SAT
Formulas, Definitions, and Theorems
Geometry
Similar Triangles:
Corresponding angles are equal in measurement and corresponding
sides are proportional.
Equilateral Triangles:
all three angles measure 60 degrees and all three sides are
congruent.
Ve
rtical angles
>< are congruent.
Supplementary
angles add to 180 degrees.
Complementary
angles add to 90 degrees.
Area of a square:
s^2
Slope of a line:
(Y
2
–
Y
1
)/(X
2
–
X
1
) = m
Equation of a line:
y = mx + b, where m is the slope and b is the y

interce
pt.
The sum of the
interior angles of a polygon
= (n

2) x 180, where n = the number of
sides.
Algebra
Direct Proportionality:
y is directly proportional to x if y = kx, for some constant k.
Inverse Proportionality:
y is inversely proportional to x if
y = k/x, for some constant k.
Factoring the
difference of two squares
: a^2

b^2 = (a + b)(a
–
b)
The
distribution
of (x + y)^2 = x^2 + 2xy + y^2
Converting
exponents to roots
: x^(1/2) = √x and x^(1/3) =
3
√x
Numbers & Operations
Sum of Consecutive Integers:
x + (x+1) + (x+2) + (x+n), where (x+n) represents the last
integer.
Distance
= rate x time
Percents:
a% of n = a/100 x n
Percent Change:
(original amount
–
new amount)/
original amount x 100%
Rational Number:
a number that can be expressed as a ratio of two integers
Irrational Number:
a number that cannot be precisely expressed as a fraction or decimal
(ex. √2, √3,
Π
)
Domain:
the set of values for which a function is
defined. For the function y = f(x), the
domain is the set of all x values for which f(x) is defined.
Range:
the set of outputs, or results, of the function. For the function y = f(x), the range
is the set of all possible y values.
Statistics/Data Anal
ysis/Probability
Permutation:
The number of ways to organize r out of n different objects (order matters)
= n!/(n

r)!
Combination:
The number of combinations of r out of n different objects (order does not
matter) = n!/[(n

r)!r!]
Average/mean:
sum of al
l data points/total number of data points
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