Number worksheet — GCSE Higher

1.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?

2.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

3.Round 0.006482 to 2 significant figures.

4.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

5.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

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

7.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

8.Work out 3.7 × 24.

9.Write 0.875 as a fraction in its simplest form.

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

11.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

12.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

13.Write 7/12 as a decimal, showing clearly which digit is recurring.

14.Work out the reciprocal of (2 + 3)

15.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?