Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.
1)
Evaluate: –325
1)
A)
–15
B)
15
C)
5i 3
D)
–75
2)
x + 6 +2 – x = 4
2)
A)
2, –2
B)
No solution
C)
0
D)
–2
Solve the problem.
3)
In the study of electrical circuits, the impedance of electron flow in an alternating–current (AC)
circuit is expressed as a complex number. The total impedance in an AC circuit connected in series
is the sum of the individual impedances. If the impedance in one part of the circuit is (5 –10i) ohms
and in another part is (1 +15i) ohms, what is the total impedance in the circuit?
3)
A)
(6 +5i) ohms
B)
(6 –5i) ohms
C)
(4 +25i) ohms
D)
6 ohms
Divide.
4)
97
4+9i
4)
A)
4+9i
B)
4–9i
C)
–1
9+13
9
D)
1
9+i
9
Use a calculator to approximate the root to the nearest thousandth.
5)
–82
5)
A)
–9.052
B)
–9.055
C)
–9.060
D)
–82.000
Rationalize the denominator.
6)
2 a –b
a–2 b
6)
A)
2a +3ab +2b
a –2b
B)
2a +3ab –2b
a –4b
C)
2a +3ab –2b
a +4b
D)
2a +3ab –2b
a –2b
Solve the problem.
7)
The radius, r, of a sphere can be found using the formula r =S
4, where S is the surface area. If
the surface area is 13,854 square inches, what is the radius? (Use
3.14 and round to the nearest
tenth.)
7)
A)
66.4 in.
B)
33.2 in.
C)
58.9 in.
D)
104.3 in.
Solve.
8)
3216–x3=6– x
8)
A)
0, 36
B)
0, 6, –6
C)
0, –6
D)
0, 6
1
Rationalize the denominator.
9)
3
2–5x
9)
A)
6–3 5x
4+5x
B)
6+3 5x
4–5x
C)
3
2+5x
D)
6+3 5x
4–25x
Solve.
10)
x2+3x = –4x –12
10)
A)
–3, 4
B)
–1
2, 3
4
C)
3, 4
D)
–3, –4
Multiply and simplify.
11)
15 108
11)
A)
18 5
B)
–18 5
C)
–30 3
D)
30 3
Divide.
12)
5y3
51024
12)
A)
5y3
4
B)
5y
4
C)
5y3
1024
D)
y
4
Solve the problem.
13)
The period P of a pendulum in seconds is given by the formula P = 2L
11 , where L is the length
of the pendulum. Solve the formula for L in terms of P.
13)
A)
L =P 11
2
B)
L =11 P2
42
C)
L =4 P2
11 2
D)
L =2 P
Divide.
14)
–6
–49
14)
A)
6i
7
B)
6
7i
C)
–6i
7
D)
6i
49
Write using radical notation. Then, simplify, if possible.
15)
a1
b2
1/2
15)
A)
a1/2
b
B)
a1/2
b1/2
C)
a1/2 ·b
D)
a1/2
b12
2
Evaluate, if possible
16)
–3729
16)
A)
–9
B)
–729
C)
9
D)
81
Combine, if possible.
17)
100 +64
17)
A)
18
B)
9
C)
3 2
D)
241
Multiply.
18)
–245· –5
18)
A)
35
B)
–1225
C)
–35
D)
–7 5
Evaluate.
19)
i5
19)
A)
–i
B)
i
C)
1
D)
–1
Divide.
20)
6+ 2i
2– 4i
20)
A)
–5
3+7
12i
B)
1
5+7
5i
C)
–1
12 +7
12i
D)
4+ 4i
Simplify.
21)
3+ 8 t
5t
21)
A)
15 – 8 5
5
B)
15t+ 8t 5
5t
C)
15t+ 8t 5
5
D)
15 + 8t 5
5t
Divide and simplify.
22)
3y2
8
22)
A)
y
2
B)
3y2
8
C)
3y
2
D)
3y2
2
Multiply.
23)
(6 – 9i)(5+ 3i)
23)
A)
57 – 27i
B)
–27i2– 27i + 30
C)
3– 63i
D)
57 + 27i
Solve the problem.
24)
The length of the diagonal of a box is given by D =L2+W2+H2 where L, W, and H are the
length, width, and height of the box. Find the length of the diagonal, D, of a box that is 1 ft long, 6 ft
high, and 4 ft wide. Give the exact value.
24)
A)
11 ft
B)
53 ft
C)
2 6 ft
D)
24 ft
3
Evaluate, if possible
25)
–100
25)
A)
10
B)
10
100
C)
10,000
D)
Not a real number
Simplify.
26)
3u4
16v
26)
A)
u3u
4v
B)
u34uv2
4v
C)
u34uv2
v
D)
u3u
16v
27)
14
3
27)
A)
14 3
3
B)
14 3
C)
23
D)
196 3
3
Combine, if possible.
28)
410x –9+310x –9
28)
A)
710x –9
B)
7(10x –9)
C)
720x –18
D)
40 10x –9
Divide and simplify.
