integers test

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

sample test questions on integers

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Write an addition statement represented by this number line. Find the sum.

a. (+2) + (−3); –1 b. (−3) + (+2); +5 c. (+2) + (−3); +1 d. (+2) + (+3); +5

____ 2. Use a number line to add. (+2) + (–1)

a.

+3

c.

+1

b.

–2

d.

–1

____ 3. Add. (+18) + (+19)

a. +1 b. –37 c. –1 d. +37

____ 4. Add. (–28) + (–14)

a. –14 b. +42 c. –42 d. +14

____ 5. Add. (–41) + (+11)

a. +52 b. –52 c. +30 d. –30

____ 6. Gail owns a small business. There was a profit of $17 on Saturday and a loss of $11 on Sunday. Find the total profit or loss for the weekend.

a. $6 loss b. $28 profit c. $6 profit d. $28 loss

____ 7. During the day the temperature was 16°C. At night, the temperature dropped 19°C. What was the temperature at night?

a. 35°C b. 3°C c. –35°C d. –3°C

____ 8. Add. (–10) + (–5) + (–6)

a. –9 b. –11 c. –1 d. –21

Name: ________________________ ID: A

2

____ 9. Add. (–218) + (+157) + (–162)

a. –223 b. –537 c. +537 d. +223

____ 10. Add. (+9) + (–23) + (+14) + (–10)

a. +36 b. –10 c. +10 d. +18

____ 11. Add. (–9) + (+27) + (–22) + (–14)

a. –18 b. +10 c. –72 d. +26

____ 12. The temperature of a town is 18°C. The weather forecast says that the temperature will drop 9°C. Write an expression to find the predicted temperature. What will the temperature be?

a. (+9) + (–18); –27°C c. (+18) + (+9); 14°C

b. (+9) + (+18); 27°C d. (+18) + (–9); 9°C

____ 13. Rewrite as an addition statement. (+10) – (–14) – (+17)

a. (–10) + (+14) + (–17) c. (+10) + (+14) + (–17)

b. (–10) + (–14) – (–17) d. (+10) + (+14) – (+17)

____ 14. Which number line model can you use to simplify –5 − (–6)?

a.

–5 − (–6) = –1

b.

–5 − (–6) = –11

c.

–5 − (–6) = +1

d.

–5 − (–6) = +11

Name: ________________________ ID: A

3

____ 15. Use a number line to subtract. (+3) – (–5)

a.

(+3) – (–5) = +8

b.

(+3) – (–5) = +8

c.

(+3) – (–5) = –8

d.

(+3) – (–5) = –8

____ 16. Use a number line to subtract. (–1) – (+3)

a.

(–1) – (+3) = –4

b.

(–1) – (+3) = –4

c.

(–1) – (+3) = +4

d.

(–1) – (+3) = +4

____ 17. Use a number line to subtract. (+9) − (–7)

a. –16 b. +16 c. +2 d. –2

Name: ________________________ ID: A

4

____ 18. Write (+58) – (–31) as an addition statement. Then find the sum.

a. (+58) + (+31); +89 c. (+58) + (+66); +124

b. (+58) − (+66); –8 d. (+58) − (+31); +27

____ 19. Subtract. (+2) − (+31)

a. –29 b. –33 c. +29 d. +33

____ 20. Subtract. (+8) − (–42)

a. –34 b. +34 c. –50 d. +50

____ 21. Evaluate. (+9) − (–9) − (–2)

a. –2 b. +16 c. +20 d. –20

____ 22. Evaluate. (+12) + (+5) − (+4)

a. +11 b. –3 c. +13 d. +3

____ 23. The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is

192 m below sea level.a) Find the difference of the 2 elevations.

b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point?

