Number worksheet — GCSE Higher

1.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

2.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

3.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.

4.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

5.Work out the value of 6² − 4³.

6.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

7.Work out (−3) × 4 + 2 × (−5)

8.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

9.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

10.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

11.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

12.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.

13.Simplify (3a²)² × (2a)³

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

15.Work out −4.5 + 2.8.