Number worksheet — GCSE Higher

1.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

2.Work out how many factors 100 has.

3.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

4.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

5.Work out 3 + 4 × (−2).

6.Work out the exact value of √(2² + 3²)

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.Simplify (x⁻²)³, giving your answer as a fraction.

9.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

10.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.

11.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

12.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

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

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

15.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.