Ratio, proportion and rates of change worksheet — GCSE Higher

1.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.

2.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.

3.A crate exerts a force of 84 N on the floor through a base with an area of 2.4 m². Work out the pressure on the floor, in N/m².

4.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.

5.The strength of a radio signal, in units, is inversely proportional to the square of the distance from the transmitter, in km. At a distance of 2 km the signal strength is 20 units. Construct the equation connecting signal strength S and distance d, then work out the distance at which the signal strength is 5 units.

6.A taxi journey of m miles costs C pounds, where C = 2.5m + 3. A driver says the ratio C : m is the same for every journey. Is the driver correct? Give a reason for your answer.

7.A novel has 312 pages. A comic has 48 pages. Write the number of pages in the novel as a fraction of the number of pages in the comic, giving your answer in its simplest form.

8.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

9.Simplify the ratio 45 : 30 : 75 to its simplest form.

10.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.

11.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.

12.To make orange paint, red and yellow paint are mixed in the ratio 6:15. Write the amount of red paint as a fraction of the amount of yellow paint, in its simplest form.

13.A cyclist's speed, in metres per second, is plotted against time, in seconds, since she sets off. Which statement correctly pairs the gradient of a tangent to this graph, and the area between the graph and the time-axis, with what each one represents?

14.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.

15.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.