Ratio, proportion and rates of change worksheet — GCSE Higher

1.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.

2.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.

3.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.

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

5.The depth of water in a tank, in cm, is recorded every 10 seconds: at t = 10, depth = 32; at t = 20, depth = 45; at t = 30, depth = 56. Use the most appropriate chord from these readings to estimate the instantaneous rate of change of depth at t = 20.

6.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.

7.A loan of £3000 has interest added at 2% each month, and then a fixed repayment of £200 is made. This is modelled by the recurrence B_{n+1} = 1.02B_n − 200, where B_n is the balance after n months and B_0 = 3000. Work out the balance after 2 months.

8.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.

9.y is directly proportional to √x. When x = 25, y = 20. Construct the equation connecting x and y, then work out the value of x when y = 32.

10.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.

11.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.

12.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.

13.A photo is enlarged so that its new width is 1.4 times its original width. Write the multiplier that would scale the new width back down to the original width, as a fraction in its simplest form.

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.A curve has equation y = x² + 2x. Work out the average rate of change of y with respect to x over the interval from x = 1 to x = 4.