SPM (2005 - 2013) Past Year Questions on Trigonometric Function Graphs

SPM Past-Yr Questions on Trigonometric Function Graphs (Yrs: 2005 – 2013):

(with a peek at similar questions from IGCSE Cambridge Add-Maths 0606 and Edexcel 4PMO (Further Pure Maths)

(Note: SPM 2013 P2 Q4 on trigonometric functions does not involve graphs unlike the years before)

The SPM Past Year Questions:

1)        2012 P2 Q6:

(a)    Prove that 2/(cos 2x + 1) = sec² x.                                          (2)

(b)   (i) Sketch the graph of y = cos 2x + 1 for 0 ≤ x ≤ 2π.               (3)

(ii) Hence, use the same axes, sketch a suitable straight line to find the number of solutions to the equation 2/sec² x = x/4π + 1 for 0 ≤ x ≤ 2π.

State the number of solutions.                                          (3)

2)        2011 P2 Q6:

(a)   Sketch the graph of y = -3 sin (3/2)x for 0 ≤ x ≤ 2π.               (4)

(b)   Hence, using the same axes, sketch a suitable graph to find the number of solutions to the equation π/x + 3 sin (3/2)x = 0 for 0 ≤ x ≤ 2π.      

State the number of solutions.                                                 (3)

3)        2010 P2 Q2:

(a)    Sketch the graph of y = 1 + 3 cos x for 0 ≤ x ≤ 2π.                  (4)

(b)   Hence, using the same axes, sketch a suitable straight line to find the number of solutions to the equation 6π cos x = 4π – 3x for 0 ≤ x ≤ 2π.

State the number of solutions.                                                   (3)

4)        2009 P2 Q4:

(a)    Sketch the graph of y = (3/2) cos 2x for 0 ≤ x ≤ (3/2)π.            (3)

(b)   Hence, using the same axes, sketch a suitable straight line to find the number of solutions to the equation (4/3π)x – cos 2x = (3/2) for 0 ≤ x ≤ (3/2)π.

State the number of solutions.                                                   (3)

5)        2008 P2 Q4:

(            a)    Prove that (2 tan x)/(2 - sec² x) = tan 2x.                                              (2)

(            b)   (i) Sketch the graph of y = - tan 2x for 0 ≤ x ≤ π.         

(ii) Hence, using the same axes, sketch a suitable straight line to find the number of solutions to the equation 3x/π + (2 tan x)/(2 - sec² x) = 0

for 0 ≤ x ≤ π.

State the number of solutions.                                            (6)

6)        2007 P2 Q3:

(a)      Sketch the graph of y = ׀3 cos 2x׀ for 0 ≤ x ≤ 2π.                    (4)

(b)      Hence, using the same axes, sketch a suitable line to find the number of solutions to the equation 2 - ׀3 cos 2x׀ = x/2π for 0 ≤ x ≤ 2π.

State the number of solutions.                                                   (3)

7)        2006 P2 Q4:

(a)      Sketch the graph of y = -2 cos x for 0 ≤ x ≤ 2π.                        (4)

(b)      Hence, using the same axes, sketch a suitable graph to find the number of solutions to the equation π/x + 2 cos x = 0 for 0 ≤ x ≤ 2π.                   

State the number of solutions.                                                    (3)

8)        2005 P2 Q5:

(a)      Prove that cosec² x – 2 sin² x – cot² x  = cos 2x.                      (2)

(c)      (i) Sketch the graph of y = cos 2x for 0 ≤ x ≤ 2π.       

(ii) Hence, using the same axes, draw a suitable straight line to find the number of solutions to the equation 3 (cosec² x – 2 sin² x – cot² x) = (x/π) – 1 for 0 ≤ x ≤ 2π.

State the number of solutions.                                              (6)

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Try this question of mine before you proceed further:

My Q. For 0^o ≤ x ≤ 180^o, find to 3 significant figures the range of values of x for

           5 sin x > cos x.                     (Answer given at the end of this post)

                                   

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Let's take a look at a Cambridge IGCSE question on trigonometric function graphs:

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Let's take a look at a Edexcel IGCSE Add-Maths (4PMO) question on trigonometric function graphs:

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(Ans to My Q: 11.3^o < x ≤ 180^o - posed after the SPM Past-Yr Qs)

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Let's take a break and go jogging:

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P/S: If You Need Help In Physics, Chemistry, Add-Maths and/or O-Maths (IGCSE Yr 10/11 or SPM or CIE AS/A2 Chemistry 9701)

Help is Available in or around Petaling Jaya, Selangor:
1) Just email tutortan1@gmail.com; or WhatsApp: 018-3722 482. Act early to avoid disappointment! Currently in May 2016, existing students are about to finish their Summer exams. Their slots are up for grab starting now! All slots are normally taken up by end-June. Act now to avoid disappointment!

2) Those far-away can follow my student-friendly blog(s) for free. :).

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