29)
3625x4
35x
29)
A)
5x3x
B)
x3125
C)
5x
D)
5x35
Multiply and simplify.
30)
3 9y 5 3y5
30)
A)
45y43
B)
45 3y5
C)
45y33
D)
15y327
For the given functions f(x) and g(x), find the product or quotient as indicated.
31)
If f(x) =3+z and g(x) =3–z, find f(x) · g(x).
31)
A)
3– 2 z
B)
3– z
C)
3– 2 3z
D)
3z
Solve the problem.
32)
The cost, C, in dollars, of producing n clocks can be found using the formula C =25 n + 16. What is
the cost when no clocks are produced?
32)
A)
$400
B)
$20
C)
$25
D)
$100
Write using radical notation. Then, simplify, if possible.
33)
x1/5· x4/5
33)
A)
x4/5
B)
x–1
C)
x4/25
D)
x
4
Evaluate, if possible
34)
1
25
34)
A)
1
25
B)
25
C)
5a
D)
1
5
35)
–481
35)
A)
–2
B)
–9
C)
Not a real number
D)
–3
Write using radical notation. Then, simplify, if possible.
36)
(243x15)2/5
36)
A)
9x6
B)
243x3
C)
9x2
D)
9x3
37)
274/3
37)
A)
81
B)
243
C)
2187
D)
729
Given f(x) and g(x), find the sum or difference as indicated.
38)
If f(x) =74x7 and g(x) =3x4x3, find f(x) – g(x).
38)
A)
4x4x7
B)
104x3
C)
44x3
D)
4x4x3
Solve.
39)
Simplify: 200k7q8.
39)
A)
10k3q42
B)
10k2q42k
C)
10k7q82k
D)
10k3q42k
Evaluate, if possible
40)
49
64
40)
A)
7
8
B)
7
8
C)
0
D)
7
8
Write using radical notation. Then, simplify, if possible.
41)
125–1/3
41)
A)
1
6
B)
1
5
C)
–1
5
D)
–5
5
Simplify.
42)
36x
125y6z9
42)
A)
36x
5y3z2
B)
Cannot be simplified
C)
36x
5y2z3
D)
36x
125y2z3
Perform the indicated operation.
43)
12x3
25y6
43)
A)
2 3x3
5y3
B)
2x23xy3
5y3
C)
2x33
5y3
D)
2x 3x
5y3
Solve.
44)
Simplify: 256x8y6.
44)
A)
15x4y3
B)
17x4y3
C)
16x8y6
D)
16x4y3
Simplify.
45)
2
r4
45)
A)
2r4
r4
B)
2
r
C)
2
r4
D)
2
r2
Solve.
46)
x +8=x –8
46)
A)
16
B)
No solution
C)
0
D)
–16
Write using radical notation. Then, simplify, if possible.
47)
x1/6
47)
A)
x6
B)
x–6
C)
1
6x
D)
6x
Evaluate.
48)
i23 ·i19
48)
A)
–i
B)
i
C)
–1
D)
1
6
Solve.
49)
Rewrite in radical notation and simplify: (8x6)4/3
49)
A)
3(8x6)4; 16x8
B)
3(8x6)4; 64x8
C)
3(8x6)4; 128x24
D)
48x6)3; 32x8
Divide and simplify.
50)
311
x6
50)
A)
311
x2
B)
11
x2
C)
311
x
D)
311
x3
Simplify.
51)
25 u4v10
51)
A)
50u2v5
B)
25u2v5
C)
5u2v5
D)
5u4v10
Divide.
52)
10 + –25
2+ –16
52)
A)
2–3
2i
B)
2
C)
–3
2i
D)
–3
2+ 2i
Evaluate, if possible
53)
–64
121
53)
A)
–8
11
B)
8
11
C)
Not a real number
D)
–8
15
Simplify.
54)
481x5
y18z12
54)
A)
3x
y4z34x
y2
B)
3x 4x
y18z12
C)
3x
y16z12 4x
y2
D)
81x
y4z34x
y2
55)
38k6
55)
A)
–2k2
B)
2k2
C)
2k9
D)
8k2
7
For the given functions f(x) and g(x), find the product or quotient as indicated.
56)
If f(x) =325x and g(x) =349x, find f(x) · g(x).
56)
A)
31225x2
B)
12x
C)
374x2
D)
35x
Find the distance between the two points on the coordinate plane. Give an exact answer.
57)
(6, 2) and (15, –10)
57)
A)
14 units
B)
16 units
C)
15 units
D)
17 units
Multiply and simplify.
58)
( 7a +b)2
58)
A)
49a2+7ab +b2
B)
7a +7ab +b
C)
7a + 2 7ab +b
D)
49a2+ 2 7ab+b2
Divide.
59)
324
9
59)
A)
36
B)
3
C)
6
D)
18
Solve the problem.
60)
Find the area of a square piece of cardboard for which the length of the side is 713 cm.
60)
A)
49 13 sq cm
B)
8281 sq cm
C)
91 sq cm
D)
637 sq cm
Use a calculator to approximate the root to the nearest thousandth.
