VCE Specialist Mathematics/Units 3 and 4: Specialist Mathematics/Common Math Hacks

Preface
This page serves to categorize and organize commonly used mathematical hacks, which allow their users to complete questions faster, and with a greater deal of accuracy.

Ellipses, Hyperbolas
The values $$a$$ and $$b$$ can be fractional, as can be seen by taking the following equation:


 * $$\frac{4(x)^2}{1} + \frac{16(y)^2}{1} = 1$$ where $$ a = \frac{1}{2}, b = \frac{1}{4}$$

Equations found in questions may not be in the general form, and may need to be transformed via the complete the square method::

Circles
Equations found in questions may not be in the general form, and may need to be transformed via the complete the square method, in conjunction with extricating all variables from under root symbols; an example follows:

Circular Functions
j