suggested answer stpm 2011 mathematics t paper 2

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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-yIi't t-*(etBJsin'u-s) l : 119n 1(,4 -9 ) L t"n'1aT 9)-t@\b (A"Uf = fsm?(|-B) L r l h- su't/+ " B) t I r rl G,wn b.Q-'{) =O \s.(- -V.4 =Q -l- "^d c.Cd- b1t o rt| - c.V rr *"1 = /4- r "^,\o " c F o d '>-a4 I I l ht S.rVs[,t.'* " O t "v 9v o.J --il 9,"-r '*L"O BCr *.te 0D J L LJlL= 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 YI g =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'

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STPM 2011 Mathematics T Paper 2 Suggested Answer

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Page 1: SUGGESTED ANSWER STPM 2011 MATHEMATICS T Paper 2

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'

Page 2: SUGGESTED ANSWER STPM 2011 MATHEMATICS T Paper 2

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 ?

Page 3: SUGGESTED ANSWER STPM 2011 MATHEMATICS T Paper 2

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

Page 4: SUGGESTED ANSWER STPM 2011 MATHEMATICS T Paper 2

(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

Page 5: SUGGESTED ANSWER STPM 2011 MATHEMATICS T Paper 2

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@

Page 6: SUGGESTED ANSWER STPM 2011 MATHEMATICS T Paper 2

=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