Number worksheet — GCSE Higher

1.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

2.Write 5/6 as a decimal, showing clearly which digit recurs.

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

4.Work out the value of 6² − 4³.

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

7.Work out √3 × √12, giving your answer as an integer.

8.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.

9.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

10.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

11.Work out (−6) + (−4) × 3

12.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

13.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

14.Work out 36 ÷ (2 × 3)

15.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.