Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
A company will enclose a rectangular area of 12,800 square feet in the rear of its plant. One side
will be bounded by the building and the other three sides by fencing. Suppose that 400 feet of
fencing will be used and that the side of the building has a length of 100 ft. What will be the
dimension (in feet) of the side of the rectangle that is opposite the building?
1)
A)
20
B)
40
C)
60
D)
80
E)
90
2)
One of the most important defoliating insects is the gypsy moth caterpillar, which feeds on foliage
of shade, forest, and fruit trees. A homeowner lives in an area in which the gypsy moth has become
a problem. She wishes to spray the trees on her property before more defoliation occurs. She needs
128 ounces of a solution made up of 3 parts of insecticide A and 5 parts of insecticide B. The
solution is then mixed with water. How many ounces of insecticide A should be used?
2)
A)
16
B)
52
C)
68
D)
38.4
E)
48
3)
If x lies in the interval (–2, 8), then
3)
A)
x– 3 5
B)
x– 3 > 5
C)
x– 3 < 5
D)
x– 3 5
E)
none of the above
4)
A group of biologists studied the nutritional effects on rats that were fed a diet containing 10%
protein. The protein was made up of yeast and corn flour. By changing the percentage P (expressed
as a decimal) of yeast in the protein mix, the group estimated that the average weight gain g (in
grams) of a rat over a period of time was given by g = – 200P2+ 200P+ 20. What percentage of yeast
gave an average weight gain of 70 grams?
4)
A)
50%
B)
60%
C)
65%
D)
70%
E)
80%
5)
Imperial Educational Services (I.E.S.) wants to offer a workshop in pollution control to key
personnel at Acme Corporation. I.E.S. will offer the course to thirty persons at a charge of $50 each.
Moreover, I.E.S. will agree to reduce the charge for everybody by $1.00 for each person over the
thirty who attends, up to a total group size of fifty. It has been determined that the greatest revenue
the I.E.S. can receive is $1600. What group size will give this revenue?
5)
A)
34
B)
36
C)
40
D)
44
E)
48
6)
The solution of 4x+ 9 = 3 is
6)
A)
–3 x–3
2
B)
x= – 3, –3
2 only
C)
no solution
D)
x= – 3
2 only
E)
–<x<
2
7)
A good oiled furniture finish contains two parts boiled linseed oil and one part turpentine. If you
need a pint (16 fluid ounces) of this furniture finish, how many fluid ounces of turpentine are
needed?
7)
A)
42
3
B)
3
C)
31
2
D)
51
3
E)
2
8)
A company will manufacture a total of 5000 units of its product at plants A and B. At plan A the
unit cost for labor and material combined is $2.50, while at plant B it is $3.00. The fixed costs at
plant A are $6000 and at plant B they are $8000. Between the two plants the company has decided
to allot no more than $28,000 for total costs. The minimum number of units that must be produced
at plant A is
8)
A)
2545.
B)
2500.
C)
2546.
D)
1871.
E)
2000.
9)
The “current ratio” of a company is the ratio of its current assets to its current liabilities. Suppose a
company has current assets of $250,000 and current liabilities of $100,000. If the company wants to
make a short–term loan and have their current ratio no less than 2.2, what is the maximum amount
it can borrow? (Note: The funds they receive are considered as current assets and the loan as a
current liability.)
9)
A)
$15,000
B)
$20,000
C)
$25,000
D)
$30,000
E)
$33,000
10)
If x– 2 is less than 4 units from 0, then
10)
A)
x
< 6.
B)
x
– 2 > 4.
C)
x
– 6 < 0.
D)
x
– 2 < 4.
E)
x
– 6 > 0.
11)
The solution of 2x– 3 –2 is
11)
A)
–1
2x1
2
B)
1
2x5
5
C)
–<x<
D)
x –1
2, x 1
2
E)
no solution
12)
The solution of 4 – 3x– 5 is
12)
A)
–3 x 3
B)
x 3
C)
–<x<
D)
x< – 3, x> 3
E)
no solution
13)
The solution of 2 –x 5 is
13)
A)
0 x 3
B)
x– 3, x 7
C)
x–7, x 3
D)
–3 x 7
E)
–7 x 3
14)
Suppose consumers purchase q units of a manufacturer’s product when the price per unit (in
dollars) is 60 – 0.5q. If no more than 75 units can be sold, then the number of units that must be sold
in order that sales revenue be $1000 is
14)
A)
20.
