Download 2nd-Semester-Final

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Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the next term of the arithmetic sequence.
8, –9, –26, –43...
a. –60
b. –53
____
c. –57
d. 731
2. Find the next term of the geometric sequence.
8, 32, 128, 512...
a. 2,158
b. 1,909
c. 1,936
d. 2,048
____
3. Brian, a scientist, is writing a research paper on projectile motion. During one of his experiments, he throws a
ball from a point marked as Point A, with a certain velocity in the horizontal direction. The ball travels a total
horizontal distance of 0.6 meter after 1 second, 1.2 meters after 2 seconds,
1.8 meters after 3 seconds, and so on. It hits the ground on the 8th second. Brian marks the point where the
ball landed as Point B. Calculate the distance between Point A and Point B.
a. 4.2 m
c. 5.4 m
b. 4.8 m
d. 9.0 m
____
4. Maria drops a stone from the top of a building. The stone falls 4.9 meters in the first second,
14.7 meters in the second second, and 24.5 feet in the third second, regardless of its weight. How many feet
would an object fall in the tenth second?
a. 102.9 m
c. 83.3 m
b. 93.1 m
d. 88.2 m
____
5. A ditch contains 10 centimeters of water. The total amount of rainwater in the ditch is as follows:
10 centimeters of water after 1 second, 15 centimeters after 2 seconds, 20 centimeters after 3 seconds, and so
on. Assuming that the ditch has sufficient capacity for storage, how many centimeters of water will it have
after 10 seconds?
a. 55 cm
c. 75 cm
b. 65 cm
d. 110 cm
____
6. James covers a distance of 8 meters in the first second of a 100 meter race. Then, he sprints at a speed of 9
meters per second. How far is James from the finish line 9 seconds after the race has started?
a. 11 m
c. 28 m
b. 20 m
d. 80 m
____
7. A scientist rolls two balls A and B down two different ramps. Ball A rolls 4 meters in the 1st second, 9 meters
in the 2nd second, 14 meters in the 3rd second, and so on. Ball B rolls 3.5 meters in the 1st second, 6.5 meters
in the 2nd second, 9.5 meters in the 3rd second, and so on. How many meters would each ball roll in 10
seconds?
a. A: 49 m; B: 30.5 m
c. A: 59 m; B: 36.5 m
b. A: 54 m; B: 33.5 m
d. A: 85 m; B: 72 m
____
8. Two elevators begin descending from the same height. Elevator A has descended 4 feet after one second, 9
feet after two seconds, 14 feet after three seconds, and so on. Elevator B has descended
3.5 feet after one second, 6.5 feet after two seconds, 9.5 feet after three seconds, and so on.
How many feet would each elevator descend in 10 seconds?
a. A: 49 ft; B: 30.5 ft
c. A: 59 ft; B: 36.5 ft
b. A: 54 ft; B: 33.5 ft
d. A: 85 ft; B: 72 ft
____
9. Two cars, A and B, 100 miles apart, move toward each other. Car A covers 0.7 mile in the first minute, and
then moves with an average speed of 0.8 mile per minute. Car B covers 0.6 mile in the first minute, and then
moves with an average speed of 0.7 mile per minute. How many miles apart are the cars after 10 minutes?
a. 85.2 mi
c. 83.7 mi
b. 14.8 mi
d. 16.3 mi
____ 10. A bus moves away from a bus stop in a straight line. It moves a total of 10 meters after 1 second,
20 meters after 2 seconds, and 30 meters after 3 seconds. How many meters away is the bus from the bus stop
after 10 seconds?
a. 100 m
c. 120 m
b. 110 m
d. 190 m
____ 11. After a gas-filled balloon is released, it rises to 90 feet in the first minute. In the second minute, the balloon
rises to 120 feet, and in the third minute, it rises to 150 feet. How many feet would the balloon rise in 8
minutes?
a. 300 ft
c. 390 ft
b. 330 ft
d. 660 ft
____ 12. A landscaper is designing a wall made of white bricks. The pattern consists of 130 white bricks in the bottom
row, 110 white bricks in the second row, and 90 white bricks in the third row. How many white bricks will
the 6th row have?
a. 10
c. 80
b. 30
d. 230
____ 13. Two objects in outer space drift apart at an average rate of 25 kilometers every year. If the objects continue to
drift apart from each other at the same rate, how many kilometers will they drift in
10 years?
a. 250 km
c. 300 km
b. 275 km
d. 475 km
Find the arithmetic means in the given sequence.
____ 14. 105, ?, ?, ?, 165
a. 125, 145, 155
b. 120, 135, 150
c. 115, 125, 135
d. 150, 135, 120
____ 15. –3, ?, ?, ?, 93
a. 21, 45, 69
b. 21, 46, 71
c. 13, 29, 45
d. 69, 45, 21
Find S for the given arithmetic series.
