# HSC Mathematics Advanced, Extension 1, and Extension 2

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This book requires that you are familiar with mathematics up to Stage 5. |

*HSC Mathematics (Advanced, Extension 1 and Extension 2)*

*An Open Source Guide to Acing the HSC*

This book covers the New South Wales mathematics syllabi for Advanced, Extension 1 and Extension 2 levels. This aims to be a comprehensive guide to the course and heavily encourages contributions to improve its usefulness and keep it current in the face of more syllabus changes.

## Outline edit

### Advanced course (assumed knowledge for both Extensions) edit

#### 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

### Extension 1 course edit

- Graphs
- Complex numbers
- Conics
- Integration
- Volumes
- Mechanics
- Polynomials
- Harder 3-Unit Topics
- /4-Unit/Mathematical inductions

#### 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)* - [[HSC Mathematics Advanced, Extension 1, and Extension 2/3-Unit/HSC/Projectile motion|Projec\
- Further probability
- Iterative methods for numerical estimation of the roots of a polynomial equation
- Harder applications of HSC 2-Unit topics