Number worksheet — GCSE Higher

1.Write down the symbol that makes this statement true: −2/3 ___ −5/6

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

3.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

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

5.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

6.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

7.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

8.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

9.Work out the value of 6² − 4³.

10.Simplify √8 + √18, giving your answer in the form k√2.

11.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

12.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

13.Estimate the value of √45, giving your answer to the nearest whole number.

14.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

15.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.