34235

1uru nr?nsr fls ro uuriulsrsif; Yu n:r

rjrsuirilnr:finul 2ss1

nmfiil-rgr. oioaoldi z nrfi(:a do)nvuuurdl 100nyuuuz. riolsroun'rorr.tdsc.iuudo ratfiu'rdou eurrudouuayrioldouorlun:sorsuriudunslu

n:vnrsrirno yrSolr?l:slru:ri'arnrfiutlrtor :nYailr uarqnrloaorl#n:lniulnrToauufiiu:. doaorfl I nou

noufi r rfluoiocol :u-uu:"ru + sr-rr6on druru r+ r?o (dol-14) doac 2 nvuuunoufi z riludoao {:u-r,uru + n-rr6on riruru r+ do (dol5-28) doay 3 ncuuunoufi : riludoaouo-nfuuursr^urirnor riruru to do dons 3 nuuuu

4. lunr:nou tildnuaorilrof zn

noufi t uav z bi:v ruernaudrrf,o" C) @ @ niu @ fis,:.rn-urircrorfirirurf,on1un:vnrurftnot lnrlrituuvu'r1un:ynrurirnol)'luuciayrlofifirnstlfionds.:v€ontrrvclfi qnrfi urrirorou16ur

4 ^ q v - i c , " o , i8gu-vD hin:onrtav:crrud'ttatfr rilurireroulurioc?ru6ul unyrlnalfi riinun}ito.:unav{s1un:vors firsroil Inadolnronuocrsurenfl ura,uiiruaurdiru n rffnfiunqfi sxr5n z ya"nrato orruriruusdrlun:snrsrirfi ou

s. fi ttt rirrioaouunvn:snrsrirnsloonlrn#olcou, ! f I c 9 ! , 9e . hlorlqrn}i{rdraoloonornriolaouriounareolriru'hJ t d.lhc ro urfi

[0fl6l' l:u[1J laf]d15f, 1:

#rru rHuuyri drso'.i il3orqao riouiuii 19 i'u?rnrl 25s0

l\/fr\

/^\frl\\

rffi$].===wnr : do u ffnrfi o nu n o ar{1f, nHlq ,

,t,uen,, 04{saouin nfistarani6fld)

nd I yrqninlsu 2550

raar 09.00 - 11.00 1{.

:riairr 04 2

f;oisr nfiflnrasr{ 6ndl

iuorm-ndfi + nqao-nruu zsso

lxal 09.00 - 1 1.00 u.

l2l -p + -q

I4l -q + -p

ffi r?oaoud:#suuu I sY'rra^on iiruru tc do < rio r - r+ I {oov 2 nvltuu

1. 1# p rrvrurJ:rnmf 'drvirdruruo:-l x 4nd'r dr x < 2 *dt x2 < 4-

q uvrurJ:vvtoti "drriudrueuo?l x 4ndrfi iruauoi'r y lrldrfi x'y=x-

rJ:cilodludolneioudfi riroruoiqfl urff o

ll l -p =r q

l3 l q+-p

2.d"r A={plp rflu'iruaurql\tsrrdv p nr: (504-2p)3 nld'rJ ttdrflnurncrosc rBn

ts'r e dodolosiolrjd

ttl e [2] 10 [3] 11 l4l 12

3. ,f,rururdrLlrndrururujsfifiudn uavnr:dru 90 nrsr'r drdrurudfid'rrnoltn'nr{urflu 2 uav

" Nfrn3ourflu r uda nfrnfildodolooiobjd

lrl 6 t2l 7 t3l B l4l e

. a /o ,, o ' u ,jo r4. nrvrin"iludolneiohJfr fi grJrruuduriulnulluor (row echelon form)

