Number worksheet — GCSE Higher

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

2.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.

3.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

4.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.

5.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

6.Round 0.006482 to 2 significant figures.

7.Write ∛(x²) as a single power of x.

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

9.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.

10.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

11.Simplify √45.

12.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

13.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

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

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