Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the numerical value of the rational expression for the given value of x.
1)
9x - 1
,x=3
7x
A)
2)
B)
2
7
C)
26
21
D)
92
73
3 - 4x
,x=2
6x
A)
3)
4
3
1)
11
12
2)
B)
5
12
C) -
5
12
10
3
D) -
(- 7 x)3
,x=3
4x + 6
A)
1029
2
3)
B)
3087
2
C) -
1029
2
3087
2
D) -
Find all values that make the expression undefined.
5
4)
x+9
4)
A) -9
C) 9
5)
b-5
5b - 20
A) 4
6)
5)
B) -5
C) 0
D) 20
x2 - 81
6)
x2 + 11x + 28
A) -4, -7
7)
B) 0
D) Never undefined
B) 9, -9
C) 0
D) 4, -7
-6q - 6
q2 + 36
7)
A) 0
C) -6
B) Never undefined
D) 6, -6
Write the rational expression in lowest terms.
y2 + 10y + 16
8)
y2 + 11y + 24
A)
10y + 16
11y + 24
B)
8)
y+2
y+3
C)
1
10y + 2
11y + 3
D) -
y2 + 10y + 16
y2 + 11y + 24
9)
y2 - 4y - 12
y2 - 6y - 16
A)
10)
12)
B)
-4y - 3
-6y - 4
C)
-4y - 12
-6y - 16
D) -
y2 - 4y - 12
y2 - 6y - 16
tx + t + 8x + 8
2x + 2
A)
11)
y-6
y-8
9)
t-2
8
10)
B)
t+8
2
C)
t-8
2
D)
t+2
2
pq - 5p + 2q - 10
qr + 3q - 5r - 15
11)
A)
p-2
r+3
B)
p+2
q-3
C)
pq - 5p + 2q - 10
qr + 3q - 5r - 15
D)
p+2
r+3
x2 - y2
y-x
12)
A) -x - y
B) -1
C) x + y
D) -x + y
Multiply. Write the answer in lowest terms.
5r - 15
6r + 12
·
13)
2
30
- 10r
12r + 24r
A) -
1
4r
B)
13)
r- 3
4r(3 - r)
C)
1
4
D) -
5
4(3 - r)
Divide. Write the answer in lowest terms.
x2 - 36 4x + 24
÷
14)
x
x-6
A)
(x - 6)2
4x
B)
14)
4(x + 6)2
x
C)
4x
(x - 6)2
D)
(x - 6)2
x
Multiply or divide as indicated. Write the answer in lowest terms.
k2 + 9k + 18
k2 + 8k
·
15)
k2 + 11k + 24 k2 - 2k - 48
A)
k2 + 8k
k- 8
B)
k
2
k + 11k + 24
C)
2
15)
k
k-8
D)
1
k-8
16)
17)
25x2 - 1 5x - 1
÷
x-4
x2 - 16
A)
5x - 1
x-4
B)
5x + 1
x+4
C)
(5x - 1)(25x2 - 1)
(x2 - 4)(x - 4)
D)
x+4
5x + 1
y3 - 10y
y2 + 0y - 9
÷
2
y - 100 y2 + 7y - 30
A)
18)
16)
(y - 10)(y + 3)
y(y2 - 10)
17)
B)
y
y+3
C)
y(y2 - 10)
(y - 10)(y + 3)
D)
(y + 10)(y - 3)
y(y2 - 10)
t- 7
t+ 2
·
2
2
t - 3t - 10 t - 9t + 14
18)
A)
t
(t + 5)(t + 2)
B)
(t - 7)
(t - 5)(t - 2)(t + 7)
C)
1
(t - 5)(t - 2)
D) -
1
5(t + 2)
Add or subtract. Write the answer in lowest terms.
6
8
19) +
r r+ 8
A)
20)
22)
B)
14r + 48
r(-8 - r)
C)
-48r - 14
r(r + 8)
D)
14r + 48
r(r + 8)
6x
2
+
x+4 x-4
A)
21)
-48r - 14
r(-8 - r)
19)
6x2 - 22x + 8
x2 - 8x + 16
20)
B)
6x2 - 22x + 8
x2 - 16
C)
6x2 - 22x + 8
x2 + 8x + 16
4
7
+
2
2
y - 3y + 2 y - 1
D)
6x + 2
(x + 4)(x - 4)
21)
A)
10y - 11
(y - 1)(y + 1)(y - 2)
B)
56y - 10
(y - 1)(y + 1)(y - 2)
C)
11y - 10
(y - 1)(y + 1)(y - 2)
D)
11y - 10
(y - 1)(y - 2)
x
4
2
2
x - 16 x + 5x + 4
22)
A)
x2 - 3
(x - 4)(x + 4)(x +1)
B)
x2 + 3x + 16
(x - 4)(x + 4)(x + 1)
C)
x2 - 3x + 16
(x - 4)(x + 4)
D)
x2 - 3x + 16
(x - 4)(x + 4)(x + 1)
3
Simplify the complex fraction.
