Ratio, proportion and rates of change worksheet — GCSE Higher

1.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.

2.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.

3.A graph shows y plotted against x. The graph is a curve that gets closer to both axes but never touches them, and y decreases as x increases. Write down whether this graph could show direct proportion, inverse proportion, or neither.

4.Two mathematically similar picture frames have perimeters 30 cm and 45 cm. The area of the smaller frame is 40 cm². Work out the area of the larger frame.

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

6.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

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

8.The total cost, in pounds, of manufacturing a batch of components is plotted against the number of components produced. A tangent to this graph at a particular point has gradient 3.60. What does the value 3.60 represent?

9.Write 45 minutes : 2 hours as a ratio in its simplest form.

10.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.

11.6 identical printers can print a batch of exam papers in 40 minutes, all working at the same rate. Working at the same rate, work out how many minutes 4 of these printers would take to print the same batch.

12.A rectangular room is drawn on a plan with a scale of 1 : 50. On the plan, the room measures 8 cm by 6 cm. Work out the real area of the room, in square metres.

13.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.

14.A garden centre sells two mathematically similar sacks of grass seed. The amount of lawn a sack can treat is proportional to the volume of seed inside it. The smaller sack is 20 cm tall and treats a lawn of area 30 m². The larger sack is 40 cm tall. A gardener needs to treat a lawn with an area of 500 m² using only the larger sacks. Work out the minimum number of larger sacks needed.

15.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.