Course curriculum

  • 1

    WEEK 1 - Inequalities

    • Quadratic Inequalities 1

    • Quadratic Inequalities 2

    • Quadratic Inequalities 3

    • Quadratic Inequalities 4

    • Rational Inequalities 1

    • Rational Inequalities 2
  • 2

    WEEK 2 - The Discriminant

    • Introduction to Discriminant

    • Calculating The Discriminant

    • The Discriminant And Real Roots

    • The Discriminant And Equal Roots

    • The Discriminant And No Real Roots
  • 3

    WEEK 3 - Surds

    • Surds Intro

    • Surds Simplification 1

    • Surds Simplification 2a

    • Surds Simplification 2b

    • Surds Simplification 2c

    • Surds Simplification 3

    • Surds Rationalisation 1

    • Surds Rationalisation 2a

    • Surds Rationalisation 2b
  • 4

    WEEK 4 - Indices

    • Multiplication

    • Division

    • Raising A Power To A Power

    • Negative Indices

    • Zero Index

    • Fractional Indices

    • Equations with Indices 1

    • Equations with Indices 2
  • 5

    WEEK 5 - Disguised Quadratic Equations

    • Equation with Squares

    • Equations with Cubes

    • Equations with Square Roots

    • Equations with Cube Roots

    • LESSON 5

    • Equation with Unknown Index 2

    • Equation with Unknown Index 3
  • 6

    WEEK 6 - Functions

    • Graphs of Functions

    • The Range of a Polynomial

    • The Range of Quadratic

    • The Range of a Square Root Function

    • The Range of a Rational Function

    • The Relationship Between a Function and Its Inverse

    • The Graphical Relationship Between a Function and Its Inverse

    • Inverse of a Quadratic
  • 7

    WEEK 7 - Polynomials

    • Introduction to Polynomials

    • How To Use Synthetic Division

    • How To Factor Using Synthetic Division

    • Non Factorisable Quadratic Factor

    • Modified Synthetic Division

    • Introduction To The Factor And Remainder Theorem

    • Factor And Remainder Theorem 1

    • Factor And Remainder Theorem 2

    • Factor And Remainder Theorem 3

    • Factoring without a Factor
  • 8

    WEEK 8 - Sum and Product

    • Introduction To Sum And Product of a Quadratic

    • Sum And Product of a Quadratic 1

    • Sum And Product of a Quadratic 2

    • Sum And Product of a Quadratic 3 Part 1

    • Sum and Product of a Quadratic 3 Part 2

    • Sum and Product of a Quadratic 4
  • 9

    WEEK 9 - Logarithms I

    • Introduction to Logarithms

    • Logarithmic Form and Unknown Values

    • Numbers to Logs of a Given Base

    • Proofs of Logarithmic Properties

    • Applications of Logarithmic Properties 1

    • Applications of Logarithmic Properties 2

    • Logarithmic Equations 1

    • Logarithmic Equations 2

    • Logarithmic Equations 3

    • Logarithmic Equations 4

    • Logarithmic Equations 5

    • Logarithmic Equations 6
  • 10

    WEEK 10 - Logarithms II

    • Linearising a Curve Introduction

    • Linearising a Curve 1

    • Linearising a Curve 2

    • Linearising a Curve 3

    • Determining An Unknown Index
  • 11

    WEEK 11 - Sequences and Series

    • Introduction To Sequences

    • Writing The Terms of a Sequence

    • Introduction To Series

    • Writing a Series Using Sigma Notation

    • Properties of Sigma Notation

    • Standard Formulae 1

    • Standard Formulae 2

    • Standard Formulae 3

    • Standard Formulae - Factorised Form 1

    • Standard Formulae - Factorised Form 2
  • 12

    WEEK 12 - Arithmetic Progressions

    • Introduction to Arithmetic Progressions

    • Finding the Common Difference

    • Proving an Arithmetic Progression

    • Finding an Unknown Term

    • Proof Involving the Sum of an Arithmetic Progression

    • Sum of an Arithmetic Progression 1

    • Sum of an Arithmetic Progression 2

    • Sum of an Arithmetic Progression 3
  • 13

    WEEK 13 - Geometric Progressions

    • Introduction to Geometric Progressions

    • Proving a Geometric Progression

    • Finding an Unknown Term

    • A Real World Problem

    • Proof Involving the Sum of a Geometric Progression

    • Using the Sum Formula for a Geometric Progression

    • Introduction to the Sum to Infinity

