Number worksheet — GCSE Higher

1.Work out 3.7 × 24.

2.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?

3.Work out ⁴√16

4.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.

5.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

6.Work out √225 ÷ 3.

7.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.

8.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

9.4ˣ = 64. Work out the value of x.

10.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.

11.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

12.Work out (−36) ÷ (−6) × 2

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

14.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

15.Work out 100 − 4 × 5²