Exam
Name___________________________________
Practice Math 55 Final
I will drop 45 problems before the final draft
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve.
1) -

1 1
< x-5
3 9

1
3

A) (-48, -42]

1)
B) (42, 48]

C) [2, -2)

D) (2, 8]

2) A plane traveling 410 mph in still air encounters a 65-mph headwind. How long will it take the plane to travel 675 mi into the wind? Round your answer to the nearest tenth of an hour, if necessary. A) 2 hr
B) 232,875 hr
C) 1.4 hr
D) 0.5 hr

2)

3) 3(3x - 4) - 13 6x - 1
A) (- , 8)

3)

B) (- , 8]

C) (-8, )

D) [-8, )

4) At the end of the day, a storekeeper had $1155 in the cash register, counting both the sale of goods and the sales tax of 5%. Find the amount that is the tax.
A) $50
B) $55
C) $60
D) $45
Solve using the addition and multiplication principles together.
5) -3x + 3(-2x - 2) = -11 - 4x
A) 1

6)

17
C)
13

B) - 1

17
D)
5

2
1
x- x=2
5
3

A) -60

4)

5)

6)
B) -30

C) 60

1

D) 30

Solve and graph. Write the result in interval notation.
7) f - 2 < -11

7)

A) (- , -9)

B) [-9, )

C) (-9, )

D) (- , -9]

Solve the absolute value inequality. Write the solution set using interval notation.
8) 6 x - 4
1
25
23
23
25
,
,
A) - ,
B) - ,
6
6
6
6
C) - , -

23
6

-

Solve and graph.
9) 6x - 4 < 2x or -4x

25
,
6

D)

8)

25 23
,
6 6

9)

-12

A) [1, 3]

B) (- , 1) [3, )

C) (1, 3)

D)
Determine the slope and the y-intercept.
10) f(x) = -7x + 1
A) Slope 1, y-intercept (0, 7)
C) Slope 1, y-intercept (0, -7)

B) Slope 7, y-intercept (0, 1)
D) Slope -7, y-intercept (0, 1)

2

10)

Simplify.

11) -9x2

A) 9 x2

B) 9x2

C) 9x

Determine the slope and the y-intercept.
12) 18y + 3x + 1 = 7 + 3x
1
A) Slope 0, y-intercept (0, )
3
C) Slope 0, y-intercept (0, -

D) -9x2

1
1
B) Slope , y-intercept (0, )
6
3

1
)
3

D) Slope -

Write an equation of the line described.
13) Through (5, -5), perpendicular to 3x - 5y = -10
3
3
A) y = - 1x - 2
B) y = - x 5
5

5
10
D) y = x +
3
3

7
61
C) y = - x +
6
6

13
13
xD) y = 6
6

Tell whether the lines are "parallel", "perpendicular", or "neither."
15) 3x - 6y = -6
18x + 9y = -6
A) Perpendicular
B) Parallel

13)

14)

15)
C) Neither

Find the function value.
16) f(1)

A) 3

12)

1
, y-intercept (0, 1)
6

5
10
C) y = - x +
3
3

14) Through (1, -9), parallel to 7x - 6y = 13
6
9
7
61
A) y = x B) y = x 7
7
6
6

11)

16)

B) 5

C) 7

3

D) 6

Determine whether the graph is the graph of a function.
17)

17)

A) Not a function

B) Function

4

Graph the linear equation.
18) y = 2x + 4

18)

A)

B)

C)

D)

5

For the function represented in the graph, determine the domain or range, as requested.
19) Find the range.

A) [-3, 3]
C) [-4, 3]

19)

B) [3, -3]
D) {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

20) Find the domain.

