Number worksheet — GCSE Higher

1.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

2.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.

3.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

4.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

5.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

6.Simplify x⁶ ÷ x²

7.Work out ⁴√81

8.Work out ∛(−27) + ∛8

9.Simplify √8 + √18, giving your answer in the form k√2.

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

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

12.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

13.Write down the exact decimal value of the fraction 1/6.

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

15.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.