Number worksheet — GCSE Higher

1.Expand and simplify √3(2 + √12).

2.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

3.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

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

5.4ˣ = 64. Work out the value of x.

6.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

7.Work out (−3) × 4 + 2 × (−5)

8.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

9.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

10.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.

11.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

12.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

13.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

14.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

15.Work out ⁴√16