# GCSE Maths Revision

### Calculations

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.

#### Process

• 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

### Shapes

#### 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

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

#### Circles

$\mathrm{Circumference} = 2\pi r$ $\mathrm{Area} = \pi r^2$

#### Spheres

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

Created: 2018-10-05 Fri 00:19