Number worksheet — GCSE Higher

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

3.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.

4.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.

5.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

6.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

7.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

8.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

10.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

11.Write 7/12 as a decimal, showing clearly which digit is recurring.

12.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

13.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

14.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

15.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.