a. 4717 m; lowest c. 4333 m; highest

b. 4333 m; lowest d. 4717 m; highest

____ 24. What is the result of 8 subtract negative 7?

a. –1 b. –15 c. 15 d. 1

____ 25. Find the result of 6 add negative 8 then subtract negative 5.

a. –7 b. 7 c. 3 d. –3

____ 26. Evaluate. 50 − 32

a. 18 b. –18 c. 82 d. –82

____ 27. Evaluate. 16 − 7 − 6

a. 15 b. 3 c. –15 d. –3

____ 28. Evaluate. −17 + 9 − 7

a. 15 b. 19 c. –15 d. 1

____ 29. Evaluate. 10 − 6 + 7

a. 11 b. 9 c. 3 d. –3

____ 30. Find the missing integer that makes this statement true. 2 − = –9

a. 7 b. –11 c. 11 d. –7

____ 31. Add brackets to make this an addition statement of integers. –5 – 20 + 13

a. (–5) − (+20) + (+13) c. (−5) + (−20) + (+13)

b. (−5) + (−20) + (−13) d. −(+5) − (+20) + (+13)

____ 32. Evaluate. 5 − 10 + (–8)

a. +3 b. +7 c. –13 d. –3

Name: ________________________ ID: A

5

____ 33. Evaluate. 4 + (−7) − (−5)

a. 2 b. 16 c. 6 d. –8

____ 34. Lynn has $169 in her savings account. She withdraws $91, deposits $52, and then withdraws $85. Find the balance of Lynn’s account.

a. $397 b. −$59 c. $293 d. $45

____ 35. Write this sum as a product and evaluate. (–5) + (–5) + (–5) + (–5)

a. 4 × (–5); –20 c. 5 × (–5); –25

b. 2 × (–5) + 2(–5); +22 d. (–5) × (–5); –18

____ 36. Find this product. (+9)(−5)

a. –47 b. –45 c. –43 d. +81

____ 37. Find this product. (−6)(−8)

a. +48 b. +46 c. +50 d. +47

____ 38. Find this product. (− 15) × (+11)

a. –165 b. –26 c. –4 d. +165

____ 39. Find this product. (−8)(+5)(+7)

a. –278 b. –281 c. –40 d. –280

____ 40. Find this product. (+7)(−3)(+3)

a. –21 b. –64 c. –61 d. –63

____ 41. Find this product. (+12) × (−4) × (−6)

a. +288 b. –288 c. –36 d. +36

____ 42. Which pair of expressions has the same value?

a. (−2) × (+6)

(+16) + (−4)

b. (−2) × (−6)

(+4) + (−16)

c. (+2) × (−6)

(+4) − (+16)

d. (+2) × (+6)

(+4) + (+16)

____ 43. An arctic air current moved into a region where the temperature was originally 25°C.

The temperature began to fall at a steady rate of 4°C per hour.

What was the temperature after 9 h?

a. –7°C b. 36°C c. –11°C d. –15°C

____ 44. A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. Suppose a diver started at 27 m below the water surface and rose in 5 steps of 5 m each. Use an integer to describe his new position in relation to the water surface.

a. –2 m b. +2 m c. +25 m d. –25 m

____ 45. Find this product. (− 2) × (− 3) × (− 5)

a. –10 b. +13 c. +1 d. –30

____ 46. Find this product. (− 2) × (+10) × (+1) × (+11)

a. +108 b. –9 c. –219 d. –220

Name: ________________________ ID: A

6

____ 47. Divide. (−42) ÷ (−7)

a. +6 b. –6 c. −1

6d. +

1

6

____ 48. Divide. (+50) ÷ (−5)

a. +10 b. –10 c. +250 d. –250

____ 49. Divide. (–54) ÷ (+9)

a. –6 b. –8 c. –5 d. –1

____ 50. Divide. (+40) ÷ (+8)

a. +48 b. –5 c. +5 d. –48

____ 51. Divide. (− 20) ÷ (− 10)

a. +2 b. +30 c. –2 d. –30

____ 52. Find this quotient. − 84

+12

a. −1

7b. +7 c. –7 d. +

1

7

____ 53. Find this quotient. +24

− 8

a. +1

3b. −

1

3c. –3 d. +3

____ 54. A mountain climber is at an elevation of 3640 m. After 5 h, he is at an elevation of 1215 m. Use this formula to find the climber’s vertical speed.

