SAT Math
a^2 + 2ab + b^2
(a+b)^2
a^2 - 2ab + b^2
(a-b)(a-b)
length of arc
(n degree / 360 degrees) · 2 · pi · r
area of sector
(n degree / 360 degrees) · pi · r^2
FOIL
(x+a)(x+b) = x^2 + (b+a)x + ab
multiplying exponents
(x^a)^b = x^(a·b)
slope formula
(y₂- y₁) / (x₂- x₁)
integers
..., -3, -2, -1, 0, 1, 2, 3, ...
x^0
1
negative exponents
1 / x^b = x^(-b)
isosceles
2 equal sides, 2 equal angles
circle perimeter
2 pi r
circle circumference
2 · pi · r
prime factors
2, 3, 5, 7, 11, ...
full circle
= 360 degrees
Central Angle
An angle whose vertex is the center of the circle
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
order of opperations
PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)
arc
Part of a circle connecting two points on the circle.
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.
Dividing by a negative number in an inequality
You must flip the sign
mid-point formula
[(x₁+ x₂)/2 , (y₁+ y₂)/2]
quadratic formula
[-b ± √(b² - 4ac)] / (2a)
difference of squares
a^2 -b^2 = (a+b)(a-b)
angles of triangle
add up to 180 degrees
area of triangle
area = (1/2)bh
trapezoid area
area = [(base1 + base2) / 2] · h
parallelogram area
area = lh
rectangle area
area = lw
average
average = sum of terms / number of terms
average speed
average speed = total distance / total time
Graphing < or > on a coordinate plane
dotted line
Greatest Common Factor
ex. GCF of 200 and 60 is 20
Least Common Multiple
ex. LCM of 200 and 60 is 600
Factors
ex. factors of 52 are 2, 4, 13, and 26
Multiples
ex. multiples of 20 are 40, 60, 80, 100, ...
rationals
fractions (anything expessable as a ratio of integers)
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.
reals
integers, rationals, plus special #s (like √2 or pi)
length of triangle sides
length of 1 side is always less than the sum of the other 2
median
median = middle value in the list
mode
mode = value in the list that appears most often
intersecting lines
opposite angles are equal (each pair of angles along the same line add to 180 degrees)
percentages
part = (percent / 100) x whole
circle area
pi · r^2
probability
probability = number of desired outcomes / number of total outcomes
similar
same shape, corresponding angles are equal, corresponding sides are in proportion
Graphing ≤ or < on a coordinate plane
shade downwards or to the left
Graphing ≥ or > on a coordinate plane
shade upwards or to the right
Graphing ≥ or ≤ on a coordinate plane
solid line
sum
sum = average x (number of terms)
equilateral
three equal sides, all angles = 60 degrees
Arithmetic Sequences
t₁, t₁+ d, t₁+2d, ...
Geometric Sequences
t₁, t₁· r, t₁· r², ...
rectangular solid volume
volume = lwh
right cylinder volume
volume = pi · r^2 · h
equation of circle
with midpoint (h,k) ... (x - h)^2 + (y - k)^2 = r^2
subtracting exponents
x^a / x^b = x^(a-b)
adding exponents
x^a · x^b = x^(a+b)
Point-Slope form
y - y₁= m(x - x₁)
Inverse Variation
y=k/x
Direct Variation
y=kx
Slope intercept form
y=mx+b
roots
√(xy) = √x · √y
distance formula
√[(x₂- x₁)^2 + (y₂- y₁)^2)]