Number worksheet — GCSE Foundation

1.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

2.Work out 18 − 4 × 2

3.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

4.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

5.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

6.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.

7.In a car park the ratio of vans to cars is 2 : 7. Work out the number of vans as a fraction of the number of cars.

8.Simplify (y³)⁴, giving your answer as a single power of y.

9.Work out 20 − 8 ÷ 2 + 1

10.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

11.Work out −7 − (−3).

12.A garden has flowers, herbs and vegetables in the ratio 2 : 3 : 4. What fraction of the garden is not vegetables?

13.Write these numbers in order, starting with the smallest: 5, −8, 0, −3, 2

14.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.

15.Simplify x⁶ ÷ x²