Number worksheet — GCSE Higher

1.Work out the value of (√5)⁴

2.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

3.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

4.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

5.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

6.Work out −4.5 + 2.8.

7.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

8.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

9.Find the missing number: ▢ ÷ 15 = 24

10.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

11.Write 0.005 in standard form.

12.Simplify ⁴√(16a⁸b¹²)

13.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

14.Find the missing number: 17 × ▢ = 391

15.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.