Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1)
Police use the formula s =30fd to estimate the speed s of a car in miles per hour, where d is the
distance in feet that the car skidded and f is the coefficient of friction. If the coefficient of friction on
a certain dry road is 0.81 and a car was traveling on it at a rate of 40 mph, how far will the car skid?
(Round to the nearest foot.)
1)
A)
53 ft
B)
389 ft
C)
31 ft
D)
66 ft
Simplify the expression.
2)
-7 200+ 5 98 – 4 32
2)
A)
-8 2
B)
82
C)
-51 2
D)
-7 2
Write in exponential form.
3)
x4y2
3)
A)
x4y1/2
B)
(x4y2)2
C)
(x4y2)1/2
D)
x1/4y1/2
Simplify.
4)
4512
4)
A)
442
B)
4
C)
16
D)
448
Write the radical in exponential form and then simplify. Write the answer in simplified radical form.
5)
12 x9
5)
A)
x4/3
B)
x
C)
4x3
D)
3x4
Use the FOIL method to multiply the factors, then solve the equation.
6)
(5 –x)(1+x) =5
6)
A)
x = 0, x =4
B)
x = 0
C)
x = 0, x =16
D)
x =16
Simplify the expression.
7)
375
15
7)
A)
5 3
B)
51
5
C)
25
D)
5
Simplify.
8)
3648
8)
A)
6
B)
6318
C)
18
D)
633
Simplify the expression.
9)
7
5+ 9
9)
A)
35 – 9 7
14
B)
35 – 9 7
-76
C)
35 + 9 7
-76
D)
335 + 5 7
45
Multiply.
10)
y(y3–4 y)
10)
A)
y2–4y
B)
y4–4y y
C)
y4–4 y
D)
4y3y
Solve the equation. If the equation has no real solution, so state.
11)
6q – 5 =5
11)
A)
q =5
B)
q =25
C)
q =25
6
D)
q =10
3
Simplify.
12)
7·7
12)
A)
49
B)
7
C)
2 7 · 12
D)
14
Find the product of the given binomial and its conjugate.
13)
6–2
13)
A)
10
B)
32 +4 6
C)
2
D)
2–4 6
Write in exponential form.
14)
t5
14)
A)
t5
2
B)
t5/2
C)
52/t
D)
t2/5
Simplify the expression.
15)
6
7–2
15)
A)
42 + 6 2
5
B)
42 – 6 2
47
C)
6
7–62
D)
42 + 6 2
47
Is the radical expression completely simplified?
16)
6 x
x
16)
A)
Yes
B)
No
Find the product of the given binomial and its conjugate.
17)
2+3
17)
A)
-1
B)
2 6
C)
-1 –6
D)
5
Write the expression in radical form and then evaluate.
18)
811/4
18)
A)
36
B)
243
C)
3
D)
12
Solve the equation. If the equation has no real solution, so state.
19)
9x +22 = x
19)
A)
x =– 11
4
B)
x =-2, x =11
C)
x =11
D)
No solution
Solve the problem.
20)
Find the height of the cliff. Round to the nearest hundredth meter.
45 m
20 m
20)
A)
25 yd
B)
49.24 yd
C)
41.14 yd
D)
40.31 m
Simplify the expression.
21)
x15
64
21)
A)
x x13
8
B)
x15
8
C)
x7x
8
D)
x7x
8
Solve the equation. If the equation has no real solution, so state.
22)
x + 6 +2 – x = 4
22)
A)
x =31, x = –2
B)
x = –2
C)
x = 2, x = –2
D)
x = 0
5
Simplify the expression.
23)
8
25
23)
A)
2
5
B)
8
5
C)
4 2
D)
2 2
5
Evaluate the square root.
24)
–49
100
24)
A)
-7
B)
–7
10
C)
7
100
D)
Not a real number
Use the Pythagorean Theorem to find the indicated quantity. Round your answer to the nearest hundredth.
25)
a
8
10
25)
A)
a =9
B)
a =36
C)
a =6
D)
a =18
Simplify.
