Year 8 Computation with integers: free practice test with answers

Sample computation with integers questions with answers

Try each one before you open the answer.

1. Adding and subtracting positive integers

   Use a mental strategy to find $487 + 296$.

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   Key idea: $296$ is close to $300$, so add $300$ and then take away the extra $4$.

   1. $487 + 300 = 787$
   2. $296 = 300 - 4$, so subtract $4$: $787 - 4 = 783$

   Answer: $783$

2. Multiplying and dividing positive integers

   Use a mental strategy to find $36 \times 25$.

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   Key idea: $4 \times 25 = 100$, so split $36$ into $9 \times 4$.

   1. $36 \times 25 = 9 \times 4 \times 25$
   2. $= 9 \times 100$
   3. $= 900$

   Answer: $900$

3. Number properties

   Evaluate $\sqrt{196}$.

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   Key idea: Find the number that multiplies by itself to give 196.

   1. $14 \times 14 = 196$
   2. So $\sqrt{196} = 14$

   Answer: $14$

4. Divisibility and prime factorisation

   Write $360$ as a product of its prime factors in index form.

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   Key idea: Keep dividing by prime numbers (a factor tree) until every factor is prime.

   1. $360 = 2 \times 180 = 2 \times 2 \times 90 = 2 \times 2 \times 2 \times 45$
   2. $45 = 3 \times 15 = 3 \times 3 \times 5$
   3. So $360 = 2 \times 2 \times 2 \times 3 \times 3 \times 5 = 2^3 \times 3^2 \times 5$

   Answer: $2^3 \times 3^2 \times 5$

5. Negative integers

   Write these integers in ascending order (smallest to largest):

   $$-7, 4, -12, 0, -3, 9$$
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   Key idea: On a number line, numbers further to the left are smaller. The negative number with the larger size is the smaller number.

   1. Negative integers, from furthest left: $-12, -7, -3$
   2. Then zero, then the positive integers: $0, 4, 9$

   Answer: −12, −7, −3, 0, 4, 9

6. Adding and subtracting negative integers

   Evaluate $-14 + 9 - (-5)$.

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   Key idea: Subtracting a negative is the same as adding its positive. Then work left to right.

   1. Rewrite the subtraction of a negative: $-14 + 9 - (-5) = -14 + 9 + 5$
   2. Add the positive integers first as a mental strategy: $9 + 5 = 14$, so $-14 + 14$
   3. Evaluate: $-14 + 14 = 0$

   Answer: $0$

7. Multiplying and dividing negative integers

   At midnight the temperature in a town was $-6{°}$C. By noon it had risen by $11{°}$C, then during the afternoon it fell by $3{°}$C for each of the next $4$ hours. What was the temperature at the end of those $4$ hours?

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   Key idea: Rise means add, fall means subtract. A repeated fall can be written as multiplication.

   1. Temperature at noon after the rise: $-6 + 11 = 5 \text{ °C}$
   2. Total drop over 4 hours: $3 \times 4 = 12 \text{ °C}$
   3. Temperature after the fall: $5 - 12 = -7 \text{ °C}$

   Answer: $-7{°}$C

8. Order of operations and substitution

   Evaluate $3 - (-2)^3 \div 4 \times (-1)$.

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   Key idea: Follow BODMAS: evaluate the power first, then division and multiplication left to right, then subtraction.

   1. Evaluate the power: $(-2)^3 = -8$, so the expression becomes $3 - (-8) \div 4 \times (-1)$
   2. Division (left to right): $(-8) \div 4 = -2$, giving $3 - (-2) \times (-1)$
   3. Multiplication: $(-2) \times (-1) = 2$, giving $3 - 2$
   4. Subtract: $3 - 2 = 1$

   Answer: $1$

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 8 algebra worksheet
• Year 8 integer operations worksheet