verbaluri nawili

analogiebi

am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva,

romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. daadgineT, ra

saxisaa es mimarTeba.

savaraudo pasuxTa yovel variantSi aseve mocemulia mniSvnelobiT

urTierTdakavSirebuli sityvebis wyvili. airCieT maTgan is wyvili, romelSic

sityvaTa mniSvnelobebs Soris mimarTeba gamuqebul sityvaTa urTierTmimarTebis

msgavsia (analogiuria). pasuxis arCevisas gaiTvaliswineT wyvilebSi sityvaTa

Tanmimdevroba.

1. sastiki : lmobieri

(a) bejiTi : warmatebuli

(b) maRali : axovani

(g) zarmaci : zanti

(d) mxdali : mamaci

2. veziri : cbieri

(a) wyali : mineraluri

(b) zebra : zoliani

(g) haeri : gamWvirvale

(d) naZvi : maradmwvane

3. estumra : Causaxlda

(a) ixila : esizmra

(b) aTxova : aCuqa

(g) gadaemtera : daumoyvrda

(d) daicva : gamoeqomaga

4. gamagreba : mtkice

(a) dapirispireba : mZafri

(b) SeSineba : saxifaTo

(g) gardaqmna : Secvlili

(d) gacxadeba : saidumlo

2

5. gapartaxeba : dampyrobeli

(a) kerva : qsovili

(b) naTeba : sanTeli

(g) dnoba : yinuli

(d) krefa : yvavili

6. mxatvari : damTvalierebeli

(a) wigni : mkiTxveli

(b) leqcia : momxsenebeli

(g) reJisori : mayurebeli

(d) fexburTeli : mwvrTneli

7. Ruza : floti

(a) xmali : muzaradi

(b) afra : ialqani

(g) lula : artileria

(d) paraSuti : vertmfreni

8. diriJori : simfoniuri musikis koncerti

(a) amomrCeveli : saparlamento arCevnebi

(b) mayurebeli : kalaTburTis matCi

(g) mZRoli : sagzao SemTxveva

(d) mosamarTle : sasamarTlo procesi

3

winadadebebis Sevseba

am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa

gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiT aris aRniSnuli.

erTi xazi zogjer erT sityvas gulisxmobs, zogjer ki _ ramdenimes.

savaraudo pasuxTa yovel variantSi mocemulia sityvaTa jgufi, romlis

nawilebi erTmaneTisgan daxrili xazebiTaa (/) gamijnuli. airCieT pasuxis is

varianti, romlis TiToeuli nawilis Tanmimdevrulad Casma Sesabamis

gamotovebul adgilebSi azrobrivad gamarTul winadadebas mogvcems.

9. adamianis uflebebis dacva zogadsakacobrio zrunvis sagans _____ , Tumca, zogierTi mTavroba _____ moqalaqeTa fundamentur uflebebs _____ .

(a) ar warmoadgens / ucxo qveynis / mxolod saSinao saqmed miiCnevs

(b) warmoadgens / ucxo qveynis / saerTaSoriso saqmed miiCnevs

(g) warmoadgens / sakuTari / mxolod saSinao saqmed ganixilavs

(d) ar warmoadgens / sakuTari / saerTaSoriso saqmed ar miiCnevs

10. zogjer _____ ukavSireben konfliqtsa da Zaladobas, xolo _____ _ mSvidobasa da TanamSromlobas, _____ , sinamdvileSi arsebobs uamravi _____

qali.

(a) mamakacs / qals / miuxedavad amisa / mSvidobismoyvare

(b) qals / mamakacs / miuxedavad amisa / Zaladobis momxre

(g) mamakacs / qals / marTlac / Zaladobis momxre

(d) qals / mamakacs / Tumca / mSvidobismoyvare

11. _____, rom es Tqmulebebi im adamianebs miaCniaT ______ , vinc poseidonis kunZuls atlantis okeaneSi daeZebs, radgan ______ cnobebi kunZulis swored

am okeaneSi mdebareobis Sesaxeb.

