Number worksheet — GCSE Higher

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

2.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.

3.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

4.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.

5.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.

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

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

8.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

9.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.

10.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.

11.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

12.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

13.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

14.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

15.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.