Number worksheet — GCSE Higher

1.Write 0.35 as a fraction in its lowest terms.

2.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

3.Work out −4.5 + 2.8.

4.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

5.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

6.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

7.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

8.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.

9.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.

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

11.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

12.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.

14.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

15.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.