Number worksheet — GCSE Higher

1.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

2.After a price increase of 10%, a laptop costs £330. Work out the original price.

3.Simplify x⁶ ÷ x²

4.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

5.Work out ∛(−27) + ∛8

6.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.

7.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

8.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

9.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

10.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.

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

12.Work out ⁴√81

13.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

14.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

15.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.