Pythagoras' Theorem

 

${\displaystyle a^2+b^2=c^2}$

 

 

Volume of a cone = ${\displaystyle \frac{1}{3}\pi r^{2}h}$

 

Curved surface area of a cone = ${\displaystyle \pi rl}$

 

 

Volume of a sphere = ${\displaystyle \frac{4}{3}\pi r^3}$

 

Surface area of a sphere = ${\displaystyle 4\pi r{r}^2}$

 

 

${\displaystyle \text{adj = hyp}\times \cos \theta }$

${\displaystyle \text{opp = hy }\times \sin \theta }$

${\displaystyle \text{opp = adj}\times \tan \theta }$

Or

${\displaystyle \sin \theta =\frac{\text{opp}}{\text{hyp}}}$

${\displaystyle \cos \theta =\frac{\text{adj}}{\text{hyp}}}$

${\displaystyle \tan \theta =\frac{\text{opp}}{\text{adj}}}$

 

 

In any triangle ${\displaystyle ABC}$

Sine rule: ${\displaystyle \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}}$

Cosine rule: ${\displaystyle a^2=b^2+c^2-2bc\cos A}$

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

 

 

Volume of a prism = area of cross section ${\displaystyle \times }$  length

 

 

Circumference of a circle = ${\displaystyle 2\pi r}$

 

Area of a circle = ${\displaystyle \pi r^2}$

 

 

Curved surface area of a cylinder = ${\displaystyle 2\pi rh}$

 

Volume of a cylinder = ${\displaystyle \pi r^{2}h}$

 

 

Area of a trapezium = ${\displaystyle \frac{1}{2}(a+b)h}$

 

 

The Quadratic Equation

The solutions of ${\displaystyle a{x}^2+bx+c=0}$,

where ${\displaystyle a\ne 0}$, are given by

${\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$

 

 

Arithmetic series

The sum of ${\displaystyle n}$ terms, ${\displaystyle S_n=\frac{n}{2}[2a+(n-1)d]}$

 

Compound interest

Where ${\displaystyle P}$ is the principal amount, ${\displaystyle r}$ is the interest rate over a given period and ${\displaystyle n}$ is number of times that the interest is compounded:
Total accrued ${\displaystyle =P{(1+\frac{r}{100})}^n}$

 

Probability

Where ${\displaystyle P\left(A\right)}$ is the probability of outcome ${\displaystyle A}$ and ${\displaystyle P\left(B\right)}$ is the probability of outcome ${\displaystyle B}$:
${\displaystyle P\left(A\text{or}B\right)=P\left(A\right)+P\left(B\right)-P\left(A\text{and}B\right)}$
${\displaystyle P\left(A\text{and}B\right)=P\left(A\text{given}B\right)P\left(B\right)}$