Number worksheet — GCSE Higher

1.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

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

3.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

4.Write ∛(x²) as a single power of x.

5.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

6.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.

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

8.Work out 3.7 × 24.

9.Expand and simplify √3(2 + √12).

10.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

11.Find the missing number: ▢ ÷ 15 = 24

12.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

13.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

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

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