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Math152

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Jarinya Jantra
Jarinya Jantra
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a'/ A dA aJ ?%o1r1nun 21 6%?1stEJ y,l .G1. 2551 214 05 nrfisrs[1cila{ 1 tyj 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*'2y zx*y222 x*Y) 21 x*zy)39 x)o v)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*?u9ld 9Ya vt'.:fiu 4 vl;Tn ci.:{an-n:iurdanqr'.:ll::nne 3 nu o.:nliruruifidfi'lqi'iunr:rdanotrororjcI ql - -qt tv& 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=Q eq 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 ?40J. 7 4. lz a+1 a+1 I lo a a+3 I I L1 1 2 ud'r rruuflun'rr 2. AA n. zuo $ny lJ. 29t 2. ri'rut,tqt A - ri'r detA - T 1. 5 [*l "_lul L;l AX-B frFi 38 7 [Lnv j 'l9tOuTl 3. ri'rut*otd'A-fr,2,3,.. ,1oI B-{+,s,0} I r ct o,r da.' A , A F - {r, n + nlr lilurd.lrifurail.: qi silfrr rud'r n(F) rvir n-urioto 1. 10! 2. 3! 7t 3. 1. sx2 * gy2 : 4s 3. gx2 * 2sy2 : 22s un3 rLnv (b) - b 7l ?ln b€Bl -4 LLnr (*-u)'*y2 -e 3! unrYilruil 30oq 4. 4. tri' r- riJur#uar.rfi rJrt,t1eroTqr0.r?{nnil ^2 + y2q #ur#usr:r x = 5 fliln1Tto.rr#uq:{ L fiafoto 1 y-+x-+r/s r/s 3. y:.ft" - 2^l; 4. y--'.6"-2",[; 5. r.:3r.:radtfiooTrln-aoqjfi (*c,o) oouooarjfi 1r1c*r1,01 rfio c rilu:su;yrr.::;u'jr.: o er u o q rrn so oh^l rYst a.: nt:rlu nr *2 + t zy = o fl il nlTt o.lr.rfu :J dd oriolet 2 y-+x*+ r/s r/s 2. 7x2 * 16y2 - 112 4. 13x2 * 36y2 : 46g ln u8 g e,r a a ut#inlun m ar i
a.r A da L/ ?%a1Yl nttn 21 fi?t?'lGtil yl .6.2551 216 os nrfinc['16{n{ 1 rarirf{ + o. tri' t- ril ur#uq:.r fi fr nm ilfuryir n-u m un r r.ir uo o surin nrrr a rnlarn aflu nrq9 (*-2)2 -(v -1)2 - r ud'rrir r i4*rtri r- lrid'olarna{Iunr:rJddariote 4' 1.m=0.52.m=1.03.m=1.54.m=2.5 (z ) < B[t--J d odoter (- m, 21 3. (2, 7 . rtarirsrouro.to6[iln17 1. (- oc, 2) ) - tn(x + 1) - ln9 6oriotcr X {r} 3. {2,3} 8. L{gtri'rqrouro.t6[run1T 1 t) 3.1. 1 7 i-j+2k A 9,/ 6l Ftofl 0 Lo 8 "l r 2*' (*-g) 2. ln(x2 - 1 2. @) m)4, fz, G 7 4. 4. fz,3) -9 2 9. eirr o.: 10. o n'lilltgl u - 2i- j+ k ri'r 6+(u.v)-alu"vl 8 1. 11 [,.,;),,{,,,ccos ft) 2.: A e,/ 6l 9tolj 0 [9t z"l-2 7 LLNg V _ C,/ r tLn?nl a 2. 4.3. 11 . drr o.: x tdriltrl' ^+x2 +x3 +.. .....*xn 2 1. 13 Ae)61 9t01J 0 L9t 3. fotofio '[n rfr s il aa?bl#inlluelrT eri T 6 + 2. aa = 0.18 4.-4 12. rirrauo 6rrJnr:u#uTri'.: y - ,2 ., d-y - 25 | :-r' ,2 3 OX 4(1 - 5*)2 2. 3. 4. Ft?'rrud'uto.:r#uki'..rfr1o (0 , 1) 6o +2 frrri'fu y: {EA rflufr.:rid'udorfio.rfr x-0 6nJnlrro.tr#u#rurisTri'.:fdnr (0 , 1) 6o 2y *5x * 2:0
iuarfi n$fr z'l f;'r,nrail il .Gl.2ss1 217 05 nrfisrorasr{ 1 tvi 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'r 9rutu 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.ullru 9 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 uryr tor.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 11 1. 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{ 1 tyj 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 I AVATI 9{ArunAn?[mao'0lilaEJ r ?r ma [5 ! rl a?'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$:rn.jrtei.rqt d { q . e ---"' cl v Ay j - t u j j q q y 6r{ tR 9t yt lt 0 u n fl o n u n1 fl .l [n o m il'l n m fl q [1t1, 0 3,J fl Tgt 1.{1.[ t fl il 0 2. rirfoilnqotqfidrfiq:JnG nairr6ofieirq'rrfiu'l:Jratooirrfiul:J ovfirunn:smuqiofiuoru usiqrql|l'@ l4 ra [tJ u il n nrsytu qr aoluiiu ru 3. t{nr?iluo{runsir{:sn'irruqinveirro.:riarunir-urirradurnrnfinrotrioai*mtit* fisirryirn-uq| d _,,,_. d fll,lutflila,u 4. nir rur m:orur o.:rio il nrqlo I oseior fi rir lr nn.ir sufraru aa qt q ) qi--- --- ln rfr s il 6r a ll'l#intun ?'r il ;