26)
4x ·8x
26)
A)
4 2x2
B)
4x22
C)
4 2x
D)
4x 2
Evaluate.
27)
3125
27)
A)
±5
B)
11
C)
5
D)
25
Write the radical in exponential form and then simplify. Write the answer in exponential form.
28)
3x·4x3
28)
A)
x1/3
B)
x5/9
C)
x1/4
D)
x13/12
Simplify the expression.
29)
3 x
x+ 2 y
29)
A)
3 x( x + 2 y)
x –4y
B)
3 x( x + 2 y)
x +4y
C)
3 x( x – 2 y)
x –2y
D)
3 x( x – 2 y)
x –4y
30)
7 5 + 5 20
30)
A)
12 5
B)
35
C)
-17 5
D)
17 5
Is the radical expression completely simplified?
31)
13
31)
A)
Yes
B)
No
Multiply.
32)
( 5 +6)( 5–6)
32)
A)
11
B)
5– 2 5
C)
5– 2 6
D)
–1
Solve the problem.
33)
The formula v =2.5r can be used to estimate the maximum safe velocity v, in miles per hour, at
which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest
whole number, find the radius of curvature if the maximum safe velocity is 40 miles per hour.
33)
A)
640 ft
B)
4000 ft
C)
1600 ft
D)
256 ft
Simplify the expression.
34)
3
5
34)
A)
15
5
B)
15
C)
15
25
D)
3
Multiply.
35)
(8 2 – 7)2
35)
A)
79 – 112 2
B)
177+ 112 2
C)
177– 112 2
D)
121– 112 2
Simplify the expression.
36)
x+y+ x +6 x
36)
A)
x +5 x +y
B)
x +7 x +y
C)
9 x +y
D)
x +8 x
8
Solve the equation. If the equation has no real solution, so state.
37)
x–3=x +33
37)
A)
No solution
B)
x =-4
C)
x =16
D)
x =-16
Write the radical in exponential form and then simplify. Write the answer in exponential form.
38)
4x53
38)
A)
x5/12
B)
x12/5
C)
x4/15
D)
x15/4
Is the radical expression completely simplified?
39)
10
10
39)
A)
Yes
B)
No
Simplify the expression.
40)
121
5
40)
A)
121 5
5
B)
11 5
5
C)
11 5
D)
36
Find the area of the figure.
41)
611
5
41)
A)
30
2 square units
B)
15 square units
C)
30 square units
D)
15 square units
Use the Pythagorean Theorem to find the indicated quantity. Round your answer to the nearest hundredth.
42)
7 c
9
42)
A)
c =65
B)
c =11.4
C)
c =130
D)
c =8
Simplify the expression.
43)
2
7+ 4
43)
A)
14 – 4 2
11
B)
14 – 4 2
-9
C)
14 + 4 2
-9
D)
314 + 14 7
2
Use the Pythagorean Theorem to find the indicated quantity. Round your answer to the nearest hundredth.
44)
12 20
b
44)
A)
b =16
B)
b =19
C)
b =14
D)
b =20
Simplify.
45)
3·2
45)
A)
6
B)
6
C)
5
D)
3+ 2
Indicate whether the statement is true or false.
46)
(2)2 is an integer
46)
A)
True
B)
False
Simplify.
47)
180x2
47)
A)
6x 5
B)
180x
C)
6 5x
D)
5x26
48)
108x5y5z3
48)
A)
6x2y2z3z
B)
6x3y3z3z
C)
6x2y2z3xyz
D)
6xyz 3x3y3z
Write in exponential form.
49)
5
49)
A)
21/5
B)
51/2
C)
52
D)
51/5
Find the product of the given binomial and its conjugate.
50)
4+3
50)
A)
7–8 3
B)
19 +8 3
C)
13
D)
19
Solve the problem.
51)
Abigail needs to determine the distance at certain points across a lake. Her crew and she are able to
measure the distances shown on the diagram below. Find the width of the lake.
150 meters
70 meters
51)
A)
132.66 m
B)
80 m
C)
8.94 m
D)
165.53 m
Use the Pythagorean Theorem to find the indicated quantity. Round your answer to the nearest hundredth.
