Number worksheet — GCSE Higher

1.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

2.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

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

4.Work out how many factors 36 has.

5.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

6.Work out 35% of 180.

7.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

8.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

9.Which of these is written correctly in standard form?

10.Work out the value of (√5)⁴

11.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

12.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

13.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

14.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

15.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.