Math Rules Flashcards
what is the area of a triangle
A=(1/2)bh
what is the area of a rectangle
A=bh
what is the area of a trapezoid
A=(1/2)(b1+b2)(h)
what is the area of a circle
A=pi*r^2
what is the circumference of a circle
C=2pir
How do you calculate the volume of a cylinder or cube?
Take the area of the base X the height
What is the equation to find the mean of a group of numbers?
(mean = average) = (sum of #)/(total number of #)
What is the “mode” of a group of numbers?
the value that recurs the most
What is the “median” of a group of numbers?
the middle value when in order
What is the “range” of a group of numbers?
The largest # minus the smallest #
In an arithmetic sequence, you ___ to get the next term, while in a geometric sequence you _____ to get the next term.
arithmetic = add geometric= multiply
How do you find the reciprocal of a fraction?
You flip it over,
i.e. 2 -> 1/2
and 4/3 -> 3/4
etc.
What is/ how do you use the triple fraction method?
method:
(A/B)=(fact #1 for A / fact #1 for B) = (fact #2 for A / fact #2 for B)
use:
This is used for math problems where a constant relationship is metioned. For ex: Car A is driving at 2mph while car B drives at 3mph. If the speed relationship is maintained, and car A increases its speed to 4mph how fast must car B be going?
(2/3)=(4/x) -> x=6mph
USE THIS FOR ALL RELATION PROBLEMS
What is the probabilty that an event “x” happens, when the total number of possible events is “y”?
probability = (# of winners)/(total)=x/y
what is the equation for a line
y=mx + b
what is the equation for the slope of a line
slope=m=rise/run=(y2-y1)/(x2-x1)
What is “b” in the equation y=mx+b
b is the y-intercept, in other words, this is the value of y when x=0
When two lines are parallel their slopes ____ while when they are perpendicular their slopes _____
parallel lines: slopes are the same
perpendicular lines: slope= the negative reciprocal of the other line
To add or subtract fractions, first:
manipulate the fractions to have a common denominator. After this they can be added/subt. as follows:
ex: (1/2) + (3/4) = (2/4)+(3/4) =(5/4)
To multiply fractions
multiply the top number together to get the numerator and the bottom numbers together to get the denominator. ex) (1/2)*(3/4)= (3/8)
3/(2/5) = ? (in other words how do you divide by a fraction)
To divide by a fraction, multiply by the reciprocal:
3/(2/5)= 3 * (5/2) = (15/2)
what is the scientific notation of 300454?
3.00454 * 10 ^5
How do you FOIL? ex) (x+1)(x-2)=0
(x+1)(x-2)= 0
x^2 -2x +1x-2=0
reduce: x^2 -x -2 =0
How do you reverse FOIL (factor) ex) x^2 -7x +10=0
1) get in format where RHS=0:
x^2-7x+10=0
2) Look for a number combo where they add to the coefficient for x (-7), but they multiply to the coef. of x^2 times the non-x term (1 * 10 =10)
(-2) + (-5) =-7 and (-2) *(-5)= 10
3) Then put the number combo into (x + ….) format:
(x-5)(x-2)=0
4) If asked to solve, solve each portion w/ an x component:
x=5 and x=2
What is the equation for a right triangle?
a^2 + b^2 = c^2 where c is the hypotenuse
sin(x) = ?
sin(x) = opposite/hypotenuse
cos(x)=?
cos(x) = adjacent/hypotenuse
tan(x)=?
tan(x)=opposite/adjacent
what does sin^2(x) + cos^2(x) equal
sin^2(x) + cos^2(x) = 1
5! = ?
5! = 54321
-3 | = ?
-3 | = 3
What is the equation for distance?
distance= rate* time
notice that this may also be used by being given the distance and being asked to find the rate or the time
this one was an ACT favorite when back when I took it , there was always atleast 1 question so make sure you know how to use this
How do you find the distance between two points?
