AQA Maths Core 2

1. a^m x aⁿ = a^m+n

2. a^m / aⁿ = a^m-n

3. (a^m)ⁿ = a^mn

4. a^-n = 1/aⁿ

5. a⁰ = 1

6. a^1/n = ⁿÖa

7. a^m/n = ⁿÖa^m

If y=xⁿ then dy/dx  = nx^n-1

 If y=cxⁿ then dy/dx  = cnx^n-1

 If y=f(x)+g then dy/dx = f’(x)+g’(x)

 Tangent to (x₁,y₁) is given at y-y₁ = m(x-x₁) when m=gradient at the point

 Normal to a point has gradient of 1/m where m = gradient of tangent

 Stationary point ® second derivative: negative = maximum , positive = minumun

If dy/dx=xⁿ then y=(1/n+1)xⁿ⁺¹ +c

In definite integral ® no limits ® need a +c

Definite integral has limits ® then do F(b)-F(a)

Trapezium rule:        where h=(b - a)/n

y=sinθ crosses at 0, 180, 360

y=cosθ crosses at 90, 270

y=tanθ crosses at 0, 180, 360 heading up

Area = ½ ab sinC

A translation of         transforms the graph of y=f(x) to y=f(x)+b

A translation of         transforms the graph of y=f(x) to y=f(x-a)

A translation of         transforms the graph of y=f(x) to y=f(x-a)+b

A reflection in y=0 transforms the graph of y=f(x) to y=-f(x)

A reflection in x=0 transforms the graph of y=f(x) to y=f(-x)

A stretch of scale factor d in the y direction transforms the graph of y=f(x) to y=df(x)

A stretch of scale factor c in the x direction transforms the graph of y=f(x) to y=f(x/c)

To solve sin bx=k substitute u for bx to simplify, find interval of u, solve sin u=k, substitute back in

cos²θ + sin²θ = 1

tanθ=sinθ/cosθ

n!= n x (n-1) x (n-2) ... x 2 x 1

n!= n x (n-1)!

0!=1

ⁿC_r is the number of ways of taking r objects out of n objects

Pascal’s Triangle adds the two numbers above to get the number below

Inductive relates one to the previous         eg u_n=u_n-1+4n³

Arithmetic have first term a, common difference d , last term l 

 eg a + (a+d) + (a+2d)...

A series is an added sequence, sigma notation means series - used as short hand

1° = 2p/360 ^C

l=rθ

A= 0.5r²θ

30=p/6

45=p/4

60=p/3

90=p/2

180=p

360=2p

The curve y=a^x will always pass through (0,1) when x is positive

Logarithm of y to base a is written as log_ay

y=a^x  ® x=log_ay

log_aa=1    log_a1=0

log_ax + log_ay = log_axy

log_ax - log_ay = loga(x/y)

k log_ax = log_a(x^k)

a^x=b   ®   x= logb/loga          ß Take logs of both sides, rearrange and solve by calculator

a+ar+ar²+ar³+ar⁴….  First term a, common ratio r

S_¥=a/(1-r)