Unit 3 Exam Review Questions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Some Useful Formulas:
Compound interest formula:
r nt
A=P 1+
n
Continuously compounded interest formula:
A=Pert
Find all numbers that must be excluded from the domain of the rational expression.
x-8
1)
x2 + 13x + 40
A) x
2)
0
C) x
8, x
5
D) x
-8, x
-3, x
2)
-5
B) x
0
C) x
3, x
5
D) x
3
x-6
3)
x2 + 4x - 12
6
B) x
0
C) x
-6, x
2
D) x
-2, x
x+7
x2 - 16
4
B) x
4, x
C) x
-4
-7
D) x
16
Multiply or divide as indicated. Simplify completely.
x2 - 8x + 16 10x - 40
÷
5)
8x - 32
80
A)
7)
x2 - 8x + 16
(x - 4)2
5)
B) 1
C) 80
D)
(x - 4)2
64
2x - 2 6x2
·
x
7x - 7
6)
A)
14x2 + 28x + 14
6x3
B)
12x3 - 12x2
7x2 - 7x
C)
12x
7
D)
7
12x
x3 + 1
10x
·
3
2
-30x
- 30
x -x +x
A) -
6
4)
A) x
6)
-5
x-3
A) x
4)
8
x2 + 8x + 15
A) x
3)
B) x
1)
1
3
7)
B) -
x2 + 1
3
C) -
1
x3 + 1
3(x + 1)
D)
x+1
3(-x - 1)
8)
x2 + 8x + 16
x2 + 9x
·
x2 + 13x + 36 x 2 - 3x - 28
A)
9)
1
x-7
8)
B)
x
x-7
C)
x(x + 9)
x-7
D)
x
x2 + 13x + 36
4x
10x + 5
·
8x + 4
4
A)
9)
5x
4
B)
5x
16
C)
x
4
D)
5
4
Add or subtract as indicated.
2
6
10)
x+4 x-4
A)
11)
12)
13)
-4x + 32
(x + 4)(x - 4)
C)
-4x + 16
(x + 4)(x - 4)
D)
-4x - 32
(x + 4)(x - 4)
11)
A)
6x + 1
2
2x + 6x - 20
B) 6x + 1
C)
6x2 + 35x - 4
(x + 2)(x - 6)(x - 4)
D)
6x2 + 35x - 4
(x - 2)(x + 6)(x + 4)
2
7
+
2
2
x - 3x + 2 x - 1
12)
A)
28x - 12
(x - 1)(x + 1)(x - 2)
B)
9x - 12
(x - 1)(x + 1)(x - 2)
C)
12x - 9
(x - 1)(x + 1)(x - 2)
D)
9x - 12
(x - 1)(x - 2)
5x - 1
x2 + 5x + 4
+
5 - 4x
13)
x2 + 5x + 4
1
2
x + 5x + 4
B)
1
x+4
C)
x-4
2
x + 5x + 4
D)
1
x+1
7x
42
x-6 x-6
A)
15)
B)
x+5
5x - 4
+
2
2
x + 4x - 12 x + 2x - 8
A)
14)
-4
(x + 4)(x - 4)
10)
1
7
14)
B)
7x - 42
x - 12
C) 7x
D) 7
3
9
+
x x-6
A)
12x - 18
x(x - 6)
15)
B)
12x - 18
x(6 - x)
C)
2
18x - 12
x(6 - x)
D)
18x - 12
x(x - 6)
Solve the equation.
x
2x - 3
-2x
=
+
16)
2x + 2 4x + 4
x+1
A) -
17)
12
5
3
2
C) {-3}
17)
B) { -10 }
C) { 10 }
D) { -32 }
18)
B) { 34}
C) {54}
D) {-18}
-3
1
2
+
=
x+6 x+3
2
x + 9x + 18
A) {0}
19)
B) {-6}
C) {3}
Find the vertical asymptotes, if any, of the graph of the rational function.