____ 16.
,
a. –560
b. 880
,
c. –800
d. –400
____ 17.
,
a. –2520
b. –5040
,
c. –630
d. –2541
Find the sum of the given arithmetic series.
____ 18.
a. 5008
b. 2352
c. 2504
d. 2592
a. 1,446,309
b. 1,439,100
c. 1,372,410
d. 1,440,855
____ 19.
____ 20. Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on. He continues to double
his savings each day. Find the amount that he will save on the fifteenth day.
a. $16,384
b. $29
c. $32,768
d. $8192
____ 21. Last year, 150 cases were reported of a new infectious disease. It has been predicted that the number will
double every year. How many cases will be reported in the ninth year?
a. 38,400
b. 166
c. 76,800
d. 256
____ 22. A pool was sprayed with insecticide, and 2400 mosquitoes were killed on the first day, 600 on the second day,
150 on the third day, and so on. What number of mosquitoes was killed on the sixth day after the spraying?
(Round the answer to the nearest whole number.)
a. 2
b. 2401
c. 1
d. 0
____ 23. Frank has a sheet of paper which is
thick. If the sheet is folded in half, the total thickness will be
A second fold will produce a total thickness of
Frank folds it 8 times?
a. 14.001 in.
b. 0.41 in.
What will be the thickness of the sheet if
c. 0.205 in.
d. 128 in.
____ 24. One minute after it is released, a hot-air balloon rises 120 feet. In each succeeding minute, the balloon rises
only 60% as far as it rose in the previous minute. How far will the balloon rise in the fourth minute?
a. 25.92 ft
b. 121.8 ft
c. 15.552 ft
d. 0.216 ft
Find the geometric means in the following sequence.
____ 25.
a. –144, –576, –2,304, –9,231
b. 36, 144, 576, 2,304
c. –720, –1,080, –1,440, –1,800
d. –36, –144, –576, –2,304
a. –6,580, –9,870, –13,160, –16,450
b. 329, 2,303, 16,121, 112,847
c. 2,303, –16,121, 112,847, –789,944
d. –329, 2,303, –16,121, 112,847
____ 26.
Find S for the given geometric series. Round answers to the nearest hundredth, if necessary.
____ 27.
a. 435.4
b. 51.4
c. 311.08
d. 874.94
a. –4,774
b. –2,870
c. –1,190
d. –8,995
____ 28.
Find a for the given geometric series. Round to the nearest hundredth if necessary.
____ 29.
____ 30.
,
a. 2,385.58
b. 3,056.70
,
,
a. 12,951.89
b. 11,375.61
,
c. 5,325.87
d. 16,258.27
c. 4,646.30
d. 21,704.20
Find the sum of the given infinite geometric series. Round to the nearest hundredth, if necessary.
____ 31.
a. 25
b. 26.4
c. 27.08
d. 51
a. –9.71
b. –9.7
c. –10.31
d. –43.33
____ 32.
Write the given repeating decimal as a fraction.
____ 33. 0.27
a. 11
3
b. 3
11
____ 34. 0.3
c.
27
101
d. 27
100
a.
c. 3
33
101
b. 33
100
d.
1
3
Find the first five terms of the given sequence.
____ 35.
a.
b.
, 3,
, 25,
, 3,
,
c.
d.
,
, 3,
,
, 3,
,
,
,
____ 36.
a.
b.
c.
, 1, 9, 33,
, 1,
,
d.
,
, 7,
,
, 49,
,
,
,
____ 37.
a.
b.
, 0, 0, 0, –4
,
,
,
,
c.
d.
,
,
,
,
, 0, 0, 0, 0
____ 38.
a.
–5,
b.
–5, –
, 0, 0, 0
, 0, 0, 0
c.
–5,
d.
–5, –
,
,
,–
,
,–
,0
____ 39.
a. 1, 1, 1, 1, 1
b. 1, 1, 2, 3, 4
c. 1, 2, 9, 64, 625
d. 1, 2, 3, 4, 5
a. –5, 7, 10, 14, 19
b. –5, 15, 10, 5, 0
c. –5, 0, 5, 10, 15
d. –5, 10, 15, 20, 25
a. 2, –5, –12, –19, –26
b. 2, –26, –19, –12, –5
c. 2, –9, –16, –23, –30
d. 2, –5, –4, –3, –2
a. 4, 9, 13, 16, 18
c. 4, –2, –7, –11, –14
____ 40.
____ 41.
____ 42.
b. 4, 10, 15, 19, 22
d. 4, 7, 7, 7, 7
a. 4, 24, 84, 264, 804
b. 24, 84, 264, 804, 2424
c. 4, 12, 36, 108, 324
d. 4, 15, 47, 153, 471
a. 9, 7, 5, 3, 1
b. 9, 8, 7, 6, 5
c. 9, 16, 14, 12, 10
d. 9, 1, 2, 3, 4
____ 43.
____ 44.
Expand the given power by using Pascal’s triangle.
