Number worksheet — GCSE Higher

1.Work out (2/3)² + (1/2)². Give your answer as a fraction.

2.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

3.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

4.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.

5.Work out the reciprocal of (2 + 3)

6.Work out (−3) × 4 + 2 × (−5)

7.Work out ⁴√16

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.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

10.Write 0.875 as a fraction in its simplest form.

11.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

12.Work out (−6) + (−4) × 3

13.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

14.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

15.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.