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:9541L,950/1 ,,iMathematicsTlS.,Paperl 2009 :i3 hours :; .i ' 't i{.:a, , , -_,{. t : ;- r' I

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' . . ,1. : lJABATAN PELAJARAI\ NEGERINEGERI SEMBILAN DARUL KIIUSUS

PEPERIKSAAN PERCUBAANSIJIL TINGGI PERSEKOLAHAN MALAYSIA2ga9

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MATHEMATICS TMATHEMATICS S

Paper LThree hours

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DO NOT OPEN THIS BOOKLET I]NTIL YOU ARE TOLD TO DO SOInstructions o candidates:

Anywer all questions.Answers may be written in either English ar BahasaMalaysia.AII necessary orking shouldbe shownclearly.Non-exactnumeriealanswersmsy begivencorrect o threesignificantfigures,or onedecimalplace in the caseof angles n degrees, nlessa dffirent levelofaccuracy s specified n thequestion.

This question paper has 3 printed pages [TurnOverCONFIDENTIAL*

gS+/ r, gSo/ t @ aoog CopyrightPPDSeremban {:r7i

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Find''theolution tofthe inequality'l 3x'2 [ -< + 5 .Find the vallg of a f one,of herootsof theequation6x + q2 -9x -2= Q is -l',2"With this valueof a, find the remainingootsof the equation..Showthatthematrix= e I isarootofthe quation -lx+2I=O,t.s 4)where and O are he 2x2 identity mahix andnull ma.ffix espectively

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4. Express3xz -6x-5 in partialfractions.(x+lXr-1) 'znf5)Solvetheequat ionl t -* +J+.+, ="1-4x-3.w

the root correct to threedecimal places.7. Thefunction /is periodic with period'2'andf it defined'byf(x) = x' for, g5.r

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9. ThevariablepointP(x, y)moves n suchawayhat AP2 =48P'?whereA isthepoint (1,3) andB is thepoint 4 , -3).

(a) Find he equation f the ocusof Pwhich s a circle.Stateheradiusand he centrethe circle.

(b) Find he equation f the angento thecircle at thepoint (1,-3).@ fn. [ne OT is a tangent o thecircle,whereO is theorigin.

12. (a) The third term of an arithmetic progression s 10, the nfr term is 8 and the(2tt)th erm is 9. Findthesumofthefirst 2nterms-.2

(b) In a geometricprogression, he first term is 2 andthe sum of the first threetermsequal o thirteen times of the third term. Find two possiblevaluesof the commonratior.Thesum of the first n terms*d ttt. sum o infinity of thegeometricserieswith r > 0areSnandS* respectively.Determinehe valueof S* and he smallest alueof n such

oftslt4l

Calculatehe engthof OT.10.Expand(1-")-2 1+ ax2 7' in ascendingowersof x up to and ncluding he erm in x3.1S1

(a)Find hevalueof a if the first four terms n the aboveexpansion re| +Zx+ 4:l.f+ x3.Statehesetof valuesof x for which heexpansions valid.$

(b) BV aking x: Ys, ind thevalueof tln conect o threesignificant igures.

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11. Find he coordinates f the stationary ointson thecurve y = x'(x-3) anddeterminetheirnature.Sketchhe curve. 7('Find he areaof the regionbounded y the curveand hex-axis.Calculatehevolume -*of thesolid ormedwlienthe region s rotatedhrough2nrudianabouthex-axis. (j9

tsltzJ

t8lis

r8l

Vt

that S* - Sn< 0.002.

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ru'EK'LAHwLn, f"" Yqtn MENENGAH KtrBANGSAANSTPAULSEREMBAI{Tingkatan: Wl Jangan ulisapa-apa. iruangan m.Nothing isto be writ-ten in thismargin.

x-(sZf -LLy+t"wLn

t

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[ (r- ') '1rftrr)(x-t) c (x+r)= x'-6x-rX. l fra= X' l )c =-8A= c='l+(o*gar oo,$$urrt-t A* B=3l+ B=-:

B=.J 23r ' -6x-r I * , - b f \ /

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SEKOLAH MENENGAH KtrBANGSAANSTPAULSERBMBAN

I a _fincl.oro-. wlNama:- -!11--?---! l1?1 Tingkatan:

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x: -r1t IT.1 ; -r\1f,1-E-)o tr IIo{=)-x' d et tx ' - ) to dr7i eu+r -)J++t*.*+*Xn*, " Xn --"t; i- +)xYn { )r4 ct {x'- l ,/-Ex /)( 0.(X, , A.Szt) Ix! : 0-83124 (l '1 /r-\Ir =o s!1r74 I L II

r"o1 o.r3l , /v

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nt' t ' Ia) fff= sf'n (x ' l+ q-r) ' .[ (*-0*+,{*s)" ]"

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\ / =f.i[1 u,nrf'rT=i6)"-$;F 6- tr1ttOC"'O{'3 i3o =[r)itot9';:EO

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:: f f ia=, : '3t : . : : :: , :r :.-: r; : ; , : - ' rtr: : '-\r7

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l - r l

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jangantulisapa-apa. iruangan nl.Nothing isto be writ-ten in thismiifgln.

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ftub@ ulo @ = t.'JLi,( -* - . )d = '[_::#)a -r ,4-\-{ ] +:a)"-r -7t-T-3d'--+ tv/

d.- : /Jr} d-i into CI

a+)[ ' i ) ' ro /;= *-7-n=1t" t /

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t lt - gQ")lzo'ut>g ( j , )< o.uot'.tr / l

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