Number worksheet — GCSE Higher

1.Which of these statements about −0.7 and −0.25 is true?

2.Work out the value of √(16 + 9)

3.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

4.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

5.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

6.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

7.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

8.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

9.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

10.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

11.Simplify √45.

12.Work out (5 + 2) × 3²

13.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

14.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

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