B)
50.
C)
25.
D)
75.
E)
40.
15)
The solution of 2(4 – 3x) 10 + 4(x+ 1) is
15)
A)
x
3
5
B)
x
–1
5
C)
x
–3
5
D)
x
1
5
E)
x
3
10
16)
If x> 10 or x< – 10, then
16)
A)
x> 10.
B)
x– 10 < – 10.
C)
x– 10 < 10.
D)
x< 10.
E)
x– 10 < 0.
17)
The solution of –2(x– 3) <x is
17)
A)
–<
x
<
B)
x
< 2
C)
x
< – 2
D)
x
> 2
E)
x
> – 2
18)
If x–2 or x 8, then
18)
A)
x– 3 5
B)
x– 3 < 5
C)
x– 3 5
D)
x– 3 > 5
E)
none of the above
19)
The solution of 2x– 1
–2<4x– 3
2 is
19)
A)
x
> 1
B)
x
< 1
C)
x
< – 2
3
D)
x
>2
3
E)
x
<2
3
20)
The solution of 2x– 9 < 3 is
20)
A)
x> 3
B)
x< 3, x > 6
C)
0 <x< 3
D)
3 <x< 6
E)
x< 6
21)
The solution of 3x– 5 x– (4 – 2x) is
21)
A)
x–1
6
B)
x1
6
C)
no solution
D)
x1
4
E)
–<x<
22)
The solution of 3 – 4(x+ 5) < 3x+ 7(4 –x) is
22)
A)
x< 45
B)
x< – 28
17
C)
x>28
17
D)
no solution
E)
–<x<
23)
The solution of 5x+ 1
3 2 is
23)
A)
–1 x7
5
B)
x 1
C)
x–7
5, x 1
D)
x– 1, x7
5
E)
–7
5x 1
7
24)
An electric utility company is going to locate its new power plant along a straight road connecting
the towns of Exton and Whyton, which are 10 miles apart. For political reasons, the utility company
will buy coal from both towns. The price of coal per ton from Exton is $72.65 plus $0.45 per mile for
delivery. The price per ton from Whyton is $72.25 plus $0.25 per mile for delivery. How far (in
miles) from Exton should the plant be located if the price of coal per ton delivered from Exton is to
be equal to that from Whyton? (Hint: If d is the distance of the plant from Exton, then 10 –d is the
distance from Whyton.)
24)
A)
3
B)
61
2
C)
21
2
D)
4
E)
32
3
25)
The solution of 2x– 3
–4 2 – 7x is
25)
A)
x
5
26
B)
x
5
26
C)
D)
x
1
E)
x
1
26)
The solution of 5x>2x is
26)
A)
x
<1
3
B)
–<
x
<
C)
x
> 0
D)
x
> – 3
E)
x
< 0
27)
The solution of 1 – 3x
2>4x+ 2
5 is
27)
A)
x
<1
23
B)
x
< – 1
23
C)
x
>1
23
D)
x
> – 1
23
E)
x
<4
9
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28)
Solve: Two times x plus nine is a number 13 units from zero.
28)
29)
A rectangular deck attached to a ski lodge is 22 m long and 10 m wide. Planter boxes will
be added along the 3 open sides, which include 1 long side and both short sides. How wide
can the boxes be to leave 180 sq m of deck space?
29)
30)
The owners of a bakery need to borrow money to purchase a new oven. The bakery has
current assets of $52,000 and current liabilities of $15,000. How much can they borrow if
they want their current ratio of assets to liabilities to be no less than 2.6? (Note: The funds
they receive are considered as current assets and the loan as a current liability.)
30)
31)
Evaluate
112
i=21
(i3 + 4i2 + 7i + 10)
31)
32)
The president of a computer company decides to borrow money to expand their research
facility. The company has current assets of $24,920,000 and current liabilities of $6,000,000.
