Number worksheet — GCSE Higher

1.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.

2.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

3.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

4.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

5.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

6.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

7.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.

8.Work out 3³ + 2⁴.

9.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.

10.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

11.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

12.Work out 100 − 4 × 5²

13.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

14.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

15.Work out √144 − 2 × 3 + √25