61)
0.000241
61)
A)
0.016
B)
0.16
C)
1.600
D)
0.002
Write using radical notation. Then, simplify, if possible.
62)
(27y12)1/3
62)
A)
27y4
B)
3y12
C)
3y4
D)
Cannot be simplified
Solve the problem.
63)
The radius, r, of a right circular cone can be found using the formula r =3V
h, where V is the
volume and h is the height. If the volume is 1714 cubic inches and the height is 3 inches, what is the
radius? (Use
3.14 and round to the nearest tenth.)
63)
A)
23.4 in.
B)
13.5 in.
C)
11.7 in.
D)
24.5 in.
Divide.
64)
23 +11i
8+ i
64)
A)
3
65 +11i
65
B)
3+ i
C)
8– i
D)
8
63 +i
63
8
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
65)
9r·5s
65)
A)
5rs
B)
45 rs
C)
Cannot be simplified
D)
9rs
Solve the problem.
66)
An object will take t seconds to drop d ft, where t =d
16 . What distance will the object drop in
21
2 sec?
66)
A)
84 ft
B)
168 ft
C)
21 ft
D)
42 ft
Write using radical notation. Then, simplify, if possible.
67)
(255/2)1/5
67)
A)
51/2
B)
125
C)
25
D)
5
Evaluate the radical function at the indicated value.
68)
f(x) =3x +5; f(22)
68)
A)
3
B)
4
C)
27
D)
9
Solve.
69)
Multiply: (8+ –25)(8– –49)
69)
A)
No solution
B)
99 +16i
C)
99 –16i
D)
16 –99i
Evaluate, if possible
70)
2 9
70)
A)
6
B)
12
C)
18
D)
3
Write in terms of i.
71)
–192
71)
A)
–8i 3
B)
8 3
C)
8i 3
D)
–8 3
Simplify.
72)
243x2
72)
A)
243x
B)
9x
C)
9x 3
D)
9 3x
Use a calculator to approximate the root to the nearest thousandth.
73)
1.27
73)
A)
1.142
B)
1.127
C)
1.146
D)
1.114
Simplify, if possible.
74)
–5128 – 3 200 – 6 18
74)
A)
716 2
B)
–716 2
C)
–5 2
D)
–88 2
9
Combine, if possible.
75)
83u+103u
75)
A)
183u
B)
186u
C)
1832u
D)
803u
Evaluate, if possible
76)
49
76)
A)
Not a real number
B)
2401
C)
7
D)
1
49
Simplify.
77)
4256a4
77)
A)
4a2
B)
4a
C)
4 a
D)
256a
For the given functions f(x) and g(x), find the product or quotient as indicated.
78)
If f(x) =x+ 14 and g(x) =x– 14, find f(x)
g(x).
78)
A)
x +196
x –196
B)
x + 28 x+196
x –196
C)
–1
D)
28 x
Write in terms of i.
79)
–4
144
79)
A)
–1
6i
B)
1
6
C)
–1
6
D)
1
6i
Write using radical notation. Then, simplify, if possible.
80)
9–7/2
80)
A)
–2187
B)
1
2187
C)
Cannot be simplified
D)
–63
2
81)
84/3
81)
A)
128
B)
64
C)
32
D)
16
Simplify.
82)
98
x
82)
A)
72x
B)
7x
x
C)
72x
x
D)
72
x
10
Find the distance between the two points on the coordinate plane. Give an exact answer.
83)
(6, 1) and (6, 10)
83)
A)
9 units
B)
10 units
C)
15 units
D)
8 units
Find the complex conjugate of the complex number. Then find the product of each complex number and its complex
conjugate.
84)
–17 + 4i
84)
A)
–17 – 4i; 273
B)
–17 – 4i; –21
C)
–17 – 4i; 305
D)
–17 + 4i; –13
Solve.
85)
8a – 5 =2a + 6
85)
A)
11
6
B)
11
10
C)
1
6
D)
6
11
86)
x2+92 = 2 5x – 1
86)
A)
–4, 18
B)
4, 18
C)
8, –12
D)
8, 12
87)
The demand equation for a particular item manufactured at a factory is p = 27 –x –5, where p is
the price of the item in dollars and x is the daily demand. What is the daily demand when the price
is $23?
87)
A)
17 units
B)
9 units
C)
16 units
D)
21 units
Evaluate, if possible
88)
3125
88)
A)
25
B)
–5
C)
11
D)
5
Given f(x) and g(x), find the sum or difference as indicated.
89)
If f(x) =3625x8 and g(x) =x2340x2, find f(x) + g(x).
89)
A)
735x2
B)
7x35x2
C)
7x235x2
D)
7x23x2
Write in terms of i.
90)
4–10
144
90)
A)
i10
3
B)
i10
9
C)
–i10
3
D)
4i 10
3
Solve the problem.
91)
Find the perimeter of a lot with sides measuring 550, 2 8, 232, and 412 yards.
91)
A)
37 + 8 3 yd
B)
37 2+ 8 3 yd
C)
45 2 yd
D)
74 + 8 3 yd
Solve.
