Number worksheet — GCSE Higher

1.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.

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

3.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

4.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

5.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

6.Work out √25 + 4² − 12 ÷ 3

7.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

8.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

9.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

10.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

11.Which statement about the number 91 is correct?

12.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

13.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

14.Work out −(−3)⁴ + (−3)³

15.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.