Number worksheet — GCSE Higher

1.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

2.Write 5/6 as a decimal, showing clearly which digit recurs.

3.Write down the symbol that makes this statement true: −2/3 ___ −5/6

4.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.

5.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

6.Work out 5/6 × 2/9, giving your answer in its simplest form.

7.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

8.Expand and simplify √3(2 + √12).

9.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

10.Write ∛(x²) as a single power of x.

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

12.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

13.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

14.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

15.Write 0.325 as a fraction in its simplest form.