Number worksheet — GCSE Higher

1.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

2.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.

3.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

4.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

5.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

6.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

7.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

8.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

9.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

10.Work out √144 − 2 × 3 + √25

11.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

12.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

13.Write 0.06 as a fraction in its simplest form.

14.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

15.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.