Number worksheet — GCSE Higher

1.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.

2.Write 12 as a product of its prime factors.

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

4.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

5.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

6.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

7.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.

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

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

10.Which of these statements about −0.7 and −0.25 is true?

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

12.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

13.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

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

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