11 2341 [1 23 4 ltr l los67l t21 lo912l

t00011 l -0 10 6 l

[1 2 3 4l . . I1 I 9 olte1 lo o 1 ?l t+t 19 9 9 ol

r .oooot l -ool.ol

5. rirrunlr? T = {r,2,3,4,s,6} uavnarrLdrn-ui , --{(r,i eT xTlx> sulov <z}

! [as s = { (x ,y ) e T xT lx< 5nSoY > 2}

dolnciohJdfro[1] R.-R,-o l2l D,vD"-r

[3 ] rus=TxT [4] rns=O

6. firn:rr'hosalRr: y = /(r) rflufl.rrii'utfiuuag c rfluirueul€slo 1 udr n:rv'ltolclnr:1u

rieln ei o bJdld rfl lfl r df u rvr"l

t l l y=f (x- r ) I2 l Y=f(x)+c

t3 l y=f( -x) -c [4 Y-- f ( -x)+c

:riaiyr 04

6ioim nfinqrasri t?ndl

2 - a r AJ ?uolvrgruvr 41r61fl0n'ru1l 2550

[?a1 09.00 - 11.00 u.

7. rirnunb{xnaloqjlun':on:-uoifi r fiisfirvirfii 3 urj:tr uasdlricunu x uny unu y fiqnA uns B nrrLiirri! dr I rflurduor:,rfidounu X rrasunu y fiEo .4 uav B nriliira'u udr:vovrirr:vrjrrqngurtnor.iro.r?{nalri'rrdusr:r r 6o{olneiohJd,., ,lZ ztljtll ; urjro t2l ; r.njau

' I3l z'/-z uuta 141 3"lZ vriTu

_ 8. rri;ilnur'rfinrrlur'lro.iunuronryirfiunarrarlto.rra6'ar:n6'rto.onr:rll.tar

x2 - 4x - By+ 28 - 0 drrr5fi'finluruiorgudnar,rrvirriu ] ,,d.l o.ruu,rnournulnroro i o y o , , , o '

?.t:u flo10 lnflo [uu

[1] 2 rilru tzl 2,/3 niletr

[3] 4 nil?u t4l 4,h rdeu

9. riruun}? IR uflurrynclol,i-ruaunis uny A = {x e IR | Se(z')-z = 6252"} r.tau?nlo.l

flrJr$fl1o{ a no,flolnsiohjfi' rrl -1 t21 + t3l o I4r I

10. rirtor .o, l,u..,un (])) Au+utmuttlc"\ \ 3 . / /

1l :1 ' ^ ' -3 t g l !, t r iT tJ l E . , s

I l. rirnuo}i tL '.Lay o rfluranrnofdl lu + ol2 + la - vlz = 22 ucty, lal = V3 drql

:cfldl t uny t rflu 60. ude rirrol t.a n'odolnriolild

f ia Pl ' /6' t3l vTz t4t Jm

r ̂ , , / r+V3i\10 n -- 12.d't z = (i-") udrdrarnfiutolnlru?nro{ z fiodolnciolild

r . , r_1*f 1 V5., . ' r , , l i l2 l - ; - ; i

. r . t \ . r Vs .t3l ;+; i r4l ; - ; i

13.d'rlf i ' A-U,2,3j rrav B = {1,2,3,4,5J udrdrururolfl ld{uorn A tJ a firf luq t v A o y o , , t ' iv{.:fllutll n010 t9ct0 tlJl.l

lrl 10 l2l 12

[3] 14 I4l 1.6

:riain 04 4 iuorfisrdii 4rlqf,6nruu 2550

doicr afinnrcni 6ildl [?a1 09.00 - 11.00 u.

I 4. duunnr:xtrtnrro{nrrrr6sio'lild

ngtIuu

2t -30 9031 -40 A

41 -50 5051 -60 B6I -70 10

drnsuuuludrunri.:rdeirdulndd 50 fio 40.5 udr rirts* a - r fiodslnrishjd

tll -40 [2] -30 t3l 30 I4l 40

ffi l?ocrsuil:rYrrruu t fi'ardonuiruru tl {a tdot5-28) doev 3 Rsttuu

' 15. 1i p, q, r rrae s rflurJ:slrtriler 'l

. lt'or:anrlsnlrldslild

n) 6'r t(-p (- s) ̂ (-r + q)l + (rv -s) frrirnrrltisrflurfit udrrirn'rrlriltor

p, q, r LLav s rilu li'r rfio rfin uav oil srruiirfii

t) dr fu + -q)vr fiiirnrrlri.rrfluuioud'r (p <+ r) + (gvs) frrirn'rrloiuflurir

rioloeiohlfiqn

[1 ] n qn nnr t qn [2] n qn ttaY t n'n

[3] n fin trav n qR [4] n n'n ttav'u fin

' I 6.r i rnunld IR uyurrynrosdrulusFluoy /={x€ Rl2lr+21 < l r+31},B-{xeRl/ tTT-- , l i=t}t d I u r dtJ0 tnno llluQn

l l l AcB l2 l BcA [3] A 'cB l4 l BcA'