20)

A) all real numbers
C) [-3, 3]

B) [-5, 5]
D) [-18, 18]

Find an equation of the line containing the given pair of points
21) (2, -4) and (5, -13)
A) y = -3x + 2
B) y = 2x - 3
C) y = 2x + 3

D) y = 3x + 2

Find a linear function whose graph has the given slope and y-intercept.
9
22) Slope , y-intercept (0, -4)
5
A) f(x) = -

9 x+4 5

B) f(x) = -

9 x-4 5

C) f(x) =

21)

22)
9
x-4
5

D) f(x) =

9 x+4 5

Find the domain.
23) f(x) =

-1 x-3 A) {x x is a real number and x
C) {x x is a real number and x

23)
3}
-3}

B) {x x is a real number and x
D) {x x is a real number and x

6

1}
-1}

Graph.

24) y = -x2 + 3

24)

A)

B)

C)

D)

Find the slope of the line containing the two given points.
25) (2, -2) and (-4, -7)
6
9
A)
B)
5
2

5
C) 6

5
D)
6

Divide and simplify. x2 - 1
6x - 6
÷
26) x2 - 14x + 49 x2 - 4x - 21
A)

x-7
(x + 1)(x + 3)

25)

26)
B)

(x + 1)(x + 3) x-7 C)

7

(x - 1)(x - 3)
6(x + 7)

D)

(x + 1)(x + 3)
6(x - 7)

27)

8x12
12x5
÷
12y10 12y8

A)

Simplify.
28)

3y7
2x2

4x17
6y18

C)

4x7
6y2

D)

2x7
3y2

28)

3 2 x y

B)

2y + 3x
3y - 2x

C)

y+x x D)

x+y y-1 m 2 - 25m
25 - m

A) -m
4+

30)

B)

2 3
+
x y

A) -y

29)

27)

29)
B) m + 5

C) -(m + 5)

D) m

2 s 30)

s 1
+
4 8

A) 16

B)

16 s C)

s
16

D) 1

Add or subtract. Then simplify. If a denominator has two or more factors (other than monomials), leave it in factored form. Express the answer using the denominator of the first fraction when applicable.
7y2
7y
31)
31) y-1 y-1

A)

32)

B) 0

C) 7y

D)

7y y-1 3
1
+
2-m m-2

A)

33)

7y(y + 1) y- 1

2
2-m

32)
B)

3
2-m

C)

4
2-m

2
5
+ y2 - 3y + 2 y2 - 1

D)

-2
2-m

33)

A)

7y - 8
(y - 1)(y + 1)(y - 2)

B)

20y - 8
(y - 1)(y + 1)(y - 2)

C)

8y - 7
(y - 1)(y + 1)(y - 2)

D)

7y - 8
(y - 1)(y - 2)

8

Multiply and simplify. z 2 + 4z + 4 z 2 + 7z
·
34) z+2 z2 - 49
A)

z(z + 2) z-7 Use synthetic division to divide.
35) (3x2 + 16x + 21) ÷ (x + 3)
A) x + 7
Divide.
36)

34)
B)

z(z + 2) z+7 C)

B) 7x + 3

C) 3x + 7

37)

14
5

B) 3 + 3x2 y3 - 3x3 y2
D) 3 + 3xy4 - 3x2y

37)

B) -7

C) 4

D) no solution
38)

B) -7

C) 35

D) 7
39)

B) 2

C) 3

D)

5
13

x x
- =3
2 9

A) 6

40)
B) 27

54
7

C) 18

Rewrite without rational exponents, and simplify, if possible.
41) (9y8 )3/2
A) 2717

35)

36)

14
1
=5x x A)

40)

D) -3x - 7

3
8
2
=
y + 3 y - 3 y2 - 9

A) 31
39)

(z + 2) z-7 1
3
-3
+
= x+7 x+4
2 + 11x + 28 x A) 0
38)

D)

6x3y4 + 6x5y8 - 6x6y5
2x3y4

A) 3 + 3x2 y4 - 3x3 y
C) 3xy + 3x2y4 - 3x3y
Solve.

z z+7 B) 9y24

Use rational exponents to write a single radical expression.
42) 7p 15q
A) 22pq
B) 105(p + q)

