Gibilisco S. Everyday Math Demystified: A Self-Teaching Guide
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per second. What is the forward force causing this acceleration?
Neglect the effects of friction, and assume there is no wind.
(a) 1000 newtons.
(b) 10,000 newtons.
(c) 100,000 newtons.
(d) 1,000,000 newtons.
(e) More information is needed to answer this question.
60. Suppose you graph two different equations in two variables.
Both of the equations have graphs that look like parallel, straight
lines. How many common solutions are there to this pair of equa-
tions?
(a) There are no solutions.
(b) There is one solution.
(c) There is more than one solution.
(d) There are infinitely many solutions.
(e) More information is needed to answer this.
61. Which of the following numbers is expressed in binary form?
(a) 2E5F
(b) 722
(c) 989880
(d) 10101
(e) 123210
62. Suppose you’re sailing a motorboat from south to north across
a river that runs exactly east–west. If there were no current in the
river, your boat would travel at 12 knots with respect to the
riverbank. (A knot is a nautical mile per hour, and a nautical mile
is 6080.20 feet.) But there is a current in the river, and it flows at
a steady 5 knots from west to east. What is the speed of your boat
relative to the riverbank?
(a) 7 knots.
(b) 12 knots.
(c) 13 knots.
(d) 17 knots.
(e) More information is necessary to answer this question.
63. Suppose you have a standard 52-card deck. The deck is complete,
and there is exactly one of each card (4 suits with 13 cards in each
suit, and no jokers). You draw a card from this deck, then put the
card back, shuffle the deck several times, and then draw another
card. Then you put the card back, reshuffle the deck again several
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times, and draw a third card. What is the probability that you’ll get
three cards of the same suit?
(a) 1/128
(b) 1/64
(c) 1/32
(d) 1/16
(e) 1/8
64. The quotient of two negative real numbers is
(a) always negative
(b) negative if the denominator is greater than 1, and positive if the
denominator is less than 1
(c) negative if the denominator is less than 1, and positive if the
denominator is greater than 1
(d) always positive
(e) equal to 0
65. Which, if any, of the following (a), (b), (c), or (d) cannot be defined
as a scalar quantity?
(a) The mass of an apple.
(b) The temperature of the water in a swimming pool.
(c) The speed of the wind.
(d) The brightness of a light bulb.
(e) All of the above (a), (b), (c), and (d) can be defined as scalar
quantities.
66. Suppose you are standing exactly 500 feet away from the base of a
vertical communications tower. Your eyes are exactly 5 feet above
the ground, which is flat and level in the vicinity of the tower.
There is a flashing light on the top of the tower, and this light is
exactly 400 feet above the ground. You look up at the light. At
what elevation angle is your line of sight, relative to the horizon?
Round the answer off to the nearest tenth of a degree.
(a) 38.38
(b) 38.78
(c) 51.38
(d) 51.78
(e) More information is needed to answer this question.
67. Suppose the communications tower in the scenario of Question 66
is blown out of vertical alignment by a high wind. You stand
the same distance away from the base as before, that is, 500 feet.
Your eyes are still exactly 5 feet above the ground. If you look at
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the flashing light now, what is the angle of your line of sight relative
to the horizon?
(a) 38.38
(b) 38.78
(c) 51.38
(d) 51.78
(e) More information is needed to answer this question.
68. What is the value of the quotient (6 10
5
)/(2 10
2
)?
(a) There is no way to know because the expression is ambiguous.
(b) 3 10
10
(c) 3 10
3
(d) 12 10
3
(e) 3 10
7
69. In Fig. Exam-4, the independent variable is
(a) time
(b) temperature
(c) location
Fig. Exam-4. Illustration for Final Exam Questions 69 and 70.
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(d) the absolute frequency
(e) the cumulative absolute frequency
70. In Fig. Exam-4, the dependent variable is
(a) time
(b) temperature
(c) location
(d) the absolute frequency
(e) the cumulative absolute frequency
71. In the hexadecimal number system:
(a) the set of possible digits is {0, 1}
(b) the set of possible digits is {0, 1, 2, 3}
(c) the set of possible digits is {0, 1, 2, 3, 4, 5, 6, 7}
(d) the set of possible digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
(e) the set of possible digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
72. What is 150% of 20?
(a) 10
(b) 20
(c) 30
(d) 40
(e) It is meaningless; percentages can never be greater than 100%.