Vertical speed =Finalelevation − Initial elevation

Time

a. –2425 m/h b. –728 m/h c. –485 m/h d. –971 m/h

____ 55. One day at 3 p.m., the temperature was −6°C in a city in Alaska.

At 10 p.m., the temperature was −20°C. What was the average change in temperature per hour?

a. −14°C b. −3°C c. −4°C d. −2°C

____ 56. Evaluate. 5 × 7 + 2a. –4 b. 14 c. 45 d. 37

____ 57. Evaluate. 15 − 40 ÷ 5a. 7 b. –5 c. –185 d. 23

____ 58. Evaluate. 8 × (−4) ÷ 1

a. –32 b. 33 c. –33 d. 32

____ 59. Evaluate. (–5) × (9 − 7) + (–5)

a. –15 b. –14 c. –58 d. –57

Name: ________________________ ID: A

7

____ 60. Evaluate. 8 + (−42) ÷ 7 + 7 × 3

a. 27 b. −1 c. 7 d. 23

____ 61. Evaluate. −(−4) + 3(11 − 3)

a. 20 b. –28 c. 56 d. 28

____ 62. Evaluate. −4 × (−6) − (−24) ÷ (−6)

a. 28 b. 0 c. –8 d. 20

____ 63. Evaluate. −16 + 18 ÷ (−6) + 7

a. 12 b. –6 c. 6 d. –12

____ 64. Write 2 expressions to describe the total area of this figure. Then find the total area of the figure.

a. 8(6) − 2(6); 6 × (8 − 2); area = 36

b. (8 × 6) + (2 × 6); 6 × (8 + 2); area = 60

c. 6 × 10; (8 + 2) + 6; area = 60

d. (8 + 6) × (2 + 6); 6 + (8 × 2); area = 60

Short Answer

65. Use a number line to add (+6) + (–6) + (+7) + (–4)

66. An elevator on the 10th floor goes down 9 floors. Then it goes up 19 floors, down 3, and finally up 12.

What floor does it end up on? Explain your answer.

67. Add. (–172) + (+257) + (–132) + (+195)

68. Find the missing integer that completes this equation. (–42) = (–13) +

69. Use <, >, or = to complete this sentence. (+10) + (–22) (–28) + (–11)

70. State if this statement is always, sometimes, or never true. Use examples to explain.“The result of subtracting a positive integer from a positive integer is a positive integer.”

71. State if this statement is always, sometimes, or never true. Use examples to explain.“The result of subtracting a positive integer from a negative integer is a positive integer.”

72. State if this statement is always, sometimes, or never true. Use examples to explain.“The result of subtracting a negative integer from a negative integer is a positive integer.”

Name: ________________________ ID: A

8

73. State if this statement is always, sometimes, or never true. Use examples to explain.

“The result of subtracting a negative integer from a positive integer is a positive integer.”

74. Use a number line to evaluate. (–5) – (–7)

75. Evaluate. (–16) – (–11) + (–6)

76. Evaluate. 20 − 9 − 10

77. Evaluate. 155 − 91 − 106 + 61

78. Draw a number line to evaluate. 6 − 9 + 5

79. Find the missing integer that makes this statement true.

–28 − = 52

80. In an experiment, the temperature change was –3°C every 30 min.

If the initial temperature was 8°C, what was the temperature after 21

2 h?

81. Predict the sign of this quotient. (–2) ÷ (+10)

82. Add brackets to make this statement true.(−32) ÷ (−4) ÷ (+2) = +16

83. Add brackets to make each statement true.(−128) ÷ (+8) ÷ (−4) ÷ (+2) = +8

(−128) ÷ (+8) ÷ (−4) ÷ (+2) = +32

(−128) ÷ (+8) ÷ (−4) ÷ (+2) = +128

84. Which resulting integer is greater?

(+144) ÷ (−3) × (+8) or (+144) × (−3) ÷ (+8)?

85. Which expression has a value closer to −1? Explain.

A: 3 × (−7)2 − 4 × 6 2 − (−4)ÈÎÍÍÍ

˘˚˙̇̇

B: (−3)3 −(6)(−12)(−3)

(−9)

86. Which expression has a greater value? Explain.

(−3)2 + (−9)2 or (−3 − 9)2

87. Evaluate. (−4)3 − (+4)3

88. Evaluate. (–8)(–8) + (–5)(6 + 11)

Name: ________________________ ID: A

9

89. Evaluate. (–4) + (–4)2 + (–4)3 + (–4)4

90. Find the mean of this set of data. –4, 5, –10, –7, 6

Problem

91. In a board game, 3 players can gain or lose points. Here are the results for 3 games.

Game 1 Game 2 Game 3

Player 1 –139 +303 –123

Player 2 +269 –187 –33

Player 3 –170 +127 +169

a) Which player won each game?b) Who had the highest total score after 3 games? What was the score?

