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

Solve a quadratic equation by:

1. Rewriting the equation in the form ax² + bx +c = 0.

2. Factorise.

3. Make each bracket = 0 to solve the equation

Alternatively: you can use the quadratic formula after step 1.

1. Rewrite in the form x² + bx +c = 0, (if necessary divide by the multiple of x²)

2. Rewrite the x² + bx as (x - b/2)² -(b/2)² so that x² + 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:

x² - (sum of roots) x + product of roots

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.)