Number worksheet — GCSE Higher

1.Write ∛(x²) as a single power of x.

2.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

3.Find the missing number: ▢ ÷ 15 = 24

4.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

5.Estimate the value of √45, giving your answer to the nearest whole number.

6.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

7.Simplify x⁷ × x⁴, giving your answer as a single power of x.

8.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

9.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

10.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

11.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

12.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

13.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

14.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.

15.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.