Number worksheet — GCSE Higher

1.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.

2.Estimate the value of √45, giving your answer to the nearest whole number.

3.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

4.Round 0.006852 to 2 significant figures.

5.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

6.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

7.Work out 3.7 × 24.

8.Work out the exact value of √(2² + 3²)

9.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.

10.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.

11.Work out 36 ÷ (2 × 3)

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

13.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.

14.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

15.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.