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LAMC
Yun
Exam 3-A
Chapter 5 and 6
Math 125
Spring 2009
Is:£l
Your name:
.
.
.
Please show your work clearly.
Points are assigned for the answer and the work shown.
Calculators are not allowed.
a.
=
3
1. Simplifythefollowing.
'f[3"
la.
ID
b.
=
b.
:5J
(-2)3
@
a. ~24x4y3
:::.J 4 -6 .('Xz.J2. 'd'l. Cj :
2X?'
2. Simplify the following. All vanables represent pOSitivt
.
b.- sJ18
3m
~
~
{ G ~,
XSJf 13 15Jb
b.
~
1
~ Ltg
492 =
ill
_
-
I]
3a.
I
-3'1-
-
(~)-4=
is
[5:-]
I"fy the following:
3. Simp
a.I
b.
_
GJ3.f3.
2a.
b.
'2.Lf
4. Rationalizethe denominator. Simplify your answers.
1
a.
.~
J3.
=[1
13
4a.
..
4
b. \. 15 -
(
IS +~
)
J3 )( IS + J3~
-=
<i ( IS + 13)
==
5 -~
4 (J; +J3)
-
b.
2-
::
2
(fi5 1"0) Df<.
{ 2JS + 213
5. Perform the addition, subtraction, or multiplication. Simplify your answers.
5a.
b. (2-3v'5f
~
(1-3~) (2-315)
4 --GIS-6 JS +- q."5
-:: 4 - I~J5 t- 4sr
l
~F-(1-12JS
(3h -~)( 3h +~) 7- ~ IT):l. -lSS)
c.
.
q.~ -5
co
.J45;3+ v'18x2-
d.
:
J
q .5
)( ~)(
=3X~
~
c.
~
18 -E,
~0
J5Q;2 - v'20x3
;- J q .2,)(
~
d.
- J2; .2X ~
+2>XJ2 - 5)( Ji
:="X
- J5"i
b.'
=:.
-2X
J2.
J 4-. S ,(~ X-
- '2XJ5><
I
6a.
5::(-01 =- 3;(
2-~
j
+~
c~€(k: 6(;) -2 ~) 3(5)t~
=-10
J23
J ?( =- 51
b.lJX~€-2
= J 2~ yes v'
b.
)L
(17 )
~
()(
X
-::-
)C2_2X-~)(+4
- L) ( )(-2 )
"
K~
2
X ~'/.2._ 4x-t- 4o :=.'{~
o
~
C)(
X=4-
X=-I
SX T if
- LL)
Ot'
(>C
-
,
)
it-2~
go
,/e~ v'
[I -~ 1-2-
'I-I
)(~\.
2-
I t<~4 J
No
7. Use scientific notation to and the properties of exponents to calculate the following. Write the answer in
scientific notation.
(300)(0.0004)
-::
(
'3
. ID 2.
) . (4
/0 -f)
0
-'1)
0.0002
(20
10
8. Solvefor b. Simplifyyouranswers.
a. b2 = 200
J bJ- :: + J 200
=)
f.? .
b'
f
i
~
102- t
_
8a.
..2-
tOD
. =-ft fO J2:.
b-"'~
7.
;:: '3" 102 0 2.
1
b.
h-3=4 0" h-3=-4
.:t4~
h~q
~=-I
Or
9. Perform the operations. Write your answersln standard form (a + bi).
a. (6+2i)
- (5+i)
:=
-
6t-'2.;
::
~~
c. (2-3i)(5+6i)
=
\0 + 12 j
~
~
(4- 2i
(4+-2]2
) (4 t'2J )
10
-=.T,
-+;
P j 2. ::. ?J",- -12
b. (3i)(1+4i)
d.
5 -j.
-t
_ l~
9a.
1
-=-1.-12-+3
J 1_
;.. _ I ~ j
2-
- 3 J + 18 -=[jg- - 3 v\J
-)
b (4 t ~ -: 6 (t./-+
2J) = '2LI- + 12J
16t4-
W
-20
-::=. G_
+ '3
r (-1).2
)(-~
11. Solve.
X2
r:
- 4x -12 = 0
lK-b)
k-b
.).
