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.
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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.
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To both decimal places and "sig figs" (significant figures).
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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.
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Simplifying the buggers, adding them together, rewriting them with a common denominator...
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i.e., applying your 1337 mathematics skillz to "real-life" problems.
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Aka "order of operations" - brackets first, then powers, then division, multiplication, then addition and finally subtraction.
Basic algebraic manipulations
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ax, ax+c, x2, xa, x/a, 1/a and the like.
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Knowing what equations are and being able to solve them.
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As with equations, but change the = to a < or a >.
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Being able to find formulae for sequences, and continue a given sequence; you must be able to do this for linear and quadratic sequences.
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But no derivatives, luckily.
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Direct proportion and inverse proportion.
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Learn how to solve simultaneous linear equations. While you're at it, learn how to solve simultaneous linear and quadratic equations.
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Knowing how to write expressions like 4x3 + 9.
This basically covers properties of shapes, angles, measures and the stuff you can do with them, like constructions.
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Fortunately, you don't actually have to memorise the cosine rule; it's in the list of formulae on the exam.
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Measuring, in other words.
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Rotational symmetry, reflectional symmetry and bilateral symmetry.
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The three you need to know are reflections, translations, and rotations.
Problems in R3
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Given a straight line AB, straight edge, and compass, construct another line which is perpendicular to AB and bisects it.
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Given a straight line AB, straight edge, compass and a point P, construct another line perpendicular to AB and going through point P.
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Given an angle ABC, straight edge and compass, bisect ABC.
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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 A-level.
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Recognising surveys with obvious bias, and being able to write questionnaires which avoid bias.
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Picking an unbiased sample of people to collect data on.
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It's the square root of the variance!
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You need to understand pie charts, scatter diagrams and histograms. Oh, and line graphs.
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Mean, median and mode.
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Don't worry, they're not expecting you to do linear regression.
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You must be able to recognise and describe positive, negative and no correlations.
The contents of this writeup are in the public domain.