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.

1. ## Number

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.

1. ### Rounding

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

4. ### Operations with integers

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.

5. ### Fractions

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

7. ### Problem solving

i.e., applying your 1337 mathematics skillz to "real-life" problems.

10. ### BODMAS

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

2. ## Algebra

2. ### Graphs

2. #### Recognising graphs of common functions

ax, ax+c, x2, xa, x/a, 1/a and the like.

4. ### Equations

Knowing what equations are and being able to solve them.

5. ### Inequalities

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

7. ### Sequences

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.

10. ### Simultaneous equations

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

11. ### Index notation

Knowing how to write expressions like 4x3 + 9.

3. ## Space, Shape and Measures

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

5. ### Trigonometry

3. #### The sine rule and cosine rule

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

8. ### Mensuration

Measuring, in other words.

10. ### Transformations

The three you need to know are reflections, translations, and rotations.

18. ### The Four Constructions

1. #### Perpendicular bisection of a straight line

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

2. #### "Dropping a perpendicular"

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

3. #### Bisection of an angle

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

4. #### Construction of a 60° angle

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

4. ## Data Handling

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

3. ### Collecting data

1. #### Questionnaires

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

2. ### Sampling

Picking an unbiased sample of people to collect data on.

4. ### Processing and representing data

2. #### Standard deviation

It's the square root of the variance!

4. #### Charts

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

5. #### Averages

Mean, median and mode.

6. #### Lines of best fit

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

6. ### Correlations

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

The contents of this writeup are in the public domain.