Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Choose the number that is a solution of the inequality.
1)
a – 5 <-15
A)
11
B)
-6
C)
-11
D)
-8
2)
f + 11 <2
A)
–10
B)
–6
C)
–9
D)
–7
3)
12n + 9 >11n + 4
A)
–7
B)
–8
C)
–4
D)
–6
4)
7n + 3 6n – 9
A)
–11
B)
–10
C)
–12
D)
–9
5)
6t – 1 5t + 2
A)
0
B)
3
C)
2
D)
1
Write interval notation.
6)
{x
x >6}
A)
(6, )
B)
(–, 6]
C)
(–, 6)
D)
[6, )
7)
{x
x <-5}
A)
(-5, )
B)
(–, -5)
C)
(–, -5]
D)
[-5, )
8)
{x
x -4}
A)
(–, -4]
B)
(–, -4)
C)
[-4, )
D)
(-4, )
9)
{x
x -5}
A)
(–, -5]
B)
[-5, )
C)
(-5, )
D)
(, -5)
10)
{x
2 x 6}
A)
(2, 6]
B)
(2, 6)
C)
[2, 6)
D)
[2, 6]
11)
{x
-6 < x < – 2}
A)
(-6, –2)
B)
[-6, –2)
C)
(-6, –2]
D)
[-6, –2]
12)
{x
2 x <6}
A)
(2, 6)
B)
(2 ,6]
C)
[2, 6)
D)
[2, 6]
Write interval notation for the graph.
13)
A)
[-2, 2]
B)
[-2, 2)
C)
(-2, 2]
D)
(-2, 2)
14)
A)
(-6, -2]
B)
[2, 6)
C)
(2, 6]
D)
[-6, -2)
15)
A)
(2, 6]
B)
[2, 6)
C)
(2, 6)
D)
[2, 6]
16)
A)
[0, 4)
B)
[-4, 0)
C)
(0, 4]
D)
(-4, 0]
17)
A)
(-2, )
B)
(–, -2]
C)
[-2, )
D)
(–, -2)
18)
A)
[-2, )
B)
(–, -2]
C)
(-2, –)
D)
(–, -2)
19)
A)
(–, -6]
B)
(-6, )
C)
[-6, )
D)
(–, -6)
20)
A)
(0, )
B)
[0, )
C)
(–, 0]
D)
(–, 0)
Solve and graph. Write the result in interval notation.
21)
z– 4 <-6
A)
[-2, )
B)
(–, -2]
C)
(-2, )
D)
(–, -2)
22)
a + 4 >6
A)
(2, )
B)
[2, )
C)
(–, 2]
D)
(–, 2)
23)
f – 8 -2
A)
[6, )
B)
(–, 6]
C)
(–, 6)
D)
(6, )
24)
f + 8 <18
A)
(–, 10]
B)
(10, )
C)
[10, )
D)
(–, 10)
25)
0.5b>3
A)
(–, 6]
B)
(–, 6)
C)
[6, )
D)
(6, )
26)
4x 32
A)
(–, 8]
B)
(8, )
C)
[8, )
D)
(–, 8)
27)
3x <-6
A)
[-2, )
B)
(–, -2)
C)
(–, -2]
D)
(-2, )
28)
5
8x 5
A)
[5, )
B)
(, 5]
C)
(, 8]
D)
[8, )
29)
7
8x < – 9
A)
, –72
7
B)
, –
7
72
C)
–, 8
63
D)
–
63
8,
Solve.