____ 45.
a.
b.
c.
d.
____ 46.
a.
b.
c.
d.
Expand the given power using the Binomial Theorem.
____ 47.
a.
b.
c.
d.
____ 48.
a.
b.
c.
d.
____ 49. The salaries of some of the employees of MegaMall departmental store are given below.
Employee
Annie
Harris
Sarah
Cherry
Mini
Trish
Salary
$1700
$1600
$1600
$1500
$1500
$1400
Employee
David
Dennis
Roger
Rebecca
Michael
Salary
$1600
$1300
$1600
$1200
$1000
Find the mean, median, and mode of the salaries.
a. 1400, 1500, and 1600
c. 1454.5, 1500, and 1500
b. 1454.5, 1500, and 1600
d. 1454.5, 1600, and 1600
____ 50. The table shows the heights (in centimeters) of students of class IX.
145
155
155.5
158
160.6
165
170
175
175
175.9
180
Find the mean, median, and mode of the heights to the nearest tenth.
a. 165.0, 165.0, and 155.5
b. 165.0, 165.0, and 175.0
c. 166.5, 165.0, and 175.0
d. 165.0, 170.0, and 175.0
____ 51. The table shows the prices (in dollars) of the latest models of cars of different motor companies.
20,000
20,000
25,000
30,000
32,000
35,000
40,000
40,000
40,000
48,000
50,000
Find the mean, median, and mode of the prices.
a. 34,000, 35,000, and 40,000
b. 34,545.45, 40,000, and 40,000
c. 34,545.45, 35,000, and 40,000
d. 34,545.45, 35,000, and 20,000
____ 52. The table shows the weights (in pounds) of some newborn babies.
4.2
4.5
4.8
5.0
5.5
6.5
6.5
6.5
6.5
7.0
7.4
8.0
8.6
Find the mean, median, and mode of the weights.
a. 6.2, 6.5, and 8.6
b. 6.2, 7.0, and 6.5
c. 6.5, 6.5, and 6.5
d. 6.2, 6.5, and 6.5
____ 53. The table shows the number of children (in hundreds) visiting the McDonalds counter outside Jackson High
School on thirteen different days.
1.2
1.5
2.5
2.5
2.3
2.5
2.5
2.1
2.5
2.2
Find the mean, median, and mode (in hundreds) of the number of children.
a. 2.3, 2.5, and 2.2
c. 2.4, 2.5, and 2.5
b. 2.4, 2.1, and 2.5
d. 2.4, 2.5, and 3.5
2.8
3.5
3.5
____ 54. The table shows the difference between the actual and the estimated production of a home product (in
percentage) by a company for the last seven years.
Year
1997
1998
1999
2000
2001
2002
2003
Difference in Production
(percent)
4.5
4.6
4.2
4.7
4.2
2.4
2.9
Find the mean, median, and mode of the percentage difference in production.
a. 3.9, 4.2, and 4.2
c. 3.8, 4.2, and 4.6
b. 3.9, 4.6, and 4.5
d. 3.9, 4.5, and 4.2
____ 55. The table shows the population (in millions) of five continents.
Continents
Africa
Asia
Australia
Europe
North America
Population (millions)
826.835
3758.725
31.862
726.169
494.394
Find the mean and median of the population in millions.
a. 1167.60 and 726.17
c. 1167.60 and 826.84
b. 1160.46 and 726.17
d. 726.17 and 1167.60
____ 56. The table shows the rate of literacy (in percent) of the following countries.
Country
Australia
China
France
Germany
Japan
United Kingdom
United States
Literacy Rate
99.5%
88%
98.3%
100%
100%
100%
95.2%
Find the mean, median, and mode of the literacy rate.
a. 97.7%, 98.3%, and 100%
c. 97.3%, 100%, and 99.5%
b. 97.3%, 99.5%, and 100%
d. 97.6%, 99.5%, and 95.2%
____ 57. The table shows the areas (in thousand square miles) of five continents. Find the mean and median of these
areas.
Continents
Africa
Area (thousand square miles)
11,717.218
Asia
Australia
Europe
North America
a.
b.
c.
d.
12,268.332
3287.609
8892.753
6882.128
8609.608 sq. miles and 6882.128 sq. miles
8609.608 sq. miles and 8892.753 sq. miles
9609.608 sq. miles and 6882.128 sq. miles
9,609.608 sq. miles and 8,892.753 sq. miles
____ 58. The table shows the gross national product (in thousands) of the following countries.
Country
Australia
China
France
Germany
Japan
United Kingdom
United States
GNP ($)
400
1000
1400
2100
4100
1400
8900
Find the mean, median, and mode of the gross national product.
a. 2757, 1400, and 1400
c. 2757, 2100, and 1400
b. 3587, 1400, and 400
d. 3587, 1400, and 1400
Find the variance and standard deviation of the given set of data to the nearest tenth.
