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).

    2. Estimation

    3. Ratios

    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...

    6. Orders of magnitude

    7. Problem solving

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

    8. Decimals

    9. Calculator methods

    10. BODMAS

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

  2. Algebra

    1. Basic algebraic manipulations

    2. Graphs

      1. Plotting graphs

      2. Recognising graphs of common functions

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

    3. Functions

      1. Transformation of functions

      2. Recognising common functions

    4. Equations

      Knowing what equations are and being able to solve them.

    5. Inequalities

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

    6. Factorisation, expansion and simplification of expressions

    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.

    8. Gradients

      But no derivatives, luckily.

    9. Proportions

      Direct proportion and inverse proportion.

    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.

    1. Angles

    2. Geometry and properties of the circle

    3. Geometry and properties of 3-D shapes

    4. Geometry and properties of polygons

      1. Area

      2. Perimeter

      3. Pythagoras' theorem

    5. Trigonometry

      1. Sines, cosines and tangents

      2. Opposites, adjacents, and hypotenuses

      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.

    6. Coordinates

    7. Bearings

    8. Mensuration

      Measuring, in other words.

    9. Symmetry

      Rotational symmetry, reflectional symmetry and bilateral symmetry.

    10. Transformations

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

    11. Volume

    12. Arcs and sectors

    13. Loci

    14. Vectors

    15. Problems in R3

    16. Congruency

    17. Similar shapes

    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.

    1. Probability

    2. Measures of spread

    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

      1. Frequency diagrams

      2. Standard deviation

        It's the square root of the variance!

      3. Range

      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.

    5. Interpreting raw data

    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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