# HSC Extension 1 and 2 Mathematics

This is a book about the Australian extension mathematics syllabi, in particular the New South Wales course (Extension 2), though most other states' courses are very similar. The book aims to be useful as a revision guide for students doing the course, but it may also be of interest to others. It is assumed that the reader has done at least up to Year 10 mathematics.

## Contents

## Course Outline[edit]

### 2-Unit course (assumed knowledge for 3/4-Unit)[edit]

This book might not cover the 2-Unit course in any depth because this book is supposed to focus on extension maths, so it is assumed that the reader grasps the basic concepts required in the beginnings of the 3-Unit course. But feel free to add as much detail as you want to this section. If you are using this book and find that an explanation is unclear then you can always try wikipedia, and rewrite the explanation to make more sense.

#### Preliminary[edit]

- Basic arithmetic and algebra
- Real functions
- Trigonometric ratios
- Linear functions
- The quadratic polynomial and the parabola
- Plane geometry — geometrical properties
- Tangent to a curve and derivative of a function

#### HSC[edit]

- Coordinate methods in geometry
- Applications of geometrical properties
- Geometrical applications of differentiation
- Integration
- Trigonometric functions (including applications of trigonometric ratios)
- Exponential and logarithmic functions
- Applications of calculus to the physical world
- Probability
- Series and series applications

### 3-Unit course[edit]

#### Preliminary[edit]

- Other inequalities
- Circle geometry
- Further trigonometry (sums and differences, t-formulae, identities and equations)
- Lines and linear functions
- Internal and external division of lines into given ratios
- Parametric representation
- Permutations and combinations
- Polynomials
- Harder applications of the Preliminary 2-Unit course

#### HSC[edit]

- Methods of integration
- Primitive of sin²α and cos²α
- Equation
*dN / dt = k(N - P)* - Velocity and acceleration as a function of
*x* - Projectile motion
- Simple harmonic motion
- Inverse functions and inverse trigonometric functions
- Induction
- Binomial theorem
- Further probability
- Iterative methods for numerical estimation of the roots of a polynomial equation
- Harder applications of HSC 2-Unit topics