Number worksheet — GCSE Higher

1.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

2.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?

3.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.

4.Work out the value of (1/3)⁻²

5.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.

6.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.

7.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

8.Work out (−3) × 4 + 2 × (−5)

9.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

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

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

12.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

13.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.

14.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

15.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.