92. Describe the signs of the results of adding integers with the same signs and with different signs.

93. Aaron will buy a stock only if it shows an overall increase over the next 3 days. A stock has a daily increase of $30 in the first day, a decrease of $45 in the next day, and an increase of $25 on the third day. Will Aaron buy the stock? Explain.

94. The sum of 3 consecutive integers is –693. Find the integers.

95. The table shows the monthly income and expenses of a new business over 6 months.a) Which months show a profit? Explain your answer.b) Did the business make a profit or loss over the 6 months?

Month Income (I) Expenses (E)

1 $258 $335

2 $287 $367

3 $427 $330

4 $359 $314

5 $333 $383

6 $504 $449

96. Write the next 3 terms in this pattern. Then write a pattern rule.

+3, –1, –5, ...

97. Write add or subtract symbols to make this statement true.

(–18) (+39) (–32) = (+53)

98. Find 2 negative integers that have a sum of –11 and a difference of 3. Explain your answer.

Name: ________________________ ID: A

10

99. x is an integer greater than –45 but less than –20.

y is an integer greater than –75 but less than –50.

a) What is the greatest possible value of x − y?

b) What is the greatest possible value of y − x?Justify your answers.

100. Find a value of n such that (–5) − (–7) > (+9) + (n)

101. A dodecahedron is a solid with 10 faces. You have a blue dodecahedron labelled 1 to 10 and a red one

labelled −1 to −10. You roll the 2 dodecahedrons and add the integers that show.a) What is the highest possible sum that will show? Justify your answer.b) How many ways can you get a sum of –6?

102. This table shows the depths reached by a submersible recorded at 15 min intervals.Describe and show the vertical movements of the submersible on a number line.

Time (min) 0 15 30 45 60 75 90

Depth (m) 0 –9 –12 –5 –6 –4 0

103. In a board game, the letters of the alphabet are given these integer values.

–5 A E I O U

+7 D G L N R S T

–9 B C M P

+11 F H K V W Y

+13 J X

–15 Q Z

Find words from the list below that have:a) the same valueb) the least valuec) the greatest valued) a value of 0

NUMBER, MULTIPLY, SUBTRACT, QUESTION, QUIZ

104. Jake borrowed $25 from his mother and spent $21. He then earned $22 and spent $15.

Does Jake have enough money to repay his mother? Explain.

105. This pattern continues. (–10 + 8), (–11 + 7), (–12 + 6), ...

a) Evaluate the first 3 terms in the pattern. b) Write the next 3 terms in the pattern.c) Calculate the sum of the first 6 terms.

Name: ________________________ ID: A

11


5, –20, 80, –320, ....


–4, +16, –64, ...

108. A loan for a motorbike requires equal payments of $150 per month for 3 years.

a) What is the total amount paid over the 3 years?

b) Suppose a down payment of $1000 was made in addition to the monthly payments. What was the total cost of the motorbike?

109. These statements show that product of negative integers could be positive or negative.

(−1) × (−1) = +1

(−1) × (−1) × (−1) = −1

(−1) × (−1) × (−1) × (−1) = +1

How can you predict the sign of the product without multiplying? Give 2 another statements that justify your prediction.

110. Explain how you could predict the sign of the product of −8, +9, +7, and −4 without actually multiplying.

111. The product of 3 integers is −24. The sum of the integers is −12.What are the 3 integers? Show your work.


+729, –243, +81, ...

113. Simplify. −30

+14×

+42

−7×

−14

+10

114. Find 2 integers that make this statement true.

(+16) ÷ ÷ = –1

115. Luther and Nicole were on a hiking trip. They began at an elevation of 139 m above sea level and descended

to an elevation of 21 m below sea level in 8 h.a) Write a division expression that can be used to find their average change in elevation per hour.b) Use an integer to represent their average change in elevation per hour.

