Number worksheet — GCSE Higher

1.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

2.Find the missing number: 17 × ▢ = 391

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

4.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

5.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

6.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

7.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

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

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

10.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

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

12.Work out the exact value of √(2² + 3²)

13.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.

14.Work out 5/6 × 2/9, giving your answer in its simplest form.

15.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.