Binomial expansion
Manipulation of surds
![]() |
![]() |
![]() |
Rationalise denominators
![]() |
![]() |
![]() |
Quadratic formula
Complete the square
Factor theorem
Factor theorem solves cubic equation (ax3+bx2+cx+d=0)
Given that (x – 5) is a factor of x3 – 8x2 + 17x – 10, work out the quadratic factor.
Domain & range of a function
Composite functions
Express (5x + 6)4 in the form fg(x), stating the expressions corresponding to f(x) and g(x).
Starting with x gives the flow chart x → 5x + 6 → (5x + 6)4
This is the same as x → g(x) → fg(x) giving g(x) = 5x + 6, f(x) = x4 so fg(x) = (5x + 6)4
Given that f(x) = x + 1 and g(x) = x2 – 1. Find the composite function of fg(x) and gf(x).
Inverse functions
Graphs of exponential functions
Graphs of quadratic functions
General formula of quadratic function
Linear inequalities
When solving a linear inequality, if you multiply or divide by a negative, you reverse the sign.
Quadratic inequalities
To solve a quadratic inequality, find the critical values, then use a sketch to interpret these values as solution regions.
Index laws
Disguised quadratic equations
Algebraic proof
![]() |
![]() |
Sequences
Number sequence A number sequence is a set of numbers listed in a specific order, where the numbers can be found by a specific rule. |
Arithmetic progression (AP)
An arithmetic progression is a linear sequence in which the next term is obtained by adding a fixed common difference d, to the previous term
|
Sum of arithmetic progression (AP)
The sum of the first n terms of an AP with first term a and common difference d is given by
|
The difference method
Use of a difference method to find the formula for a linear sequence, a quadratic sequence or a cubic sequence is required. For the linear sequence, For the quadratic sequence, For the cubic sequence, |
Limiting value
Find the limiting value of