Number worksheet — GCSE Higher

1.Work out (−2)² − 3

2.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

3.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

4.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

5.Work out the value of 2⁻⁴

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

7.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.

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

9.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

10.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

11.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

12.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.

13.Simplify (3a²)² × (2a)³

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

15.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.