Number worksheet — GCSE Higher

1.Work out the value of √(16 + 9)

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

3.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

4.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

5.Write 0.06 as a fraction in its simplest form.

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

7.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

8.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

9.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

10.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

11.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

12.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

13.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

14.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

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