Number worksheet — GCSE Higher

1.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

2.√700 lies between which two consecutive integers?

3.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

4.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

5.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

6.Round 0.006482 to 2 significant figures.

7.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

8.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

9.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

10.Write 0.35 as a fraction in its lowest terms.

11.Expand and simplify √3(2 + √12).

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

13.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

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

15.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.