IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Functions-Weighted Networks
Topic :Function- Weightage : 21 %
All Questions for Topic : Representation and shape of more complex functions,Transformation of quadratic functions,Rational functions,Graphing trigonometric functions,Linear programming, including inequalities,Networks-edges and arcs, nodes/ vertices, paths,Calculating network pathways,Weighted networks,Domain and range
Question
In this question, you will make calculations for changes that individuals can make to save water on a daily basis.
Question (a)
Write down the missing percentage for drinking and cooking on the pie chart.
▶️Answer/Explanation
Ans:
Sum of all percentage is equal to $100$
$(100-40-9-12)\%$=remaining
$=39 \%$
Question (b)
It is estimated that the daily water usage per person is 120 litres.
A regular shower has a flow rate of 8 Litres (L) per minute.
Using your answer from part (b), determine the duration of a regular shower.
▶️Answer/Explanation
Ans:
To determine the amount of water used for showering, we need to calculate $40\%$ of the daily water usage per person, which is $\rm{120~ litres}$.
To find $40\%$ of a quantity, we can multiply that quantity by $0.40$ (or $40\%$).
Water used for showering $= 120 \text{ liters} \times 0.40 = 48 \text{ liters}$.
Therefore, the amount of water used for showering is 48 liters.
Now, to determine the duration of a regular shower, we can divide the amount of water used by the flow rate:
\[\text{Duration of shower} = \frac{\text{Amount of water used}}{\text{Flow rate}}\]
Plugging in the values:
\[\text{Duration of shower} = \frac{48 \text{ liters}}{8 \text{ L/min}}\]
Simplifying the expression:
\[\text{Duration of shower} = 6 \text{ minutes}\]
Therefore, the duration of a regular shower is 6 minutes.
Question (c)
In a water-saving condition the flow rate of a shower can be reduced to be $5 \mathrm{~L}$ per minute. Given that the duration of the shower does not change:
Determine the amount of water used for showering in a water-saving condition.
▶️Answer/Explanation
Ans:
To determine the amount of water used for showering in a water-saving condition, we can use the new flow rate of 5 L per minute and the duration of the shower.
Let’s denote the amount of water used for showering in the water-saving condition as $x$ liters.
Using the equation:
\[\text{Amount of water used} = \text{Flow rate} \times \text{Duration}\]
In the original condition, we found that the duration of the shower is 6 minutes. So, in the water-saving condition, the duration of the shower remains the same.
Substituting the values into the equation:
\[x = 5 \text{ L/min} \times 6 \text{ min}\]
Simplifying the expression:
\[x = 30 \text{ liters}\]
Therefore, in a water-saving condition, the amount of water used for showering is 30 liters.