Factorising quadratics: 2 term quadratic
(PART ONE | PART TWO)

(Video Links - LINK 1 - LINK 2 -  )

Factorising quadratics: 3 term quadratic a = 1
(PART ONE | PART TWO | PART THREE )


(Video Links - LINK 1 - LINK 2 -  )

Factorising quadratics: 3 term quadratic a ≠ 1
(PART ONE  )

(Video Links - LINK 1 - LINK 2 -  LINK 3 - )

Factorising quadratics: Difference of two squares
(PART ONE | PART TWO | PART THREE)

(Video Links - LINK 1 - LINK 2 -  )
 
Expanding brackets: 1 brackets
(PART ONE)

Expanding brackets: 2 brackets
(PART ONE | PART TWO)


(Video Links - LINK 1 - LINK 2 -  ) 

Expanding brackets: How it works
(PART ONE)

Factorsing quadratics: How it works (Under construction)
(PART ONE)

Completing the square: How it works
(PART ONE )

(Video Links - LINK 1 - LINK 2 -  )

Completing the square: Method 
(PART ONE | PART TWO | PART THREE | PART FOUR)

(Video Links - LINK 1 - LINK 2 - LINK 3 - )
 
Completing the square: Properties (vertex and line of symmetry)
(PART ONE | PART TWO)

Completing the square: How to sketch quadratics using transformations
(Under construction)
(PART ONE)

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 -)

 Solving quadratic equations: Introduction
(PART ONE)

Solving quadratic equations: Factorisation
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  )

Solving quadratic equations: Completing the square
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  )

Solving quadratic equations: Quadratic formula
(PART ONE )

(Video Links - LINK 1 - LINK 2 -  )

Factorising using the quadratic formula

(Video Links - LINK 1 - LINK 2 -  )

Quadratic formula proof
(PART ONE)

Solving quadratic equations: Plotting quadratics (Under construction)
(PART ONE)

Solving quadratic equations: Graphical solutions (Under construction)
(PART ONE)

Solving quadratic equations: Almost or hidden quadratics
(PART ONE | PART TWO)

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - )

Solving quadratic equations: Graphical solutions
(PART ONE | PART TWO)

The discriminant: Introduction
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  )

The discriminant: General problems
(PART ONE | PART TWO )
(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 - LINK 5 - )


Simultaneous equations

Introduction
(PART ONE)
 
Coordinate geometry of two lines 
(PART ONE)

Forming simultaneous equations (Under construction)

Sketching simultaneous equations (Under construction)

Solving simultaneous equations graphically (Under construction)
(PART ONE | PART TWO)
 
Solving by substitution
(PART ONE | PART TWO)

(Video Links - LINK 1 -  -  )

Solving by elimination 
(PART ONE | PART TWO | PART THREE | PART FOUR )

(Video Links - LINK 1 - LINK 2 -  ) 


Why elimination method works (Under construction)

Solving one linear and one quadratic equations
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  ) 

Solving a line and a non linear equation (Under construction)

Solving 2 non linear equations (Under construction)


Polynomials and Transformations


 Division, factor and remainder theorem
Multiplication, addition, subtraction, binomial theorem
 
Polynomials: Introduction  
(PART ONE | PART TWO | PART THREE )


(Video Links - LINK 1 - LINK 2 -  )

Polynomials: Simplifying (Adding and subtracting) polynomials
(PART ONE | )

Polynomials: Multiplying polynomials (Expanding brackets)
(PART ONE | PART TWO | )

(Video Links - LINK 1 - LINK 2 -  )

Polynomials: Raising polynomials to a power
(PART ONE | )

Polynomials: Dividing polynomials - Long Division Method
(PART ONE | PART TWO ) 

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - LINK 5 - )

Polynomials: Dividing polynomials - Multiplication Method
 
(Video Links - LINK 1 - LINK 2 -  )
 
Polynomials: Why study Polynomials
(LINK ONE | LINK TWO | LINK THREE |


Polynomials: Evaluating Cubic Polynomials (Substitution)
(PART ONE |

(Video Links - LINK 1 - LINK 2 -  )

Polynomials: Factor Theorem
(PART ONE  | PART TWO | PART THREE

(Video Links - LINK 1 - LINK 2 -  )

