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derriviative of sin
cos
derivative of cos
-sin
integral of cos
sin x + c
integral of sin
-cos x +c
derrivative of -cosx
sin x
integral of -cosx
-sinx + c
derrivative of -sin x
-cos x
integral of -sinx
cos x + c
cosine rule
a2 =b2+c2- 2*b*c*cos(A)
area of non right triangle
½absin(C)
sec2x=
1+tan2(x)
cosec2x=
1+cot2(x)
arc length radians
rθ
sector area radians
1/2r2θ
range
all the y values
domain
all the x values
what transformation maps f(x) to f-1(x)
reflect in y=x
formula for nth term of arithmetic sequence
un=a+(n-1)d
nth term for geometric sequence
un=ar(n-1)
derrivative of a^x (a is constant non e)
lna times a^x
derriative of arcsin(x)
1/(1-x2)1/2
derrivative of arccos(x)
-1/(1-x2)1/2
derrivative of arctan(x)
1/(1+x2)
how to find point of inflection
find second derivative check its 0 then check either side and if sign changes its inflection point.
how to check if concave
if second derivative is negative when sub in x value its concave
how to check if convex
if second derivative is positive when sub in x value its convex.
factor theorem
(x-a) is a factor of f(x) IF f(a)=0
how to find binomial p(x<n)
binomial cd with x value as n-1
how to find binomial prob x less than or equal to n
x value = n this is default for calculator
how to find binomial prob (x>n)
1-p(x</=n)
how to find binomial P(x>/=n)
1-P(x</=n-1)
simple random sampling
every member equally likely, assign each number and random number generate
systemic sampling
take every k member from a population, e.g every 10th person
stratified sampling
split into groups e.g gender then sample each group in proportion to size
opportunity sampling
take whoever you can get until you have enough
quota sampling
use opportunity sampling until you meet a set quota for each group e.g 10 women 10 men
cluster
split population into clusters you expect to be similar then take sample from each cluster