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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the set by listing its elements.

1)


The set of states that border California.


1)


_______ A)


{ Oregon, Nevada, Utah}


B)


{ Oregon, Nevada, Arizona} C)


{ Washington, Utah, Arizona}


D)


{ Nevada, Utah}

2)


The set of letters needed to spell these words: toot, tot, too, to.


2)


_______ A)


{ t, t, o}


B)


{ t, t, o, o}


C)


{ t, o, o}


D)


{ t, o}

3)


{x ∈ N∣ 0 < x < 4}


3)


_______ A)


{ 1, 2, 3}


B)


{ 1, 2, 3, 4} C)


{ 0, 1, 2, 3}


D)


{ 0, 1, 2, 3, 4}

4)


The set of whole numbers greater than 2 and less than 6.


4)


_______ A)


{ 2, 3, 4, 5, 6}


B)


{ 2, 3, 4, 5} C)


{ 3, 4, 5}


D)


{ 3, 4, 5, 6}

5)


{x∣ x = 5n for some n ∈ N}


5)


_______ A)


∅


B)


{ 10, 15, 20, . . .} C)


{0, 5, 10, 15, . . .}


D)


{ 5, 10, 15, . . .}

Write the set in set builder notation. 6)


{ 7}


6)


_______ A)


{x∣ 7 < x < 7}


B)


{x∣ x > 7} C)


{x∣ x ≤ 7}


D)


{x∣ 7 ≤ x ≤ 7}

7)


{2, 4, 6, 8}


7)


_______ A)


{x ∈ N∣ x is even and x < 10}


B)


{x ∈ N∣ x < 10} C)


{x ∈ N∣ x is even}


D)


{x ∈ N∣ x is even and x ≤ 10}

8)


{ 13, 14, 15, 16}


8)


_______ A)


{x ∈ N∣ 12 < x < 17}


B)


{x∣ 13 < x < 16} C)


{x ∈ N∣ x < 17}


D)


{x ∈ N∣ 13 < x < 16}

9)


{ 10, 15, 20, 25, . . . , 60}


9)


_______ A)


{x∣ x = 5n for n ∈ N} B)


{x ∈ N∣ x = 5n for n ∈ N and 10 < x < 60} C)


{x ∈ N∣ x = 5n for n ∈ N and x ≥ 10} D)


{x ∈ N∣ x = 5n for n ∈ N and 5 < x < 65}

10)


The odd natural numbers less than 29.


10)


______ A)


{x ∈ N∣x < 29}


B)


{x ∈ N∣x < 28} C)


{x ∈ N∣x is odd and x ≤ 27}


D)


{x ∈ N∣x is odd and x ≤ 29}

Let A = {1, 3, 5, 7}, B = {5, 6, 7, 8}, C = {5, 8}, D = {2, 5, 8}, and U = {1, 2, 3, 4, 5, 6, 7, 8}. Decide if the set relationship is true or false.

11)


C ⊆ D


11)


______ A)


False


B)


True

12)


D ⊆ B


12)


______ A)


False


B)


True

13)


A ≠ {7, 5, 3, 1}


13)


______ A)


False


B)


True

14)


{5} ⊆ D


14)


______ A)


False


B)


True

15)


{0} ⊆ U


15)


______ A)


False


B)


True

16)


C ⊂ D


16)


______ A)


False


B)


True

17)


C ⊂ A


17)


______ A)


True


B)


False

Let U = {q, r, s, t, u, v, w, x, y, z}, A = {q, s, u, w, y}, B = {q, s, y, z}, and C = {v, w, x, y, z}. List the elements in the following set.

18)


A ∩


18)


______ A)


{t, v, x}


B)


{r, s, t, u, v, w, x, z} C)


{q, s, t, u, v, w, x, y}


D)


{u, w}

19)



19)


______ A)


{r, t, v, x}


B)


{t, v, x} C)


{r, s, t, u, v, w, x, z}


D)


{s, u, w}

20)



20)


______ A)


{t, v, x}


B)


{r, t, u, v, w, x, z} C)


{s, u, w}


D)


{q, s, t, u, v, w, x, y}

21)


∪ B


21)


______ A)


{r, s, t, u, v, w, x, z}


B)


{q, r, s, t, v, x, y, z}C)


{q, s, t, u, v, w, x, y}


D)


{s, u, w}

22)


A ∪ (B ∩ C)


22)


______ A)


{q, s, u, w, y, z}


B)


{q, w, y} C)


{q, r, w, y, z}


D)


{q, y, z}

23)


A ∩ (B ∪ C)


23)


______ A)


{q, r, w, y, z}


B)


{q, y, z} C)


{q, s, u, w, y, z}


D)


{q, s, w, y}

24)


∪


24)


______ A)


{s, t}


B)


{q, r, s, t, u, v, x, z} C)


{w, y}


D)


{q, s, u, v, w, x, y, z}

25)


∩


25)


______ A)


{q, r, s, t, u, v, x, z}


B)


{r, t} C)


{q, s, u, v, w, x, y, z}


D)


