AQA a level maths - core formulae

how do you work out arc length?

r0 when in radians

how do you work out area of a sector?

1/2r²0

how do you work out area of a triangle?

½ ab SinC

what is the cosine rule?

a²= b² + c² -2bc CosA

what is the sine rule when finding out a missing side?

a/SinA = b/sSinb

what is the sine rule when working out a missing angle?

SinA/a = SinB/b

how do you work out distance between two points?

sqr (x2-x1)² + (y2-y1)

what is the nth term of an arithmetic sequence?

Un = a + (n-1)d

what is the nth term of a geometric sequence?

Un = ar^n-1

what are the log rules?

• log a + log b = log ab

• log a - log b = log (a-b)

• log a^x = x log a

• loga 1 = 0

what are the trig identities that are derivied from the compound angel formulae?

sin2x = 2sinxcosx

cos2x = cos2x - sin2x which can then be further rearranged into 2cos2x-1 and 1-2sin2x

tan2x = 2tanx/1-tan2x

how do you work out tan using harmonic form?

for example,

Rsin(x+a) = acosx + bsinx

R= sqr a2 + b2

tana = a/b

what are the standard differentials?

• a^kx = ka^kx x (lna)

• tan kx = ksec2 kx → in formula booklet

• ln f(x) = f’(x)/f(x)

how do you differentiate an exponential term?

multiply by ln(base) and then multiply by the derivative of the power

what are the standard integrals?

• sin kx = -1/k cos kx

• sec2kx = 1/k tank kx → in formula booklet

• e^kx = 1/k e^kx

how do you reverse chain rule in integration?

1. let u = ()

2. find the differential; of u and rearrange to get dx=

3. replace all x functions with u and cancel if possible before integrating to make it easier by doing things like looking for expanding brackets and splitting fractions

4. change to limits from x= limits to u= limits

what is the rule for wheat should be u when intergrating by parts?

Log

Algebra

trigonometry

e

how do you determine the nature of a stationary point?

work out f’’(x)

if its more than 0 then its a minimum

if its equal to 0 then it could be a point of inflection

if its less then 0 then its a maximum

hwo do you work out if a stationary point is a point of inflection?

if f’’(x) is equal to 0

use x coordinates before and after the coordinate of the stationary point and if there is a change in sign of f’’(x) then there is a point of inflection at that coordinate