____ 59. {490, 130, 240, 400, 170, 630, 730}
a. variance = 214.2, standard deviation = 45,898
b. variance = 45,898, standard deviation = 22,949
c. variance = 53,547.6, standard deviation = 231.4
d. variance = 45,898, standard deviation = 214.2
____ 60. {9.1, 13.6, 24.4, 35.7, 30, 45, 12.7, 47.8, 29, 66}
a. variance = 289, standard deviation = 17
b. variance = 289, standard deviation = 144.5
c. variance = 321.1, standard deviation = 17.9
d. variance = 17, standard deviation = 289
____ 61. Find the probability that a student’s score on a college admissions test improved on their second attempt,
given that he or she took a test score improvement program after their first attempt.
Test Score
Improved
Did Not Improve
a. 67%
b. 73%
Number of Students
Took Program
No Program
317
149
158
327
c. 72%
d. 59%
____ 62. Find the probability that a marathon runner is female given that she is an adult.
Age Group
Teen
Adult
Number of Marathon Participants
Male
Female
29
15
90
113
a. 60%
b. 61%
c. 52%
d. 56%
There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected
for a stage performance. Find the probability of the following selection.
____ 63. P(2 brown-haired children)
a.
b.
____ 64. P(2 black-haired children)
a.
b.
____ 65. P(1 brown-haired and 1 black-haired child)
a.
b.
c.
d.
c.
d.
c.
d.
Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag
during the move. Four books are of mathematics, three are English, and six are science. If Laura opens the
bag and selects books at random, find the given probability.
____ 66. P(3 mathematics books)
a.
b.
____ 67. P(3 English books)
a.
b.
____ 68. P(1 science and 2 mathematics books)
c.
d.
c.
d.
a.
c.
b.
d.
____ 69. P(1 English and 2 science books)
a.
c.
b.
d.
____ 70. P(1 book of each subject)
a.
c.
b.
d.
____ 71. P(2 science and 2 mathematics books)
a.
c.
b.
d.
____ 72. P(2 mathematics and 1 history book)
a. 0
c.
b.
d. 1
Three tickets are selected at random from a box of tickets bearing numbers from 1 to 30. The table and the
relative-frequency histogram show the distribution of the number of even-numbered tickets chosen. Find the
given probability.
Tickets with Even Numbers
Probability
0
1
2
3
____ 73. P(0 even-numbered tickets)
a.
b.
____ 74. P(1 even-numbered ticket)
a.
b.
____ 75. P(2 even-numbered tickets)
a.
b.
____ 76. P(3 even-numbered tickets)
a.
b.
____ 77. P(2 odd-numbered tickets)
a.
b.
____ 78. P(1 odd-numbered ticket)
a.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
c.
b.
d.
Two pens are selected at random from a pen stand containing three blue and two black pens. The table and
the relative-frequency histogram show the distribution of the number of blue pens chosen. Find the
probability.
Blue Pens
0
1
2
Probability
____ 79. P(0 blue pens)
a.
c.
b.
d.
____ 80. P(1 blue pen)
a.
c.
b.
d.
____ 81. P(1 black pen)
a.
c.
b.
d.
____ 82. P(2 black pens)
a.
c.
b.
d.
The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a
standard deviation of 5 points.
____ 83. About what percent of students have scored between 55 and 65 points?
a. 2.5
c. 47.5
b. 34
d. 68
____ 84. About what percent of students have scored between 60 and 65 points?
a. 13.5
c. 50
b. 34
d. 95
____ 85. About what percent of students have scored less than 45 points?
a. 0.5
c. 15.5
b. 2.5
d. 34
____ 86. About what percent of students have scored more than 65 points?
a. 2.5
c. 34
b. 16
d. 47.5
____ 87. About what percent of students have scored more than 75 points?
a. 0.5
c. 15.5
b. 2.5
d. 34
The measurement of the height of 600 students of a college is normally distributed with a mean of
175 centimeters and a standard deviation of 5 centimeters.
____ 88. What percent of students are between 170 centimeters and 180 centimeters in height?
a. 16
c. 68
b. 34
d. 81.5
____ 89. What percent of students are between 180 centimeters and 185 centimeters in height?
a. 12.5
c. 34
b. 13.5
d. 68
____ 90. What percent of students are less than 170 centimeters in height?
a. 0.5
c. 15.5
b. 2.0
d. 16.0
____ 91. What percent of students are taller than 175 centimeters?
a. 34
c. 68
b. 50
d. 84
____ 92. What percent of students are taller than 180 centimeters?
a. 0.5
c. 15.5
b. 2.0
d. 16.0
Find a 95% confidence level. Round to the nearest hundredth.