x
20) h(x) =
x(x - 4)
A) x = 0 and x = -4
C) x = 0 and x = 4
21) f(x) =
22) g(x) =
x
x2 + 1
20)
21)
B) x = -1, x = 1
D) no vertical asymptote
x
22)
x2 - 4
A) x = 2
C) x = 2, x = -2, x = 0
B) x = 2, x = -2
D) no vertical asymptote
x-4
2
x - 12x + 27
23)
A) x = - 4
C) x = 3, x = 9, x = - 4
24) g(x) =
D)
B) x = 4
D) no vertical asymptote
A) x = 1
C) x = -1
23)
D) {3}
4
7
10
=
y + 4 y - 4 y2 - 16
A) {18}
19)
B)
m+ 4
4
m- 4
=
2
2
2
m + 2m - 8 m + 8m + 16 m + 2m - 8
A) { -40 }
18)
16)
B) x = -3, x = -9
D) x = 3, x = 9
x
x-1
24)
A) x = 0 and x = -1
C) x = 1
B) x = 0 and x = 1
D) no vertical asymptote
3
Find the horizontal asymptote, if any, of the graph of the rational function.
5x2 - 3x - 6
25) g(x) =
6x 2 - 4x + 7
A) y =
5
6
B) y =
C) y = 0
26) f(x) =
D) no horizontal asymptote
26)
5
2
B) y = 0
C) y = 1
27) g(x) =
3
4
2x
2x + 5
A) y = -
D) no horizontal asymptote
4x2
2x 2 + 1
27)
1
2
A) y = 2
B) y =
C) y = 0
D) no horizontal asymptote
28) f(x) =
-15x
3
5x + x2 + 1
A) y = -
25)
28)
1
3
B) y = -3
C) y = 0
D) no horizontal asymptote
Use the horizontal line test to determine whether the function is one-to-one.
29)
A) Yes
B) No
4
29)
30)
30)
A) No
B) Yes
31)
31)
A) No
B) Yes
32)
32)
A) No
B) Yes
Find the inverse of the one-to-one function.
33) f(x) = (x + 8)3
A) f-1 (x) =
C) f-1 (x) =
3
33)
B) f-1 (x) =
x+8
D) f-1 (x) =
x-8
5
3
3
x - 512
x-8
34) f(x) =
3
7x - 2
34)
2
3
+
A) f-1 (x) =
7y 7
B) f-1 (x) =
2
3
+
7x 7
2
3
C) f-1 (x) = - 7
7x
7x - 2
D) f-1 (x) =
3
35) f(x) = (x + 5)3
35)
3
A) f-1 (x) = x + 5
C) f-1 (x) =
36) f(x) =
3
B) f-1 (x) = x - 5
3
D) f-1 (x) = x - 125
x-5
5x + 1
8
8x + 1
A) f-1 (x) =
5
36)
B) f-1 (x) =
8
5x - 1
C) f-1 (x) =
8
5x + 1
Write the equation of the graph in its final position.
37) The graph of y = ex is translated 6 units to the right and then 4 units upward.
A) y = ex + 6 + 4
B) y = ex - 4 + 6
C) y = ex + 4 + 6
8x - 1
D) f-1 (x) =
5
D) y = ex - 6 + 4
The graph of an exponential function is given. Select the function for the graph from the functions listed.
38)
A) f(x) = 4 x
B) f(x) = 4 x - 2
C) f(x) = 4 x - 2
6
D) f(x) = 4 x + 2
37)
38)
39)
39)
A) f(x) = - 4 x
B) f(x) = - 4 -x
C) f(x) = 4 -x
D) f(x) = 4 x
40)
40)
A) f(x) = - 4 -x
B) f(x) = - 4 x
C) f(x) = 4 x
D) f(x) = 4 -x
Solve the problem..
41) An initial investment of $480 earns interest for 7 years in an account that earns 13% interest,
compounded quarterly. Find the amount of money in the account at the end of the 7 year period.
A) $1138.34
B) $1129.25
C) $1175.34
D) $695.340
41)
42) Suppose that you have $4000 to invest. Which investment yields the greater return over 9 years:
7.5% compounded continuously or 7.6% compounded semiannually?
A) Both investment plans yield the same return.
B) $4000 invested at 7.6% compounded semiannually over 9 years yields the greater return.
C) $4000 invested at 7.5% compounded continuously over 9 years yields the greater return.
42)
43) Find the accumulated value of an investment of $20,000 at 12% compounded semiannually for 8
years.
A) $50,807.03
B) $39,200.00
C) $31,876.96
D) $49,519.26
43)
44) Suppose that you have $10,000 to invest. Which investment yields the greater return over 7 years:
6.6% compounded monthly or 6.7% compounded quarterly?
A) Both investment plans yield the same return.
B) $10,000 invested at 6.6% compounded monthly over 7 years yields the greater return.
