General Things to remember Flashcards
(30 cards)
what is the range of a function?
it is the set of y values the function can give.
what is the domain of a function
it is the set of x values a function could have.
for inverse functions, what is the domain of it?
the range of the original function.
for an inverse function, what is the range of it?
it is the domain of the original function.
What should you do for sketching.
y = |f(x)|
- Sketch y = f(x)
- reflect anything below the x-axis in the x axis.
What should you do for sketching.
y = f(|x|)
- sketch y = f(x) for x >= 0.
- Reflect your sketch in the y-axis.
when having multiple combinations of transformations of a graph, what order do you do them for the example below?
af(bx+c)+d where abcd are transformations.
BIDMAS
B = 1st
C = 2nd
A = 3rd
D = 4th
what is the equation for an arithmetic series.
Un = a + (n-1)d
where a is the first item in the series n is the nth term and d is the common difference.
what is the equation for a geometric series.
Un = ar^n-1
what should you do when you have to differenciate the following problem.
6xy
when an xy is used, you should use product rule for differentiation.
dy/dx = (6x X 1dy/dx) + (y X 6)
= 6dy/dx + 6y
what are the properties of a Standard normal distribution?
it has a mean of 0 and a varience of 1^2 (or standard deviation of 1)
on which two conditions can you link a binomial distribution and a normal distribution?
If number of trials is large AND if probability is close to 0.5.
what are the two formulas for finding stanard deviation or mean when a binomial and a normal distribution are linked?
mean = number of trials x probability
standard deviation = sqrt(np(1-p)) - where p is probability and n is number of trials.
6 steps for finding a hypothesis testing solutions for a normal distribution.
- Define your random variable.
- Distribution for x
- Distribution for the sample mean of x.
- Write down your H0 and H1.
- Calculate the probability.
- Compare the probability with the significance level and state the conclusion with context.
What are the hypothesis testing conditions for a binomial distribution? (one tailed)
Reject H0 and Accept H1
If the probability < significance level
Accept H0 and Reject H1
If the probability > significance level
What are the hypothesis testing conditions for a binomial distribution? (two tailed)
Accept H0 and reject H1
If the probability > significance level
Reject H0 and Accept H1
If the probability < Significance level
What are the hypothesis testing conditions for a normal distribution? (using normal distribution)
Reject H0 and Accept H1
if the probability < significance level
Accept H0 and Reject H1
if the probability > significance level
What suvat equation is used for an object with constant velocity (vectors)?
r(t) = r(o) + vt
r(t) is the position of the object at time t
r(0) is the initial position of the object.
What is the equation for the horizontal part of projectiles with vectors.
S = vt
s = horizontal displacement
v = horizontal initial velocity
t = time
what is the suvat equation used for constant acceleration (vectors)?
R(t) = R (0) + ut + 1/2at^2
R(t) = position of R at time t
R(0) = inicial position of R
(ut + 1/2at^2) = displacement vector at time t.
what does r~ mean in vectors?
It is a postion vector, it can be differentiated to find velocity vector and again to find accelation vector.
what does v~ mean in vectors?
it is a velocity vector, it can be differenciated to find the acceleration vector and integrated to find the position vector.
what does a~ mean in vectors?
It is the acceleration vector, it can be integrated to find the velocity vector and integrated again to find the position vector.
when using double differenciation, what is the comparison for a local maximum?
d^2y/dx^2 < 0
