Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
Determine which of the following is used to solve the inequality ax + b > c , for c > 0.
1)
A)
ax + b > c or ax + b > – c
B)
ax + b > c and ax + b < – c
C)
ax + b > c or ax + b < – c
D)
ax + b < c and ax + b > – c
2)
Determine which of the following is used to solve the equation ax + b = c , for c > 0.
2)
A)
ax + b = c or ax + b = – c
B)
ax + b = – c
C)
ax + b = c
D)
ax + b = c and ax + b = – c
3)
Determine which of the following is used to solve the inequality ax + b < c , for c > 0.
3)
A)
ax + b < c or ax + b < – c
B)
ax + b < c
C)
–c < ax + b > c
D)
–c < ax + b < c
1
Each of six decorators has to paint a room (walls only) and put a wallpaper border around the room at the ceiling. One
gallon of paint covers 400 sq ft, and one roll of border contains five yards. Each decorator has one gallon of paint and
three rolls of border.
4)
The list gives the name of each decorator and the size of the room.
Jane
Roger
Noriko
Sun Woo
Juanita
Manuel
9′ x 12′
10′ x 12′
12′ x 12′
12′ x 13′
14′ x 17′
13′ x 15′
Give the names of the decorators who will have either enough paint or enough border or both.
(Assume a ceiling height of 8‘ for each room.)
4)
A)
{Jane, Roger, Noriko, Sun Woo}
B)
All
C)
{Juanita, Manuel}
D)
None
For the compound inequality, give the solution set in both interval and graph forms.
5)
x –3>3 or x +3<2
5)
A)
(–, 1) (6, )
B)
(–, –1) (6, )
C)
(–1, )
D)
(–, 6)
B
Graph the solution set of the inequality or system of inequalities.
2
A
6)
y –2x – 1
x – y –1
6)
A)
B)
C)
D)
7)
4x – 9 7
7)
A)
–, 1
24,
B)
–, – 4 –1
2,
C)
1
2, 4
D)
4,
For the compound inequality, give the solution set in both interval and graph forms.
8)
13x + 4 and 4x – 9 <3
8)
A)
[–1, 3]
B)
[–1, 3)
C)
(–1, 3]
D)
(–1, 3)
Solve the equation.
9)
9+1
4x=3
9)
A)
{–48, –24}
B)
[48, –24}
C)
{24, 48}
D)
5
Solve the inequality. Give the solution set in both interval and graph forms.
10)
33x – 1
79
10)
A)
–22
3,64
3
–22
3
64
3
B)
22
3, 64
3
22
3
64
3
C)
–64
3, 22
3
–64
3
22
3
D)
22
3,64
3
22
3
64
3
Graph the linear inequality in two variables.
11)
y < – 3
11)
A)
B)
6
C)
D)
For the compound inequality, give the solution set in both interval and graph forms.
12)
4x – 1 –13 and 4x – 1 3
12)
A)
[–3, 1]
B)
[–3, 1)
C)
(–3, 1)
D)
(–3, 1]
Solve the equation.
13)
10 –3x =3
13)
A)
–13
3, 7
3
B)
{–13, 7}
C)
13
3, 7
3
D)
{7, 13}
The boundary of the graph of the linear inequality will be a _____ line, and the shading will be _____ the line. Fill in the
first blank with either solid or dashed. Fill in the second blank with above or below.
14)
y –2
3x + 1
14)
A)
dashed; above
B)
solid; below
C)
dashed; below
D)
solid; above
Solve the equation.
15)
1–0.01x=1
15)
A)
{0, 200}
B)
{200}
C)
{100}
D)
{0, 100}
16)
5m + 4 =5
16)
A)
B)
1
4, –9
4
C)
–1
5, 9
5
D)
1
5, –9
5
Let A = {q, s, u, v, w, x, y, z}, B = {q, s, y, z}, C = {v, w, x, y, z}, and D = {s}. Specify the following set.
17)
A
17)
A)
B)
{q, s, u, v, w, x, y, z} or A
C)
{w, y}
D)
{q, s, u, v, x, z}
For the compound inequality, decide whether intersection or union should be used. Then give the solution set in both
interval and graph forms.
18)
x <1 or x > – 1
18)
A)
Intersection;
B)
Intersection; (–, 1)
C)
Intersection; [–1, 1)
D)
Union; (–, )
Solve the inequality. Give the solution set in both interval and graph forms.
19)
7x – 10
–4< – 18
7
19)
A)
–18
49 ,
–18
49
B)
142
49 ,
142
49
C)
–, –18
7
–18
7
D)
142
7,
142
7
True or false?
20)
The intersection of the set of positive numbers and the set of negative numbers is {0}.
20)
A)
True
B)
False
Graph the system of inequalities.
10
21)
x + 2y 2
x – y 0
21)
A)
B)
C)
D)
True or false?
