Number worksheet — GCSE Foundation

1.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

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

3.Which of these numbers is a common factor of 18 and 24?

4.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

5.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

6.Work out ∛(−27) + ∛8

7.Using only 20p coins and 10p coins, and at least one of each, work out how many different ways there are to make exactly 60p. List the possibilities systematically.

8.Write 0.36 as a fraction in its simplest form.

9.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

10.In a choir, 2/9 of the members are boys and the rest are girls. Write down the ratio of girls to boys, in its simplest form.

11.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

12.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

13.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

14.Which of these numbers lies between −8 and −5 on a number line?

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.