D)

C) 27y3/2

D) 27y12

41)

42)
C)

9

22(p + q)

D)

105pq

Add or subtract. Then simplify by collecting like radical terms, if possible. Assume that no radicands were formed by raising negative numbers to even powers.
3
3
43) 2 81x - 3 24x
43)
3
3
3
A) 0
B) 12 x
C) cannot simplify
D) 6 x - 3 24x

Multiply. Assume that no radicands were formed by raising negative numbers to even powers.
44) ( 5 + z)( 5 - z)
A) 5 - 2 z
B) 5 - 2 5z
C) 5 - z
D) 5z

44)

Solve.
45)

Simplify.
46)

47)

q+5=4
A) 16

B) 21

C) 81

-576
A) does not exist as a real number
C) 24

45)

D) 11

46)

B) 288
D) 25

3 y23
27

A)

47)

y7 +

3
3

y2

3 y7 y2
B)
3

C) 3y7

3

y2

D) y7 - 3

3

y2

Rationalize the denominator. Assume that no radicands were formed by raising negative numbers to even powers.
5
48)
48)
7- 5
A)

35 + 5 5
44

B)

5
5
7
5

C)

35 + 5 5
-2

Rewrite with rational exponents.
49) x9
A) -x2/9

B) x-9/2

C) x-2/9

Rewrite with positive exponents, and simplify, if possible.
50) 11x-10/11z 11/12
A)

z11/12

(11x 10/11)

B)

11z 11/12

C)

x11/10

11z 11/12 x10/11 D)

35 - 5 5
44

D) x9/2

D)

11z 1/12

1 y B) y3/4

C) y

10

50)

x10

Use the laws of exponents to simplify. Write the answer with positive exponents. y3/4 51) y1/4 A)

49)

51)
D) y1/2

52) (b7 )2/7
A) b1/7

B) b2

C) b2/49

D) b9/7

Simplify by factoring. Assume no radicands were formed by raising negative numbers to even powers.
53) 405k7 q8
A) 9k7 q8 5k

B) 9k3 q4 5k

C) 9k3 q4 5

52)

53)

D) 9q4 5k7

Use rational exponents to simplify. Write the answer in radical notation if appropriate.
54)

12

x8

A)

54) x2 Graph.
55) g(x) = 4 +

B)

4

x

C)

x+3

4

x2

D)

3

x2

55)

A)

B)

11

C)

D)

Without graphing, find the line of symmetry.
56) f(x) = -(x - 5)2 + 5
A) x = -5
B) x = 4
Solve.

C) x = 5

D) x = 6

56)

57) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18 ft. Find the length of the ladder if the length is 6 ft more than its distance from the wall.
A) 24 ft
B) 30 ft
C) 18 ft
D) 36 ft

57)

58) 3x2 + 12x = - 5
-6 ± 21
A)
6

58)

59)

-12 ± 21
B)
3

-6 ± 21
C)
3

-6 ± 51
D)
3

6
6
+
=1
x x+9

A) 6

59)
B) 9

C) -6, 9

13 9
,
C)
2 2

60) (2m - 7)2 - 8(2m - 7) + 12 = 0
13
9
1
5
,A) B) , 2
2
2
2
61) 5n 2 = -12n - 5
-6 ± 61
A)
5

D) 6, -9

1 5
D) - ,
7 2

60)

61)
B)

-6 ± 11
10

C)

12

-12 ± 11
5

D)

-6 ± 11
5

Graph.

