Ratio, proportion and rates of change worksheet — GCSE Foundation

1.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.

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

3.A textbook is reduced from £60 to £45. Work out the percentage reduction.

4.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.

5.A cyclist travels 45 km in 3 hours at a constant speed. Work out the cyclist's average speed, in km/h.

6.A map has a scale of 1 : 100 000. Two railway stations are 8 km apart in real life. Work out the distance between the stations on the map, in centimetres.

7.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².

8.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.

9.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.

10.£3000 is invested in a savings account that pays 4% compound interest each year. Work out the value of the investment after 2 years.

11.Two mathematically similar cubes have edge lengths 2 cm and 6 cm. Write the ratio of the volume of the smaller cube to the volume of the larger cube in its simplest form.

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

13.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.

14.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.

15.Write the ratio 4 : 9 in the form 1 : n.