## Course curriculum

• 1

• 2

### Chapter 1 - The Nature Of Proof

• Chapter 1 - The Nature of Proof Worksheet

• 1.1 - The Language of Proof

• 1.2 - Simple Proofs

• 1.3 - Contrapositive Proofs

• 1.4 - Proof by Contradiction

• 1.5 - Inequality Proofs

• 1.6 - Mathematical Induction

• 1.7 - Harder Mathematical Induction

• 1.8 - Inequality Induction

• Chapter 1 - The Nature of Proof Worksheet ANNOTATED

• Chapter 1 Quiz

• 3

### Chapter 2 - Complex Numbers

• Chapter 2 - Complex Numbers Worksheet

• 2.1 - Introduction to Complex Numbers

• 2.2 - Arithmetic With Complex Numbers

• 2.3 - Roots of Polynomials With Real Coefficients

• 2.4 - Roots of Polynomials With Complex Coefficients

• 2.5 - The Argand Diagram

• 2.6 - Polar Form

• 2.7 - Curves and Regions

• 2.8 - Harder Curves and Regions

• 2.9 - Exponential Form and De Moivre_s Theorum

• 2.10 - Further Roots

• Chapter 2 - Complex Numbers Worksheet ANNOTATED

• 2.11 - Applications of De Moivre_s Theorum

• Chapter 2 Quiz

• 4

### Chapter 3 - Integration

• Chapter 3 - Integration Worksheet

• 3.1 - Algebraic Manipulation

• 3.2 - Further Algebraic Manipulation

• 3.3 - Substitution

• 3.4 - Further Substitution

• 3.5 - Partial Fractions

• 3.6 - Denominators With Quadratics

• 3.7 - Integration By Parts

• 3.8 - Further Integration By Parts

• 3.9 - Trigonometric Integrals

• 3.10 - Further Trigonometric Integrals

• 3.11 - Reduction Formulae

• 3.12 - Further Reduction Formulae

• Chapter 3 - Integration Worksheet ANNOTATED

• Chapter 3 Quiz

• 5

### Chapter 4 - Vectors

• Chapter 4 - Vectors Worksheet

• 4.1 - The Three Dimensional Plane

• 4.2 - The Dot Product

• 4.3 - Further Dot Products

• 4.4 - Geometric Proofs

• 4.5 - The Vector Equation Of A Line

• 4.6 - Vector Equations Of Circles And Spheres

• 4.7 - Further Vector Geometry

• Chapter 4 Vectors Worksheet ANNOTATED

• Chapter 4 Quiz

• 6

### Chapter 5 - Mechanics

• Chapter 5 - Mechanics Worksheet

• 5.1 - Forces And Acceleration

• 5.2 - Simple Harmonic Motion

• 5.3 - Further Simple Harmonic Motion

• 5.4 - Differential Equations For Simple Harmonic Motion

• 5.5 - Horizontal Resisted Motion

• 5.6 - Further Horizontal Resisted Motion

• 5.7 - Vertical Resisted Motion

• 5.8 - Further Vertical Resisted Motion

• 5.9 - Projectile Motion

• Chapter 5 - Mechanics Worksheet ANNOTATED

• Chapter 5 Quiz