Number worksheet — GCSE Foundation

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

2.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

3.Work out 4π + 2π, giving your answer as a multiple of π.

4.Write these numbers in order, starting with the smallest: 5, −8, 0, −3, 2

5.Work out (−2)³ + (−3)² − (−4)

6.Write 200 as a product of its prime factors, using index notation.

7.A number line runs from 0 to 1 and is divided into 4 equal parts. Which mark on the line represents 1/4?

8.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

9.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

10.A laptop costs £720. A carrying case for it costs 1/9 of the price of the laptop. Work out the cost of the carrying case.

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

12.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

13.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

14.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

15.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.