Number worksheet — GCSE Higher

1.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.

2.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

3.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

4.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

5.Work out 5/6 × 2/9, giving your answer in its simplest form.

6.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

7.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.

8.Simplify x⁶ ÷ x²

9.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

10.Write ∛(x²) as a single power of x.

11.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

12.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

13.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

14.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

15.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.