Integers

21 Grade 9 Mathematics questions on Integers, with worked marking schemes. 21 questions are available on this topic in full.

1. Question 1

   1 mark

   Temperature in Nairobi at night is −2°C. By morning it rose by 9°C. What is the morning temperature?

   A. 7°C

   B. −11°C

   C. 11°C

   D. −7°C

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

2. Question 2

   1 mark

   (−2)³ = ___

   A. 6

   B. 8

   C. −8

   D. −6

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

3. Question 3

   1 mark

   (−6) × (−9) = ___

   A. 54

   B. 15

   C. −15

   D. −54

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

4. Question 4

   1 mark

   (−3) × 4 × (−2) = ___

   A. 24

   B. −24

   C. −9

   D. 9

   (1 mark)

   Marking scheme

   A. $24$ — work left to right: $(-3)\times 4=-12$, then $-12\times -2=24$. With two negative factors the result is positive; an odd number of them would make it negative.

5. Question 5

   1 mark

   Calculate: 12 − (−7) = ___

   A. 5

   B. −5

   C. −19

   D. 19

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

6. Question 6

   3 marks

   Work out: 5 − 8 + (−3) − (−6) = ___

   (3 marks)

   Marking scheme

   Subtracting a negative is the same as adding, so $-(-6)$ becomes $+6$, and the expression is $5-8-3+6$. (1)

   Work left to right: $5-8=-3$, then $-3-3=-6$. (1)

   Finally $-6+6=0$. (1)

   Final answer: $0$.

7. Question 7

   1 mark

   What is the absolute value of −15?

   A. −15

   B. 0

   C. 15

   D. $\frac{1}{15}$

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

8. Question 8

   1 mark

   What is the sum of all integers from −3 to 3?

   A. −6

   B. 0

   C. 21

   D. 6

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

9. Question 9

   1 mark

   36 ÷ (−4) = ___

   A. −9

   B. −12

   C. 12

   D. 9

   (1 mark)

   Marking scheme for this question

   Create a free account to see it

10. Question 10

    2 marks

    The product of two integers is −36. One integer is −4. Find the other integer.

    (2 marks)

    Marking scheme

    Let the other integer be $n$, so $(-4)\times n=-36$. Division undoes multiplication: $n=-36÷(-4)$. (1)

    A negative divided by a negative gives a positive, so $n=9$. (1)

    Final answer: $9$. Check: $(-4)\times 9=-36$.

11. Question 11

    1 mark

    (−48) ÷ 6 = ___

    A. −8

    B. 8

    C. −6

    D. 6

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

12. Question 12

    1 mark

    Which of the following is the correct order from least to greatest: −5, 3, −2, 0, 7?

    A. 7, 3, 0, −2, −5

    B. −5, 0, −2, 3, 7

    C. −2, −5, 0, 3, 7

    D. −5, −2, 0, 3, 7

    (1 mark)

    Marking scheme

    D. $-5,-2,0,3,7$ — order by position on the number line, where further left is smaller. Among negatives the bigger-looking number is the smaller one, which is what C gets wrong.

13. Question 13

    1 mark

    Evaluate: −4 + 9 − 3 = ___

    A. −2

    B. −10

    C. 10

    D. 2

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

14. Question 14

    1 mark

    A submarine dives 200 m below sea level, then rises 75 m. What is its new position?

    A. −125 m

    B. −275 m

    C. 125 m

    D. 275 m

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

15. Question 15

    2 marks

    List all integers x such that −3 ≤ x < 2.

    (2 marks)

    Marking scheme for this question

    Create a free account to see it

16. Question 16

    3 marks

    A lift in a building starts at floor 0 (ground floor). It goes down 3 floors, then up 7 floors, then down 2 floors. At which floor is it now?

    (3 marks)

    Marking scheme for this question

    Create a free account to see it

17. Question 17

    3 marks

    Evaluate: (−4) × 3 + (−2) × (−5) = ___

    (3 marks)

    Marking scheme

    Multiplication comes before addition, so work out the two products first. (1)

    $(-4)\times 3=-12$, because a negative times a positive is negative. (1)

    $(-2)\times (-5)=+10$, because a negative times a negative is positive. Then $-12+10=-2$. (1)

    Final answer: $-2$.

18. Question 18

    1 mark

    Calculate: (−8) + (−5) = ___

    A. 13

    B. −13

    C. 3

    D. −3

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

19. Question 19

    1 mark

    Evaluate: (−5)² = ___

    A. −25

    B. 25

    C. 10

    D. −10

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

20. Question 20

    1 mark

    Evaluate $-8+5\times (-3)-(-6)$.

    A. $15$

    B. $-29$

    C. $-17$

    D. $9$

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

21. Question 21

    1 mark

    Which integer is between −10 and −6?

    A. −5

    B. 0

    C. −11

    D. −8

    (1 mark)

    Marking scheme for this question

    Create a free account to see it

22. 16 more marking schemes are on this page. A free account opens all of them, and lets you build your own paper on the topics you have actually taught, laid out in KNEC format with its full marking scheme.

    Create a free account

More Grade 9 Mathematics topics