Number worksheet — GCSE Higher

1.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

2.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

3.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

4.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

5.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

6.Work out the value of (√5)⁴

7.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.

8.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

9.Work out ⁴√16

10.Simplify √8 + √18, giving your answer in the form k√2.

11.Round 0.006852 to 2 significant figures.

12.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

13.Work out the value of 6² − 4³.

14.Work out (−6) + (−4) × 3

15.Simplify x⁷ × x⁴, giving your answer as a single power of x.