Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor.
1) 12z 2 - 60z
A) 12(z 2 - 5z)
1)
B) 12z(z - 48)
C) 5z(12z - 1)
D) 12z(z - 5)
2) 12x2 y6 - 6x2 y3 - 24x6 y3
2)
A) 6x2 y3 (2y3 - 4x4)
B) 6x2 y3 (2y3 - 1 - 4x4 )
C) 6x2 y3 (6y3 - xy - 18x4 )
D) x2 y3(12y3 - 6 - 24x4 )
3) 3x + dy + dx + 3y
3)
A) 3(x + y) + d(x + y)
B) 3d(x + y)
C) (x + y)(3 + d)
D) cannot be factored
4) 6x2 + 23x - 18
A) (2x + 9)(3x - 2)
4)
B) (2x - 9)(3x + 2)
C) (6x - 23)(x + 18)
D) (6x - 2)(x + 9)
5) a 3 + 6a 2 - ab2 - 6b2
5)
A) (a - 6)(a 2 + b2 )
B) (a 2 + b2 )(a + 6)
C) (a +b)2 (a + 6)
D) (a + b)(a - b)(a + 6)
6) 25k2 - 36j2
6)
A) (5k - 6j)2
B) 30(k - j)(k + j)
C) (5k - 6j)(5k + 6j)
D) cannot be factored
7) y3 - 512
7)
A) (y - 8)(y + 8)2
B) (y + 8)(y2 - 8y - 64)
C) (y - 8)3
D) (y - 8)(y2 + 8y + 64)
Solve the equation.
8) 3x2 + 19x = -28
A) {-4, -7}
9) 4x2 - 8x = 0
1
A) 1,
2
8)
7
C) -4, 3
B) {7, 12}
7
D) 4,
3
9)
B) 2
C) 0, 2
C-1
D) {0, 8}
10) 2m(m - 7) = 3(7 - m)
3
A)
2
10)
2
C)
,7
3
B) {0, 1}
3
D) - , 7
2
Solve the problem.
11) The area of the rectangle shown is 42 in. 2 . Find the length and the width of the rectangle.
11)
x+5
2x + 5
A) length: 17 in.; width 1 in.
B) length: 6 in.; width 7 in.
C) length: 21 in.; width 21 in.
D) length: 7 in.; width 6 in.
Find the domain of the rational function.
x2 - 7x
12) r(x) =
2
x + 4x - 12
A) { x x ≠ -7, 7}
12)
B) { x x ≠ -2, 6}
C) { x x ≠ 0, 7}
D) { x x ≠ -6, 2}
Simplify the rational expression.
a2 - 25
13)
a 2 + 8a + 15
A)
a-5
a-3
13)
B)
a+5
a-3
C)
a-5
a+3
D)
a+5
a+3
Multiply.
14)
x-6
(x + 4)2
A)
15)
·
x2 - 2x - 24
(x - 6)2
x-6
x+4
14)
B)
1
x+4
C)
1
x-6
D) x + 4
6x + 12 4x2 - 8x + 4
·
x-1
x2 - 4
A)
24(x - 1)
x-2
15)
B)
24(x - 1)
x+2
C)
24(x + 2)(x - 1)
x2 - 4
D)
6(x - 1)
x-2
Divide.
16)
4x - 4y
2y - 2x
÷
40 - 10z
z-4
A)
1
20
16)
B) -
1
5
C)
C-2
2(x - y)
10
D)
1
5
17)
x2 - 9
4x - 12
÷
2
2
x - 2x + 1 x - 8x + 7
A)
(x - 3)(x + 7)
4(x + 1)
17)
B)
x-1
(x + 3)(x - 7)
C)
(x + 3)(x - 7)
4(x - 1)
D)
(x + 3)(x - 7)
x-1
Perform the indicated operation and express in lowest terms.
3
9
18)
+
10x 14x2
A)
19)
21)
B)
140x2
108
70x2
C)
12
10x + 14x2
D)
3(7x + 15)
70x2
1
11
4xy
8x4 y2
A)
20)
12
18)
19)
1 - 22x
8x4 y2
x
x2 - 16
-
B)
9 - 22x5
8x4 y
C)
11 - 22x4 y
8x5 y3
D)
1 - 22x3 y
8x4 y2
3
20)
x2 + 5x + 4
A)
x2 - 2
(x - 4)(x + 4)(x + 1)
B)
x2 - 2x + 12
(x - 4)(x + 4)(x + 1)
C)
x2 - 2x + 12
(x - 4)(x + 4)
D)
x2 + 2x + 12
(x - 4)(x + 4)(x + 1)
2
x
x2 + 6
+
x + 5 x - 3 x2 + 2x - 15
A)
-3x
(x - 5)(x + 3)
21)
B)
-3x
(x + 5)(x - 3)
C)
7x
(x + 5)(x - 3)
D)
2x2+ 7x - 12
(x - 5)(x + 3)
Simplify the complex fraction.
12x + 15
7
22)
16x + 20
4
A)
4
7
22)
B)
3
4
C)
1
7
D)
3
7
23)
23)
5 x
x 5
1 1
5 x
A) -(x + 5)
B) -(x - 5)
C) 5x(x + 5)
C-3
D) x + 5
Rewrite as a complex fraction and simplify.
a -2 - b-1
24)
8a -1 + 3b-2
A)
ab2 - a 2
8b2 + 3a2 b
B)
24)
b2 - a2 b
8b2 + 3a 2
C)
b2 - a2 b
8ab2 + 3a 2
D)
b2 - a 2
8ab2 + 3a 2
Solve.
25)
2
t
=
t
5t - 12
A) 0,
26)
24
9
25)
B) {0}
C) {4, 6}
D) {0, 36}
5
9
10
=
y + 5 y - 5 y2 - 25
A) {-20}
26)
B) {20}
C) {60}
D) ∅
Solve for the indicated variable.
h(B + b)
27) A =
for b
2
A) b = 2A - Bh
27)
B) b =
A - Bh
h
C) b =
2A - Bh
h
D) b =
2A + Bh
h
Solve.
28) Sandi can make a quilt in 11 days and Eva can make a quilt in 8 days. In how many days can they
make a quilt working together?
1
2
19
12
A) 4 days
B) 5 days
C) 3
days
D) 4
days
2
9
88
19
28)
29) The speed of a stream is 5 mph. If a boat travels 78 miles downstream in the same time that it takes
to travel 39 miles upstream, what is the speed of the boat in still water?
29)
A) 17 mph
B) 10 mph
C) 15 mph
D) 18 mph
Solve the problem. Round your answer, as needed.
30) Dr. Wong can see 9 patients in 3 hours. At this rate, how long would it take her to see 54 patients?
A) 17 hours
B) 162 hours
C) 18 hours
C-4
D) 27 hours
30)
Answer Key
Testname: MATH0312TEST2
1) D
2) B
3) C
4) A
5) D
6) C
7) D
8) C
9) C
10) D
11) B
12) D
13) C
14) B
15) A
16) D
17) C
18) D
19) D
20) B
21) B
22) D
23) A
24) C
25) C
26) A
27) C
28) D
29) C
30) C
C-5