# GCSE Maths Formulae

All lengths are in cm.

## Volume of a Prism

$$V = \text{area of cross section} × \text{length}$$

## Volume of a Cylinder

$V = \pi r^2h$

## Volume of a Pyramid

$$V = \frac{1}{3} × \text{area of base} × h$$

## Circumference of a Circle

$C = \pi D\$ $\text{ or }$ $C = 2 \pi r$

## Area of a Circle

$A = \pi r^2$

## Speed, Distance, Time

$\text{speed} = \frac{\text{distance}}{\text{time}}$

## Density, Mass, Volume

$\text{density} = \frac{\text{mass}}{\text{volume}}$

## Trigonometric Ratios

$\sin x° = \frac{opp}{hyp}$ $\cos x° = \frac{adj}{hyp}$ $\tan x° = \frac{opp}{adj}$

## Sine Rule

$$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$

## Cosine Rule

$$a^2 = b^2 + c^2 - 2bc \cos A$$

## Area of a triangle

$$\text{Area of triangle} = \frac{1}{2}ab \sin C$$

## Pythagoras Theorem

$$\text{For a right-angled triangle,}$$ $$a^2 + b^2 = c^2$$

$\text{If } ax^2 + bx + c = 0 \text{ then:}$ $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$ $\text{where } a \ne 0.$