Number worksheet — GCSE Higher

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

2.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

3.Which of these decimals lies between 1/4 and 2/5?

4.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

5.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.

6.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

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

8.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

9.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

10.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

11.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

12.Work out √144 − 2 × 3 + √25

13.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

14.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.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.