Ratio, proportion and rates of change worksheet — GCSE Higher

1.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.

2.5 decorators paint 3 rooms in 6 hours. All the decorators work at the same rate. Work out how long it takes 10 decorators to paint 5 rooms.

3.Write 250 g : 2 kg as a ratio in its simplest form.

4.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.

5.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.

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

7.An oven is preheating. Its temperature, T °C, is plotted against time, t minutes, on a straight-line graph. The line passes through the points (2, 60) and (6, 140). Work out the gradient of the line.

8.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.

9.Two quantities, P and Q, are in inverse proportion. A graph is drawn with P on the vertical axis and Q on the horizontal axis. Write down which description fits the shape of this graph.

10.The table shows values of x and y. x: 3, 5, 8. y: 12, 20, 32. Which statement correctly describes the relationship between x and y?

11.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.

12.The height of a candle, in cm, is measured as it burns: t = 0 min, height = 20.0; t = 3 min, height = 18.7; t = 5 min, height = 17.5; t = 6 min, height = 16.6; t = 7 min, height = 15.4; t = 9 min, height = 13.4. Which pair of readings gives the best estimate of the instantaneous rate of change of the height at t = 6 minutes, and why?

13.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.

14.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.

15.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.