Number worksheet — GCSE Higher

1.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

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

3.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.

4.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

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

6.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

7.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

8.Work out −4.5 + 2.8.

9.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

10.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

11.Work out 100 − 4 × 5²

12.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

13.Work out √225 ÷ 3.

14.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

15.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.