Number worksheet — GCSE Higher

1.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

2.Work out (−2)² − 3

3.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.

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 metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

6.Work out (−6) + (−4) × 3

7.Write down the symbol that makes this statement true: −2/3 ___ −5/6

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

9.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

10.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

11.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.

12.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

13.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

14.Write 0.35 as a fraction in its lowest terms.

15.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.