Number worksheet — GCSE Higher

1.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

2.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

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

4.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

5.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

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

7.Find the missing number: ▢ ÷ 15 = 24

8.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.

9.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

10.Given that 2⁵ = 32, work out 2⁶.

11.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

12.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

13.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.

14.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.

15.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.