Pythagoras' Theorem

 

`a^2+b^2=c^2`

 

 

Volume of a cone = `1/3pir^2h`

 

Curved surface area of a cone = `pirl`

 

 

Volume of a sphere = `4/3pir^3`

 

Surface area of a sphere = `4pirr^2`

 

 

`"adj = hyp"xxcostheta`

`"opp = hy "xxsintheta`

`"opp = adj"xxtantheta`

Or

`sintheta="opp"/"hyp"`

`costheta="adj"/"hyp"`

`tantheta="opp"/"adj"`

 

 

In any triangle `ABC`

Sine rule: `a/sinA=b/sinB=c/sinC`

Cosine rule: `a^2=b^2+c^2-2bc cosA`

Area of a triangle = `1/2 ab sinC`

 

 

Volume of a prism = area of cross section `xx`  length

 

 

Circumference of a circle = `2pir`

 

Area of a circle = `pir^2`

 

 

Curved surface area of a cylinder = `2pirh`

 

Volume of a cylinder = `pir^2h`

 

 

Area of a trapezium = `1/2(a+b)h`

 

 

The Quadratic Equation

The solutions of `ax^2+bx+c=0`,

where `a ne 0`, are given by

`x=(-b pm sqrt(b^2-4ac))/(2a)`

 

 

Arithmetic series

The sum of `n` terms, `S_n = n/2[2a+(n-1)d]`

 

Compound interest

Where `P` is the principal amount, `r` is the interest rate over a given period and `n` is number of times that the interest is compounded:
Total accrued `=P(1+r/100)^n`

 

Probability

Where `P(A)` is the probability of outcome `A` and `P(B)` is the probability of outcome `B`:
`P(A " or "B)=P(A)+P(B)- P(A" and "B)`
`P(A " and " B) = P (A " given " B) P(B)`