MGF 1106 Summer C 11 Ref: 625150
Review for Exam 1
Mr. Guillen
Exam 1 will be on 05/26/11 and cover the following sections: 2.1, 2.2, 2.3, 2.4, 2.5, 12.1, 12.2, 12.3.
Write the set in set-builder notation.
1) {2, 4, 6, 8}8}
1)
2) {}{
24, 28, 32, 36,..., 64}
2)
3) {}{
13, 14, 15, 16}
3)
4) {}{
9, 12, 15, 18,..., 39}
4)
5) {}{
42, 49, 56, 63,..., 112}
5)
Express the set in roster form.
6) {x | x is an integer between n
6 and 10}
6)
7) {x | x is a natural number multiple of f4}
7)
8) {x | x is a natural number multiple of f2}
8)
9) The set of the days of the week
9)
10) The set of seasons in a year
10)
TRUE/FALSE. Write ʹTʹ if the statement is true and ʹFʹ if the statement is false.
Tell whether the statement is true or false.
11) 16 ∉ {15, 13, 12, ..., 1}
11)
12) 9 ∈ {18, 27, 36, 45, 54}
12)
13) {}{
6} = {x | x is an even counting number between 8 and 14}
13)
14) 7 ∉ {x | x is an even counting number}
14)
Find n(A) for the set.
15) A = {100, 101, 102, . . ., 1000}
15)
16) A = {x | x is a month in the year}
16)
17) A = {x | x is a second in a minute}
17)
18) A = {x | x is a number on a clock face}
18)
19) A = {7, 9, 11, 13, 15}
19)
20) A = {700, 701, 702, . . ., 7000}
20)
Determine whether the sets are equal, equivalent, both, or neither.
21) {L, M, N, O} and {l, m, n, o}o}
21)
22) {}{
87, 85, 35} and {85, 35, 87}
22)
23) {}{
3, 12} and {3, 1, 2}
23)
24) {first, second, third} and {1, 2, 3}3}
24)
List all subsets or determine the number of subsets as requested.
25) Determine the number of subsets of {0}
25)
26) Determine the number of subsets of {mom, dad, son, daughter}
26)
27) Determine the number of subsets of {1, 2, 3, ..., 9}
27)
28) List all the subsets of {fox, dog, pig}.
28)
29) List all the subsets of {2}.
29)
30) List all the subsets of {wolf, hen, pig}.
30)
For the given sets, construct a Venn diagram and place the elements in the proper region.
31) Let U = {c, d, g, h, k, u, q}
A = {d, h, g, q}
B = {c, d, h, u}
31)
32) Let U = {1, 2, 3, 4, 5, 6, 7, 8}
A = {3, 6, 8}
B = {4, 6}
C = {1, 6, 7, 8}
Use the Venn diagram to find the requested set.
33) Find A ∩ B.
i
d
b
p
g
t
32)
33)
k
34) Find (A ∪ B)ʹ.
34)
7
z
r
6
3
f
35) Find A ∩ Bʹ.
35)
R
>
+
$
Z
@
F
36) Find Aʹ ∪ B.
36)
R
H
<
&
%
Y
#
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
37) A ∩ (B ∪ C)
37)
38) Cʹ ∩ Aʹ
38)
39) A ∪ (B ∩ C)
39)
40) (A ∩ B)ʹ
40)
41) A ∩ Bʹ
41)
42) (A ∪ B)ʹ
42)
Use the Venn diagram shown to list the set in roster form.
43) B
43)
44) A ∩ C
44)
45) (A ∪ B)ʹ
45)
46) (A ∩ B)ʹ
46)
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.
Let A = {1, 3, 5, 7}
B = {5, 6, 7, 8}
C = {5, 8}
D = {2, 5, 8}
U = {1, 2, 3, 4, 5, 6, 7, 8}.
Determine whether the statement is true or false.
47) C ⊆ D
48) A ⊄ A
47)
48)
49) {5} ⊆
} D
49)
50) C ⊂ A
50)
51) { } }⊂ U
51)
Solve the problem.
52) Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly
beans, and 17 like both red and green jelly beans. How many of the students surveyed like
neither red nor green jelly beans?
52)
53) Mrs. Bolloʹs second grade class of thirty students conducted a pet ownership survey.
Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5
students own both a cat and a dog. How many of the students surveyed own only a cat?
53)
54) Monticello residents were surveyed concerning their preferences for candidates Moore
and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor
Allen, 100 support both Moore and Allen, and 250 support only Moore. How many
residents support Moore or Allen?
