midpoint
add end points together and divide by two
distance
√(x-x)²- (y-y)²
slope
rise/run
slope-intercept
y=mx+b
point slope
y-y1=m(x-x1)
circle
(x-h)²+(y-k)²=r²
ellipse
((x-h)²/a²)+((y-k)²/b²)=1
volume of cube
s³
volume of rectangular prism
lwh
volume of triangular prism
1/2lwh
volume of cylinder
πr²h
volume of cone
1/3πr²h
volume of sphere
4/3πr³
area of square
s²
area of rectangle
lw
area of triangle
1/2bh
area of trapezoid
1/2(b1+b2)*h
surface area of rectangular prism
2lw+2wh+2lh
surface area of cube
6s²
circumference of circle
2πr
area of circle
πr²
degrees to radians
180°=1 radian
similar triangles
same angles different side lengths
Imaginary (complex) numbers
i²=-1
i^4=1
Integers
positive whole numbers
Absolute Value
The positive distance on a number line from 0
[3]=3, [-3]=3, [3-5]=[-2]=2
Logarithm
logB A=P, B^P=A
log2 8=3, 2³=8
PEMDAS
The preformed order of operations
1.Parentheses, 2.Exponents, 3.Multi, 4.Divide, 5.Add, 6. Subtract
Commutative Property
a + b = b + a
a x b = b x a
Associative Property
a+(b+c) = (a+b)+c
a x (b x c)=(a x b) x c
Distributive Property
a x (b+c)=(a x b) + (a x c)
Percent Change
% Change= (amount of change/original amount) x 100%
Sale Price
initial $ - discount OR
(initial $ - % discount) x initial price
FOIL (First, Outer, Inner, Last)
(x+5) (x+2)= x² - 2x + 5x - 10 → x² + 3x - 10
Factoring Quadratic
Given: ax² + bx + c = 0
x² + 9x + 18 = 0 → (x+6) (x+3) = 0 → x = -6,-3
Quadratic Formula
x = -b + √b² - 4ac / 2a
Discriminant
b² - 4ac
b² - 4ac > 0, there are 2 solutions
b² - 4ac < 0, there are NO solutions
b² - 4ac = 0, there are 1 solution
vertical angles
m<1 = m<3, m<2 = m<4
m<1 + m<3 = 180° , m<2 + m<4 =180°
SOH CAH TOA
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent
CSC SEC COT
csc = hypotenuse/opposite
sec = hypotenuse/adjacent
cot = adjacent/opposite
triangle degrees of SOH CAH TOA
sin 30° = ½ sin 60°=√3/2
cos 30° = √3/2 cos 60°= 1/2
tan 30°= 1/√3 tan 60°=√3
special right triangles
45° - 45° - 90°,
hypotenuse = x√2 , sides = x
30° - 60° - 90°
hypotenuse = 2x , adjacent(of 30°)= x√3 , opposite(of 30°) = x