eaaz1EqaAg/4 Oaaan1:6Iaud'otfionrlnr:EJ%tlttgnflfl%1R1on4t$o[ilta[z1G[nr*1t1ta,n41?ytu'lng]rg\ttilfliA

eJulTn u1 n'EJs oo igun s ro nfit,u tl nr:fin w't 2ss2

ila6rauisr o5 orrfisrcrlr[a 4 t

cfauilrorfi n$fr zt #urraru yr.Fr. 2ss1

9v

?,aae 4 aeur,tltlr,/

?,ons 3 Ft&[rt,t-lu

[?n1 12.00 - 14.00 ?[.

OA@1AfrU1EI

1. riaaouariudfin"orur go fo r?rJ 7 n#r uriroonriju z aou Frnrt*urdru too nsuuu el-tdiatYU

aor+fi 1fi 1o zTo oT.ruqirio 1- 10

aa%{d 2 6i zo ila oi.:udria 1 - zo

2. rioaousrolti4 r rio 1 - 10 tilurioeouuuutrfrForiruenr tr{riTrirsrarfinnoior Torr1t

qY a otgmflr{ssJ6[oaeirunr.dolrif,srfiernz '[:Jnoutun:carrr*rirnaunoufi t n"odtti'rt r?",aruq4 AA q

' v , o Y A^- " yA

sfn t}1? DnlTn a u lilTo.J q? 0 u1{ a'lst oufl an 25 uun:;ol :*ritq oufi il1fr 1

(ti3. rTaaou sraufi z rio 1-20 riaaouuuurdonoou uqinsrioosfirirqrautri'udon 4 rirqou

6a 't. z.3. unv +. lrdfiqr:il'rtfionrirqoufirfiu'ir nnsiaofiaqutarililrsaaJfiaorfis.r{qq

rirooutdse u#rlfGuaasir ze fitaairn'ir:curutur.:nnrufioiornr:tun:corr*rirnau;

oallYi 2 q{CI?ou't{

vta?a EJ10 n1:aou

(0) 2 + 3 = ?

1. 2

2.33.44.5

e./ X o i a1JA1,[ fllnoU?lnnno 5

fl

6..:t:J a ou si'r rfr on + tunrrol:*rirfl ou oifl

(0) o@oon1:n gr rfl rr tr{vr otucl-rfo ao u un ;#r rut#rotor 6 o rir ue nrlo 1 Io u r6ozr olYog/o9/f€

14'l E t 1,[1 ?t o 6t o u ua & n :e ol1 t}fl 1 st o u o o n o r n il a 0 a o u [o sJ r o o g 1 slt v qevv o d A", - qy d q vnaila0u1aflou tfir.tr?J1flourflull dounerasfir,r,raou tr4aeru:nl nr [uil1n:sqr]gnrnou.u-

ffiaeitunhLod u#e I#ao fraritilavlau

ila6fauariufi uulan s1fi's rfiso'[uil 6hr?%Rvr dr'rilnguil1u

4.

5.

6.

IATO u'l lJ 6[n n.. i .. .

I

ttAv

... r. .... LnTn1[.16[0U

r6bn er#o 6[auTq EJ o1o1:stor;n1 nfi'o

'[ n rfr s il 6[ a t,ut#in'[r,u Fr ?1 r,r i

vA€Aq.-?ldalYtagYt 21 filt?"laeJ il ,d.2551

213

05 errf,srrf'ldn{ 1 rn#rfi r

srol,[fd 1

(6i to r?a #oas 4 asu%r+)

AOtaila'laou

1. td'p, q ,r,s rilurJ:sy{of

ft ufi oil:nnror.fi t fidrn?1ruo3.,:riJuoirutnsdlnuer (t) : { -!-

-[o rfi o:J:vvrorf t fidro?'rru03.: uflurfio

rYr f(p) .f(q) = 0 Ltns f(r) + f(p) = 2 rrd'r

o.tn'tritto.: f(p -) r) + f(q -) s) * f(r)

h rfiox(oI

4. rirHuotri'f(x) :1" rfioo<x(1 unyg(x) =*2+1l^2 rfiax)1L

ri'"r n: .f o g ud'r o.ln't h(3)

2, td' A - {0, 1, 2,... ..., 99}

B - {too, 101 , 102 .., tss}

rirHuqtd' A.B - {"ola € A rny o = a}

o.:urdlu?unrutfinr 0.,: rssr A. B

3. td' p(x) - x5 + gx4 * 2x3 * ox2 - 2x- 6

LLns x + 3 rilusiril;ynoufid.:oot p(x)

oi.,rriurirqr oufi riludruruo?{?J a{ niln1r p(x) = 0 fr frtru?t*

o. d'r zk: dk +bki tilu:rnfd 6 to.t G4u#r o.rn'r EFnl

la ufr g eu a a ut#intuer m ru i

s. x. , = [] t.l u* s2 +ge-1 - ["" "'f udr oru.reilr'{ a12

[o -t] l.r, ^zz )

a'/ A dA aJ

?%o1r1nun 21 6%?1stEJ y,l .G1. 2551

214

05 nrfisrs[1cila{ 1tyj

H%',I?l 2

T. a{H'tni't c fdri'.rtnl' tim [.*+l -ux+0[ ./*+4-2)

B. e.r14'rtfluiduSn ilfd urr{llr+ril qiotrtfiqt

9. u3:inruviuad.:ru6ql6'vao.:tfiq6o A uns e Iqudr{finld'grfiq n,iruru x sTr unsnrfiqrld's