116. Find the greatest possible negative integer that can be divided completely by −2, −3, −4, −5, −6, or −7.

Explain your answer.

117. Write 3 integers such that the sum of the first 2 integers divided by the third integer gives this result:

a) 0

b) −1

c) +1Describe how the 3 integers are related in each case.

Name: ________________________ ID: A

12

118. Add brackets to make each statement true.8 + 5 × (−6) − 4 = −82

8 + 5 × (−6) − 4 = −42

8 + 5 × (−6) − 4 = −130

119. I think of a number.

I multiply it by 6.

I subtract 8.

I multiply the result by 3.I subtract 16.

The answer is –4.

What number did I think of? Justify your answer.

120. Write an expression for each statement and evaluate.

a) Divide the sum of –13 and 37 by 6.

b) Subtract the square of –10 from the product of 5 and 10.

121. Evaluate each expression.

A: (−1) + (−1)2

B: (−1) + (−1)2 + (−1)3

C: (−1) + (−1)2 + (−1)3 + (−1)4

If this pattern was continued, when would you get answers of 0?

122. Describe the steps you would use to evaluate this expression. Then evaluate the expression. 3 + (−8) − (10 + 4) × 2

ID: A

1

sample test questions on integers

Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: Easy REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

2. ANS: C PTS: 1 DIF: Easy REF: 9.1 Adding Integers

STA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

3. ANS: D PTS: 1 DIF: Easy REF: 9.1 Adding Integers


4. ANS: C PTS: 1 DIF: Easy REF: 9.1 Adding Integers


5. ANS: D PTS: 1 DIF: Moderate REF: 9.1 Adding Integers


6. ANS: C PTS: 1 DIF: Moderate REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Application

7. ANS: D PTS: 1 DIF: Moderate REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Application

8. ANS: D PTS: 1 DIF: Moderate REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

9. ANS: A PTS: 1 DIF: Moderate REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

10. ANS: B PTS: 1 DIF: Moderate REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

11. ANS: A PTS: 1 DIF: Moderate REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

12. ANS: D PTS: 1 DIF: Moderate REF: 9.1 Adding IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

13. ANS: C PTS: 1 DIF: Easy REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

14. ANS: C PTS: 1 DIF: Easy REF: 9.2 Subtracting Integers


15. ANS: B PTS: 1 DIF: Easy REF: 9.2 Subtracting Integers


16. ANS: A PTS: 1 DIF: Easy REF: 9.2 Subtracting Integers


17. ANS: B PTS: 1 DIF: Easy REF: 9.2 Subtracting Integers


18. ANS: A PTS: 1 DIF: Moderate REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

19. ANS: A PTS: 1 DIF: Moderate REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

20. ANS: D PTS: 1 DIF: Moderate REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

ID: A

2

21. ANS: C PTS: 1 DIF: Moderate REF: 9.2 Subtracting Integers


22. ANS: C PTS: 1 DIF: Moderate REF: 9.2 Subtracting Integers


23. ANS: D PTS: 1 DIF: Difficult REF: 9.2 Subtracting Integers

STA: 8m22 TOP: Number Sense and Numeration KEY: Application

24. ANS: C PTS: 1 DIF: Easy REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding


26. ANS: A PTS: 1 DIF: Easy REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

27. ANS: B PTS: 1 DIF: Easy REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding


29. ANS: A PTS: 1 DIF: Easy REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

30. ANS: C PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

31. ANS: C PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

32. ANS: C PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting Integers


33. ANS: A PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting Integers


34. ANS: D PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting Integers


35. ANS: A PTS: 1 DIF: Easy REF: 9.4 Multiplying Integers


36. ANS: B PTS: 1 DIF: Easy REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

37. ANS: A PTS: 1 DIF: Easy REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