Polynomials: Factorising Polynomials
(PART ONE | PART TWO | PART THREE |

(Video Links - LINK 1 - LINK 2 -  )

Polynomials: Solving Cubic Polynomial equations
(PART ONE | PART TWO

Why method for factorising works? (Under construction)

Polynomials: Division theorem 
(PART ONE | PART TWO

Polynomials: Dividing polynomials - Comparing Coefficients Method
(PART ONE|
 
Polynomials: Remainder Theorem
(PART ONE | PART TWO 

(Video Links - LINK 1 - LINK 2 -  LINK 3 - )  

Why remainder theorem works?
(PART ONE |

 Why factor theorem works?
(PART ONE |

Polynomials: Sketching Cubic Polynomials (Under construction)
(PART ONE

(Video Links - LINK 1 - LINK 2 -  )

Polynomials: Sketching Cubic Polynomials in factored form
(Under construction)
(PART ONE

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - LINK 5 - LINK 6 - LINK 7 -)

Polynomials: Sketching Cubic Polynomials in standard form
(Under construction)
(PART ONE

(Video Links - LINK 1 - LINK 2 -  )

Polynomials: Transformations of Cubic Polynomials
(Under construction)
(PART ONE

(Video Links - LINK 1 - LINK 2 -  )

Sketching and Transformations of curves (Under Construction)



Sketching curves introduction
(PART ONE |  

(Video Links - LINK 1 - LINK 2 -  )

Sketching the straight line curve
(PART ONE |

Sketching the quadratic curve
(PART ONE | 

Sketching the cubic curve
(PART ONE | 

Sketching the reciprocal curve (1/x)
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )

Finding asymptotes 

Finding undefined points on a curve

Sketching the exponential curve (ax)
(PART ONE |

Sketching the logarithm curve 
(PART ONE |  

Transformations of curves: Translation
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )

Transformations of curves: Reflection
(PART ONE |  

(Video Links - LINK 1 - LINK 2 -  )


Transformations of curves: Stretch or Enlargement
(PART ONE |  

(Video Links - LINK 1 - LINK 2 -  )

General problems with transformations
(PART ONE |  

(Video Links - LINK 1 - LINK 2 -  LINK 3 -)

 
Single transformation of the straight line curve
(PART ONE | 

Combined transformation of the straight line curve
(PART ONE | 

Single transformation of the quadratic curve
(PART ONE | 

Combined transformation of the quadratic curve
(PART ONE | 

Using transformations to sketching a general quadratic curve
(PART ONE | 

Single transformation of the cubic curve
(PART ONE | 

Combined transformation of the cubic curve
(PART ONE | 

Single transformation of the reciprocal curve (1/x)
(PART ONE | 

Combined transformation of the reciprocal curve (1/x)
(PART ONE | 

Single transformation of the the exponential curve (ax)
(PART ONE | 

Combined transformation of the the exponential curve (ax)
(PART ONE | 

Single transformation of the logarithm curve
(PART ONE | 

Combined transformation of the logarithm curve 
(PART ONE |

Sketching combinations of curves on same axes
(PART ONE |

Sequencing of combined transformations
(PART ONE | 

Solving points of intersection of curves on same axes
(PART ONE |


Inequalities

Introduction
(PART ONE)

(Video Links - LINK 1 - LINK 2 -  )

 Sketching inequalities
(PART ONE | PART TWO)
 
Solving linear inequalities
(PART ONE | PART TWO)

(Video Links - LINK 1 - LINK 2 - LINK 3 -  )
 
Why flip the inequality sign?
(PART ONE
 
Sketching double sided linear inequalities
(PART ONE | PART TWO | PART THREE)
 
Solving double sided linear inequalities
(PART ONE)
 
Solving 2 linear inequalities (simultaneous)
(PART ONE | PART TWO)

(Video Links - LINK 1 - LINK 2 -  )  
 
Sketching quadratic inequalities
(PART ONE)

(Video Links - LINK 1 - LINK 2 -  )  
 
Solving quadratic inequalities
(PART ONE | PART TWO )

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - LINK 5 -)  
 
Why method for solving quadratic inequalities work? (Under construction)
(PART ONE)
 