{w, y}

Draw and shade a Venn diagram that corresponds to the set. 26)


∩


26)


______ A)



B)


27)


∪


27)


______ A)



B)


28)


(A ∪ B) ∩


28)


______ A)



B)


29)


(A ∩ B) ∪


29)


______ A)



B)


30)


∩ (A ∪ B)


30)


______ A)



B)


31)


( ∪ B) ∩ C


31)


______ A)



B)


32)


A ∪ (B ∩ )


32)


______ A)



B)


Find the number of subsets. 33)


{ 8, 9, 10}


33)


______ A)


7


B)


6


C)


8


D)


3

34)


{x∣x is an even number between 15 and 29}


34)


______ A)


256


B)


128


C)


6


D)


64

35)


{0}


35)


______ A)


2


B)


4


C)


1


D)


0

36)


{x∣x is a day of the week}


36)


______ A)


127


B)


256


C)


124


D)


128

37)


{1, 2, 3, . . . , 9}


37)


______ A)


1024


B)


512


C)


508


D)


16

Provide an appropriate response. 38)


If A ∩ B = A ∩ C, is it necessarily true that B = C?


38)


______ A)


No


B)


Yes

39)


Yes or no? If = for nonempty sets A and B, must


39)


______ A)


Yes


B)


No

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

40)


Given the objects revealed below, consider the following definitions.L = {large objects}B = {black objects}T = {triangular objects}Place the objects in the correct regions of the Venn diagram.

Objects:


40)


_____________

41)


Given the objects revealed below, consider the following definitions.S = {small objects}C = {circular objects}B = {black objects}Place the objects in the correct regions of the Venn diagram.

Objects:


41)


_____________

42)


Given the objects revealed below, consider the following definitions.R = {rectangular objects}S = {striped objects}L = {large objects}Place the objects in the correct regions of the Venn diagram.

Objects:


42)


_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify by type (cardinal, ordinal, or nominal) the number that appears in the sentence.

43)


Monti ordered catalog item number 96325.


43)


______ A)


Cardinal


B)


Nominal


C)


Ordinal

44)


The baby gained four ounces since his last check-up.


44)


______ A)


Ordinal


B)


Cardinal


C)


Nominal

45)


The prize in the raffle is five-hundred dollars.


45)


______ A)


Nominal


B)


Ordinal


C)


Cardinal

46)


Max placed fourteenth in the cross-country race.


46)


______ A)


Nominal


B)


Cardinal


C)


Ordinal

47)


The physician prescribed five different types of pills for Aunt Martha.


47)


______ A)


Ordinal


B)


Nominal


C)


Cardinal

48)


The novel has 594 pages.


48)


______ A)


Nominal


B)


Ordinal


C)


Cardinal

49)


The math assignment is on page 594.


49)


______ A)


Nominal


B)


Ordinal


C)


Cardinal

50)


The savings account number is 01059637.


50)


______ A)


Ordinal


B)


Nominal


C)


Cardinal

51)


Hal's birthday is on the fifteenth day of the month.


51)


______ A)


Nominal


B)


Cardinal


C)


Ordinal

52)


Move the box to the fifth floor.


52)


______ A)


Nominal


B)


Cardinal


C)


Ordinal

Decide if the sets are equivalent to one another. 53)


{ 24, 58, 51, -58} and {x|x is a letter in the phrase "I AM A MAN"}


53)


______ A)


Not equivalent


B)


Equivalent

54)


{ 4, 2, 5, 7} and { -4, 2, -5, 7}


54)


______ A)


Equivalent


B)


Not equivalent

55)


{0, 7, 10, 19} and { 7, 10, 19}


55)


______ A)


Equivalent


B)


Not equivalent

56)


{Mon, Tue, Wed} and {Oct, Nov, Dec}


56)


______ A)


Not equivalent


B)


Equivalent

57)


{a, b, c, d} and {A, B, C, D}


57)


______ A)


Not equivalent


B)


Equivalent

58)


{0} and { 874}


58)


______ A)


Not equivalent


B)


Equivalent

59)


∅ and


59)


______ A)


Equivalent


B)


Not equivalent

Use counting to determine the whole number that corresponds to the cardinality of the set. 60)


A = { 8, 10, 12, 14, 16}


60)


______ A)


16


B)


5


C)


4


D)


2

61)


A = { 400, 401, 402, . . . , 4000}


61)


______ A)


3601


B)


3600


C)


4000


D)


4

62)


A = {x∣x is a month in the year}


62)


______ A)


1


B)


12


C)


24


D)


52

63)


A = {x∣x is a number on a clock face}


63)


______ A)


12


B)


3


C)


6


D)


24

64)


A = {x∣x is a second in a minute}


64)


______ A)


60


B)


120


C)


Infinite


D)


12

65)


A = {x∣x ∈ N and 12 ≤ x ≤ 31}


65)


______ A)


18


B)


20


C)


44


D)


43

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Show that the sets are equivalent by carefully describing a one-to-one correspondence between the sets.

