Number worksheet — GCSE Higher

1.Work out (−36) ÷ (−6) × 2

2.Expand and simplify √3(2 + √12).

3.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.

4.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

5.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

6.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

7.After a price increase of 10%, a laptop costs £330. Work out the original price.

8.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.

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

10.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

11.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

12.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

13.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

14.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

15.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.