HSC Mathematics Advanced, Extension 1, and Extension 2

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.

Preliminary

 * Basic arithmetic and algebra
 * /Real functions/
 * Trigonometric ratios
 * /Linear functions/
 * The quadratic polynomial and the parabola
 * Plane geometry &mdash; 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 sin&sup2;&alpha; and cos&sup2;&alpha;
 * 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