Number worksheet — GCSE Higher

1.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

2.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

3.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

4.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

5.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

6.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

7.Work out −4.5 + 2.8.

8.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

9.Work out (−36) ÷ (−6) × 2

10.Work out √225 ÷ 3.

11.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.

12.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

13.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

14.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.

15.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.