iuarfi n.ffr zt fiueralu n .d.2ss1 219 05 nrfisrrrran{ 1 s,/ j 14}t1?1 7 te. riorynoiolrJduaqrrirtd'sirutunr:Ts.iunnRudr lrar.iru : uauurm) rotuS:iyruvicadt turirril u.st.2545 - 2549 tl Tr.Ff. oir'l#Eir er 2545 2546 2547 2548 2549 1 2 4 5 7 f,rnmru#rur{uf':sra'ir'reirt:fi'sirutunr:TruururRu6'rn-udrrrrnrro.:riorunfr fin:llrilur#uq:r rf,rnre'irrirlfdrutunr:Izur*rur?uri'rtufl fl.sr.2553 osrfiruduornfl n.s.zsst rvirriurioto (Hr.iru : LL6[uu'lYr) 1. 1.5 2. 3.0 3. 9.8 4, 12.8 v a u a y t f a & A t dv a u &X 19. n1:fl0unqtn0nunliuu[{lT?ri[n:{n1:i5'rnr:er:ttailr lruirilun[5EJurfrsouiliRu tZO ou 6l -.:..-.--.3.*t-.-y' a u a a f A v a at t1.t01t{?tnt[1]ilun trullr'r u 70 nu t,tn rruul4cu{ 50 nil [q ufi o r uuuaour orun iSuutr u fr eir i{rutdurtuutJlarg'n{?a{nruuuflourvirrir 12 nsuuu unsfroir#rurl:sRnfnr:ru:J:r.r-uryi'rri':-r 0.24 airun;uul.lflau?JOrrinGrurnfi.rftri'rradrrvirriu oz osuilu o-.:rfunsuuuradurarfinGuu Ao&taeqv 7l tlj',r fl 0u?1itfi tJo t?11nulj I t9l 1. 55 2. 60 3. 63 4. 66 zo. lri A uns e rilurn nnr:rrflo 1 dld rnodaru fr'ulu:Jin fi sl-r o Eirr fir p(A) = s.3 unr p(B) - o.+ u#r eirro.: e1R'n e'; rvirn-uriotor 1. 0.3 2. 0.4 3. 0.5 4. 0.6 nf { #jk '[n rfi s N 6t o lt'l#intr,ra x1 EJ {
22I eiT rinirrnr:'lnufisil rads ntf,neirasr{ t rans imsrrfisrf,'rcleli r no$fi t 1) 3 7)2 naltfi z 1.) 2 7)1 13).3 1e) 1 2) 6,126 p' 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.,ruiluo3r A L}[0.lQln f (r) LLflY f (p) T do alnlovruri'rnuotd'f (p) .f (q) = 0 lLnsLT'llTru'jt f (p) = a.t U el.l}[ltf(q)=0 &AArAdrd 1,[U9t 0 q 3J gt',l gt?'l 3.JaT.,] nJl,tLma p-)r p->s ? dA o tuo r ruoi'tot?'1ru03.:uiluufio d A r A 1 lfio p fiei'rn?1il03{riluoSr o rfio p frdrfl?'lru03.:rflurfio ={ ={ T6-o6lc,' 01n IOYIU nlilUq LH f (r) + f (p) = I a,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.:jl t1.[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 AtACra r 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-nf1 Aau,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 - rl runffnf,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':u il 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 A rflotorn 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 -2 a2 + 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 f 9t.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.] lo1 1 [-t_t -3*oLo tl l ?tz = ln rfi er ru aout#in'lr,lsrrT rui
r6rasJ nrf,ngrasr{ 1 22s eirrinisrnr:'[arfrsru aou I oQtv n1nugt 114 Z Yrul al s$aartYi I k-2 k=3 k=4 =64 1r/ ,i -.1 I a & eto.lrunuu z tu:rj ufrflr$ nu'ir r = l=l frae [rn3 e a.t & O',11t1{ Z .'. Z =0 : r(cosO * isin0) = 64(cos0 + isin0) tl r ! *r .l ?lrdna$n 2 gTa.,:n1Tnaor1nfr 6tsl:ts zk k=1 6 ta.,: Z V;( "or2kr*o + isinSl"-fo) n "-) 1r2r"" n W(cos 2(1)n+o + isin 2(1)ru+o) 6 +lsln 6 ) z( "o"L +isinr) = ,( I.{,.] 3 3) [2 2 ) z1 / W(cos 2(2)n+o + isinz(z)n+o) 66) z( "o"?n + isin'"] t 3 3) / .6.) 2l -! + = -1+ ,.6i t-2 2) W(cos 2(3)n+o + isin K"+o) 6 +lsrn 6 ) z(cosn + isinru) -2 ?l*(cos 2@)T*o + i sin z(+)l + o) 66) z( "o"!n + i sin o"') 3 3) / "6.) . t:2l -! - -1-"6i t2 2) z2= zg= zg= z4= : zt = r*16 z2 la rfr s rr a a ul#intun er ru i
