Number worksheet — GCSE Higher

1.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

2.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

3.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.

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

5.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

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

7.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.

8.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

9.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

10.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

11.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

12.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

13.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.

14.After a price increase of 10%, a laptop costs £330. Work out the original price.

15.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.