Past-Year Questions on Cosine Formula/Rule, Sine Formula/Rule (including ambiguous case)...

Edexcel Past-Year Questions (involving Sine Formula, Cosine Formula, Etc.)

A) Given 2 sides and 1 angle of Δ:

1)        In ΔABC, AB = 7 cm, AC = 6 cm, angle ABC = 42^o and angle ACB = Ө^o.

Find, to 1 decimal place, the 2 possible values of Ө.           (24/3/2004 P1 Q1)

2)        In ΔABC, AB = 5.7 cm, BC = 8.4 cm, angle ACB = 42^o.

Find, to the nearest 0.1^o, the 2 possible sizes of angle BAC.  (15/01/2010 P1 Q1)

3)    In triangle ABC, AB = 4.6 cm, AC = 5.7 cm and angle C = 52^o. Angle B is acute.

Calculate, to the nearest 0.1^o, the size of angle B.   (14/01/2011 P1 Q2)

4)    In ΔABC, BC = 12 cm, AC = 10 cm, angle ACB = 48^o.

Find, to 3 significant figures,

(a)    the length of AB,

(b)   the size of angle BAC                                      (27/05/2004 P1 Q3)

5)        In ΔLMN, LM = 5.6 cm, LN = 8.2 cm, angle MLN = 57^o.

Find, to 3 significant figures,

a)      the length of MN,

b)      the size of angle LMN                                      (17/05/2007 P2 Q3)

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B) Given 2 angles and 1 side of Δ:

6)        In ΔABC, angle A = 45^o and B = 60^o and AB = 7 cm.

Calculate to 3 significant figures, the length of BC.   (26/05/2006 P2 Q1)

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C) Given 3 sides of Δ

7)        A triangle has sides of lengths 4.6 cm, 5.3 cm and 6.5 cm.

Find, to the nearest degree, the size of the largest angle of the triangle.

                                                                                         (23/01/2007 P2 Q1)

8)        Triangle LMN has LM = 5 cm, LN = 8.2 cm and MN = 6.4 cm

Calculate, in degrees to the nearest 0.1^o, the size of angle LMN.

                                                                                         (21/01/2008 P1 Q1)

9)        The lengths of the sides of a triangle are 4 cm, 5 cm and 6 cm.

Find, in degrees to 1 decimal place, the size of the largest angle of the Δ.

                                                                                         (12/05/2008 P1 Q1)

10)    The lengths of the sides of a triangle are 5 cm, 6 cm and 8 cm.

(a)    Find, in degrees to 1 decimal place, the size of the smallest angle of the Δ.

(b)   Find, to the nearest cm², the area of the Δ.                   (13/05/2010 P1 Q4)

11)    In ΔABC, AB = 5 cm, BC = 8.3 cm and AC = 6.9 cm

(            a)    Find, in degrees to the nearest 0.1^o, the size of angle ACB.

(            b)   Find, in cm², to 3 significant figures, the area of ΔABC.

(18/01/2010 P2 Q2)

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Q12 to Q14 have to be scanned and shown below because the blogging software cannot produce the drawn triangles as they are - perhaps certain plug-in needed:

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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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Help is Available in or around Petaling Jaya, Selangor:
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