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.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

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

4.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.

5.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.

6.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.

7.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.

8.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

9.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.

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

11.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

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

13.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

14.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

15.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?