Math Booklet of Formulas
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GREEK ALPHABET
cL
centiliter
MASS / WEIGHT
Capital
А
В
Γ
∆
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
dL
deciliter
1 kg = 2.2 lb
L
liter
1 lb = 16 oz
daL
dekaliter
hL
hectoliter
SUBSETS OF REAL NUMBERS
Natural Numbers = {1,2,3,4,...}
kL
kiloliter
Whole Numbers = {0,1,2,3,4,...}
cc
cubic centimeter
Small
α
β
γ
δ
ε
ζ
η
θ
ι
κ
λ
µ
ν
ξ
ο
π
ρ
σ
τ
υ
φ
χ
ψ
ω
Name
Alpha
Beta
Gamma
Delta
Epsilon
Zeta
Eta
Theta
Iota
Kappa
Lambda
Mu
Nu
Xi
Omicron
Pi
Rho
Sigma
Tau
Upsilon
Phi
Chi
Psi
Omega
ABBREVIATIONS
Length
In.
inch
Integers
= {..., − 3, − 2, − 1,0,1, 2,3, 4,...}
Rational
Weight
mg
milligram
cg
centigram
dg
decigram
g
gram
dag
dekagram
hg
hectogram
kg
kilogram
pond
lb
ounce
oz
a
= { | a and b are int egers}
b
with a ≠ 0
Irrational = { x | x in not rational }
PROPERTIES OF REAL NUMBERS
For all real numbers a, b and c we can write
a+b = b+a
The addition is commutative
a⋅b = b⋅a
The multiplication is commutative
(a + b) + c = a + (b + c)
The addition is associative
ft
foot
RATES OF CONVERSION BETWEEN
UNITS
yd
yard
mile
mi
mm
millimeter
cm
centimeter
(a ⋅ b)c = a(b ⋅ c)
The multiplication is associative
LENGTH
a(b + c) = ab + ac
1 mi = 5280 ft
Distributive property of multiplication over
addition
1 mi = 1.609 km
1 mile = 1760 yd
dm
decimeter
1 in. = 2.54 cm
m
meter
1 yd = 0.9144 m
dam
decameter
ORDER OF OPERATIONS
First evaluate within the grouping symbols
such as parentheses
1.
Exponential expressions
2.
Multiplication and division
3.
Addition and subtraction
1 yd = 3 ft
1 m = 3.281 ft
hm
hectometer
km
kilometer
VOLUME / CAPACITY
1 mile squared = 640 acres
ABSOLUTE VALUE
1 cubic foot = 7.481 gal
x for x ≥ 0
| x |=
− x for x < 0
Volume
pt
pint
gal
gallon
mL
milliliter
1 gal = 3.785 L
1 mL = 1cc
1
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EXPANDING - FACTORING FORMULAS
2
2
2
2
2
2
( x + y ) = x + 2 xy + y
ARITHMETIC AND GEOMATRIC
SEQUENCES
The n th term of an arithmetic sequence
( x − y ) = x − 2 xy + y
( x + y ) 3 = x 3 + 3 x 2 y + 3 xy 2 + y 3
with first term a1 and common difference d
( x − y ) 3 = x 3 − 3 x 2 y + 3 xy 2 − y 3
The sum S n of the first n terms of an
is given by
arithmetic sequence is given by
SLOPE OF A LINE
•
The slope m of a line through the
points ( x1 , y1 ) and ( x2 , y 2 ) is
given by
m=
y 2 − y1
when x1 ≠ x2
x2 − x1
The slope of a horizontal line is equal
to zero.
The slope of a vertical line is
undefined.
•
•
MIDPOINT AND DISTANCE FORMULAS
The coordinates of the midpoint M of
( x + y ) n = x n + n C1 x n −1 y +
n
a n = a1 + (n − 1)d
( x − y )( x + y ) = x 2 − y 2
BINOMIAL THEOREM
Sn =
C 2 x n − 2 y 2 + K+ n C r x n − r y r
+K+ yn
Where n C r =
n
( a1 + a n )
2
n!
r!(n − r )!
