maths

Differentiation

Tell you the gradient of tangent

Normal = -1/gradient of curve

y-y1=m(x-x1)

Times then take

Stationary points - how to find

Differentiate to see where dy/dx = 0

Then substitute that x value into original equation (not the dy/dx equation).

Stationary point - max min or turning

Use d2y/dx2 to find if max min or turning.

Same as rate of change

If f’’ > 0 then min

If f’’ < 0 then max

If f’’ = 0 then any

To find if decreasing/ increasing

Find f’(x)

If increasing then find when f’(x)>0

If decreasing find when f’(x)<0

Then rearrange

Integration

Add 1, then divide

+C

Definite integrals give the area under the graph of the function you integrate. Then add or subtract.

Circles

(x-a)²+(y-b)²=r²

Complete the square if not in right form:

X² +bx+c = (x+(b/2))²-(b/2)²+c

Factor theorem harder

If f(b/a)=0 then (ax-b) is a factor of f(x)

Discriminant

(b²-4ac)

If b²-4ac>0 then 2 real roots

If b²-4ac=0 then 1 real root

If b²-4ac<0 then 0 real roots

Inequalities

If multiply or divide by a negative then flip sign

Proportion

Direct: y infinity x then y=kx

Inverse: y infinity (1/x) then y=k/x

Proof

Even is 2n

Odd is 2n+1

Vectors

Ex and logs

Ex logs 2

Ex logs 3