Number worksheet — GCSE Higher

1.4ˣ = 64. Work out the value of x.

2.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

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

4.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

5.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

6.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.

7.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.

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

9.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

10.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

11.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

12.Work out how many factors 100 has.

13.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

14.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

15.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.