Number worksheet — GCSE Higher

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

2.Which of these statements about −0.7 and −0.25 is true?

3.Work out the value of (1/3)⁻²

4.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

5.Write down the symbol that makes this statement true: −2/3 ___ −5/6

6.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

7.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

8.Work out 100 − 4 × 5²

9.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

10.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

11.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

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

13.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.

14.Last year a company made a profit of £5,200,000. Write this amount in standard form.

15.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.