Number worksheet — GCSE Higher

1.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.

2.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

3.3/5 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.

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 distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

7.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

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

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

10.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

11.2/3 of an amount of money is £30. Work out the amount.

12.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

13.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

14.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

15.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.