92)
3x – 1 + 9 = 0
92)
A)
– 9
B)
6561
C)
– 6561
D)
No solution
11
Rationalize the denominator.
93)
x–y
5x +2y
93)
A)
x 5 –2xy –5xy + y 2
5x –2y
B)
5x –7xy +2y
5x –2y
C)
5x –7xy +2y
5x +2y
D)
x 5 –2xy –5xy + y 2
5x +2y
Simplify, if possible.
94)
1052x3y6+1052x3y
94)
A)
2052x3y
B)
(10y +10)52x3y
C)
(10y2+10)52x3y
D)
Cannot be simplified
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
95)
14 v5·14 v9
95)
A)
v2
B)
v
C)
v
D)
v4
Solve.
96)
q +1=5
96)
A)
36
B)
25
C)
26
D)
24
For the given functions f(x) and g(x), find the product or quotient as indicated.
97)
If f(x) = x –25 and g(x) =x+ 5, find f(x)
g(x)
97)
A)
x+ 5
B)
x – 5
C)
x + 5
D)
x– 5
Simplify.
98)
245
98)
A)
7
B)
15
C)
7 5
D)
49 5
Multiply and simplify.
99)
3xy5·3x19y11
99)
A)
x6y63xy
B)
x6y73x2y2
C)
x6y53xy2
D)
x6y53x2y
Divide.
100)
7
i
100)
A)
7– i
B)
7i
C)
–7i
D)
i –7
12
Solve.
101)
Divide: 9+ 3i
2– 5i
101)
A)
–1
7+17
7i
B)
–11
7+17
7i
C)
33
29 +39
29i
D)
3
29 +51
29i
Simplify.
102)
332
102)
A)
234
B)
2 +34
C)
2
D)
4 2
Solve.
103)
Simplify: (16p1/3)3/2
4p1/3
103)
A)
166p
B)
16 p
C)
163p
D)
46p
Solve the problem.
104)
The formula I =V
Z is used in electrical engineering. The variables I, V, and Z are complex
quantities. Find V if I =7+6i and Z =8+8i. Express the answer in standard form.
104)
A)
104– 8i
B)
8+104i
C)
8–104i
D)
104+ 8i
105)
Given the area A of a circle, the formula A
can be used to calculate the radius of the circle.
Rewrite the formula by rationalizing the denominator.
105)
A)
r =A
B)
r =A
A
C)
r =A
D)
r =A
2
Multiply and simplify.
106)
( 7 +10)( 7–10)
106)
A)
7–270
B)
7+ 2 70
C)
–3
D)
17
Solve.
107)
4x + 5 =2x – 2 – 3
107)
A)
1, 19
B)
– 1, 4
C)
No solution
D)
19
Evaluate.
108)
i12
108)
A)
–i
B)
–1
C)
i
D)
1
Perform the indicated operation.
109)
(4 – 7i) + (9+ 2i)
109)
A)
13 + 5i
B)
–13 + 5i
C)
13 – 5i
D)
–5+ 9i
13
Evaluate, if possible
110)
–0.0121
110)
A)
–0.11
B)
Not a real number
C)
0.11
D)
–0.011
Perform the indicated operation.
111)
(–8+6–100) – (–4–10 –1)
111)
A)
70i
B)
–4+50i
C)
–4+70i
D)
–12 +70i
Solve the problem.
112)
Given the area A of a circle, the formula r =A
can be used to calculate the radius of the circle.
Find the area when the radius is 5.2 cm.
112)
A)
A =27.04 sq cm
B)
A =27.04 sq cm
C)
A =27.04 2 sq cm
D)
A =28.30 sq cm
Solve.
113)
Multiply: 34xy ·39xy.
113)
A)
5xy
B)
313x2y2
C)
336x2y2
D)
6xy
Divide.
114)
22z
2
114)
A)
44z
B)
11 z
C)
11z
D)
z11
Solve the problem.
115)
The period of a pendulum, in seconds, is given by the formula 2L
11 , where L is the length of
the pendulum. Rewrite the formula, by rationalizing the denominator.
115)
A)
P =211L
11
B)
P = 2L
C)
P =411L
11
D)
P =22L
11
Combine, if possible.
116)
711 +311
116)
A)
110
B)
21 11
C)
10 22
D)
10 11
Evaluate, if possible
117)
3–27
8
117)
A)
3
2
B)
9
4
C)
–27
8
D)
–3
2
Use a calculator to approximate the root to the nearest thousandth.
118)
313
118)
A)
2.351
B)
13.009
C)
2.355
D)
12.996
14
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
119)
10 v7
12 v5
119)
A)
v
B)
10 v7
12 v5
C)
60 v17
D)
120 v34
Solve.
120)
5x +2=7
120)
A)
5
B)
25
C)
53
5
D)
1
Perform the indicated operation.
121)
(–1– i) – (–1+11i)
121)
A)
10i
B)
–2+12i
C)
12i
D)
–12i
Solve.
