Number worksheet — GCSE Higher

1.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.

2.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

3.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.

4.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.

5.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

6.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.

7.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

8.Round 0.006852 to 2 significant figures.

9.Work out (−36) ÷ (−6) × 2

10.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

11.Work out 5⁰ + 5¹ + 5²

12.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

13.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

14.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

15.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.