(a) ucnauria / nakleb sarwmunod / am TqmulebebSi dasturdeba

(b) bunebrivia / nakleb sarwmunod / am TqmulebebSi Semonaxulia

(g) bunebrivia / sarwmunod / am TqmulebebiT baTildeba

(d) ucnauria / sarwmunod / am TqmulebebSi dasturdeba

12. statiaSi mkacrad aris gakritikebuli axalgazrda mwerlis moTxroba; _____ , bolo dros kritikaSi SemoWrili cinikuri kilos _____ , am werilSi _____

kilo _____ .

(a) Sesabamisad / mibaZviT / Semwynarebluri / udavod igrZnoba

(b) Sesabamisad / miuxedavad / damcinavi / aSkarad igrZnoba

(g) miuxedavad amisa / sapirispirod / damcinavi / namdvilad ar igrZnoba

(d) miuxedavad amisa / sapirispirod / Semwynarebluri / sruliad ar igrZnoba

4

13. A firmis mier gamoSvebuli saTamaSoebis fasi aseTi _____ rom ar yofiliyo, maTze moTxovna _____ iqneboda, vinaidan cnobilia, rom dRes

momxmareblebi did mniSvnelobas _____ saTamaSoebis xarisxs da fiqroben, rom

nawarmis fasi pirdapirproporciuladaa dakavSirebuli mis xarisxTan.

(a) maRali / gacilebiT didi / aniWeben

(b) dabali / gacilebiT didi / aniWeben

(g) dabali / gacilebiT didi / ar aniWeben

(d) maRali / gacilebiT naklebi / ar aniWeben

logika

am saxis davalebebi gansxvavdeba erTmaneTisgan winaswari monacemebisa da

gamosatani daskvnebis TvalsazrisiT. amitom gansakuTrebuli yuradReba miaqcieT

SekiTxvas, romelic axlavs TiToeul davalebas da mocemuli variantebidan

airCieT Sesabamisi pasuxi.

zogierT SekiTxvaze pasuxis gacemas gagiadvilebT monacemebis gamosaxva

naxazis formiT.

14. ucxoplanetelTa kosmosur xomaldze kapitnis garda kidev oTxi wevria: alfa, beta, gama da Teta. dedamiwaze Camosvlisas xomaldis kapitanma ekipaJi or

jgufad gayo (TiToeul jgufSi ori wevri iyo). man gadawyvita, rom:

1. gama da beta iqnebian erTsa da imave jgufSi

2. beta da alfa ar iqnebian erTsa da imave jgufSi

3. alfa da Teta iqnebian erTsa da imave jgufSi

4. beta da Teta iqnebian erTsa da imave jgufSi

ganawilebis am oTxive wesis erTdroulad ganxorcieleba SeuZlebelia. zemoT

CamoTvlilTagan ganawilebis romeli wesi unda gamoiricxos, raTa ekipaJis

wevrebis jgufebSi ganawileba SesaZlebeli gaxdes?

(a) 4

(b) 3

(g) 2

(d) 1

15. cotne da kote megobrebi arian. cnobilia, rom erT-erTi maTgani yovelTvis simarTles ambobs, xolo meore – yovelTvis cruobs.

megobrebidan erT-erTma ganacxada:

“me cotne ar var”

Tu am sityvebis warmomTqmeli aris _____ , maSin _____ aris matyuara.

(a) cotne / kote

(b) kote / kote

(g) cotne / kote ar

(d) kote / cotne ar

5

16. cnobilia, rom: • gamomZiebeli arasodes cruobs, magram amomwurav informaciasac arasodes

gvawvdis

• eWvmitanili arasodes gvawvdis amomwurav informacias, Tanac man SeiZleba

icruos

alekos ZaRlebis gamofenaze mxolod senbernari da kavkasiuri nagazi moewona.

kiTxvaze, Tu ra jiSis ZaRlebi moewona mas, alekom upasuxa, rom moewona nagazi

da doberman-pinCeri.

aqedan aucileblad gamomdinareobs, rom aleko:

(a) SeiZleba gamomZiebeli iyos, magram ar SeiZleba iyos eWvmitanili

(b) SeiZleba eWvmitanili iyos, magram ar SeiZleba iyos gamomZiebeli

(g) SeiZleba iyos rogorc eWvmitanili, aseve gamomZiebeli

(d) ar SeiZleba iyos arc eWvmitanili da arc gamomZiebeli

17. adamianis qcevas pirovnul Tvisebebze metad situacia ganapirobebs. magram xdeba xolme, rom zogierTi adamiani, romelic, vTqvaT, Tamamad iqceva erT

situaciaSi, aseve iqceva sruliad gansxvavebul viTarebaSi.

romeli daskvna gamomdinareobs am msjelobidan aucileblad?

