Number worksheet — GCSE Higher

1.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.

2.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

3.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

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

5.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

6.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

7.Find the missing number: 17 × ▢ = 391

8.Write down the reciprocal of 0.2

9.Write down the symbol that makes this statement true: −2/3 ___ −5/6

10.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

11.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.

12.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

13.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

14.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

15.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.