Integers

12 Grade 8 Mathematics questions on Integers, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   1 mark

   Evaluate: $(-6)+(+9)-(-4)$

   A. -1

   B. 7

   C. 11

   D. -7

   (1 mark)

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2. Question 2

   1 mark

   Arrange in ascending order: -5, 3, -8, 0, -1

   A. -8, -5, 0, -1, 3

   B. 3, 0, -1, -5, -8

   C. -8, -5, -1, 0, 3

   D. -1, -5, -8, 0, 3

   (1 mark)

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3. Question 3

   1 mark

   Evaluate: $(-12)÷(+4)\times (-2)$

   A. -6

   B. 6

   C. -1.5

   D. 24

   (1 mark)

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4. Question 4

   1 mark

   Evaluate: $-20+(-5)-(-8)$

   A. -17

   B. -33

   C. -7

   D. 17

   (1 mark)

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5. Question 5

   3 marks

   A diver starts at the surface (0 m). She descends 18 m, rises 7 m, then descends a further 5 m. Find her final position relative to the surface.

   (3 marks)

   Marking scheme

   Take the surface as $0$, downwards as negative and upwards as positive. (1)

   Descending $18$ m gives $0-18=-18$ m; rising $7$ m gives $-18+7=-11$ m. (1)

   Descending a further $5$ m: $-11-5=-16$ m. (1)

   Final answer: $-16$ m, that is $16$ m below the surface.

6. Question 6

   3 marks

   Evaluate: $(-7)\times (+4)+(-6)\times (-5)-(-2)$

   (3 marks)

   Marking scheme

   Do the multiplications first. $(-7)\times (+4)=-28$, since a negative times a positive is negative. (1)

   $(-6)\times (-5)=+30$, since a negative times a negative is positive. (1)

   Subtracting $-2$ is the same as adding $2$: $-28+30+2=4$. (1)

   Final answer: $4$.

7. Question 7

   1 mark

   Evaluate: $-15-(-7)+(-3)$

   A. -25

   B. -5

   C. -1

   D. -11

   (1 mark)

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8. Question 8

   1 mark

   Evaluate: $(-4)\times (-6)÷(+3)$

   A. -8

   B. 2

   C. -2

   D. 8

   (1 mark)

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9. Question 9

   3 marks

   The temperature in a town was -4 degrees C at 6 a.m. It rose by 11 degrees C by midday, then fell by 9 degrees C by midnight. Work out the temperature at midnight.

   (3 marks)

   Marking scheme

   A rise is added and a fall is subtracted, starting from $-4{}^{\circ }$C. (1)

   By midday: $-4+11=7{}^{\circ }$C. (1)

   By midnight it falls $9$ degrees: $7-9=-2{}^{\circ }$C. (1)

   Final answer: $-2{}^{\circ }$C.

10. Question 10

    1 mark

    A submarine is at -250 m. It rises 90 m, then descends 40 m. What is its new depth?

    A. -200 m

    B. -380 m

    C. -120 m

    D. -300 m

    (1 mark)

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11. Question 11

    1 mark

    Find the value of $(-3{)}^2$

    A. -9

    B. -6

    C. 9

    D. 6

    (1 mark)

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12. Question 12

    1 mark

    The temperature at night was -3 degrees C. By noon it had risen by 8 degrees C. What was the noon temperature?

    A. -11 degrees C

    B. 11 degrees C

    C. 5 degrees C

    D. -5 degrees C

    (1 mark)

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