maths

how to work out when a sequence converges

set u.n and u.n+1 equal to L and solve for L

artithmetic sequence

u.n = a + (n-1)d

geometric sequence

u.n = ar^(n-1)

chain rule

easy

product rule

hard

differentiate (a^x)

a^x ln(a)

integrate 1/(ax+b)

1/a(ln(ax+B)) +c

differentiate tanx

sec^2(x)

sin2a

2sinAcosA

cos2A

2cos^2(a) - 1

1 - 2sin^2(a)

cos^2(a) - sin^2(a)

tan2a

(2tanA)/(1-tan^2(a))

secx =

1/cosx

cosecx =

1/sinx

cotx =

1/tanx or cosx/sinx

1 + cot^2(x) =

cosec^2(x)

tan^2(x) + 1

sec^2(x)

arc length

l = xr

area of a sector

a = 1/2(r^2)(x)

percentage error

|actual - estimate|/actual * 100

if f(b/a) = 0

ax-b is a factor

nC2

n(n-1)/2

how to find the mean from a frequency table

(Sum of the frequency of each x value multiplied by the x value) divided by the total frequency

how to find the variance from a frequency table

(Sum of the frequency of each x value multiplied by the x value squared) divided by the total frequency, all take away the mean squared

bivariate data

data that comes in pairs

simple random sampling

every possible sample has an equal chance of being selected

opportunity sampling

choosing respondents based on availability and convinience

systematic sampling

choosing participants at regular intervals from the population starting randomly

stratified sampling

dividing the population into subgroups and randomly sampling from each in proportion

quota sampling

splitting into groups depending on factors of the investigation then opportunity sampling from those groups

cluster sampling

splitting into clusters based on convinience then randomly choosing some clusters to study furhter

ABCD is a parralelogram IF

AB = DC

if ABCD is a parralelogram, it is a rhombus IF

magnitude of AB = magnitude of BC

midpoint of line segment connecting points with position vectors a and b has position vector

1/2(a+b)