Number worksheet — GCSE Higher

2.Simplify ⁴√(16a⁸b¹²)

3.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

4.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

5.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

6.Work out the value of √(16 + 9)

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

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

9.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

10.Write 7/12 as a decimal, showing clearly which digit is recurring.

11.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

12.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

13.Work out √25 + 4² − 12 ÷ 3

14.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

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