22)
The intersection of the set of rational numbers and the set of whole numbers is the set of rational
numbers.
22)
A)
True
B)
False
Solve the equation.
23)
3s + 5 =s – 1
23)
A)
– 3
B)
3, 1
C)
– 3, – 1
D)
24)
7x =35
24)
A)
{0, 5}
B)
{5}
C)
{–5, 0}
D)
{–5, 5}
Graph the system of inequalities.
25)
3x – 2y –6
x – 1 < 0
25)
A)
B)
12
C)
D)
Solve the inequality. Give the solution set in both interval and graph forms.
26)
8x <40
26)
A)
(–, –5)
B)
(–, 5)
C)
(–5, )
D)
(5, )
Solve the equation.
27)
n – 2 =2– n
27)
A)
B)
{4}
C)
0
D)
2
Graph the union or intersection of the two sets, as requested.
28)
Intersection
28)
A)
B)
C)
Solve the absolute value equation or inequality. Give the solution set in interval form.
29)
|3x + 3| =4
29)
A)
( , )
B)
C)
–7
3, 1
3
D)
3, –3
7
C
True or false?
30)
The union of the sets (–, –15] and (–15, ) is (–, )
30)
A)
True
B)
False
A
14
B
Solve the inequality. Give the solution set in both interval and graph forms.
31)
15(4x – 14) >6(10x – 9)
31)
A)
B)
(–, 0)
C)
(0, )
D)
(-, )
Graph the linear inequality in two variables.
32)
2x + 4y 8
32)
A)
B)
15
C)
D)
True or false?
33)
“You win if your card contains the number 23 or the number 45″ is an example of union applied to
a real–life situation.
33)
A)
True
B)
False
Solve the inequality and graph the solution set.
34)
r + 7 >6
34)
A)
(–1, )
B)
(–13, –1)
C)
(–, –13) (–1, )
D)
16
Solve the inequality. Give the solution set in both interval and graph forms.
35)
–5(x – 2) – 2x <1(–5x + 8) – 3x
35)
A)
(2, )
B)
(–, 2)
C)
(–2, )
D)
(–, –2)
For the compound inequality, give the solution set in both interval and graph forms.
36)
x 4 or x 7
36)
A)
[–7, –4]
B)
(–4, 7)
C)
(4, 7)
D)
(–, 4] [7,)
Each of six decorators has to paint a room (walls only) and put a wallpaper border around the room at the ceiling. One
gallon of paint covers 400 sq ft, and one roll of border contains five yards. Each decorator has one gallon of paint and
three rolls of border.
37)
The list gives the name of each decorator and the size of the room.
Jane
Roger
Yong Sun
Sergey
Consuela
Manuel
9′ x 12′
10′ x 12′
12′ x 12′
12′ x 13′
14′ x 17′
13′ x 15′
Give the names of the decorators who will have enough paint, but will not have enough border for
their rooms. (Assume a ceiling height of 8′ for each room.)
37)
A)
{Consuela, Manuel}
B)
{Yong Sun, Sergey}
C)
{Jane, Roger}
D)
None
Graph the union or intersection of the two sets, as requested.
38)
Union
38)
A)
B)
C)
C
B
Solve the equation.
39)
|12 –3p|=21
39)
A)
{– 3, 11}
B)
{–11, – 3}
C)
{11}
D)
{–11, 3}
The boundary of the graph of the linear inequality will be a _____ line, and the shading will be _____ the line. Fill in the
first blank with either solid or dashed. Fill in the second blank with above or below.
40)
y > – 3x +7
3
40)
A)
dashed; above
B)
solid; below
C)
dashed; below
D)
solid; above
A
For the compound inequality, give the solution set in both interval and graph forms.
41)
9x – 6 <3x or –4x –12
41)
A)
(–, 1) [3, )
B)
[1, 3]
C)
D)
(1, 3)
A
A
Each of six decorators has to paint a room (walls only) and put a wallpaper border around the room at the ceiling. One
gallon of paint covers 400 sq ft, and one roll of border contains five yards. Each decorator has one gallon of paint and
three rolls of border.
42)
The list gives the name of each decorator and the size of the room.
Jane
Sam
Irina
Ajay
Juanita
Pedro
9′ x 12′
10′ x 12′
12′ x 12′
12′ x 13′
14′ x 17′
13′ x 15′
Give the names of the decorators who will not have enough paint, but will have enough border for
their rooms. (Assume a ceiling height of 8′ for each room.)
42)
A)
{Jane, Sam}
B)
{Irina, Ajay}
C)
{Juanita, Pedro}
D)
None
Solve the inequality and graph the solution set.
43)
4x + 3 <4
43)
A)
–, –7
41
4,
B)
–7
4, 1
4
C)
–, –7
4
D)
(–, 4)
20