How much can they borrow if they want their current ratio of assets to liabilities to be no
less than 3.2? (Note: The funds they receive are considered as current assets and the loan as
a current liability).
32)
33)
Simplify: |9–1|
33)
34)
A company is establishing a dental plan for its employees. Under this plan the company
will pay the first $20 of an employee’s dental–care expenses and 80% of all additional
dental–care expenses up to a maximum total benefit payment of $700. For an employee,
find the total dental–care expenses covered by this program.
34)
35)
A person wishes to deposit a total fo $10,000 in two accounts. The savings account pays
yearly interest of 4% and fixed certificates of deposit pay a yearly interest rate of 7%. How
much should the person deposit in each account so that he gets a total of $502 interest at
the end of the year?
35)
36)
Solve: 4x– 3 = 7
36)
A zoo veterinarian can purchase 4 different animal foods with various nutrient values for the zoo’s grazing animals. Let
x1 represent the number of bags of food 1, x2 represent the number of bags of food 2, and so on. The number of bags of
each food needed can be described by the following:
x1= 150 –x4
0
x2= 3x4– 210
0
x3=x4+
60 0
37)
Determine an interval for x4 that satisfies all of these inequalities.
37)
Provide an appropriate response.
38)
The IQ (intelligence quotient) of a person is found by dividing his or her mental age by his
or her chronological age and then multiplying that result by 100. For example, a person
with a a mental age of 11 and a chronological age of 10 has an IQ of 11
10 · 100 = 110. Find the
mental age of a person with a chronological age of 12 and an IQ of 125.
38)
39)
Evaluate
120
k=1
(3k2– 6)
39)
40)
Solve: 0.2 5(x– 1) – 4 < 0.8(x+ 1)
40)
41)
An elder brother is twice as old as his younger brother at the present. Six years ago the
elder brother was three times as old as the younger brother. Find the present age of the
brothers.
41)
42)
Evaluate
74
j=1
(6j + 2)
42)
43)
A student receives grades of 63, 75, 66 in three midterms (out of 100 points). The final exam
is worth 200 points. The student needs at least 70% to get a grade of C in the course. How
many points, at least, must the student obtain (out of 200 points) to get a grade of C?
43)
44)
A painting contractor completed two jobs at $480 each. For one of them, this represented a
20% loss; for the other it was a 20% profit (based on his cost for each job). How much did
he make or lose on the two jobs?
44)
45)
The sum of two real numbers is 12. The sum of their reciprocals is 1
3. Find the two
numbers.
45)
46)
A teenager has $10,000 invested in a checking account paying 2.5% per year and a savings
account paying 6.5% per year. The total interest earned in the two accounts at the end of
the year was equivalent to an annual rate of 6% on the entire $10,000. How much was
invested in each account?
46)
47)
A woodworker must decide whether to buy or rent a table saw. If he rents the saw, the
rental fee is $30 per weekend, and the charge for delivery and pickup is $15. If he were to
buy the saw, the purchase price is $960 plus $5 each weekend for new saw blades and
maintenance. After how many weekends of use would it cost less to buy the saw than rent
it?
47)
48)
Solve: –2(x– 1) – 7 9x– (3 –x)
48)
49)
Solve: 4 – 2x
–5>x+ 2
49)
50)
The number x minus four is less than 6 units from zero. What are the possible values for x?
50)
51)
A metallurgist is preparing 63 kg of an alloy. It must consist of 3 parts aluminum and 4
parts copper. How much of each metal should be used?
51)
52)
Evaluate
20
j=1
(j2 + 5j + 7)
52)
4060
53)
A manufacturer has 4000 units of product x in stock and is now selling it at $10 per unit.
Next month the unit price will increase by $2. The manufacturer wants the total revenue
received from the sale of the 4000 units to be no less than $45,000. What is the maximum
number of units that can be sold this month?
53)
1500
54)
Party supply store A rents tables for $10 per day and chairs for $1.50 per day. Party supply
store B rents tables for $9 per day and chairs for $1.25 per day, plus a $36 delivery charge.
