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 | edit source]Advanced course (assumed knowledge for both Extensions)
[edit | edit source]Preliminary
[edit | edit source]- 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 | edit source]- 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 | edit source]- Graphs
- Complex numbers
- Conics
- Integration
- Volumes
- Mechanics
- Polynomials
- Harder 3-Unit Topics
- /4-Unit/Mathematical inductions
Preliminary
[edit | edit source]- 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 | edit source]- 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