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.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

3.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

4.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

5.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.

6.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

7.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

8.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

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

10.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

11.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.

12.Simplify x⁶ ÷ x²

13.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

14.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

15.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.