Ratio, proportion and rates of change worksheet — GCSE Higher

1.The mass of a length of copper pipe is proportional to its length. A pipe of length 4.5 m has a mass of 12.6 kg. Work out the mass of a pipe of the same type of length 9.5 m.

2.In a fruit squash mix, the ratio of squash to water is 2 : 9. A shop wants to make up the mix using 3.4 litres of squash. Work out how many litres of water are needed.

3.A metal sample has a mass of 342.6 g and a volume of 18 cm³. Work out the density of the sample, in g/cm³, to 1 decimal place.

4.A charity fun run raises money through entry fees and donations. Entry fees raise £1,260, which is 60% of the total amount raised. Work out how much money was raised through donations.

5.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

6.6 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.

7.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.

8.A scale drawing of a park has a scale of 1 : 2500. On the drawing, the distance between the entrance and the lake is 4.4 cm. A jogger runs from the entrance to the lake and then back to the entrance. Work out the total distance the jogger runs, in kilometres.

9.Write the ratio 8 : 15 in the form 1 : n.

10.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.

11.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.

12.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.

13.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.

14.A photo is enlarged so that its new width is 1.4 times its original width. Write the multiplier that would scale the new width back down to the original width, as a fraction in its simplest form.

15.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.