Number worksheet — GCSE Higher

1.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

2.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

3.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

4.Simplify x⁷ × x⁴, giving your answer as a single power of x.

5.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

6.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.

7.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

8.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

9.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.

10.Simplify (x⁻²)³, giving your answer as a fraction.

11.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.

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

13.Work out 35% of 180.

14.Work out √144 − 2 × 3 + √25

15.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.