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Integers

20 questions: addition, subtraction, multiplication, division, comparing, absolute value and order of operations.

For questions 1–17 choose one answer. For questions 18–20 enter a number only, e.g. -13. When you finish, select Check answers.

1. The set of integers is denoted by the letter …

A. ℕ

B. ℤ

C. ℚ

Solution: The integers are ℤ = {…, −3, −2, −1, 0, 1, 2, 3, …}.

2. Which of these numbers is not an integer?

A. −5

B. 0

C. 3/4

D. 12

Solution: 3/4 is a fraction, not an integer. −5, 0 and 12 are integers.

3. What is 5 + (−2)?

A. 3

B. 7

C. −3

Solution: 5 + (−2) = 5 − 2 = 3

4. What is −6 − 9?

A. −15

B. −3

C. 3

D. 15

Solution: Both numbers are negative, so add their absolute values and keep the minus sign: −6 − 9 = −(6 + 9) = −15

5. What is 8 − (−5)?

A. 3

B. 13

C. −13

Solution: Subtracting a negative number is adding: 8 − (−5) = 8 + 5 = 13

6. What is (−3) · 4?

A. 12

B. −12

C. −7

Solution: Negative times positive is negative: (−3) · 4 = −12

7. What is (−5) · (−2)?

A. −10

B. 10

C. −7

Solution: Negative times negative is positive: (−5) · (−2) = 10

8. What is 18 : (−3)?

A. −6

B. 6

C. 15

Solution: The signs are different, so the quotient is negative: 18 : (−3) = −6

9. What is (−36) : (−4)?

A. −9

B. 9

C. −40

Solution: The signs are the same, so the quotient is positive: (−36) : (−4) = 9

10. Which of these numbers is the greatest?

A. −8

B. −2

C. −10

Solution: Among negative numbers, the greatest is the one closest to zero: −10 < −8 < −2.

11. Which order goes from smallest to greatest?

A. −7 < −3 < 0 < 4

B. −3 < −7 < 0 < 4

C. 0 < −3 < −7 < 4

Solution: On the number line, numbers increase from left to right: −7 < −3 < 0 < 4.

12. What is the absolute value of −7, that is |−7|?

A. −7

B. 0

C. 7

Solution: Absolute value is the distance from zero, so it is never negative: |−7| = 7

13. What is the opposite of 9?

A. −9

B. 9

C. 0

Solution: The opposite has the same absolute value and the other sign: the opposite of 9 is −9, because 9 + (−9) = 0.

14. What is (−2)³?

A. −8

B. 8

C. −6

Solution: (−2)³ = (−2) · (−2) · (−2) = 4 · (−2) = −8. An odd power of a negative number is negative.

15. What is (−3)²?

A. −9

B. 9

C. 6

Solution: (−3)² = (−3) · (−3) = 9. An even power of a negative number is positive.

16. What is −2 · (3 − 7) + 5?

A. −3

B. 3

C. 13

Solution: Brackets first, then multiplication, then addition: −2 · (3 − 7) + 5 = −2 · (−4) + 5 = 8 + 5 = 13

17. In the morning the temperature was −4 °C. By midday it had risen by 9 °C. What was the temperature at midday?

A. 5 °C

B. −13 °C

C. 13 °C

Solution: −4 + 9 = 5, so it was 5 °C at midday.

18. −15 + (−8) − (−10) =Enter a number only

Solution: −15 + (−8) − (−10) = −15 − 8 + 10 = −23 + 10 = −13

19. (−6) · (−4) : (−3) =Enter a number only

Solution: Work from left to right: (−6) · (−4) = 24, then 24 : (−3) = −8.

20. A lift is on floor −2 (the car park). It goes up 7 floors. Which floor is it on now?Enter a number only

Solution: −2 + 7 = 5, so the lift is on floor 5.

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See also

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State Matura tests

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