1. Algebra & Functions

1.1 Modulus Functions

1.1.1 Modulus Functions - Sketching Graphs

1.1.2 Modulus Functions - Solving Equations

1.2 Polynomials

1.2.1 Polynomial Division

1.2.2 Factor & Remainder Theorem

1.2.3 Factorisation

1.2.4 Rational Expressions

1.2.5 Top Heavy Rational Expressions

1.3 Partial Fractions

1.3.1 Linear Denominators

1.3.2 Squared Linear Denominators

1.3.3 Quadratic Denominators

1.4 Further Modelling with Functions

1.4.1 Further Modelling with Functions

1.5 General Binomial Expansion

1.5.1 General Binomial Expansion

1.5.2 General Binomial Expansion - Subtleties

1.5.3 General Binomial Expansion - Multiple

1.5.4 Approximating values

2. Logs & Exponentials

2.1 Logarithmic & Exponential Function

2.1.1 Exponential Functions

2.1.2 Logarithmic Functions

2.1.3 "e"

2.1.4 Derivatives of Exponential Functions

2.2 Laws of Logarithms

2.2.1 Laws of Logarithms

2.2.2 Exponential Equations

2.3 Modelling with Logs & Exponentials

2.3.1 Exponential Growth & Decay

2.3.2 Using Exps & Logs in Modelling

2.3.3 Using Log Graphs in Modelling

3. Trigonometry

3.1 Reciprocal Trigonometric Functions

3.1.1 Reciprocal Trig Functions - Definitions

3.1.2 Reciprocal Trig Functions - Graphs

3.1.3 Trigonometry - Further Identities

3.2 Compound & Double Angle Formulae

3.2.1 Compound Angle Formulae

3.2.2 Double Angle Formulae

3.2.3 R addition formulae Rcos Rsin etc

3.3 Further Trigonometric Equations

3.3.1 Strategy for Further Trigonometric Equations

3.4 Trigonometric Proof

3.4.1 Trigonometric Proof

4. Differentiation

4.1 Further Differentiation

4.1.1 Differentiating Other Functions (Trig, ln & e etc)

4.1.2 Product Rule

4.1.3 Quotient Rule

4.2 Implicit Differentiation

4.2.1 Implicit Differentiation

4.3 Differentiation of Parametric Equations

4.3.1 Parametric Equations - Basics

4.3.2 Parametric Equations - Eliminating the Parameter

4.3.3 Parametric Equations - Sketching Graphs

4.3.4 Parametric Differentiation

5. Integration

5.1 Further Integration

5.1.1 Integrating Other Functions (Trig, ln & e etc)

5.1.2 Integrating with Trigonometric Identities

5.1.3 f'(x)/f(x)

5.1.4 Substitution (Reverse Chain Rule)

5.1.5 Harder Substitution

5.1.6 Integration by Parts

5.1.7 Integration using Partial Fractions

5.1.8 Integration Decision Making

5.2 Differential Equations

5.2.1 General Solutions

5.2.2 Particular Solutions

5.2.3 Separation of Variables

5.2.4 Modelling with Differential Equations

5.2.5 Solving & Interpreting Differential Equations

6. Numerical Methods

6.1 Numerical Solutions of Equations

6.1.1 Change of Sign

6.1.2 Change of Sign Failure

6.1.3 x = g(x) Iteration

7. Vectors

7.1 Vectors in 2 Dimensions

7.1.1 Basic Vectors

7.1.2 Magnitude & Direction

7.1.3 Vector Addition

7.1.4 Position Vectors

7.1.5 Problem Solving using Vectors

7.2 Vectors in 3 Dimensions

7.2.1 Vectors in 3 Dimensions

7.2.2 Problem Solving using 3D Vectors

7.3 Further Vectors

7.3.1 Equation of a Line in Vector Form

7.3.2 Parallel, Intersecting & Skew Lines

7.3.3 The Scalar ('Dot') Product

7.3.4 Uses of the Scalar Product

8. Complex Numbers

8.1 Complex Numbers

8.1.1 Intro to Complex Numbers

8.1.2 Complex Conjugation & Division

8.1.3 Square Roots of a Complex Number

8.1.4 Complex Roots of Polynomials

8.2 Argand Diagrams

8.2.1 Argand Diagrams - Basics

8.2.2 Geometry of Complex Addition, Subtraction & Conjugation

8.2.3 Modulus & Argument

8.2.4 Loci in Argand Diagrams

8.2.5 Inequalities & Regions in Argand Diagrams

8.3 Further Complex Numbers

8.3.1 Exponential Form of Complex Numbers

8.3.2 Geometry of Complex Multiplication & Division

8.3.3 Square Roots of a Complex Number - Advanced