73. Let S be the sequence of all the positive whole numbers divisible by 7,
considered in ascending order. That is:
S ¼ 7ó 14ó 21ó 28ó 35ó ...
This is an example of
(a) a finite arithmetic sequence
(b) an infinite arithmetic sequence
(c) a finite geometric sequence
(d) an infinite geometric sequence
(e) none of the above
74. What is wrong with Fig. Exam-5?
(a) The curve should represent a function, but it does not.
(b) The curve should be a straight line, but it is not.
(c) The horizontal axis does not portray a reasonable independent
variable.
(d) The vertical axis does not portray a reasonable dependent
variable.
(e) Nothing is wrong with Fig. Exam-5.
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75. Which of the following is not a circular function?
(a) Sine.
(b) Cosine.
(c) Logarithm.
(d) Tangent.
(e) Cosecant.
76. Consider a point (x,y,z) in 3D rectangular coordinates. The distance
d of this point from the origin can be found using this formula:
d ¼ðx
2
þ y
2
þ z
2
Þ
1=2
Imagine the origin of a 3D rectangular coordinate system as the
point where two walls intersect the ceiling in a room whose walls
run north–south and east–west. A spider has built a web in the
northwestern corner of this room, near the ceiling. The spider sits
in its web, waiting for a fly to get caught. As the spider lurks, it is
at a point 30 centimeters below the ceiling, 20 centimeters to the
south of the north wall, and 40 centimeters to the east of the west
wall. How far, in a straight line, is the spider from the origin?
Round the answer off to the nearest centimeter.
(a) 9 centimeters.
(b) 29 centimeters.
(c) 30 centimeters.
(d) 54 centimeters.
(e) More information is needed to answer this question.
77. Suppose, in the scenario described in Question 76, a fly gets caught in
the web, 10 centimeters away from the spider. How far, measured in
Fig. Exam-5. Illustration for Final Exam Question 74.
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a straight line, is the fly from the origin? Round the answer off to
the nearest centimeter.
(a) 9 centimeters.
(b) 29 centimeters.
(c) 30 centimeters.
(d) 54 centimeters.
(e) More information is needed to answer this question.
78. If you want to design a stool so it won’t wobble, even if the floor is
not flat, how many legs should the stool have?
(a) 3
(b) 4
(c) 5
(d) 6
(e) 8
79. Suppose you are standing 200 yards away from a communica-
tions tower that is 150 yards high. The ground between you and
the tower is flat and level. You draw this situation and get
Fig. Exam-6, where d represents the distance of your shoes
from the tower, e represents the height of the tower, and f represents
the distance of your shoes from the top of the tower. According to
the Theorem of Pythagoras, you know this:
d
2
þ e
2
¼ f
2
You also know that there are exactly 3 feet in a yard. How far are
your shoes from the top of the tower? Express the answer to the
nearest 10 feet.
(a) 450 feet.
(b) 600 feet.
(c) 750 feet.
Fig. Exam-6. Illustration for Final Exam Questions 79 and 80.
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(d) 900 feet.
(e) More information is necessary to answer this question.
80. Suppose, in the situation shown by Fig. Exam-6, and described by
Question 79, you move twice as far away from the tower as you
were before. How far are your shoes from the top of the tower
now? Express the answer to the nearest 10 feet.
(a) 1170 feet.
(b) 1220 feet.
(c) 1280 feet.
(d) 1440 feet.
(e) More information is necessary to answer this question.
81. Suppose you are grocery shopping and you come across apples on
sale for $0.50 (50¢) a pound. The scale for weighing them, however,
shows kilograms (kg). You place apples on the scale until it reads
3.50 kg. What is the price of this mass of apples?
(a) 80¢
(b) $1.59
(c) $3.85
(d) $7.70
(e) It cannot be determined without more information.
82. A continuous variable
(a) can attain only certain values over a specified range
(b) can attain infinitely many values over a specified range
(c) can always be portrayed as a straight line
(d) can only be portrayed as a series of points
(e) is a bell-shaped curve
83. Suppose a truck weighs 8459 kilograms (kg). How many grams (g) is
this, written in scientific notation?
(a) 8459 g
(b) 8.459 g
(c) 8.459 10
3
g
(d) 8.459 10
6
g
(e) 8.459 10
9
g
84. Let q represent a set of items or objects taken r at a time in a specific
order. The possible number of combinations in this situation is
symbolized
q
C
r
and can be calculated as follows:
q
C
r
¼ q!=½r!ðq rÞ!
