Number worksheet — GCSE Higher

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

2.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

3.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

4.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

5.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

6.Work out the value of √(16 + 9)

7.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

8.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.

9.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

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

11.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

12.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

13.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

14.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

15.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.