Number worksheet — GCSE Higher

1.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

2.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

3.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

4.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

5.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

6.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

7.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

8.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

9.Write 90 as a product of its prime factors.

10.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

11.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

12.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

13.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

14.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

15.Write 0.325 as a fraction in its simplest form.