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Formula Memorization Sheet - Precalculus I | MATH 121, Study notes of Pre-Calculus

Lansing Community CollegePre-Calculus
Prof. Barbara Bolin

formula memorization sheet Material Type: Notes; Professor: Bolin; Class: Precalculus I; Subject: Mathematics; University: Lansing Community College;

Typology: Study notes

2011/2012

Uploaded on 03/04/2012

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MATH 121 Formulas
Properties of Exponents
1. n m n m
a a a
2.
n
nm
m
aa
a
3. r
n m nr mr
a b a b



4.
r
n nr
m mr
aa
bb
1
5. r
r
bb
Quadratic Formula
24
2
b b ac
xa
Vertex of Parabola







,
22
bb
f
aa
Vertex at
( , )hk
Circle
2 2 2
( ) ( )x h y k r
( , )center h k
radius r
Properties of Logarithms
1. log y
b
y x iff b x
2. log 1
bb
3. log p
bbp
4. log 1 0
b
log
5. bp
bp
6. log log
p
bb
m p m
7. log log log
b b b
mn m n




8. log log log
b b b
mmn
n
10
9. log( ) logaa
10. ln( ) loge
aa
Change of Base Formula

10
10
log ln
log log ln
b
xx
xbb
Properties of Radicals
1.
m
mm
n
nn
b b b
2. n n n
b b ab
3. mn mn
bb
4. , 0
n
n
n
aa
b
b
b
Distance Formula
2
2
2 1 2 1
d x x y y



12
12
,
22
yy
xx
M
Equations for Graphing Lines
21
21
,
yy
m y mx b
xx
11
y y m x x
Exponential Growth Model:
0
() kt
P t P e
Doubling Time:
ln 2
Tk
Exponential Decay Model:
0
() kt
P t P e
Half Life:
ln 2
Tk
Special Product Formulas
2 2 2
1. ( ) 2a b a ab b
2 2 2
2. ( ) 2a b a ab b
22
3. ( )( )a b a b a b
Sum or Difference of Cubes
3 3 2 2
4. ( )( )a b a b a ab b
3 3 2 2
5. ( )( )a b a b a ab b
Absolute Value Inequalities
E k iff k E k
E k iff E k or E k
Interest Formulas
Compound




1
nt
r
AP n
Continuous
rt
A Pe
Remainder Theorem: For any polynomial
()Px
, the remainder obtained when dividing
()Px
by
xr
is
()Pr
.
Rational Root Theorem: Let
1
1 1 0
() nn
nn
P x a x a x a x a
, where all coefficients are
integers and n is a positive integer. If
c
d
is a root of
()Px
then c is a factor of
0
a
and
d
is a factor
n
a
.
Note: Students are not allowed to use this formula sheet during any tests or final exams.

Partial preview of the text

Download Formula Memorization Sheet - Precalculus I | MATH 121 and more Study notes Pre-Calculus in PDF only on Docsity!

MATH 121 Formulas

Properties of Exponents

  1. a an^ m an^ m 2.^ n  n^ m m

a (^) a a

a bn^ m r anr bmr   

  1.  

n r nr m mr

a a b b

  1. ^ r 1 b (^) br

Quadratic Formula ^ ^2 ^4 2 x b^ b^ ac a

Vertex of Parabola   (^)     ^   

b (^) f b a a f x ( )  a x(  h) 2 k Vertex at( ,h k )

Circle ( x  h) 2  ( y  k) 2 r^2  

center ( ,h k ) radius r

Properties of Logarithms

  1. y  log (^) bx iff b yx
  2. log (^) b b 1
  3. log (^) b bp p
  4. log 1b  0
  5. b logb^ pp
  6. log (^) b mp p logbm

7. log b  mn  log b m logbn

  1. log (^) b m^ log (^) b m logbn n

9. log( )a  log 10  a

10. ln( )a loge a

Change of Base Formula  10  10

log log^ ln b log ln x x^ x b b

Properties of Radicals

m (^) n m^ m n (^) b b bn

  1. n^ b n^ b nab
  2. m n^ b mnb
  3.  ,  0

n n^ a^ na^ b b b

Distance Formula

d   x 2  x 1  2   y 2  y 1 ^2

 ^   

^1 2 2 ,^1 22 

M x^ x^ y^ y

Equations for Graphing Lines     

2 1 2 1

m y^ y , y mx b x x

y  y 1  m x x 1 

Exponential Growth Model: P t( )  P e 0 kt Doubling Time: T  ln 2 k Exponential Decay Model: P t( )  P e 0 kt Half Life: T  ln 2 k

Special Product Formulas

  1. ( a  b) 2  a 2  2 ab b^2
    1. ( a  b) 2  a^2  2 ab b^2
    2. ( a  b)( a  b)  a^2 b^2

Sum or Difference of Cubes

  1. a^3  b^3  ( a  b)( a 2  ab b^2 )
  2. a^3  b 3  ( a  b)( a^2  ab b^2 )

Absolute Value Inequalities E  k iff  k  E k E  k iff E   k or E k

(^) Interest Formulas Compound  ^    

r^ nt A P n Continuous A  Pert

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

Rational Root Theorem: Let P x( )  a xn n  an (^)  1 xn ^1   a x 1 a 0 , where all coefficients are

integers and n is a positive integer. If c d is a root of P x( )then c is a factor of a 0 and dis a factor an.

Note: Students are not allowed to use this formula sheet during any tests or final exams.