Number worksheet — GCSE Higher

1.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

2.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.

3.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

4.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

5.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

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

7.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

8.Which of these is written correctly in standard form?

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

10.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.

11.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

12.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

13.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

14.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

15.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.