Ratio, proportion and rates of change worksheet — GCSE Higher

1.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.

2.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.

3.A curve has equation y = 2x² + 5. Work out an estimate for the gradient of the curve at x = 3, using a chord between the points where x = 2 and x = 4.

4.y is directly proportional to x. When x = 8, y = 20. Work out the value of y when x = 12.

5.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.

6.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.

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

8.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

9.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.

10.An ice-cream van's daily takings, in £, are modelled by a curve plotted against the average temperature that day, in °C. At a temperature of 22°C, the gradient of the tangent to this curve is 14. What does this gradient tell you about the takings at 22°C?

11.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.

12.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.

13.A market stall sells apples at a fixed price per kilogram. Priya buys 3 kg for £5.40. Write the ratio of the mass in kilograms to the cost in pounds, in its simplest form.

14.Write 400 g : 1.5 kg as a ratio in its simplest form.

15.A process is modelled by the recurrence P_{n+1} = 0.6P_n + 40. As n increases, P_n approaches a long-run value L, which satisfies L = 0.6L + 40. Solve this equation to find L.