Number worksheet — GCSE Higher

1.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

2.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

3.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

4.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.

5.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

6.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.

7.Write 7/12 as a decimal, showing clearly which digit is recurring.

8.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

9.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

10.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

11.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

12.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

13.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

14.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

15.Simplify 2³ × 2⁴, giving your answer as a single power of 2.