ranEJ Frrflsrrfran{ 1 226 ei'r ri'n i rr n r :'[ a rfi s e,r W(cos 2(5)zu+o + isin K)n+o) 6 +rsln 6 ) ,( "o"-sn + i sin u") . 3 3) ,( r-s,l : r-",8 [2 2) w(cos 2(6)rc + o + i sin z(6)ru + o) 66) z(coszn + isin2ru) 2 + l-rl + l-,1 + l,l + lrl +1+1+2 = I z5 .'. Z6 : : : lorl : l,l + l-,1 = 1+1+2 k:5 k:6 6 14'l Ik-1 Tra 7 nou 2 tx-l01n lim rc* ,- | x-)0[ r/x +4 -2) limc+ lim - r+0 x-)0r/x +4 -2 ffi+2lim - x *50 ^l **+ -2 ffi +2 c+ c a oa c+ lim x-)0 -6X +4 = 6 c=2 x+ 4-4 ln rfi s sr a a ut#intr,rn m ru i
rans ertflsrgfran{ 1 227 eir fini gr n'l :'t a tfi et eJ etou I x iA j 1^l UYI U T t? TUYI LLT.I t.] 1 2 (2 - 7r*2d* + I - J- -2d^ I o l.d ) : [+F] +[L+F]) : T.[ L:]) 16 B 24I- T 333 r?a s r?o g =8 9tou 48 9 o (x,y) (x,y) (3 , 18) (12 , 9) @ @ a"t 0 9t9t9rq AJ aoaoq o n1il}b91 27+ 21+ 30 -+ LLny @ LLflU @ rYirrTu +a 3x+y x+y : x+2y : ttti:vuuflalnr: O uuti':ruu6[un1T @ eir c ri'tidqer I T{U't1 qoqru (x,y) c (0 ,27) (3 , 18) (12 , 9) (30 , 0) 54 48 66 120 ln ufi s il a a ?t'[#in'[nner al f,
r6rnE a$srrrran{ 1 228 ei'r rin?gr nr :'ta 16 s ar ly ?lo 10 aou 108 g d- A A fl%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)=Q A tilo.:ornx€luflr 2(x(5 x*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} -&rt otuu Anc = {x€ t I z <x (S uoyqr-lnr:jrrururnloit x rtnr 6 6o z] = {+) +A A tflo.: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 -Yt y-0 v = tan60o =rG m(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+9 7 01n
rerns errfiodran{ 1 231 iirrinirrnr:'tarfrsil froe -A 6tr,In1:?07 *2 u2 J-t : 0 16 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 ^J tl.to.,lotn L lilqlortaul r ofTu nl unsn?'r rufur#uri'rri'u uvirrYu e.. & ol.,rriu m>2 Hto m<-2 ln rfr e, il a a %'[#in'Lr,rn er eu i A 9t0 2 LLny -2
r6las ntf,nerrasr{ 1 232 eiT #nirrnr:'[nrfisau lv nau so 1 Ton ri vvel 9l',11{1,[ (-@, 2l l)/ 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=3 Uns 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 Ntv IN2 =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 I 7 rirHuo A = arccos cosA = ila io nou fra g 'Jn a1n u = 2l-j*[LLnv V = i-j-zk U'V = 2+1+2-5 2 Jt 2 Jt q,& Tt t 2lo.,tul* sin- sinf2arccos T ) .77 sin- x sin2A 3 = sinl x 2sinA cosA 3 t- t- r/g A r/g 2 ^, G-/-,t:. j 2 "lt "lt =97 6+5 = t 11 = .Jna .'.a=L t- 4tt = .Jn uXV = ijRl 2 -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 11 tv aou ?to fd a1n Lam u A 9t0 nlTn'l 1-x 99x 117x X - o i8 a,/douA O,}|nTil01*1,[A?l0.1n1quLTlJ'lFltUgl f -X , a1 =X a, AlnfTAT S - | ', 1-r x = 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) -t 25 d- rllouunt,l x=o tu tr 1) = -',2 2+(1 -s*) d25 d_ (1 - 5x) _ -;(1 - 5x) X j d; 7d (,- s*)t:;(,' -s*)- d'y ;F I 4(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 _E 2 @ @ 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=#=Po ririluq'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 =5ii aA 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 .yu sa 15 glou ra 4 86.41 fd- 0'ln[Anu x=50t1fl3S:12 nE': Z - *-r ts a d utv 74-50 finufnou"ld'z+ :.2^ "-'- "u-2 frnur 12 o:*rfi:grnould az .'