SAT Math Terms & Formulas
full circle
= 360 degrees
Central Angle
An angle whose vertex is the center of 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.
difference of squares
a^2 -b^2 = (a+b)(a-b)
angles of triangle
add up to 180 degrees
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
special sin cos relationship
sin^2(angle) + cos^2(angle) = 1
Graphing ≥ or ≤ on a coordinate plane
solid line
sum
sum = average x (number of terms)
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)
x^0
1
circle perimeter
2 pi r
equilateral
three equal sides, all angles = 60 degrees
Direct Variation
y=kx
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
rectangle area
area = lw
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
logarithms
y = log(little b)x asks b^y = x
Inverse Variation
y=k/x
Slope intercept form
y=mx+b
roots
√(xy) = √x · √y
distance formula
√[(x₂- x₁)^2 + (y₂- y₁)^2)]
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, ...
negative exponents
1 / x^b = x^(-b)
isosceles
2 equal sides, 2 equal angles
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
mid-point formula
[(x₁+ x₂)/2 , (y₁+ y₂)/2]
quadratic formula
[-b ± √(b² - 4ac)] / (2a)
trapezoid area
area = [(base1 + base2) / 2] · h
circle area
pi · r^2
Arithmetic Sequences
t₁, t₁+ d, t₁+2d, ...
order of opperations
PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)
arc
Part of a circle connecting two points on the circle.
degree to radian
degree# · (pi / 180 degrees)
median
median = middle value in the list
circle circumference
2 · pi · r
prime factors
2, 3, 5, 7, 11, ...
Chord
The distance from one point on the circle to another point on the circle.
cos of an angle
adj / hyp
area of triangle
area = (1/2)bh
parallelogram area
area = lh
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)
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
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
mode
mode = value in the list that appears most often
tan of an angle
opp / adj
sin of an angle
opp / hyp
intersecting lines
opposite angles are equal (each pair of angles along the same line add to 180 degrees)
percentages
part = (percent / 100) x whole
probability
probability = number of desired outcomes / number of total outcomes
radian to degree
radian# · (180 degrees / pi)