After how many days is it more expensive to rent 3 tables and 24 chairs from store A?
54)
55)
Three minus three times x is a number that is more than 6 units from zero. What are the
possible values for x?
55)
56)
Solve: t – 1
4+ 3 >t
3
56)
57)
Evaluate
5
i=1
13i
57)
58)
A company manufactures two types of prefabricated houses: ranch and colonial. Last year
they sold three times as many ranch models as they did colonial models. If a total of 2640
houses were sold last year, how many of each model were sold?
58)
59)
The CEO of an office equipment company decides to borrow money to expand their
manufacturing facility. The company has current assets of $4,000,000 and current liabilities
of $640,000. How much can they borrow if they want their current ratio of assets to
liabilities to be no less than 3? (Note: (1) The current ratio is the ratio of a business’ current
assets to its current liabilities; (2) The funds they receive are considered as current assets
and the loan as a current liability.)
59)
60)
Solve: 3 –x> 5
60)
61)
Solve: 2x– 3 < – 2
61)
62)
A homeowner needs to make a cover for a circular pool with a diameter of 18 feet. How
much cover fabric should be ordered if the cover must extend 2 feet beyond the edge of the
pool? (Hint: The area A of a circle is r2, where r is the radius. Assume = 3.14, and round
to the nearest square foot.)
62)
63)
Express the sum in summation notation.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + … + 37
63)
64)
Solve: 11(3 –x) + 2 2(3 – 5x) + 29 –x
64)
65)
Give the bounds of summation and the index of summation for
21
k=4
(13k + 2)
65)
66)
Give the bounds of summation and the index of summation for
15
m=5
(9m4– 4m)
66)
67)
Evaluate
n
j=1
k
n·2k
n– 5
67)
68)
The number x plus eight is at least 4 units from zero. What are the possible values for x?
68)
69)
A computer keyboard retails for $48.54, which includes a markup of 40% for the retailer
and a markup of 20% for the wholesaler. What did the keyboard cost the wholesaler?
69)
70)
Evaluate
80
i=1
25
70)
2000
71)
Three minus x is a number at least 6 units from zero. What are the possible values for x?
71)
72)
Evaluate
6
i=1
i
6
2 + 2 i
6·i
6
72)
73)
Solve: 3(x– 5) + 7 < 4(3 –x) + 7x– 20
73)
74)
Six minus four times x is a number that is at most 14 units from zero. What are the possible
values for x?
74)
75)
Solve: 4 –x= 10
75)
76)
Evaluate
60
k=1
k
76)
77)
A chemist must prepare 540 ml of a chemical solution. It is to be made up of 4 parts acid
and 5 parts distilled water. How much of each should be used?
77)
Express the problem using absolute value notation.
78)
A number is always at least as large as the negative of its absolute value and at most as
large as its absolute value.
78)
Provide an appropriate response.
79)
Two resistors R1 and R2 are connected in parallel in an electrical circuit. The net resistance
R is given by 1
R=1
R1
+1
R2. If R1= 20 ohms, what values of R2 will create a net resistance
of less than 10 ohms?
79)
80)
A flower border of uniform width is to be added to a rectangular lawn, 30 feet by 40 feet.
How wide should the border be so that 600 sq ft of lawn remains?
80)
81)
A fence is to be placed around a rectangular plot so that 2700 sq ft are enclosed. How much
fencing must be used if the plot is 3 times as long as it is wide?
81)
The 1996 tax brackets for a single person are given in the following table.
Taxable Income 1 Tax T
1. 0 – 24,000 15% (I)
2. 24,000 – 58,150 28% (I – 24,000) +
3600
3. 58,150 – 121,300 31% (I – 58,150) +
13,162
4. 121,300 – 263,750 36% (I – 121,300) +
32,738.50
5. over 263,750 39.6% (I – 263,750) +
84,020.50
Source: 1040 Forms and Instructions, IRS, 1996
82)
Write the income range for line 3 as an inequality. Write the inequality that represents the
tax owed.
82)