Number worksheet — GCSE Higher

1.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.

2.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.

3.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

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

5.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

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

7.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

8.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

9.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

10.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

11.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

12.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

13.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

14.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

15.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.