Solving one linear and one quadratic inequalities
(PART ONE | PART TWO)

Solving rational inequalities (Under construction)

General method of solving inequalities (Under construction)

Solving inequalities using critical values table (Under construction)
 
Using the discriminant  (Under construction)
( PART ONE | PART TWO)

(Video Links - LINK 1 - LINK 2 -  ) 
 
Finding regions (Under construction)
 

Coordinate Geometry (Under Construction)


 Straight Lines and Gradients
Distance between two points
Mid point between two points
Circles
Intercept between lines and circles


(General Video Links - LINK 1 - LINK 2 -)

Introduction and prior knowledge

Geometric objects and properties (point, line, circle, angles, length, area)

Coordinates and Cartesian axes

Pythagoras' Theorem

(Video Links - LINK 1 - LINK 2 -  )


Distance between two points

(Video Links - LINK 1 - LINK 2 -  )

Why Pythagoras' theorem is used to find the distance?
 
Mid point between two points

(Video Links - LINK 1 - LINK 2 -  )
 
Geometry of a single line

Gradients of lines

(Video Links - LINK 1 - LINK 2 -  )
 
Horizontal and vertical straight lines

Diagonal straight lines

Equations of lines (y = mx+ c form)

(Video Links -  LINK 1 -  LINK 2 - )

Finding the equation of the line (point slope method)

(Video Links - LINK 1 - LINK 2 -  )

Finding the equation of the line (2 point method)
 
Different forms of equations of lines

(Video Links - LINK 1 - LINK 2 -  )


Intercept of line and x and y axes

(Video Links - LINK 1 - LINK 2 -  )

Transformations of straight lines  

Geometry of two lines

(Video Links - LINK 1 - LINK 2 -  ) 

Intersection of two lines

Parallel lines

(Video Links - LINK 1 - LINK 2 - LINK 3 -  ) 

 Perpendicular lines

(Video Links - LINK 1 - LINK 2 -  ) 

 Why the product of the gradient of two perpendicular lines equal -1

General problems with two lines

(Video Links - LINK 1 - LINK 2 -  LINK 3 - ) 

 Geometry of Circles and circle theorems

(Video Links - LINK 1 - LINK 2 -  )

Equation of circle

(Video Links - LINK 1 - LINK 2 - LINK 3 - ) 

 Centre and radius of a circle

(Video Links - LINK 1 - LINK 2 -  LINK 3 - )

Sketching circles

(Video Links - LINK 1 - LINK 2 -  )

Transformation of circles 

Properties of circles (circle theorems)

General problems with circles

(Video Links - LINK 1 - LINK 2 -  )

Geometry of circles and lines (Tangents and Normals)

(Video Links - LINK 1 - LINK 2 -  )

General problems with circles and lines

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - LINK 5)

Sequences and series


 Introduction
Recurrence Relations
Arithmetic Progression
Geometric Progression
Sequences: Introduction

(Video Links - LINK 1 - LINK 2 -  )

Sequences: Convergent, Divergent, Periodic


(Video Links - LINK 1 - LINK 2 -  )

Sequence: The Nth term

Recurrence relations: Introduction

(Video Links - LINK 1 - LINK 2 -  )


Recurrence relations: Generating a sequence

(Video Links - LINK 1 - LINK 2 -  LINK 3 -)

Recurrence relations: Finding the recurrence relation from a sequence

 (Video Links - LINK 1 - LINK 2 -  )

Recurrence relations: Limit of a sequence

(Video Links - LINK 1 - LINK 2 -  )

Recurrence relations: General problems

(Video Links - LINK 1 - LINK 2 -  )

Sequences: Arithmetic Progression (A.P.)


(Video Links - LINK 1 - LINK 2 - LINK 3 -  )

Arithmetic Progression (A.P.): Finding the Nth term formula

(Video Links - LINK 1 - LINK 2 -  ) 

Arithmetic Progression (A.P.): Using the Nth term formula

(Video Links - LINK 1 - LINK 2 -  )

Arithmetic Progression (A.P.): Deriving the Nth term formula

(Video Links - LINK 1 - LINK 2 -  )

Arithmetic Progression (A.P.): General problems

(Video Links - LINK 1 - LINK 2 - LINK 3 -  )

Sequences: Geometric Progression (G.P.)

