Number worksheet — GCSE Higher

1.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

2.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.

3.Round 592.5 to the nearest 10.

4.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

5.Write 200 as a product of its prime factors, using index notation.

6.Work out the value of √(16 + 9)

7.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.

8.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

9.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

10.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

11.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

12.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

13.Which of these is written correctly in standard form?

14.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.

15.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.