HSC Mathematics Advanced, Extension 1, and Extension 2

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

Advanced course (assumed knowledge for both Extensions)

Preliminary

• 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

• 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

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

Preliminary

• 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

• Methods of integration
• Primitive of sin²α and cos²α
• Equation dN / dt = k(N - P)
• Projectile motion
• Further probability
• Iterative methods for numerical estimation of the roots of a polynomial equation
• Harder applications of HSC 2-Unit topics