Number worksheet — GCSE Higher

1.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

2.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

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

4.Work out 6² − 4².

5.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

6.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

7.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

8.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

9.Work out (−36) ÷ (−6) × 2

10.2/3 of an amount of money is £30. Work out the amount.

11.Work out √3 × √12, giving your answer as an integer.

12.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

13.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

14.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.

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