Number worksheet — GCSE Higher

1.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

2.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.

3.Simplify x⁷ × x⁴, giving your answer as a single power of x.

4.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.

5.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

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

7.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

8.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

9.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

10.Work out the value of √49 + ∛27

11.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

12.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

13.√700 lies between which two consecutive integers?

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

15.Work out √3 × √12, giving your answer as an integer.