Number worksheet — GCSE Higher

1.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

2.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

3.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

4.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

5.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

6.Work out how many factors 36 has.

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

8.2/3 of an amount of money is £30. Work out the amount.

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

10.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

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

12.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

13.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

14.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

15.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.