66)


The set of whole numbers and the set of even natural numbers:W ={0, 1, 2, 3, . . . } and E = {2, 4, 6, 8, . . . }.


66)


_____________

67)


The set of natural numbers and the set of powers of 6:N = {1, 2, 3, 4, . . . } and { , , , , . . . }.


67)


_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide if the set is finite.

68)


{ 6, 7, 8, . . . , 24}


68)


______ A)


Finite


B)


Infinite

69)


{x∣x is a counting number larger than 562}


69)


______ A)


Infinite


B)


Finite

70)


{x∣x is an odd counting number}


70)


______ A)


Finite


B)


Infinite

71)


{x∣x is a 12-headed lizard}


71)


______ A)


Infinite


B)


Finite

72)


{whole numbers divisible by 38 and 51}


72)


______ A)


Finite


B)


Infinite

73)


{the hairs on your head}


73)


______ A)


Infinite


B)


Finite

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. A and B designate finite sets. Decide whether the statement is true or false.

74)


n(A ∪ B) = n(A) + n(B)


74)


______

75)


If A ⊆ B, then n(A) < n(B).


75)


______

76)


If n(A ∪ B) = n(A), then B ⊂ A.


76)


______

77)


If n(A) > n(B), then A ⊈ B


77)


______

78)


n(A ∩ B) = n(B ∩ A)


78)


______

79)


n(A ∪ B) = n(A) + n(B) - n(A ∩ B)


79)


______

80)


n(A ∩ B) = n(A) - n(B)


80)


______

81)


n(A ∪ B) + n(A ∩ B) = n(A) + n(B)


81)


______

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. Use a Venn diagram to find your answer.

82)


The subsets A, B, and C of the universe U satisfy the following conditions:n(A) = 70n(B) = 78n(C) = 72n(A ∩ B) = 14n(A ∩ C) = 16n(B ∩ C) = 10n(A ∩ B ∩ C) = 8n( ∩ ∩ ) = 141

Find n(U).


82)


______ A)


258


B)


329


C)


188


D)


339

83)


The subsets A, B, and C of the universe U satisfy the following conditions:n(U) = 202n(A) = 68n(B) = 88n(A ∩ B) = 29n(A ∩ C) = 32n(A ∩ B ∩ C) = 15n( ∩ B ∩ ) = 44n( ∩ ∩ ) = 51

Find n(C).


83)


______ A)


40


B)


24


C)


41


D)


71

84)


The subsets A, B, and C of the universe U satisfy the following conditions:n(A ∪ B ∪ C) = 149n(A ∩ B ∩ C) = 20n(A ∩ B) = 42n(A ∩ C) = 39n(B ∩C) = 37n(A) = 101n(B) = 74n(C) = 72n(U) = 149

Find n( ∩ B ∩ C).


84)


______ A)


17


B)


19


C)


18


D)


16

Solve the problem. Use a Venn diagram, as needed. 85)


A local television station sent out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 600 responses with the following results:

180 were interested in an interview show and a documentary, but not reruns; 24 were interested in an interview show and reruns but not a documentary; 84 were interested in reruns but not an interview show; 144 were interested in an interview show but not a documentary; 60 were interested in a documentary and reruns; 36 were interested in an interview show and reruns; 48 were interested in none of the three.

How many are interested in exactly one kind of show?


85)


______ A)


268


B)


278


C)


298


D)


288

86)


A survey of 220 families showed the following:

83 had a dog; 64 had a cat; 28 had a dog and a cat; 84 had neither a cat nor a dog nor a parakeet; 6 had a cat and dog and a parakeet.

How many had a parakeet only?


86)


______ A)


32


B)


17


C)


27


D)


22

87)


A survey of a group of 111 tourists was taken in St. Louis. The survey showed the following:

61 of the tourists plan to visit Gateway Arch; 45 plan to visit the zoo; 9 plan to visit the Art Museum and the zoo, but not the Gateway Arch; 12 plan to visit the Art Museum and the Gateway Arch, but not the zoo; 18 plan to visit the Gateway Arch and the zoo, but not the Art Museum; 6 plan to visit the Art Museum, the zoo and the Gateway Arch; 15 plan to visit none of the three places.

How many plan to visit the Art Museum only?


87)


______ A)


45


B)


14


C)


96


D)


33



Let A, B, and C be finite sets, with A ⊆ B ⊂ C and n(B) = 3. What are the possible values of n(A) and n(C)?


88)


______ A)


n(A) = 0, 1, or 2; n(A) = 3, 4, 5, . . . B)


n(A) = 1 or 2; n(A) = 3, 4, 5, . . . C)


n(A) = 0, 1, 2, or 3; n(A) = 4, 5, 6, . . . D)


n(A) = 1, 2, or 3; n(A) = 4, 5, 6, . . .


89)


Use the concept of cardinality of sets to explain why 2 < 5.


89)


_____________

90)


Explain why the sets {a, b, c} and {1, 2, 3} are equivalent but not equal.


90)


_____________

91)


Explain why no one-to-one correspondence can be established between the elements of {4, 7, 9} and {w, x, y, z}.


