Number worksheet — GCSE Higher

1.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

2.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.

3.Simplify √45.

4.Simplify x⁶ ÷ x²

5.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

6.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

7.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

8.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.

9.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

10.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

11.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

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

13.Simplify (3a²)² × (2a)³

14.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

15.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?