[Edu.joshuatly.com] Sam Tet STPM Trial Maths T [w Ans]

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    SMJKUpper

    SAM TET, IPOH, PERAK.Sir STPMTrialExam2010Mathematics( Time : 3 Eours)

    Answerall questions.1, Prove romfirstprinciplshat he valueofthedcdvative fthe fiEctionf(z) = 'la 611x = d rs;J;2- Using he Algebraicnws ofsct, show hat, or anysetA andB,[(AnB)' n/] u [(/4nB)' nB] = (A B) u (B - A)

    l_1\ ' 'Yr-r3. Evaluatel-#. 3Then find the setofvalues t such hat theseriesXl=1

    3Hence, iDd tho sum o i4fitrity when r = t4, Given that

    is continuousat r = I, find a andc ,(5Marks)

    Preparedby : Mr Wong Mook CheongMs ODgSiewEngchecked& ApprcvedbY

    L...9* 72'..MschciMei LinHeadof Mathematicsepartmed

    (4Marks)(5 Marks)

    $ cotrvergent.(6 Mark )

    .EJsinx-@, :>ElL t t/ ( rJ = 1 -; , x=;lx+c x

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    7. /3 1 -3\Misthematix[1 2k 1].\0 2 k, /(a)Fird the wovalueof k if M is singular,O) Solve he equatio[M

    (3Marlc)(6 Markg

    Ialio ofthc geometric progressioD"bxi) Express;* in partial fractions(ii) Hence sbow tbat lot-I- 4a = tnm - a . Stating he value ofm andn (fMarks)

    9. civen that thpolynomial p(r) = x3 + a;x2+ bx + 70 has hc faotor(l + z) aldwhen divided by (r - 3), the remaindcrs 10.(a) Find the values ofa andD

    /-a \I " , \=[s: Jwnenz\5 /a)The ust andsecondermsof anaridurcticprogressiooqualo the ust sndsecondtermsof I geoEretric rogression.he hid termofthe geometricrogressionxceedsth lftd lerm ofthe arifhmetic rogressiony 4. Thccornmon ifference fthearithmetic rogressions positiveand he surn fthe first lhroeermsofthearithmeticprogressions 72.Find he cornmon ifference fthe arithmetic rogressionndcommon

    @)Find the otho real actorofp(r)all realvalueofx.fc, Find the setofvaluos of.x for which (r - l)p(r) < 0.

    andshow hat this

    (5Marks)

    (4Marks)factorspositivc or(3Marks)(3Marks)10. Expand(1 - :f wlere n is apositive integer o ascendiogpowers ofx until tle

    1lerm n xJ . tf the coemcient f rr is -rr:, fi-nd .Withthis valueof ,, obtainhecxpansionf (1powersofr u[til the ermr3.

    ll. The circle S with centre C, passeshrcugh the point A( l, 7 ) andB ( 9,(a) Find the equationofthe perpendicutar isector of the cord AB(b) IfC lies or the ine 3x.+ 4y = z+,find,t*Ecoordinate fc andshow hat equation fthe circlcS s -I2+ y2 - Bx-6y =O(c) Find the equation ofthe two taDgentso Swhich areparallelto the chordAB.12,On the salneaxes, ketch he iney = x and 4y2 = 7.(a) Find rho coordiaateofthe point of inte.section,(b) Find the area-ofthe region boundedby tlte line y = aandcurve 4Y' = x(c) Calculatc the volumeof solid formed$fien the region is rotatedcompletely bout hey-axis

    (6Marks)(1 - x)i in asconding(5Marks)

    3).(3Marks)(4Marks)(6Mark)(4 Marks)(4 M6rks)(5Malks)

    http://edu.joshuatly.com/http://www.joshuatly.com

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    M a. ,n1

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    3 - ,t + llt o. . . k/"h'( r1 .t?."rJ -.3c/- c-t)"J---;7:T*t , - Gt)"J

    r-.(-/ I.J lJ

    : . ln l a 3d:

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    3^, i rn*- - - &+tc4Ar*t lAt ht-t.22 l2t/4.er ' t /4a : g, y. h- f t 'a , , /=8aA

    (h

    -'. +i ary /ry'2/cre., -

    (a./ Lt j , . A-/r t .) =z ArVl= a.{t; = .I = - l '+s. ' - A-a) - )( zt) , )( >of, t / , ' ' rxtJ = f,( >t '+t) ;

    f ,h- ' : X- 1-t ( Iz.rz)(L./

    d)f r

    ( v/-ev) ' , r d.7";Ar:4 4./ri /> O ,t-att gr= O&/ , t*4)/ . r , =O: 1:- I 'I .r/,2?e - / ^4a./

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    I

    )

    I="

    )

    t )R

    /i- \,- (.J

    . ro

    /3 | -1\M. | , )K i \\o s K/3l)K I I - | | l | - 2tr Kl lo Rl

    3(.zrt-s) - K - 6 , O6K'-K-t2.o( 3k +f X)k-3)tO

    " ' O' tSr itu4tat=)t , , / :\a. ' . t ,4 l - - J(6) -) _ j( .