. z ^ : 62-50 = 1 q ot*rut*..I 12 n:rilrrso.:'irururirrireoudaould'nyttuurioun'irourfl:*rniorurnn'irurufiiluf,.uq cr vX tu1,[o.11{ 9,/ I AA 1 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.Adtet vl 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 flO il U 91,/ 9Y ?to 16 aou ?to 1 184.5 ALAi,vt h fl zunan? Liln 0.1 tan un 0 LT j 9t?1iln 6 10 18 14 2 ln rfr u E r 6{ o %61#in'[r,la ?1 il { A gt?'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 - 219 oJaArurts-A r{nilfiqnxrfi6olradueialdg.:n'jr o-.:nr"q6u I rJxrurruiauni zs 6a pru druur.it Pzc : tn = 75x50 :37.5 100 100 ('"-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 rnsnlfiorsaoU 9/ & ar ! s d ?l o il atro}[l.[ 3.t Ft1 [?11 n u G{$El t6tet o O figr til:rs orufiuruaroovfinirtvirn-ueir#.rrnqfifoudqo ntoo'roorrvirriurir#{rnsrI il ilil1nflfl9r @ fio tn:'tg ri'rriapnrotqfi€irfioilnG os'lrifirunn:rvrusion-r'us'nr unrolufiuil usios . ,.1 t, a c, iu , 4 yt't lil n1 tiln il tnlj n ilq tu iln1 n n1 { 71 [u [14 tJ't r fl tJ N/- @ en !r{r1t I F' - *)= o rntJo i=1 @ fio rn:r; eirilre:oru 1z; ro.:riorunfiritioun'jr niorvi'rriugurl'loi' 9'/ 9r'/ ?lo 18 aou %a 2 3.0 ilarJn rfjualrnral r?n1qq Tl T{.F1. X cir'l#Eirs (y) xy 2 x 2545 -2 1 -2 4 2546 -1 ,2 -2 1 2547 0 4 0 0 2s48 1 5 5 1 2549 2 7 14 4 ailnr:tffuq:.: y = ax+b NNn arunr::Jn6 It, = "I"i +Nb-O ilil.lrrp4st I*, =0 i=1 ' F1 i4' 19 = 5b .:.b = 19 : . 5 .I",u, = "I*,' * o$*, -@i-,1 ' ' l-l l:l I:l 15 = 10a 3 ,.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 u n1t501Utun1:lnl]9rU',tflUFt't 1r{.fl.2553 tlytlr x = 6 .'. Yl =it l.f -e r 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 .2ss1 r vi r riu Y'r -Y z= ]rut -|et _.)_) tt/ I sa 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 = 0.24 x5'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(AJB) = 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) :

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  • 1. eaaz1EqaAg/4 Oaaa n1:6Iaud'otfionrlnr:EJ%tlttgnflfl%1R1on4t$o[ilta[z1G[nr*1t1ta,n41?ytu'lng]rgttilfli A eJulTn u1 n'EJs oo igun s ro nfit,u tl nr:fin w't 2ss2 ila6rauisr o5 orrfisrcrlr[a 4 t cfauilrorfi n$fr zt #urraru yr.Fr. 2ss1 9v ?,aae 4 aeur,tlt lr,/ ?,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-td iatYU 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 o tgmflr{ssJ6[oaeirunr.dolrif,srfiernz '[:Jnoutun:carrr*rirnaunoufi t n"odtti'rt r?",aruq 4 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 (ti 3. 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{ vt a?a EJ10 n1:aou (0) 2 + 3 = ? 1. 2 2.3 3.4 4.5 e./ X o i a 1JA1,[ fllnoU?lnnno 5fl 6..:t:J a ou si'r rfr on + tunrrol:*rirfl ou oifl (0) o@oo n1:n gr rfl rr tr{vr otucl-rfo ao u un ;#r rut#rotor 6 o rir ue nrlo 1 Io u r6ozr o lYog/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 sl t v qevv o d A", - qy d q v naila0u1aflou tfir.tr?J1flourflull dounerasfir,r,raou tr4aeru:nl nr [uil1n:sqr]gnrnou.u- ffiaeitunhLodu#e I#ao fraritilavlau ila6fauariufi uulan s1fi's rfiso'[uil 6hr?%Rvr dr'rilnguil1u 4. 5. 6. I A TO u'l lJ 6[n n.. i .. . I tt Av ... 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
  • 2. 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+) AO taila'laou 1. td'p, q ,r,s rilurJ:sy{of ft ufi oil:nnror.fi t fidrn?1ruo3.,:riJuoir utnsdlnuer (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(o I 4. rirHuotri'f(x) :1" rfioo<x(1 unyg(x) =*2+1 l^2 rfiax)1 L 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 )
