Number worksheet — GCSE Higher

1.Work out √144 − 2 × 3 + √25

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

3.Simplify (3a²)² × (2a)³

4.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.

5.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

6.Work out 4368 ÷ 12.

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

8.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

9.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.

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

11.Last year a company made a profit of £5,200,000. Write this amount in standard form.

12.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

13.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

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

15.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.