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)
Mean= 132+125+137+130+128 5   = 652 5  cm   =130.4 cm



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)
Translation (  5 1 )

(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:
Distance of PQ=x, QR=25, RS= 1 5 ×25=5 PQ= 1 3 PS x= 1 3 ( x+25+5 ) 3x=x+30 2x=30 x=15 Distance PS=15+25+5    =45 km Distance PR=15+25    =40 km Wasted distance = 1 4 ×PR = 1 4 ×40 =10 km  Fraction of wasted distance = 10 45 = 2 9


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