Number worksheet — GCSE Higher

1.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

2.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

3.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.

4.Work out how many factors 100 has.

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

6.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

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

8.Work out (2/3)² + (1/2)². Give your answer as a fraction.

9.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

10.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

11.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

12.Work out 3 + 4 × (−2).

13.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

14.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

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