Number worksheet — GCSE Higher

1.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.

2.Work out the value of √(16 + 9)

3.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

4.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

5.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

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

7.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.

8.Work out −(−3)⁴ + (−3)³

9.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

10.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

11.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

12.Work out √25 + 4² − 12 ÷ 3

13.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

14.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

15.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.