3e am term 3 common test (2011)

8/4/2019 3E AM Term 3 Common Test (2011)

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- ~ ; v c h 4-/\-\ ( \ t - ) ' ~ A \2.1) Without using a calculator, given that tan A = t and that f ~ U t A and COS"/1 I ' ) . , C u . ~ 12l ~ find the value of(a) cos A, [2](b) tan(-A), [2](c) cos(90 - A). [2](d) sin (180 + A) [2]

2) Without using a calculator, find the value of each of the following:(a) tan330, [1](b) cos 225, [1](c) . ( 2ff) [2]SIll -3'

3) Solve the following equat ion forl3x - 51 + 2110 - 6x I = 10. . [4]

4) Solve the following equat ions for 00 S;; x S;; 360 0... 1

cos 2x+200: : : : - )-. .... .2(a) [4](b) 2 stn x - tan K =0 .{3l.

5) Find all the angles, between 0 and 2JT inclusive, whichsatisfy the equationS-tany=3sec 2 y [4]

1+ cos x Sill X 2 .- - - + = cos:ec x6) Prove the identity Sill x 1+ cos x [4]7) Sketch the graph of j (x ) = 12x - 91+ 1 for the domain 0 S; x S; 6,

Hence state the corresponding range ofj(x). [4]

3E AM Term 3 Common Test 2011


2/8

8) On the same axes, sketch, for 0 x 360 0 , the graph of(a) y;;;; 2C0:5 x(b) y;;;; 1+sin 2x [4JHence, state the number of solutions in this interval of the equation2 cos x = 1-+ sin 2x .. [1}

******End of Paper ******


3/8

J-3/, II25" (Am) CGwtM"Y17exr C T 3) Date: No.-

2+ 6 f ~ c .....l.#0

I 7.J:;) T I ~ ~ - ~ /1/r

12

I.,).a) ws A -= I 1,) -ret l'\ C- ~ =:

-- . r - -S"-C) LQJ C ~ '-A )

)) ~ w Cl8r> -t f1) :

(Q;..1-l;i", S3o til) -

..-:,) ~ \ 9 ~ 225"::

..~ [_ L ~ 9 /

- ~ r fl12

::!' ~ . . ; It- S13- SIV, A

- /3- f r ; ? ~ 30 '

..l.-n- ces Cf'S _Ji.--.

4..

,- - s;h/f ):. -2-

AZONE


4/8

Date: No,

[ ~ - \ t .2.7 [0 - CA.! z: 10137L -s / + 4 131C- - S I = l (J

5" I 3 - 5 I :: 10I I( 6X -.> J=-, 2

3x. -s ~ 2 tIV s x - S - ~ -2- =f. x={ /----.A:. - ~ / #

0 0 z, 360 .,

lOS ( 2 T U;. ) - I.. - -2.( l ~ t r O ) . vv $ vA (Que:u;{ . .fltkvf L oU-!S IV\, .., u

ri.=- CCf) -\ IT)= , . -

2x. -t h ) ::: ISO -bo l t{, 0 I 3bO f l -'0 .?,ot(so+ "0

ro>

19


5/8

.

Date: No.

b)

lis

:::.2. 9 t n: - ~ V l ~


6/8

Date: No.

( if W 'K...~ f \ ? c .

f, $l1 )(.-l+ (,OS:lt 2 ( [+ ( ,e j )(.. ) { sit" 1 X

9 l 'X.. ( (-t clSx..)/- \+ 2- zes >c..~ : - ,

+ ces x , + S 1 x (l+ U>fj; X-} 2.#'(.....

- [+ ')ic,os 'L Ts>J X ( l-t- t s r>t..)/

. ~

2-t MS '):,~ x: ( ( T U > ~ . ' ) ( . . )

....- lC 1 + u > ~ J ( . . ) S1 V)-x. ( It- ~ " > l - ) .--=.

2-$lrix.2 C o ( S h ~ J

/f\... / -

AZO


7/8

Date' No

~ i {C?t,)'-= r 2 x ~ 1 I+- I@ ~ I ~ _ " I :'). 0

X 4s l. ( 't.!" J I )l.1 :; I JV

(i;) (sf r*. ~ . : : 0C ~ I Y o 4 IV\1 ) 1.1:: I -q I+ I ( 0 I 10 )I: T V J= 10

@ (""rl br.{-. 2.::.


8/8

Date: No.

' & t ~ i ~ \if ;) l.6S x , ~ {+VJn 2:>

3e am term 3 common test (2011)

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