SPM 2016 Additional Mathematics (Forecast Paper)


SPM 2016 Additional Mathematics (Forecast Paper)

Section B
[40 marks]
Answer any four questions from this section.


Question 7
(a)  Prove that  ( cosec xsecx secx cosec x ) 2 =1sin2x    
[3 marks]
(b)(i) Sketch the graph of y = 1 – sin2x for 0 ≤ x ≤ 2π.

(b)(ii) Hence, using the same axes, sketch a suitable straight line to find the number of solutions to the equation 2 ( cosec xsecx secx cosec x ) 2 = x π  for 0 ≤ x ≤ 2π.
State the number of soultions.
[7 marks]

Answer and Solution:
(a)
LHS = ( cosec xsecx secx cosec x ) 2 = ( cosec x secx  cosec x secx secx  cosec x ) 2 = ( 1 secx 1 cosec x ) 2 = ( cosxsinx ) 2 = cos 2 x2cosxsinx+ sin 2 x =1sin2x (RHS)

(b)(i)


(b)(ii)
2 ( cosec xsecx secx cosec x ) 2 = x π 2( 1sin2x )= x π From 7(a) 2y= x π From 7(b)(i) y=2 x π  (suitable straight line)

x
0
π
y
2
1
0

From the graph, there is 3 number of solutions.