____ 93.
a.
b.
c.
d.
a.
b.
c.
d.
____ 94.
Short Answer
Determine whether the sequence is arithmetic or geometric. Write the next four terms.
95. 2, 4, 8, 16...
96. 13, –1, –15, –29...
97. 2.7, 3.3, 3.9, 4.5...
98. –5, 15, –45, 135...
99. 16, 4, 1,
...
100. Aponi has joined a new job. She is paid $8.50 an hour. She has been told that every year she will receive a
raise of $1.50 an hour. What will her hourly wage be during the seventh year?
101. A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the
second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50
rows. Find the number of people that can be accommodated in the sixteenth row.
102. Makya was conducting a physics experiment. He rolled a ball down a ramp and calculated the distance
covered by the ball at different times. The ball rolled a distance of 1 foot during the first second, 3 feet during
the next second, and so on. If the distances the ball rolled down the ramp each second form an arithmetic
sequence, determine the distance the ball rolled down during the fifteenth second.
103. Isaac is practicing for an upcoming cycling competition. The first day he practiced for 45 minutes. He
increases his practicing time by 15 minutes each day. How much time will he spend practicing on the 25th
day?
104. If a student loses a book issued from the school library, he or she pays for the book. If the book is returned
late, the student pays a fine of 50 cents for each day. Charles returned a book on April 30. The book was due
on April 21. Find the overdue fine that Charles paid for the late return of the book.
Find
105.
for each arithmetic series described.
106.
107.
108.
109.
110. Anoki has just been employed at an annual salary of $35,000. If he expects to receive an annual increase of
5%, what will his salary be as he begins his sixth year?
111. Bradley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces
the previous
height. Find the height the ball will bounce after hitting the ground the fourth time.
112. Mr. Cameron has recently purchased a new car that costs $14,450. He estimates that the value of the car will
depreciate at a rate of 16% per year. He is planning to trade the car after 6 years. Determine the value of the
car at that time to the nearest dollar.
113. From 1991 through 2000, the annual revenue for an electronics company increased at an average rate of
16.5% per year. The annual revenue generated by the company in 1991 was 465 million dollars. Determine
the revenue generated by the company in the year 2000.
114. On the first day of college, Sophia tells a rumor to three of her friends. Each of those friends tells the rumor to
three of their friends the next day. Each person who hears the rumor on the second day shares it with three
more people on the third day, and so on. So, every day, the number of people who hear the rumor is three
times the number who heard it the previous day. Determine the number of people who hear the rumor on the
sixth day.
115. The population of a certain microbe triples every 15 minutes. The initial population is 230. Determine the
number of microbes that would exist after 14 hours.
116. A frog at the base of a 40-foot deep well is leaping the wall to reach to its top. The first jump
is 10 feet, the second jump is 7.5 feet, the third jump is 5.625 feet, and so on. In each leap, the frog jumps
one-fourth of the remaining distance. Determine the distance the frog leaps in 10 jumps. Will the frog be able
to come out of the well in 10 leaps?
117. Namid conducted an experiment on the growth of plants. He took four-inch-tall plants and exposed them to
sunlight for 8 hours each day. He found that the plants grow 3% each week. Predict how tall the plants will be
at the beginning of the ninth week.
118. An art museum has been investing in sculptures for many years. Ten years ago, the director of the museum
purchased a sculpture from a gallery for $135,000. It has been found that the value of the sculpture
appreciates at a rate of 12% per year. Find the value of the sculpture after 35 years, assuming that the rate of
appreciation remains constant.
119. A vacuum pump removes 30% of the air from a sealed jar on each stroke of its piston. The jar contains 32
liters of air before the pump starts. What percent of the original amount of air in the jar will be removed if the
jar passes through six strokes?
120. The bob of a pendulum swings through an arc of 45 inches on its first swing. Each succeeding swing is 95%
of the length of the previous swing. Determine the total distance the bob will travel.
121. Austin is conducting an experiment on the movement of spheres over a smooth trail. He rolled down a sphere
on a smooth track with some initial velocity and calculated the distances traveled by the sphere every minute.
The ball moved a distance of 146 feet in the first minute. Every minute, the ball travels only 35% as far as it
moved during the preceding minute. Determine the total distance covered by the sphere.
122. Tracy is working on a science experiment and is making loops of a string. The first loop of the string is 36
inches long. The length of the second loop is
the length of the first. The length of the third loop is
the
length of the second, and so on. Assuming the string has infinitely many loops, determine the length of the
string.
123. Drew dropped a tennis ball from a 42-foot-high terrace. After striking the ground, the ball rebounds 30% of
the height from which it fell. For every rebound of the ball, there is another rebound, 30% as high. Determine
the vertical distance the ball travels before coming to a rest.
