Download Exam 1 Review KEY

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Math 1005 Exam 1 Review Fall 2013
Exam 1 covers sec R.1-1.7. This includes material from the guided notebook, homework, quizzes, and this review. You
must show all your work to earn full credit. calculators are allowed on this exam, but phones or computers may not be
used as a calculator.
1. Write the Interval in set-builder notation and graph the set on a number line.
S"
a) [-2,4)
("
I -z ')( "- u-1
1\
,·...:
e1
-2
-...;-
2. Write the set in interval notation and graph the set on a number line.
a){xli S x S 20}
2.o1
(
(:
•
a1,_
b){xlx<O)
1
1
0
0
i
!
!
?X l )( ') -S '
b)(-5,oo)
l1
(- "°• 0)
. .1--------...,,
.
0
.
I
I
II
)
II
0
(
0
3. Find
I!
a) (1,3,5,7,9} u {1,2,5,8,12}
:;
h1, 3,
b) (-8,3]
u (-10,1)
(-IOJ
::
s ..,, i1"\1 \1.
31
4. Find
a) {1,3,5,7,9} n {l,2,5,8,12}
!:'
f \, 5
b)(-8,3)
n c-10,1)
\)
S. Find the distance between -10and15.
\-\O -\S \ ::
\-2s \
'::
12s-J
6. Simplify the expression. Write any numbers in your answer as an integer or fraction in lowest terms.
a) 2 + 83
+ (-56) - 7
'2 +
_..,
-Sl.P
-7 1
s 7
b)-·-+-+6 2
9
6
c) 102 - 4(8 - 3) 2
d)p2 -36-(4{p2 -9)+1]
c
pi.
I
-
I
• (-31"'"- I J
II
7. Simplify each expression using positive exponents only. Assume all variables represent nonzero numbers.
a) sy-10
rn
I
3
=(
'j..?>-t
'=
\:)·'2..
ri
((). '-(\o . ,)l
':.""
c.
(J-U
o
-2-(-Z)
:aobo
fl\
e)
.. 1'
( x-al•yit•)-8
x-•I•
• t./u.
'l'Y't
ll
<j
JalJ• S (i.2)1 y.
::
fi\g fS J(!.1)' f i
r
.
V16S·'t
ef4 if,f ·
=
x>. ·(t.f")S
•
)' =
=
1:"
l.JJ5 X ;.JY..
:: {[;VS T fij.,J3
(Vs
m>ff Vt<-j")s
lf
'I.'\
2"3
_ fi'o
f5.JS-fr;J3-tl3R"-$J3 -
(v'S-"3)(fS-+{5)
..
.,.,
JS.;-2/3
't
&
2.fS-t
x >.+II\( +S -3)1.... 1S l<.-1\ =[ "h3 -
f :;s ><.1.t+
+ 3)(x2 -
I 0)(-1]
7x + 6)
3
.. X
=\x3 -'i"J('"- ISi<..+\ 'il
"t
l\J)( -
_ _ _,
ra +t JS+']
-
•
a) (9x 3 -12x 2 +11.x + S)-(3x 2 -Sx+11)
j
5lj
.
fio-+ 3E. +:>.JS +2 J3
10. Perform the indicated oitation, and write your
b) -sx4 (7x2 - 2)
'1 {
5"
9. Rationalize the denominator. Assume all variables represent positive real numbers.
c) (x
y_.1-
• /yx2[5; ]
•
(..fl,+ 2)
.. i.
i.
8. Simplify each radical expression. Assume all VJ.riables represent positive real numbers.
a)J180x5
'/..
-:.:
Lr\
1
r:::.
V
3
I
d){8x+y)(8r-y)
"' lJL\x'2. -
::
(4 x-q )l"' '(-'1)
T
I
\
ll
l.
• \ I Lo-1. 2
f}
(6x 5 - Sx 2 +1x + 6) + (2x3 -1)
auo t'\eY\ t'
2'( 3 -\
"f"
- -, 1.
UX'S' -t
- ( .!:! '1.5
'3 "')(.-a
-z'l(. 2 -4>1J1..+\.D
11. Completely factor or state that the polynomial is prime.
a) 3x 2 + 3xy - 2x - 2y
')l.•Hfl -
;;! ( )Vt'1\
=[('!,
'<.- 2.)(
'><.-+<·f)
1
f(
c)x 2 -6x+ 10
d) 12y2 +29y+15
e}64x2 -100
12.Simplify the following rational expressions.
a)x2 -64
s+x
..
8.N
I
-Lj '2.
=- (J
e)(4x - 9)2
-
i')<.
"
L:-..:-J
J
f' \
"\ S' \
0'1-.
1
-S'""i
-3
l. )
x 3-125
) -c
=
,, ( -;. . ;)5) ( ')(. 1. ... s x + 2 5) -:;
(x
3x-15
d)
?;,( 1'tS-')
4x 2 -7x-2
= ( 4}.
