Number worksheet — GCSE Higher

1.Work out (−6) + (−4) × 3

2.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.

3.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

4.Work out 100 − 4 × 5²

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

6.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

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.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.

9.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

10.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.

11.Work out ⁴√81

12.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

13.Simplify √45.

14.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

15.Simplify (x⁻²)³, giving your answer as a fraction.