Number worksheet — GCSE Higher

1.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

2.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

3.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

4.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

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

6.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

7.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

8.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

9.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

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

11.Work out 3.7 × 24.

12.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

13.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

14.Write 0.005 in standard form.

15.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.