math Flashcards
to pass
Calculate E(x)
Formula: E(X * P(x))
-add all the sum of X*P(X))
what is the equation of circles?
(x-h)^2+(y-k)^2 =r^2
(-h,-k)=(x,y)square root r to find gradient.
concavity formulas:
if f(x)>0, this means that the graph is concave up. If f(x)<0, this means that the graph is concave down.
what is concavity used for?
concavity point is used for determining whether the stationary point is a local maximum or minimum. If is it concave down, it is the local maximum. If it is concave up, it is the local minimum.
P(A∪B), non-mutually? Also, what is it used for? For addition rule
P(A)+P(B)−P(A∩B) - used to calculate the probability that either event A or event B or both) will happen. (If the event happens at the same time we subtract P(A∩B) ).
what is the formula for odd function
f(-x)=-f(x)
what is the formula for even function
f(-x)=f(x)
P(A∪B), mutually? Also, what is it used for?For addition rule
P(A)+P(B)- used to calculate when the event cannot happen at the same time.
what is the formula for P(A∣B), conditional probability.
P(A∩B)/P(B) - used to find the probability of event A happening given that event B has already occur.
formula for P(A∩B)-multiplication independent(also explain what independent is)
P(A)×P(B)- Means the probability of A does not affect the probability of B. It is used for finding a and b at the same time.
Formula for P(A∩B)-multiplication dependent event.
P(A)×P(B∣A)- Means the probability of both A and B happening takes into the likely hood that B may change if A occur. Used to find the probability of both a and b happening
formula for P(A∣B)
P(BIA) * P(A)/P(B)- generally used in questions life if a patient were to test positive, what is the probability that they have a disease.
what is the formula for at least one?
P(at least one)= 1-P(none)
nature test?
f”(x)>0 the function is a local minimum
f”(x)<0 the function is a local maximum
f”(x)= 0 then test for concavity, typically point of inflexion.
transformation trigs formular
f(x) = a*sin(k( x + c) )+d
first principal
f(x+h) - f(x)/h
what is the steps to find point of inflexion
- find the second derivative
- set the second derivative to 0
- Check for the sign change in the second derivative by pluggin in the x-value(in f”(x)) slightly smaller and bigger than the f”(x) value and look for changes sign (from positive to negative or vice versa).