38. ANS: A PTS: 1 DIF: Easy REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

39. ANS: D PTS: 1 DIF: Moderate REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

40. ANS: D PTS: 1 DIF: Moderate REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

41. ANS: A PTS: 1 DIF: Moderate REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

42. ANS: C PTS: 1 DIF: Moderate REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

43. ANS: C PTS: 1 DIF: Moderate REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Application

ID: A

3

44. ANS: A PTS: 1 DIF: Moderate REF: 9.4 Multiplying Integers


45. ANS: D PTS: 1 DIF: Moderate REF: 9.4 Multiplying Integers


46. ANS: D PTS: 1 DIF: Moderate REF: 9.4 Multiplying Integers


47. ANS: A PTS: 1 DIF: Easy REF: 9.5 Dividing IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

48. ANS: B PTS: 1 DIF: Easy REF: 9.5 Dividing IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding


50. ANS: C PTS: 1 DIF: Easy REF: 9.5 Dividing IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding




54. ANS: C PTS: 1 DIF: Moderate REF: 9.5 Dividing IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Application

55. ANS: D PTS: 1 DIF: Moderate REF: 9.5 Dividing Integers


56. ANS: D PTS: 1 DIF: Easy

REF: 9.6 Order of Operations with Integers STA: 8m23TOP: Number Sense and Numeration KEY: Knowledge and Understanding

57. ANS: A PTS: 1 DIF: Easy






60. ANS: D PTS: 1 DIF: Moderate






ID: A

4



64. ANS: B PTS: 1 DIF: Difficult


SHORT ANSWER

65. ANS:

(+6) + (–6) + (+7) + (–4) = +3

PTS: 1 DIF: Moderate REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication

66. ANS:

Find the sum of all the up and down movements of the elevator.

(+10) + (–9) + (+19) + (–3) + (+12) = +29

The elevator will be on the 29th floor.

PTS: 1 DIF: Moderate REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication

67. ANS:

+148

PTS: 1 DIF: Moderate REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

68. ANS:

–29

PTS: 1 DIF: Moderate REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

69. ANS:

(+10) + (–22) > (–28) + (–11)


ID: A

5

70. ANS:

It is sometimes true.Examples may vary. Sample:

(+17) – (+10) = +7

(+10) – (+17) = −7

PTS: 1 DIF: Moderate REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Communication

71. ANS: It is never true.Examples may vary. Sample:

(–17) – (+10) = –27

(–10) – (+17) = –27


72. ANS: It is sometimes true.Examples may vary. Sample:

(–17) – (–10) = –7

(–10) – (–17) = +7


73. ANS:

It is always true.Examples may vary. Sample:

(+17) – (–10) = +27

(+10) – (–17) = +27


74. ANS:

(–5) – (–7) = +2


75. ANS:

–11

PTS: 1 DIF: Moderate REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

ID: A

6

76. ANS:

1

PTS: 1 DIF: Easy REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

77. ANS:

19

PTS: 1 DIF: Easy REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

78. ANS:

6 − 9 + 5 = 2

PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Communication

79. ANS:

–80

PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

80. ANS:

–7°C

PTS: 1 DIF: Moderate REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Application

81. ANS:

negative

PTS: 1 DIF: Easy REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

82. ANS:

(−32) ÷ (−4) ÷ (+2)ÈÎÍÍÍ

˘˚˙̇̇ = +16

PTS: 1 DIF: Moderate REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

83. ANS:

(−128) ÷ (+8) ÷ (−4) ÷ (+2)ÈÎÍÍÍ

˘˚˙̇̇ = +8

(−128) ÷ (+8) ÷ (−4)ÈÎÍÍÍ

˘˚˙̇̇ ÷ (+2) = +32

(−128) ÷ (+8) ÷ (−4) ÷ (+2)ÈÎÍÍÍ

˘˚˙̇̇ = +128


ID: A

7

84. ANS: (+144) ÷ (−3) × (+8) = −384

(+144) × (−3) ÷ (+8) = −54

(+144) ÷ (−3) × (+8) < (+144) × (−3) ÷ (+8)


85. ANS: Value of A: +3

Value of B: −3

The value of B is closer to −1.

PTS: 1 DIF: Moderate REF: 9.6 Order of Operations with IntegersSTA: 8m23 TOP: Number Sense and Numeration KEY: Communication

86. ANS:

(−3)2 + (−9)2 = 90

(−3 − 9)2 = 144

The value of (−3 − 9)2 is greater.

