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.

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