Math Equations Flashcards
Rule of Imaginary Numbers
i=√-1, hence imaginary number, since you can’t normally take the square root of a negative number
This rule would then imply the following:
I^2= -1
I^3= -i
I^4= 1
To find i^x, divide x by four and look at the decimal value:
-if .25 it’s √-1
-.5 –> -1
-.75 –> -i
-.00 –> 1
Exponential Growth Model
y= a( 1 + r)^x
a= initial value
r- rate of growth –> write rate in decimal form
x= time changes based on the problem, but will usually be in years
Exponential Decay Model
y= a( 1 - r)^x
a= initial value
r- rate of decay –> write rate in decimal form
x= time changes based on the problem, but will usually be in years
Simple Interest
A=Prt
-P = starting amount
-r = rate (in decimal form)
-t = time
Compound Interest
A= P(1+ r/n)^nt
-n = # of times compounded in one “t”
Example: How much total amount of money is owed on a 1000 loan at 6% if compounded 2 times per year after 4 years?
n=2
Rule For Interest
you have to look at what the question is asking for. If it’s just asking for the interest owed, don’t use the isolated rate. If it’s asking for the total amount owed, you would add 1 to the rate.
How should surveys be taken?
The need to be random. This means that samples need to be taken randomly, without any biases. Survey’s should not be taken based on categorized groups unless it’s being compared. For instance, if you were trying to find the average child number in the household in a given city, you shouldn’t take samples from adults in a playground, because it’s more likely for these adults to have children.
–> pick most generalized answer!!!
How do you find Standard Deviation based on graph?
Find the difference in spread. A greater spread means a greater SD. This means that the SD will automatically have a greater range.
–> a double-top plot will automatically have a very high spread so look out for those graphs
How can you estimate the center of the data?
Look at where the clusters are, that’s typically where the mode, mean, median are located in
Tips for Exponential Growth Graphs
The vertical shift of an exponential graph is equal to the horizontal asymptote
Area of an equilateral triangle
(S^2√3)/4
Circle Equation
r^2=(x-h)^2+ (y-k)^2
-h and k are the center of the circle
-If given in an expanded form, group together like terms and complete the square to get into this format
Degrees/Radians
Degrees to radians –» degree # * (pi/180)
Radians to degree –»> # pi radians * (180/pi)
Area Of Sector of A Circle
Central Angle/360 * piR^2
–> think of multiplying the area of total circle by the shaded fraction (central angle/360)
If central angle is given in radians:
-1/2r^2* angle measure in radians
Arc Length of a Circle
Radians: radian angle measure * radius
Degrees: Central angle/360 * piD (multiplying entire circumference by the fraction of circle)
–> even if given degrees, you can still use the radian measure by converting. It could take faster to do it that way
