7/29/2019 STPM Trials 2009 Math T Paper 1 (SMJK Sam Tet Ipoh)

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SMJK SAM TET IPO HS ' F P M 4 ' r i . t - ~ 2 0 0 9

Mathematics TAnswer all questions Time: 3hours

. . . . 1 i1. Find the solulton set of he tnequality -; . > 8+ ; ,where", O.

2. a) lfy =In,Jx+Y, f i n d t h e v a l u e O f ~ MlenX aO andy = l.

b) BysubslilUtingu'. x, ewluate t ~ <Ix.(I - x)vx

3. Given tha tf(z) = ( 7 - ~ ) wherez = 1+2i, s b o w t h a t ~ = 2 l ! ( 4(1 - : )

Determine the&g\U11Clt of

4  Using the trapezium rule, with fiveordinatcs. evaluate f 2 ~ " dx,

giving your answer 10 tlueedccimal places.

Setby: ( )

Miss Ong Siew Eng ~Me' Wang Yaw Weng J l " t '

[4 marlcs]

[4 marlcs]

[6 marlcs]

[6 marlcs]

S. I f a andP are the roots of he equation ar' +1r<+c=O, ~ in tams of a and Pthe sum and products of ile roolSofme equation

( i ~ Tb'x.,..b!-4ac=O. [6m:uksl

Express a' +tJ in thelcnnsofa,08iid c. [2 marlcs]

6. Find JiOi=10 ive decirnaJ pI8c<s by using the binomial expansion of JlOO +x.

7. Provethat thecin:les 1"+y' +Zx-8y+8=O

1" +y' + IOx-2y +22=O

touch _another. Find

. ) thepoiot ofcontact . [4marlcs]

b) the equation to thecorraron tangent.t this point. [3 marlcs]

c) the area of the triangle enclosed by this commdD tangen, the line of oentru and the y-axis. [3 marlcs]

8 Ms the Imuix ~o 2 •

(aJ Find two values ofa for whicb M s singular.

-l!(b) Solve the equation M;]= li wbena=2.

[2 marlcs]

[6 marlcs]

7/29/2019 STPM Trials 2009 Math T Paper 1 (SMJK Sam Tet Ipoh)

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9 . Given Ihatth e fun ctio n g {x } is def:ned as

- q cos x O:sx <3-

r.X " 3"

~ 21r x ,

where q :lL Fi nd the value of q if lim g(x) exists .

x-·tWith thi s value of q . determ ine whether is g(x) contin uous at x =f.Sketch the graph.

[3 marks)

[ 3 mark s)

[3 marks ]

10. a) The roth term, U r . ofa series is given by

11 .

(13r-2 (13r-1

Ur = "5 -+ 5Express rt Urn the fo rm A( 1- 1 2 ~ f l ) where A and B are constants .

rInd the sum to infi nity of the series.

b) Express - -;- in part ial fnctions.r ( r - I )

n I n2+n - 2Hen ce. pro ve ; (r2 - 1) - 4n(n -+ I) .

Find the s:.Im when r. approach es infin ity.

~ ' .".-.

Th,di.gram ' b O Y ' ~ind the coordinates o f the turning poi nts on the c urve .

[3 marks )

[ I marks]

(3 marks)

[3 mark s1

( I marks ]

[3 marks1

Th e .r-coo rd ina te of the point of interse ction of the curves y • .r 2t·-.r and y "" - x + 3,

where x < 0 is p. Show that - 1 < P < - 2 . [3 marks )

Us e the Ne w ton -R aphson method 10 determine the value of p correct to .hree decima l p lac es and,

hence , find the point of intersection . {7 marks)

12 . Sketch, on the same coo rdinate axes, the curves y = xl - Jx 2 + 2x and )' = 4(.r 3 _)x2 - 2x).

(4 marks ]

Find the coo rdinl!. ;es of the points ofintef$ection . [2 marks]

Find the area of the region bounded by !,he cu rves y = xl - 3x2 + 2x and y = 4(x 3 _)x2 + 2x )~ (4 marks}

Ilf'p roved b.!l : ( : : . . ~ ~. l ! ' t t "