The n th term of a geometric sequence with
EXPONENTS AND RADICALS
first term a1 and common ratio r is given
x0 = 1
by
a n = a1 r n −1
The sum S n of the first n terms of a
geometric sequence is given by
a (1 − r n )
Sn = 1
(1 − r)
The sum S of an infinite geometric
sequence with | r |< 1 is given by
S=
segment PQ where points P ( x1 , y1 ) and
a1
(1 − r )
Q ( x 2 , y 2 ) are given by
x −r =
1
1
= ( )r
r
x
x
1
= xr
−r
x
x r x s = x r+s
( x r ) s = x rs
x
xr
( )r = r
y
y
xr
= y r −s
s
y
The distance d(PQ) between points P and
Q is given by
EXPONENTAILS AND LOGARITHMS
( xy) r = x r y r
x
y
( ) −r = ( ) r
y
x
y = log b ( x) if and only if b y = x
x n =n x
( x 2 − x1 ) 2 + ( y 2 − y1 ) 2
log b ( xy) = log b ( x) + log b ( y )
x
log b ( ) = log b ( x) − log b ( y )
y
log b x r = r log b ( x)
M(
x1 + x 2 y1 + y 2
,
)
2
2
d(PQ) =
QUADRATIC FORMULA
The solutions to the quadratic equation
2
ax + bx + c = 0 ( a ≠ 0 ) are given
by
2
− b ± b − 4ac
2a
2
If b − 4ac > 0 , then there are two real
x=
solutions.
2
If b − 4ac = 0 , then there is one real
solutions
(or a repeated solution).
b log b ( x ) = x
log b (b x ) = x
1
n
xy = n x n y
n
x m = (m x ) n
n
x n x
=
y n y
INEQUALITIES
log b (1) = 0
If a > b and b > c then a > c
log b (b) = 1
log a ( x)
log b ( x) =
log a (b)
If a > b , then a + c > b + c
If a > b and c > 0 , then ac > bc
If a > b and c < 0 , then ac < bc
2
If b − 4ac < 0 , then there are two
complex solutions.
2
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ABSOLUTE VALUE INEQUALITIES
If | x |≤ b if and only if − b ≤ x ≤ b
If | x |≥ b if and only if x ≥ b or
x ≤ −b
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GROWTH AND DECAY EXPONENTIAL
FUNCTIONS
Assuming that P is positive
f ( x) = Pe kx is increasing if k > 0 ,
growth function.
RECTANGULAR EQUATIONS FOR
CONIC SECTIONS
Circle of center ( h, k ) and radius r
f ( x) = Pe kx is decreasing if k < 0 ,
LINEAR FUNCTION
f of the
form f ( x) = ax + b with a ≠ 0 is called
( x − h) 2 + ( y − k ) 2 = r 2
decay function.
Function
Ellipse of center ( h, k )
a linear function because its graph is a line
that has a slope equal to a and b is the y
intercept of the line.
Domain: ( −∞ ,+∞ )
COMPOUND INTEREST FORMULA
If r is the rate of interest and the principal
(the amount you begin with) P is
compounded n times per year then after t
years the total amount A is given by
Range: ( −∞ ,+∞ )
r
A(t ) = P (1 + ) nt
n
( x − h) 2 ( y − k ) 2
+
=1
a2
b2
Parabola of vertex ( h, k ) - Axis
parallel to y axis
( x − h) 2 = 4 p ( y − k )
QUADRATIC FUNCTION
Function
f of the form
f ( x) = ax 2 + bx + c with a ≠ 0 is
called a quadratic function. Its graph is a
parabola that has a vertex.
The coordinates ( h, k ) of the vertex are
FRACTIONS AND RATIONAL
EXPRESSIONS
a c a+c
+ =
b b
b
( y − k ) 2 = 4 p ( x − h)
given by
h=
−b
and k = f (h)
2a
if a > 0 , the graph opens upward and the
vertex is a minimum point. The range of f is
given by the interval [ k ,+∞ )
if a < 0 , the graph opens downward and
the vertex is a maximum point. The range of
f is given by the interval ( −∞ , k ]
Parabola of vertex ( h, k ) - Axis
parallel to x axis
Hyperbola of center ( h, k ) - Axis
a c a −c
− =
b b
b
parallel to x axis
( x − h) 2 ( y − k ) 2
−
=1
a2
b2
a c ad + cb
+ =
b d
bd
Hyperbola of center ( h, k ) - Axis
a c ac
⋅ =
b d bd
parallel to y axis
( y − k ) 2 ( x − h) 2
−
=1
a2
b2
a c a d ad
÷ = ⋅ =
b d b c bc
Domain of given by ( −∞ ,+∞ )
Function
f may also be written in vertex
form as follows
ac a
=
bc b
f ( x ) = a ( x − h) 2 + k
3
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