Number worksheet — GCSE Higher

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

2.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

3.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

4.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

5.Work out 35% of 180.

6.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

7.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.

8.A country has an area of 25,000,000 hectares. Write this area in standard form.

9.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

10.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

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 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.

13.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

14.Work out 100 − 4 × 5²

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