Number worksheet — GCSE Higher

1.√700 lies between which two consecutive integers?

2.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

3.Write 5,000,000 in standard form.

4.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

5.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.

6.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

7.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

8.Work out (−2)² − 3

9.Simplify √45.

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

11.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

12.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.

13.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

14.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

15.Simplify (y³)⁴, giving your answer as a single power of y.