Number worksheet — GCSE Higher

1.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

2.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.

3.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

4.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

5.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

6.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.

7.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

8.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

9.Simplify (y³)⁴, giving your answer as a single power of y.

10.Find the missing number: 17 × ▢ = 391

11.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

12.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

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

14.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

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