Number worksheet — GCSE Higher

1.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.

2.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?

3.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

4.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

5.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.

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

7.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

8.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

9.Write 90 as a product of its prime factors.

10.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

11.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

12.2/3 of an amount of money is £30. Work out the amount.

13.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

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

15.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.