Ratio, proportion and rates of change worksheet — GCSE Higher

1.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.

2.Last week Priya worked 5 shifts of 7 hours. This week she worked 4 shifts of 8 hours. Write the number of hours she worked last week as a fraction of the number of hours she worked this week.

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

4.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

5.A trust fund contains £8000. Each year, 5% interest is added, and then £600 is paid out to a charity. Work out the amount remaining in the fund after 2 years.

6.A cyclist rides 17.5 km on Saturday and 12.25 km on Sunday. Write the distance ridden on Saturday as a fraction of the distance ridden on Sunday, giving your answer in its simplest form.

7.A spring's extension is directly proportional to the force applied to it. A force of 5 N produces an extension of 12 mm. Work out the extension produced by a force of 20 N.

8.A greenhouse's temperature, in °C, is recorded every hour during the day: 09:00, 15.0; 10:00, 18.4; 11:00, 20.1; 12:00, 19.8; 13:00, 17.2. Work out between which two consecutive readings the instantaneous rate of change of the temperature is most likely to have been zero.

9.An architect builds a scale model of a staircase before construction. The model is mathematically similar to the real staircase, at a scale of 1 : 10. The model covers a floor area of 0.4 m² on the plan. Work out the floor area the real staircase will cover, giving your answer in m².

10.A runner's speed is 8 m/s. Given that there are 3600 seconds in an hour and 1000 metres in a kilometre, work out the runner's speed in km/h.

11.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.

12.y is inversely proportional to x², and x is positive. When x = 2, y = 45. Construct the equation connecting x and y, then work out the value of x when y = 5.

13.y is directly proportional to √x. When x = 4, y = 8. Construct the equation connecting x and y, then work out the value of y when x = 9.

14.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.

15.A recipe needs 1.2 kg of flour. Dan has 750 g of flour in his cupboard. Write the mass of flour the recipe needs as a fraction of the mass of flour Dan has. Give your answer in its simplest form.