tfiq e 'iruru y or-r ri'rtri'c riluoi'u4unr:rufio unsfiria,irriqelieialild

C=4x*'2yzx*y222x*Y) 21

x*zy)39x)ov)o

o ltr'r oi'uyr unr:ar 6 n fi #o ufi acr

I

10. nr:tfionoto.:slt8nnnr{rrnu:r:*4Tta{o-.n4?-gradrd.:finrurfin'lsi' 3 nu fin::ernr:rfiovi.n*?u9ld9Ya

vt'.:fiu 4 vl;Tn ci.:{an-n:iurdanqr'.:ll::nne 3 nu o.:nliruruifidfi'lqi'iunr:rdanotrororjcI ql - -qttv&

al{1lTTnnilfl{fiilo

-x

'[n lfr s s,r 6{ o t,t'[#in'[r,la ?1 sJ i

e/ A da e.,

?%o"lYt nun 21 fi%?1nil n .F1.2551

215

05 nrfisrr{'16[n{ 1 rarirfi s

aa:v'fr2

1ii zo ila ilane 3 nerr,tr,t)

1. drnun A = {x e nl ,2 - 7x * 10 < o} olfior:rurriaormrusio'l:Jd

n. tir a - {r.l I x il1r 25 uns 5l udrfirqurrdorrirfi'u} u#r n .rr= Q

fl. rYr c-{-=Ilsr-'rrr:drilrnnra{ xunco6oz} rrd'r aac=Qeq ct

lJ0 tOHJIAOT.I

1. n.en unr r. nn 2. n.Qn unc r. fio g. n. fio une r. 0n 4.

B-[;]

fidr z 6 orioter

?40\J.

74.

lz a+1 a+1I

lo a a+3I

I

L1 1 2

ud'r rruuflun'rr

2.

AA

n. zuo $ny lJ. 29t

2. ri'rut,tqt A -

ri'r detA - T

1. 5

[*l

"_lulL;l

AX-B frFi

38

7

[Lnv

j'l9tOuTl

3. ri'rut*otd'A-fr,2,3,.. ,1oI B-{+,s,0}I r ct o,r da.' A , A

F - {r, n + nlr lilurd.lrifurail.: qi silfrr

rud'r n(F) rvir n-urioto

1. 10! 2. 3! 7t 3.

1. sx2 * gy2 : 4s

3. gx2 * 2sy2 : 22s

un3

rLnv (b) - b

7l

?ln b€Bl

-4 LLnr (*-u)'*y2 -e

3!

unrYilruil 30oq

4.

4. tri' r- riJur#uar.rfi rJrt,t1eroTqr0.r?{nnil ^2

+ y2q

#ur#usr:r x = 5 fliln1Tto.rr#uq:{ L fiafoto

1 y-+x-+r/s r/s

3. y:.ft" - 2^l; 4. y--'.6"-2",[;

5. r.:3r.:radtfiooTrln-aoqjfi (*c,o) oouooarjfi 1r1c*r1,01 rfio c rilu:su;yrr.::;u'jr.:

o er u o q rrn so oh^l rYst a.: nt:rlu nr *2 + t zy = o fl il nlTt o.lr.rfu :J dd oriolet

2 y-+x*+r/s r/s

2. 7x2 * 16y2 - 112

4. 13x2 * 36y2 : 46g

ln u8 g e,r a a ut#inlun m ar i

a.r A da L/

?%a1Yl nttn 21 fi?t?'lGtil yl .6.2551

216

os nrfinc['16{n{ 1 rarirf{ +

o. tri' t- ril ur#uq:.r fi fr nm ilfuryir n-u m un r r.ir uo o surin nrrr a rnlarn aflu nrq9

(*-2)2 -(v -1)2 - r ud'rrir r i4*rtri r- lrid'olarna{Iunr:rJddariote4'1.m=0.52.m=1.03.m=1.54.m=2.5

(z )

< B[t--J d odoter

(- m, 21 3. (2,

7 . rtarirsrouro.to6[iln17

1. (- oc, 2)

) - tn(x + 1) - ln9 6oriotcrX

{r} 3. {2,3}

8. L{gtri'rqrouro.t6[run1T

1 t)

3.1. 17

i-j+2kA 9,/ 6l

Ftofl 0 Lo

8

"l r

2*' (*-g)

2.

ln(x2 - 1

2.

@) m)4, fz,

G7

4.

4. fz,3)

-92

9. eirr o.:

10.on'lilltgl u - 2i- j+ k

ri'r 6+(u.v)-alu"vl8

1.11

[,.,;),,{,,,ccos ft)2.:

A e,/ 6l

9tolj 0 [9t

z"l-2

7

LLNg V _C,/ r

tLn?nl a

2. 4.3.

11 . drr o.: x tdriltrl'

^+x2 +x3 +.. .....*xn2

1.13

Ae)619t01J 0 L9t

3.

fotofio

'[n rfr s il aa?bl#inlluelrT eri

T6

+

2.

aa

= 0.18

4.-4

12. rirrauo 6rrJnr:u#uTri'.: y -,2., d-y - 25| :-r' ,2 3

OX

4(1 - 5*)2

2.

3.

4.