122)
4q –3=3
122)
A)
No solution
B)
9
C)
3
D)
3
2
Evaluate, if possible
123)
–100
123)
A)
10
B)
–10
C)
Not a real number
D)
–50
Divide.
124)
31296x4
36x
124)
A)
x3216
B)
6x
C)
6x36
D)
6x3x
Solve the problem.
125)
The length of the diagonal of a rectangle is given by D =L2+W2 where L and W are the length
and width of the rectangle. What is the length of the diagonal, D, of a rectangle that is 69 inches
long and 16 inches wide? Round your answer to the nearest tenth of an inch, if necessary.
125)
A)
70.8 in.
B)
9.2 in.
C)
33.2 in.
D)
67.1 in.
Find the distance between the two points on the coordinate plane. Give an exact answer.
126)
(1, 2) and (–1, –7)
126)
A)
85 units
B)
77 units
C)
–7unit
D)
18 units
Multiply and simplify.
127)
17(17 +2)
127)
A)
17 +34
B)
51
C)
17 +34
D)
323
15
Simplify.
128)
z18
128)
A)
z9
B)
2z
C)
z36
D)
z
2
Simplify, if possible.
129)
27 + 2 75
129)
A)
–3
B)
13 3
C)
5 3
D)
8 3
Simplify.
130)
50x3
y5
130)
A)
x50xy
y3
B)
5x 2xy
y3
C)
5x32
y5
D)
5x
y2 2x
y
Simplify, if possible.
131)
6 5 + 8 20
131)
A)
10 5
B)
14 5
C)
–22 5
D)
22 5
Multiply.
132)
2·3
132)
A)
46
B)
5
C)
45
D)
6
Perform the indicated operation.
133)
(5 7 +5)(5 7 +7)
133)
A)
60 7+35
B)
35 +25 72+35 7
C)
210+60 7
D)
95 7
Combine, if possible.
134)
1133+ 733
134)
A)
1833
B)
1839
C)
1836
D)
33
135)
7 x +6 x
135)
A)
12 x
B)
x
C)
13 x
D)
14 x
Simplify, if possible.
136)
1
4512–162+1
362
136)
A)
–5 2 +2
B)
4 2 +2
C)
13 2+2
D)
–3 2
Use a calculator to approximate the root to the nearest thousandth.
137)
4101
137)
A)
3.192
B)
3.202
C)
3.184
D)
3.170
16
Perform the indicated operation.
138)
Rationalize the denominator: 3 x
x– 2 y.
138)
A)
3x + 6 xy
x +2y
B)
3x + 6 xy
x –4y
C)
3x + 6 xy
x +4y
D)
3x + 6 xy
x –2y
Solve.
139)
2k + 1 =13
139)
A)
42
B)
–84
C)
84
D)
168
Write using radical notation. Then, simplify, if possible.
140)
31254/5
140)
A)
78,125
B)
625
C)
390,625
D)
1,953,125
Multiply and simplify.
141)
y y3+3y
141)
A)
y2+3y
B)
y2+ y 3
C)
y4+ y 3
D)
y1+ y 3
Solve.
142)
Divide: 60n
3n
142)
A)
2n 5
B)
20
C)
20n
D)
2 5
Evaluate, if possible
143)
4256
625
143)
A)
64
125
B)
4
5
C)
256
625
D)
16
25
Evaluate the radical function at the indicated value.
144)
f(x) =2x – 1;f(5)
144)
A)
3
B)
10
C)
3.2
D)
9
Solve the problem.
145)
Police use the formula s = S l
L , where S is the test–car speed and L is the test–skid length, to find
the actual speed s in an accident which left a skid mark of length l. Solve the formula for l in terms
of s, L,
and S.
145)
A)
l =s2
S2L
B)
l =S2L
s2
C)
l =s2L
S2
D)
l = L
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
146)
10 x
146)
A)
12 x
B)
x10
C)
5x
D)
20 x
17
Solve.
147)
The radius of a sphere with surface area S is given by the expression S
.
a) Simplify the expression.
b) Find the radius of a beach ball if its surface area is 128in.2. Express the answer in radical form.
147)
A)
a) S
; b) 8
in.
B)
a) S
; b) 4
in.
C)
a) S
; b) 8
in.
D)
a) S
; b) 4
in.
Solve the problem.
148)
Some functions have the set of complex numbers for their domain. These functions play a role in
fractal geometry, which is important in nature and art. If the function f(z) = 2z + 5 + 2i, find
f(–2+5i).
148)
A)
1+12i
B)
–4+12i
C)
1+7i
D)
–3+20i
Evaluate, if possible
149)
–3–64
149)
A)
–4
B)
8
C)
–16
D)
4
Write using radical notation. Then, simplify, if possible.
150)
9611/2
150)
A)
124
B)
31
C)
62
D)
15.5
Simplify.
151)
3128
151)
A)
432
B)
11
C)
5
D)
234
Solve the problem.
152)
Is the complex number 7–5i a solution of the equation x2–14x = –74 ? Explain.
