GCSE Maths Syllabus

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, x^a, 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.