(Video Links - LINK 1 - LINK 2 - LINK 3 - )

Geometric Progression (G.P.): Using the Nth term formula

(Video Links - LINK 1 - LINK 2 -  )


Geometric Progression (G.P.): Deriving the Nth term formula


(Video Links - LINK 1  - LINK 2 -  )

Geometric Progression (G.P.): General problems

(Video Links - LINK 1 - LINK 2 - LINK 3 - )

Series: Introduction

(Video Links - LINK 1 - LINK 2 -  )

Series: Sigma notation

 
(Video Links - LINK 1 - LINK 2 - LINK 3 -  )

Arithmetic Series: Finding the Nth term of a series

(Video Links - LINK 1 - LINK 2 -  )


Arithmetic Series: Sum of N terms

(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 - LINK 5 - LINK 6 - )


Arithmetic Series: Deriving the Sum of N terms formula

(Video Links - LINK 1 - LINK 2 -  )


General problems with Arithmetic Series and sequences

(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 - LINK 5 - LINK 6 - LINK 7 - LINK 8 - )

Geometric Series: Sum of N terms


(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 -)

Geometric Series: Deriving the Sum of N terms formula

(Video Links - LINK 1 - LINK 2 -  )

Geometric Series: Sum to infinity and Limit of series

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - )

Geometric Series: Deriving the Sum to infinity formula

(Video Links - LINK 1 - LINK 2 -  )

General problems with Geometric Series and sequences 

(Video Links - LINK 1 - LINK 2 -  )

 


Binomial Expansion (Under Construction)


 Expanding Brackets
Expanding Multiple Brackets using Pascals triangle
Combinations and expanding brackets
Introduction
 
Expanding a binomial using Pascal's Triangle

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 )

Combinations and Pascal's Triangles

(Video Links - LINK 1 - LINK 2 -  )

Expanding (a + b)n form

(Video Links - LINK 1 - LINK 2 -  )

Finding specific terms or coefficients of a binomial expansion

(Video Links - LINK 1 - LINK 2 -  )
 
Expanding (1 + x)n form
 
Combinations of binomials

(Video Links - LINK 1 - LINK 2 -  )

Using binomial expansion to find an estimate of powers of numbers
(Video Links - LINK 1 - LINK 2 -  )
 
General problems

(Video Links - LINK 1 - LINK 2 -  )

Trigonometry (Under Construction)


 Right Angle Triangles
Any Triangle (cosine and sine rule)
Area of triangles
Bearings 
Functions and Graphs
Transformations
Equations and Identities (Part PART 1 | PART 2 | PART 3 | PART 4)


Angles in Degrees

Angles in Radians

(Video Links - LINK 1 - LINK 2 -  )

Why use radians instead of degrees? 

Converting between degrees and radians


(Video Links - LINK 1 - LINK 2 -  )

Triangle properties (notation, angles and area)

Naming and notation of triangles

(Video Links - LINK 1 - LINK 2 -  )


Trigonometry in right angle triangles

(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 - )


 How trigonometric formula work

Trigonometry in any triangles (sine and cosine rule)

Use of sine rule 

(Video Links - LINK 1 - LINK 2 -  )

Use of cosine rule 

(Video Links - LINK 1 - LINK 2 -  )

Proof of sine rule

Proof of cosine rule

Area of any triangle using trigonometric formula

(Video Links - LINK 1 - LINK 2 -  )

General problems using trigonometry

(Video Links - LINK 1 - LINK 2 -  )

Bearings

Problems in 3 dimensions

Recap of circle properties (names of parts, areas, circumference)

Arc length

(Video Links - LINK 1  - LINK 2 -  )

Derivation of the arc length formula

Area of a sector

(Video Links - LINK 1 - LINK 2 -  )

Derivation of the area of a sector formula


(Video Links - LINK 1 - LINK 2 -  )

General problems with circles (areas of segements, perimeter of sector, length of chord, etc)

(Video Links - LINK 1 - LINK 2 - LINK 3 -  )

Trigonometry for any angle (trig functions)

