Number worksheet — GCSE Higher

1.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

2.Write down the exact decimal value of the fraction 1/6.

3.A country has an area of 25,000,000 hectares. Write this area in standard form.

4.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

5.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

6.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

7.Work out ∛64.

8.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

9.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

10.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

11.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

12.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.

13.Work out the reciprocal of (2 + 3)

14.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

15.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.