91)


_____________

92)


Let A and B be finite sets. Explain why


92)


_____________

93)


Let A and B be finite sets. Explain why


93)


_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

94)


Sets A and B match. Therefore, sets A and B are _________.


94)


______ A)


equivalent


B)


finite C)


equal


D)


All of the above


95)


Use number strips to illustrate the transitive property of "less than."


95)


_____________

96)


Use sets to illustrate the transitive property of "less than."


96)


_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem.

97)


Let A = { p, q, r, s, t} and B = { p, r, t, u, v}. Find n(A ∪ B).


97)


______ A)


2


B)


3


C)


10


D)


7

98)


Let n(A) = 6, n(B) = 13, and n(A ∩ B) = 4. Find n(A ∪ B).


98)


______ A)


14


B)


16


C)


15


D)


19

99)


Let A = {x∣x is a natural number divisible by 3 and x < 100 }, and let B = {x∣x is a natural number divisible by 11 and x < 100 }. Find n(A ∪ B).


99)


______ A)


42


B)


45


C)


3


D)


39

100)


Let n(A) = 8, n(B) = 21, and n(A ∪ B) = 25. Find n(A ∩ B).


100)


_____ A)


6


B)


4


C)


12


D)


2

101)


Let n(B) = 48, n(A ∩ B) = 9, and n(A ∪ B) = 84. Find n(A).


101)


_____ A)


45


B)


36


C)


47


D)


43

102)


Let n(A) = 15, n(A ∪ B) = 43, and n(A ∩ B) = 11. Find n(B).


102)


_____ A)


38


B)


40


C)


28


D)


39

Answer the question. 103)


Which property of addition of whole numbers is illustrated?


103)


_____ A)


Additive-identity property B)


Associative property C)


Commutative property

104)




104)


_____ A)


Associative property B)


Additive-identity property C)



105)




105)


_____ A)




Commutative property C)


Additive-identity property

106)




106)


_____ A)


Commutative property B)




Associative property

107)




107)


_____ A)


Additive-identity property B)


Associative property C)



108)


Draw number strips to illustrate 3 + 5 = 8.


108)


_____ A)



B)



C)


109)


Illustrate (3 + 2) + 4 = 3 + (2 + 4) with a number-line diagram.


109)


_____ A)


B)


C)


110)


Illustrate 8 + 0 = 8 with a number-line diagram.


110)


_____ A)


B)


C)


111)


Illustrate 7 + 4 = 11 with a number-line diagram.


111)


_____ A)


B)


C)


Determine if the given set of whole numbers is closed under addition. 112)


{1, 3, 5, 7, . . . }


112)


_____ A)


Not closed


B)


Closed

113)


{ 6}


113)


_____ A)


Closed


B)


Not closed

114)


{0}


114)


_____ A)


Not closed


B)


Closed

115)


{0, 1}


115)


_____ A)


Closed


B)


Not closed

116)


{ 6, 12, 18, 24, . . . }


116)


_____ A)


Closed


B)


Not closed

117)


{n ∈ N|n ≤ 37}


117)


_____ A)


Not closed


B)


Closed

118)


{n ∈ N|n ≥ 59}


118)


_____ A)


Closed


B)


Not closed

What property of addition is used in the equality? 119)


3 + 7 = 7 + 3


119)


_____ A)




B)


Closure property C)




D)



120)


( 2 + 2) + 1 = 2 + ( 2 + 1)


120)


_____ A)


Closure property


B)






D)



121)


0 + 8 = 8


121)


_____ A)




B)


Closure property C)




D)



122)


1253 + 23,618 is a whole number


122)


_____ A)


Closure property


B)






D)



123)


21 + ( 34 + 58) = 21 + ( 58 + 34)


123)


_____ A)




B)


Closure property C)




D)



SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. What is the fact family that contains the equality?

124)


8 + 6 = 14


124)


____________

125)


0 + 9 = 9


125)


____________

126)


6 - 1 = 5


126)


____________

127)


1 - 0 =1


127)


____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which subtraction model (take-away, missing addend, comparison, or measurement) corresponds best to the problem?

128)


Jane has $ 10 in her wallet. If she spends $ 3 on a book, how much money will she have left?


128)


_____ A)


Measurement


B)


Take-away C)


Comparison


D)


Missing addend

129)


Last year the hatch-back model of a new car cost $16,322. This year's model costs $16,383. How much more does this year's model cost?


129)


_____ A)


Comparison


B)


Take-away C)


Measurement


D)


Missing addend

130)


Jim had 15 oranges and gave away 2 of them. How many oranges did he have left?


130)


_____ A)


Comparison


B)


Take-away C)


Missing addend


D)


Measurement

131)


Sonya is driving 520 miles to get home from college. If she drives 305 miles the first day, how many miles remain?


131)


_____ A)


Missing addend


B)


Comparison C)


Take-away


D)


Measurement

132)


Sam drove from home to his grandmother's who lives 209 miles away. On the way back home, he drove 93 miles before his car broke down. How far away from home was he?


