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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)
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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
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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
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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
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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
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, ,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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