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8/8/2019 math1 + N9
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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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Jangzrnulislna-aol diruangannr .Nothing isto be rvritten in thisn.)afgln.
3" A)-ae1JI=oT=f o,) , o' [3 :) 4'- { +rIl6l t t R'11 :) A'-1A )[ : ?)= : 3 =(i ) ' - r l l)4 +r ( j :)(,'a\l{l})=(tt : ) - , i i ) ' r ;?) -G x)t;" )a'+ bc[ab + bd 6a+tdl f l { ' }b\ /bc+ ',f\rc al( ; i ) -- ( o 00 \t
ab bd +c=0 :Q / YVI A'-lA+rrfro *A='= i) {n ,#, d eadr-Q,-]n2L =AA'- R+ I = o
l ' :TR-)IS 11-:A- '
)A-t" :1i- 4 IA-'=+t- tq=+ : i ) -i t : i )_ /)- L--r ; ) / A*'= -s 3lj Jr ' '6x 5 A B c ,7[xrr) r r) ' I x_r . Cr""rl
[ (r- ') '1rftrr)(x-t) c (x+r)= x'-6x-rX. l fra= X' l )c =-8A= c='l+(o*gar oo,$$urrt-t A* B=3l+ B=-:
B=.J 23r ' -6x-r I * , - b f \ /
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SEKOLAH MENENGAH KtrBANGSAANSTPAULSERBMBAN
I a _fincl.oro-. wlNama:- -!11--?---! l1?1 Tingkatan:
Jangan ulisapa-apa. iruanganrnl.Nothing isto be writ-ten in thismargin.
5_ Jl-r + Jlrx = J-qr-3t l i ; { Jff i l ' . [-r, 's) ' |)hcu,,q'"[ tzq+rf iTJAu \*X= -4r-l x=-+,r-A+)lrfr:I) lfr-91-3rJfi-x)t,r$')-4X-8 x -3, J6 1 1ffi; "'1-s(+)-3
Jtrr)['r-rx)-)x -4 c e: x=-S ba{.4(' -r)tltn) lrr+l[x + {I t)r-4x-x' ttr '-tlx+ltr
Sx'+l1r-{r to gf - t {x tr13o \\=+.9 n=! o, 4r1 / t,1/
x: -r1t IT.1 ; -r\1f,1-E-)o tr IIo{=)-x' d et tx ' - ) to dr7i eu+r -)J++t*.*+*Xn*, " Xn --"t; i- +)xYn { )r4 ct {x'- l ,/-Ex /)( 0.(X, , A.Szt) Ix! : 0-83124 (l '1 /r-\Ir =o s!1r74 I L II
r"o1 o.r3l , /v
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--E-r\- \J \ \Jangan ulisapa-apa diru:rngan ni.Nothing isto be writ-ten in thismargln.
{ tx)=x' {or o(r
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SEKOLAHMENENGAH KEBANGSAANSTPAULSEREMBAN
Ice f* K"an t^xlJangan ulisapa-apa. iruangan nl.Nothing isto be writ-ten in thismargrn.
nt' t ' Ia) fff= sf'n (x ' l+ q-r) ' .[ (*-0*+,{*s)" ]"
x'- x-r+q'-q+1 h(f-fr +l[+l'th4 4]0 11 I'-h 'ly'-6q1r9= ftI'-31x 4r4"'+)trlt00
I- t *b qltl:loy +3014{o 0X'{t4'- l0x l fPq { la:o
$$iZ ---t-- I X'- l t l l t t4'{ f0q= -to4 (r.,-$ (x s)'-Ysr,4tx)'-r-=ro a)(x-r)i 1l'J'; p | 5Gn+e 1s, sf ,/ l/
radl,^s Apo "..IJr[b) k) \o,o)
_ _-t- f , . / i \+t' "i o1Xra{ry1l, ^l^y't =[P" ' , . r , "1t+ [ t , - r) J-r' I = +\
U{3 = rLx-t) f \q* 3 = )x-)- =s \Y=Jx s/v-u'+r--/ Actancrc Ji,r-of{-r-oJ'= JITh\ q..@-'tm'lJ/ -,n'
\ / =f.i[1 u,nrf'rT=i6)"-$;F 6- tr1ttOC"'O{'3 i3o =[r)itot9';:EO
f i ,6rCalon-calon estimenggunakanedua-duaelahmuka.
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:: f f ia=, : '3t : . : : :: , :r :.-: r; : ; , : - ' rtr: : '-\r7
Jangan ulisapa-apa diruangan ni .Nothing isto be writ-te n in thismargin.
IrJ. I t-r)- '( t ' f4x') if f iE-r)-'=+.tr -t+ [-x)'-t {-!-il+*'j(+J"r+rr+a}l ;; < -(r+afltt+!ay'+ ry [ox')'+@ = +l{-* a'x+ +Ct-r)"Il+ar')i.ru*sr+ryi)lti^ '-* o'x7' * .. )= | try *da1'{3x'+At '*ox'{ .= lt Jr t (3rta)r',t(t tio)il.
( I t -x) ' ' t ' rar ') i | * Jx Gtialx'+0+L)r'= l - t r r I 4r ' - l I ) r3
Co*garc .n4{i.,.r,1, 3t ia "4dq. { /1 /o=E/ l ,
l - r l
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SEKOLAHMENENGAHKEBANGSAANSTPAULSEREMBAN
uLlTingkatan:= '(x 3)= x3-bx'
=3x'-6x=3rtx r)"o [ 0, o) i s a 'v'axist4dh4 o]^tX:Q 61 [:)
X=0, q= l)f i :J , t4: f[0, o") t [r, '4) 04 $al,w^ norY 6 r r -4 ) is a Mtnirn rzvvr
lotvri tl inler(r{r,,'1 .5"r ' tx- x' [x-s)o
N:0 pr x: J
r'(r-r1t 1= J'"x'-3r'V*)' l l+ ^' l i=1-?-olJl . i=T uni l
v,4 Vot,rur=u|tufu'-lr)a^=n '" [xt-tr'+/) dr= ,1+*^+'l:= 7,{to"t f -o): )0. t la yni f ]" 6s.,13
jangantulisapa-apa. iruangan nl.Nothing isto be writ-ten in thismiifgln.
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Y)Jangan ulisapa-apa diruanganni .Nothing isto be writ-te n in thismrroin
t) [4 A f ,6=4+al l0 / -(0/uq= =a+6-i{0 S,,=*[l^+ [)'-') fl, rn.1:a+Ll i lJd-{ =n la+fa+[')d]]0-o (n-t)d -- > -o =n[ar{]f.r\.-/ fr nd, : / - I [ l++)_t4= Id -A il1 I=7,/
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 /
Ib 6.7. q=l , S.=tg i ls=13qrz t : 0lt- rIffi
??0/ If? Jl -r ' .- a- : t . tYl- r l l p ' -p-1 '0 s^-f t /l -v]= lSrr-13rs t ' t , r , - 'T ='3 /
l?ri l3r1+ l=0-- - -\ l a . - i r \\ ' r rLFt r . r i - ' . , if : lor -h ott- - t - " , / S* - (n lo.oozr*1, ' t r i , / r- t )ucf)-Tr l- I { o.our
t lt - gQ")lzo'ut>g ( j , )< o.uot'.tr / l
nt.r5f< 'q* , - \7h 7 LL\-7n= t
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