  • 3. a'/ A dA aJ ?%o1r1nun 21 6%?1stEJ y,l .G1. 2551 214 05 nrfisrs[1cila{ 1 tyj 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*'2y zx*y222 x*Y) 21 x*zy)39 x)o v)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*?u9ld 9Ya vt'.:fiu 4 vl;Tn ci.:{an-n:iurdanqr'.:ll::nne 3 nu o.:nliruruifidfi'lqi'iunr:rdanotrororjcI ql - -qt tv& al{1lTTnnilfl{fiilo -x '[n lfr s s,r 6{ o t,t'[#in'[r,la ?1 sJ i
  • 4. 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=Q eq 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 ?40J. 7 4. lz a+1 a+1 I lo a a+3 I I L1 1 2 ud'r rruuflun'rr 2. AA n. zuo $ny lJ. 29t 2. ri'rut,tqt A - ri'r detA - T 1. 5 [*l "_lul L;l AX-B frFi 38 7 [Lnv j 'l9tOuTl 3. ri'rut*otd'A-fr,2,3,.. ,1oI B-{+,s,0} I r ct o,r da.' A , A F - {r, n + nlr lilurd.lrifurail.: qi silfrr rud'r n(F) rvir n-urioto 1. 10! 2. 3! 7t 3. 1. sx2 * gy2 : 4s 3. gx2 * 2sy2 : 22s un3 rLnv (b) - b 7l ?ln b€Bl -4 LLnr (*-u)'*y2 -e 3! unrYilruil 30oq 4. 4. tri' r- riJur#uar.rfi rJrt,t1eroTqr0.r?{nnil ^2 + y2q #ur#usr:r x = 5 fliln1Tto.rr#uq:{ L fiafoto 1 y-+x-+r/s r/s 3. y:.ft" - 2^l; 4. y--'.6"-2",[; 5. r.:3r.:radtfiooTrln-aoqjfi (*c,o) oouooarjfi 1r1c*r1,01 rfio c rilu:su;yrr.::;u'jr.: o er u o q rrn so oh^l rYst a.: nt:rlu nr *2 + t zy = o fl il nlTt o.lr.rfu :J dd oriolet 2 y-+x*+ r/s r/s 2. 7x2 * 16y2 - 112 4. 13x2 * 36y2 : 46g ln u8 g e,r a a ut#inlun m ar i
  • 5. a.r A da L/ ?%a1Yl nttn 21 fi?t?'lGtil yl .6.2551 216 os nrfinc['16{n{ 1 rarirf{ + o. tri' t- ril ur#uq:.r fi fr nm ilfuryir n-u m un r r.ir uo o surin nrrr a rnlarn aflu nrq9 (*-2)2 -(v -1)2 - r ud'rrir r i4*rtri r- lrid'olarna{Iunr:rJddariote 4' 1.m=0.52.m=1.03.m=1.54.m=2.5 (z ) < B[t--J d odoter (- m, 21 3. (2, 7 . rtarirsrouro.to6[iln17 1. (- oc, 2) ) - tn(x + 1) - ln9 6oriotcr X {r} 3. {2,3} 8. L{gtri'rqrouro.t6[run1T 1 t) 3.1. 1 7 i-j+2k A 9,/ 6l Ftofl 0 Lo 8 "l r 2*' (*-g) 2. ln(x2 - 1 2. @) m)4, fz, G 7 4. 4. fz,3) -9 2 9. eirr o.: 10. o n'lilltgl u - 2i- j+ k ri'r 6+(u.v)-alu"vl 8 1. 11 [,.,;),,{,,,ccos ft) 2.: A e,/ 6l 9tolj 0 [9t z"l-2 7 LLNg V _ C,/ r tLn?nl a 2. 4.3. 11 . drr o.: x tdriltrl' ^+x2 +x3 +.. .....*xn 2 1. 13 Ae)61 9t01J 0 L9t 3. fotofio '[n rfr s il aa?bl#inlluelrT eri T 6 + 2. aa = 0.18 4.-4 12. rirrauo 6rrJnr:u#uTri'.: y - ,2 ., d-y - 25 | :-r' ,2 3 OX 4(1 - 5*)2 2. 3. 4. Ft?'rrud'uto.:r#uki'..rfr1o (0 , 1) 6o +2 frrri'fu y: {EA rflufr.:rid'udorfio.rfr x-0 6nJnlrro.tr#u#rurisTri'.:fdnr (0 , 1) 6o 2y *5x * 2:0
  • 6. iuarfi n$fr z'l f;'r,nrail il .Gl.2ss1 217 05 nrfisrorasr{ 1 tvi 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'r 9rutu 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.ullru 9 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 uryr tor.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 11 1. 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$nsu'r{fl't?o:Erf,ut rilufirrirnautun*.:dq9t unsaou'loi 74 rtng*o2 nruul.r srtruiiror-u qi'.:riuiosJnrro.:firdrnaufiaould'nr"rruurioln'ir ur.: sm a :*rfl ut ui a rur n n'ir ur u fi ?n uf rvir riu rioterq rir ra uot# duiitol'r *t*LYr :l n 6 sYr qr :r r z 0.00 - 1.00 0.00 - 1.50 0.00 - 2.00 0.00 - 2.50 ftr,r{dt sTr #uTrTo rJ n 6 0.3413 0.4332 0.4772 0.4938 1 . 1 3.59 2. 79.15 3. 84.13 4. 86.41 ln rfr s il 6r a %:L#in'[r,ra x1 il f