3
8x +2x2+4x+1
j ( X -2 )
2 '1- 2.(U., '/- + \') -T ( Y'!-+I)
+I
(Y
{ '1...-2-)
'*4\) ( 1 )(.-i+ I)
+x-6
) xe
2
x+3
f) 6x- 1 +6y- 1
xy-1-x-1y
==\ (5--r---s'X.
1(2
a) 4(2x + 5) = 10 - 2(x - 5)
i'J.-n..
-z._o
+2.')(
/0'1.. '""
i2x
-2.-0
0
10-+10-2...Q
10
10
)( '1 +I)
a) 2 less than three times the sum of a number and 7
b) 3 less than four times the quotient of a number and 7 is equal to the product of the number and 8 more than
the number.
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L\(-=;-)-3
=
16. SOive the following problems algebraically by writing and solving an appropriate equation. Clearly define all
variables.
a) The perimeter of a rectangular garden is 32 feet. The length of the garden is 4 feet less than three times the
width. Find the dimensions of the garden •
p ,.. ....t +J. + W+W
.L
"" -;;JJ..-+ ') W
3;i .. d-{3w-4) +2w
31
40 =
w'!:S 4 J: 3<s)-'1
,.).
-g T
. . ,,
b) Laura and Eric had a contest to see who could sell more pumpkins for a fundralser. Together, they sold 121
pumpkins. Laura sold l more than twice as many pumpkins as Erle. How many pumpkins did each person sell?
TbW ...
£. ,,.
L
f,-t L
fbW!:
*
¥-c\l\.D E--V\t.. s.-o\o\
f>JVV\f>
\1\.1
\d
LaUvtA
L= \-t2£.,
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lt
=- 40 \
L
i \ }
-
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3
3
-
'-i\) ::. t;:
.; L. : \-+1.l LI OJ
c) A coffee shop owner decides to blend a gourmet brand of coffee with a cheaper brand. The gourmet coffee
usually sells for $9/lb. The cheaper brand sells for $5/lb. How much of each type should he mix in order to have
30 lb of coffee that is worth $6.50/lb?
X = I b)
'b iaovv
B 0-x
bn:H"
Cf X + s ( -?>o -x) = Lt ..')O
"\'{-+ISl)-5)(=
°b cv...ocv.p
=-
V\d
l \."J.5
(
\O\S-
1'°vvY\l\.A..k
l \:J "()
l\a'(:,
\Q.l'S""
d) A freight train leaves the train station 2 hours before a passenger train. The two trains are traveling in the
same direction on parallel tracks. If the rate of the passenger train is 20 mph faster than the freight train, how
fast is each train traveling if the passenger train passes the freight train in 3 hours?
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C{)
'/..'41..0:.:
V\-\--
"'r
pevh
d==
= :, (
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-io')
\.
o
S'X:::.
1-vduN
cA =- &--+ w) 3
=
:
pCA.
-> o
:
V'V'\
f'"'
)0
If"'(\
pV\ \}-
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V-=- LP o =>\ )( =VV'!'f>"-' ) 'i(+'U) =
:- SU ¥Vi P'-'
e) Fred can paint a fence in 5 hours. If his friend George helps, they can paint the fence in 1 hour. How fast could
George paint the fence by himself?
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i-4 J,-:::\
x
'5 'l
(
".)
J=S't ( 1)
+
S+ ·"- =S""
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Y')(
l\
QI V"v\.Q\,/ll'V\:
+ \)
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r C• ""
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l
...
t.
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i l
. c;
l
13
c) f-6
"::'.
l!J.t_U::
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=
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l
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l
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l
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l
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l
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12.. • i..
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rm
V\.Jl
(
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UV"'
Q
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Q.
17. Write each power of i as i, -1, -i, or 1.
b) i- 5 • i4
.ro\o
=8
.
\.(... \"'\..
l
- (.2.
a 11'\ V...O
V\
18. Perform the desired operations. Write each answer In the form a + bi.
a) ( "'5 - 4i) + (3"'5 + 2i)
=
"1S - '-\
3
JS- 4-- ?..
2
'!:!'
.
s--"\ -
\.
l
I
I
!
I
!
19. Find the product of the given complex number and its conjugate. Write each answer in the form a + bi.
ali-3t
-'H-1) •
=
4,
= ..!.
....
.
3
:: - - -
11
(2.-2..\.) :.
(2-+2{) ( 2-Z.l)
a)i+ii
u l. -
lol"2..
-4( •Y\-4 (-i
::
=
(!>\I) -
ui. - u ( -,)
=
<-I - 4 ( -1)
Le\.-+ \.Q = u
q 4 '-\
g
J.e.
