Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Graph the solution set of the system of inequalities or indicate that the system has no solution.
1)
x 0
y 0
2x – 3y –6
3x + 2y 12
1)
A)
B)
1
C)
D)
Solve the problem.
2)
2)
A company that manufactures bicycles has a fixed cost of $125,000. It costs $100 to produce each
bicycle. The selling price is $350. Let x represent the number of bicycles produced and sold and
write the profit function, P. More than how many bicycles must be produced and sold for the
company to make money?
A)
P(x) =250x –125,000; more than 500 bicycles
B)
P(x) =200x –125,000; more than 450 bicycles
C)
P(x) =450x –125,000; more than 278 bicycles
D)
P(x) =250x +125,000; more than 500 bicycles
3)
3)
Given the cost function, C(x), and the revenue function, R(x), more than how many units must be
produced and sold for the business to make money?
C(x) =0.5x +600
R(x) =1.1x
A)
more than 353 units
B)
more than 1000 units
C)
more than 1010 units
D)
more than 1020 units
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
4)
4)
–11 –3x +
4 < – 8
A)
(4, 5]
B)
(–, 4]
(5, )
C)
[4, 5)
D)
Graph the inequality.
5)
5)
x + 2y –1
A)
B)
3
C)
D)
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
6)
6)
9<3x 15
A)
[3, 5)
B)
(–, 3)
[5, )
C)
(3, 5]
D)
(–, 3]
(5, )
Solve and graph the solution set on a number line.
7)
7)
5(5x – 4) <30x – 30
A)
[2, )
B)
( , 2]
C)
(2, )
D)
( , 2)
8)
8)
|x – 8| > 0
A)
B)
(8, )
C)
(–8, 8)
D)
(–, 8)
(8, )
Solve the inequality. Other than
, graph the solution set on a number line.
9)
9)
4x + 10 + 6x <2+ 8x + 2
A)
( , –3]
B)
( , –3)
C)
(–3, )
D)
[–3, )
Solve the problem.
10)
10)
A company is planning to manufacture copy machines. The fixed cost will be $77,000 and it will
cost $6000 to produce each copier. Each copier will be sold for $13,000.
a. Write the cost function, C, of producing x copiers.
b. Write the revenue function, R, from the sale of x copiers.
c. Write the profit function, P, from producing and selling x copiers.
d. More than how many copiers must be produced and sold for the business to make money?
A)
a. C(x) =13,000x +77,000
b. R(x) =6000x
c. P(x) =7000x –77,000
d. 11 copiers
B)
a. C(x) =6000x +77,000
b. R(x) =13,000x
c. P(x) =7000x –77,000
d. 110 copiers
C)
a. C(x) =6000x +77,000
b. R(x) =13,000x
c. P(x) =7000x +77,000
d. 11 copiers
D)
a. C(x) =6000x +77,000
b. R(x) =13,000x
c. P(x) =7000x –77,000
d. 11 copiers
Find the solution set for the equation.
11)
11)
|8x – 8| = |x – 6|
A)
2
7, –10
9
B)
C)
–2
7, –14
9
D)
2
7, 14
9
Graph the solution set of the system of inequalities or indicate that the system has no solution.
12)
y < x
2x +10y >10
12)
A)
B)
C)
D)
7
Answer:
B
Graph the inequality.
13)
13)
y > x + 5
A)
B)
C)
D)
Answer:
D
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
14)
14)
9x <45 and x +9>7
A)
[–2, 5]
B)
(–, –2) (5, )
C)
D)
(–2, 5)
Graph the inequality.
15)
15)
y –5x – 2
9
A)
B)
C)
D)
Solve and graph the solution set on a number line. Express the solution set in both set–builder and interval notations.
16)
16)
|3x + 1| + 7 <4
A)
–, –4
3
B)
C)
–4
3, 2
3
D)
–, 2
3
Solve.
17)
17)
Benjamin never has more than 20 hours free during the week. He is trying to make a weekly plan
for dividing his free time between reading and working out. He wants to spend at least 5 hours
per week reading. Write a system of inequalities to describe the situation. Let x represent the
number of hours for reading and y represent the number of hours for working out.
A)
x + y 20, x 5y, x 0, y 0
B)
x + y 20, y 5, x 0
C)
x + y 20, x 5y, x 0, y 0
D)
x + y 20, x 5, y 0
Graph the inequality.
11
18)
x
5+y
2 1
18)
A)
B)
C)
D)
Solve the problem.
19)
19)
Using data from 2010–2012, the annual number of cars sold at a certain dealership can be
modeled by the formula y =2x +1, where y is the number of cars, in thousands, sold x years after
2010. According to this formula, in which years will the number of cars sold exceed 19 thousand?
A)
Years after 2017
B)
Years after 2023
C)
Years after 2019
D)
Years after 2021
Solve the inequality. Other than
, graph the solution set on a number line.
20)
x –2
24 x –1
30 +1
120
20)
A)
(–, 7]
B)
(7, )
C)
[7, )
D)
(–, 7)
Solve the compound inequality. Other than
, graph the solution set on a number line.
21)
21)
8x – 2 –10 and 3x + 1 16
A)
[–1, 5]
B)
[5, )
C)
(–, –1] [5, )
D)
[–1, )
14
Solve and graph the solution set on a number line.
22)
22)
|8x + 5| – 2 >4
A)
1
8, –11
8
B)
–, –11
81
8,
C)
–11
8, 1
8
D)
Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the
solution set in interval notation.
23)
23)
x >7 or x <7
A)
(–, 7)
B)
C)
(–, 7)
(7, )
D)
(7, )
Solve. Use interval notation to express the range.
24)
24)
The formula for converting Celsius temperature, C, to Fahrenheit temperature, F, is
F =9
5C + 32.
If Fahrenheit temperature ranges from 5° to 131°, inclusive, what is the range for the Celsius
temperature?
A)
(–15, 55)
B)
[–15, 55]
C)
(41, 268)
D)
[41, 268]
Solve and graph the solution set on a number line.
25)
25)
|6x – 1| 6
A)
–5
6, 7
6
B)
, 7
6
C)
–5
6, 7
6
D)
, –5
67
6,
Graph the inequality.
16
26)
26)
y < x + 6
A)
B)
C)
D)
27)
27)
y < – 5x
A)
B)
C)
D)
Graph the solution set of the system of inequalities.
18
28)
x + 3y –12
2x – y 8
28)
A)
B)
C)
D)
Solve and graph the solution set on a number line.
29)
3+1 –x
25
29)
A)
(–, –6] [2, )
B)
[–6, 2]
C)
(–, –2] [6, )
D)
[–2, 6]
30)
30)
|x + 3| 0
A)
B)
{3}
C)
{–3}
D)
(–, –3)
20