Number worksheet — GCSE Higher

1.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.

2.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

3.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

4.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

5.Work out 3 + 4 × (−2).

6.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

7.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

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

9.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

10.Work out the value of 2⁻²

11.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

12.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

13.Work out (−2)³ + (−3)² − (−4)

14.Work out 35% of 180.

15.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.