30)
–0.8x –0.6
A)
(–, 0.2]
B)
(–, 0.75]
C)
[–0.2, )
D)
[0.75, )
31)
–2
3 x –10
11
A)
–, 20
33
B)
20
33 ,
C)
–, 15
11
D)
15
11 ,
32)
4x +8<32
A)
[6, )
B)
( , 6]
C)
( , 6)
D)
(6, )
33)
9x – 12 3x + 18
A)
(–, -5]
B)
(–, 5)
C)
[5, )
D)
(-5, )
5
34)
20z+ 20 >4(4z + 13)
A)
(8, )
B)
(–, 8)
C)
(–, 20)
D)
(20, )
35)
2(6w +8) 4(2w +12)
A)
(–, 8]
B)
(–, 16]
C)
[8, )
D)
[16, )
36)
1.4x + 2.2 >0.6x – 3.16
A)
(-6.7, )
B)
(-6.8, )
C)
(–, -6.8)
D)
(–, -6.7)
37)
1.2x – 3 0.7x +13.5
A)
(–, 33]
B)
(3.3, )
C)
[33, )
D)
(–, 33)
38)
4(5x + 2) – 29 14x + 3
A)
(-4, )
B)
(–, 4]
C)
[-4, )
D)
(–, 4)
39)
-5(k – 9) <-2 + (-6k – 5)
A)
( , 52)
B)
( , – 2)
C)
( , 48)
D)
( , – 52)
40)
–3x – (6x + 3) >7– (2x + 9)
A)
, 13
5
B)
, – 1
7
C)
, – 13
7
D)
– 1
7 ,
41)
3(4x + 1) <7– 5(4x – 3)
A)
– 7
32 ,
B)
, 7
32
C)
19
32 ,
D)
, 19
32
42)
–3(2x + 3) 2[4x – 3(x – 2)]
A)
–, 3
4
B)
–, 21
8
C)
–, – 21
8
D)
– 21
8,
43)
1
2(x – 2) >1
6(7x – 5)
A)
– 1
4,
B)
–, 1
4
C)
1
4,
D)
–, – 1
4
44)
1
21 (3x + 2) –1
3+1
7(3x + 1)
A)
–1,
B)
–, 1
C)
1,
D)
1,
45)
5
2(4x – 5) >35
A)
9
4,
B)
, 9
4
C)
19
4,
D)
, 19
4
46)
22 – (3x +2) 4(x –4) +5x
A)
, 10
3
B)
( , 3]
C)
[3, )
D)
10
3,
47)
1
4(12x +40) –48 > – 1
3(6x –21)
A)
, 31
5
B)
( , 9]
C)
31
5,
D)
[9, )
48)
0.2(4x –3) <1.5 – (x +4)
A)
, 61
18
B)
– 19
18 ,
C)
, – 19
18
D)
61
18 ,
49)
In order for a chemical reaction to take place, the Fahrenheit temperature F of the reagents must be at least
151.81° F. At what Celsius temperatures C will the reaction occur? F =9
5C + 32
A)
{C
C <305.26°}
B)
{C
C 66.56°}
C)
{C
C 66.56°}
D)
{C
C 305.26°}
50)
In order for a chemical reaction to remain stable, its Celsius temperature C must be no more than 126.25°C. At
what Fahrenheit temperatures F will the reaction remain stable. F =9
5C + 32
A)
{F
F 259.25°}
B)
{F
F 52.36°}
C)
{F
F 259.25°}
D)
{F
F 52.36°}
51)
The equation y =0.002x – 0.30 can be used to determine the profit y, in dollars, of producing x items. How many
items x must be produced so the profit will be at least $3075?
A)
{x
0 < x 1,537,649}
B)
{x
x 1,537,350}
C)
{x
x 1,536,650}
D)
{x
x 1,537,650}
52)
A salesperson has two job offers. Company A offers a weekly salary of $560 plus commission of 16% of sales.
Company B offers a weekly salary of $1120 plus commission of 8% of sales. What is the amount of sales above
which Company A‘s offer is the better of the two?
A)
$3500
B)
$7000
C)
$7100
D)
$14,000
53)
Company A rents copiers for a monthly charge of $120 plus 8 cents per copy. Company B rents copiers for a
monthly charge of $240 plus 4 cents per copy. What is the number of copies above which Company A’s charges
are the higher of the two?
A)
3100 copies
B)
1500 copies
C)
6000 copies
D)
3000 copies
54)
Jon has 1101 points in his math class. He must have 84% of the 1500 points possible by the end of the term to
receive credit for the class. What is the minimum number of additional points he must earn by the end of the
term to receive credit for the class?
A)
159 points
B)
1260 points
C)
925 points
D)
399 points
55)
Photography reprints cost $0.52 each at a local photo shop. Through the mail, they cost $0.44 each plus $1.20
postage and handling. How many reprints must a customer purchase to make it less expensive to use mail
order?
