SPM Additional Mathematics 2017, Paper 2 (Question 1 – 3)


Question 1:
Solve the following simultaneous equations:
x – 3y = 1,
x2 + 3xy + 9y2 = 7


Solution:
x3y=1……………….( 1 ) x 2 +3xy+9 y 2 =7……………….( 2 ) From ( 1 ):x=3y+1……………….( 3 ) Substitute ( 3 ) into ( 2 ): ( 3y+1 ) 2 +3( 3y+1 )y+9 y 2 =7 9 y 2 +6y+1+9 y 2 +3y+9 y 2 7=0 27 y 2 +9y6=0 9 y 2 +3y2=0 ( 3y1 )( 3y+2 )=0 y= 1 3  or  2 3 Substitute y into ( 3 ): When y= 1 3 x=3( 1 3 )+1=2 When y= 2 3 x=3( 2 3 )+1=1 Hence, the solutions are x=2,y= 1 3  or x=1,y= 2 3 .



Question 2:
It is given that the equation of a curve is y= 5 x 2 .  
(a) Find the value of dy dx when x = 3.
(b) Hence, estimate the value of 5 ( 2.98 ) 2 .  

Solution:
(a)
y= 5 x 2 =5 x 2 dy dx =10 x 3 = 10 x 3 When x=3 dy dx = 10 3 3 = 10 27

(b)
δx=2.983=0.02 δy= dy dx .δx = 10 27 ×( 0.02 ) =0.007407 Values of  5 ( 2.98 ) 2 =y+δy = 5 x 2 +( 0.007407 ) = 5 3 2 +( 0.007407 ) =0.56296


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