Number worksheet — GCSE Higher

1.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.

2.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

3.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

4.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

5.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

6.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

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

8.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

9.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.

10.Work out −(−3)⁴ + (−3)³

11.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.

12.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

13.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

14.Work out (−2)³ + (−3)² − (−4)

15.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.