52)
3 c
4
52)
A)
c =5
B)
c =3.5
C)
c =4
D)
c =2.65
Solve the problem.
53)
If you drive 16 miles south, then make a left turn and drive 12 miles east, how far are you, in a
straight line, from your starting point?
53)
A)
10.58 mi
B)
20 mi
C)
5.29 mi
D)
2 mi
54)
Classify the number as rational, irrational, or imaginary.
6
64
54)
A)
imaginary
B)
rational
C)
irrational
Simplify the expression.
55)
189x5y6
3y4
55)
A)
63xy x
B)
9x2y7x
C)
3x2y7x
D)
3x4y27xy
Solve the problem.
56)
Classify the number as rational, irrational, or imaginary.
–49
56)
A)
rational
B)
imaginary
C)
irrational
Simplify the expression.
57)
-6 5+5– 2 x–3 x
57)
A)
-10 5– x
B)
-5 5–5 x
C)
-4 5–5 x
D)
-5 5–1 x
Evaluate the square root.
58)
196
25
58)
A)
3
B)
7
3
C)
49
6
D)
14
5
Write the radical in exponential form and then simplify. Write the answer in simplified radical form.
59)
18 x12
59)
A)
x3
B)
3x2
C)
x3/2
D)
3x2/3
Solve the equation. If the equation has no real solution, so state.
60)
x=7
60)
A)
x =7
B)
x = –49
C)
x =14
D)
x =49
Simplify the expression.
61)
1
23
61)
A)
1 +23
23
B)
23
C)
1 +23
D)
23
23
Multiply.
62)
( 7 +11)( 3–11)
62)
A)
21 +33 +77 +11
B)
21 +33 –77 +11
C)
21 +33 +77 –11
D)
21 +33 –77 –11
Find the product of the given binomial and its conjugate.
63)
x– y
63)
A)
x – 2y x+y2
B)
x –2y
C)
x –y2
D)
x +y2
Simplify.
64)
63
64)
A)
7
B)
7 3
C)
21
D)
3 7
Write the radical in exponential form.
65)
r5
65)
A)
r5
2
B)
52/r
C)
r2/5
D)
r5/2
Solve the problem.
66)
The maximum distance d in kilometers that you can see from a height h in meters is given by the
formula d = 3.5 h. How far can you see from the top of a 471–meter building? (Round to the
nearest tenth of a kilometer.)
66)
A)
40.6 km
B)
21.7 km
C)
76 km
D)
881.2 km
Simplify the expression.
67)
3 7 + 8 7
67)
A)
–5 7
B)
11 14
C)
24 14
D)
11 7
D
Use the distance formula to find the length of the line segment between the pair of points.
68)
(5, -4) and (0, -1)
68)
A)
3
5
B)
213 7.21
C)
2 2 2.83
D)
34 5.83
D
Multiply.
69)
5( 3 –7)
69)
A)
50
B)
10 5
C)
15 –35
D)
5 3 + 5 7
C
Simplify the expression.
70)
100
9
70)
A)
10
3
B)
10
3
C)
3
D)
10
3
A
C
Indicate whether the statement is true or false.
71)
(–4)2 is a rational number
71)
A)
True
B)
False
Solve the equation. If the equation has no real solution, so state.
72)
(x +4)1/2 =3
72)
A)
x =5
B)
x =1
C)
x =2
D)
x =13
Indicate whether the statement is true or false.
73)
49 is a rational number
73)
A)
True
B)
False
Simplify.
74)
332
74)
A)
1
B)
234
C)
16
D)
354
Write the expression in radical form and then evaluate.
75)
64–3/2
75)
A)
512
B)
–512
C)
–1
512
D)
1
512
Simplify the expression.
76)
2
49
76)
A)
2
7
B)
2
7
C)
2
7
D)
27
Simplify.
77)
5·9
77)
A)
3
B)
3 5
C)
15
D)
45
Solve the problem.
78)
Find the perimeter of the rectangular window below.
11 ft
211 ft
78)
A)
622 ft
B)
611 ft
C)
311 ft
D)
411 ft
Solve the equation. If the equation has no real solution, so state.