17. rirruo}{ r rfiudrururdllrnfiirirlrnfiqerdfir: 16, 40 tras 100 rrd'lirsurvdsrdrriu

uav y rfluirururdllrnfifirirrloofiqodrr:dau 16, 40 trnc 100 rtdrfirqsrfi6otflu 19 o r u r a r

n110{ y -x no to taoo luu

tll 3Be .

[2] 4oo [3] 4Be [4] soo

6

:riair 04

deir nfinR1crfli 6fldl

5 iuorfindfi a uqrrn'nluu 2550

r?al 09.00 - I1.00 u.

lE. lnunts!?un1:s1luunl:Fl1![lo? v{1.1?1

-s 4 -3. |10 -7 6lB _6 5J

. rirxo{ r+y+z fio{olneiohJfilrl -e t21 -7 I3l s t4l I

' 19. drraun}i f (n) n'o tflufitinornnr: r: n dro 4 unr g(n) = n2 + |

rirrw Xi11o (f " dfu) 6o'ils1ecio1ildlll zsso 12) 382s [3] sloo l4l 6275

20.1# Ll rflutdusr:r 2x-3y-6=0 fidnunu x tlatrrntr f f i1n a ttcs B nrldtdu

rir c rflulnd.rnnrr:;u'irl1n A Lrcw B unv 1,, rflurduer:siioicqlnriu L, fi1n c uarer'n

runu X fi1o p udr dufitelautu6ul lCn n"sdslqeiel:Jd. - . 1 3 1 3

. f l f rrrr :rrnjru [2] f ,nt: trrdru' . ^ , 1 3 , . , , 1 3'"

t3J f nr:rwtjru [4] f nt:tuilru

2L 1o'roi6ar;ilnuid1n1dfi'aoqifi (+3,0) gnrilruqn (5,4) $iufi1o'tfirrl6o:rt*nrna 4gu6nnrs ns{o1neiolrJfi

ll] 2V5 nr:tcx ru t2l 4lE nt:r'trrjru

t3l 816 str:t.lfl ru t4l 16G etr:rqnriru

22. dr1o.l 25i*:s + gtos2764 +2i;**a- 5uoiu1r6u11t''

trl 2s l2l 26 t3l 27 t4l 28

. 23.rirruerlfi a-{e e[0,2] | cotd(1 -cosd) =-#:9J rrnrrnroqarrinror\ ,

- a t q I ! r a4 n010tnno t u

1l 3 ,n2J r?r . , , w! !. 3 Lzl T Lvl . 3

l x 2 -317 0 0 l 11 0 0lz y o lo r ol- lo 1.0L4-2z l001 lL001

24. firintorlnludolneiobJiifuyrqlto.rvr:rfiru6ulrprnrnfiiqorluds (1,2,9), (1,2,4),(2,2,3), (r,3,3)

trl (3,1,2) l2l G,2,4) [3] (2,3,4) l4J Q'4'3)

:riair 04

doisr nfinnrasr{ t?ndl

6 ?u0lytgluyr 4 flqflnnluu 2550

t?dl 09.00 - 11.00 U.

