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 ax2 + 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 x2 + bx +c = 0, (if necessary divide by the multiple of x2) 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 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.)