152)
A)
No; because (7 –5i)2–14(7 –5i) –74
B)
Yes; because (7 –5i)2–14 = –74
C)
No; because (7 –5i)2–14 –74
D)
Yes; because (7 –5i)2–14(7 –5i) = –74
153)
The manufacturer’s cost, C, in dollars, can be found using the formula C =3003n+ 1300, where n is
the number of parts produced. Find the cost when 125 parts are produced.
153)
A)
$60
B)
$4654
C)
$2050
D)
$2800
Simplify.
154)
–640
154)
A)
12 10
B)
–12 10
C)
–415
D)
–240
18
Multiply and simplify.
155)
(9 3 +6 7 )(2 3 +3 7)
155)
A)
18 3+18 7
B)
180 +39 21
C)
–72 +39 21
D)
18 3+18 7+39 21
Solve the problem.
156)
One television has a rectangular screen that is 9 inches by 17 inches. Another has a rectangular
screen that is 6 inches by 10 inches. The size of a television set is commonly given by the length of
the screen’s diagonal. What is the difference of the diagonal lengths for these two sets ?
156)
A)
370+ 2 136
B)
234
C)
234
D)
370– 2 34
Write using radical notation. Then, simplify, if possible.
157)
(u–3)–1/6
157)
A)
u
B)
1u
C)
u2
D)
3u
Multiply.
158)
37xy·32y
158)
A)
14xy2
B)
39xy2
C)
314xy2
D)
314xy
For the given functions f(x) and g(x), find the product or quotient as indicated.
159)
If f(x) =3x and g(x) =3–64x2, find f(x)
g(x).
159)
A)
3x2
4x
B)
3x2
4
C)
3x2
–4x
D)
3x2
–4
Simplify.
160)
73125p12q3
160)
A)
35p4q
B)
35p4q3
C)
7q3125p12
D)
353p12q3
161)
252w4x7y6z
2xy
161)
A)
3wx3y22yz
B)
3w2x3y214yz
C)
42w2x3y2yz
D)
3w2x3y214z
Multiply.
162)
(5i)(10i)
162)
A)
–15
B)
–50
C)
15
D)
50
Write using radical notation. Then, simplify, if possible.
163)
165/4
163)
A)
128
B)
512
C)
32
D)
256
19
Divide and simplify.
164)
24x3
25y6
164)
A)
2x26xy3
5y3
B)
2x 6x
5y3
C)
2x36
5y3
D)
2 6x3
5y3
Graph the function.
165)
f(x) =x+ 3
165)
A)
B)
C)
D)
20
Multiply.
166)
34x ·39x
166)
A)
313x2
B)
6x
C)
5x
D)
336x2
Use a calculator to approximate the root to the nearest thousandth.
167)
5–66
167)
A)
–2.324
B)
–2.312
C)
–2.342
D)
–2.333
Solve.
168)
3z+4=6
168)
A)
–8
B)
No solution
C)
316
D)
8
Write using radical notation. Then, simplify, if possible.
169)
5p2/7
p1/7
169)
A)
5
p7
B)
57p
C)
Cannot be simplified
D)
5p3/7
Evaluate, if possible
170)
3–216
170)
A)
36
B)
15
C)
–6
D)
6
Solve the problem.
171)
The owner of a factory finds that the price, p (in dollars), of an item is given by the equation
p =0.75 x –8, where x is the daily demand. Find the price of the item when the daily demand is 71
units.
171)
A)
$6.67
B)
$13.89
C)
$5.95
D)
$47.25
21
Graph the function.
172)
g(x) =x – 4
172)
A)
B)
C)
D)
Find the distance between the two points on the coordinate plane. Give an exact answer.
173)
(–1, –7) and (–4, 2)
173)
A)
12 units
B)
72 2 units
C)
310 units
D)
72 units
Evaluate.
174)
i3
174)
A)
1
B)
i
C)
–i
D)
–1
22
Multiply and simplify.
175)
35 (6 35–325)
175)
A)
635–535
B)
635–5
C)
6325 –5
D)
5325
Solve the problem.
176)
The velocity of a fluid flowing out of a tank through a small opening d ft below the surface is given
by the expression 2d
72 . Simplify the expression.
176)
A)
d
36
B)
d
2
C)
d
6
D)
d
6
Write using radical notation. Then, simplify, if possible.
177)
(–8)2/3
177)
A)
–2
B)
–4
C)
Not a real number
D)
4
Solve the problem.
178)
An object will take t seconds to drop d ft, where t =d
16 . Solve the formula for d in terms of t..
178)
A)
d = 4t2
B)
d = 16t2
C)
d =t2
4
D)
d =t2
16
Solve.
179)
4x – 2 + 7 = 0
179)
A)
–7
2
B)
–2401
2
C)
2401
2
D)
No solution
Rationalize the denominator.
180)
7
9 –5
180)
A)
7
9 – 7
5
B)
63 +7 5
76
C)
63 –7 5
76
D)
63 +7 5
–4
Simplify.
181)
19x
64
181)
A)
19x
8
B)
19
8x
C)
19x
64
D)
152x
8
Divide and simplify.