A)
{n|n > 15 reprints}
B)
{n|n > 16 reprints}
C)
{n|n > 18 reprints}
D)
{n|n > 19 reprints}
Find the indicated intersection or union.
56)
{2, 9, 14, 15, 22}
{9, 15, 22, 27}
A)
{2, 9, 14, 15, 22, 27}
B)
{9, 15, 22, 27}
C)
{9, 15, 22}
D)
{2, 9, 15, 22}
57)
{3, 8, 13, 18} {8, 18, 20, 28}
A)
{8, 18}
B)
{3, 8, 13, 18, 20, 28}
C)
{3, 8, 18, 20}
D)
{8, 18, 20}
58)
{q, s, u, v, w, x, y, z}
{q, s, y, z}
A)
{v, x}
B)
{s, u, v, w, x, z}
C)
{q, s, u, v, w, y}
D)
{q, s, y, z}
59)
{q, s, u, v, w, x, y, z} {q, s, y, z}
A)
{v, x}
B)
{s, u, v, w, x, z}
C)
{s, u, w}
D)
{q, s, u, v, w, x, y, z}
60)
{q, s, u, v, w, x, y, z}
{s}
A)
{q, s, u, v, w, x, y}
B)
{s}
C)
{v, x}
D)
{s, u, w}
61)
{v, w, x, y, z} {q, s, y, z}
A)
{q, s, v, w, x, y, z}
B)
{s, u, v, w, x, z}
C)
{q, s, u, v, w, x, y}
D)
{s, u, w}
62)
{q, s, u, v, w, x}
A)
{q, s, u, v, w}
B)
C)
{q, s, u, v, w, x}
D)
{q}
63)
{q, s, u, v, w, x}
A)
{q}
B)
{q, s, u, v, w}
C)
{q, s, u, v, w, x}
D)
Graph and write interval notation.
64)
3 x 7
A)
(3, 7]
B)
(3, 7)
C)
[3, 7]
D)
[3, 7)
65)
3< x <7
A)
[3, 7]
B)
[3, 7)
C)
(3, 7)
D)
(3, 7]
66)
-3 x <1
A)
[-3, 1)
B)
(-3, 1]
C)
(-3, 1)
D)
[-3, 1]
67)
x 2 and x –2
A)
(–2, 2)
B)
[–2, 2]
C)
[–2, 2)
D)
(–2, 2]
68)
x 2 and x –3
A)
(–, –3]
B)
[2, )
C)
(–, 2]
D)
(2, )
69)
x > 0 and x < 5
A)
(0, 5)
B)
[0, 5]
C)
[0, 5)
D)
(0, 5]
70)
x < 3 and x > – 1
A)
(–1, 3)
B)
[–1, 3]
C)
[–1, 3)
D)
(–1, 3]
Solve and graph.
71)
8x – 7 9 and 8x – 7 41
A)
[2, 6]
B)
(2, 6)
C)
(2, 6]
D)
[2, 6)
72)
-6 <3x + 9 and 4x + 5 <1
A)
[-5, -1]
B)
[-5, -1)
C)
(-5, -1)
D)
(-5, -1]
73)
-15 4x + 9 and 3x + 7 <1
A)
[-6, –2)
B)
(-6, –2]
C)
[-6, –2]
D)
(-6, –2)
74)
9x + 7 -2 and 4x – 8 12
A)
[-1, )
B)
[5, )
C)
(–, -1] [5, )
D)
[-1,5]
11
75)
3x + 6 <-9 and -1 – 6x >17
A)
(–, -5) (-3, )
B)
(–, -5)
C)
(-5, -3)
D)
(–, -3)
76)
4x – 10 18 and 2x – 1 13
A)
(7, )
B)
[7, )
C)
(–, 7)
D)
{7}
77)
4x > 4 and x + 5 < 5
A)
(–1, 0)
B)
C)
(0, 1)
D)
(–1, )
78)
5x – 1 < 4 and x – 2 > – 1
A)
[0, 1]
B)
{1}
C)
(0, 1)
D)
Solve.