25. d't z1 uar z, rfludruaurS.rdoufi (2 * d) + (t + i.)4= 3 + 2i rras21l.2* (l -2i)72-2 - 0 udtrirror lz;11 6odo1npio1ilfi, r , ' 3 ,^, 3At t t , l z l - ;

[3] 3 tq 3a

26. neiosllr.rur.rfifq: 9 tu lnurifl:udasluocfifld{firLrornr uavfirar 1,2,... , g srrrurirdl ti

eiln8rrin:duuaorll ud: narrLrirocrflufiHnr?r.Jro{fi!1urnr#rao.rl-o:rrnn.jr 10 6o{oo t n , ilo0t0 tllu

nr 1 ra9- - 3 ' ' 3 6

r31 ; vti

27.d"t xr, x2, x3, xa, rfludoryaXnrdrdidrgrufioluavritugru6o 0 fifidufio 12 unsirirrniurnl,nru'ndo 1 udr rirtor Ef=r(xi -r)'? 6o{elnsio1r1fi

tll 76

[3] Bo[2] 78

l4l Bz

ffi r?oaouirnrTsuililrfiilrireroil druru r0 qio doas 3 nvuuu

L rirnuolr? x rfludrururfirLuenfirj:vnoudruratlnn 4 ndnd.t 2,3,4,S,6,lO,7t,1z,lzruac 15 fi'r: r alda udr rlnrrirro.r x

z.riruunl# a - [] l] o*nrirtor der(A+ A2+13 +...+/4s0)

I

g t - , n r !zd. nlriunt,o{no{9r0 tulr

l r I 3.s[3] 4.s

x 0 1 2 5

l 1. r t . 5

rirdo{alndficlnr:fildrj:srLrorri 'r y 6o y=2x*t udrrirro.r s n'odolnciolildI2l 4

[4] s

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y = (f " f ' f)(72.34567) udr olririrlo.r [y]4. 1& AG,s) rflulorunr:rll a't y2 - 2y - 4x * ! - 0. dri r tflulcrooounv r rfluyrb'{fio

dr t, rflurdun:rfiriruEn A unz F

:yov?irs:sx'ir{rdun:{ 11 lras L2

5. rirnuol# a, b rflurirqrouto{duflr:

L, rflurduer:.:fir.i'luna y unstururYr L, rtd'l o.lvr

rsr,irururfrur':n uav A = {x e I+ lx1o{[sn ,4

log5r*2 log*5=3lnuf i a<b f r r 1+ t rmurrysr

e [a, b] unv 3 rr: r n.:fir] ud'l olurdrueuelrfin

O.lfresco rflufirfiduildruluru M uas N rfluyrrudru BC uas cD srrrLiird'lloufi

dn:rc i ' ru BM:MC -DN:NC - l :2 d ' t Td -aert+PTfr r tdar ' rmrr i r tor a+p

7. 1# I = {zlz2 - (2 - t)z - 2i = 0} uav B - {zlz2 - 5 - tzi} fr'1 6 - {lzl2 lz e A u B}

rudr olurrirrosnauanrorflrrfintor c

8. lf c rflun:rr'l fiirvewo.rlooontvirtirtryntoviru?urqfllv nn'xtt:n lnofi1nuon d uat j fiq r j , j a , , t l j v i - . . i

tdur'gtt :vtt ' lNao{lf iuonunaoluo i +j l tnsi + i < 10 o{f i ln1u?uldul luot qnYl

arur:our^r1#fiu c u,r'orirl# 6 rflun:rr'loouraof

9. drrurrlo 9 qnlurdu:orrunuuronuu.onutl dr r rtnc y rflu'iru,ugrJvnrorufiolfil::1

nrulur.rnnllotrldlorxrirdrflulne,onrlrunvfi6rurunr6uilrflu6 uav { orrliirrir rtde olnrrir

10{ . r - y

10. ncrruueouisrn'flqren{rrncnrsr'lnufinr:unnuourrrilnFunvfiritunrurvirriu 16nnt!'rnra

nrl.jrnvuuuluitrnfi orqrcnfto'teruoqirilofrdulvrdfi 78.81 drrvirdtrrlofrdulvrdto.r

nvuuunrsr'hufi'ldyro6 usiovuuunfisrqrcnidurrnn'itnvttuuntgtlvruoqi zo nstruu dr ,4

uac B rflurirurfiu{rlrurrq:nlurornvuuuirrnfingranfunsnrur'luuoudtdtr ttdr l.rttrir

to r / -B

Z 0.70 0.80 0.90i . i c y t , s y

u?'l t$rrdu tfl.t 0.2580 0.2881 0.3159