Number worksheet — GCSE Higher

1.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

2.Simplify (y³)⁴, giving your answer as a single power of y.

3.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

4.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.

6.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

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

8.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

9.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

10.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

11.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

12.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

13.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

14.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

15.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.