132)


_____ A)


Take-away


B)


Measurement C)


Comparison


D)


Missing addend

133)


A coffee can comes packed with enough ground coffee to make 80 cups of coffee. After 35 cups have been made, how many cups of coffee can be made with the remaining ground coffee?


133)


_____ A)


Comparison


B)


Measurement C)


Missing addend


D)


Take-away

134)


Dinah promised to make fruit baskets for her school bazaar. On Monday, she made 136 baskets and on Tuesday, she made 177 baskets. How many more baskets did she make on Tuesday than on Monday?


134)


_____ A)


Take-away


B)


Measurement C)


Missing addend


D)


Comparison

Place parentheses, if needed, to turn this into a true statement. 135)


10 - 4 - 3 = 9


135)


_____ A)


( 10 - 4) - 3 = 9


B)


( 10 - 4 - 3) = 9 C)


10 - ( 4 - 3) = 9


D)


No parentheses needed

136)


10 + 5 - 6 = 9


136)


_____ A)


10 + ( 5 - 6) = 9


B)


( 10 + 5 - 6) = 9 C)


( 10 + 5) - 6 = 9


D)



137)


8 - 2 - 5 + 3 = 14


137)


_____ A)


( 8 - 2) - 5 + 3 = 14


B)


8 + 2 - ( 5 + 3) = 14 C)


8 - ( 2 - 5) + 3 = 14


D)



138)


10 - 3 - 7 - 1 = 1


138)


_____ A)


( 10 - 3) - 7 - 1 = 1


B)


10 - ( 3 - 7) - 1 = 1 C)


10 - 3 - ( 7 - 1) = 1


D)



139)


8 + 10 - 8 + 3 = 7


139)


_____ A)


( 8 + 10) - 8 + 3 = 7


B)


8 + 10 - ( 8 + 3) = 7 C)


8 + ( 10 - 8) + 3 = 7


D)



Solve the problem. 140)


Follow the pattern in the first array to fill in the missing entries in the second array.


140)


_____ A)


From upper left to lower right: 10, 33, 43 B)


From upper left to lower right: 26, 27, 53 C)


From upper left to lower right: 6, 13, 19

141)


Follow the pattern in the triangle on the left to place the numbers 4, 5, 6, 7, 8, 9, in the triangle on the right.


141)


_____ A)


B)


C)


142)


Use the pattern of tiles to find the sum of 1 + 3 + 5 + . . . + 201


142)


_____ A)


10,200


B)


10,201


C)


10,000

Complete the puzzle, as instructed. 143)


Insert numbers so that all rows, columns, and diagonals sum to the same constant.


143)


_____ A)


B)


C)


D)


144)




144)


_____ A)


B)


C)


D)


145)




145)


_____ A)


B)


C)


D)


146)


Complete the following chart using the numbers 0 to 9, each only once, so that the sum of each of the horizontal rows is 9 and the sum of the numbers in the second column is one more than the sum of the numbers in the first column.


146)


_____ A)



B)


C)



D)


SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.

147)


Make up a word problem that uses the set model of addition to illustrate 20 + 17.


147)


____________

148)


Make up a word problem that uses the measurement model of addition to illustrate 13 + 25.


148)


____________

149)


Make up a word problem thath uses the comparison model of subtraction to illustrate 25 - 13.


149)


____________

150)


Make up a word problem which uses the missing-addend model of subtraction to illustrate 250 - 130.


150)


____________

151)


Make up a word problem which uses the take-away model of subtraction to illustrate 85¢ - 27¢.


151)


____________

152)


Make up a word problem which uses the measurement model of subtraction to illustrate 18 - 11.


152)


____________

153)


Addition problems arise in everyday living. Make up an addition problem that might occur when planning a party, and name the conceptual model of addition that best corresponds to your problem.


153)


____________

154)


Addition problems arise in everyday living. Make up a subtraction problem that might occur when preparing a meal, and name the conceptual model that best corresponds to your problem.


154)


____________

155)


In order to add 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12, Mary wrote the sum as (5 + 12) + (6 + 11) + (7 + 10) + (8 + 9) = 17 + 17 + 17 + 17 = 68. What properties of addition justify Mary's procedure?


155)


____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. What property of multiplication is illustrated in the diagram below?

156)


The shaded rods represent 2-rods.The unshaded rods represent 3-rods.


156)


_____ A)




B)


Closure property C)




D)


Distributive property

157)



157)


_____ A)




Multiplication-by-zero property C)


Distributive property D)



158)



158)


_____ A)




B)


Distributive property C)


Closure property


D)



159)



159)


_____ A)


Distributive property B)




Multiplicative-identity property D)



160)



160)


_____ A)


Multiplicative-identity property B)




Associative property D)



161)



161)


_____ A)


Multiplication-by-zero property B)


Multiplicative-identity property C)





162)



162)


_____ A)






Distributive property D)


Multiplicative-identity property

Identify the multiplication model that best fits the problem. Do not solve the problem. 163)


Suppose there are 2 roads connecting town A to town B and 3 roads connecting town B to town C. In how many ways can a person travel from A to C via B?