54)
55) A survey of a group of 114 tourists was taken in St. Louis. The survey showed the
following:
55)
62 of the tourists plan to visit Gateway Arch;
47 plan to visit the zoo;
9 plan to visit the Art Museum and the zoo, but not the gateway Arch;
14 plan to visit the Art Museum and the Gateway Arch, but not the zoo;
16 plan to visit the Gateway Arch and the zoo, but not the Art Museum;
9 plan to visit the Art Museum, the zoo, and the Gateway Arch;
16 plan to visit none of the three places.
How many plan to visit the Art Museum only?
56) A survey of 140 college students was done to find out what elective courses they were
taking. Let A = the set of those taking art, B = the set of those taking basketweaving, and C
= the set of those taking canoeing. The study revealed the following information.
n(A) = 45 n(A ∩ B) = 12
n(B) = 55
n(A ∩ C) = 15
n(C) = 40 n(B ∩ C) = 23
n(A ∩ B ∩ C) = 2
How many students were not taking any of these electives?
56)
57) A local television station sends out questionnaires to determine if viewers would rather
see a documentary, an interview show, or reruns of a game show. There were 350
responses with the following results:
57)
105 were interested in an interview show and a documentary, but not reruns.
14 were interested in an interview show and reruns but not a documentary
49 were interested in reruns but not an interview show.
84 were interested in an interview show but not a documentary.
35 were interested in a documentary and reruns.
21 were interested in an interview show and reruns.
28 were interested in none of the three.
How many are interested in exactly one kind of show?
Construct a frequency distribution for the given qualitative data.
58) The blood types for 40 people who agreed to participate in a medical study were as
follows.
O
A
A
O
A
O
B
A
A
A
O
O
O
B
A
O
O
O
A
A
AB
O
O
B
O
O
O
O
B
AB
B
O
A
A
O
A
58)
O
A
O
AB
Construct a frequency distribution for the data.
Construct the requested grouped-data table. Use classes based on a single value.
59) The following data represent the total number of years of formal education for 40
employees of a bank.
13
16
14
12
17
18
15
17
13
13
13
17
14
11
15
16
12
19
17
16
17
19
18
17
19
12
17
15
13
14
14
13
15
13
13
13
59)
13
13
17
14
Construct a grouped-data table for the number of years of education.
60) A teacher asked each of her students how many novels they had read in the previous six
months. The results are shown below.
0
2
1
7
0
1
7
2
1
2
5
2
6
4
1
4
5
0
2
1
2
0
2
3
0
1
1
3
1
6
3
0
1
7
1
2
1
2
0
7
Construct a grouped-data table for the number of novels read.
60)
Construct the requested histogram.
61) The table gives the frequency distribution for the data involving the number of television
sets per household for a sample of 100 U.S. households.
61)
# of TVs Frequency
1
25
2
45
3
15
4
10
5
5
Construct a relative frequency histogram.
0.5
0.4
0.3
0.2
0.1
1
2
3
4
5
6
62) The table gives the frequency distribution for the data involving the number of radios per
household for a sample of 80 U.S. households.
# of TVs Frequency
1
5
2
10
3
30
4
25
5
10
Construct a relative frequency histogram.
0.625
0.5
0.375
0.25
0.125
1
2
3
4
5
62)
Find the mean for the list of numbers.
63) 5, 5, 10, 6, 11, 9 (Round to the nearest tenth)
63)
64) 20, 42, 71, 43, 125, 72 (Round to the nearest tenth)
64)
65) 8.776, 7.094, 6.809, 13.242, 5.370 (Round to the nearest thousandth)
65)
66) 1.38, 11.59, 13.81, 7.11, 4.85, 7.80, 15.89, 19.86 (Round to the nearest hundredth)
66)
Find the median.
67) 7, 2, 29, 14, 49, 34, 32
67)
68) 1, 10, 23, 29, 35, 45
68)
69) 10, 5, 21, 18, 24, 43, 32, 32
69)
Find the mode or modes.
70) 20, 22, 46, 22, 49, 22, 49
70)
71) 85, 50, 32, 50, 29, 85
71)
72) 65, 25, 65, 13, 25, 29, 56, 65
72)
Solve the problem. Round to the nearest hundredth, if necessary.
73) The following data gives the number of applicants that applied for a job at a given
company each month of 1999: 65, 68, 93, 77, 79, 81, 87, 89, 91, 93, 72, 65. What is the mode of
the data?
