Number worksheet — GCSE Higher

1.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

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

3.Write 0.35 as a fraction in its lowest terms.

4.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

5.Work out (−36) ÷ (−6) × 2

6.Work out ∛64.

7.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.

8.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

9.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.

10.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

11.4ˣ = 64. Work out the value of x.

12.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

13.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

14.Simplify x⁶ ÷ x²

15.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.