Common trigonometric ratios and their derivations

(Video Links - LINK 1 - LINK 2 -  )

Sketching trigonometric functions

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - )

Using the graphs of the trigonometric functions

(Video Links - LINK 1 - LINK 2 -  )

Transformations of trigonometric functions 

(Video Links - LINK 1 - LINK 2 -  )

Solving trigonometric equations 

(Video Links - LINK 1 - LINK 2 -  LINK 3 - )

Trigonometric identities

(Video Links - LINK 1 - LINK 2 -  )

Proof of trigonometric identities for tan and Pythagoras 

(Video Links - LINK 1 - LINK 2 -  )

Proving trigonometric identities 

(Video Links - LINK 1 - LINK 2 - LINK 3 -  )

Solving complex trigonometric equations

(Video Links - LINK 1 - LINK 2 - LINK 3 -  LINK 4 - LINK 5 - LINK 6 - )

Trigonometric ratios and the unit circle

Using CAST diagram to solve trigonometric equations

How the trigonometric curves are generated

Use of general formulae to solve trigonometric equations

How the trigonometric general formulae are derived?




Logarithms and exponentials (Under Construction)


 Exponential curve sketching
Rules of logs
Solving log and exponential equations
Reducing exponential equations to linear form

 Exponential function: Introduction

 Exponential function:Sketching

(Video Links - LINK 1 - LINK 2 -  )

Exponential function: Transformations

Exponential function:  Rules and indices

Exponential function: Simplifying 

Exponential function: Evaluating and substitution

Logarithm function: Introduction

 (Video Links - LINK 1 - LINK 2 -  )
  
Logarithm function: Inverse of exponential 

(Video Links - LINK 1 - LINK 2 -  )


Logarithm function: Sketching 

Logarithm function: Transformations

Logarithm function: Rules 

(Video Links - LINK 1 - LINK 2 -  )

Logarithm function: Derivations of rules

(Video Links - LINK 1 - LINK 2 -  )

Logarithm function: Simplifying

 (Video Links - LINK 1 - LINK 2 -  )

Logarithm function: Evaluating and substitution

Solving exponential and logarithm equations

(Video Links - LINK 1 - LINK 2 -  )

      






Differentiation 


 First Principles
Power Rule
Increasing and Decreasing functions
Tangents and Normals
Stationary points
Maxima and Minima
Point of Inflexion
Applications

(General Video Links - LINK 1 -

 Introduction and gradients of straight lines
(PART ONE |  

(Video Links - LINK 1 - LINK 2 -  LINK 3 - )

Gradients of non straight lines
(PART ONE | PART TWO

(Video Links - LINK 1 - LINK 2 -  )

Differentiation of  y = xn (power rule) and notation
(PART ONE | 

(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 - )

Differentiation from first principles (Derivation of power rule and proof)
(PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE


(Video Links - LINK 1 - LINK 2 -  )

Why use dy/dx notation?(Under construction)

Limits (Under construction)

 Differentiation of  y = axn (multiplicative constant rule)
(PART ONE | 
 
(Video Links - LINK 1 - LINK 2 -  )

Proof of multiplicative constant rule
(PART ONE | 

Differentiation of Sum rule (Differentiating polynomials)
(PART ONE | 
 
(Video Links - LINK 1 - LINK 2 -  )

Proof of Sum rule
(PART ONE | 

Differentiation of complex functions (surds, fractions, brackets)
(PART ONE | PART TWO | PART THREE
 
(Video Links - LINK 1 - LINK 2 -  )

Gradient at a point
(PART ONE | 
  
(Video Links - LINK 1 - LINK 2 -  )

Rates of change (Under construction)
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )

Tangents and Normals to a curve
(PART ONE | PART TWO | PART THREE | PART FOUR | PART FIVE | PART SIX | PART SEVEN | PART EIGHT | PART NINE | PART TEN

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - LINK 5 -)

Increasing and decreasing functions (Under construction)
(PART ONE | 
 
(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 -  )

Derivative equations (solving when dy/dx = a) (Under construction)
(PART ONE | 


Second derivatives and notation (Under construction)
(PART ONE | 
 
(Video Links - LINK 1 - LINK 2 - LINK 3 -  )

