Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.

2.The number of members of a running club increases from 45 to 54. Work out the percentage increase.

3.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.

4.A cordial drink is made by mixing cordial concentrate and water in the ratio 1 : 6. Freya says that a 700 ml jug of this drink contains 100 ml of concentrate. Is she correct? Give a reason for your answer.

5.In a bag, the ratio of green counters to yellow counters is 3 : 8. There are 24 yellow counters. A student says, 'There must be 9 green counters.' Is the student correct? Choose the correct verdict and reason.

6.In a fruit drink, cranberry juice and apple juice are mixed in the ratio 3:7. Write the amount of apple juice as a fraction of the amount of cranberry juice, in its simplest form.

7.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.

8.Which of these ratios is equivalent to 6 : 10 : 14?

9.A jug holds 3 litres of a drink that is 60% fruit juice. 1 litre of water is added to the jug. Work out the percentage of the new mixture that is fruit juice.

10.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.

11.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.

12.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.

13.In a class, 50% of the students study French, 30% study Spanish and the rest study German. Write down the ratio of French : Spanish : German students, in its simplest form.

14.A metal alloy is made from copper and tin in the ratio 7:3. Work out the mass of tin in 250 g of the alloy.

15.A hiker's distance from the start of the trail, in kilometres, is plotted against time, in minutes, since she set off. At t = 45 minutes she stops to rest, so her distance from the start is neither increasing nor decreasing at that instant. Which statement about the tangent to the distance–time graph at t = 45 minutes is correct?