Number worksheet — GCSE Higher

1.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

2.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

3.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

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

5.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

6.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

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

8.Write 0.875 as a fraction in its simplest form.

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

10.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

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

12.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.

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

14.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

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