Stationary points (Under construction)
(PART ONE | 
 
(Video Links - LINK 1 - LINK 2 -  LINK 3 - )

Maximums and Minimums (Under construction)
(PART ONE | 
 
(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 - LINK 5 - )

Points of inflection (Under construction)
(PART ONE | 
 
(Video Links - LINK 1 - LINK 2 -  )

Finding vertices on quadratics and cubics (Under construction)
(PART ONE | 
 
Sketching quadratics and cubics including turning points (Under construction)
(PART ONE | 
 
Optimisation problems (maximising or minimising) (Under construction)
(PART ONE |   
 
(Video Links - LINK 1 - LINK 2 - LINK 3 -  LINK 4 - )


Integration (Under Construction)


 Indefinite

Definite

(General Video Links - LINK 1 -

Introduction
(PART ONE | 

Reversing differentiation: the anti deriviative
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )

Integrating y = xn (power rule) and notation
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  LINK 3  - LINK 4 - )

Derivation of integration power rule (using limits)
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )

Why the constant of integration exists?

(Video Links - LINK 1 - LINK 2 -  )


Integrating  y = axn (multiplicative constant rule)
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )


Integrating complex functions
(PART ONE |

(Video Links - LINK 1 - LINK 2 -  )

Integrating using Sum rule (integrating polynomials)
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )


Finding the constant of integration
(PART ONE | 

(Video Links - LINK 1 - LINK 2 - LINK 3 - ) 


Solving differential equations (integrating and finding the constant)
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )

Definite integration introduction
(PART ONE |


(Video Links - LINK 1 - LINK 2 -  )

Evaluating definite integration 

(Video Links - LINK 1 -  LINK 2 -  )

Definite integration and areas bounded by the curve, x axis and limits
(PART ONE | 

(Video Links - LINK 1 - LINK 2 - LINK 3 - )

Why constant of integration disappears?
(PART ONE | 
 
Derivation of integration
(PART ONE | 

Derivation of why differentiation and integration are inverse of each other (The fundamental theorem of calculus)
(PART ONE |


Finding areas below the x axis
(PART ONE |

(Video Links - LINK 1 - LINK 2 - LINK 3 -  LINK 4 - )

Finding areas bounded by two curves
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  LINK 3 - LINK 4 -  )
 
Finding areas between a curve and the y axis
(PART ONE |

Trapezium rule (numerical integration)
(PART ONE | 

(Video Links - LINK 1 - LINK 2 -  )

Derivation of Trapezium rule formula
(PART ONE |

Using Trapezium rule
(PART ONE |  
 
(Video Links - LINK 1 - LINK 2 - LINK 3 - LINK 4 - )

   

Proof and language of mathematics (Under Construction)

What is mathematics
What is doing mathematics
Common notation
Statements and truth
Implication (=>) including necessary or sufficient
if and only if (<=>)
What is proof and logic
How to prove by exhaustion
How to prove by contradiction
How to prove by counter example 
How to prove by deduction
Proof by induction
Disproving by contradiction
Disproving by counter example
Disproving by deduction
Problem solving ideas
How to lay out work



EDEXCEL Module C2 textbook book work
2.1 Algebra and Functions
2.2 Sine and Cosine Rule
2.3 Exponentials and Logarithms
2.4 Coordinate Geometry
2.5 Binomial Expansion
2.6 Radians, Sectors and Arcs
2.7 Geometric Sequences and Series
2.8 Trigonometric Functions
2.9 Differentiation
2.10 Trigonometric Identities and Equations
2.11 Integration






Topic Maps


(Under Construction)

Indices
Binomial Expansion
Circles
Coordinate Geometry (Under Construction)
Differentiation (Under Construction)
Inequalities (Under Construction)
Integration (Under Construction)
Polynomials (Under Construction)
Pre A Level (Under Construction)
Quadratics (Under Construction)
Simultaneous Equations (Under Construction)
Sketching Curves(Under Construction)
Transformations (Under Construction)

2 comments:

  1. Anonymous5 May 2014 at 09:09

    Hi I would really appreciate it if you could cover transformations soon!

    ReplyDelete
  2. TEACHERLOOKUP. COM30 November 2018 at 22:28

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