'3
-5 + -J
5
-:::-th
!S
Complex numbers as solutions are possible.
10. Solve. (X_3)2 =-36
d.
~
,
=:
b.
c.
+- J
.::
=.
'
10.
-3b
:Z 6 j
=r!~bj'l
11.
()(+Z.)=O
0 «.
'k= -2.
12.
12. Solve by completing the square. 3y2 + 5y -1 = 0
3y~+s y
;.
L(+'; Y
lf2-+ ~ ~-t
(~t-%)L
I
_
~
-L
~+f
:3
_ ..i+§
-
3
-
-3b
V\ -;. -'5
36
12 t2-f:
+ J.2i
36
=-
o
::
2!l
3fo
+-
~
rr
+ .J~ry
6
6- u.:L
::.r t)-J:[3~
6
13. Solve by using the quadratic formula. 2x2 - 6x + 1= 0 .
(simplify your answer)
13.
(}.,-=1- . b~ --b , c=-I
X-=. -bt
rb~-Lt-OtL
= -(-b/.i
'20\.
f 36 - 4 (l.)(t)
=
-
::J.(l)
36x2 - 4 = 0
14. Solve by the method of your choice.
~iJ '36-~~
61:4'2fFi
-;
6::!:~
.:r
~
~~+0
2-14.1
4 ( qX:>'-I ) =0
1- (':3X-f-j)C:;X-() =-0
'/_ -1-L
"--
3
1
3>
J
15. Find all real solutions.
~
15.
( 12 -t 16) C)( ~ 4-).-::: D
X~16 =0 or< X~- 4 =-0
X~ +-4.1
Y Ci-t,y
~
t
ft;J~)
3 ()(-+I )
+ 2:t
3)( +3
+-2-X
SX+3
4X
=:
-=-
::::
p&:!:'21
~x + ~x+1 = 4
16. Find all real solutions.
-=-)
«0 )(-=1=0.-I
6JL-C.D )«('I.-tf)
(j)
.
16.
-3
o 41:2-X
I. (,(11)
~
()(+I)
= (4 X +- 3)(X
41 +4 x..
-
I)
X-I =-0
tfX,+4K
Oy )(-:.1
17. For the equation x2 - 5x + 6 = 0
a. Find the value of b2 - 4ac
.
{-C;))..~
4(
.2i: -21
f)
( 6)
fl
17a.
b. Based on your answer to part (a), how many real solutions will the equation have?
Aiin (Q.
b:"40- c.> 0
, !-fw0
r e6d $0 It4-lOYJ 5
1 b.
18
l'l--q)CKtb)LO.
(>(-+6)
(;£-q)
_
I
-
\
-
-£
-
i
)
t
\ +-
- _.~ -
-t- I EJ
({4)(t~)
I
+- '++
--..)
C(
L-6,Cf]
19. Graph the solutionset and writeyour answer in intervalnotation.
x+221
-\
xt2
x
1-
~
D
19.
!:E-
X:f(J==-
-.6-'f.-;/'>:0
()
)<+2- f--_ //0
2-
i
i----
2-
-40
'f
-\
+--\\
-\
"
g
I
1-
+-
-\
-leD
C
0,<M)
20. The sum of two numbers is 6 and their product is 4. Find the larger of the two numbers.
20.
be ~
W
'X
~
6-X
II
r
~ (b -~)
Grx -x~::-
4
~
Lf
or< 0;:;. 1(2.-6'X
'BUt
-\11£
a~ ( I b=- -b
l~rqYl :jf.
7
X -=-6 i
-q{ 3tJ!)
r
36 -4{f)l4)
+ J.I..
/
c::=-4~
bz j 36 -1£
:2(t)
~
~
6:t J20 .::: 6i 215
2-
::;2-
~
-=3 1-
IS
)