Ft?'rrud'uto.:r#uki'..rfr1o (0 , 1) 6o +2

frrri'fu y: {EA rflufr.:rid'udorfio.rfr x-06nJnlrro.tr#u#rurisTri'.:fdnr (0 , 1) 6o 2y *5x * 2:0

iuarfi n$fr z'l f;'r,nrail il .Gl.2ss1

217

05 nrfisrorasr{ 1tvi

14%111 5

13. drnuo f(x)- x4 -4x3 + qx2 +r riotoon,u

1. eirinqnra.:t6o t uR;2 2. trilufirri'fudTrfiruuuri?{(1 ,2)3. tfirirqrqofifinf,'fi x:r 4. uurir{ilq[0,1] tfirirg.:qo#ru!:nlfi '-oqlqq.U

14. #rts::lrRusTruvi.:nd.: d'ofionrrilfluurnilnnrYrfifirordr"rur'rufiouh qirunr:trinnrY'r9rutu

cirunfiunn uon,iruru 3 nn ornneio.:turadrdrurraflnu0flnuroryirn-ufifn:*rucrilfioun1uq lll { q.u

,iruru 10 nR tu'irurudfinnuonf,rm'iruru s nR unvnnuonfruor''iril?u 5 nn Torritauo'ir,u(u.ullru9 a llv a e Vleu r a- d'rn Eu'[si'n nu o nRuo.: n nriros'lqi'fu et:J o.l unurT uao ru neir t 00 uryrtor.tot.u.-t,^t- d'rnEu'[d'n nr o nRrm n n riro s'[d'fu n:J o.: rrmuriuno ru n rir 50 ur n

nrrrurirosrituduna'rou"dodfiurrrf,rr'ruf$,u1, .rrt*0unnuanel-rncimunsleinilot$q.ug

um u ti uao r n rir :r er n-u'l ai rio s n'ir 2oo u'r yr rvir riuriater.u

.5_5^7 111. 2.6121212

1 5. nl:fl o u n-o tfi o n u n er n tririu:rrnr: tui m nm ruin rr ru ar ur:n vir'[:l n s uuur6 r 1 00 n s uuil

nu'irnsuuuaauto.:firrirnoufinr:uonuo.::JnG firirrqfrurngflrf,qryirfiu 50 nsrtuu unsfict

airutfiu.:tuutllarolr{lvirn-u '12 nru]tu urrfiGnuf$nsu'r{fl't?o:Erf,ut rilufirrirnautun*.:dq9t

unsaou'loi 74 rtng*o2 nruul.r srtruiiror-u qi'.:riuiosJnrro.:firdrnaufiaould'nr"rruurioln'ir

ur.: sm a :*rfl ut ui a rur n n'ir ur u fi ?n uf rvir riu rioterq

rir ra uot# duiitol'r *t*LYr :l n 6 sYr qr :r r

z 0.00 - 1.00 0.00 - 1.50 0.00 - 2.00 0.00 - 2.50

ftr,r{dt sTr #uTrTo rJ n 6 0.3413 0.4332 0.4772 0.4938

1 . 1 3.59 2. 79.15 3. 84.13 4. 86.41

ln rfr s il 6r a %:L#in'[r,ra x1 il f

iuo'rfi n$fr zt fir,lmaal ilr .Fr. zss1

218

os orfisrrlran{ 1tyj

14%1?1 6

1 o. en:'r.J uo R ua { n ?'r rr d ri rll n usq.: r{ n r{fi q rad u ei oti lrar.ir u : fi In niru ;,i

or n un si r fi il n n vir il :y ryr g,ir ur u so o-.: n l-err o.l :J :g ryt fi '[n EJ

L A i A ue,/lJO.ln?tilnO.lnzunA LO

IAVATI

9{ArunAn?[mao'0lilaEJr ?r

ma [5

!rla?'liln

120 - 139

140 - 159

160 - 179

180 - 199

200 - 219

6

10

18

14

2

v v af, & A , !- -,q e y y - Aa ^ & a A r u,n1T0u1nil [Frr.]n1TTU'tu1^rl{mn1:tlr''rvilnRn?riln0{ 6nnru0.:nrofilil.rnrudnnrtndottafruqio'[iru

q.:n'jr {rilr-qdu 1 :Jxrurr*iounv 75 toro-rfifqfifidufd:Jnnilu?ra 50 o-.:nfo erifu6'tfir-qfiqr / ----ri'!tee, t u t v d a L a j , u, ,l^s u

0 r [9t rlj't:? rl tFtT{ nl:q { n nl ? 0 r qt 0.] rj ru n ru ri n n I rnd o.: ta6 u qi 0 -tiat nir fl fl [n nfit

1. 184.5 2. 182.0 3. 159.5 4. 146.0

tz. rioqrlrrulonn9t

1. nr:foreirnnr.:to.:t"orynoi":ugrufiururorriarynqoter l rirgrufiuruossio.rfiriro$:rn.jrtei.rqt d { q . e ---"' cl

v Ay j - t u j j q q y6r{ tR 9t yt lt 0 u n fl o n u n1 fl .l [n o m il'l n m fl q [1t1, 0 3,J fl Tgt 1.{1.[ t fl il 0

2. rirfoilnqotqfidrfiq:JnG nairr6ofieirq'rrfiu'l:Jratooirrfiul:J ovfirunn:smuqiofiuoru usiqrql|l'@l4 ra[tJ u il n nrsytu qr aoluiiu ru