    • Sum to Infinity Problem
  • 14

    WEEK 14 - Vectors

    • i, j Representation

    • The Unit Vector 1

    • The Unit Vector 2

    • The Angle Between Two Vectors

    • The Angle Between Two Vectors 2
  • 15

    WEEK 15 - The Equation of a Circle

    • Derivation of the Equation of a Circle

    • Finding The Centre and Radius of a Circle

    • Tangents and Normals 1

    • Proving a Tangent

    • Tangents and Normals 2

    • Length of Tangent
  • 16

    WEEK 16 - Radian Measure

    • Introduction to Radian Measure

    • Converting From Degrees to Radians

    • Arc Length

    • The Area of a Sector

    • The Shaded Area 1

    • LESSON 5 - Exam Question 2

    • The Shaded Area 3
  • 17

    WEEK 17 - Trigonometry I

    • Trigonometric Identities

    • Proving Trigonometric Identities

    • Trigonometric Graphs

    • Sketch of Sine Graph

    • Sketch of Cosine Graph

    • Sketch of Tan Graph

    • Relationship Between Sine and Cosine

    • Unit Circle and Quadrant Rule

    • General Solutions 1

    • General Solutions 2

    • Trigonometric Equations 1

    • Trigonometric Equations 2

    • Trigonometric Equations 3

    • Trigonometric Equations 4

    • Trigonometric Equations 5
  • 18

    WEEK 18 - Trigonometry II

    • Compound Angle Formulae 1

    • Compound Angle Formulae 2

    • Compound Angle Formulae 3

    • Double Angle Formulae 1

    • Double Angle Formulae 2

    • Double Angle Formulae 3
  • 19

    WEEK 19 - DIFFERENTIATION I

    • Introduction to Differentiation

    • How To Differentiate Simple Functions

    • Differentiating Combined Funtions 1

    • Differentiating Combined Funtions 2

    • How To Use The Chain Rule

    • The Chain Rule and Rational Functions

    • The Chain Rule and Trigonometric Functions 1

    • The Chain Rule and Trigonometric Functions 2

    • Introduction To The Product Rule

    • The Product Rule and a Coefficient

    • Introduction to The Quotient Rule

    • The Quotient and Chain Rule

    • Trigonometric Functions Example 1

    • Trigonometric Functions Example 2

    • The Quotient Rule (Algebraic Simplification)
  • 20

    WEEK 20 - Differentiation II

    • How to Find the Gradient of a Curve

    • The Equation of a Tangent

    • The Equation of a Normal

    • Determining an Unknown Value

    • Introduction to Increasing and Decreasing Functions

    • The Sign Change Test

    • The Second Derivative Test

    • Maxima and Minima Worded Problem

    • Rate Of Change (Area of a Square)

    • Rate of Change (Area of a Sector)

    • Rate Of Change (Volume of a Sphere)

    • Rate Of Change (Volume of a Cone)
  • 21

    WEEK 21 - Integration

    • Introduction to Integration

    • How to Integrate Part 1

    • How To Integrate Part 2

    • Trigonometric Integration

    • Equation of a Curve 1

    • Differential Equations

    • Equation of a Curve 2

    • Equation of a Curve 3

    • The Definite Integral Part 1

    • The Definite Integral Part 2
  • 22

    WEEK 22 - Applications of Integration

    • Area Under a Curve 1

    • Area Under a Curve 2

    • Area Under a Curve 3

    • Area Between 2 Curves 1

    • Area Between 2 Curves 2

    • Area Below The x Axis 1

    • Area Below The x Axis 2

    • Area Below The x Axis 3

    • Volume About The x Axis 1

    • Volume About The x Axis 2
  • 23

    WEEK 23 - Kinematics

    • Displacement Time Graph

    • Velocity Time Graph 1

    • Velocity Time Graph 2

    • Motion In A Straight Line 1

    • Motion In A Straight Line 2

    • Motion In A Straight Line 3
  • 24

    WEEK 24 - Statistics

    • Stem And Leaf Introduction

    • Stem and Leaf With Mode And Mean

    • Stem and Leaf With Quartiles

    • Back to Back Stem and Leaf

    • Box Plot

    • The Mean

    • Standard Deviation Intro

    • Standard Deviation For Ungrouped Data

    • Standard Deviation For Grouped Data

    • Variance
  • 25

    WEEK 25 - Probability

    • Introduction to Probability

    • Sample Space

    • Tree Diagrams

    • Mutually Exclusive Events

    • Non Mutually Exclusive Events

    • Independent Events

    • Conditional Probability