Number worksheet — GCSE Foundation

1.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

2.Work out how many factors 36 has.

3.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.

4.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

5.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

6.A tin of beans has a mass of 650 g. A bag of rice has a mass of 1.35 kg. Work out the total mass, in kilograms.

7.Work out 3 + 4 × 2²

8.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.

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

10.A jar of jam costs £2.35. Tom buys 3 jars. He says the total cost is more than £7. Work out the exact total cost, and state whether Tom's claim is correct.

11.Oliver uses his calculator to work out 25% of 80 and writes down 320. Without using a calculator, work out the correct value of 25% of 80.

12.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

13.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

14.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

15.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.