C) $10,000 invested at 6.7% compounded quarterly over 7 years yields the greater return.
44)
7
Solve the equation.
45) log1/3 x = -4
A)
45)
1
81
B)
1
64
C) 64
D) 81
46) log (4 + x) - log (x - 3) = log 2
A)
B) {10}
47) log 3x = log 5 + log (x - 4)
A) {-10}
1
B)
2
48) log (3x + 5) = log (3x + 2)
5
5
7
A)
B) {3}
3
Simplify the expression.
log (6x)
49) 8 8
A) 8
1
2
C) {-10}
D)
C) {10}
5
D) 2
47)
48)
C) {0}
D)
49)
B) 8 6
C) 1
D) 6x
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
50) log 6
A) 0.6389
46)
B) 0.2810
C) 1.5652
50)
D) 1.2753
51) log
51)
47
13
A) 2.7860
B) 0.5582
52) log4 (31.85)
A) 7.9625
C) 0.6662
D) 1.5011
52)
B) 2.4966
C) 0.4005
D) 1.5031
B) -12
C) -6
D) 6
Solve the equation.
53) 9
3x-12
A) 12
=(3)
2x
Solve the exponential equation. Express the solution set in terms of natural logarithms.
54) 4 x + 4 = 5 2x + 5
5 ln 5 - 4 ln 4
ln 4 - 2 ln 5
A) {ln 5 - ln 4}
B)
C) {7 ln 5 - 5 ln 4}
D) ln
8
55
4
4
4
52
53)
54)
55) 5
9x
= 4.7
ln 4.7
A)
9 ln 5
4.7 ln 9
B)
ln 5
C)
9 ln 4.7
ln 5
55)
ln 4.7
D)
5 ln 9
Solve the equation by expressing each side as a power of the same base and then equating exponents.
1
56) 3 (3x + 6) =
27
A)
1
9
57) 64x = 16
A) {4}
B) {3}
C) {-3}
D) {9}
4
B)
5
3
2
2
D)
3
C)
56)
57)
1
58) ex + 3 =
e2
58)
A) {-1}
B) {5}
C) {-5}
D) {1}
Solve the equation. Round your answer to three decimal places.
59) 3
(x-2)
=9
A) 4.800
B) -1.635
C) 3.588
59)
D) 4
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
60) 4ex = 17
60)
A) -1.45
B) -0.63
C) 0.63
Rewrite the expression as a single logarithm.
61) 6 logm (y )- 3 logm (x2 )
y6
6y
A) logm
B) logm
5
x
3x 2
62) ln x + 9ln y
x
A) ln
y9
61)
y6
2x 3
C) logm
D) logm
y6
x6
62)
B) ln (x + 9y)
63) 4logby + 6logbz
A) logby4 z 6
64)
D) 1.45
C) ln 9xy
D) ln xy9
63)
B) 10logbyz
C) 24logbyz
D) logb(yz)10
1
(log7 (r - 2) - log7 r)
2
A) log7
r-2
2r
64)
B) log7
r-2
r
C) log7
9
r-2
r
D) log7
r-2
r
Rewrite the expression as a sum or difference of logarithms or multiples of logarithms.
x9 y8
65) log3
7
A) 9 log3 (x) + 8 log3 (y) - log3 (7)
65)
B) 9 log3 (x) - 8 log3 (y) - log3 (7)
C) (9 log3 (x))(8 log3 (y)) - log3 (7)
D) 9 log3 (x) + 8 log3 (y) + log3 (7)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
x3
66) log
66)
3 y8
A) 3 log x - 8 log y
3
3
B) 8 log y - 3 log x
3
3
C) 3 log x + 8 log y
3
3
D)
67) log
2
3
x
log ( )
3 y
8
x
4
67)
B) 4 -
A) log x - 2
2
1
log x
2
2
C)
1
log x - 2
2
2
D) - 2 log x
2
8
68) log
11
13 y2 x
A)
68)
1
log 11 - 2 log y - log x
13
13
13
8
C) 8 log
13
11 - 2 log
13
y - log
13
B)
1
log 11 - 2 log y - 2 log x
13
13
13
8
D) log
8
13
11 - log
13
y - log
Use properties of logarithms to expand the logarithmic expression as much as possible.