62) f(x) = -(x + 3)2

62)

A)

B)

C)

D)

13

63) f(x) = 5(x - 3)2 - 1

63)

A)

B)

C)

D)

14

64) f(x) = -6(x + 7)2 + 1

64)

A)

B)

C)

D)

Without graphing, find the vertex.
65) f(x) = -(x + 6)2 - 3
A) (-6, 3)

B) (6, 3)

C) (-6, -3)

D) (6, -3)

Without graphing, find the maximum value or minimum value.
66) f(x) = -(x + 5)2 - 7
A) 4
B) -7
C) 6

D) 5

Solve. Give exact solutions.
67) x2 + 2 = 146
A) ±11

D) 73

B) 12

C) ±12
15

65)

66)

67)

68) x2 - 6x + 9 = 16
A) 19

B) -1, -7

C) 7, -1

Find the x-intercepts.
69) f(x) = x2 - 2
A) No x-intercepts
C) x-intercepts (0, 2) and (0, -2)

D) 4, -4

68)

69)
B) x-intercepts ( 2, 0) and (- 2, 0)
D) x-intercepts (0, 2) and (0, - 2)

Solve the problem. Give the answer to the nearest tenth.
70) The hang-time function V(T) = 48T2 , relates vertical leap to hang time. A player has a vertical leap of 29 in. What is his hang time?
A) 0.8 sec
B) 37.3 sec
C) 1.3 sec
D) 0.6 sec

16

70)

Graph the inequality on a plane.
71) 4x + y 4

71)

A)

B)

C)

D)

17

72) y < -2x + 1

72)

A)

B)

C)

D)

18

Solve and graph.
73) 6x - 4 < 2x or -3x

73)

-9

A)
B) [1, 3]

C) (- , 1) [3, )

D) (1, 3)

Solve.

74) x - y + z = -3 x+y+z= 7 x+y-z= 9
A) (3, -1, 5)
75) x + y + z = 2 x - y + 3z = 8
5x + y + z = -10
A) (4, 1, -3)

74)

B) (3, 5, -1)

C) (-1, 3, 5)

D) No solution
75)

B) (4, -3, 1)

C) No solution

D) (-3, 1, 4)

76) Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.
The total income from all 3 investments is $1600. The income from the 5% and 6% investments is the same as the income from the 8% investment. Find the amount invested at each rate.
A) $10,000 at 5%, $10,000 at 6%, $5000 at 8%
B) $8000 at 5%, $10,000 at 6%, $7000 at 8%
C) $10,000 at 5%, $5000 at 6%, $10,000 at 8%
D) $5000 at 5%, $10,000 at 6%, $10,000 at 8%
Solve the system of equations by the elimination method.
77) 5x + 8y = 64
-2x + 4y = 32
A) (-1, 9)
B) no solution
78) x - 6y = 5
3x - 5y = 15
A) no solution
79)

77)
C) (0, 8)

D) (0, 9)
78)

B) (-5, -1)

C) (6, 5)

D) (5, 0)

3
1
x - y = -18
2
3

79)

3
2
x + y = -9
4
9

A) (-12, 0)

76)

B) (12, 0)

C) (0, 12)

19

D) (0, -12)

Solve the problem.
80) Walt made an extra $9000 last year from a part-time job. He invested part of the money at 7% and the rest at 6%. He made a total of $600 in interest. How much was invested at 6%?
A) $7000
B) $4500
C) $3000
D) $6000
Solve using the substitution method.
81) x + y = 5 y = 3x - 3
A) (3, 2)
B) (3, 3)

81)
C) (1, 5)

82) x = 3 + -6y x + 6y = 4
1 21
A) (- , )
5 5
C) (-

80)

D) (2, 3)
82)

B) No solution

1
21
,)
5
5

D) Infinitely many solutions

20

Graph the system of inequalities, and find the coordinates of the vertices.
83) 3x - 2y 6 x-1 0

A)

B)

C)

D)

21

83)

Graph.

