GCSE Maths Revision

Table of Contents

General advice


Checking your answer

There are many ways in which you can check whether you got the right answer. This is one of the most useful skills to have, and can save you a lot of marks in the exam. Some ways to do this are:

  • Ask yourself if the answer makes sense. If I am calculating the mass of a football, does it make sense if I get an answer of \(10^{23}\ \mathrm{kg}\)?!
  • If you are solving an equation, substitute your answer back in and see if it satisfies the equation.
  • Units can be a lifesaver. Check to see if the units of your answer make sense. (If I am expecting a volume, and I multiplied a time and a distance together, I've done something wrong!). In addition, I can't add two things together that have different units/dimensions.


  • Write down each step you do in an ordered way, one step after the other. If I make a mistake and need to go back, well-structured working will make that a lot easier. (Also you get marks for working ;)
  • Do not round until the end of a calculation. You will get rounding off errors and probably end up with the wrong answer!

Maths is like life – you should always ask:

  • Can I do it?
  • Should I do it?

Formula sheet


Right angled triangles


  • Trigonometry

    \[\mathrm{sin}\ A = \frac{\mathrm{a}}{\mathrm{c}}\] \[\mathrm{cos}\ A = \frac{\mathrm{b}}{\mathrm{c}}\] \[\mathrm{tan}\ A = \frac{\mathrm{a}}{\mathrm{b}}\]

  • Pythagoras' theorem

    \[a^2 + b^2 = c^2\]

Any triangle


  • Law of Sines

    \[ \frac{a}{\mathrm{sin\ } A} = \frac{b}{\mathrm{sin\ } B} = \frac{c}{\mathrm{sin\ } C} \]

  • Law of Cosines

    \[ c^2 = a^2 + b^2 - 2 a b \ \mathrm{cos\ } C \]


\[\mathrm{Circumference} = 2\pi r\] \[\mathrm{Area} = \pi r^2\]


\[\mathrm{Surface \ Area} = 4\pi r^2\] \[\mathrm{Volume} = \frac{4}{3}\pi r^3\]

Author: Laurence Sebastian Bowes

Created: 2018-10-05 Fri 00:19