79)
k+ 9 =8
79)
A)
k =289
B)
k = 1
C)
No solution
D)
k = –1
Simplify the expression.
80)
5 5x + 3 5x
80)
A)
2 5
B)
85x
C)
8x10
D)
15 10x
81)
294x9
6x
81)
A)
7x46
B)
7 x9
C)
7x4
D)
7x8
Write the radical in exponential form and then simplify.
82)
4x32
82)
A)
x8
B)
x4
C)
x9
D)
8x
Multiply.
83)
(9 x +10 )( x–5)
83)
A)
9x – 35 x+50
B)
9x – 35 x–50
C)
9x + 55 x–50
D)
9x + 35 x–50
19
Solve the problem.
84)
A square sheet of paper measures 39 centimeters on each side. What is the length of the diagonal of
this paper?
84)
A)
3042 cm
B)
55.15 cm
C)
78 cm
D)
39 cm
Solve the equation. If the equation has no real solution, so state.
85)
x –3x – 2 = 4
85)
A)
x = 1, x = 2
B)
x = 9
C)
x = 2, x = 9
D)
x = –1
Write the radical in exponential form and then simplify.
86)
3x6
86)
A)
2x
B)
x3
C)
x4
D)
x2
Solve the equation. If the equation has no real solution, so state.
87)
(x –8)1/2 =(2x –15)1/2
87)
A)
x =49
B)
x =7
C)
x =23
D)
No Solution
Simplify the expression.
88)
3 5 + 8 20
88)
A)
13 5
B)
-19 5
C)
19 5
D)
11 5
20
Indicate whether the statement is true or false.
89)
20 is a rational number
89)
A)
True
B)
False
Simplify.
90)
38192
90)
A)
4096
B)
313 2
C)
8
D)
1632
Solve the equation. If the equation has no real solution, so state.
91)
2x + 5 –x – 2 = 3
91)
A)
x = 2
B)
x = 2, x = 38
C)
x = –2
D)
x = 3, x = 8
Write the radical in exponential form and then simplify.
92)
8624
92)
A)
216
B)
36
C)
336
D)
36
Multiply.
93)
2 3( 11 +3)
93)
A)
233 + 3
B)
211 + 3
C)
233 + 6
D)
611 + 6
21
Solve the problem.
94)
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 60 feet from where the rope is
staked down. Find the altitude of the balloon if the rope is 80 feet long. (Leave answer in simplified
radical form.)
94)
A)
2 5 ft
B)
100 ft
C)
270 ft
D)
20 7 ft
Simplify.
95)
28
95)
A)
4 7
B)
28
C)
2 7
D)
14
Solve the equation. If the equation has no real solution, so state.
96)
x–2=x –20
96)
A)
x =-36
B)
No solution
C)
x =6
D)
x =36
Simplify the expression.
97)
6
10 +3
97)
A)
610 +18
B)
610 –3
C)
610 +18
20
D)
610 –18
Simplify.
98)
x6
98)
A)
x3
B)
x4
C)
x3
2
D)
x12
Solve the problem.
99)
Police use the formula s =30fd to estimate the speed s of a car in miles per hour, where d is the
distance in feet that the car skidded and f is the coefficient of friction. If the coefficient of friction on
a certain gravel road is 0.21 and a car skidded 310 feet, find the speed of the car, to the nearest mile
per hour.
99)
A)
96 mph
B)
44 mph
C)
1953 mph
D)
242 mph
Is the radical expression completely simplified?
100)
14
2
100)
A)
Yes
B)
No
Use your calculator to evaluate the square root. Write your answer to seven decimal places.
101)
78
101)
A)
8.8317609
B)
6084
C)
31.8433667
D)
21.6333077
Simplify the expression.
102)
6
7+ 2
102)
A)
42 – 2 6
9
B)
42 + 2 6
3
C)
42 – 2 6
3
D)
342 + 7 14
6
103)
1
3x
103)
A)
3x
3x
B)
1
C)
3x
9x2
D)
3x
Solve the equation. If the equation has no real solution, so state.