(a) situacias yovelTvis naklebi mniSvneloba aqvs pirovnul TvisebebTan

SedarebiT

(b) arseboben adamianebi, romelTa qceva naklebad aris damokidebuli situaciaze

(g) arseboben adamianebi, romelTa qceva arasodes araa damokidebuli pirovnul

Tvisebebze

(d) situacia yovelTvis meti zegavlenis mqonea, vidre pirovnuli Tvisebebi

18. sawarmom A da B qalaqebSi arsebul Tavis safirmo maRaziebSi gasayidad Seitana sportis moyvarulTa Soris popularuli maisurebi. A qalaqSi gacilebiT meti maisuri gaiyida, vidre _ B qalaqSi. sawarmos xelmZRvanelobam amaSi B qalaqis sadistribucio qselis menejeri daadanaSaula.

qvemoT CamoTvlilTagan romeli faqti matebs damajereblobas sawarmos

xelmZRvanelTa pozicias?

(a) A qalaqSi gacilebiT meti sportuli klubia, vidre _ B qalaqSi (b) B qalaqSi imave periodSi sxva firmamac Seitana msgavsi maisurebi (g) A qalaqSi am periodSi axalgazrduli rok-festivali imarTeboda (d) B qalaqSi am firmas ufro meti safirmo maRazia aqvs, vidre _ A qalaqSi

6

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis

mixedviT (saWiroebis SemTxvevaSi SegiZliaT danomroT abzacebi).

enis warmoSobis sakiTxi mZafr interess iwvevda enaTmecnierebis

Camoyalibebamde mravali saukuniT adre. jer kidev Zvel saberZneTSi (V-IV

saukuneebSi Zv.w.) didi gatacebiT kamaTobdnen am problemis erT-erTi

umniSvnelovanesi aspeqtis Sesaxeb. kerZod, berZen moazrovneebs ainteresebdaT,

ratom ewodeba sagans es da ara sxva saxeli.

erTni amtkicebdnen, rom sagnis saxeli gansazRvrulia sagnis bunebiT. “Tu es ase ar aris, _ ambobdnen isini, _ maSin ratom xdeba, rom ama Tu im sagans

nebismier saxels ver vuwodebT?” meore Teoriis mimdevrebi amtkicebdnen, rom saxeli sagans eZleva “SeTanxmeba_dakanonebiT”. saxeli rom sagnis bunebiT

ganisazRvrebodes, sagnebs sxvadasxva saxeli ar erqmeoda, erTsa da imave sagans

yvela enaSi erTi da igive saxeli eqneboda; maSasadame, saxeli ar ganisazRvreba

sagniTo, ambobdnen isini. arsebiTi is ki ar aris, am TvalsazrisTagan romeli

ufro Seefereba sinamdviles. aq mTavaria Tavad sakiTxis dasma _ ratom iwodeba

sagnebi ase da ara sxvagvarad, es ki enis filosofiis erT-erT ZiriTad sakiTxs

warmoadgens.

enis warmoSobis sakiTxiT dainteresebuli iyvnen aRmosavleTis qveynebSic.

herodotes gadmocemiT, egviptis faraonma fsametiqma (Zv. w. VI s.) enis

warmoSobis sakiTxis gasarkvevad Turme aseTi cda Caatara: ori bavSvi ise

aRzardes, rom maT ar gaugoniaT adamianis metyveleba. bavSvebi mainc

alaparakdnen da pirveli sityva, romelic orivem warmoTqva, iyo _ “bekos”. faraonma gasca gankarguleba, gaegoT, romel enaSi arsebobs es sityva. gairkva,

rom aseTi sityva arsebobs frigiul enaSi da niSnavs “purs”. faraonma aqedan daaskvna, rom uZveles enad frigiuli unda miviCnioT.