3. t{nr?iluo{runsir{:sn'irruqinveirro.:riarunir-urirradurnrnfinrotrioai*mtit* fisirryirn-uq| d _,,,_.d

fll,lutflila,u

4. nir rur m:orur o.:rio il nrqlo I oseior fi rir lr nn.ir sufraru aa qt q ) qi--- ---

ln rfr s il 6r a ll'l#intun ?'r il ;

iuarfi n.ffr zt fiueralu n .d.2ss1

219

05 nrfisrrrran{ 1s,/ j

14}t1?1 7

te. riorynoiolrJduaqrrirtd'sirutunr:Ts.iunnRudr lrar.iru : uauurm) rotuS:iyruvicadt turirrilu.st.2545 - 2549

tl Tr.Ff. oir'l#Eir er

2545

2546

2547

2548

2549

1

2

4

5

7

f,rnmru#rur{uf':sra'ir'reirt:fi'sirutunr:TruururRu6'rn-udrrrrnrro.:riorunfr fin:llrilur#uq:rrf,rnre'irrirlfdrutunr:Izur*rur?uri'rtufl fl.sr.2553 osrfiruduornfl n.s.zsst rvirriurioto

(Hr.iru : LL6[uu'lYr)

1. 1.5 2. 3.0 3. 9.8 4, 12.8

v a u a y t f a & A t dv a u &X19. n1:fl0unqtn0nunliuu[{lT?ri[n:{n1:i5'rnr:er:ttailr lruirilun[5EJurfrsouiliRu tZO ou

6l -.:..-.--.3.*t-.-y' a u a a f A v a att1.t01t{?tnt[1]ilun trullr'r u 70 nu t,tn rruul4cu{ 50 nil [q ufi o r uuuaour orun iSuutr u fr eir

i{rutdurtuutJlarg'n{?a{nruuuflourvirrir 12 nsuuu unsfroir#rurl:sRnfnr:ru:J:r.r-uryi'rri':-r

0.24 airun;uul.lflau?JOrrinGrurnfi.rftri'rradrrvirriu oz osuilu o-.:rfunsuuuradurarfinGuuAo&taeqv7l tlj',r fl 0u?1itfi tJo t?11nulj I t9l

1. 55 2. 60 3. 63 4. 66

zo. lri A uns e rilurn nnr:rrflo 1 dld rnodaru fr'ulu:Jin fi sl-r o Eirr

fir p(A) = s.3 unr p(B) - o.+ u#r eirro.: e1R'n e'; rvirn-uriotor

1. 0.3 2. 0.4 3. 0.5 4. 0.6

nf

{

#jk

'[n rfi s N 6t o lt'l#intr,ra x1 EJ {

22I eiT rinirrnr:'lnufisilrads ntf,neirasr{ t

rans imsrrfisrf,'rcleli r

no$fi t

1) 3

7)2

naltfi z

1.) 2

7)1

13).3

1e) 1

2) 6,126p' g)8

2)4

8)2

14) 4

20) 1

4) 100

10) 108

4)3

10) 3

16) 1

3)3

e) 48

5)e

5)2

11) 1

17) 3

6)8

6)4

12) 4

18) 2

3)3

e)2

15) 4

1 n rfi s ru a a r,t1#5n'[r'ln er ru f

rans arfiqorasr{ 1 222 atT rlnirT nr:larfisil

A CIY?ra:1s14ua6{0u imnrfisrrt16ta{ r

grar,tfi 1

lv?ro 1 aou 3

1 ufio '.

fid'rn?lruq3.,ruiluo3rA

L}[0.lQln f (r)

LLflY f (p)

T doalnlovruri'rnuotd'f (p) .f (q) = 0 lLnsLT'llTru'jt f (p) =a.t Uel.l}[ltf(q)=0&AArAdrd

1,[U9t 0 q 3J gt',l gt?'l 3.JaT.,] nJl,tLma

p-)r p->s

?

dAo tuo r ruoi'tot?'1ru03.:uiluufio

d A r A1 lfio p fiei'rn?1il03{riluoSr

o rfio p frdrfl?'lru03.:rflurfio

={

={

T6-o6lc,'01n IOYIU nlilUq LH f (r) + f (p) = Ia,t &9l.lltl.tf (r)=1IIflUf (p) =1;)A&ArcrA

1*1[nA n.l r LLflY p u9l'l9l?'lilLUltQT.l

( 1 rfi o q fi drfl?'lruo3.: rfluoS.:jlt1.[0.]01n f (q) = I

Lo rfio q fidrn?'rru03.:rflurfro

r)= 1

s)= 1

.'. f (p -+.'. f (q -+1+1+1 = 3

e.t &gt.rul,l p -+unr q -+.'. f (p -+

a{TACtA

r il Fl'l Ft?'l il a T.,l t:.J l.to T.l

AtACrar tl Fl'l 9l?'l il 0 T.l tU }[A T.1

r)+f(Q-)s)+f(r)=

'[ n ufr s a,r a a ut#intr,ln m ar i

raas nrfinnran{ 1 223 atr#nirrnr:'ta rfrs,il

ila z oou orzo flfTrtruR:ilnoilfierooflarnna-nf1Aau,av

tflo.:orna b e R6orrfifiaunr:6'uci:sn'irr a uns o uqiosfirunfi'rrftor aofidrrTu

.'. fir',iru'runrnfirfga.: au = [n(A)xn(B)] - f ,iruruusincHnnufro.r ab ddln-u - tI

= [rooxroo] - 1'ilru'luttoinsrunfft'tfiio.: ao f4"i'rrYu - rlrunffnf,io.: ao i4d'rrTu

rriu0 X 100 =0, 0 X 101 = 0, ..., 0 X 199= 0

.'. druruHna'lrfdfirirrvirn-u o 6a too'iruru

rriuz x 150 = 300, uns 3 x 1oo = 300

.'. 'ilruruHnfir#ficirrvirn-u eoo 6o 2'iru':uil il'r u ril sr ru n #r r f,r o.: au d"i'r ri'ufi il nr u,irur u rir'lril#rr nrtunr:6 our ururn

