Ratio, proportion and rates of change worksheet — GCSE Higher

1.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.

2.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.

3.The volume of fuel remaining in a storage tank, in thousands of litres, is plotted against time, in hours, since a leak was detected. A tangent to the graph at t = 2 hours has gradient −8.75 thousand litres per hour. A tangent at t = 8 hours has gradient −3.5 thousand litres per hour. Work out by what factor the instantaneous rate of change is greater in size at t = 2 hours than at t = 8 hours.

4.A straight-line graph shows the number of pages printed, p, plotted against the time in minutes, t, since a printer started a print job. The line passes through the points (2, 30) and (5, 90). Work out the gradient of the line.

5.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.

6.A shop sells ribbon by the metre. 2 m costs £3.00, 4 m costs £6.00, and 7 m costs £10.50. Does this data show that the cost is directly proportional to the length of ribbon bought? Choose the correct verdict and reason.

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

8.A car travels at a constant speed. It travels 150 miles in 3 hours. At the same speed, work out how far it travels in 5 hours.

9.A laptop costs £800 when new. Its value decreases by 25% of its value at the start of each year. Work out how much value the laptop loses in the second year.

10.A patient is given a dose of 200 mg of a drug. Each hour, 30% of the drug remaining in the bloodstream is eliminated, and then a further dose of 50 mg is given. Using the recurrence D_{n+1} = 0.7D_n + 50, with D_0 = 200, work out the amount of drug in the bloodstream after 2 hours.

11.A recipe for 8 muffins needs 200 g of sugar. Sam wants to make 20 muffins for a bake sale, and he already has 350 g of sugar. Work out how many more grams of sugar he needs to buy.

12.The width, the length and the height of a box are in the ratio 3:4:5. The length of the box is 16 cm. Work out the height of the box.

13.Maya buys a vintage car for £15000. Its value is expected to increase by 4% each year for 2 years. She then plans to sell the car and use £2000 of the money from the sale to buy a trailer. Work out how much money she will have left after selling the car and buying the trailer.

14.Two quantities are connected by the formula y = 0.8x. Write down the ratio y : x in its simplest form.

15.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.