Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
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.)
1)
A)
$15,000
B)
$20,000
C)
$25,000
D)
$30,000
E)
$33,000
2)
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?
2)
A)
50%
B)
60%
C)
65%
D)
70%
E)
80%
3)
The solution of 5x>2x is
3)
A)
x
> – 3
B)
x
> 0
C)
–<
x
<
D)
x
< 0
E)
x
<1
3
4)
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?
4)
A)
48
B)
68
C)
38.4
D)
52
E)
16
5)
The solution of 5x+ 1
3 2 is
5)
A)
x–7
5, x 1
B)
x– 1, x7
5
C)
–7
5x 1
D)
–1 x7
5
E)
x 1
6)
The solution of 4x+ 9 = 3 is
6)
A)
–3 x–3
2
B)
x= – 3
2 only
C)
no solution
D)
x= – 3, –3
2 only
E)
–<x<
2
7)
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?
7)
A)
34
B)
36
C)
40
D)
44
E)
48
8)
If x–2 or x 8, then
8)
A)
x– 3 5
B)
x– 3 5
C)
x– 3 < 5
D)
x– 3 > 5
E)
none of the above
9)
The solution of 2x– 3 –2 is
9)
A)
x –1
2, x 1
2
B)
–1
2x1
2
C)
1
2x5
5
D)
–<x<
E)
no solution
10)
The solution of –2(x– 3) <x is
10)
A)
x
< – 2
B)
–<
x
<
C)
x
> – 2
D)
x
> 2
E)
x
< 2
11)
The solution of 1 – 3x
2>4x+ 2
5 is
11)
A)
x
>1
23
B)
x
< – 1
23
C)
x
> – 1
23
D)
x
<1
23
E)
x
<4
9
12)
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
12)
A)
50.
B)
25.
C)
40.
D)
20.
E)
75.
13)
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
13)
A)
1871.
B)
2000.
C)
2545.
D)
2500.
E)
2546.
14)
If x> 10 or x< – 10, then
14)
A)
x> 10.
B)
x– 10 < – 10.
C)
x< 10.
D)
x– 10 < 0.
E)
x– 10 < 10.
15)
If x lies in the interval (–2, 8), then
15)
A)
x– 3 5
B)
x– 3 < 5
C)
x– 3 > 5
D)
x– 3 5
E)
none of the above
16)
The solution of 2 –x 5 is
16)
A)
0 x 3
B)
–3 x 7
C)
x–7, x 3
D)
–7 x 3
E)
x– 3, x 7
17)
If x– 2 is less than 4 units from 0, then
17)
A)
x
– 2 > 4.
B)
x
– 6 > 0.
C)
x
< 6.
D)
x
– 6 < 0.
E)
x
– 2 < 4.
18)
The solution of 2(4 – 3x) 10 + 4(x+ 1) is
18)
A)
x
1
5
B)
x
3
5
C)
x
–1
5
D)
x
3
10
E)
x
–3
5
5
19)
The solution of 3 – 4(x+ 5) < 3x+ 7(4 –x) is
19)
A)
x< 45
B)
x>28
17
C)
no solution
D)
x< – 28
17
E)
–<x<
20)
The solution of 2x– 3
–4 2 – 7x is
20)
A)
x
5
26
B)
x
1
C)
D)
x
5
26
E)
x
1
21)
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?
21)
A)
20
B)
40
C)
60
D)
80
E)
90
22)
The solution of 3x– 5 x– (4 – 2x) is
22)
A)
x1
6
B)
no solution
C)
x–1
6
D)
x1
4
E)
–<x<
23)
The solution of 4 – 3x– 5 is
23)
A)
x< – 3, x> 3
B)
–3 x 3
C)
x 3
D)
–<x<
E)
no solution
24)
The solution of 2x– 1
–2<4x– 3
2 is
24)
A)
x
> 1
B)
x
>2
3
C)
x
< 1
D)
x
<2
3
E)
x
< – 2
3
25)
The solution of 2x– 9 < 3 is
25)
A)
x< 3, x > 6
B)
3 <x< 6
C)
x> 3
D)
0 <x< 3
E)
x< 6
26)
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.)
26)
A)
32
3
B)
3
C)
61
2
D)
21
2
E)
4
27)
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?
27)
A)
3
B)
42
3
C)
51
3
D)
2
E)
31
2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
28)
Evaluate
10
i=1
7
28)
29)
Solve: 3 –x> 5
29)
30)
The product of two consecutive integers is 42. Find the integers.
30)
31)
Evaluate
j=15
(j2– 9j)
31)
32)
Evaluate
k=1
(3k2– 6)
32)
33)
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.)
33)
34)
Express the sum in summation notation.
10 + 13 + 16 + 19 + 22 + 25 + 28 + 31
34)
35)
Evaluate
74
j=1
(6j + 2)
35)
36)
A company manufactures water filters that cost $15 for labor and material, plus $50,000 in
fixed costs. If they sell the water filter for $20, how many must be sold to make a profit?