84) f(x) = 4 x - 2

84)

A)

B)

C)

D)

22

85) f(x) =

1 x
+1
4

85)

A)

B)

C)

D)

Solve the problem.
86) Suppose that $60,000 is invested at 2% interest, compounded annually. Find a function A for the amount in the account after t years.
A) A(t) = $60,0000.02t
B) A(t) = $60,000(0.02)t
C) A(t) = $60,000(1.02)t

86)

D) A(t) = $60,0001.02t

87) The number of bacteria growing in an incubation culture increases with time according to
B(x) = 6500(5)x, where x is time in days. Find the number of bacteria when x = 0 and x = 2 .
A) 32,500 ; 162,500
C) 6500 ; 65,000

B) 6500 ; 20,312,500
D) 6500 ; 162,500

23

87)

Convert to a logarithmic equation.
1
88) 4 -3 =
64
A)

88)

1
= log 4 -3
64

B) -3 = log 4
D) 4 = log -3

C) -3 = log1/ 64 4
Convert to an exponential equation.
89) log 8 512 = 3
A) 8 3 = 512

90) log 7 1 = 0
A) 7 1 = 0
Convert to a logarithmic equation.
91) 5 2 = 25
A) 2 = log 5 25
Solve.

92) log 4 x = 3
A) 81
93) log 243 = 5 x A) 3

1
64
1
64

89)
B) 512 3 = 8

C) 3 8 = 512

D) 8 512 = 3
90)

B) 1 0 = 7

C) 0 7 = 1

D) 7 0 = 1

B) 25 = log 5 2

C) 5 = log 2 25

D) 2 = log 25 5

92)
B) 64

C) 7

D) 12
93)

B) 5

C) 3 or -3

D) 5 or -5

94) log 3 x = -4
A) -81

94)
B) 64

C) -12

Express as a sum of logarithms.
95) log (12x)
2
A) log 12 + log x
1
1
C) log 12 + log x
2
2
Express as a single logarithm.
96) log x + log y b b
A) log (x + y) b 91)

D)

1
81

95)
B) log 12 - log x
1
1
D) log 12 - log x
2
2

96)
B) log xy b C) log

2b

97) 2 log b q - log b r

(x + y)

D) log

2b

xy

97)

A) log b q 2 ÷ log b r

B) log b

C) log b ( q 2 - r )

D) log b

24

q2 r 2q r 98) 3 log

c

5 + 2 log

A) log
C) log

99)

c

52 · log

c

98)

9

c

c

92

B) log

49
54

D) log

c

c

53 9 2

(15 + 15)

1
1
1 log x4 + log x4 - log x
2
2
2
2
4
6

A) log x7
2
Solve the equation.
100) 5x = 625
A) 5
101) 27x = 8
2 ln 2
A)
7

B)

99)

7 log x8
2
6

C) log x9/2
2

B) 3

C) 125

B) 343

C)

102) 4x + 1 = 7 (Round to the nearest thousandth.)
A) 1.698
B) 2.404
103) log x = -5
8
1
A)
32,768
104) log (x - 3) = 1 - log x
A) -5, 2

C) 0.404

D) 4

D)

7
3

D) 1.404

100)

101)

102)

103)
1
390,625

B) 32,768

C)

B) 5

C) -5

D) -2, 5

C)

1
D)
2

105) log ( 4 + x) - log (x - 2 ) = log 3
A) - 5

3
7

D) log x17/6
2

B) 5

25

D) 390,625

104)

105)

Answer Key
Testname: UNTITLED1
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)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)

B
A
B
B
A
D
A
B
B
D
B
A
C
B
A
B
A
A
C
C
A
C
A
D
D
D
D
B
A
B
C
A
A
A
C
A
D
B
C
D
D
D
A
C
D
A
B
A
D
C
26

Answer Key
Testname: UNTITLED1
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
81)
82)
83)
84)
85)
86)
87)
88)
89)
90)
91)
92)
93)
94)
95)
96)
97)
98)
99)
100)

D
B
B
D
A
C
B
C
C
C
D
D
A
A
C
B
C
C
B
A
C
C
C
B
D
C
C
D
A
C
D
B
A
C
A
C
D
B
A
D
A
B
A
D
C
B
B
B
D
D
27

Answer Key
Testname: UNTITLED1
101)
102)
103)
104)
105)

C
C
A
B
B

28