PTS: 1 DIF: Moderate REF: 9.6 Order of Operations with IntegersSTA: 8m23 TOP: Number Sense and Numeration KEY: Communication

87. ANS:

–128

PTS: 1 DIF: Moderate REF: 9.6 Order of Operations with IntegersSTA: 8m23 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

88. ANS:

–21


89. ANS:

204


90. ANS:

−2


ID: A

8

PROBLEM

91. ANS: a) Game 1: Player 2 Game 2: Player 1 Game 3: Player 3

b) Player 3; the score was +126 points.


92. ANS:

Descriptions may vary. Sample:Integers with the same sign: The sum of 2 positive integers is positive. The sum of 2 negative integers is negative.Integers with different signs:To add integers with different signs, find the difference of their number values. The sum has the sign of the integer with the greater number value.

PTS: 1 DIF: Difficult REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication

93. ANS: Yes. (+$30) + (−$45) + (+$25) = +$10

There was an overall increase of $10 over 3 consecutive days.


94. ANS:

–232, –231, –230

PTS: 1 DIF: Difficult REF: 9.1 Adding Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

ID: A

9

95. ANS:

a) Methods may vary. Sample: Make a table that shows the balance of each month. The 3rd, 4th, and 6th months show a profit.

Month Balance (I −−−− E) Profit/Loss

1 −$77 Loss

2 −$80 Loss

3 +$97 Profit

4 +$45 Profit

5 −$50 Loss

6 +$55 Profit

b) The business made a profit of $–10 over the 6 months.


96. ANS:

–9, –13, –17

Pattern rule: Start with +3. Subtract +4 each time.

PTS: 1 DIF: Moderate REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

97. ANS:

(–18) + (+39) – (–32) = (+53)

PTS: 1 DIF: Difficult REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

98. ANS:

Find pairs of negative integers that have a sum of –11:

−1 and –10, −2 and –9, −3 and –8, ..., and so on.

Look for pairs of integers that have a difference of 3:

–7 and –4

PTS: 1 DIF: Difficult REF: 9.2 Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Communication

99. ANS: a) Subtract the least value of y from the greatest value of x

(−21) − (−74) = +53b) Subtract the least value of x from the greatest value of y

(−51) − (−44) = −7


ID: A

10

100. ANS:

n is any number less than –7.


101. ANS:

a) The highest possible sum is 10 + (−1) = 9.

It is the sum of the greatest positive integer (10) and the greatest negative integer (−1).b) Four ways:

(−10) + 4 = −6

(−9) + 3 = −6

(−8) + 2 = −6

(−7) + 1 = −6

PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

102. ANS: Sea level is at 0 m.

PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Communication

103. ANS:

a) NUMBER and QUESTION have the same value of −14.

b) QUIZ has the least value of −40.c) MULTIPLY has the greatest value of +4.d) SUBTRACT has a value of 0.

PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

ID: A

11

104. ANS:

No. Explanations may vary. Sample:Calculate the money that Jake has:

$25 − $21 + $22 − $15 = $11

Jake has $11 but this is not enough to repay his mother.

PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Communication

105. ANS:

a) −2, −4, −6

b) (–13 + 5), (–14 + 4), (–15 + 3)

c) (−2) + (−4) + (−6) + (−8) + (−10) + (−12) = −42

PTS: 1 DIF: Difficult REF: 9.3 Adding and Subtracting IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

106. ANS:

The next 2 terms are: 1280, –5120

Pattern rules may vary. Sample:

Start at 5. Multiply by –4 each time.

PTS: 1 DIF: Moderate REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

107. ANS:

The next 3 terms are: +256, –1024, –4096Pattern rules may vary. Sample:

Start at –4. Multiply by −4 each time.

PTS: 1 DIF: Moderate REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

108. ANS:

a) $5400

b) $6400

PTS: 1 DIF: Difficult REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Application

109. ANS: If the number of negative integers being multiplied is even, then the product is positive. If the number of negative integers being multiplied is odd, then the product is negative.Examples may vary. Sample:The number of negative integers being multiplied is odd:(−1) × (−1) × (−1) × (−1) × (−1) = −1

The number of negative integers being multiplied is even:(−1) × (−1) × (−1) × (−1) × (−1) × (−1) = +1

PTS: 1 DIF: Difficult REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Communication

ID: A

12

110. ANS:

The sign of the product of (−8)(+9)(+7)(−4) is positive.

