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PAST YEAR SPM QUESTIONS

PAPER 1 /2009:

16. Solve the equation 3sin x cos x cos x = 0 for 0o x 360o.

[3 marks]

PAPER 1 /2008:

17. Given that sin = p, wherep is a constant and 90o x 180o. Find in

terms ofp:

(a) cosec ,

(b) sin 2. [3 marks]

PAPER 1 /2007:

18. Solve the equation cot x + 2cos x = 0 for 0o x 360o.

[4 marks]

PAPER 1 / 2006:

15. Solve the equation 15 sin2 x = sin x + 4 sin 30o for 0o x 360o.

[4 marks]

PAPER 1 / 2005:

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17. Solve the equation 3cos 2x = 8 sin x 5 for 0o x 360o.

[4 marks]

PAPER 1 / 2004:

18. Solve the equation cos2 x sin2x = sin x for 0o x 360o.

[4 marks]

PAPER 1 / 2003:

20. Given that tan = t, 0

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PAPER 2 / 2004 / SECTION A:

3. (a) Sketch the graph ofy = cos 2x for 0o x 180o. [3 marks]

(b) Hence, by drawing a suitable straight line on the same axes, find the

number of solutions satisfying the equation 2 sin2 x = 2 180

x for 0o x 180o.

[3marks]

PAPER 2 / 2005 / SECTION A:

5. (a) Prove that cosec2 x 2 sin2 x cot2 x = cos 2x. [2 marks]

(b) (i) Sketch the graph ofy = cos 2x for 0 x 2.

(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

1 for 0 x 2.State the number of solutions. [6 marks]

PAPER 2 / 2006 / SECTION A:

4. (a) Sketch the graph ofy = 2 cos 2x for 0 x 2. [4 marks]

(b) Hence, using the same axis, sketch a suitable graph to find the number

of solutions to the equationx

+ 2 cos x = 0 for 0 x 2.

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State the number of solutions. [3 marks]

PAPER 2 / 2007 / SECTION A:

3. (a) Sketch the graph ofy = |3cos 2x | for 0 x 2. [4 marks]

(b) Hence, using the same axis, sketch a suitable graph to find the number

of solutions to the equation 2 - |3cos 2x | =2

x

for 0 x 2.

State the number of solutions. [3 marks]

PAPER 2 / 2008 / SECTION A:

4. (a) Prove that xx

x

2tan2

sec2

tan2=

[2

marks]

(b) (i) Sketch the graph ofy = tan 2x for 0 x .

(ii) Hence, using the same axis, sketch a suitable graph to find the

number of solutions to the equation 02

sec2

tan23=

+

x

xx

for

0 x .

State the number of solutions. [6 marks]

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PAPER 2 / 2009 / SECTION A:

4. (a) Sketch the graph ofy =2

3

cos 2x for 0 x 2

3

. [3

marks]

(b) Hence, using the same axis, sketch a suitable straight line to find the

number of solutions to the equation2

32cos

3

4= xx

for 0 x

2

3.

State the number of solutions. [3 marks]

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