Number worksheet — GCSE Higher

1.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

2.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

3.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

4.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

5.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

6.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

7.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

8.Write 60 as a product of its prime factors, using index notation.

9.Expand and simplify √3(2 + √12).

10.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

11.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

12.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

13.√700 lies between which two consecutive integers?

14.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

15.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.