Explanations may vary. Sample:Since there are 2 negative integers being multiplied, their product will be positive. The product of any number of positive integers is always positive.

PTS: 1 DIF: Difficult REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Communication

111. ANS:

Methods may vary. Sample:Find the 3 natural numbers that will multiply to give 24.There are 6 possible combinations.1, 1, 24; 1, 2, 12; 1, 3, 8; 1, 4, 6; 2, 2, 6; 2, 3, 4Since the product is negative, 1 or all 3 of the integers are negative integers.

(−2)(−4)(−6) = −24

(−2) + (−4) + (−6) = −12

So, the 3 integers are −2, −4, and −6.

PTS: 1 DIF: Difficult REF: 9.4 Multiplying IntegersSTA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

112. ANS:

The next 3 terms are: –27, +9, –3Pattern rules may vary. Sample:

Start with +729. Divide by –3 each time.


113. ANS: –18

PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Knowledge and Understanding

114. ANS: Answers may vary. Sample:(+16) ÷ (+4) ÷ (−4) = −1

PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Thinking

115. ANS:

a) Average change of elevations per hour: (−21) − (+139)ÈÎÍÍÍ

˘˚˙̇̇ ÷ 8

b) −20 m/h

PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Application

ID: A

13

116. ANS:

Explanations may vary. Sample:A number that is divisible by –6 is also divisible by –2 and –3.

−4 and −6 are multiples of −2. So, only 1 factor of −2 is needed to ensure divisibility by −4.

The greatest possible negative integer is: −(2 × 5 × 6 × 7) = −420

PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication

117. ANS:

Answers may vary. Sample:

a) (−2) + (+2)ÈÎÍÍÍ

˘˚˙̇̇ ÷ (−1) = 0

b) (−2) + (+3)ÈÎÍÍÍ

˘˚˙̇̇ ÷ (−1) = −1

c) (−3) + (+2)ÈÎÍÍÍ

˘˚˙̇̇ ÷ (−1) = +1

In a), the first two integers must be opposites of each other.In b), the sum of the first 2 integers must be the opposite of the third integer.In c), the sum of the first 2 integers must equal the third integer.

PTS: 1 DIF: Difficult REF: 9.5 Dividing Integers STA: 8m22 TOP: Number Sense and Numeration KEY: Communication

118. ANS:

8 + 5( ) × (−6) − 4 = −82

8 + 5 × (−6) − 4ÈÎÍÍÍ

˘˚˙̇̇ = −42

8 + 5( ) × (−6) − 4ÈÎÍÍÍ

˘˚˙̇̇ = −130

PTS: 1 DIF: Difficult REF: 9.6 Order of Operations with IntegersSTA: 8m23 TOP: Number Sense and Numeration KEY: Thinking

119. ANS:

Work backwards to find the number.Add 16 to –4 to get 12.

Divide 12 by 3 to get 4.

Add 8 to 4 to get 12.

Divide 12 by 6 to get the original number, 2.

PTS: 1 DIF: Difficult REF: 9.6 Order of Operations with IntegersSTA: 8m23 TOP: Number Sense and Numeration KEY: Communication

120. ANS:

a) (−13) + 37

6= 4

b) 5 × 10 − (−10)2 = −50


ID: A

14

121. ANS:

A: 0

B: −1

C: 0If there are an even number of terms in the expression, the answer will be 0.

PTS: 1 DIF: Difficult REF: 9.6 Order of Operations with IntegersSTA: 8m23 TOP: Number Sense and Numeration KEY: Thinking

122. ANS:

Methods may vary. Sample:Add 10 + 4 in brackets.3 + (−8) − (10 + 4) × 2 = 3 + (−8) − 14 × 2

Multiply 14 × 2. 3 + (−8) − 14 × 2 = 3 + (−8) − 28

Add or subtract in order from left to right.

3 + (−8) − 28 = −5 − 28

= −33

3 + (−8) − (10 + 4) × 2 = −33


Documents

integers test