Maths A level stuff

Chain rule

dy/dx = dy/du x du/dx

Product rule

if y=uv then

dy/dx = v(du/dx) + u(dv/dx)

Quotient rule

if y=u/v

dy/dx = (v(du/dx) - u(dv/dx))/v^2

Differentiate y = e^x

dy/dx = e^x

Differentiate y = lnx

dy/dx = 1/x

Differentiate y = tanx

dy/dx = sec^2x

Differentiate y = cotx

dy/dx = -cosec^2x

Differentiate y = secx

dy/dx = tanxsecx

Differentiate y = cosecx

dy/dx = -cotxcosecx

Differentiate y = sinx

dy/dx = cosx

Differentiate y = cosx

dy/dx = -sinx

Small angle approximation of sinx

x

Small angle approximation of cosx

1-x^2/2

identity linking cos and sin

cos^2x + sin^2x = 1

Identity linking tan and sec

1 + tan^2x = sec^2x

Identity linking cot and cosec

1 + cot^2x = cosec^2x

sin addition identities

cos addition identities

tan addition identities

sin double angle formula

sin2A = 2sinAcosA

cos double angle formulae

cos2A = cos^A - sin^A

cos2A = 2cos^A - 1

cos2A = 1 - 2sin^A

tan double angle formula

tan2A = 2tanA/(1 - tan^2A)

Binomial: (1+ax)^n

1 + ax + n(n-1)(ax)^2/2! + n(n-1)(n-2)(ax)^3/3!

Power reduction formula: cos

cos^2A = (1 + cos2A)/2

Power reduction formula: sin

sin^2A = (1-cos2A)/2

Power reduction formula: tan

conditional probability formula

basic probability formulae

mean and standard deviation formulae

Expected value for discrete probability distributions

E(X)=Σx*P(X=x)

Binomial and geometric distribution

Conditions needed for binomial distribution

1. A fixed number of trials

2. Each trial must be independent of the others.

3. There are only two mutually exclusive outcomes for each trial (success or failure).

4. Constant probability of success.

Geometric sequence Un

Geometric sequence Sn

Geometric sequence sum to infinity

-1<r<1

Coding

Y= aX+b

E(Y)=aE(X)+b

Var(Y)=a²Var(X)

Normal distribution: finding Z

conditions for binomial to be approximated to normal

1. np>5

2. nq>5

Normal distribution of the sample mean