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Now suppose you have a pair of standard 6-faced dice. If you toss
both dice at once, how many different combinations of numbers is
it possible to get?
(a) 15
(b) 30
(c) 360
(d) 720
(e) More information is necessary to answer this question.
85. Suppose you build a canvas teepee. The floor is circular with a radius
of 3 meters, as shown in Fig. Exam-7. The teepee is a right circular
cone supported by a central pole 4 meters high (pole not shown).
The slant height is 5 meters. The surface area of a right circular
cone, not including the base, is equal to p times the radius of
the base, times the slant height. How much canvas will you need
to construct this teepee? Neglect the small area of the exhaust
fan hole at the top. Assume that the door will be a flap of canvas,
that there will be no windows, and that the floor will be dirt.
Let p ¼ 3.14.
(a) 15 square meters.
(b) 28.26 square meters.
(c) 47.1 square meters.
(d) 37.68 cubic meters.
(e) 60 cubic meters.
86. The volume of a right circular cone is equal to p times the square of
the radius of the base, times the height, divided by 3. How much air is
Fig. Exam-7. Illustration for Final Exam Questions 85 through 87.
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enclosed by the teepee shown in Fig. Exam-7? Neglect the small
volume taken up by the supporting pole. Let p ¼ 3.14.
(a) 15 square meters.
(b) 28.26 square meters.
(c) 47.1 square meters.
(d) 37.68 cubic meters.
(e) 60 cubic meters.
87. The area of a circle is equal to the product of p and the square of its
radius. How much floor area does the teepee shown in Fig. Exam-7
have? Neglect the small area taken up by the base of the supporting
pole. Consider the value of p to be 3.14.
(a) 15 square meters.
(b) 28.26 square meters.
(c) 47.1 square meters.
(d) 37.68 cubic meters.
(e) 60 cubic meters.
88. Suppose you graph two different equations in two variables. Both of
the equations have graphs that look like circles. How many common
solutions are there to this pair of equations?
(a) There are no solutions.
(b) There is one solution.
(c) There is more than one solution.
(d) There are infinitely many solutions.
(e) More information is needed to answer this.
89. Imagine that you are a dedicated lap swimmer, and you are used
to swimming 3000 meters every day, which is 30 round-trip laps
(a lap is two one-way lengths) in your local 50-meter pool. You
are in a strange town and you go to their local pool, and discover
that it is 25 yards long. You happen to remember that there are
approximately 39.37 inches in 1 meter, and that 1 yard is exactly
36 inches. Based on this information, how many round-trip laps of
the 25-yard pool should you swim in order to be sure you get your
3000-meter workout, but without swimming any more laps than
necessary?
(a) More information is necessary in order to answer this question.
(b) 28
(c) 33
(d) 55
(e) 66
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90. The median for a discrete variable in a statistical distribution is
(a) the smallest value
(b) the largest value
(c) the mathematical average of all the values
(d) the value in the exact middle
(e) the value that occurs most often
91. In the octal number system:
(a) the set of possible digits is {0, 1}
(b) the set of possible digits is {0, 1, 2, 3}
(c) the set of possible digits is {0, 1, 2, 3, 4, 5, 6, 7}
(d) the set of possible digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
(e) the set of possible digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
92. In a major-league baseball diamond, the distance between home
plate and first base is 90 feet. The same is true of the distance between
first base and second base, between second base and third base, and
between third base and home plate. The pitcher’s rubber is 60.5 feet
from home plate. Suppose a triangle is laid out with straight ropes
between home plate, first base, and the pitcher’s rubber. What is
the sum of the measures of the interior angles of this triangle?
(a) 1728
(b) 176.58
(c) 1808
(d) 183.58
(e) More information is needed to answer this question.
93. Suppose that major-league baseball officials decide to change the
dimensions of a standard baseball diamond. The motivation is to
make it more difficult for pitchers, causing higher-scoring games.
According to the new regulations, the pitcher’s rubber will be 70
feet, rather than 60.5 feet, away from home plate. Further imagine
that the distances between the bases will be left the same, at 90
feet. Suppose a triangle is laid out with straight ropes between
home plate, first base, and the pitcher’s rubber in a diamond with
the new official dimensions. What is the sum of the measures of
the interior angles of this triangle?
(a) 1728
(b) 176.58
(c) 1808
(d) 183.58
(e) More information is needed to answer this question.
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