Number worksheet — GCSE Higher

1.Work out the value of √49 + ∛27

2.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

3.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

4.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

5.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.

6.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

7.Work out √225 ÷ 3.

8.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

9.2/3 of an amount of money is £30. Work out the amount.

10.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

11.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

12.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

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

14.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.

15.Work out (2/3)² + (1/2)². Give your answer as a fraction.