Number worksheet — GCSE Higher

1.Write down the reciprocal of 0.2

2.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

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

4.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

5.Work out 3 × (−2)² − 5

6.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

7.Write 0.325 as a fraction in its simplest form.

8.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

9.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

10.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

11.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

12.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

13.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.

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