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 - Disguised Quadratic Equations

    • Laws of Indices - Multiplication

    • Laws of Indices - Division

    • Laws of Indices - Raising A Power To A Power

    • Laws of Indices - Negative Indices

    • Laws of Indices - Zero Index

    • Laws of Indices - Fractional Indices

    • Laws of Indices - Equations 1

    • Laws of Indices - Equations 2

    • Disquised Quadratic Equations 1

    • Disquised Quadratic Equations 2

    • Disquised Quadratic Equations 3

    • Disquised Quadratic Equations 4

    • Disquised Quadratic Equations 5

    • Disquised Quadratic Equations 6

    • Disquised Quadratic Equations 7
  • 5

    WEEK 5 - Functions

    • Mapping Diagrams

    • Ordered Pairs

    • Graphs of Functions

    • The Vertical Line Test

    • The Range of a Polynomial

    • The Range of a Quadratic

    • The Range of a Square Root Function

    • Range of a Rational Function

    • Injections (Equations)

    • Injections (Mapping Diagrams)

    • Injections 3 (Equations 2)

    • Injections 4 (Counter - Example)

    • Injections 5 (Domain Restriction)

    • Injections 6 (Horizontal Line Test)

    • Surjections (Mapping Diagrams)

    • Surjections (Equations 1)

    • Surjections (Equations 2)

    • Bijections

    • Inverse Functions (Mapping Diagrams)

    • The Relationship Between A Function And Its Inverse

    • The Graphical Relationship Between A Function And Its Inverse

    • Inverse of a Quadratic

    • Piece - Wise Functions 1

    • Piece - Wise Functions 2
  • 6

    WEEK 6 - Polynomials I

    • 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
  • 7

    WEEK 7 - Polynomials II

    • 11 - Introduction To Sum And Product Of A Quadratic

    • 12 - Sum And Product Of A Quadratic 1

    • 13 - Sum And Product Of A Quadratic 2

    • 14 - Sum And Product Of A Quadratic 3 Part 1

    • 15 - Sum And Product Of A Quadratic 3 Part 2

    • 16 - Sum And Product Of A Quadratic 4

    • 17 - Introduction To Sum And Product Of A Cubic

    • 18 - Sum And Product Of A Cubic 1

    • 19 - Sum And Product Of A Cubic 2

    • 20 - Sum And Product Of A Cubic 3 Part 1

    • 21 - Sum And Product Of A Cubic 3 Part 2

    • 22 - Sum And Product Of A Cubic 4 Part 1

    • 23 - Sum And Product Of A Cubic 4 Part 2

    • 24 - Sum And Product Of A Cubic 5

    • 25 - Factoring Polynomials
  • 8

    WEEK 8 - Logarithms

    • 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
  • 9

    WEEK 9 - Logarithms II

    • Introduction To Exponential Functions

    • Introduction To The Exponential Function

    • Sketching The Graph of an Exponential Function

    • Equations Involving The Exponential Function

    • Simultaneous Equation Involving The Exponential Function

    • Equation Involving The Natural Logarithm

    • A Modelling Problem

    • Unknown Indices

    • Unknown Indices (alternative Method)
  • 10

    WEEK 10 - The Modulus Function

    • Modulus Equations 1

    • Modulus Equations 2

    • Modulus Equations 3

    • Modulus Inequalities 1

    • Modulus Inequalities 2

    • Graphs of Modulus Functions

    • How to Graph a Modulus Graph
  • 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 - Mathematical Induction

    • The (k+1) Term

    • First Look At Mathematical Induction

    • Mathematical Induction (Summation 1)

    • Mathematical Induction (Summation 2)

    • Mathematical Induction (Summation 3)

    • Mathematical Induction (Divisibility 1)

    • Mathematical Induction (Divisibility 2)
  • 13

    WEEK 13 - Binary Operations

    • Cayley Table

    • Closure

    • Commutavity

    • Associativity

    • Identity And Inverse
  • 14

    WEEK 14 - Reasoning and Logic

    • Introduction to Reasoning and Logic

    • Truth Tables

    • Truth Tables 2

    • Truth Tables 3 (Implications)

    • Truth Tables 4 (Logical Equivalence)

    • Laws of Boolean Algebra 1

    • Laws of Boolean Algebra 2
  • 15

    WEEK 15 - Vectors

    • i, j Representation

    • i, j, k Representation

    • The Unit Vector 1

    • The Unit Vector 2

    • The Unit Vector 3

    • The Dot Product For 2 Dimensional Vectors

    • The Dot Product For 3 Dimensional Vectors

    • The Angle Between Two Vector (2 Dimensional Vectors)

    • The Angle Between Two Vectors 2 (2 Dimensional Vectors)

