Number worksheet — GCSE Higher

1.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

2.√700 lies between which two consecutive integers?

3.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

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

5.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

6.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

7.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.

8.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

9.Write 7/12 as a decimal, showing clearly which digit is recurring.

10.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

11.Work out 6² − 4².

12.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

13.After a price increase of 10%, a laptop costs £330. Work out the original price.

14.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

15.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.