Tavi rom davaneboT sakiTxs, Tu ramdenad kanonzomieria am

“eqsperimentidan” (Tuki aseTi ram odesRac marTlac moxda) gamotanili daskvna, an ramdenad safuZvliania kvlevis meTodika, herodotes monaTxrobi erTi mxriv

mainc sagulisxmoa: enis warmoSobis sakiTxi axlo aRmosavleTis Zvel qveynebSi

berZnebze ufro adre ainteresebdaT.

saxeldebis problemis mecnieruli kvleva gasuli saukunis ociani wlebidan

iwyeba. erT-erTi gamokvlevis mixedviT, sityva SemTxveviT ar ukavSirdeba im

obieqts, romelsac aRniSnavs, anu is SemTxveviT rodi iRebs saxelwodebis

funqcias. am Tvalsazrisis Tanaxmad, sityvisa da obieqtis kavSiri emyareba

erTgvar Sesabamisobas sityvis bgeriT Sedgenilobasa da obieqtis vizualur

xats Soris. eqsperimentSi cdispirebs sTavazobdnen ori figuris naxazs,

romelTagan erTi texili, xolo meore _ mrudi xazebisgan iyo Sedgenili, da

sTxovdnen SeerCiaT maTTvis saxelwodeba ori xelovnurad Seqmnili bgeraTa

kompleqsidan _“takete” da “maluma”. cdispirTa didi umravlesoba texili

xazebisgan Sedgenil figuras “taketes” uwodebda, mrudi xazebisgan Sedgenil

figuras ki _ “malumas”. Tumca, saxeldebis problema jer kidev araa sabolood gadawyvetili. is kvlav iwvevs mkvlevarTa mZafr interess da biZgs aZlevs

mravali, zogjer sruliad gansxvavebuli mecnieruli koncefciis SemuSavebas.

7

19. raze kamaTobdnen enis warmoSobis sakiTxiT dainteresebuli Zveli berZnebi (upasuxeT I-II abzacebis mixedviT)?

(a) sagnis an movlenis saxeldeba enaTmecnierebis Camoyalibebamde ufro mZafr

interess iwvevda Tu misi Camoyalibebis Semdeg

(b) ra ufro arsebiTia _ berZeni moazrovneebis gansxvavebul TvalsazrisTagan

romelia marTebuli Tu Tavad saxeldebis sakiTxis dasma

(g) sagnis an movlenis saxeldeba sagnis bunebis Sesabamisad xdeba Tu erToblivi

gadawyvetilebis safuZvelze

(d) ratom iwodeba sagnebi ase da ara sxvagvarad _ enaTmecnierebis erT-erTi

ZiriTadi sakiTxia Tu enis filosofiis

20. qvemoT CamoTvlilTagan romeli uaryofs II abzacSi warmodgenil orive

Teorias?

(a) sagnis saxeli gansazRvrulia misive bunebiT

(b) sagans saxeli eniWeba SeTanxmeba-dakanonebiT

(g) sagnis saxeli ar ganisazRvreba arc misi bunebiT da arc

SeTanxmeba_dakanonebiT

(d) sagans saxeli eniWeba SeTanxmeba-dakanonebiT an saxelwodeba ganisazRvreba

sagnis bunebiT

21. romeli mosazrebis argumentad gamoiyena faraonma fsametiqma mis mierve

Catarebuli cdis Sedegi?

(a) metyvelebis aTvisebis sawyis etapze dakvirvebiT SesaZlebelia ama Tu im enis

warmoSobis sakiTxis garkveva

(b) aRmosavleTis qveynebSi ufro daxvewili iyo kvlevis meTodika, vidre _

saberZneTSi

(g) ufrosebisagan gancalkevebiT bavSvebis aRzrda xels ar uSlis maT

ametyvelebas

(d) pirveli sityva, romelic frigiul enaSi warmoiSva, iyo _ "bekos"

22. teqstidan gamomdinare, herodotes monaTxrobTan dakavSirebiT danamdvilebiT SeiZleba iTqvas is, rom:

(a) faraonis mier Catarebuli eqsperimentis daskvnebi misaRebi da kanonzomieria

(b) bavSvebi, romlebzec fsametiqma Caatara cda, namdvilad alaparakdnen frigiul

enaze da warmoTqves sityva "bekos" (g) fsametiqis kvlevis meTodi Seesatyviseba Tanamedrove mecnieruli kvlevis erT-

erT meTods

(d) enis warmoSobisa da saxeldebis sakiTxebi axlo aRmosavleTis Zvel qveynebSi

berZnebze ufro adre ainteresebdaT

8

23. ra mimarTebaa sityvis bgeriT Sedgenilobasa da obieqtis vizualur xats Soris bolo abzacSi aRwerili eqsperimentis mixedviT?

