SPM Mathematics 2019, Paper 2 (Question 7 & 8)


Question 7:
Diagram 3 shows the straight lines PR, SQ, QT and ST drawn on a Cartesian plane. It is given that PR and ST are parallel and SQ = QT – 10 units.

Diagram 3

Find the equation of the straight line PR. [4 marks]


Solution:
Q=( x, 8 ) SQ=10 [ x( 2 ) ] 2 + 8 2 =10 ( x+2 ) 2 +64=100 ( x+2 ) 2 =36 x+2= 36 x+2=±6 x=4   or    x=8 Q=( 4, 8 )

QT=10 units T=( 4+10, 8 ) T=( 14, 8 ) Gradient of ST= 80 14( 2 ) = 8 16 = 1 2

m PR = m ST = 1 2 ( 4, 5 ):x=4, y=5 y 1 =m x 1 +c 5= 1 2 ( 4 )+c 5=2+c c=7 The equation of the straight line PR y= 1 2 x+7



Question 8:
Diagram 4 shows a distance-time graph for the journey of Rina by train from Rawang to Serdang.

Diagram 4

(a)(i) It is given that the speed of the train from Kuang to Serdang is 1.25 km min
-1.
Find the value of t.      [2 marks]
(ii) How long it takes, in minutes, to reach Serdang from Kuang?    [1 mark]
(b) Calculate the average speed, in km h-1, of the train for the whole journey. [2 marks]


Solution:
(a)(i)
Speed= Distace Time =1.25  km min 1 ( 4010 ) km t11 =1.25 30 1.25 =t11 t11=24        t=35

(a)(ii)
Time taken = t – 11
= 35 – 11
= 24 minutes

(b)
Average speed= Total distance Totak time                   = 40 km 35 60  h                   =68.57  kmh 1


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