Ratio, proportion and rates of change worksheet — GCSE Foundation

1.300 g of a salt solution of concentration 10% is poured into 200 g of a salt solution of concentration 25%. Work out the concentration of salt in the mixture.

2.Triangle A and triangle B are mathematically similar. A side of triangle A is 5 cm long, and the corresponding side of triangle B is 15 cm long. Write the ratio of the length in triangle A to the length in triangle B in its simplest form.

3.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.

4.In a recipe the mass of chocolate to the mass of milk is in the ratio 1:4. Amelia uses 200 g of milk. Work out the mass of chocolate she needs.

5.Line P passes through the origin and the point (3, 21). Line Q passes through the origin and the point (5, 45). Both lines represent the distance, in metres, run by an athlete against the time, in seconds. Work out the gradient of the steeper line.

6.Simplify the ratio 12 : 18 : 30 to its simplest form.

7.A recipe for pancakes uses 240 g of flour to make pancakes for 6 people. Work out how many grams of flour are needed to make pancakes for 15 people, using the same recipe.

8.A table shows three pairs of values: when x = 2, y = 6; when x = 5, y = 15; when x = 8, y = 24. In every pair the ratio y : x is the same. Write down a formula for y in terms of x.

9.A car travels 180 miles in 3 hours. A lorry travels 160 miles in 4 hours. Write the car's average speed as a fraction of the lorry's average speed, giving your answer in its simplest form.

10.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.

11.Write the ratio 4x : 6x in its simplest form, where x is a positive number.

12.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?

13.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.

14.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.

15.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.