79)
–8< x +4<6
A)
(-4, 10)
B)
(-10, 4)
C)
(-12, 10)
D)
(-12, 2)
80)
9<3x 18
A)
[–3, -6)
B)
(3, 6]
C)
(–3, -6]
D)
[3, 6)
81)
3–x > – 7
A)
[–3, 7)
B)
(–3, 7]
C)
(–7, 3]
D)
[3, 7)
82)
22t – 2 12
A)
[-7, -2]
B)
(-7, -2)
C)
[2, 7]
D)
(2, 7)
83)
-18 -2c – 2 <-6
A)
[2, 8)
B)
(-8, -2]
C)
[-8, -2)
D)
(2, 8]
84)
-31 -5z – 1 -11
A)
(2, 6)
B)
(-6, -2)
C)
[2, 6]
D)
[-6, -2]
85)
–7<3– 5x
10 8
A)
77
5,73
5
B)
– 77
5,73
5
C)
77
5, 73
5
D)
– 77
5, 73
5
86)
62
3x + 4 <10
A)
(3, 9]
B)
[3, 9)
C)
(3, 4]
D)
[3, 4)
87)
–14 <3x –12
4–1
A)
– 44
3, 8
3
B)
– 44
3, 8
3
C)
– 44
3, 16
3
D)
– 44
3, 16
3
88)
–1
33x – 1
9<1
3
A)
– 2
3, 4
3
B)
– 8
9, 10
9
C)
– 2
3, 4
3
D)
– 2
3, 4
3
89)
–3
4<1
12 x –53
4
A)
(-69, -51]
B)
(-4, 14]
C)
[-4, 4)
D)
(51, 69]
Solve the compound inequality. Express the solution using interval notation. Graph the solution set.
90)
x 3 or x 6
A)
(-3, 6)
B)
(–, 3] [6, )
C)
(3, 6)
D)
[-6, -3]
91)
x < – 3 or x >6
A)
(-3, 6)
B)
(–, –6) (3, )
C)
[-6, -3]
D)
(–, –3) (6, )
92)
x <2 or x <8
A)
(2, 8)
B)
(2, )
C)
(–, 8)
D)
(–, 2) (8, )
93)
x >4 or x <4
A)
(4, 4)
B)
(–, 4)
C)
(4, )
D)
(–, 4) (4, )
Solve and graph.
94)
x 2 or x 5
A)
(-2, 5)
B)
(–, 2] [5, )
C)
[-5, -2]
D)
(2, 5)
95)
x <1 or x <5
A)
(–, 1) (5, )
B)
(–, 5)
C)
(1, 5)
D)
(1, )
96)
x >2 or x <2
A)
(–, 2) (2, )
B)
{2}
C)
(–, 2)
D)
(2, )
97)
12x – 8 <4x or -4x -12
A)
B)
(1, 3)
C)
(–, 1) [3, )
D)
[1, 3]
98)
–7x + 1 15 or 4x + 3 -13
A)
[–2, )
B)
[–4, –2]
C)
(–,)
D)
[–4, )
Solve.
99)
1 –6x 13 or 7x + 3 -25
A)
[–2,)
B)
[–4,)
C)
(–,)
D)
[–4,–2]
100)
9x – 5 -50 or 3x + 7 1
A)
[-5, –2]
B)
[–2, )
C)
[-5, )
D)
(–, -5] [–2, )
101)
52t – 3 or 11 2t – 3
A)
( , 4] [7, )
B)
[-7, -4]
C)
[4, 7]
D)
(–,)
102)
-4c – 2 -26 or -4c – 2 >-10
A)
( , 2) [6, )
B)
( , -6] (-2, )
C)
(–,)
D)
(2, 6]
103)
1 – 4x 6 or 1 – 4x <4
A)
–5
4, 3
4
B)
–5
4, –3
4
C)
, –3
45
4,
D)
, –5
4–3
4,
104)
10 – 8x
6< – 5 or 10 – 8x
65
A)
, – 5
25,
B)
– 5
2,5
C)
(–,)
D)
, – 5
25,
105)
4x – 1
15 < – 1
3or 4x – 1
15 1
3
A)
, – 1 3
2,
B)
– 7
6, 4
3
C)
– 1, 3
2
D)
(–,)
106)
7
3x + 3 10 or 7
3x + 3 >17
A)
[3, 6)
B)
(–,)
C)
( , –3] (6, )
D)
( , 3] (6, )
107)
3x –24
4< – 17 or 3x –24
4–2
A)
– 44
3, 16
3
B)
, – 44
332
3,
C)
(–,)
D)
, – 44
316
3,
108)
Using the formula to find Fahrenheit (F) in terms of Celsius (C), F =9
5 C + 32, find the range (to the nearest
tenth) of the Fahrenheit temperature when the range of the Celsius temperature is between 2°C and 10°C,
inclusive.