124. Anoki is doing an experiment to draw conclusions about the motion of an object hanging on a tensioned coil.
He took a tensioned coil spring and attached a weight to it. He pulled the weight downward and then let it go.
The weight traveled a distance of 2.5 feet upward. It changed direction and moved only 75% as far as it did in
the previous direction. Every time the weight changed its direction, it traveled a distance 75% of the distance
it moved in the previous direction. Determine the total distance covered by the weight.
125. April drew a card from a standard deck. Find the probability of her drawing a red queen given that she drew a
face card.
126. Beet Na rolled two dice. Find the probability of her rolling two even numbers given that the sum of the roll is
8.
127. Jose bought a book from a bookstore's clearance table. Find the probability of him buying a paperback if the
book he bought was 30% off.
Sale
Number of Clearance Books
Paperback
Hardback
45
18
66
22
14
35
20% Off
30% Off
50% Off
128. A student was selected from a city-wide high school tennis tournament. Find the probability of the player
being a sophomore given that he or she was not from the Southern District.
District
Northern
Southern
Freshman
5
2
Sophomore
7
10
Junior
10
8
Senior
8
12
Eastern
Western
3
7
8
2
9
7
15
12
129. A packet contains 4 green thumbtacks, 5 blue thumbtacks, and 3 yellow thumbtacks. If the thumbtacks are
chosen randomly, what is the probability that 2 green thumbtacks, 2 blue thumbtacks, and 2 yellow
thumbtacks will be selected?
130. Mana has a candle box containing 6 red candles and 6 white candles. What is the probability that she will pull
out three red candles and two white candles?
131. Tyee buys 4 shirts, 5 pairs of pants, and 3 jackets. He puts the shirts, pants, and jackets randomly on a shelf.
Find the probability of putting 4 shirts, 5 pairs of pants, and 3 jackets in the same order as he bought them.
132. A combination lock of a locker requires a four-digit code made up of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9. No
number can be used more than once. What is the probability that all the digits are even numbers?
133. The scores of written tests for a job is normally distributed with a mean of 70 marks and a standard deviation
of 2 marks. About what percent of candidates scored more than 70 marks?
The heart rates of a number of people are normally distributed with a mean of 85 beats per minute and a
standard deviation of 5 beats per minute.
134. About what percent of the heart rates lies between 85 beats per minute and 90 beats per minute?
135. About what percent of the heart rates lies between 75 beats per minute and 80 beats per minute?
136. About what percent of the heart rates is more than 90 beats per minute?
137. About what percent of the heart rates is less than 75 beats per minute?
Find a 95% confidence level. Round to the nearest hundredth.
138.
139. Sixty managers at a company were asked the average number of hours a week they worked. The mean time
was 47.3 hours with a standard deviation of 4.9 hours.
t
Answer Section
MULTIPLE CHOICE
1. A
2. D
3. B
Use the formula
.
4. B
Use the formula
.
5. A
Use the formula
.
6. B
Use the formula
.
7. A
Use the formula
.
8. A
Use the formula
.
9. A
Use the formula
.
10. A
Use the formula
.
11. A
Use the formula
.
12. B
Use the formula
.
13. A
Use the formula
.
14. B
Use the formula for the nth term of an arithmetic sequence:
.
15. A
Use the formula for the nth term of an arithmetic sequence:
.
16. D
Calculate a using the formula for the nth term of an arithmetic sequence and then apply the formula for the
sum of an arithmetic sequence.
17. A
Calculate a using the formula for the nth term of an arithmetic sequence and then apply the formula for the
sum of an arithmetic sequence.
18. C
Find a and a and substitute these values in the formula for the sum of an arithmetic sequence.
19. A
Find a and a of the given arithmetic series and substitute these values in the formula for the sum of an
arithmetic sequence.
20. A
Apply the formula for the nth term of a geometric sequence:
where
is the first term,
is
the nth term, and r is the common ratio.
21. A
Apply the formula for the nth term of a geometric sequence:
where
is the first term,
is
the nth term, and r is the common ratio.
22. A
Apply the formula for the nth term of a geometric sequence:
where
is the first term,
is
the nth term, and r is the common ratio.
23. C
Apply the formula for the nth term of a geometric sequence:
where
is the first term,
is
the nth term, and r is the common ratio.
24. A
Apply the formula for the nth term of a geometric sequence:
where
is the first term,
is
the nth term, and r is the common ratio.
25. D
Use the formula
to find the nth term of a geometric sequence.
26. D
Use the formula
to find the nth term of a geometric sequence.
27. A
Use the formula
for the sum of a geometric series.
28. A
Use the formula
for the sum of a geometric series.
29. B
Use the formula
for the sum of a geometric series.
30. C
Use the formula
for the sum of a geometric series.
31. A
Use the formula
for the sum of an infinite geometric series.
32. A
Use the formula
for the sum of an infinite geometric series.
