Number worksheet — GCSE Higher

1.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

2.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

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.Write 0.35 as a fraction in its lowest terms.

5.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

6.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

7.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.

8.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

9.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

10.Work out how many factors 100 has.

11.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

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

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.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.

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