A)
Between 19.6°F and 34°F, inclusive
B)
Between 3.6°F and 18°F, inclusive
C)
Between 33.1°F and 32.8°F, inclusive
D)
Between 35.6°F and 50°F, inclusive
109)
Assume that the mathematical model C(x) =14x +180 represents the cost C, in hundreds of dollars, for a certain
manufacturer to produce x items. How many items x can be manufactured while keeping costs between
between $410,000 and $606,000?
A)
{x 280 < x <420}
B)
{x 420 < x <560}
C)
{x 300 < x <450}
D)
{x 450 < x <600}
110)
Suppose that the sales of a particular brand of appliance satisfy the relationship S(x) =170x +1600, where S(x)
represents the number of sales in year x, with x = 0 corresponding to 1990. For what years will sales be between
2280 and 2790?
A)
Between 1993 and 1996
B)
Between 5 and 8
C)
Between 1994 and 1996
D)
Between 1994 and 1997
111)
Body mass index is given by the formula I =704.5W
H2. Mary’s height is 69 in. What weights W will allow Mary to
keep her body mass index I between 18.5 and 25?
A)
{W|147.6 lb < W <176.2 lb}
B)
{W|1.8 lb < W <2.4 lb}
C)
{W|125 lb < W <168.9 lb}
D)
{W|114.3 lb < W <152.4 lb}
Simplify.
112)
17.5z
A)
–17.5 z
B)
17.5 z
C)
–17.5z
D)
17.5z
113)
9x2
A)
9x2
B)
9 x2
C)
9 x2
D)
9x
114)
-11x2
A)
11x2
B)
-11x2
C)
11x
D)
11 x2
115)
-4x
A)
4x
B)
4 x
C)
-4x
D)
4 x
116)
-9
x
A)
-9
x
B)
9
x
C)
9
x
D)
-9
x
117)
x
5
A)
x
5
B)
x
-5
C)
x
-5
D)
x
5
118)
x6
–y
A)
x6
y
B)
x6
–y
C)
x6
y
D)
x6
–y
119)
-14x2
7x
A)
-2x
B)
2x
C)
2 x
D)
2x
120)
30y
10y2
A)
3
y
B)
3 y
y2
C)
3
y
D)
3 y
y2
Find the distance between the points on a number line.
121)
8, -15
A)
–23
B)
–7
C)
23
D)
7
122)
-1, 3
A)
4
B)
2
C)
–4
D)
–2
123)
17, -15
A)
32
B)
–2
C)
2
D)
–32
124)
-3, 14
A)
–17
B)
11
C)
–11
D)
17
D
125)
19.2, 9.2
A)
28.4
B)
14.2
C)
10
D)
5
C
126)
2
9, 4
9
A)
2
3
B)
9
2
C)
3
2
D)
2
9
D
Solve.
127)
x=8
A)
{8}
B)
{-8}
C)
{8, -8}
D)
{64}
C
128)
x= – 9
A)
{-9}
B)
{9, -9}
C)
D)
{9}
C
129)
x=7.5
A)
{-7.5}
B)
{5625}
C)
{7.5, -7.5}
D)
{7.5}
C
130)
x + 3 =8
A)
{5}
B)
C)
{-5, 11}
D)
{5, -11}
D
131)
t – 3 = 0
A)
{3, -3}
B)
C)
{-3}
D)
{3}
D
132)
5x –8=7
A)
– 1
4, 3
2
B)
– 3, – 1
5
C)
1
5, 3
D)
– 3
2, 1
4
C
133)
|2x –4|=20
A)
– 8, 12
B)
12
C)
-12, 8
D)
–12, – 8
A
A