... Yi:
a>
8
/i-,)
"
'O
d)
4+-:=9
L-\ .-\
Jt\) · L · '--\
:::
L\ -tr-\ [4 {2_
'1
-
. '")
• v:; .fi1.r H ,ru.°' = i.. u - i ·l · w-1 i.
c)(iH)
l 4 M ·T-'--\
= i. z. JH). J:1 . J::\" {;:;: : l 2 • l L · v 2 " '-l i. 'I
'-I {I)
2
-@]''1
-
4
=
b) .J-36 - ../-49
""
""'
20. Write each expression in the form a + bi.
3t
•
'1
'-l
+
-1 ( )
Q
8)
I
-_,
___ -
21. Solve each of the following equations.
a. 8n 7
H
!' t.
yY\_ '2
-rs : . I
M
{4M
b. x 2 -64
=O
c. (2x + 1) 2 + 4
e. 9x 2
-
\"Jtl'\-'$" '::: 0
)( ;l\"V\ -5) --0
.;-
9 q \;'y\4
I
-
-
,
rvp
$" -::...0
S/L}
=o
6x = -1
"h<'L-L.Dx-+1 =o
I) = o
( 3 '>< - I) f 3
f.
2p 3 + 4p 2
30p
-
3 "--' = 0
=0
2f>lj0 2<+2.\D-lS) ::-0
2pl p-+<:)('(J-o) =o
g. 2x 3 + 3x 2
=Bx+ 12
p+S-=-o / p-3 -=-o
--'> p =-o) f> : - s f r 3 }
2p 1-0
l
j
J
;).y, 3 .;. 3')(. 7. -g'')(- fl :::: 0
::.Q
-->i ( --+2), ..,,.-2') r2 "-+-')
.:::\
\ x--2, -21
ik-l.S
t' //lbw
i.
fa CA-t;,,, YVt ( e-1'1
C>tAJl. d
IA
../32 - 4x - x
wu
to
=o
(
x. "24y
j.
'V2x - 1
=-2
"'= X. ':: 0
-
1i.e.
d. oh 1t-
lv<...
r
•
('f,--+
\ )<\
f) { )(-1..4)
-:.-g J
')(-: \..\
:: 0
\
l
=o
22. Use the discriminant to determine the number and nature of the solutions to the equation 2x 2 + x - 5
( =
D==
I) ) D
L\ (2--)l-5)
v-eo&.
""' [
=O.
Li\
-: \+ 40 :
u. M OVU> \
23. If a rocket's height after t seconds is given by the equation: h = -4. 9t2 + 18.9t + 2.8, find how long it will take
for the rocket to hit the ground.
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\,\ =-t)
:JVOU. \l'\d,
-<-\.'\t 4 -t\i.°\t-+z..-g :.a
i -:; - \'l.q
.:t
t
J
lJ
(-'i.tt)(z..<t)
-t
.f:-
ys
24. A 35ft by 20ft rectangular swimming pool ls surrounded by a uniform width walkway. If e total area o the
walkway is 434ft, how wide is the walkway?
q 2.. -t \\
-4
Aw::. A-r -A(!)
Lt ?Y =--'u..> - "20 { ;.,-)
1. .3S"'t2 )(
4
2.l\(\
(3s+2.><) (U>+l ')() - 100
+"-' o"' + 4 x' - ')Oo -
'¢> + '1
,.
x-'-Ho :t /w.>1 ..
\
4 '! \.f ..,
25. A car travels 280 miles at a certain average speed. If the car would have gone 5 mph faster, the trip would
taken an hour less. Find the average speed of the car.
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t:>
,
tU. '- t=t vt U2....
M-<l/'\A...Q....
1
t:--=-
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2 'CO /Y-
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2V:O/'f'-1r'5
2. 'iO
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\<.,,
z. "°
\'ti
+ll..lOO-V'"l.-5V"-"'Z. j*'Y
y.
'-l =o
r
o
i
Il
-
2.iQ - \ "' f=B 0
r
v--+- sr(V--t5""\('Z..i9- ' : Y'"(V-"""'t)(.1.i?
)
'\:../
V""
\ J
y-+-S-"\:'> J"
:'}
- V'"(<-t-S-) :=- 2.U<"
26. Solve each inequality. Graph each solution and express the solution in both set builder and interval notation.
y'L-+5
a. 11- 2a s 4a + 35
-ua 1Y
;; -;
(o )! - )
<
..
) o. \ o.
-i;
(·Y,
4v..-\
t0/7
l- oC) I 10/,.)
< .,... e>"'
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< .!.:!:.!
..... t
12 .;;::,
c. !4
14-{'/"-I)
t-tl
3< t-t\
3-'
<:.
I; S.\2.t-\
tl It..)
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ts \1..t-\
;i<t S..12..t-\
2.
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-5
d. -<y+l
6 -
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e. 4k + 2 ::; -10
m:
l.D
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y
3k - 4
>8
'1
11.
3b - 5 ::; 1 and 1 - b
3'Q-SS.\
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w
5 -12.
/1<-s-3
f.
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(..-.l.)
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1
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< -3
1-'a<-..3
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0
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Y'-\o
'oS
27. Laura and Cassie went to Branson for a week. They had two options for rental cars. Company A charges $40 per
day plus 5 cents per mile. Company B charges $200 per week plus 30 cents per mile. How far do they need to
drive for Company A to be the cheaper option?
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wt:..Q,\c
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CA
+ . O'S
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1'Z..S'
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28. Your scores on three exams were 91, 92, and 85. What must you get on the forth exam to average at least 90 on
the four exams?
C)\-+92-+
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