73)
74) The following data gives the number of applicants that applied for a job at a given
company each month of 1999: 65, 67, 94, 76, 79, 83, 86, 88, 90, 94, 75, 65. What is the mean of
the data?
74)
75) The following data gives the number of applicants that applied for a job at a given
company each month of 1999: 62, 71, 68, 74, 83, 77, 79, 86, 81, 68, 65, 62. What is the median
of the data?
75)
Find the standard deviation.
76) 42, 82, 77, 57, 82, 83, 60, 24, 57
76)
77) 290, 221, 260, 220, 111, 160, 174, 151, 110
77)
78) 17, 12, 10, 17, 17, 8, 16, 10, 7, 20
78)
79) 1, 2, 7, 6, 6, 19, 20, 5, 18
79)
Find the standard deviation for the given data.
80) Christine is currently taking college astronomy. The instructor often gives quizzes. On the
past seven quizzes, Christine got the following scores:
50 11 38.0 24 17 44 72
Round results to one decimal place.
80)
81) The manager of a small dry cleaner employs six people. As part of their personnel file, she
asked each one to record to the nearest one-tenth of a mile the distance they travel one
way from home to work. The six distances are listed below:
19.1 16.5 45.0 38.4 22.4 10.0
Round results to two decimal places.
81)
82) To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of
a specific model. The prices he was quoted are listed below:
$367 $210 $232 $276 $169 $162 $388 $325
Round results to the nearest ten cents.
82)
Find the range for the set of data numbers.
83) 28, 40, 19, 43, 58
83)
84) 114, 490, 131, 637, 359, 301
84)
85) 54, 136, 24, 91, 160
85)
Answer Key
Testname: MGF_1106_SUMMER_11_EXAM_1_REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
{x | x is an even natural number less than 10}0}
{x | x is a multiple of f4 between 20 and 68}
{x | x is an integer between n
12 and 17}
{x | x is a multiple of f3 between 6 and 42}
{x | x is a multiple of f7 between 35 and 119}
{}{
7, 8, 9}
{}{
4, 8, 12, . . .}
{}{
2, 4, 6, . . .}
{Friday, Monday, Saturday, Sunday, Thursday,y,
Tuesday, Wednesday}
{winter, spring, summer, fall}l}
TRUE
FALSE
FALSE
TRUE
n(A) = 901
n(A) = 12
n(A) = 60
n(A) = 12
n(A) = 5
n(A) = 6301
Equivalent
Both
Neither
Equivalent
2
16
512
{}{
fox, dog, pig}, {fox, dog}, {fox, pig}, {dog, pig}, {fox}, {dog}, {pig}, { }
{}{
2}, { }
{}{
wolf, hen, pig}, {wolf, hen}, {wolf, pig}, {hen, pig}, {wolf}, {hen}, {pig}, { }
32)
33) {}{
d, g}
34) ∅
Answer Key
Testname: MGF_1106_SUMMER_11_EXAM_1_REVIEW
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
54)
55)
56)
57)
58)
{}{
>, $}
{}{
Y, R, #, H, &}
{q, s, w, y}y}
{r, t}t}
{q, s, u, w, y, z}z}
{r, t, u, v, w, x, z}z}
{u, w}w}
{r, t, v, x}x}
{4, 7, 11, 12, 14}4}
{11, 13}3}
{1, 2, 5, 8, 10}0}
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14}4}
TRUE
TRUE
TRUE
FALSE
TRUE
8
3
500
14
48
168
Blood type
Frequency
O
A
B
AB
19
13
5
3
59)
Number of
years of
education Frequency
11
1
12
3
13
11
14
5
15
4
16
3
17
8
18
2
19
3
Answer Key
Testname: MGF_1106_SUMMER_11_EXAM_1_REVIEW
60)
Number of
novels Frequency
0
7
1
11
2
9
3
3
4
2
5
2
6
2
7
4
61)
0.6
0.5
0.4
0.3
0.2
0.1
1
2
3
4
5
6
62)
0.625
0.5
0.375
0.25
0.125
1
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
7.7
62.2
8.258
10.29
29
26
22.5
22
85, 50
65
2
3
4
5
Answer Key
Testname: MGF_1106_SUMMER_11_EXAM_1_REVIEW
73)
74)
75)
76)
77)
78)
79)
80)
81)
82)
83)
84)
85)
93 and 65
80.17
72.5
20.5
63.3
4.5
7.5
21.2
13.55
$87.20
39
523
136
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