[-b ± √(b² - 4ac)] / (2a)
(y₂- y₁) / (x₂- x₁)
..., -3, -2, -1, 0, 1, 2, 3, ...
fractions (anything expessable as a ratio of integers)
integers, rationals, plus special #s (like √2 or pi)
order of opperations
PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)
t₁, t₁+ d, t₁+2d, ...
t₁, t₁· r, t₁· r², ...
ex. factors of 52 are 2, 4, 13, and 26
ex. multiples of 20 are 40, 60, 80, 100, ...
part = (percent / 100) x whole
average = sum of terms / number of terms
average speed = total distance / total time
sum = average x (number of terms)
mode = value in the list that appears most often
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 = number of desired outcomes / number of total outcomes
x^a · x^b = x^(a+b)
x^a / x^b = x^(a-b)
1 / x^b = x^(-b)
(x^a)^b = x^(a·b)
(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
√[(x₂- x₁)^2 + (y₂- y₁)^2)]
[(x₁+ x₂)/2 , (y₁+ y₂)/2]
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
three equal sides, all angles = 60 degrees
2 equal sides, 2 equal angles
same shape, corresponding angles are equal, corresponding sides are in proportion
2 · pi · r
= 360 degrees
length of arc
(n degree / 360 degrees) · 2 · pi · r
area of sector
(n degree / 360 degrees) · pi · r^2
area = lh
rectangular solid volume
volume = lwh
right cylinder volume
volume = pi · r^2 · h
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
y = log(little b)x asks b^y = x
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)
area = [(base1 + base2) / 2] · h
Slope intercept form
y - y₁= m(x - x₁)
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
Graphing ≥ or ≤ on a coordinate plane
Graphing ≥ or > on a coordinate plane
shade upwards or to the right
Graphing ≤ or < on a coordinate plane
shade downwards or to the left
The distance from one point on the circle to another point on the circle.
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.
Part of a circle connecting two points on the circle.
An angle whose vertex is the center of the circle
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