#o g erou 3

Arflotorn x + 3 rilusr-til:;nouto.: e(x)

u&gt.trlu x = -3 rijurhnautoitfltlR't: P(x) = O Eiru

nr rir qr oudu 6JT o{ fl il n1: P(x) = o'loilo u nt:uu n qt-l :J:;n oilT o.i 1 t U u1 il P(x)

-2 -6

.\1..,2

2x6

-3

-6

-2

=0=0

-0=0

O1nfliln'lT P(x) = 0

x5 + 3xa + 2x3 +6x2

(x+s) ("t +2x2 -2)LL u n qir :J :s n o uhjld'oi'o .,rtd'g or :tfii atri'rri'rto ir u rir H uqtd' a

x4 +2x2 -2a2 + 2a-2

x2

-2+2(1)

ln rfi s il 6r a ltl#intua?1 er i

22 - 4(1)(-2)

7

ranlJ arfisrrrlan{ 1 224 eirrinisrnr:la rfisil

rrqi a = ^2>09t/a./ aJ f9t.l,1,b1,[ a = -1 + r/g

*2 = -1 +,16,x - + {-r*"6

rirsrau?Jo{fliln1T P(x) = 0

9'/ra4

9v

?la 5

OU

'l

9t

H

=

=

da-3,ffiLLnv-ffi

100

h (3)

fos (3)

r (g(3))

f (10)

102 =

aou 9

oln 82

LLflY B-1

82 + 3B-1 _

82 + 3B-1 -

oln g (3) = 32 +1

"' g (3) = 10

L: :,1 [: :,]1 [-t -s.l

oetalo 3l

[: ;] +{ t[;'

[: :] .[;

:]rro e

]L' -z)["', 1 a,r]

l^r, 'rr)I

ornloyrri

rs.]lo11 [-t_t

-3*oLo

tl l

?tz =

ln rfi er ru aout#in'lr,lsrrT rui

r6rasJ nrf,ngrasr{ 1 22s eirrinisrnr:'[arfrsru

aou IoQtv

n1nugt 114 ZYrul al

s$aartYi I

k-2

k=3

k=4

=641r/ ,i

-.1 I a &

eto.lrunuu z tu:rj ufrflr$

nu'ir r = l=l

frae

[rn3 ea.t &O',11t1{ Z

.'. Z

=0: r(cosO * isin0)

= 64(cos0 + isin0)

tl r !*r .l?lrdna$n 2 gTa.,:n1Tnaor1nfr

6tsl:ts zk

k=1

6 ta.,: Z

V;( "or2kr*o + isinSl"-fo)

\ n "-)1r2r"" n

W(cos 2(1)n+o + isin 2(1)ru+o)

\ 6 +lsln

6 )

z( "o"L

+isinr) = ,( I.{,.]\ 3 3) [2 2 )

z1

/W(cos 2(2)n+o + isinz(z)n+o)

\66)z(

"o"?n + isin'"]t 3 3)/ .6.)

2l -! + = -1+ ,.6it-2 2)

W(cos 2(3)n+o + isin K\"+o)\ 6

+lsrn 6 )

z(cosn + isinru)

-2

?l*(cos 2@)T*o + i sin

z(+)l + o)

\66)z( "o"!n + i sin

o"')

\ 3 3)/

"6.) . t:2l -! - -1-"6it2 2)

z2=

zg=

zg=

z4=

:

zt = r*16

z2

la rfr s rr a a ul#intun er ru i

ranEJ Frrflsrrfran{ 1 226 ei'r ri'n i rr n r :'[ a rfi s e,r

W(cos 2(5)zu+o + isin K)n+o)\ 6

+rsln 6 )

,( "o"-sn

+ i sin u")

\. 3 3)

,( r-s,l : r-",8[2 2)

w(cos 2(6)rc + o + i sin z(6)ru + o)

\66)z(coszn + isin2ru)

2

+ l-rl + l-,1 + l,l + lrl

+1+1+2 = I

z5

.'. Z6 :

:

:

lorl : l,l + l-,1

= 1+1+2

k:5

k:6

6

14'l Ik-1

Tra 7 nou 2

tx-l01n lim rc* ,- |x-)0[ r/x +4 -2)

limc+ lim

-

r+0 x-)0r/x +4 -2

ffi+2lim

-

x*50

^l **+ -2 ffi +2

c+

ca

oa

c+

limx-)0

-6X

+4 = 6

c=2

x+ 4-4

ln rfi s sr a a ut#intr,rn m ru i

rans ertflsrgfran{ 1227 eir fini gr n'l :'t a tfi et eJ

etou Ix iA j

1^l UYI U T t? TUYI LLT.I t.] 1

2 (2 \- 7r*2d* + I - J- -2d^

Io l.d )

: [+F]

+[L+F])

: T.[ L:])16 B 24

I-

T333

r?a s

r?o g

=8

9tou 48

9

o

(x,y)

(x,y)

(3 , 18)

(12 , 9)

@

@a"t

0 9t9t9rq

AJ

aoaoq

o

n1il}b91 27+21+30 -+LLny @

LLflU @

rYirrTu +a

3x+y

x+y :x+2y :

ttti:vuuflalnr: Ouuti':ruu6[un1T @

eir c ri'tidqerI

T{U't1

qoqru (x,y) c

(0 ,27)

(3 , 18)

(12 , 9)

(30 , 0)

