Basically, Extension Mathematics builds on the 2 unit course. You go through more or less the same topics as Mathematics 2 Unit, but in Extension there are more concepts that are learnt on the same topic. There are some topics that are unique to Mathematics Extension 1 and is not covered in 2 unit Mathematics.
If you've done some Preliminary work already, then here's a little preview of the syllabus: (*means only covered in 3/4 unit)
1. Basic Arithmetic and Algebra
*Extension students also do "other inequalities" such as x/(x + 1) > 1 where you need to consider the possibility of the unknown being negative and whether or not to change the sign if you put the denominator on the other side.
2. Plane Geometry
*Extension students would do circle geometry in addition to this.
3. Probability
4. Real Functions of a Real Variable and Their Geometrical Representation
5. Trigonometric Ratios
*Extension students also do sums and differences of angles (i.e. sin(A+B) and cos(A+B)) as well as t-formulae, trigonometric identities and general solutions
6. Linear Functions and Lines
*Extension students will in learn in addition to this, the angle between two lines (in terms of co-ordinate geometry) as well as internal and external division of an interval in a given ratio
7. Series and Applications
*Extension students will do Mathematical Induction and applications in addition to this
8. The Tangent to a Curve and the Derivative of a Function
9. The Quadratic Polynomial and the Parabola
*Extension students will also do Parametric representation of the parabola as well as proving properties of chords, normals and tangents etc
10. Geometrical Applications of Differentiation
11. Integration
*Extension students will learns methods of integration, including reduction to standard forms by very simple substitutions
12. Logarithmic and Exponential Functions
13. The Trigonometric Functions
*Extension students will also do primitive functions of sin²x and cos²x
14. Applications of Calculus to the Physical World
*students doing Extension will cover the equation dN/dt = k (N – P), where k is the population growth constant, and P is a population constant as well as simple harmonic motion and projectile motion
*The following topics are ONLY covered in Extension Mathematics, so if you take 2 Unit Mathematics, you will not have to learn, or will miss out on these topics:
15. Inverse Functions and the Inverse Trigonometric Functions
16. Polynomials
17. Binomial Theorem
18. Permutations, Combinations and Further Probability
The hardest topic will depend on the individual. For me, it is usually Permutations, Combinations and Further Probability.
