SPM Mathematics 2018, Paper 2 (Questions 7 & 8)


Question 7 (6 marks):
Diagram 6 shows two parallel straight lines, JK and LM, drawn on a Cartesian plane.
The straight line KM is parallel to the x-axis.

Diagram 6

Find
(a) the equation of the straight line KM,
(b) the equation of the straight line LM,
(c) the value of k.



Solution:
(a)

The equation of the straight line KM is y = 3

(b)
Given, equation of JK: 2y=4x+3 y=2x+ 3 2 Thus,  m JK =2 m LM = m JK =2 y=mx+c At M( 5, 3 ) 3=2( 5 )+c 3=10+c c=7  Equation of the straight line LM is y=2x7.


(c)

Substitute ( k,0 ) into y=2x7 0=2( k )7 7=2k k= 7 2



Question 8 (6 marks):
Given A=( 4    2 3    1 ), B=m( 1    n 3    4 ) and I=( 1    0 0    1 ).
(a) Find the value of m and of n if AB = I.
(b) Write the following simultaneous linear equation as matrix equation:
4x – 2y = 3
3xy = 2
Hence, by using matrix method, calculate the value of x and of y.

Solution:
(a)
If AB=I, then B= A 1 A 1 = 1 4( 1 )( 2 )( 3 ) ( 1    2 3    4 ) A 1 = 1 2 ( 1    2 3    4 ) By comparison: B= A 1 m( 1    n 3    4 )= 1 2 ( 1    2 3    4 ) m= 1 2  ; n=2


(b)

4x2y=3 3xy=2 ( 4    2 3    1 )( x y )=( 3 2 )                ( x y )= 1 2 ( 1    2 3    4 )( 3 2 )                ( x y )= 1 2 ( ( 1 )( 3 )+( 2 )( 2 ) ( 3 )( 3 )+( 4 )( 2 ) )                ( x y )= 1 2 (   1 1 )                ( x y )=(    1 2 1 2 ) x= 1 2  and y= 1 2


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