Number worksheet — GCSE Higher

1.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

2.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

3.Find the missing number: 17 × ▢ = 391

4.4ˣ = 64. Work out the value of x.

5.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.

6.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.

7.Simplify x⁷ × x⁴, giving your answer as a single power of x.

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

9.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

10.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

11.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

12.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

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

14.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.

15.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.