Algebraic skills

Removing brackets is to multiply the term outside the brackets by each term inside - also known as the distributive law. Use FOIL to remove a pair of brackets then simplify by collecting like terms.

Factorising an expression is to write it as a product of its factors. There are 4 methods: common factor, difference of two squares, trinomial/quadratic expression and completing the square.

Completing the square is a method used to solve quadratic equations that will not factorise.

Like other fractions, algebraic fractions can be simplified by cancelled down by dividing the numerator and the denominator by a common factor.

Algebraic fractions can be added, subtracted, multiplied or divided using the same basic rules as working with other fractions.

The equation of a straight line can be worked out using coordinates and the gradient, and vice versa.

As with other equations and inequations, when working with algebraic equations and inequations it is key to change operation when you change side.

Simultaneous equations can be solved algebraically by first eliminating one of the unknowns so the other can be found.

To change the subject of a formula the terms are rearranged following the general rule, change side, change operation.

The equation of a a quadratic function can be determined from a graph showing the turning point and another point on the graph.

To sketch a quadratic function you must first determine the roots, nature and coordinates of the turning point and the y-intercept.

The key features of a quadratic function are the y-intercept, the axis of symmetry, and the coordinates and nature of the turning point (or vertex).

Revise the methods of solving a quadratic equation, including factorising and the quadratic formula. See a worked example of how to solve graphically.

The quadratic formula can be used to solve any quadratic equation but is best saved for when an equation cannot be factorised.

Whether the discriminant is greater than zero, equal to zero or less than zero can be used to determine if a quadratic equation has no real roots, real and equal roots or real and unequal roots.