Number worksheet — GCSE Foundation

1.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

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

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

4.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

5.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

6.Write 0.0038 in standard form.

7.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.

8.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.

9.A shelf is 60 cm long, correct to the nearest 10 cm. Write down the upper bound for the length of the shelf, in centimetres.

10.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

11.Write 260,000 in standard form.

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

13.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

14.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

15.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.