###
quadratic formula

[-b ± √(b² - 4ac)] / (2a)

###
slope formula

(y₂- y₁) / (x₂- x₁)

###
integers

..., -3, -2, -1, 0, 1, 2, 3, ...

###
rationals

fractions (anything expessable as a ratio of integers)

###
reals

integers, rationals, plus special #s (like √2 or pi)

###
order of opperations

PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)

###
Arithmetic Sequences

t₁, t₁+ d, t₁+2d, ...

###
Geometric Sequences

t₁, t₁· r, t₁· r², ...

###
Factors

ex. factors of 52 are 2, 4, 13, and 26

###
Multiples

ex. multiples of 20 are 40, 60, 80, 100, ...

###
percentages

part = (percent / 100) x whole

###
average

average = sum of terms / number of terms

###
average speed

average speed = total distance / total time

###
sum

sum = average x (number of terms)

###
mode

mode = value in the list that appears most often

###
median

median = middle value in the list

###
fundamental counting principle

if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways.

###
probability

probability = number of desired outcomes / number of total outcomes

###
adding exponents

x^a · x^b = x^(a+b)

###
subtracting exponents

x^a / x^b = x^(a-b)

###
negative exponents

1 / x^b = x^(-b)

###
multiplying exponents

(x^a)^b = x^(a·b)

###
FOIL

(x+a)(x+b) = x^2 + (b+a)x + ab

###
difference of squares

a^2 -b^2 = (a+b)(a-b)

###
a^2 - 2ab + b^2

(a-b)(a-b)

###
distance formula

√[(x₂- x₁)^2 + (y₂- y₁)^2)]

###
mid-point formula

[(x₁+ x₂)/2 , (y₁+ y₂)/2]

###
intersecting lines

opposite angles are equal (each pair of angles along the same line add to 180 degrees)

###
area of triangle

area = (1/2)bh

###
angles of triangle

add up to 180 degrees

###
length of triangle sides

length of 1 side is always less than the sum of the other 2

###
equilateral

three equal sides, all angles = 60 degrees

###
isosceles

2 equal sides, 2 equal angles

###
similar

same shape, corresponding angles are equal, corresponding sides are in proportion

###
circle circumference

2 · pi · r

###
full circle

= 360 degrees

###
length of arc

(n degree / 360 degrees) · 2 · pi · r

###
area of sector

(n degree / 360 degrees) · pi · r^2

###
parallelogram area

area = lh

###
rectangular solid volume

volume = lwh

###
right cylinder volume

volume = pi · r^2 · h

###
prime factors

2, 3, 5, 7, 11, ...

###
Greatest Common Factor

ex. GCF of 200 and 60 is 20

###
Least Common Multiple

ex. LCM of 200 and 60 is 600

###
equation of circle

with midpoint (h,k) ... (x - h)^2 + (y - k)^2 = r^2

###
logarithms

y = log(little b)x asks b^y = x

###
complex numbers

i^0 = 1; i^1 = i; i^2 = -1; i^3 = -i; i^4 = 1; i^5 = i; i^6 = -1; i^7 = -i

###
sin of an angle

opp / hyp

###
cos of an angle

adj / hyp

###
tan of an angle

opp / adj

###
special sin cos relationship

sin^2(angle) + cos^2(angle) = 1

###
degree to radian

degree# · (pi / 180 degrees)

###
radian to degree

radian# · (180 degrees / pi)

###
trapezoid area

area = [(base1 + base2) / 2] · h

###
Slope intercept form

y=mx+b

###
Point-Slope form

y - y₁= m(x - x₁)

###
standard form

Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative

###
Dividing by a negative number in an inequality

You must flip the sign

###
Graphing < or > on a coordinate plane

dotted line

###
Graphing ≥ or ≤ on a coordinate plane

solid line

###
Graphing ≥ or > on a coordinate plane

shade upwards or to the right

###
Graphing ≤ or < on a coordinate plane

shade downwards or to the left

###
Chord

The distance from one point on the circle to another point on the circle.

###
Sector

The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.

###
arc

Part of a circle connecting two points on the circle.

###
Central Angle

An angle whose vertex is the center of the circle

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