36)
37)
A chef must prepare 10 cups of a sauce. The recipe calls for 1 part wine and 4 parts beef
stock. How much of each ingredient should be used?
37)
38)
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?
38)
39)
The relationship between Fahrenheit and Celsius temperature is given by the formula
F– 32
180 =C
100. Normal body temperature is F 98.6. Find the corresponding Celsius
temperature.
39)
40)
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.)
40)
41)
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?
41)
42)
Approximately 21% of the air we breathe is oxygen. To the nearest milliliter, how many
milliliters of air contain 1 milliliter of oxygen?
42)
43)
Researchers at a university need a 10,000 square meter rectangular plot on which to grow
three hybrids of corn. The plot is to be enclosed by fencing and divided into three equal
subplots by a pair of fences both parallel to the same pair of sides of the rectangle. If 600
meters of fencing are to be used for the project, what are the dimensions of the plot?
43)
44)
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.
44)
45)
Solve: 11(3 –x) + 2 2(3 – 5x) + 29 –x
45)
10
46)
Hooke’s Law of springs states that the force F (in pounds) required to stretch a spring x
inches beyond its natural length is F=kx, where k is the “spring constant” for a given
spring. If a certain spring has a spring constant k of 6.5 and 13 F 26, what are the
corresponding values for x?
46)
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
47)
Solve each inequality for x4.
47)
Provide an appropriate response.
48)
Solve: 4 –x= 10
48)
49)
Solve: Six plus three times x is a number 12 units from zero.
49)
50)
A father wants to invest $50,000 in order to earn $4000 per year to help pay for his
daughter’s college education. He places $30,000 in a savings account earning 5% per year.
He wants to place the rest of his investment in a mutual fund. How much will the mutual
fund have to earn for him to make his goal?
50)
51)
Solve: 2x– 3 < – 2
51)
52)
Solve: x+ 7 > – 2
52)
53)
A corporation plans to buy back some of its stock in 2 years for $1,081,600. It plans to invest
$1,000,000 this year to have the necessary capital for this move. At what annual rate of
interest, compounded annually, should it invest this million dollars to earn enough for its
stock re–purchase?
53)
54)
Give the bounds of summation and the index of summation for
13
i=2
(2i2– 3i)
54)
55)
Solve: 7 – 2x< 9
55)
56)
A woman has $90,000 to invest in two mutual funds. One fund is low–risk and has an
annual yield of 10%. The second fund is medium–risk and has a 15% annual yield. How
much should she invest in each fund if she would like to earn $10,000 per year from her
investments?
56)
Express the problem using absolute value notation.
57)
For safety reasons, the arrival time of commuter train A at a station must be at least 6
minutes different from the 6:00 P.M. arrival of train B.
57)
Provide an appropriate response.
58)
A recliner costs a wholesaler $189 and her markup is 10% of her selling price. If the
retailer’s markup is 30% of his selling price for the item, what is the retailer’s selling price?
58)
59)
A car dealer has 20 new automobiles which she purchased for $12,000 each. If she sells 16
of them at a profit of 20%, for how much must she sell the remaining 4 to have an average
profit of 18%?
59)
60)
The owner of a 20–room motel, which is 70% occupied, decides to charge $8 more than the
single occupancy rate if two or more people occupy the room. This situation occurs in 75%
of the occupied rooms, on the average. What should the two rates be so that the owner
receives $160,000 in annual income to cover expenses and yield a reasonable profit?
(Assume that a year has 365 days and give your answer to the nearest dollar.)
60)
61)
Evaluate
50
i=1
(i + 2)2
61)
12
62)
Solve: –2 2x–1–.6
62)
63)
A person deposits $50 in a bank and in two years it increases to $56.18. If the bank
compounds interest annually, what annual rate of interest does it pay?
63)
Express the problem using absolute value notation.
64)
The absolute value of the product of two numbers is equal to the product of the absolute
values of the numbers.
64)
Provide an appropriate response.
65)
A company produces a product at a cost of $6 per unit. If fixed costs are $20,000 and each
unit sells at $8, at least how many units must be sold in order to earn a profit?
65)
66)
The concentration of a certain drug in the bloodstream t hours after it is injected is given by
C=5.4t
t+ l mg/L. Determine when the concentration reaches the maximum therapeutic level
of 1.8 mg/L.
66)
67)
A homeowner must decide whether to buy or rent a garden rototiller. If she rents the
machine, the rental fee is $25 per day, and the daily cost to use it is $5 for gas. If she were to
buy the machine, the purchase price is $650, and the daily cost is $7 for gas, oil, and
maintenance. On which day of use would the rental costs become greater than the
ownership costs?
67)
68)
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?
68)
69)
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?
69)
70)
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?
70)
71)
Solve: 2(x– 8) + 5 –42 –x
2
71)
72)
Evaluate
n
j=1
k
n·2k
n– 5
72)
73)
Evaluate
30
i=1
i2
73)
74)
Solve: 6x– 2
3–1
4
74)
75)
Solve: 2x– 3
4 1
75)
76)
Evaluate
4
n=0
(3n– 7)
76)
77)
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?
