stpm trials 2009 math t paper 1 (smjk sam tet ipoh)
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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 "