Number worksheet — GCSE Higher

1.Work out ∛(−27) + ∛8

2.Work out (−3) × 4 + 2 × (−5)

3.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

4.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

5.Work out (−2)³ + (−3)² − (−4)

6.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.

7.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.

8.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.

9.Work out −(−3)⁴ + (−3)³

10.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

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

12.Round 0.006852 to 2 significant figures.

13.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

14.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

15.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.