Number worksheet — GCSE Higher

1.Simplify √8 + √18, giving your answer in the form k√2.

2.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

3.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

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

5.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

6.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

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

8.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

9.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

10.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

12.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

13.Write 5,000,000 in standard form.

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

15.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.