Intermediate Algebra
Test II Review
1.- Add/subtract the following rational expressions.
3
(a)
1
=
+
4
x + 2 x2
x
(
⇒
3-
1×12)
.
(b)
1
x
-
1×-4
Xtz
4) ( X
(
×
.
1
4) ( xtz
Xtz
)
3×+6
⇒
1
)
×
=
-
4
3×+6=2×-4
⇒
✓
X
+
⇒
X=@
)
2×1×+7
D=
LC
4
6x
= 2
x+7
2x + 14x
2×1×+7
4) (
.
2)
+
+
)
( X
=
8
1. i.
41×+2
(1)
=
)
X.
X
LCD
x
2x
)
÷si¥÷x÷÷¥=I÷⇒⇒¥'III:
⇒
⇒
X
14=12
÷@
✓
2.- Multiply/divide the following fractions.
Ylx
(a)
-
1)
+41×-1
)
ytz )
X(
1
+1
ytz )
xy y + 4x
xy 3y + 4x
4
xy + 2x + y + 2
÷
0
12 xy 3y + 2x 6
ylx
)
-
|
Ylx
'
3)
+21×-3
x
x3
X(
.
)
2) (
4)
x(X23
125
x
4x
· 2
10x x + 5x + 25
3x2
1/2-3×-10 )
1) (
-
3) (
⇒
Xxx
511×+4
x#
#
(b)
3
-
)
Flip
1×2*+25
x
s
+41×-3
3)
(
⇒
-
⇒
x@
¥+€|
# #
¥4
)
.
)
)
-
1×+1 )
3- Multiply (and simplify) the following.
⇒
2)(x3
(a) (4x
4×4
5x2 + 4x
20×3+16×2
-
24X
-
2×3+10×2
-
6)
8×+12
-
.
(b) (2x3
3
.
⇒
4×6
⇒
3)2 + (x3
=3)
(2×3-3)
4)(x3 + 4)
(
t
3-
X
4)
X3t4 )
(
6+4×3*-16
6×3.6×3+9
-
X
+
5×6-12×3=7
4.- Simplify the following.
(a)
'iI¥ax⇒¥¥⇒xg
75x 4 x12
(5x)2 [3x(5x)0 ]
4114.22×3+26112.32×+1
(b) (2x4 y 3 z 5 )5 (6x 2 y 3 z 7 )2
⇒
⇒
⇒
(c)
25×20
25.62
y
.
'5z25(
62×-4
y6z' 4)
X16y21z39
115211162212£
✓
36x3 y 5 z
12x6 y 5 z 9
◆4
(
⇒
3×-35
'0zn)4
⇒
z4×- 2y-4°z4°
⇒
;t÷o
1
5.- Write the following in Scientific Notation.
(a) 0.000000054
⇒
Wrynn
(b) 3, 000, 000, 000 ⇤ 10
-3.0*109*-10-4
4
⇒
3.O*@
-14
-
C-
8)
←
(c)
⇒
0.000000000000065
1.5 ⇤ 10 8
www.m
6.51¥
-
1.
14
-
=
6
>
5*10-8
5.4*€
4.3¥
6.- Solve the following by factoring.
(a) x(x
(
X
p) + 7(x
(
D)
-
(b) x3
p) = 0
xt7)=o
5x2
⇒
4x + 20 = 0
-
XYX
⇒
⇒
(
X
-
(
×
-
-41×-53=0
5)
-
5)
( X2-
5)
(
4)
=
0
X=p,X#)
⇒
×
.
2) (
xtz
)=°
⇒
(c) x2
7x = 0
-77=0
XCX
⇒
⇒
X=o,l#
X.es/x=2,X=-Z7
(d) 3x3
{
28x
=0
3×(1/2.9)=0
⇒
⇒
3X
(
x
-
3) (
Xt3)=O
⇒xIot×⇒t⇐@
(e) (x + 3)2 = 25
(1/+371×+3)=25
⇒
X2t
⇒
6×+9=25
1/2+6×-16=0
⇒
(
⇒
(
8)+
X
X
2)
-
=
0
⇒
(f) (x + 4)(x
3) = 12x
X2
3×+4×-12=1221
⇒
-
X2+
⇒
X
×2
⇒
⇒
(
×
-
11×-12=0
-
.