54

48

66

120

ln ufi s il a a ?t'[#in'[nner al f,

r6rnE a$srrrran{ 1 228 ei'r rin?gr nr :'ta 16 s ar

ly?lo 10 aou 108

g d- A Afl%ao}svr 1 rfionilTTgtn1Trila\: 3 yr::n o1n 4 y,t:Tgt

.,iruruifi = C+,g

rYt rrt fi z o1n y{rrn g nttofd'lui'lurlrur*urn r6onfinl-n:v{r:nnr 1 nr{

'iruruifr = Ce,r XCs,r XGs,r

^aAilrv- a &.'. 'irurui3m{1oi'iurdaner-roraqjoirryl::nfiu = cc,e X cs,r X cs,r X ce,r

= toe if

sraufiz

ila 1 oou ila z n. Bn rrn& s. fio

o1n A-{"eRl/x2 Tx+10

x2 7x + 10

(x-2) (x-5)

H

A = (2,5)

ria n gn o1n g = {x€t / x nr:2b uns st fire:*ru6orvirfiu}-&er.lilu AnB = {x€tlz<x(5 unrnl:2sunrs1 firer:*rn6ormfru)=QAtilo.:ornx€luflr 2(x(5x*3 rlt:1r 3141:2s rnfiorerr* 1 unr 3 n1T s1 n{qr-r

x* 4 ry{:1s 4 141: Z5 rndorerr* 1 ttns 4 il1T St rilfiorqs g

fa s fio o1n g = {xct / qr-rnr:iailil1nra{ x rns o 6o z}-&rtotuu Anc = {x€ t I z <x (S uoyqr-lnr:jrrururnloit x rtnr 6 6o z]

= {+) +AAtflo.:otnx€luns2(x(5

x*3 [y{:'13 t4.T.rJ. Ta{ 3 un; O 6o g

x = 4 [?{T'li 14.T.il. ljoil 4 Unv O 6O Z

ln ufr sr N 6r o ilt#intr,ra ?1 il i

r6rner nrf,nerran{ 1 229 rtrrinirrnr:-[n rfrgn

l)'/

%a2

9L/sa3

lv%a4aou

2

detA A =

Q1n det A

.'. 5a-3

a

6

a+1 2 a+1

&- gcu1jl.[

+ 4a* 3l -b'z

n.1

a2

3

'2

tu

+

fl

lo^5a

7

7

2

.11J

11

+ a +2a* 6l

&niln{ - nculuq, qr

Z= = 40 - (-2)

7

Z =6

aou #a g 7l

rirHt,ter t(4)= (4) LLnvf =(5) =5LLnrf -(6)=6!- - -" ri'fuo'rn A+A lijufi.rri'd'urad.:qi oHdr0'11*?u1 l.tnTl,[Qln A+A LUl+l l.]nTuulti

= 7 x q x q x L x I x I x I x E

A-+o@@@@@@@X Z X T@@

7!

ilat aou #as y= "6*-2"[39"/ &

H't o q a q fl a { ? { n n il n .t 6[8.: Tq u n'] T Llti;y u u 6ril nl Tq

^2+y2 - 4-O(*-5)'+y2 = e-@(*-s)'+^2 - 5

- 10x +25 - 5

5

@-o

'[ a rfi g er a a r+t#in'[r,r or er ar i

rcrner nrfisroT asr{ 1 230 eirrinirrnr:'tnrfrsru

ttYlil x

4+y'

v

L p.iru qooi'ollo.t?.tnnurionol6o e, 0) =q

Ft?'le.Juu (m) 10.1 L

= -2 tuO=4=0

(xr,Yr )

X=5

6[iln17 Y -Yty-0

v

= tan60o

=rGm(x-xr)

"6t* -2)

"[g* -2-rli

ly?lA5 aau ila Z 7x' + lily' = 112

6[iln']Tnr;rTun1 *2 + 12y = o

^2 _ -12y.'. 4C = -12

C - -3

ArJ rruu dil nr: ?'tr: rlunr

do *2 = 4cy

C:3

?=4

u fi o .t a'l nIo vr riri r H uotri' c r fl u:y u y yr 1 .: :s u'i 1 .r n

o u o q u n y o qlill n-fl

gY..:riu c)0 .'. c = 3

si'.,:riuoeTillrinto.,:r.:3 (t .,0) : (t s,o)

unsarurerro{r.ri (* G + r)o) - (r 4,0)

a2 - b2+c

16

b2

la ufi s ru a a ul#intuerer au i

a

aa

a

aa

= b2+97

01n

rerns errfiodran{ 1 231 iirrinirrnr:'tarfrsil

froe

-A6tr,In1:?07*2 u2J-t : 016 7

7x2 +16y2 - 112

gtou ilal m = 2.5

nilnlrlarr{oflunr (x - z)2 -(y -1)2 = 1

4

olncrilnlTri'rrfu 6o y = + 2(x- 2) +1^Jtl.to.,lotn L lilqlortaul r ofTu nl unsn?'r rufur#uri'rri'u uvirrYue.. &ol.,rriu m>2 Hto m<-2

ln rfr e, il a a %'[#in'Lr,rn er eu i

A9t0 2 LLny -2

r6las ntf,nerrasr{ 1 232eiT #nirrnr:'[nrfisau

lvnau so 1

Ton ri

vvel9l',11{1,[

(-@, 2ll)/ra7

+3x -2-2

z+

ttflnri'rrj:ynouro(l *3 - 3x2

{:)

','[9-lL*-J

'[:)

'[:)

IX

0

0

-3

2

3

-2

014il'lutfiaq

t3)r7o a nau ila z

Ton ri rn("' - r)- rn(x + 1)

,n[*' - 'IL x+1J

,n(x-1Xx+t )x+1

ln(x - 1)

