Number worksheet — GCSE Higher

1.Work out (−6) + (−4) × 3

2.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

3.Simplify √45.

4.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

5.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

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

7.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

8.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.

9.Work out −4.5 + 2.8.

10.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

11.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

12.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

13.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.

14.Write 5/6 as a decimal, showing clearly which digit recurs.

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