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STPM 2011 Mathematics T Paper 2 Suggested Answer
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Pt (sin 24- ri\ Lilz
I
sl:g sLA-.,sLs)?6^r+'r;n79)z - ,
-v7s,4 4 \zt+t6)'iirn f,L&4 "ni * L':',!(wTzfi)'''n L (u-LilJ'
=Lqgin? (A +e:) gnzio-yI i ' t t -*(etBJsin'u-s) l
: 119n 1(,4 -9 ) L t"n'1aT 9)-t @\b (A"Uf
= fsm?(|-B) L r lh- su't/+ " B)
t I r r lG,wn b.Q-'{) =O
\s. ( - -V.4 =Q- l -
"^d c.Cd- b1t o
r t | - c.Vr r
*"1 =/4- r
"^, \o " cF
od
'>-a4
IIl
ht
S.rVs[,t.'* " O t
"v9v
o.J- - i l
9,"-r ' *L"O
BCr *. te 0D
J
LLJlL=
La JL =
co..,sl,ltrLT
Liu k ='Q ( a5|o_ i4 at"{<rnqft sr.5.nva{ )
LJLI = LLV-1.= ( f0 '*d-9 (ce^*n;{qs-b t^ki$le] - .
-.'. A v31 ad I icu( art; rT,-*=l
A L31 a,A I icu( arr
IT,-*=l,rLT uK YIg =E 4 st"K1 =tur)'"'*4
N \: :L Vy'.r F "q''r f 2zuw-'fl'a"L;aK=o(tco44n,s^ a1ie) /
TKt-Sv'
7-49.Jrc
x4eJK
Ig)," =tfua"-5 g-- l) tu'lStd*
ILt- d) /*'z1td"g - t"") =')J,qY + C
&ivern YrL w[<'n w= i )
Flo'n h"
ffi,4-=').9-ni*ci - Jnt=2),nl- '+c
4 - 7\n7= -7'l'u7 a c-
4 -LAn]4[l"\zc. ' -C=4' '
Fa^@ r - i.., u =T:"r -t /t
?*'x-#4t ' [ * ' ."@
,+-@a@'^'b@x b+u= ur-(urcrx)
T*- K[ ux-r)
t . . r@
...".@
t*1"u[4"1L,L J
- u X' \ (ut r ) -U nY' ,\ ' K( u-t )
v @-0"-Y/U-t ut- t
- utz+u-,,r2+Lt = ?, ' . ,- _u_
t ca_l
: ,2u ,x(u-,)
^
gq I q1=1 :lr CS.= h ?q-*'=i.
@ B=\"G#""'@s
PCr I GS: l3h
(G
EsPG'
2i -@
\q5
lc4satc
A*5L
\,1= \,t )L
i =u)c{lr^, 4 A.
GT =,(aQ
ct( =tAT
t+t-t
.-t '--t
20S = kr}+ut>_ 4 -.r --a2.KAG=bPrGR
C*t].+ GA = -Z.t^ G ?
Coa$re- b"& tXg
ztr- l =0' a^{ t - [1 =oh=t h= *
i - h =V=\
^Let S=lf tug
t$ c"qtucrt'4+Gt c*no+ f,^,{ v+t
| ,rr*-'ftti\)c z ( ca(lx+x) 'ffi-= (Co:sd' n oS 7L- fsino\J r4 4'
re.Sd-l . @ Co'-d.+,'0'1 4X
[, ^-
.li sl^ r= 7c': ( ^o t'n)
f j ,nA=G fr\cndzd..t9,r"
@, fs lTJ. - 6
6 6* '1 tAn 6*+?-,A'G 1"
"( I ' f
. 6/ z no'.xT tt:,':*
- rW{ .*= l \ N,.u2anA*PjT*
' . Co5 X.- f t5;qt= Zcostx+ 60 ) -4
J $en do{c*rrcunrsf
" tqtuu5gur 6
.-tt v- .J
zgRA= 6{* G0lt^tush1",t4 GA = -(x?-?-hfrts & = G;{+ (-c?t- tbit)
-\< cdsx 5 \
q -+^ --i1
-1 .-+
-)q h(L= Gt - cR-zu.t*lp-ts -) -.-r .-g ' ^C.&-Tle +zhc.(-.aP =2
A-'sl.Sg33*{e"fr* oaft-bt
5*te^d 2ln-t-€
h=\,
CoS I- JT rr, r. - l @ <x <242us[r+!rr)= - l
) -
tos [t t ]n)= -r.re+{-rr =3or*Ti
) r= *n,rk"
- rlSstn x ={ L
- l
-2
fr!\i^io-t''x'- l ' -
v\ = coS { -J3 SlnlC
-Xlq qr*b,/. o+ ooh "{ e1^r"{itn
is x = *-t\ ^J
tL=,"effiit" x"4
(D pb-bi\,b 4,t tt"il'o^(- sl'v4 ii t*'1t
1 $*+a+1Llacry. d:^r?