  • 7. iuo'rfi n$fr zt fir,lmaal ilr .Fr. zss1 218 os orfisrrlran{ 1 tyj 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 I AVATI 9{ArunAn?[mao'0lilaEJ r ?r ma [5 ! rl a?'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$:rn.jrtei.rqt d { q . e ---"' cl v Ay j - t u j j q q y 6r{ tR 9t yt lt 0 u n fl o n u n1 fl .l [n o m il'l n m fl q [1t1, 0 3,J fl Tgt 1.{1.[ t fl il 0 2. rirfoilnqotqfidrfiq:JnG nairr6ofieirq'rrfiu'l:Jratooirrfiul:J ovfirunn:smuqiofiuoru usiqrql|l'@ l4 ra [tJ u il n nrsytu qr aoluiiu ru 3. t{nr?iluo{runsir{:sn'irruqinveirro.:riarunir-urirradurnrnfinrotrioai*mtit* fisirryirn-uq| d _,,,_. d fll,lutflila,u 4. nir rur m:orur o.:rio il nrqlo I oseior fi rir lr nn.ir sufraru aa qt q ) qi--- --- ln rfr s il 6r a ll'l#intun ?'r il ;
  • 8. iuarfi n.ffr zt fiueralu n .d.2ss1 219 05 nrfisrrrran{ 1 s,/ j 14}t1?1 7 te. riorynoiolrJduaqrrirtd'sirutunr:Ts.iunnRudr lrar.iru : uauurm) rotuS:iyruvicadt turirril u.st.2545 - 2549 tl Tr.Ff. oir'l#Eir er 2545 2546 2547 2548 2549 1 2 4 5 7 f,rnmru#rur{uf':sra'ir'reirt:fi'sirutunr:TruururRu6'rn-udrrrrnrro.:riorunfr fin:llrilur#uq:r rf,rnre'irrirlfdrutunr:Izur*rur?uri'rtufl fl.sr.2553 osrfiruduornfl n.s.zsst rvirriurioto (Hr.iru : LL6[uu'lYr) 1. 1.5 2. 3.0 3. 9.8 4, 12.8 v a u a y t f a & A t dv a u &X 19. n1:fl0unqtn0nunliuu[{lT?ri[n:{n1:i5'rnr:er:ttailr lruirilun[5EJurfrsouiliRu tZO ou 6l -.:..-.--.3.*t-.-y' a u a a f A v a at t1.t01t{?tnt[1]ilun trullr'r u 70 nu t,tn rruul4cu{ 50 nil [q ufi o r uuuaour orun iSuutr u fr eir i{rutdurtuutJlarg'n{?a{nruuuflourvirrir 12 nsuuu unsfroir#rurl:sRnfnr:ru:J:r.r-uryi'rri':-r 0.24 airun;uul.lflau?JOrrinGrurnfi.rftri'rradrrvirriu oz osuilu o-.:rfunsuuuradurarfinGuu Ao&taeqv 7l tlj',r fl 0u?1itfi tJo t?11nulj I t9l 1. 55 2. 60 3. 63 4. 66 zo. lri A uns e rilurn nnr:rrflo 1 dld rnodaru fr'ulu:Jin fi sl-r o Eirr fir p(A) = s.3 unr p(B) - o.+ u#r eirro.: e1R'n e'; rvirn-uriotor 1. 0.3 2. 0.4 3. 0.5 4. 0.6 nf { #jk '[n rfi s N 6t o lt'l#intr,ra x1 EJ {
  • 9. 22I eiT rinirrnr:'lnufisil rads ntf,neirasr{ t rans imsrrfisrf,'rcleli r no$fi t 1) 3 7)2 naltfi z 1.) 2 7)1 13).3 1e) 1 2) 6,126 p' 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
  • 10. 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.,ruiluo3r A L}[0.lQln f (r) LLflY f (p) T do alnlovruri'rnuotd'f (p) .f (q) = 0 lLnsLT'llTru'jt f (p) = a.t U el.l}[ltf(q)=0 &AArAdrd 1,[U9t 0 q 3J gt',l gt?'l 3.JaT.,] nJl,tLma p-)r p->s ? dA o tuo r ruoi'tot?'1ru03.:uiluufio d A r A 1 lfio p fiei'rn?1il03{riluoSr o rfio p frdrfl?'lru03.:rflurfio ={ ={ T6-o6lc,' 01n IOYIU nlilUq LH f (r) + f (p) = I a,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.:jl t1.[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 AtACra r 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
  • 11. raas nrfinnran{ 1 223 atr#nirrnr:'ta rfrs,il ila z oou orzo flfTrtruR:ilnoilfierooflarnna-nf1 Aau,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 - rl runffnf,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':u il 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 A rflotorn 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 -2 a2 + 2a-2 x2 -2+ 2(1) ln rfi s il 6r a ltl#intua?1 er i 22 - 4(1)(-2)