77)
78)
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?
78)
79)
A company’s revenue from the sale of interior doors is $98 per door. The cost of producing
the doors is $48 per door with $12,000 in fixed costs. How many doors must the company
sell in order to break even?
79)
80)
A sociologist is hired by a city to study different programs that aid the education of
preschool–age children. The sociologist estimates that n years after the beginning of a
particular program, p thousand preschoolers will be enrolled, where p=5
4n(12 –n). How
many years after the start of the program will 25,000 preschoolers first be enrolled?
80)
81)
Solve: t – 1
4+ 3 >t
3
81)
82)
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?
82)
83)
Express the sum in summation notation.
1 + 8 + 27 + 64 + 125 + 216
83)
84)
Solve: x+ 4
3> 2
84)
15
85)
Give the bounds of summation and the index of summation for
15
m=5
(9m4– 4m)
85)
86)
Evaluate
100
k=1
(2k– 8)
86)
87)
Express the sum in summation notation.
73+74+75+76+77+78+79
87)
88)
Evaluate
6
i=1
i
6
2 + 2 i
6·i
6
88)
89)
A company produces a product for which the variable cost per unit is $3.50 and fixed cost
is $20,000 per year. Next year, the company wants the total cost to be $48,000. How many
units of the product should be made next year?
89)
90)
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?
90)
91)
Ohm’s Law in electrical theory states that V=IR, where R is the resistance (in ohms) of an
object, V is the potential difference (in volts) across the object, and I is the current (in
amperes) that flows through it. If the voltage is 220 volts, what values for the current will
result in a resistance that is less than 20 ohms?
91)
92)
Rooms in a 130 unit student housing complex are fully rented at $300 per month. The
university is raising rates to produce $1920 more in monthly income from these units. Each
$10 per month increase will create two vacancies with no possibility of filling them. What
should be charged for the new rent?
92)
93)
A baker must prepare 6 cups of pie filling. The recipe calls for 1
2 cup of sugar for each 4
cups of fruit. How much of each ingredient should be used?
93)
94)
Express the sum in summation notation.
1 +1
2+1
3+1
4+1
5+1
6
94)
95)
Evaluate
5
k=2
2k2
95)
96)
Express the sum in summation notation.
7 + 11 + 15 + 19 + 23 + 27 + … + 67
96)
16
97)
The number five minus two times x is less than 9 units from zero. What are the possible
values for x?
97)
98)
Solve: 0.2 5(x– 1) – 4 < 0.8(x+ 1)
98)
99)
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?
99)
100)
Evaluate
40
k=1
(k3+ 2k2)
100)
101)
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).
101)
102)
The cost of publishing each copy of a magazine is $1.75. The revenue from dealers if $1.60
for each copy. The amount received for advertising is 10% of the amount received for all
magazines sold beyond 1,000. Find the smallest number of copies that must be sold to
break even.
102)
103)
Solve: 4x– 3 = 7
103)
104)
A company makes car stereos. The manufacturing cost for each stereo is $45. The company
has fixed costs of $4150 per month. How many stereos can it make next month for a total
cost of $10,000?
104)
105)
An appliance company makes coffee makers for which the variable cost per unit is $12 and
the fixed cost is $92,000. What should the selling price be for the company to earn a profit
of $88,000 on 10,000 units?
105)
106)
Evaluate
n
k=1
2k
n + 1
106)
107)
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?
107)
108)
Solve: (1 –2x)2– 4(3 –x)2 5
108)
109)
A monthly real estate guide is published for $1.40 per issue. It is sold to real estate agents
for $1.25 each. The advertising revenue is 15% of the amount received for all guides sold
beyond 2,000. Find the fewest number of real estate guides that must be sold to break even.
109)
110)
Solve: 4x– 3 < – 2(1 –x)
110)
111)
The “current ratio” of a company is the value of its current assets divided by its current
liabilities. A company has a current ratio of 2.5 and current liabilities of $80,000. what are
its current assets?
111)
112)
A manufacturer makes CD players. If the variable costs are $25 per player and the fixed
costs are $50,000, what is the minimum number of CD players that must be sold to make a
profit of $75,000 given that the CD players sell for $45 per player?
112)
113)
Simplify: |(–3 – 7)/ 2|
113)
114)
Express the sum in summation notation.
3 + 3
10 +3
100 +3
1,000 +3
10,000 +3
100,000 +3
1,000,000
114)
19
115)
Suppose a person has $23 in his pocket. What is the maximum number of pizzas that
person can order if each pizza costs $4.39?
115)
116)
Solve: x– 6 6
116)
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
117)
Determine an interval for x4 that satisfies all of these inequalities.
117)
Provide an appropriate response.
118)
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.)
118)
119)
A theater owner charges $3 for each ticket. Currently, only 100 people attend the theater
daily. The owner believes that for each $0.10 decrease per ticket, 10 more people will
attend. If this is true and the capacity of the theater is 200, what should the price of a ticket
be if the owner wants to receive $375 daily from ticket sales?
119)
120)
Simplify: |–8|
120)