Number worksheet — GCSE Higher

1.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.

2.Write 60 as a product of its prime factors, using index notation.

3.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

4.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

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

6.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

7.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.

8.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

9.Work out how many factors 36 has.

10.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

12.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

13.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

14.Work out 3.7 × 24.

15.Work out 4368 ÷ 12.