.'. x-1

^2-x-o(x-3Xx +2)

x=3 , -2

x = -2 rfio.,ro'ln x 2 1

.'. x=3Uns x+1

q

'[ n rfi s er a a u'[#in'[uor tr er i(u

rcrds afisrorasr{ 1 233 etr rin irr nr ;-[n rfi g a,r

NtvIN2

=l-1,t,1;;1,.1;_ll,l-r zl

= (-z-r-rl) T -d-r) J* (-z-r-rl) [= -l-sJ-[

ornTonri 6+(u.v) = "lu'vl

fro e aou ilaz I7

rirHuo A = arccos

cosA =

ila io nou fra g 'Jna1n u = 2l-j*[LLnv V = i-j-zk

U'V = 2+1+2-5

2

Jt2

Jtq,& Tt t 2lo.,tul* sin- sinf2arccos

T ).77sin- x sin2A

3

= sinl x 2sinA cosA3

t- t-r/g A r/g 2

^, G-/\-,t:. j2 "lt "lt=9

7

6+5 = t11 = .Jna

.'.a=L t-4tt= .Jn

uXV =

ijRl2 -1 ,|l

1-1 2l

ln ufr sJ ar a a ul#in'[r,rn rr e.r i

r6ras arfisrnrasr{ 'l 234 itrrin?r'rnr:-tn rfrHil

9v

?to 11tvaou ?to

fda1n Lam u

A9t0 nlTn'l

1-x99x

117x

X

- o i8a,/douA

O,}|nTil01*1,[A?l0.1n1quLTlJ'lFltUgl f -X , a1 =Xa,

AlnfTAT S - |

', 1-rx = 18

99

1B - 18x

18

2

13

ila tz aou ila + 6{iln1:?ro0r#u#arfraT6.rlr*nr 1o , t; 6o zy + sx+ 2= 0

o nn !T'lT'ly(u

dy

d-d

dx

_h"(1-5x)2\

: * --Z(1-5x)-1r :;(1-5x) -t25

d-

rllouunt,l x=o tutr

1) = -\',2

2+(1 -s*)

d25d_

(1 - 5x) _ -;(1 - 5x)

X

jd;

7d (,- s*)t:;(,' -s*)-

d'y;F

I4(1- 5x) 2

nn LilT'ly(u

ar 9,/ f q.z

H't9t?'liltut6[1,[[9t.] rt[ 19t (0,

.'. Ft?'lrufur#uki'.: il qgl (0,

Bn LvrTlr

f qiotfit.:fi x:o lfio.taln

O H1(o)_1

@ (o) = *50

_E2

@

@

dy

dx

@

la 16 s ar a a r,rt#intnn m er i

1-5x

rilau nrfisrcrran{ 1 23s airrinisrnr:'tn16sru

@ figr t?lTry

nr:nfr.t6[iln1T T0.,]l#u#lrin il nq (0, 1)

O oqhiru (xr,yr) = 1o#'u#n (0, 1)

@ n?1rud'ur#u#ruein (m) = qo#rurin (0, 1)q'

@ freJnlT y-yt-m(x-xr)tr

y 1 _ -t(* 0)2

2y+5x-2 - 0

9" - 4 t e./ v eA?ro3 f e,ra16[oqo6[rJT{niiri x:1

,1,2

fio Lilrlry

r rfilufr.,rri-d'ueirufiru rfro tt(*)

4x3 -12x2 + Bx

*(*-zX*-1)

m

o0@'o2@r rilufi.rri'd'uni'rrfiiluurir.,r (0 , 1) v(2, *)

tv?ro 13 aou

o t{o Ll^lT'ly

a'ln f(x) : x4 - 4x3 + 4x2 + 1

rt(*) -4x3 -12x2 +gx

rareir?nqorTou ufi'arun1: tt(") - o

4x3 -12x2 + 8x - o

"(+*' - 12x* 8) _ o

*("'-3x*2) _ o

x(*-zX"-1) - o

X-0

@

ln rfr s e,r a o r,r1#in'[r,ln rr er i

rans afisretrasr{ t 236 iiT rlnigr nr :'tn 16 s e,r

@ en Lwr'lv

f"(*) _ *4x3-12x2+8x

- 12x2 - 24x+ 8

rir?nqorturio O unu'lu f"(*)

lru,ir f" (1) - - 4

.'. rftoir6[.tflgr#run-yrffi x - 1(Uq

@ fior LilT'tv

sirinqorturio O unutuftt(*) nu'jr rtt(o) - 8,,r

.'. rfioirqofi'ruU;nlfi x-0turir.rilq t0,1]qqJ

ila t+ aou ila+ 11

12

n(s)=Cro,g=#=Poririluq'hi E rnu uaqnT:nffi4nri"rld'n:Jorriunqilncir:?iln-uillnn'jrntorvirriu zoo

ad - ve , : t- qr ru

n:rflfi t toi'orrJo.rtiunq:rilrYu 200 ulyr 1rafiu'loinnuonfiuo.r 1 nn uncerrr 2 nn)

.rj _ T:tTut^= cs,zxcs,z = 5ifr

n:rfifi z "lsierrJottiuaq :rilriu 250 u'ryr 1ra0u'[oi'nnuonfiuq{ z nn ttn;f;sl? 1 nn)

'iruruii = Cs,zXCs,r =5iiaA ue a ^ u.d e

n:rfifi a tein:Jorriunq:riln-u 3oo uryr 1rafiu1ffiuro.:vr'.: 3 4n1ql'