163)


_____ A)


Cartesian product model


B)


Array model C)


Set model


D)


Measurement model

164)


How many months are there in 15 years?


164)


_____ A)


Measurement model


B)


Cartesian product model C)


Set model


D)


Array model

165)


Ajay can bike 68 miles a day whil he is on vacation. If he can vacation for 16 days, what is the maximum distance he can cover?


165)


_____ A)


Measurement model


B)


Array model C)


Set model


D)



166)


The school band forms 14 rows with 8 members in each row when it marches. How many members are in the school band?


166)


_____ A)




B)


Measurement model C)


Set model


D)


Array model

167)


Jama drives 13 miles round trip each day to work. If she works 6 days each week, how many miles each week does she drive to work?


167)


_____ A)




B)


Measurement model C)


Array model


D)


Set model

168)


How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not allowed?


168)


_____ A)


Measurement model


B)


Array model C)




D)


Set model

Illustrate and find the product by the indicated method. 169)


Use repeated addition on your calculator to find 6 × 378.


169)


_____ A)


378 × 378 × 378 × 378 × 378 × 378 = 2268 B)


378 + 378 + 378 + 378 + 378 + 378 = 2268

170)


Use repeated addition on your calculator to find 6384 × 5.


170)


_____ A)


6384 × 5 = 5 × 6384 = 6384 + 6384 + 6384+ 6384 + 6384 = 31,920 B)


6384 × 5 = 5 × 6384 = 6384 × 6384 × 6384 × 6384 × 6384 = 31,920

171)


A= {i, a} and B = {t, d, m}. Use a crossing-line pattern to find A × B.


171)


_____ A)


{i, a} × {t, d, m} = 6

B)


{i, t} × {a, d} × {m} = 8

172)


A = {0} and B = { 10, 20, 30}. Use a crossing-line pattern to find A × B.


172)


_____ A)


{0} × { 10, 20, 30} = 3


B)


{0, 10} × { 20, 30} = 4

173)


A = { 5, 2, 9, 6} and B = {0, 1}. Use crossing-line pattern to find A × B.


173)


_____ A)


{ 5, 0} × { 2,1} × { 9, 6} = 12

B)


{ 5, 2, 9, 6} × {0, 1} = 8

Determine if the given set of whole numbers is closed under multiplication. 174)


{1, 3, 5, 7, . . . }


174)


_____ A)


Closed


B)


Not closed

175)


{1, 2, 3, 4, . . . }


175)


_____ A)


Not closed


B)


Closed

176)


{0, 1}


176)


_____ A)


Not closed


B)


Closed

177)


{1, 2, 3, 4, . . ., 48}


177)


_____ A)


Not closed


B)


Closed

178)


{ 0, 1, 2, 4, 5, 6, . . . } (that is, the whole numbers except for 3)


178)


_____ A)


Closed


B)


Not closed

179)


{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, . . . } (that is, the whole numbers except for 12)


179)


_____ A)


Not closed


B)


Closed

180)


{1, , , , . . . }


180)


_____ A)


Closed


B)


Not closed

What property of whole-number multiplication justifies the equality? 181)


4 ∙ 1 = 4


181)


_____ A)




Multiplicative-identity property C)





182)


6(x + 6) = 6x + 6 ∙ 6


182)


_____ A)








Multiplicative-identity property

183)


( 9 ∙ 1) ∙ 1 = 9 ∙ ( 1 ∙ 1)


183)


_____ A)









184)


0 ∙ 48 = 0


184)


_____ A)


Multiplication-by-zero property B)


Closure property C)





185)


68 ∙ 78 = a whole number


185)


_____ A)


Multiplicative-identity property B)




Closure property D)


Multiplication-by-zero property

186)


23 ∙ 656 + 77 ∙ 656 = 100 ∙ 656 = 65,600


186)


_____ A)




B)






D)


Closure property

Use the indicated model of multiplication to illustrate the statement. 187)


3 ∙ (5 ∙ 2) = (3 ∙ 5) ∙ 2; array model


187)


_____ A)


3 ∙ (5 ∙ 2) has three sets of blocks with 5 rows and 2 columns in each set.

3 sets of these

(3 ∙ 5) ∙ 2 has two sets of blocks with 3 rows and 5 columns in each set.

2 sets of these B)


3 ∙ (5 ∙ 2) has three sets of blocks with 1 row and 10 columns in each set.

3 sets of these

(3 ∙ 5) ∙ 2 has two sets of blocks with 1 row and 15 columns in each set.

2 sets of these

188)


(2 ∙ 3) ∙ 4 = 2 ∙ (3 ∙ 4); array model


188)


_____ A)


(2 ∙ 3) ∙ 4 has four sets of blocks with 2 rows and 3 columns in each set.

4 sets of these

2 ∙ (3 ∙ 4) has two sets of blocks with 3 rows and 4 columns in each set.

2 sets of these B)


(2 ∙ 3) ∙ 4 has six sets of blocks with 1 column and 4 rows in each set.

