PT3 Mathematics 2016, Question 10

Question 10 (a):
Diagram 10.1 is a pie chart showing Ahmad’s monthly expenses.


(i) State the mode.
(ii) The following data are the height of students in a class.
132 cm, 125 cm, 137 cm, 130 cm, 128 cm
Calculate the mean.

Solution:
(i) Food

(ii)
$\begin{array}{l}\text{Mean}=\frac{132+125+137+130+128}{5}\\ =\frac{652}{5}\text{ cm}\\ =130.4\text{ cm}\end{array}$

Question 10 (b):
Diagram 10.2 shows a polygon HABCD and a square JKLM.
(i) Under a transformation, polygon HABCD will be transformed such that the image will be placed inside the square JKLM. The image formed based on the following conditions:


Suggest one possible complete transformation.
(ii) Using the transformation that you have suggested in (b)(i), mark the new position of point W in Diagram 10.2.

Answer:

Solution:
(i)
$\text{Translation }\left(\begin{array}{l}5\\ -1\end{array}\right)$

(ii)

Question 10 (c):
Diagram 10.3 shows a car route from P to S. The driver starts the journey from P. When he reaches R, he turns back and travels ¼ the distance of P to R and then he continues to S to finish his journey.



Table 10 shows the distance between the destinations.


Assuming that the distance travelled in the journey when the driver turns back as a wasted distance, calculate the fraction of the wasted distance to the distance of the whole journey.

Solution:
$\begin{array}{l}\text{Distance of }PQ=x,QR=25,RS=\frac{1}{5}\times 25=5\\ PQ=\frac{1}{3}PS\\ x=\frac{1}{3}\left(x+25+5\right)\\ 3x=x+30\\ 2x=30\\ x=15\\ \\ \text{Distance }PS=15+25+5\\ =45\text{ km}\\ \text{Distance }PR=15+25\\ =40\text{ km}\\ \text{Wasted distance}\\ =\left(\frac{1}{4}\times PR\right)\times 2\\ =\left(\frac{1}{4}\times 40\right)\times 2\\ =10\times 2\\ =20\text{ km}\\ \\ \therefore \text{ Fraction of wasted distance}\\ =\frac{20}{45}\\ =\frac{4}{9}\end{array}$