10x
69) log
6
1
10 + log
x
A) log 10 + log x
B) log
6
6
6
6
2
C)
70) log
5
1
log 10x
6
2
D)
w
C) log
w
w
69)
70)
B) log (x + 5) + 4 log x
5
5
D) 4 log x - log (x + 5)
5
5
7x
4
A) log
x
1
1
log 10 + log x
6
6
2
2
x+5
x4
A) log (x + 5) - log x
5
5
C) log (x + 5) - 4 log x
5
5
71) log
13
71)
7 + log
7 + log
w
w
x + log
x - log
w
w
4
B) log
4
D) log
10
w
w
7x - log
3x
w
4
Determine whether the given ordered pair is a solution of the system.
72) (-3, -4)
4x - y = -16
2x + 4y = -22
A) solution
B) not a solution
73) (3, 2)
4x - y = 14
3x - 4y = 17
A) not a solution
72)
73)
B) solution
74) (-5, 4)
3x = -11 - y
4x = -8 - 3y
A) not a solution
74)
B) solution
Solve the following systems of linear equations.
75) 2x - 2y = -2
3x + 3y = 51
A) No Solution
75)
B) (2, 45)
C) (9, 8)
D) (8, 9)
76)
76)
-2x + 4y = 12
x - 3y = 0
A) {(-6, -18)}
77)
y = 5x - 3
5y + 15x = -95
A) {(2, -13)}
B) {(-18, 6)}
C) {(-18, -6)}
D) {(-17, -6)}
77)
B) {(-13, -2)}
C) {(-2, -13)}
D)
78) 8x + 8y = 48
15x -21y = 81
78)
23 1
, )}
4 4
A) Infinitely Many Solutions
B) {(
C) No Solution
1 23
D) {( , )}
4 4
79) 6x + 21y = 21
9x - 7y = -7
A) {(0, 0)}
80) 3x + 4y = 40
3x + 2y = 44
A) {(-2, 16)}
81) -3x + 5y = -21
7x - 3y = 23
A) {(-2, -3)}
79)
B) {(0, 1)}
C) {(1, 0)}
D) {(1, 1)}
80)
B) {(-16, 3)}
C) {(16, -2)}
D) {(-16, 4)}
81)
B) {(2, 3)}
C) {(2, -3)}
11
D) {(-2, 3)}
Solve the problem.
82) The sum of two numbers is 1. If one number is subtracted from the other, their difference is 15.
Find the numbers.
A) -8, -7
B) 8, -7
C) 0, 1
D) 8, 7
82)
83) One number is 9 less than a second number. Twice the second number is 32 more than 3 times the
first. Find the two numbers.
A) -15 and -6
B) -13 and -4
C) 5 and 14
D) -14 and -5
83)
84) There were 630 people at a play. The admission price was $2 for adults and $1 for children. The
admission receipts were $950. How many adults and how many children attended?
A) 310 adults, 320 children
B) 237 adults, 393 children
C) 155 adults, 475 children
D) 320 adults, 310 children
84)
85) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 3 bags of potato
chips for $10.75. Another customer buys 2 hot dogs and 5 bags of potato chips for $9.75. Find the
cost of each item.
A) $2.00 for a hot dog; $1.50 for a bag of potato chips
B) $1.75 for a hot dog; $1.50 for a bag of potato chips
C) $1.25 for a hot dog; $1.75 for a bag of potato chips
D) $1.75 for a hot dog; $1.25 for a bag of potato chips
85)
86) A rectangular lot whose perimeter is 500 feet is fenced along three sides. An expensive fencing
along the lot's length costs $21 per foot , and an inexpensive fencing along the two side widths costs
only $6 per foot. The total cost of the fencing along the three sides comes to $4350. What are the lot's
dimensions?
A) Length 148 ft; Width 102 ft
B) Length 300 ft; Width 200 ft
C) Length 150 ft; Width 100 ft
D) Length 154 ft; Width 96 ft
86)
12
Answer Key
Testname: CA UNIT 3 PRACTICE EXAM FALL2014V259NOREGEN
1)
2)
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50)
D
A
C
B
B
C
A
B
A
D
D
B
D
D
A
D
B
D
D
B
D
B
D
C
A
C
A
C
B
B
B
A
D
B
B
D
D
B
B
B
C
C
A
C
D
B
C
D
D
C
51)
52)
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86)
13
D
B
D
B
A
C
D
C
D
D
D
D
A
B
A
A
C
A
D
C
C
B
A
B
D
C
C
A
B
C
C
B
D
D
D
C