  • 12. 7 ranlJ arfisrrrlan{ 1 224 eirrinisrnr:la rfisil rrqi a = ^2>09t/ a./ aJ f 9t.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.] lo1 1 [-t_t -3*oLo tl l ?tz = ln rfi er ru aout#in'lr,lsrrT rui
  • 13. r6rasJ nrf,ngrasr{ 1 22s eirrinisrnr:'[arfrsru aou I oQtv n1nugt 114 Z Yrul al s$aartYi I k-2 k=3 k=4 =64 1r/ ,i -.1 I a & eto.lrunuu z tu:rj ufrflr$ nu'ir r = l=l frae [rn3 e a.t & O',11t1{ Z .'. Z =0 : r(cosO * isin0) = 64(cos0 + isin0) tl r ! *r .l ?lrdna$n 2 gTa.,:n1Tnaor1nfr 6tsl:ts zk k=1 6 ta.,: Z V;( "or2kr*o + isinSl"-fo) n "-) 1r2r"" n W(cos 2(1)n+o + isin 2(1)ru+o) 6 +lsln 6 ) z( "o"L +isinr) = ,( I.{,.] 3 3) [2 2 ) z1 / W(cos 2(2)n+o + isinz(z)n+o) 66) z( "o"?n + isin'"] t 3 3) / .6.) 2l -! + = -1+ ,.6i t-2 2) W(cos 2(3)n+o + isin K"+o) 6 +lsrn 6 ) z(cosn + isinru) -2 ?l*(cos 2@)T*o + i sin z(+)l + o) 66) z( "o"!n + i sin o"') 3 3) / "6.) . t:2l -! - -1-"6i t2 2) z2= zg= zg= z4= : zt = r*16 z2 la rfr s rr a a ul#intun er ru i
  • 14. ranEJ Frrflsrrfran{ 1 226 ei'r ri'n i rr n r :'[ a rfi s e,r W(cos 2(5)zu+o + isin K)n+o) 6 +rsln 6 ) ,( "o"-sn + i sin u") . 3 3) ,( r-s,l : r-",8 [2 2) w(cos 2(6)rc + o + i sin z(6)ru + o) 66) z(coszn + isin2ru) 2 + l-rl + l-,1 + l,l + lrl +1+1+2 = I z5 .'. Z6 : : : lorl : l,l + l-,1 = 1+1+2 k:5 k:6 6 14'l Ik-1 Tra 7 nou 2 tx-l01n lim rc* ,- | x-)0[ r/x +4 -2) limc+ lim - r+0 x-)0r/x +4 -2 ffi+2lim - x *50 ^l **+ -2 ffi +2 c+ c a oa c+ lim x-)0 -6X +4 = 6 c=2 x+ 4-4 ln rfi s sr a a ut#intr,rn m ru i
  • 15. rans ertflsrgfran{ 1 227 eir fini gr n'l :'t a tfi et eJ etou I x iA j 1^l UYI U T t? TUYI LLT.I t.] 1 2 (2 - 7r*2d* + I - J- -2d^ I o l.d ) : [+F] +[L+F]) : T.[ L:]) 16 B 24I- T 333 r?a s r?o g =8 9tou 48 9 o (x,y) (x,y) (3 , 18) (12 , 9) @ @ a"t 0 9t9t9rq AJ aoaoq o n1il}b91 27+ 21+ 30 -+ LLny @ LLflU @ rYirrTu +a 3x+y x+y : x+2y : ttti:vuuflalnr: O uuti':ruu6[un1T @ eir c ri'tidqer I T{U't1 qoqru (x,y) c (0 ,27) (3 , 18) (12 , 9) (30 , 0) 54 48 66 120 ln ufi s il a a ?t'[#in'[nner al f,
  • 16. r6rnE a$srrrran{ 1 228 ei'r rin?gr nr :'ta 16 s ar ly ?lo 10 aou 108 g d- A A fl%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)=Q A tilo.:ornx€luflr 2(x(5 x*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} -&rt otuu Anc = {x€ t I z <x (S uoyqr-lnr:jrrururnloit x rtnr 6 6o z] = {+) +A A tflo.: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
  • 17. 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
  • 18. 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 -Yt y-0 v = tan60o =rG m(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+9 7 01n
  • 19. rerns errfiodran{ 1 231 iirrinirrnr:'tarfrsil froe -A 6tr,In1:?07 *2 u2 J-t : 0 16 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 ^J tl.to.,lotn L lilqlortaul r ofTu nl unsn?'r rufur#uri'rri'u uvirrYu e.. & ol.,rriu m>2 Hto m<-2 ln rfr e, il a a %'[#in'Lr,rn er eu i A 9t0 2 LLny -2
  • 20. r6las ntf,nerrasr{ 1 232 eiT #nirrnr:'[nrfisau lv nau so 1 Ton ri vvel 9l',11{1,[ (-@, 2l l)/ 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=3 Uns x+1 q '[ n rfi s er a a u'[#in'[uor tr er i(u