Make the distance you are trying to find the hypotenuse of a right triangle where the legs are values that you already know, then use a^2 + b^2 = c^2
What is the formula for a circle? Also what is the center of that circle?
formula: (x-h)^2 + (y-k)^2 = r^2
center: (h,k)
How does the imaginary number “ i “ work? ex) what does i^2 equal?
The imaginary number “i” equals the square root of -1.
ex) i^2 = (sqrt(-1))^2 = -1
advice: don’t let the “i’s” scare you, you can literally treat it like any other variable and then once you reduce the equation just plug in that i=sqrt(-1)
What is the equation for the midpoint of a line?
midpoint = [ (x1+x2)/2 , (y1+y2)/2 ]
What are the factors of a number? ex) 6
The prime numbers needed to be multiplied to make the product
ex) 6 = 2*3
What is a prime number?
A number who’s only factors are 1 and itself
What are the multiples of a number? ex) 5
They are any numbers that fit the formula: multiple=given number * integer
ex) multiples of 5 = 10, 15, 20, 25,….
What is the definition of a rational number?
Any number that can be expressed as a fraction.
NOTE: pi or sqrt(2) are examples of numbers that aren’t rational
On a sine or cosine graph, what is the amplitude and what is the period?
amplitude: the vertical distance from the middle of the function to the max or min
Period: the horizontal distance until the function repeats itself
What is an asymptote (on a graph)?
A value that a function will approach but never reach
Define domain and range
domain: allowed x-value inputs
range: possible y-value outputs
What is a perfect right triangle and what are two examples?
A perfect triangle is defined as a triangle that has a perimeter equal to its area
ex1) side lengths 3-4-5
ex2) side lengths 5-12-13
if logb(x)=a, what does x equal?
note: b stands for base and a stands for answer
ex) log4(x)=2
For logs x=b^a
ex) log4(x)=2 -> x=4^2=16
What can be done if there is an exponent in a log?
ex) log4(x)^2
It can be moved to the front of the log
ex) log4(x)^2 = 2*log4(x)
what can be done if there is a product in a log?
ex) log4(xy)
the log can be split into two parts and added
ex) log4(xy) = log4(x) + log4(y)
what can be done if there is division in a log?
ex) log4(x/y)
the log can be split into two parts and subtracted
ex) log4(x/y) = log4(x) - log4(y)
See picture of parallel axis rules
How well do you remember this?
See picture of 30-60-90 and 45-45-90 triangles
How well do you remember the side length rules?
see picture of matrix addition and multiplication by a scalar
How well do you understand these processes
See picture of the unit circle
How well do you remember the degrees/radians/quadrants?
How are exponents combined when two of the same number with different exponents are multiplied together?
ex) 8^2 * 8^4
The base number stays the same and the exponents are added together.
ex) 8^2 * 8^4 = 8^6
If a number has a negative exponent, what can be done?
ex) 7^-4
ex2) 1/6^-5
The number can be flipped to the otherside of the fraction and the exponent can be made positive
ex) 1/7^4
ex2) 6^5
What is the result when two exponents are applied to a number, (n^a)^b
ex) (8^4)^3
The base number stays the same and the exponents are multiplied together so that (n^a)^b= n^ab
ex) (8^4)^3 = 8^3*4 = 8^12
Any number with an exponent of zero equals what?
ex) 8^0
one
ex) 8^0 = 1
How can a radical [ c sqrt(d^e) ] be written in exponential form?
ex) 3 sqrt(4^5)
Notice: that I used “sqrt()” to represent the radical because I figured this notation would be familiar to you, but really this is a cube root
it can be written d^(e/c)
ex) 3 sqrt(4^5) = 4^(5/3)
How are exponents combined when two of the same number with different exponents are divided by one another?
ex) 8^2 / 8^5
The bottom exponent is subtracted from the top exponent and the base remains the same
ex) 8^2 / 8^5 = 8^(2-5) = 8^-3
