Further Applications of Mathematics Chapter 18 Further Applications of Mathematics

Use of Graphs

Graphs and information When a car comes to a junction with a “Stop” sign and then turns left, it must slow down, stop (i.e. speed  0) and then move again. Therefore the curve of the graph touches the time axis.

Graphs and information The graphs show the process of pumping a balloon up with hand pump I and hand pump II. Which hand pump is more effective?

Graphs and rates The charge for the first 500 minutes  $108 The charge rate for the next 400 minutes  $ 1.08/min The charge rate for the first 900 minutes  $ 0.6/min

Graphs and rates The step graph shows that a car park charges $25 per hour for the first-hour and $15 per hour thereafter. Parking less than one hour will be charged as one hour.

Graphs and trends Based on the trend of the above time-series graph, the average price index of local residential property keeps decreasing since the 2nd quarter of 1997. Students may use this trend to predict the average price index in the 4th quarter of 2002.

Graphs and rates of change A travel graph shows the distance travelled by an object against time. The figure shows a non-linear travel graph. Since slope of OA  slope of AB  slope of BC, the average rate of change in distance travelled increases as time increases, i.e. the average speed of the object is getting higher.

Graphs and rates of change If water fills the following containers at a constant speed, match the graphs of the water level against time to the corresponding containers.

Further Applications of Percentages

Purchase by instalments/loan When a purchase is made by instalments, interest is generally calculated at a flat rate. The total interest is thus calculated as a percentage of the initial amount owed over the entire repayment period. The sum of the interest and loan amount is generally repayable in equal instalments.

Credit Card Repayment If a credit card holder does not repay the amount owed in full before the due date, a minimum monthly repayment is required to be paid, and an interest compounded daily will be calculated on the balance due. The minimum monthly repayment is generally 5% of the balance.

Investment Mandatory Provident Fund (MPF), stocks, bonds, foreign exchange, funds etc are common investments for investors to increase their wealth quickly. However, all investments carry risk, and thus their prices may go up or down.

Determination of Laws

Convert a non-linear graph into a linear graph In real-life situations, we come across non-linear graphs more than linear ones. To make it easier to find out the relation between the variables of a non-linear graph, the non-linear graph should be transformed into a linear one.

Convert a non-linear graph into a linear graph

Convert a non-linear graph into a linear graph In example 11, the possible relation between the length of the pendulum L and the period T is pendulum

Convert a non-linear graph into a linear graph

Analyzing Data Collected in Surveys

Analyzing data Data need to be analyzed before any conclusions are drawn. Governments and corporations analyze data regularly to make predictions about future trends and help determine future plans.

Using examination results Teachers may use the statistics of the examination to help them plan appropriate activities for students of different levels.

Highlight of 03 - 04 financial budget To facilitate the recovery of local economy from the hit of the Asian Currency turmoil in 1997, the HKSAR government sharply increased public expenditure for the period 1998 - 1999, e.g. to help improve unemployment by funding training and retraining programmes. This measure contributed to the huge fiscal deficit for several years after 1997.

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