Number worksheet — GCSE Higher

1.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.

2.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

3.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

4.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

5.Round 0.006482 to 2 significant figures.

6.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

7.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

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

9.Work out the value of 6² − 4³.

10.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

11.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

12.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

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.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

15.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.