12=1211
12
)(
)=0
xtl
⇒
X=-8,X=:
7.- Solve the following word problems.
×=l2,×=-1X=lst
(a) The sum of two number is 32. One of the numbers is 4 less than 5 times the other. Find
the two numbers.
#
y=2nd
XtY=32
=>
#
y=5X
(5×-4)=32
Xt
6×-4=32
⇒
-4
⇒
6x=36
⇒
X=@
y=5(
⇒
6)
4
-
y=2@
(b) Pokemon has 20 coins totaling $1.40. If he has only dimes and nickels, how many of each
coin does he have?
Nickels
#
N=
dimes
of
D=
@eame0t
#
,
20
DtN=
~
of
0.1013+0.05
N
=L
.
40
t
low
.
/
giant
X
D=
£
D+N=20
⇒
10C
⇒
200
140
5N=
a
⇒
→
20
-
.
)
10N
+
+
Is:@
III
5N=
5N=
140
140
20
-
N
(c) Salvador can clean his house in seven hours. His wife Cindy, can clean the house in five
hours. How long will it take them to clean the house if they work together?
⇐
35£
t
P
)
t.tt
st
⇒
7t=
+
12+-35
⇒
35
t=3
⇒
LCD
12
2.916
=
8.- Factor the following.
←
(a) 3ax + 21x
a
-
3×1
⇒
7)
at
)
lcatt
-
(b) x3
7
(at7)(3#
⇒
x2(
⇒
(
⇒
⇒
PYE
x
"
5x2
x
-
5)
-
(
5)
4x + 20
-
4(
-
Xt
4)
"
"
X
5)
-
.at#teE
and
giiut.ir#=3n@
(c) x2 + 6xy + 9y 2
any
⇒
(
⇒
,→
←
,
(d) 3x2 + 19xy
(
}×
xt
2y)(
-
(e) 2x3
50x
SITEYW
8m3 + 1 =(2m)3+(1)
(f)
=
f=zm
?2¥
(
2Mt
3
1) ( 4m2
-
Zmtl
)
¥1
ex stats
,mz)⇒
.
GCF
)
Y
m
2×(112-25)
⇒
7
xt3y)2
~
⇒
14y 2
5=1
f⇐2m
g(g) 27x
3
j@tozjrn
64
¥3135,91
⇐
2
(h)
,
.×+
.
x + 10x + 25
2=9×2
5=16
FL=
IZX
p
2
-
,
(
4
a
t
"
8%516
←
(
Xt5
×
+
-
2-
⇒
P)
(
P2
Xtstp
e-
Djttggzrgg@
)
<
f
=(
E
2-
LZ
c) (
FTL
)
9.- Find the Domain of the following functions.
(a) g(x) =
1/+4=0
⇒
x=
(c) g(x) =
3
x+4
(b)
DiX#
⇒
-4
f (x) =
(b)
x
f (x) =
x2
X
-
X
512
#
2
6x + 9
3) (
X
-
3)
D:x#@
€
c-
(a) What is the initial height?
(032+6410)+80
16
-
,
5)
16t2 + 64t + 80t{ where h represents the altitude
10.- The path of a missile is given by h(t) =
of the missile after t seconds.
D=
xtz
(
¥xtY¥¥I¥f¥o⇒€x¥5
hl
(x
D:
3x + 3
x3 25x
x4 2
2)(2x
80
=
(b) What is the height after 4 seconds.
"
"
IIYI.it#YtotsEgYuE@
(c) How long does it take to hit the ground?
16+2+64++80=0
-
⇒
-
⇒
-
⇒
16
16
t24t
(
( t
€
-
5) ( t
#
5)
-
+
1)
=°
=
0
#
'Et-¥÷
FEI
~
8°
←
.