GCSE Mathematics (9-1)

Work through these on your own. Keep your working neat: the method matters as much as the answer. Questions marked H are for Higher tier.

1.4 Priority of operations and inverse operations — Practise

Work through these on your own. Keep your working neat: the method matters as much as the answer. Questions marked H are for Higher tier.

  1. Work out 6+4×36 + 4 \times 3.
  2. Work out (6+4)×3(6 + 4) \times 3.
  3. Work out 30−2×730 - 2 \times 7.
  4. Work out 42−54^2 - 5.
  5. Work out 15÷3+2×415 \div 3 + 2 \times 4.
  6. Work out 20−12÷420 - 12 \div 4.
  7. Work out 36÷6×236 \div 6 \times 2.
  8. Work out 10+2510 + \sqrt{25}.
  9. Work out 2×(9−4)22 \times (9 - 4)^2.
  10. I think of a number, add 6, then multiply by 3. The result is 36. Find the number.
  11. I think of a number, square it, then subtract 5. The result is 20. Find the possible values.
  12. Write an expression for the profit at the stall and evaluate it.
  13. H Insert brackets to make the statement true: 2+3×4−1=192 + 3 \times 4 - 1 = 19.
  14. H Work out 3+4×(7−22)3 + 4 \times (7 - 2^2).
Answers and concise solutions

1. 6+4×36 + 4 \times 3

Answer: 1818.

2. (6+4)×3(6 + 4) \times 3

Answer: 3030.

3. 30−2×730 - 2 \times 7

Answer: 1616.

4. 42−54^2 - 5

Answer: 1111.

5. 15÷3+2×415 \div 3 + 2 \times 4

Answer: 5+8=135 + 8 = 13.

6. 20−12÷420 - 12 \div 4

Answer: 1717.

7. 36÷6×236 \div 6 \times 2

Answer: 6×2=126 \times 2 = 12.

8. 10+2510 + \sqrt{25}

Answer: 1515.

9. 2×(9−4)22 \times (9 - 4)^2

Answer: 2×52=2×25=502 \times 5^2 = 2 \times 25 = 50.

10. The number

Answer: 36÷3=1236 \div 3 = 12, then 12−6=612 - 6 = 6.

11. Possible values

Answer: x2−5=20x^2 - 5 = 20, so x2=25x^2 = 25 and x=5x = 5 or x=−5x = -5.

12. Stall profit

Answer: 95×1.20+6×3.00−(120×0.65+8×1.85)=£39.2095 \times 1.20 + 6 \times 3.00 - (120 \times 0.65 + 8 \times 1.85) = £39.20.

13. Brackets to make 19

Answer: (2+3)×4−1=19(2 + 3) \times 4 - 1 = 19.

14. 3+4×(7−22)3 + 4 \times (7 - 2^2)

Answer: 22=42^2 = 4, 7−4=37 - 4 = 3, 4×3=124 \times 3 = 12, 3+12=153 + 12 = 15.

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