Number worksheet — GCSE Higher

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

2.Given that 2⁵ = 32, work out 2⁶.

3.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

4.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.

5.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.

6.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.

7.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

8.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

9.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

10.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

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

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

13.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

14.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

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