    7.

    cb)

    -e-4)( I I-':

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    1Ct firr,l j *.m,, 4/A'.t t ] l? .t'rr ala

    6a 61z a. _@A,"t- (at2-d) =4

    A? -' a, Atd,, 6 rz4p : at a/', arr

    -oAtd: z4 _@t-om O *.o Cg , a/ -- t4 -.2

    taJ"tt t -' ].L a4d d. z? - a /.Li-oa(#)"- l atz lzv-611 .yQ'- ta + 176 2c,(a-xf c-G)2o /

    Qz ?6, t6.c e4ft. A > J6 //;r-o G)J6 t d : z4d: -/z (-y '

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    6t p(.r) : ,XJ+6/, +bl +/ t )P(- 2) =(-Z )t+ ar-t22+ b(4)t /0,O

    , ' . ra- l i . - t _OP(l)= 3]+ 6(3)2 tb(.?) f lo j /o?6* -?"- - t I

    t 4A4,o

    x '-42(+t- 7o

    f )zce ,("-+,(rr- 2o ?ra.-at( zeR. ' . (z- , ) (x+2)

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    t6, I t tG4)Jn: I+ nG+)+A]1p$1'*"( '* '2a*2f i= /-t * 4 r'- ( :3q;trt*.". C/, )

    Cn -,) (4-L) |' ---a;T- : 77>f ( n-t)c t1 z)= 6n "z7( n"- J4 t2) : .6n2/ n 2- P/n f t+. O7n2- z4a .+ t& = o

    (7n-6Xn -J )ro- : - o= J/ ot 4

    -okLtrz /?: j

    I ta7- 'Lr7s- t- { .2.- j/J /7r ' -an_:_ / ,tla.

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    61 lLt 4 6e zlJ rf,.dVtt /, A B ,.._ 14 ( t, t)

    G.6Areat 4 cL.a A'A ' J -,2-vj =6-*;tot -L -r. 48 z J

    / na'r L' IoL) > a.DLtLt t

    4t o l l l'- :t-rJ f , 1

    \ + )-+/L' \'J i ; ' Lr, l, ' L,)

    A d r ^o n ^a+nae,-t "- k-,-e * , . h) L.*4n* V'^ ^ R *7 I^-^^'c'e"4- t)c" , - \4, (^>r>.)' P-t . ( P.u., ) l - , . \qr l l - t ' * f - r . t C. : -)Y L P,, x= r.1\P('i 7) -- ;' ', I i"

    , ,q ,, >,1-*4.t) =TH* .>*,o--fita L Il* 6( qs^o, o,o 1 o" l / lf t l { r l J ' ' * .e a -\ ,L (^ >r, )p_)c, i / \,^, , |L ' ^. l t , - )1o( >f ). i - - . , , r t l t lgt , to*) i , )( ^.7tn:) " p t>,rr . , t , ' r , . o rr ts? >' fJ : : " ) tL r =t(z>, t .?71)= Lt. '1 1. t -? :t 0, ' l 1/ Chttp://edu.joshuatly.com/

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    .rr'],

    ,rI

    I - lo) - - D[ - c fr r -o) : " f r JI- '>>r e, : . o t - ->\( LtJ( rz-T2,") = rLo)- eu-): 1-grhr- ,q"- L,-

    -J l t"?er l ) -' - f L 'D') J= 3

    F("-) . +, . .^= r* za"C. 'o,-* *. ( ' r ' ' * )" = L ' [ 'J

    t . t; i ( r -*) - = ' ,( r - - ; " ' Y t , )f f - r* : t Ir44. r" lJq = >\.

    w; n--eL"'-^- q, 193 c*x'X +..z1 . ..-c |)

    t

    ' :_-

    \ ) vtf 'rr ;)z^. 'l

    Ii'],1t+.)