Real-World Examples (HSC SSCE Mathematics Standard): Revision Notes

Worked Example: Motor vehicle accident statistics

Consider a table showing fatigue-related road accidents:

Question a: How many deaths occurred in road accidents during October involving fatigue?

Solution:

Look at the intersection of the October row and the Killed column.

Answer: $197$ deaths

Question b: Which month had the least number of injuries in road accidents involving fatigue?

Solution:

Scan down the Injured column to find the lowest value, which is $1488$.

Answer: September

Question c: How many deaths in road accidents involving fatigue occurred in the four months?

Solution:

Add all the values in the Killed column:

$\text{Deaths} = 112 + 197 + 89 + 134$

$= 532$

Answer: $532$ deaths

Question d: What is the percentage increase in number of injuries involving fatigue from November to December?

Solution:

First, find the increase in injuries:

$\text{Increase} = 3487 - 2019$

$= 1468$

Now express this increase as a percentage of November's injuries:

$\text{Percentage} = \frac{1468}{2019} \times 100$

$= 72.709...$

$\approx 73\%$

Answer: Approximately 73% increase

Worked Example: Rainfall data interpretation

Question a: What was the annual rainfall for Newcastle in 2015?

Solution:

Locate 2015 on the horizontal axis, then read up to the Newcastle line (dark blue) and across to the vertical axis.

Answer: $960$ mm

Question b: Which was the wettest year during this 10-year period for Wollongong?

Solution:

Look for the highest point on the Wollongong line (red), which occurs in 2013.

Answer: 2013

Question c: Which year has the largest difference in annual rainfall between the two cities?

Solution:

Find where the vertical gap between the two lines is greatest. This occurs in 2016, where Newcastle had much higher rainfall than Wollongong.

Answer: 2016

Worked Example: Household water usage analysis

Question a: How many kilolitres of water were used by this family in a year?

Solution:

Add all the values from each sector of the pie chart:

$\text{Water usage} = 36 + 6 + 49 + 5 + 19 + 13 + 9 + 12 + 11 + 7$

$= 167 \text{ kL}$

Answer: $167$ kL

Question b: What percentage of the total water use is in operating the washing machine?

Solution:

The washing machine uses $49$ kL out of a total of $167$ kL.

Calculate the percentage:

$\text{Washing machine percentage} = \frac{49}{167} \times 100$

$\approx 29.34\%$

Answer: Approximately 29%

Question c: A dual-flush toilet saves 60% of the water used in a conventional toilet. How many kilolitres per year would be saved by replacing the toilets with dual-flush toilets?

Solution:

First, find the total water used by all toilets:

$\text{Total toilet water} = 13 + 11$

$= 24 \text{ kL}$

Calculate 60% of this amount:

$\text{Water saving} = 0.60 \times 24$

$= 14.4 \text{ kL}$

Answer: Two dual-flush toilets would save $14.4$ kL per year