Number worksheet — GCSE Higher

1.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

2.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

3.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

4.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.

5.Work out the exact value of √(2² + 3²)

6.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

7.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

8.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

9.Work out ∛(−27) + ∛8

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

11.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

12.A charity raffle sells 240 tickets at £1.85 each. 40% of the money raised is given to a local hospital. Work out how much money the hospital receives.

13.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

14.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

15.Expand and simplify √3(2 + √12).