6 sets of these

2 ∙ (3 ∙ 4) has 12 sets of blocks with 1 column and 2 rows in each set.

12 sets of these

189)


3 x 4 = 4 x 3; set model


189)


_____ A)


3 x 4 has three sets of four elements each.

4 x 3 has four sets of three elements each.

B)


3 x 4 has four sets of three elements each.

4 x 3 has three sets of four elements each.

190)


7 x 1 = 1 x 7; number-line model


190)


_____ A)


7 x 1

1 x 7 B)


7 x 1

1 x 7

What fact family is associated with the rectangular array? 191)


527 by 9


191)


_____ A)


527 ∙ 9 = 4743 4743 ÷ 527 = 9 9 ∙ 527 = 4743 4743 ÷ 9 = 527

B)


527 ∙ 9 = 9 ∙ 527 4743 ÷ 527 = 527 ÷ 4743 4743 ÷ 9 = 9 ÷ 4743

Identify which of three conceptual models of division (repeated subtraction, partition, missing-factor) best corresponds to the problem.

192)


A group of 4 people wants to buy a boat. The boat costs $256. If they all pay the same amount, how much is each person's share?


192)


_____ A)


Partition B)


Missing-factor C)


Repeated subtraction

193)


The city bridge has 3 lanes, all carrying equal numbers of cars. If 192 cars drive across the bridge, how many cars cross in each lane?


193)


_____ A)


Missing-factor B)


Partition C)


Repeated subtraction

194)


A student arranges to pay off a loan with monthly payments. If the loan is for $1800 and the monthly payment is $225, how many months will it take to pay off the loan?


194)


_____ A)


Partition B)


Repeated subtraction C)


Missing-factor

195)


A wealthy patron dies and leaves her entire estate of 16 million dollars to 4 charities. If each charity receives the same amount, how much does each receive?


195)


_____ A)


Repeated subtraction B)


Missing-factor C)


Partition

Use repeated subtraction on your calculator to compute the division problem, where a remainder is possible.

196)


18 ÷ 3


196)


_____ A)


5 R 2


B)


5 R 3


C)


6


D)


7

197)


48 ÷ 8


197)


_____ A)


5 R 8


B)


6


C)


7


D)


5 R 7

198)


312 ÷ 39


198)


_____ A)


8


B)


7 R 39


C)


9


D)


7 R 38

199)


8635 ÷ 785


199)


_____ A)


11


B)


1


C)


2


D)


12

200)


327 ÷ 6


200)


_____ A)


54


B)


54 R 3


C)


57


D)


54 R 5

201)


5493 ÷ 915


201)


_____ A)


6 R 3


B)


6 R 2


C)


9


D)


6

Solve for the unknown whole number in the expression. 202)


y ÷ 5 = 5 R 2


202)


_____ A)


35


B)


25


C)


23


D)


27

203)


37 ÷ x = 6 R 1


203)


_____ A)


16


B)


6


C)


5


D)


7

Solve the problem. 204)


Rewrite the following in the form of a single exponential: ∙


204)


_____A)


42


B)



C)


12


D)


205)




205)


_____ A)


0


B)


30


C)



D)


206)


Rewrite the following in the form of a single exponential:


206)


_____ A)



B)



C)



D)


207)




207)


_____ A)



B)


C)



D)


Cannot be simplified

208)


Write the following as for some whole number m: 4 ∙ 8


208)


_____ A)



B)



C)



D)


209)


Write the following as for some whole number m:


209)


_____ A)



B)



C)



D)


210)


Find the exponent that makes the equation true: = 19,683


210)


_____ A)


18


B)


10


C)


9


D)


36

211)


Find the exponent that makes the equation true: = 1,048,576


211)


_____ A)


10


B)


50


C)


30


D)


9

212)


Find the exponent that makes the equation true: = 32,768


212)


_____ A)


30


B)


13


C)


15


D)


45

213)


Find the exponent that makes the equation true: = 216.


213)


_____ A)


9


B)


18


C)


4


D)


3



What division fact is illustrated by the diagram?


214)


_____ A)


15 ÷ 3 = 5


B)


3 x 5 = 5 x 3

215)


What division fact is illustrated by the diagram?


215)


_____ A)


12 ÷ 4 = 3


B)


4 x 3 = 3 x 4


216)


Use the distributive property of multiplication over addition for whole numbers to make it easy to compute 7 ∙ 102 mentally.


