SCool Revision Summary
SCool Revision Summary
Basic Skills
Expanding 1 and 2 brackets (Practice)
Factorising a common factor into 1 bracket
Factorising a quadratic into 2 brackets
Solving Linear Equations
Solving Simultaneous Equations
Quadratics
Solve a quadratic equation by:

Rewriting the equation in the form ax^{2} + bx +c = 0.

Factorise.

Make each bracket = 0 to solve the equation
Alternatively: you can use the quadratic formula after step 1.
Completing the square

Rewrite in the form x^{2} + bx +c = 0, (if necessary divide by the multiple of x^{2})

Rewrite the x^{2} + bx as (x  b/2)^{2} (b/2)^{2} so that x^{2} + bx +c = (x  b/2)^{2} (b/2)^{2} + c
This gives you the minimum value of a quadratic: minimum value is the constant
((b/2)^{2} + c), when x = b/2.
If you know the roots of an equation then the original quadratic was:
x^{2}  (sum of roots) x + product of roots
Inequalities
Solve linear inequalities like normal equations. Remember (multiplying by 1) or (taking reciprocals) reverses the inequality sign.
For quadratic inequalities: Solve the equation = 0, and then use the shape of the graph to finalise the answer.
Remainder Theorem:
When dividing f(x) by (x  a), the remainder is f(a).
Factor Theorem:
If f(a) = 0, then (x  a) is a factor of f(x)
(When factorising polynomials, choose numbers that multiply together to make the constant.)