Number worksheet — GCSE Higher

1.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

2.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.

3.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

4.Which one of these statements is true?

5.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

6.Work out 5/6 × 2/9, giving your answer in its simplest form.

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 highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

9.Work out (−2)³ + (−3)² − (−4)

11.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

12.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

13.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

14.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

15.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.