Number worksheet — GCSE Higher

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 (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

3.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

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

5.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.

6.Write 90 as a product of its prime factors.

7.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

8.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

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.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.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

12.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

13.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

14.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

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