Number worksheet — GCSE Higher

1.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

2.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

3.Simplify ⁴√(16a⁸b¹²)

4.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

5.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

6.Work out √144 − 2 × 3 + √25

7.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

8.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

9.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

10.Work out ∛(−27) + ∛8

11.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.

12.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

13.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

14.Simplify √45.

15.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.