(a) kavSiri sityvis bgeriT Sedgenilobasa da obieqtis vizualur xats Soris

SemTxveviTia, anu saxeldeba xorcieldeba SeTanxmeba-dakanonebiT

(b) rogorc wesi, sityvis bgeriT Sedgenilobasa da obieqtis vizualur xats

Soris garkveuli Sesabamisobaa, anu sityva SemTxveviT ar iRebs saxelwodebis

funqcias

(g) kavSiri sityvis bgeriT Sedgenilobasa da obieqtis vizualur xats Soris

kanonzomieria, radgan ama Tu im sagnis saxeli mraval enaSi msgavs bgeraTa

kompleqsidan aris Seqmnili

(d) rogorc wesi, obieqtis vizualuri xati efuZneba sityvis bgeriT

Sedgenilobas, anu bgeraTa kompleqsi SemTxveviT ar iqceva sagnis

saxelwodebad

24. teqstis mixedviT, ra kavSiria ZvelberZnul Teoriebsa da XX saukunis erT-erT kvlevas Soris?

(a) berZnuli Teoriebi saxeldebas enis filosofiis erT-erT ZiriTad sakiTxad

ganixilavs, Tanamedrove eqsperimentSi ki is miCneulia obieqtis vizualuri

aRqmis safuZvlad

(b) ZvelberZnuli Teoriebis sapirispirod, XX saukunis es eqsperimenti sruliad

axleburad gagvaazrebinebs saxeldebis problemas

(g) "taketesa" da "malumas" eqsperimenti erTgvari kompromisuli argumentia orive berZnuli Teoriis sasargeblod

(d) XX saukuneSi Catarebuli eqsperimentis Sedegebi ganamtkicebs erT-erT

berZnul Teorias da eWvqveS ayenebs meores

25. ra aris teqstis ZiriTadi daniSnuleba?

(a) dagvanaxos saxeldebis fenomenTan dakavSirebuli sirTuleebi da maTi gadaWris

gzebi

(b) daasabuTos saxeldebis sakiTxTan dakavSirebul TeoriaTagan erT-erTis

marTebuloba

(g) Seajamos enis warmoSobis erT-erTi mniSvnelovani aspeqtis _ saxeldebis _

eqsperimentuli kvlevis miRwevebi

(d) gagvacnos Teoriuli mosazrebebi da kvlevis magaliTebi enis warmoSobis

erT-erTi aspeqtis _ saxeldebis sakiTxTan dakavSirebiT

9

analogiebi

am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva,

romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. daadgineT, ra

saxisaa es mimarTeba.

savaraudo pasuxTa yovel variantSi aseve mocemulia mniSvnelobiT

urTierTdakavSirebuli sityvebis wyvili. airCieT maTgan is wyvili, romelSic

sityvaTa mniSvnelobebs Soris mimarTeba gamuqebul sityvaTa urTierTmimarTebis

msgavsia (analogiuria). pasuxis arCevisas gaiTvaliswineT wyvilebSi sityvaTa

Tanmimdevroba.

26. mxars uWers : Tanadgoma

(a) bodiSs ixdis : patieba

(b) kamaTobs : dava

(g) nebas rTavs : Txovna

(d) yoymanobs : gadawyveta

27. sibnele : mze

(a) sicxe : qurqi

(b) kiTxva : saTvale

(g) wyurvili : wyali

(d) mosavali : xorbali

28. CiraRdani : naTura

(a) sabeWdi manqana : kompiuteri

(b) etli : avtomobili

(g) Ceqma : fexsacmeli

(d) saTvalTvalo koSki : cixesimagre

29. eWviani : ndoba

(a) didsulovani : sikeTe

(b) mSvidi : SfoTva

(g) naRvliani : martooba

(d) xumara : sicili

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30. feri : wiTeli

(a) moTxovnileba : SimSili

(b) metyveleba : aqcenti

(g) gataceba : swrafva

(d) ganaTeba : sinaTle

31. teqsti : furceli

(a) dRe : kalendari

(b) ilustracia : wigni

(g) gamosaxuleba : ekrani

(d) fotosuraTi : albomi

32. Tafli : yvavili

(a) gube : wvima

(b) comi : fqvili

(g) foladi : sabado

(d) rveuli : qaRaldi

33. puris yana : jejili

(a) rto : fesvi

(b) buCqi : ekali

(g) nayofi : nergi

(d) foToli : kvirti

11

winadadebebis Sevseba

am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa

gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiT aris aRniSnuli.