9m5 n 3
4m
23)
8m2 n 9
23)
5n4
A)
4 +
24)
45m 2
32n3
B)
C)
45m 2
32n2
D)
45m 3
32n8
2
x
24)
x
1
+
3
6
A) 1
25)
45m 3
32n3
B)
12
x
C) 12
D)
x
12
3
1
k+3 k-9
25)
3
2
+
k-9 k+2
A)
(2k - 30)
(k + 3)(5k - 12)
B)
(2k - 30)(k - 2)
(k - 3)(5k - 12)
C)
(2k - 30)(k + 2)
(k + 3)(5k + 12)
D)
(2k - 30)(k + 2)
(k + 3)(5k - 12)
Solve the equation.
x
9 x+4
+ =
26)
16 8
8
26)
A) {5 }
27)
B) {1 }
27)
B) {- 5 }
5
4
D)
28)
B) {-3}
C) {40}
D) {5}
7
9
8
=
m - 4 m + 4 m2 - 16
A) {-28}
30)
C) -
1
4
+
=2
x- 4
4 x - 16
A) {1}
29)
D) {14 }
x
5
- 5 =
x- 5
x- 5
A) { 5 }
28)
C) {10 }
y
y2 + 11y + 28
A) { 8 , 0}
29)
B) {28}
+
y
y2 - 16
=
C) {28, -28}
D)
y
30)
y2 + 3y - 28
B) { 1 , 0}
C) { -8 , 0}
4
D) { -1 , 0}
Solve the formula for the specified variable.
1 1 1
for c
31) + =
a b c
A) c =
32)
a+b
ab
B) c =
31)
ab
a+b
C) c = a + b
D) c = ab(a + b)
PV pv
=
for P
T
t
A) P =
33) I =
pvT
tV
32)
B) P =
pvV
tT
C) P =
tvT
pV
D) P =
pv
tTV
E
for r
R+r
A) r =
E
- IR
I
33)
B) r =
E-R
I
C) r =
IR
E
D) r =
E - IR
I
Solve the problem.
34) Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 282 mi in the same time
that Dana travels 246 mi. If Chuck's rate of travel is 6 mph more than Dana's, and they travel the
same length of time, at what speed does Chuck travel?
A) 50 mph
B) 44 mph
C) 41 mph
D) 47 mph
34)
35) The speed of a stream is 4 mph. If a boat travels 66 mi downstream in the same time that it takes to
travel 33 mi upstream, what is the speed of the boat in still water?
A) 12 mph
B) 8 mph
C) 14 mph
D) 15 mph
35)
36) Tom Quig traveled 260 mi east of St. Louis. For most of the trip he averaged 70 mph, but for one
period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 8 hr,
how many miles did he drive at the reduced speed?
A) 115 mi
B) 120 mi
C) 140 mi
D) 130 mi
36)
37) A jet plane traveling at a constant speed goes 1200 mi with the wind, then turns around and travels
for 1000 mi against the wind. If the speed of the wind is 50 mph and the total flight took 4 hr, find
the speed of the plane.
A) 525 mph
B) 605 mph
C) 550 mph
D) 435 mph
37)
38) One printer can do a printing job in 2 hr. Another printer can do the same job in 14 hr. How long
does it take the two printers to do the job working together?
1
1
3
11
hr
hr
A) 2 hr
B)
C) 1 hr
D) 1
3
16
4
17
38)
39) Martha can rake the leaves in her yard in 3 hr. Her brother can do the job in 6 hr. How long will it
take them to do the job working together?
1
1
hr
A) hr
B) 6 hr
C)
D) 2 hr
9
18
39)
5
40) One maid can clean the house in 2 hr. Another maid can do the job in 5 hr. How long will it take
them to do the job working together?
3
1
1
1
hr
A) 1 hr
B) hr
C) 3 hr
D)
7
7
3
10
Solve the problem involving direct or inverse variation.
41) If m varies directly as p, and m = 15 when p = 3 , find m when p is 9 .
A) m = 45
B) m = 9
C) m = 81
42) If x varies inversely as v, and x = 24 when v = 8 , find x when v = 64 .
A) x = 3
B) x = 8
C) x = 24
D) m = 25
D) x = 64
Solve the variation problem.
43) The weight of a liquid varies directly as its volume. If the weight of the liquid in a cubical container
5 cm on a side is 250 g, find the weight of the liquid in a cubical container 4 cm on a side.
A) 64 g
B) 44 g
C) 128 g
D) 8 g
44) The gravitational attraction between two masses varies inversely as the square of the distance
between them. If the force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction
when the masses are 6 ft apart?
A) 2 lb
B) 3 lb
C) 1 lb
D) 4 lb
6
40)
41)
42)
43)
44)
Answer Key
Testname: MAT1033_PE1
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
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27)
28)
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30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
C
C
C
A
A
A
B
B
A
B
D
A
A
A
C
B
C
C
D
B
C
D
C
B
D
C
D
D
B
B
B
A
D
D
A
B
C
C
D
A
A
A
C
C
7