182)
21x
36
182)
A)
36 21
B)
621
C)
21x
6
D)
21
36
23
Find the distance between the two points on the coordinate plane. Give an exact answer.
183)
(–5, –3) and (5, 1)
183)
A)
84 units
B)
6units
C)
84 21 units
D)
229 units
Divide.
184)
28xy3
4x
184)
A)
y 7y
B)
y27y
C)
y27xy
D)
y228y
Write using radical notation. Then, simplify, if possible.
185)
811/4·3
185)
A)
3
B)
243
C)
9
D)
35/4
Multiply and simplify.
186)
3( 147 –27)
186)
A)
30
B)
9– 3 3
C)
3 7 – 9
D)
12
Find the complex conjugate of the complex number. Then find the product of each complex number and its complex
conjugate.
187)
9–6i
187)
A)
3; 117
B)
9–6i; 117
C)
15; 117
D)
9+6i; 117
Solve the problem.
188)
Find the perimeter of a triangle with sides measuring 575, 475, and 580 meters.
188)
A)
45 + 20 5 m
B)
45 3+ 20 m
C)
45 3+ 20 5 m
D)
65 3 m
189)
Police use the formula S l
L , where S is the test–car speed and L is the test–skid length, to find the
actual speed in an accident which left a skid mark of length l. Simplify the expression S l
L by
rationalizing the denominator.
189)
A)
S l
L
B)
S l · L
l
C)
S l · L
D)
S l · L
L
Divide.
190)
–5
–5+ 2i
190)
A)
25
29 +10
29i
B)
25
21 –10
21i
C)
25
21 +10
21i
D)
25
29 –10
29i
Use a calculator to approximate the root to the nearest thousandth.
191)
2
191)
A)
2.000
B)
1.411
C)
1.419
D)
1.414
24
Write using radical notation. Then, simplify, if possible.
192)
73/4
71/2
192)
A)
71/4
B)
1
74
C)
Cannot be simplified
D)
7
Solve.
193)
3x –2=2–3x
193)
A)
2
3
B)
–2
3
C)
3
2
D)
No solution
Write using radical notation. Then, simplify, if possible.
194)
(49m14)1/2
194)
A)
7 m14
B)
49m14
C)
7m14
D)
7m7
195)
81/3
195)
A)
48
B)
2
C)
16
D)
6
Solve.
196)
x2+7x = –6x –42
196)
A)
–7, –6
B)
–7, 6
C)
7, 6
D)
–1
2, 3
4
Simplify, if possible.
197)
–6 3 – 4 75
197)
A)
26 3
B)
–14 3
C)
–10 3
D)
–26 3
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
198)
7s·s
198)
A)
7s2
B)
9s2
C)
14 s9
D)
92s
Find the complex conjugate of the complex number. Then find the product of each complex number and its complex
conjugate.
199)
–8–9i
199)
A)
–17; 145
B)
1; 145
C)
–8–9i; 145
D)
–8+9i; 145
Multiply.
200)
x
10 y
13
200)
A)
xy
23
B)
x + y
130
C)
xy
130
D)
x + y
23
25
Perform the indicated operation.
201)
Simplify: 9p
40q.
201)
A)
310pq
20q
B)
310pq
10q
C)
310pq
D)
40 pq
Rationalize the denominator.
202)
5
2+1
202)
A)
310 +2 5
2
B)
10 +1 5
1
C)
10 –1 5
3
D)
10 –1 5
1
Solve the problem.
203)
An object will take t seconds to drop d ft, where t =d
16 . How much time will it take the object to
drop 84 ft?
203)
A)
21 sec
B)
21
2 sec
C)
2 21 sec
D)
21
4 sec
Solve.
204)
9–3x =x –3
204)
A)
12
B)
No solution
C)
3
D)
4
Multiply.
205)
(8 – 6i)2
205)
A)
64 – 60i
B)
64 – 132i
C)
100– 96i
D)
28 – 96i
Divide.
206)
5– i
5i
206)
A)
1
5– i
B)
1
5+ i
C)
–1
5+ i
D)
–1
5– i
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
207)
5v·v
207)
A)
72v
B)
7v2
C)
5v2
D)
10 v7
Simplify.
208)
–361
289
208)
A)
–19
17
B)
5
4
C)
19
17
D)
–5
4
26
Solve.
209)
x +8+3x +22 = 2
209)
A)
0
B)
7
C)
–7
D)
No solution
Divide and simplify.
210)
24a2
b2
210)
A)
2a 6
b
B)
2a 6
b2
C)
2 6a
b
D)
24a2
b
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
211)
3x21
211)
A)
x7
B)
z
3
C)
x63
D)
3z
Write using radical notation. Then, simplify, if possible.
212)
(–8)1/3
212)
A)
–2
B)
–8
C)
Not a real number
D)
2
Simplify.
213)
41280
213)
A)
544
B)
35
C)
445
D)
5
Perform the indicated operation.
