Number worksheet — GCSE Higher

1.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

2.4ˣ = 64. Work out the value of x.

3.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

4.Work out ∛(−27) + ∛8

5.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

6.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

7.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

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

9.√700 lies between which two consecutive integers?

10.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

11.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

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

13.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

14.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

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