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2013]Itr{TRICULATION EXAMINATIONDEPARTMENT OF MYANMAR
EXAMINATIONMATIIEMATICS Tine Auowcdr (3) HoursWRITE YOUR ANSWtrRS
IN TIIE ANSWERBOOKLET.sEcTtoN (A)/ \ w1 ALL qr' liJr mi ,. app-o 1
de 1lq.r { (a. , I re I o-wr. etne e r J"e.or'.ro.he io.,Fpo!
deture r
r.(\rii|pn.ts 7.r .^_4.^,:o-0.t I _ddr/, i.te.d.bA.r B.2 C I D.2
F5(2)TlebinaryoleEtion O
isdelnedbyaOb=theromaindeiwhe.a+bhdntdedb!. ne \.1 rc or IOLtO .r
.,\.0 Bt c I D.2 L_2
E.6
L.A
E49
A-l)= 12E.2lIP.T. O,
(3)wnen(x+ l)(4x 1)(4x+p)Gdirided by (2x + r), $e rcmainderjs
j./\4 B..1 C5 D_j{4) rr(r? l) haradorof4rr lxi+ar+b,thena=A. I B.1
C I D.l''. ll rl-e -pd ,o, orl -' r.l r.tr '\'Ln.o, ai.,!r,
A 3dtern D.4sren C 5i,term D 6,hte-,(6) ln L\e expusion of(k +
2x)6, lhc coeficieDt ofxl js 2160, $cn k:A.-2 8.2 C _l D.:l(7) The
solurion ser of t1
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(12)
{l])
0'1)
it5)
fr oi\Th( urll.rof 1 P'(2 ruherc P= . , , lnLlA.6 B:lx2 C2'2
A md B are l*n evenh such drat P(nor A) = 0.6A.0?t4 B 0.286
C.l.ll,r
,\ bagconli! 12vlitebdhddsone Edballs' : tle ntrnrher.fred
balltrA. 12 D.10 C 22
O is dr. cenG ofdc cncle IVIPQN Md IPQN=A. 2i B. l5 c, 55'D 65
!. 75'
I2\Q=-l I I'l4 5jD.ltl
(16)ABa dEFdelansenbrothccncleatAandFrcspectivel) iiAB=6.BC = l,
DE = I6.lhen EF =A.l5 g.l? c. 16Dro u2i
(17) T*o conespondins altitudes oltwo sinilar trianclcs re 3cm
and locm. Thena{smdlh,^) i d(largd Al =A 4:5 B. } 4 C 9:25 D.9: 16
E 16:2t'8 lepo rio..l. o olrEpo.nr'A ldB'eLiero6 ner lu{e4: u 'aI
p: e..e-\.\.llO.A,1 Br lrei rh" p
c5 Il. 6 E.1rl0,lid' "na.dre ane.r ro.. :.le G. q0 - L'
'c.rnd (/ oo len dre ol.oiJli \ 'r: r / 4b'(t 'i t't /
A.l B1 ll0' E, 15',
D1(21) If td0 = x, le 20 = lx and 0A 75" E 60'L2:)jn ^ + rmr
1nn" =B."I X
D. 45',
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(23) t hc eqution of the nonal t. thc cb,e y=le\alx =A.3x +y=9
B.x+:ly=9 C.rx y=912r)1lnsar,oNl.uhber ;-(r h)" r"
A.n Bx" C.nx^l125)thc nalonaD pointsol rhecurvcy=xr :r *: a"A.
(r,4) d("i,0) B (,t,,1)dd(l_0)D ( 1, 4) E.rooeol$ese
E \+) =cD. (n 1) x'
c. (r,0){25 harktsEcTroN{u)
2x, such thar l.s = C!f. finn thd ietxro.ship belseeh(:r m ks)dd
r -h \ - | ift d1 dcd b\ \ + n, rhflrrmJnir.neb,h dk. {l bdkt
"rr re rfe 0 rem643 Findrhe:,lrm {l dirtrl(oR)scics olposiiivc
rlnber h l0 &d rtrc si\1cenlir rern s
2. ill xe2x +b atrdsr x HlaCiven!h.t*Ienx']+ax+bequal. ExFress p
intemsol4
:l Thesixtblee olarA! is 12'lhe sixlh rem of a Ceomenic0.1
Fnrd$eeleveithlemr
4 The poinls A, B. and C halc Fosnion !{toa ? .m + n = I, show
ihar A. B, and C are couincar.
i-l.:="5 coJ x = 0,lor 0
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(l) n A. P js su.h rhal rhe 5'i tem is ttEe rnms the 2d tcrn1i6l
eighrrnns is i.!!limesrhe s!motthc tisl rbnrrumrsl0 (a) llic ftst
thRc rcms ofan ,\P are x. y, z. It thcsc nhbcs.ri. .,o. rr. :\ .,.
).
Shol lhal tI. sLm ollrexi J. z aa 4rso lhc !nsl.
cosoI]!eEI h the unit nrlfl\(5 mdkt
3nd usc ir ro sobe lhe lollOwjnet 1= 0 (5 narkt
so rhar PA dd PU cll ltret|c rantrental P inS a.d T
it5hc5Arl=2.qI1.(a) \\'ile dolvn the invese n*" t* *1. " j:
;lsinulldeous equadons 9x 2 ) l3 = 0 a.d Zx + l)
(b) Nloke a tabie oforder patu (nar dje, sccond die) tor rolting
trro c,ce. lts. rhe rrblc tofind the proba6ih! drat the slm of rhe
sloEs is .dd, lhe produor oi.rhe sc.rcs hEreater tho l5 hd rlre
produd 1)l rhe score is ! nnrltipls ot6 (5 mdts)l2 (a) IfP, Q,
RarerhFe poidsonlhe cncrnterenceequalro rcchord PR.ptule rl.r ttrc
rhgenrar olacnde chrhlrthc chods penP bsects ihc e\rerior dgte
beNrdenpe
(b)'tuo dncles inr(se.r.r A and B A point p is takcn
on.acoth-alQ ard R respeclirtly. The toec al Q ajd R
n*lrcspcctivelr. Prolc thal ZIlR= U BRQ dd IBQS is cy.|c.Ir.(a) ln
d,{llc. ZBAC = 90 and AD| BC. ltDc= I BD. provc lhar Bc = ]A! (j
mirk,
\ .ro.g, i , . " . r. ,r'l'ien,b,.r.-_.,1.,.t5.rakn4 .i. r''
".l
-.". rt .o orelaliorship behrte. bn a dd ran F. cived innher
lhar d , p = 45 , calcutar thelalueoirana , tdp. (j hark,
(b) solveAABC riltrb- r3.a= r0. c:9 ()mark9I5.(a) Sho* lhatthe
cquationof the rancen othc cun.y= (2x, at.rIhepoi *,heEy =.- N )r=
x_(ar 6x) (5 n,d(sl
(b) Ilr'y=42,lind rhem.\ihumvaluc oJ \y (j D k,