216)


____________


1)


B 2)


D 3)


A 4)


C 5)


D 6)


D 7)


A 8)


A 9)


D 10)


C 11)


B 12)


A 13)


A 14)


B 15)


A 16)


B 17)


B 18)


D 19)


A 20)


B 21)


B 22)


A 23)


D 24)


B 25)


B 26)


B 27)


A 28)


A 29)


B 30)


A 31)


A 32)


B 33)


C 34)


B 35)


A 36)


D 37)


B 38)


A 39)


A 40)


41)


42)


43)


B 44)


B 45)


C 46)


C 47)


C 48)


C 49)


B 50)


B 51)


C 52)


C 53)


B 54)


A 55)


B 56)


B 57)


B 58)


B 59)


B 60)


B 61)


A 62)


B 63)


A 64)


A 65)


B 66)


The correspondence 0 ↔ 2, 1 ↔ 4, 2 ↔ 6, . . . , w ↔ 2w + 2, . . . shows that the sets are equivalent. 67)


The correspondence 1 ↔ , 2 ↔ , 3 ↔ , . . . , n ↔ , . . . shows that the sets are equivalent. 68)


A 69)


A 70)


B 71)


B 72)


B 73)


B 74)


FALSE 75)


FALSE 76)


FALSE 77)


TRUE 78)


TRUE 79)


TRUE 80)


FALSE 81)


TRUE 82)


B 83)


D 84)


A 85)


D 86)


B 87)


B 88)


C 89)


Answers will vary. Sample answer: Let A = {a, b} with n(A) = 2, and let B = {a, b, c, d, e} with n(B) = 5. Since A is a proper subset of B, n(A) < n(B). Therefore, 2 < 5.

90)


The sets are equivalent because they both have a cardinality of three. The sets are not equal because they do not contain the same elements.

91)


A one-to-one correspondence cannot be established because the sets do not have the same cardinality. 92)


Answers will vary. Sample answer: The set contains only the elements of A that are also elements of B. Thus, cannot have more elements than A. Therefore, n(A) ≥ n(A ∩ B).

93)


Answers will vary. Sample answer: The set contains all of the different elements that are found in either set A or set B. Therefore A cannot have more elements than A ∪ B, and n(A ∪ B) ≥ n(A).

94)


A 95)


Answers will vary. Sample answer: is less than and is less than therefore is less than .

96)


Answers will vary. Sample answer: is less than and is less

than therefore is less than . 97)


D 98)


C 99)


D 100)


B 101)


A 102)


D 103)


C 104)


B 105)


B 106)


C 107)


C 108)


A 109)


C 110)


A 111)


C 112)


A 113)


B 114)


B 115)


B 116)


A 117)


A 118)


A 119)


C 120)


C 121)


D 122)


A 123)


A 124)


8 + 6 = 14 14 - 8 = 6 6 + 8 = 14 14 - 6 = 8

125)


0 + 9 = 9 9 - 0 = 9 9 + 0 = 9 9 - 9 = 0

126)


5 + 1 = 6 6 - 1 = 5 1 + 5 = 6 6 - 5 = 1

127)


1 + 0 = 1 1 - 0 = 10 + 1 = 1 1 - 1 = 0

128)


B129)


A 130)


B 131)


A 132)


B 133)


C 134)


D 135)


C 136)


D 137)


C 138)


C 139)


B 140)


C 141)


B 142)


B 143)


D 144)


C 145)


D 146)


D 147)


Answers will vary. Sample answer: Marta has two boxes of cards. One box contains 20 cards and the other box contains 17 cards. How many cards does Marta have altogether?

148)


Answers will vary. Sample answer: Sam must travel 13 miles to get to school and an additional 25 miles to get to work. How far must Sam travel altogether?

149)


Answers will vary. Sample answer: Beth has a collection of 25 dolls and Martha has a collection of 13 dolls. How many more dolls does Beth have in her collection than Amy has in hers?

150)


Answers will vary. Sample answer: Megan hopes to collect 250 cans of food for the food drive. How many more cans does she need if she already has 130 cans?

151)


Answers will vary. Sample answer: Carrie starts with 85¢ and spends 27¢ to buy some candy. How much money does Carrie have left?

152)


Answers will vary. Sample answer: On Wednesday, Benjamin rode 18 miles on the bike trail to his campsite. On Thursday, he rode back 11 miles on the bike trail. How far is Benjamin from where he started his trip?

153)


Answers will vary. Sample answer: Dan bought 8 balloons for the party at Z-mart and 5 balloons for the party at Nan's Boutique. How many balloons does Dan have altogether from his purchases? The problem illustrates the set model of addition.

154)


Answers will vary. Sample answer: Uncle Jack plans to bake bread for dinner. His recipe calls for 8 cups of flour. If there are only two cups of flour in the canister, how much more flour does uncle Jack need? This problem illustrates the missing-addend model of subtraction.

155)


Associative and commutative properties of addition 156)


A 157)


C 158)


B 159)


B 160)


B 161)


D 162)


B 163)


A 164)


C 165)


A 166)


D 167)


B 168)


C 169)


B 170)


A 171)


A 172)


A 173)


B 174)


A 175)


B 176)


B 177)


A 178)


A 179)


A 180)


A 181)


B 182)


B 183)


A 184)


A 185)


C 186)


B 187)


A 188)


A 189)


A 190)


A 191)


A 192)


A 193)


B 194)


B 195)


C 196)


C 197)


B 198)


A 199)


A 200)


B 201)


A 202)


D 203)


B 204)


D 205)


C 206)


C 207)


C 208)


C 209)


C 210)


C 211)


A 212)


C 213)


D 214)


A 215)


A 216)


7 ∙ 102 = 7(100 + 2) = 700 + 14 = 714

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