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Signed Numbers: Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is a proficiency exam to the chapter "Signed Numbers." Each problem is accompanied with a reference link pointing back to the module that discusses the type of problem demonstrated in the question. The problems in this exam are accompanied by solutions.

Proficiency Exam

Exercise 1

((Reference)) Write all integers that are strictly between –8 and –3.

Solution

−7,−6,−5,−4−7,−6,−5,−4 size 12{ left lbrace -7,-6,-5,-4 right rbrace } {}

Exercise 2

((Reference)) Write all integers that are between and including –2 and 1.

Solution

−2, −1, 0, 1−2, −1, 0, 1 size 12{ left lbrace -2, -1, 0, 1 right rbrace } {}

For problems 3-5, write the appropriate symbol (<, >, =) in place of the □ for each pair of numbers.

Exercise 3

((Reference)) –1 □ –1

Solution

=

Exercise 5

((Reference)) –1 □ –2

Solution

>

For problems 6 and 7, what numbers can replace xx size 12{x} {} so that the statement is true?

Exercise 6

((Reference)) -3≤x<0-3≤x<0 size 12{ –3 <= x<0} {}, xx size 12{x} {} is an integer.

Solution

-3,-2,-1-3,-2,-1 size 12{ left lbrace -3,-2,-1 right rbrace } {}

Exercise 7

((Reference)) -4≤x≤0-4≤x≤0 size 12{ –4 <= x <= 0} {}, xx size 12{x} {} is a natural number.

Solution

1, 21, 2 size 12{ left lbrace 1, 2 right rbrace } {}

Exercise 8

((Reference)) How many units are there between –3 and 2?

Solution

5

For problems 9-20, find each value.

Exercise 9

((Reference)) ∣−16∣∣−16∣ size 12{ lline - "16" rline } {}

Solution

16

Exercise 10

((Reference)) −∣−2∣−∣−2∣ size 12{ - lline - 2 rline } {}

Solution

−2−2 size 12{-2} {}

Exercise 11

((Reference)) −(−∣−4∣2)−(−∣−4∣2) size 12{ - \( - lline - 4 rline rSup { size 8{2} } \) } {}

Solution

16

Exercise 12

((Reference)) ∣−5∣+∣−10∣∣−5∣+∣−10∣ size 12{ lline - 5 rline + lline - "10" rline } {}

Solution

15

Exercise 13

((Reference)) −8+6−8+6 size 12{ - 8+6} {}

Solution

−2−2 size 12{-2} {}

Exercise 14

((Reference)) −3+(−8)−3+(−8) size 12{ - 3+ \( - 8 \) } {}

Solution

−11−11 size 12{-"11"} {}

Exercise 15

((Reference)) 0−160−16 size 12{0 - "16"} {}

Solution

−16−16 size 12{-"16"} {}

Exercise 16

((Reference)) (−14)⋅(−3)(−14)⋅(−3) size 12{ \( - "14" \) cdot \( - 3 \) } {}

Solution

42

Exercise 17

((Reference)) (−5−6)2(−5−6)2 size 12{ \( - 5 - 6 \) rSup { size 8{2} } } {}

Solution

121

Exercise 18

((Reference)) (−51)÷(−7)(−51)÷(−7) size 12{ \( - "51" \) div \( - 7 \) } {}

Solution

517 or 727517 or 727 size 12{ { {"51"} over {7} } " or "7 { {2} over {7} } } {}

Exercise 19

((Reference)) −42−7−42−7 size 12{ { { - "42"} over { - 7} } } {}

Solution

6

Exercise 20

((Reference)) ∣−328−−15−55∣∣−328−−15−55∣ size 12{ lline { { - "32"} over {8} } - { { - "15" - 5} over {5} } rline } {}

Solution

0

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