Number worksheet — GCSE Higher

1.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

2.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.

3.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

4.A charity raffle sells 240 tickets at £1.85 each. 40% of the money raised is given to a local hospital. Work out how much money the hospital receives.

5.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

6.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

7.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.

8.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

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

10.Work out (−36) ÷ (−6) × 2

11.Work out (−2)² − 3

12.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

13.Simplify x⁶ ÷ x²

14.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

15.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.