Number worksheet — GCSE Higher

1.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

2.Work out √25 + 4² − 12 ÷ 3

3.Given that 2⁵ = 32, work out 2⁶.

4.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

5.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

6.Simplify (3a²)² × (2a)³

7.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.

8.Work out the value of 2⁻²

9.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

10.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

11.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

12.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.

13.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

14.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

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