Number worksheet — GCSE Higher

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

2.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

3.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.

4.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

5.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.

6.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

7.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

8.Write ∛(x²) as a single power of x.

9.Work out √(4 × 9)

10.Work out (−2)² − 3

11.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

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

13.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

14.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.

15.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.