33. B
Split the decimal into a series and apply the sum formula of infinite series.
34. D
Split the decimal into a series and apply the sum formula of infinite series.
35. A
Substitute the value of a in the function and find the value of a . Repeat the same process for a
.
36. B
Substitute the value of a in the function and find the value of a . Repeat the same process for a
.
37. B
Substitute the value of a in the function and find the value of a . Repeat the same process for a
.
38. A
Substitute the value of
in the function and find the value of . Repeat the same process for
.
, a , and a
, a , and a
, a , and a
,
, and
39. A
Substitute the value of a in the function and find the value of a . Repeat the same process for a , a , and a
.
40. C
Substitute the value of a in the function and find the value of a . Repeat the same process for a , a , and a
.
41. A
Substitute the value of a in the function and find the value of a . Repeat the same process for a , a , and a
.
42. B
Substitute the value of a in the function and find the value of a . Repeat the same process for a , a , and a
.
43. A
Substitute the value of a in the function and find the value of a . Repeat the same process for a , a , and a
.
44. B
Substitute the value of a in the function and find the value of a . Repeat the same process for a , a , and a
.
45. D
Use Pascal’s triangle to expand the power.
46. C
Use Pascal’s triangle to expand the power.
47. B
Use the Binomial Theorem to expand the power.
48. A
Use the Binomial Theorem to expand the power.
49. B
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
50. B
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
C
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
D
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
C
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
A
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
A
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
B
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of values is the value which occurs most frequently in the given group.
B
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
A
Adding the given values and dividing the sum by the number of values gives the mean of the given set of
values.
The median of a group of values is the value which divides the group into two equal parts.
The mode of a group of given value is the value which occurs most frequently in the given group.
D
Apply the appropriate formula to find the mean first, and then find the variance and the standard deviation.
A
Apply the appropriate formula to find the mean first, and then find the variance and the standard deviation.
A
D
B
P(2 brown-haired children) = P(2 brown-haired children and 0 black-haired children)
64. A
P(2 black-haired children) = P(2 black-haired children and 0 brown-haired children)
65. C
P(2 black-haired children) = P(1 brown-haired child and 1 black-haired child)
66. C
Use the Fundamental Counting Principle to find the number of successes
Determine the probability P(3 mathematics books) by using the probability formula
.
.
67. B
Use the Fundamental Counting Principle to find the number of successes
Determine the probability P(3 English books) by using the probability formula
.
.
68. C
Use the Fundamental Counting Principle to find the number of successes
.
Determine the probability P(1 science and 2 mathematics books) by using the probability formula
.
69. D
Use the Fundamental Counting Principle to find the number of successes
.
Determine the probability P(1 English and 2 science books) by using the probability formula
=
.
70. D
Use the Fundamental Counting Principle to find the number of successes
.
Determine the probability P(1 English and 2 science books) by using the probability formula
=
.
71. B
Use the Fundamental Counting Principle to find the number of successes
.
Determine the probability P(2 science and 2 mathematics books) by using the probability formula
=
.
72. A
The occurrence of this event is not possible as there are no history books in the bag.
73. A
The table gives the probability of selecting different numbers of tickets bearing even numbers.
74. C
The table shows the probability of selecting different numbers of tickets bearing even numbers.
75. B
The table displays the probability of selecting different numbers of tickets bearing even numbers.
76. A
The table shows the probability of selecting different numbers of tickets bearing even numbers.
77. C
When three tickets are drawn, the probability of selecting two odd-numbered tickets is the same as the
probability of selecting one even-numbered ticket.
78. C
When three tickets are drawn, the probability of selecting one odd-numbered ticket is the same as the
probability of selecting two even-numbered tickets.
79. A
The table gives the probability of selecting different numbers of blue pens.
80. C
The table gives the probability of selecting the various numbers of blue pens.
81. C
The probability of selecting one black pen is the same as the probability of selecting one blue pen.
82. A
The probability of selecting two black pens is the same as the probability of selecting zero blue pens. This
probability can be found using the table or the given relative-frequency histogram.
83. D
Find the number of standard deviations from the mean corresponding to 55 and 65 points. Then, calculate the
percentage of data within this range of standard deviations of the mean.
84. B
Find the number of standard deviation of the mean having values 60 and 65 and then calculate the percentage
of data between these standard deviations.
85. A
Find the number of standard deviation at 45 points. Then, using the normal distribution curve, calculate the
percentage of students scoring less than 45 points.
86. B
Find the number of standard deviations above the mean, which has the value 65, and calculate the percent
data above this value using the normal distribution curve.
87. A
88.
89.
90.
91.
92.
93.
94.
Find the number of standard deviations at 75 points. Then, using the normal distribution curve, calculate the
percentage of students scoring more than 75 points.
C
Calculate the percent of data of this normal distribution lying between the values 170 centimeters and 180
centimeters.