    • The Angle Between Two Vectors 3 (3 Dimensional Vectors)

    • Introduction To The Vector Equation of a Line

    • The Vector Equation of a Line 1

    • The Vector Equation of a Line 2

    • Parallel Lines

    • The Intersection of Two Lines

    • The Vector Equation of a Plane
  • 16

    WEEK 16 - 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 a Tangent

    • Intersection of Two Circles

    • Equation Given 3 Points
  • 17

    WEEK 17 - The Locus of a Point and Radian Measure

    • The Perpendicular Bisector

    • Locus of a Point 2

    • Introduction to Radian Measure

    • Converting From Degrees to Radians

    • Arc Length

    • The Area of a Sector

    • The Shaded Area 1

    • The Shaded Area 2

    • The Shaded Area 3
  • 18

    WEEK 18 - Trigonometry I

    • Trigonometric Identities 1

    • Trigonometric Identities 2

    • Proving Trigonometric Identities 1

    • Proving Trigonometric Identities 2

    • Graphs of Trigonometric Functions

    • Relationship Between Sine and Cosine

    • The 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

    • Trigonometric Equations 6

    • Trigonometric Equations 7 (Double Angle)

    • Trigonometric Equations 8 (Negative Direction)
  • 19

    WEEK 19 - Trigonometry II

    • Derivation of Harmonic Form

    • Harmonic Form (Solving Equations 1)

    • Harmonic Form (Solving Equations 2)

    • Harmonic Form (Extreme Values)

    • Harmonic Form (Extreme Values 2)

    • Compound Angle Derivation

    • Compound Angle Formulae 1

    • Compound Angle Formulae 2

    • Compound Angle Formulae 3

    • Derivation of Double Angle Formulae

    • Double Angle Formulae 1

    • Double Angle Formulae 2

    • Double Angle Formulae 3

    • Derivation of Half Angle Formulae

    • Half Angle Formulae 1

    • Half Angle Formulae 2

    • Derivation of Factor Formulae

    • Factor Formulae 1

    • Factor Formulae 2 (Trigonometric Identity)

    • Factor Formulae 3 (Equation)
  • 20

    WEEK 20 - Parametric Equations

    • Parametric Equations 1

    • Parametric Equations 2

    • Parametric Equations 3

    • Parametric Equations 4

    • Parametric Equations 5
  • 21

    WEEK 21 - Limits

    • Introduction To Limits

    • Introduction To Limits - Tabular Approach

    • Introduction to Limits - Graphical Approach

    • Limit As X Tends To Infinity 1

    • Limit As X Tends To Infinity 2

    • Limit As x Tends To Infinity 3

    • Limit as x Tends To Zero of 1/x

    • Limit As x Tends To Zero Of Sin(x)/x Part 1

    • Limit As x Tends To Zero Of Sin(x)/x Part 2

    • Limit As x Tends To Zero Of Sin(x)/x Part 3

    • Limit As x Tends To Zero Of Sin(x)/x Part 4

    • Limit Properties

    • Limits And Continuity 1

    • Limits And Continuity 2

    • Limits And Continuity 3

    • Limits And Piecewise Functions 1

    • Limits And Piecewise Functions 2

    • Limits By Algebra 1

    • Limits By Algebra 2
  • 22

    WEEK 22 - 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)

    • Introduction to The Second Derivative

    • Equation Involving The Second Derivative 1

    • Equation Involving the Second Derivative Part 1

    • Equation Involving the Second Derivative Part 2

    • Introduction to Parametric Differentiation

    • Parametric Differentiation and Trigonmetric Equations
  • 23

    WEEK 23 - 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

    • Introduction to Inflection Points

    • Concavity

    • Inflection Point and tthe Equation of a Normal

    • Curve Sketching - Polynomial

    • Curve Sketching - Rational Function

    • 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)
  • 24

    WEEK 24 - Integration I

    • Introduction to Integration

    • How to Integrate PART 1

    • How To Integrate Part 2

    • Trigonometric Integration

    • Differential Equations

    • Integration by Substitution 1

    • Integration By Substitution 2

    • Integration By Substitution 3

    • Integration By Substitution 4

    • The Definite Integral PART 1

    • The Definite Integral PART 2

    • Integration By Substitution with Limits 1

    • Integration By Substitution with Limits 2
  • 25

    WEEK 25 - Integration II

    • Equation of a Curve 1

    • Equation of a Curve 2

    • Equation of a Curve 3

    • Area Under a Curve 1

    • Area Under a Curve 2

    • Area Under a Curve 3

    • Area Under a Curve and the Sum of Rectangles

    • 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

    • Area Between y Axis 1

    • Area Between y Axis 2

    • Volume About The x Axis 1

    • Volume About the x Axis 2

    • Volume About y Axis