'iruruif = cs,3 = 1o ifr

n(E) = 50+50+10=110

Fri.lfiu p(E) = n(E) = 110 = 11

n(S) 120 12

1 a rfr sr il 6r a %:[#intr,rrr ?1 Er ;

raa EJ Grrfisrrlran{ 1 237 siriintrT nrr'lnrfrsil

.yusa 15 glou ra 4 86.41

fd-0'ln[Anu x=50t1fl3S:12

nE': Z - *-rts

a d utv 74-50finufnou"ld'z+ :.2^ "-'- "u-2

frnur 12

o:*rfi:grnould az .'. z ^ : 62-50 = 1q ot*rut*..I 12

n:rilrrso.:'irururirrireoudaould'nyttuurioun'irourfl:*rniorurnn'irurufiiluf,.uqcr vX

tu1,[o.11{

9,/ IAA1 l1,[71ttTt.l'l Y,l.Yl e<1) +Y{.Yt e>2)

(o.u+o.341 3) +(o.s- o.4rr2)

0.8641

i[s,/9/rAA.Adtetvl fl 0 u L9t 9t v ttul{lAo u n ?'l o 19tut91 14 t 0 ul n n?1 u't u fln uf uytr n u 86.4 1

c)/ 9,/ 9,/

T0 U nf lJ0.l zu L1J'l flOil

U

91,/ 9Y

?to 16 aou ?to 1 184.5ALAi,vt

h fl zunan? Liln 0.1 tan un 0 LT

j9t?1iln

6

10

18

14

2

ln rfr u E r 6{ o %61#in'[r,la ?1 il {

Agt?'l iln 6[96[u

6

16

34

48 * Prro Ei

frr,lor:R'ln#nfi

50

120 - 139

140 - 159

160 - 179

180 - 199

200 - 219oJaArurts-A

r{nilfiqnxrfi6olradueialdg.:n'jr o-.:nr"q6u I rJxrurruiauni zs 6a pru

druur.it Pzc : tn =

75x50 :37.5100 100

('"-s )\ 100 LfL

-l r | \

-L.r|- f

- 1re.5 + ,o( st 's - "/

\\. 14-)

:184.5

6[A: Pcr 75

raall nrf,gtgrasrf 1 238 et'r ri'n irr nr :'[ a rfi s sr

lY t/ila tt oou rTa g fla:rru?roiretnsi'lo:rra'irousiasrirsoofroslariucirrodE rnsnlfiorsaoU9/ & ar ! s d

?l o il atro}[l.[ 3.t Ft1 [?11 n u G{$El t6tet o

O figr til:rs orufiuruaroovfinirtvirn-ueir#.rrnqfifoudqo ntoo'roorrvirriurir#{rnsrI

ililil1nflfl9r

@ fio tn:'tg ri'rriapnrotqfi€irfioilnG os'lrifirunn:rvrusion-r'us'nr unrolufiuil usios. ,.1

t, a c, iu ,

4

yt't lil n1 tiln il tnlj n ilq tu iln1 n n1 { 71 [u [14 tJ't r fl tJ

N/-\@ en !r{r1t I F' - *)= o rntJo

i=1

@ fio rn:r; eirilre:oru 1z; ro.:riorunfiritioun'jr niorvi'rriugurl'loi'

9'/ 9r'/

?lo 18 aou %a 2 3.0

ilarJn rfjualrnral r?n1qq

Tl T{.F1. X cir'l#Eirs (y) xy 2x

2545 -2 1 -2 4

2546 -1 ,2 -2 1

2547 0 4 0 0

2s48 1 5 5 1

2549 2 7 14 4

ailnr:tffuq:.: y = ax+bNNn

arunr::Jn6 It, = "I"i +Nb-O ilil.lrrp4st I*, =0i=1 ' F1 i4'

19 = 5b

.:.b = 19 : .

5

.I",u, = "I*,' * o$*, -@i-,1 ' 'l-l l:l I:l

15 = 10a3

,.4 =2

o1 riu sru nr::J :y rur rudrtdd'r utunr :IsJ :*rur fi usir 6 o

319y--x+-25

ln rfr s ilr 6r a r,t:[#intun ?rar i

rons arfisretrasr{ 1 239 eir rin ?rr nr :'[ a rfr s a,r

r tl vr al I un1t501Utun1:lnl]9rU',tflUFt't 1r{.fl.2553 tlytlr x = 6

.'. Yl =it l.f -er aN vr q f a e

nlttro'ru[1.[n1T[eNJ:*il'tflun1 v{.f1.2551 rryru x = 4

,. Yz=ltol.T -@ri rtfd r utunr :I"ru unn duoirlufl n .?t .2ssg ufi ru duo r nfl il .q .2ss 1 r vi r riu

Y'r -Y z= ]rut -|et_.)_\)

tt/ Isa 19 nou ?to 1 55

or n #ru :J :s?yrf,nr : u:J : niur a.: rin 6 r um r ryir riu o. 2+

.. :ro = 0.24x5'lU

12

- = 0.24

XT'I U

NnXn +Nqfq

Nn Nq

x.. = (zo t so)+ (so t oz) - 3500 + 3100

= 5s nrrr.rilv 70+50 120

ila zo aou r7o r 0.3

orn A ras B rilurilqnr:nilr t fil*rfioderufiu

"'P(AAB) = 0

plRtne'; = p(AUB)'

= l- P(A\JB)

= t_ tp(A) + p(B) _ p(AnB)l

= l- [0.3 + 0.4 - 0]

= 0.3

ln rfi u il 6r a r,lt#intua ?1 il i

.'. xT'lu = 50

ets rLuuLilfi ur o.trin 6ur*fd rrir 610 urf;o" uor fr) :