Number worksheet — GCSE Higher

1.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

2.Round 592.5 to the nearest 10.

3.Work out √3 × √12, giving your answer as an integer.

4.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

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

6.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

7.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

8.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.

9.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

10.Which one of these statements is true?

11.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

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

13.Work out 10% of 30% of £200.

14.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

15.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.