Inspired by the advice in Node More Mathematics and the lack of revision aids present on E2, I decided to come up with something which every GCSE Mathematics student will be able to enjoy. Note that I haven't made any distinctions between the foundation and higher tiers because quite often the boundary between them gets too blurred to make a distinction.
I've probably made some omissions or stupid mistakes. If so, /msg me.

Can you use the Western number system? This isn't just numbers, but also methods of calculation  these are divided into 3 parts  mental arithmetic, written calculation and calculator calculation.

To both decimal places and "sig figs" (significant figures).

This is the easy stuff, like addition, subtraction, multiplication, division and percentages, and some harder stuff like powers and roots. To a certain degree you'll be expected to do some mental arithmetic.

Simplifying the buggers, adding them together, rewriting them with a common denominator...

i.e., applying your 1337 mathematics skillz to "reallife" problems.


Aka "order of operations"  brackets first, then powers, then division, multiplication, then addition and finally subtraction.

Basic algebraic manipulations


ax, ax+c, x^{2}, x^{a}, x/a, 1/a and the like.


Knowing what equations are and being able to solve them.

As with equations, but change the = to a < or a >.

Being able to find formulae for sequences, and continue a given sequence; you must be able to do this for linear and quadratic sequences.

But no derivatives, luckily.

Direct proportion and inverse proportion.

Learn how to solve simultaneous linear equations. While you're at it, learn how to solve simultaneous linear and quadratic equations.

Knowing how to write expressions like 4x^{3} + 9.

This basically covers properties of shapes, angles, measures and the stuff you can do with them, like constructions.



Fortunately, you don't actually have to memorise the cosine rule; it's in the list of formulae on the exam.

Measuring, in other words.

Rotational symmetry, reflectional symmetry and bilateral symmetry.

The three you need to know are reflections, translations, and rotations.
Problems in R^{3}


Given a straight line AB, straight edge, and compass, construct another line which is perpendicular to AB and bisects it.

Given a straight line AB, straight edge, compass and a point P, construct another line perpendicular to AB and going through point P.

Given an angle ABC, straight edge and compass, bisect ABC.

Given a straight line AB, straight edge and compass, make a 60° angle at point A.

Data handling is generally split into two sections, probability and statistics. The connection between the two may not be immediately obvious until Alevel.

Recognising surveys with obvious bias, and being able to write questionnaires which avoid bias.

Picking an unbiased sample of people to collect data on.

It's the square root of the variance!

You need to understand pie charts, scatter diagrams and histograms. Oh, and line graphs.

Mean, median and mode.

Don't worry, they're not expecting you to do linear regression.

You must be able to recognise and describe positive, negative and no correlations.
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