A Problem-Solving Approach to Mathematics for Elementary School
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Teachers
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by Rick Billstein, Shlomo Libeskind, Johnny Lott 13 EDITION.
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,Exam
Name
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the following is a statement. If it is, then also classify the statement as true or false.
1) Why don't you come here? 1)
A) True statement B) Not a statement C) False statement
Answer: B
2) This room is big. 2)
A) False statement B) True statement C) Not a statement
Answer: C
3) 5 - 1 = 4 3)
A) True statement B) Not a statement C) False statement
Answer: A
4) 7x + y = 3 4)
A) False statement B) Not a statement C) True statement
Answer: B
5) Can you bring the book? 5)
A) False statement B) True statement C) Not a statement
Answer: C
6) x + y = x - y, where y = 0 6)
A) Not a statement B) True statement C) False statement
Answer: B
7) 12 = 3y 7)
A) False statement B) True statement C) Not a statement
Answer: C
8) 2.4 = 5.2 8)
A) Not a statement B) False statement C) True statement
Answer: B
9) The state of California is in North America. 9)
A) Not a statement B) True statement C) False statement
Answer: B
10) Brazil is in Asia. 10)
A) True statement B) Not a statement C) False statement
Answer: C
1
,Use a quantifier to make the following true or false, as indicated, where x is a natural number.
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11) x + x = 6 (make true)
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A) There is no natural number x such that x + x = 6. @f @f @f @f @f @f @f @f @f @f @f @f
B) There exists a natural number x such that x + x = 6. @f @f @f @f @f @f @f @f @f @f @f @f
C) For every natural number x, x + x = 6. @f @f @f @f @f @f @f @f @f
D) For all natural numbers x, x + x = @f @f @f @f @f @f @f @f
@f 6. Answer:
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B
12) x3 = 8 @f
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(make true) @f
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A) No natural number x exists such that x3 = 8.
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B) Every natural number x satisfies x3 = 8. @f @f @f @f @f
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C) Three natural numbers x exist such that x3 = 8.
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D) There exists a natural number x such that x3 =@f @f @f @f @f @f @f @f
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@f 8. Answer: D
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13) 2x + @f @f1 = 5 - x (make true)
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13) @ f
A) Only two natural numbers x exist such that 2x + 1 = 5 - x.
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B) No natural number x exists such that 2x + 1 = 5 - x.
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C) For every natural number x, 2x + 1 = 5 - x.
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D) There exists a natural number x such that 2x + 1 = 5
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- x. Answer:
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D
14) 12x = 5x + 7x (make false)
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A) More than one natural number x exists such that 12x = 5x + 7x.
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B) For every natural number x, 12x = 5x + 7x.
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C) There exists a natural number x such that 12x = 5x + 7x.
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D) There is no natural number x such that 12x = 5x + @f @f @f @f @f @f @f @f @f @f @f
@f 7x. Answer:
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D
15) x - 13 = 13 - x
@f @f (make false)
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15) @ f
A) There exists a natural number x such that x - 13 = 13 - x.
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B) At least one natural number x exists such that x - 13 = 13 - x.
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C) There is no natural number x such that x - 13 = 13 - x.
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D) For x = 13, x - 13 = 13 - x. @f @f @f @f @f @f @f @f @f @f
Answer: C @f
16) 4x = @f @f7x (make false) @ f @f
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A) No natural number x satisfies 4x = 7x.
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B) There is no natural number x such that 4x = 7x.
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C) For every natural number x, 4x =
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@f 7x. Answer:
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C
Write the statement indicated.
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17) Write the negation of the @f @f @f @f
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following: The test is difficult.
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A) The test is not easy. @f @f @f @f
B) The test is very difficult.
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C) The test is not difficult.
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D) The test is not very
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easy. Answer: @f @ f
C
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, 18) Write the negation of the @f @f @f @f
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following: 8 + 2 = 10
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A) 8 + 2 = 12 @f @f @f @f B) The sum of 8 and 2 is ten.
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C) 8 + 2 × 10 @f @f @f @f @f D) 8 + 2 = 2 + 8
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Answer: C @f
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the
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question. Provide an appropriate response.
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19) Negate the following: The store is sometimes open on Sunday.
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19)
Answer:
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The store is never open on Sunday.
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
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question.
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Construct a truth table for the statement.
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20) ~p A~s @f
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A) p s (~p A~s) @f @ f @f
B) p s (~p A~s)
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T T F T T F
T F F T F T
F T F F T T
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C) p @f
s (~p A~s) @f
D) p @f
s @ f
(~p A~s) @f
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T F
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Answer: D @f
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21) s V~(r Ap)
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21)
A) s r @f
p s V~(r Ap)
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B) s @f
r p s V~(r Ap)
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T T T T T T T T
T T F T T T F T
T F T T T F T T
T F F T T F F T
F T T F F T T F
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F AF
Answer: @f F T F F F F
22) (p A~q) At @f @f
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A) p q t (p A~q) At @f @f
B) p q@f
t (p A~q) At @f @f
T T T F T T T F
T T F F T T F F
T F T T T F T F
T F F F T F F F
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Answer: A @f
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