  • 21. rcrds afisrorasr{ 1 233 etr rin irr nr ;-[n rfi g a,r Ntv IN2 =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 I 7 rirHuo A = arccos cosA = ila io nou fra g 'Jn a1n u = 2l-j*[LLnv V = i-j-zk U'V = 2+1+2-5 2 Jt 2 Jt q,& Tt t 2lo.,tul* sin- sinf2arccos T ) .77 sin- x sin2A 3 = sinl x 2sinA cosA 3 t- t- r/g A r/g 2 ^, G-/-,t:. j 2 "lt "lt =97 6+5 = t 11 = .Jna .'.a=L t- 4tt = .Jn uXV = ijRl 2 -1 ,|l 1-1 2l ln ufr sJ ar a a ul#in'[r,rn rr e.r i
  • 22. r6ras arfisrnrasr{ 'l 234 itrrin?r'rnr:-tn rfrHil 9v ?to 11 tv aou ?to fd a1n Lam u A 9t0 nlTn'l 1-x 99x 117x X - o i8 a,/douA O,}|nTil01*1,[A?l0.1n1quLTlJ'lFltUgl f -X , a1 =X a, AlnfTAT S - | ', 1-r x = 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) -t 25 d- rllouunt,l x=o tu tr 1) = -',2 2+(1 -s*) d25 d_ (1 - 5x) _ -;(1 - 5x) X j d; 7d (,- s*)t:;(,' -s*)- d'y ;F I 4(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 _E 2 @ @ dy dx @ la 16 s ar a a r,rt#intnn m er i 1-5x
  • 23. 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
  • 24. 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=#=Po ririluq'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 =5ii aA 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 ;
  • 25. raa EJ Grrfisrrlran{ 1 237 siriintrT nrr'lnrfrsil .yu sa 15 glou ra 4 86.41 fd- 0'ln[Anu x=50t1fl3S:12 nE': Z - *-r ts a d utv 74-50 finufnou"ld'z+ :.2^ "-'- "u-2 frnur 12 o:*rfi:grnould az .'. z ^ : 62-50 = 1 q ot*rut*..I 12 n:rilrrso.:'irururirrireoudaould'nyttuurioun'irourfl:*rniorurnn'irurufiiluf,.uq cr vX tu1,[o.11{ 9,/ I AA 1 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.Adtet vl 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 flO il U 91,/ 9Y ?to 16 aou ?to 1 184.5 ALAi,vt h fl zunan? Liln 0.1 tan un 0 LT j 9t?1iln 6 10 18 14 2 ln rfr u E r 6{ o %61#in'[r,la ?1 il { A gt?'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 - 219 oJaArurts-A r{nilfiqnxrfi6olradueialdg.:n'jr o-.:nr"q6u I rJxrurruiauni zs 6a pru druur.it Pzc : tn = 75x50 :37.5 100 100 ('"-s ) 100 LfL -l r | -L.r|- f - 1re.5 + ,o( st 's - "/ . 14-) :184.5 6[A: Pcr 75
  • 26. 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 rnsnlfiorsaoU 9/ & ar ! s d ?l o il atro}[l.[ 3.t Ft1 [?11 n u G{$El t6tet o O figr til:rs orufiuruaroovfinirtvirn-ueir#.rrnqfifoudqo ntoo'roorrvirriurir#{rnsrI il ilil1nflfl9r @ fio tn:'tg ri'rriapnrotqfi€irfioilnG os'lrifirunn:rvrusion-r'us'nr unrolufiuil usios . ,.1 t, a c, iu , 4 yt't lil n1 tiln il tnlj n ilq tu iln1 n n1 { 71 [u [14 tJ't r fl tJ N/- @ en !r{r1t I F' - *)= o rntJo i=1 @ fio rn:r; eirilre:oru 1z; ro.:riorunfiritioun'jr niorvi'rriugurl'loi' 9'/ 9r'/ ?lo 18 aou %a 2 3.0 ilarJn rfjualrnral r?n1qq Tl T{.F1. X cir'l#Eirs (y) xy 2 x 2545 -2 1 -2 4 2546 -1 ,2 -2 1 2547 0 4 0 0 2s48 1 5 5 1 2549 2 7 14 4 ailnr:tffuq:.: y = ax+b NNn arunr::Jn6 It, = "I"i +Nb-O ilil.lrrp4st I*, =0 i=1 ' F1 i4' 19 = 5b .:.b = 19 : . 5 .I",u, = "I*,' * o$*, -@i-,1 ' ' l-l l:l I:l 15 = 10a 3 ,.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
  • 27. rons arfisretrasr{ 1 239 eir rin ?rr nr :'[ a rfr s a,r r tl vr al I u n1t501Utun1:lnl]9rU',tflUFt't 1r{.fl.2553 tlytlr x = 6 .'. Yl =it l.f -e r 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 .2ss1 r vi r riu Y'r -Y z= ]rut -|et _.)_) tt/ I sa 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 = 0.24 x5'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(AJB) = 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) :