B
Calculate the percent of data between the values 180 centimeters and 185 centimeters.
D
Find the percent of data of this distribution between the values 155 centimeters and 170 centimeters.
B
The mean of the given distribution is 175.
D
Find the percent of data of this distribution between the values 180 centimeters and 195 centimeters.
B
C
SHORT ANSWER
95.
96.
97.
98.
geometric; 32, 64, 128, 256
arithmetic; –43, –57, –71, –85
arithmetic; 5.1, 5.7, 6.3, 6.9
geometric; –405, 1215, –3645, 10935
99. geometric;
,
,
,
100. $17.50
Apply the formula for the nth term of an arithmetic sequence:
is the nth term, and d is the common difference.
101. 136 people
where
is the first term,
Apply the formula for the nth term of an arithmetic sequence:
is the nth term, and d is the common difference.
102. 29 ft
where
is the first term,
Apply the formula for the nth term of an arithmetic sequence:
is the nth term, and d is the common difference.
103. 6.75 h
where
is the first term,
Apply the formula for the nth term of an arithmetic sequence:
is the nth term, and d is the common difference.
104. $4.50
where
is the first term,
Apply the formula for the nth term of an arithmetic sequence:
is the nth term, and d is the common difference.
105. 1632
where
is the first term,
Use the formula
to find the sum of the arithmetic series.
106. 1311
Use the formula for the nth term of an arithmetic sequence:
Substitute the values of n,
and
in the formula
to find the value of n.
to find the sum of the arithmetic series.
107. 484
Use the formula for the nth term of an arithmetic sequence:
Substitute the values of n,
and
in the formula
to find the value of n.
to find the sum of the arithmetic series.
108.
Use the formula for the nth term of an arithmetic sequence:
Substitute the values of n,
and
in the formula
to find the value of
to find the sum of the arithmetic series.
109.
Use the formula for the nth term of an arithmetic sequence:
Substitute the values of n,
and
in the formula
to find the value of
to find the sum of the arithmetic series.
110. approximately $44,670
Apply the formula for the nth term of a geometric sequence:
the nth term, and r is the common ratio.
111. about 2.1 ft
where
is the first term,
is
Apply the formula for the nth term of a geometric sequence:
the nth term, and r is the common ratio.
112. approximately $5076.26
where
is the first term,
is
Apply the formula for the nth term of a geometric sequence:
the nth term, and r is the common ratio.
113. about 1838 million dollars
where
is the first term,
is
Apply the formula for the nth term of a geometric sequence:
the nth term, and r is the common ratio.
114. 729
where
is the first term,
is
Apply the formula for the nth term of a geometric sequence:
the nth term, and r is the common ratio.
where
is the first term,
is
115. approximately
Use the formula
to find the sum of the geometric series.
116. about 37.75 ft; no
Use the formula
117. about 5.07 in.
Use the formula
118. $7,127,948.64
Use the formula
119. 88.2%
Use the formula
120. 900 in. or 75 ft
Use the formula
to find the sum of the geometric series.
to find the nth term of the geometric series.
to find the nth term of the geometric series.
to find the nth term of the geometric series.
to find the sum of the infinite geometric series.
121. about 224.6 ft
Use the formula
to find the sum of the infinite geometric series.
122. 324 in. or 27 ft
Use the formula
to find the sum of the infinite geometric series.
123. 78 ft
The distance is given by the following series.
This series can be rewritten as the sum of two infinite geometric series as follows.
Use the formula
to find the sum of the infinite geometric series.
124. 10 ft
Use the formula
125.
to find the sum of the infinite geometric series.
126.
127.
128. about 18.3%
129.
Use the Fundamental Counting Principle to find the number of successes.
Determine the probability P(2 green thumbtacks, 2 blue thumbtacks, and 2 yellow thumbtacks) by using the
probability formula
=
.
130.
Use the Fundamental Counting Principle to find the number of successes.
Determine the probability P(3 red candles, and 2 white candles) by using the probability formula
=
.
131.
Use the Fundamental Counting Principle to find the number of successes.
Determine the probability P(4 shirts, 5 pairs of pants, 3 jackets) by using the probability formula
=
.
132.
There are 4 even numbers. So the probability can be obtained by simplifying
.
133. 50%
Calculate the percent of data of this normal distribution lying between 70 marks and 78 marks.
134. 34%
Calculate the percent of data of this normal distribution lying between the values 85 beats per minute and 90
beats per minute.
135. 13.5%
Calculate the percent of data of this normal distribution lying between the values 75 beats per minute and 80
beats per minute.
136. 16%
Calculate the percent of data of this normal distribution lying between the values 90 beats per minute and 110
beats per minute.
137. 2.5%
Calculate the percent of data of this normal distribution lying between the values 65 beats per minute and 75
beats per minute.
138.
139.