Printable · GCSE Higher · ages 14-16
Direct and inverse proportion worksheet — GCSE Higher
Fifteen questions on "direct and inverse proportion" — DfE statement R10. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Direct and inverse proportion worksheet — GCSE Higher
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- 1.Two cars travel at constant speeds. Car A travels 150 km in 3 hours. Car B travels 180 km in 4 hours. Which car is faster, and what is its speed?
- 2.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
- 3.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.
- 4.It takes 2 identical pumps 10 hours to empty a flooded basement. Working at the same rate, work out how many hours 5 of these pumps would take to empty the same basement.
- 5.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.
- 6.Amelia uses 2 kg of flour to bake 5 cakes. Using the same recipe, work out how many cakes she can bake with 6 kg of flour.
- 7.A factory machine produces bottles at a constant rate. In 45 minutes it produces 810 bottles. The factory needs 2,160 bottles for an order. Working at the same rate, work out how many minutes it will take to produce the order.
- 8.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.
- 9.The exchange rate is £1 = €1.15. Convert £200 to euros.
- 10.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.
- 11.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.
- 12.A 750 g box of cereal costs £2.70. A 500 g box of the same cereal costs £1.95. Work out which box is better value, and its cost per 100 g.
- 13.6 identical taps fill a paddling pool in 20 minutes. Each tap fills at the same steady rate. Work out how long 3 of these taps would take to fill the same pool.
- 14.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
- 15.A shop sells rope by the metre. 3 m costs £7.50 and 5 m costs £11.00. Does this data show that the cost is directly proportional to the length of rope bought? Choose the correct verdict and reason.
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