214)
9i + (–4– i)
214)
A)
–4+ 8i
B)
–4+ 10i
C)
4– 10i
D)
4– 8i
Combine, if possible.
215)
946+ 8 36
215)
A)
17 36
B)
72 436
C)
946+ 8 36
D)
17 46
Solve the problem.
216)
A rectangular coal bin has a length of 75 feet and a width of 48 feet. What is its perimeter?
216)
A)
9 4 ft
B)
18 3 ft
C)
9 3 ft
D)
18 4 ft
Solve.
217)
x+2= 0
217)
A)
No solution
B)
4
C)
–4
D)
2
Write using radical notation. Then, simplify, if possible.
218)
6251/2
218)
A)
25
B)
100
C)
50
D)
12.5
27
Evaluate.
219)
i6
219)
A)
–1
B)
i
C)
1
D)
–i
Solve.
220)
Simplify: 6x4y2
220)
A)
6x2y
B)
3x2y
C)
3xy
D)
3x2y2
Perform the indicated operation.
221)
5+ 7 20 – 4 20
221)
A)
332
B)
7 5
C)
732
D)
3 5
Multiply.
222)
(–9+5)( –1–5)
222)
A)
–8– 2i 5
B)
2+4i
C)
2– 2i 5
D)
2–4i
Solve the problem.
223)
It takes 50–h
4 seconds for an object to fall from a height of 50 feet to a height of h feet above the
ground. From this height, how much longer does it take for an object to drop to a height of 31 feet
above the ground than to drop to a height of 42 feet above the ground?
223)
A)
2 2 –19
4 sec
B)
19 – 2 2
4 sec
C)
11
4 sec
D)
19 – 3
2 sec
Multiply.
224)
7i(3– 4i)
224)
A)
21i + 28i2
B)
21i – 28i2
C)
28 + 21i
D)
21i– 28
Find the distance between the two points on the coordinate plane. Give an exact answer.
225)
(7, –4) and (3, –6)
225)
A)
12 3 units
B)
2 5 units
C)
12 units
D)
2units
Solve.
226)
5a – 6 –3a + 9 = 0
226)
A)
15
8
B)
15
2
C)
2
15
D)
3
2
Given f(x) and g(x), find the sum or difference as indicated.
227)
If f(x) =53a and g(x) =3–27a, find f(x) – g(x).
227)
A)
6327a
B)
8a 3a
C)
83a
D)
153a
28
Solve the problem.
228)
A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the
rope is taut while the balloon is directly above a flag pole that is 100 feet from where the rope is
staked down. Find the altitude of the balloon if the rope is 110 feet long.
228)
A)
210 ft
B)
10 221 ft
C)
10 ft
D)
10 21 ft
Solve.
229)
20x +20 = x + 6
229)
A)
4, 5
B)
4
C)
–4
D)
4, –4
Write using radical notation. Then, simplify, if possible.
230)
(3z1/3)3
9z4
230)
A)
3
z4
B)
3
z3
C)
3z3
D)
9
z
Solve.
231)
3x +3=3
231)
A)
27
B)
0
C)
6
D)
24
Evaluate.
232)
i20
i11
232)
A)
1
B)
–1
C)
i
D)
–i
Simplify.
233)
300k7q8
233)
A)
10k3q43
B)
10k7q83k
C)
10k2q43k
D)
10k3q43k
Find the complex conjugate of the complex number. Then find the product of each complex number and its complex
conjugate.
234)
–6i
234)
A)
6i; –36
B)
6i; –12
C)
–6i; 12
D)
6i; 36
29
Divide.
235)
418r3
43r2
235)
A)
46r
B)
6r
C)
Cannot be simplified
D)
46r
r
Simplify.
236)
225
484
236)
A)
15
22
B)
8
11
C)
56
121
D)
15
23
Write in terms of i.
237)
–9
237)
A)
–3i
B)
3i
C)
±3
D)
–i 3
Simplify, if possible.
238)
5– 6 80 – 5 180
238)
A)
–53 5
B)
–53 265
C)
–11 5
D)
–11 265
Use rational exponents to simplify the expression, if possible. Then, write the answer in radical form.
239)
339
239)
A)
9
B)
339
C)
27
D)
81
Evaluate, if possible
240)
4256
240)
A)
5
B)
3
C)
16
D)
4
Solve.
241)
The distance to the horizon (in miles) of a satellite h miles above Earth‘s surface is given by the
expression 1000h +h2. What is the distance to the horizon from a satellite that is 25 miles above
Earth? Express the answer in radical form.
241)
A)
250 41 mi
B)
20 41 mi
C)
25 41 mi
D)
10 mi
242)
Evaluate: 33–8
242)
A)
–233
B)
–24
C)
–6
D)
6
Multiply.
243)
–16(36 + –121)
243)
A)
24 –44i
B)
44 + 24i
C)
–44 – 24i
D)
–44 + 24i
30
Answer Key
Testname: C9
31
Answer Key
Testname: C9
32
Answer Key
Testname: C9
33
Answer Key
Testname: C9
Answer Key
Testname: C9
35