Number worksheet — GCSE Higher

1.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

2.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

3.Work out the value of (1/3)⁻²

4.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

5.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

6.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

7.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?

8.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

9.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

10.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

11.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

12.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

13.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

15.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.