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college algebra final exam cheat sheet, Cheat Sheet of Algebra

Complete cheat sheet for finel exam of college algebra

Typology: Cheat Sheet

2018/2019

Uploaded on 09/02/2019

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Formula Sheet for College Algebra Final Exam
Properties of Exponents
p
p
mp
np
p
m
n
mpnppmn
nmmn
mn
m
n
mnmn
b
b
b
a
b
a
baba
aa
a
a
a
aaa
1
.6
.5
)(.4
)(.3
.2
.1
=
=
=
=
=
=
+
Quadratic Formula
a
acbb
x2
4
2±
=
Circle
rradius
khcenter
rkyhx
=
=
=+
),(
)()( 222
Vertex of Parabola
),(
)()(
2
,
2
2
khatVertex
khxaxf
a
b
f
a
b
+=
Standard Form of Equation of
Parabola
phxdirectrix
kphfocus
khvertex
hxpky
pkydirectrix
pkhfocus
khvertex
kyphx
=
+=
=
=
=
+=
=
=
:
),(
),(
)(4)(
:
),(
),(
)(4)(
2
2
Properties of Logarithms
pb
pb
b
xbiffxy
p
b
p
b
b
y
b
b=
=
=
=
==
log
.5
01log.4
log.3
1log.2
log.1
nm
n
m
nm
mn
mpm
bb
b
bb
b
b
p
b
loglog
log.8
loglog
)(log.7
loglog.6
=
+=
=
)(log)ln(.10
)(log)log(.9 10
aa
aa
e
=
=
Change of Base Formula
b
x
b
x
x
bln
ln
log
log
log
10
10 ==
Properties of Radicals
()
0,.4
.3
.2
.1
=
=
=
==
b
b
a
b
a
bb
abba
bbb
n
n
n
mn
mn
nnn
n
m
nm
m
n
Absolute Value Inequalities
kEorkE
iffkE
kEkiffkE
Midpoint Formula
++
=2
,
2
2121 yyxx
M
Distance Formula
2
12
2
12 )()( yyxxd +=
Equations for Graphing Lines
)(
,
11
12
12
xxmyy
bmxy
xx
yy
m
=
+=
=
Interest Formulas
nt
n
r
PA
compound
+= 1
rt
PeA
continuous
=
Remainder Theorem: For any Poly. P(x), the remainder obtained when dividing P(x) by x - r is P(r).
Rational Root Theorem: Let 01
1
1...)( axaxaxaxP n
n
n
n++++=
, where all coefficients are
integers and n is a positive integer. If d
c is a root of P(x) then c is a factor of 0
a and d is a factor of n
a

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Formula Sheet for College Algebra Final Exam

Properties of Exponents

p

p

mp

p np

m

n

n m p np mp

n m nm

nm m

n

n m nm

b

b

b

a

b

a

ab a b

a a

a a

a

a a a

Quadratic Formula

a

b b ac x 2

2 − ± − =

Circle

radius r

center hk

x h y k r

2 2 2

Vertex of Parabola

2

Vertex at h k

f x a x h k

a

b f a

b

Standard Form of Equation of Parabola

directrix x h p

focus h pk

vertex hk

y k p x h

directrix y k p

focus hk p

vertex hk

x h p y k

2

2

Properties of Logarithms

b p

b p

b

y x iff b x

p

b

p b

b

y b

b (^) =

log

  1. log 1 0

  2. log

  3. log 1

  4. log

m n

n

m

m n

mn

m p m

b b

b

b b

b

b

p b

log log

  1. log

log log

  1. log ( )

  2. log log

  1. ln( ) log ( )

  2. log( ) log 10 ( )

a a

a a

= e

Change of Base Formula

b

x

b

x b x ln

ln

log

log log 10

10 = =

Properties of Radicals

b b

a

b

a

b b

a b ab

b b b

n n

n

m n mn

n n n

n

m n m n^ m

Absolute Value Inequalities

E k or E k

E k iff

E k iff k E k

Midpoint Formula

x 1 x 2 y 1 y 2 M

Distance Formula 2 2 1

2 d = ( x 2 −x 1 ) +(y −y)

Equations for Graphing Lines

1 1

2 1

2 1

y y mx x

y mx b x x

y y m

Interest Formulas

nt

n

r A P

compound

rt A Pe

continuous

=

Remainder Theorem: For any Poly. P(x), the remainder obtained when dividing P(x) by x - r is P(r).

Rational Root Theorem: Let (^10)

1 P( x) ax a 1 x ... ax a

n n

n = (^) n + + + +

− − , where all coefficients are

integers and n is a positive integer. If d

c is a root of P(x) then c is a factor of a 0 and d is a factor of an