Number worksheet — GCSE Higher

1.Work out −(−3)⁴ + (−3)³

2.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

3.£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.

4.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

5.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

6.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

7.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?

8.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

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

10.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

11.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

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

13.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

14.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

15.Work out (−3) × 4 + 2 × (−5)