104)
3x + 10 –x + 2 = 2
104)
A)
x = –2
B)
x = –2, x = 2
C)
x = 2
D)
x = –3
Solve the problem.
105)
One end guy wire is attached to the top of a 17–foot pole and the other end is anchored into the
ground 14 feet from the base of the pole. Find the length of the guy wire. Round to the nearest
tenth foot.
17 feet
14 feet
105)
A)
22 ft
B)
22.3 ft
C)
31.3 ft
D)
31 ft
Simplify the expression.
106)
25
64
106)
A)
8
5
B)
40
C)
5
8
D)
1
Write the expression in radical form and then evaluate.
107)
165/4
107)
A)
512
B)
32
C)
256
D)
128
Simplify the expression.
108)
3
3
108)
A)
3
B)
3 3
C)
1
D)
3
Multiply.
109)
( 5 + n) ( 5– n)
109)
A)
2 5 – 2n 5+n2
B)
5–n2
C)
2 5 –n2
D)
5+ 2n 5–n2
Use the FOIL method to multiply the factors, then solve the equation.
110)
( x –7)( x+7) =51
110)
A)
x =50
B)
x =10, x =-10
C)
x =100
D)
x =2500
Simplify the expression.
111)
245x2
18y3
111)
A)
7x 5y
6y2
B)
7x 10y
6y
C)
7x 10y
6y2
D)
7xy 10
6y2
Write the expression in radical form and then evaluate.
112)
274/3
112)
A)
243
B)
81
C)
2187
D)
729
Simplify the expression.
113)
72r2y
x4
113)
A)
6 2r2y
x2
B)
r72y
x2
C)
36r 2y
x2
D)
6r 2y
x2
Simplify.
114)
486x2
114)
A)
9x 6
B)
9 6x2
C)
9 6
D)
9x26
Simplify the expression.
115)
6a – 2 54a– 3 96a
115)
A)
-5 156a
B)
-5 6a
C)
-17 156a
D)
-17 6a
Solve the equation. If the equation has no real solution, so state.
116)
q + 2 =4
116)
A)
q =18
B)
q =36
C)
q =14
D)
q =16
26
Multiply.
117)
(s +3 t) (4s – 3 t)
117)
A)
4s2+9s t –9t
B)
4s2+15s t –6t
C)
5s2–6t
D)
4s2–9t
Solve the equation. If the equation has no real solution, so state.
118)
2x + 3 –x + 1 = 1
118)
A)
No solution
B)
x = 3
C)
x = –3, x = –1
D)
x = –1, x = 3
Write the radical in exponential form.
119)
5x2
119)
A)
x5/2
B)
25/x
C)
x2
5
D)
x2/5
Solve the problem.
120)
A 33–inch–square TV is on sale at the local electronics store. If 33 inches is the measure of the
diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen.
120)
A)
5.74 in.
B)
2.87 in.
C)
544.5 in.
D)
23.33 in.
Simplify the expression.
121)
2
9–2
121)
A)
18 + 2 2
7
B)
18 – 2 2
79
C)
2
9–22
D)
18 + 2 2
79
Solve the problem.
122)
For a cone, the formula r =3V
h describes the relationship between the radius r of the base, the
volume V, and the height h. Find the volume if the radius is 12 inches and the cone is 11 inches
high. (Use 3.14 as an approximation for , and round to the nearest tenth.)
122)
A)
1657.9 cubic in.
B)
14,921.3 cubic in.
C)
150.7 cubic in.
D)
138.2 cubic in.
Simplify the expression.
123)
27x2y
25
123)
A)
9x 3y
B)
3 3x2y
5
C)
x 27y
5
D)
3x 3y
5
Write the expression in radical form and then evaluate.
124)
8–4/3
124)
A)
Not a real number
B)
16
C)
1
16
D)
–1
16
Simplify the expression.
125)
7x
13y
125)
A)
91xy
13y
B)
91xy
13
C)
91xy
169y2
D)
91xy
Answer Key
Testname: C9
Answer Key
Testname: C9
Answer Key
Testname: C9