Home
Browse
Create
Search
Log in
Sign up
Upgrade to remove ads
Only $2.99/month
ACT Math
STUDY
Flashcards
Learn
Write
Spell
Test
PLAY
Match
Gravity
Terms in this set (65)
Area of circle
A=πr²
Circumference
C=2πr or C=πd
Area of a triange
A=½b×h (make sure you use a height that is perpendicular to the base!)
Area of a parallelogram
A=b×h (make sure you use a height that is perpendicular to the base! not just the side.)
Area of a rectangle
A=l×w
Area of square
A=s² (one side squared)
Area of a trapezoid
A=½(b₁+b₂)×h (make sure you use a height that is perpendicular to the base!) You can also think of it as average of the bases times the height.
Number of degrees in a circle
360
Number of degrees in a 4-sided figure
360
Number of degrees in a triangle
180
Number of degrees in any figure
(n-2)(180) where n is the number of sides
Supplementary angles
Form a straight line and add up to 180
Vertical angles
Are equal
2 parallel lines and a transversal
a=d=e=h
b=c=f=g
Volume of a rectangular prism
V=l×w×h
Volume of a cylinder
V=πr²×h (the area of the circular face multiplied by the height)
Pythagorean theorem
a²+b²=c²
45-45-90
ratio of sides: x, x, x√2
ex: 1, 1, √2 or 2, 2, 2√2
30-60-90
ratio of sides: x, x√3, 2x
ex: 1, √3, 2 or 2, 2√3, 6
Pythagorean triplet: 3, ___, ___
3, 4, 5
Pythagorean triplet: 5, ___, ___
5, 12, 13
Multiples of Pythagorean triplet: 6, ___, ___
6, 8, 10 (3, 4, 5 multiplied by 2)
Multiples of Pythagorean triplet: 9, ___, ___
9, 12, 15 (3, 4, 5 multiplied by 3)
Slope of a line going up to the right
positive
Slope of a line going down to the right
negative
Slope formula
change in y over change in x, rise over run
slope-intercept form
y=mx+b
sine
opposite over hypotenuse
(SOH)
cosine
adjacent over hypotenuse (CAH)
tangent
opposite over adjacent (TOA)
secant
1/cosine (reciprocal of cosine) (could see one question... maybe)
cosecant
1/sine (reciprocal of sine) (could see one question... maybe)
cotangent
1/tangent (reciprocal of tangent)
y=sin (x)
y=cos(x)
y=tan(x)
n²×n³
n⁵ (add the exponents)
n⁵÷n²
n³ (subtract the exponents)
(n²)⁴
n⁸ (multiply the exponents)
n⁻²
1/n² (a negative exponent is the reciprocal of that number with a positive exponent.)
fractional exponents
multiplying radicals (ex: √2×√10)
=√20=2√5
irrational numbers
cannot be made into a fraction. there are an infinite number, but a few examples are π, √2, √3...
imaginary number
because any number squared is positive √-1 is imaginary
mean
average
median
the middle number WHEN THE NUMBERS ARE IN ORDER. if there are an even number of numbers, then average the 2 in the middle.
mode
the number that appears the most
tangent of a circle
a line that intersects with a circle at just one point. it's perpendicular to the radius.
absolute value
distance from 0 on the number line. |-10|=10
prime number
has exactly 2 factors. ex: 2, 3, 5, 7...
1 is NOT prime.
similar triangles
set up a proportion. (similar triangles-> the angles are equal to each other, the sides are in ratio)
degrees in a sector of a circle
set up a proportion. x/360 = part representing the sector/ whole
midpoint
average of x's, average of y's
distance between two points
make a right triangle or use the distance formula
probability of independent events occuring
probability of first event × probability of second event × probability of third event...
translation
rotation
reflection
slopes of parallel lines
are equal
slopes of perpendicular lines
how to find where two lines intersect
set the equations equal to each other or graph with your graphing calculator
Permutation
Order matters.
n!
...! means factorial.
EX: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
2! = 2 x 1
Henry has 10 vases. He wants to pick 3 of them and put them on the mantle with one on the left, one in the middle, and one on the right. How many possible ways can he arrange them?
n!/(n-k)! (order matters)
when k objects will be selected from a set of n objects and will be placed IN ORDER from 1st to kth. (Permutation)
10!/(10-3)! = 10!/7! = (10 x 9 x 8 x 7 x 6 x5 x 4 x 3 x 2 x 1)/(7 x 6 x 5 x 4 x 3 x 2 x 1) = 10 x 9 x 8 = 720 ways
Andrew has 6 kinds of apples. He wants to choose 3 types for his applesauce. How many possible combinations does he have?
n!/[k!(n-k)!] (order doesn't matter)
when k objects will be selected from a set of n objects but will NOT be placed in order.
6!/[3!(6-3)!] = 6!/[(3!)(3!)] = (6x5x4x3x2x1)/(3x2x1x3x2x1) = (6x5x4)/(3x2x1)=5x4= 20 possible combinations of apples
OTHER SETS BY THIS CREATOR
Final Exam IR
51 terms
Chapter 15 & 16 Physics
45 terms
Chapter 15 Physics
18 terms
ACT English
22 terms