Number worksheet — GCSE Higher

1.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

2.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

3.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

4.Simplify (x⁻²)³, giving your answer as a fraction.

5.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

6.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

7.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

8.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

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

10.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

11.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

12.Work out (−2)³ + (−3)² − (−4)

13.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.

14.Work out (5 + 2) × 3²

15.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.