"yL\
=3*vzS
7 e,4081
@1-
+t'cz
n -- LsS |,= ux,".g 41*ec$re c0 .X * B (^, 1r) + x-B ( roo, o.oo 5)
np = :co (o..re s) = | (< t)@ ?";rio^ Dnrl*jutr*r., it
-rt h ,yn.x'* P.(r )
?(X= L) '= u!r . (o=e ,( , t ] , =et1\_. .r: -il
?cb.b\rg fues ns\ CP&in a9
&{.chve r iru= P(X =e= g{0
oL
^ = Qlt z O'3b?1 #
\!!J ?ob+it\ o.-cts*r^. bur c,o^funS a+tactt rt -a.'[<-1.1g orTl+ /is.: -=^p(y,>-v) = i_ ( tx<k)
ol -tq t x: o)r itx,9 + QtX , t)+\ty4S]
-' l-[o'jo?t 1 o-1t"fl t o'tY11 t 0'o 613] -
v7 AtfTstn^r4t ,r< s*,tqJ urr?{-o-#
/ro
6o
bo.t{, notto$^ s,tlrt
7J loore.16.t^,t"f
@l*i'"$tlly b"h ran-t g,[eJ
0R4oc.* oua,
=lO0r
VL
ry+1 50
: \ - e- t f t . '
' l - * t '
d!!'* Co)"t t z lt i r-.ti
k'+/
X{ Y N, ?u lL)
?(xr{ ,= 7) = 89-= 0.1-1oT x
=L+Etzx-r)=t\/ , z a
zE(x)- l> l lzqEtr) = t( ri6+r7
=[*
=9ztS
= 4L-
t736
83
a){.*r=t,tr;ili;@E (rx-,) = [i*-y. ftrl,rrr, l
i -'. 4 rlorf r) = Var[zx-r)i 4 rlar( K) = zJL?
ur"tx) = tr, .^\ +5 {ts.(9 e(zx-'F) = u (+r2-hx')
= +ElxL)-4Erx)+ |L *:: .? _+ ($)" r= 4 E(xr)_ >1 5
: ( ! - I -1 1- f gtzr rs / L3J
= 6l+5 .h
lgU vh{r^_:! = I[7orI
TlUtsS = IbZl*To
. k= 1875 *.
10.:s/ (o,r?5) (e.rs) (o.ns)/t\ld (x)= >F.ftx=r/]l
v P( lx- E(x1 [< tJ? t ( tx- r , rs l < r)= pL _ r _4 x_r,).s s l/=t( D.25< X -<?'15)= pfX--t) r tCX=>;: A-+r8+=
? : 0.625 K
Z= X- t '?e,]Z
F $r
lJegar( I5fo 2 2 ls>t Sosotfsoc?rt fSf,$ + 6 1562,56*S0{f?5crtg 16oo + LO l5g?,5 63so16oo(x€tUt,'r+ >+ ',LIL,S 2? S+5l6?,scrg loro tz 3b | 631.1l{ bSol65qr)Ls tG+S t 4lt ,tr662.5I3 3oot6?Scr( rlpo + 48 16r,5 6 ?fotloo cx < k 2 50 r+o!+K ltos+K
0* tr*reu-F.) 11,!4{{t?'s+l< I
=1625- H[zs-r+]
: 161] [ffif' ' ."'
fl,tsdg = Ue +/A\ C\dr*dr'l=l6oo.thP+tt,') = l6r,t@
=t[+ <-o.uzs)sp = ttz > i.zs)_4_= t(? > 0.6Lt -d+r.r = b,lo 565 rirs
@ p[ s n^+u r*'l']l-f o.?h.)= N (s '1 < X l . l .o)
= o.qkoXt- o,?| tkel: 0.ao6q 4.
@ P*u"t;uq b,.nfu {Lr*\-J qrts,*cu
= p( X cr-o) - 0tX zt 'o)= 'Q.LrstrJ Lo ,>ESLI)= 0,01015
...= o.otot L\s-t-.) 4
Q/ L\ y= X,+xrr t*c^rtY: \ .1t \ '2. = 2.*V0rn"{-4 y= Q.392+ Q.3}F, 0, }oktr
\ -,N [^, r ", ? __ff. +: s.nvt)@
?f Y>2fi)=ttEH?r ,. yH#)=lL+ 7*\ 'Sk1)= 0,191