erTi xazi zogjer erT sityvas gulisxmobs, zogjer ki _ ramdenimes.

savaraudo pasuxTa yovel variantSi mocemulia sityvaTa jgufi, romlis

nawilebi erTmaneTisgan daxrili xazebiTaa (/) gamijnuli. airCieT pasuxis is

varianti, romlis TiToeuli nawilis Tanmimdevrulad Casma Sesabamis

gamotovebul adgilebSi azrobrivad gamarTul winadadebas mogvcems.

34. adamianis yuradRebas izidavs yovelive is, rac misTvis _____ . magram, rodesac subieqti _____ situaciaSi imyofeba, maSin yuradRebis gamomwvev

faqtors _____ ki ara, piriqiT, _____ warmoadgens.

(a) nacnobi da Cveulia / ucnob, axal / siaxle da uCveuloba / nacnoboba da

Cveulebrioba

(b) axali da uCveuloa / nacnob, Cveul / nacnoboba da Cveulebrioba / siaxle

da uCveuloba

(g) axali da uCveuloa / ucnob, axal / siaxle da uCveuloba / nacnoboba da

Cveulebrioba

(d) nacnobi da Cveulia / nacnob, Cveul / siaxle da uCveuloba / nacnoboba da

Cveulebrioba

35. ragind _____ unda iyos raime musikaluri nawarmoebi, igi mainc Sedgeba _____ , romelTaganac agebulia "gama", anu erTgvari musikaluri anbani. _____ is kombinacia, is sinTezi, romelSic mocemulia _____ tonebi.

(a) Cveulebrivi / araCveulebrivi bgerebisagan, gansakuTrebuli tonebisagan /

nawarmoebis trafaretulobas iwvevs / es yvelasaTvis nacnobi, Cveuli

(b) Cveulebrivi / imave gansazRvruli raodenobis notebisagan, imave tonebisagan /

nawarmoebis trafaretulobas iwvevs / mxolod unikaluri

(g) originaluri / araCveulebrivi bgerebisagan, gansakuTrebuli tonebisagan /

originalobas, esTetikur Rirebulebas nawarmoebs aniWebs / mxolod

unikaluri

(d) originaluri / imave gansazRvruli raodenobis tonebisagan / originalobas,

esTetikur Rirebulebas nawarmoebs aniWebs / es yvelasTvis cnobili

elementaruli

12

36. rasakvirvelia, avTandils _____ ar aklia, _____ mxedruli siqvele mainc _____ rols asrulebs mis winaSe wamoWrili amocanebis gadawyvetisas, radgan am

amocanebs metwilad _____ .

(a) inteleqtualuri SesaZleblobebi / magram / mTavar, arsebiT / inteleqtualuri

xasiaTi aqvs

(b) meomruli Rirsebebi / magram / aramTavar, damxmare / inteleqtualuri xasiaTi aqvs

(g) meomruli Rirsebebi / miuxedavad amisa, / aramTavar, damxmare / misi mebrZoli

buneba gansazRvravs

(d) inteleqtualuri SesaZleblobebi / swored amitom / aramTavar, damxmare /

misi mebrZoli buneba gansazRvravs

37. is faqti, rom inglisuri ena ukanaskneli 500 wlis manZilze, _____ ,

SeiZleba mieweros swored am periodSi _____ . xolo, meore mxriv, unda

aRiniSnos primitiul sazogadoebaTa enebSi mimdinare _____ imis gamo, rom maT

_____ namdvili fonetikuri damwerloba.

(a) winare periodTan SedarebiT, mniSvnelovnad Seicvala / werilobiTi

komunikaciis gavrcelebis Seferxebas / sakmaod swrafi cvlilebebi / Seqmnes

(b) winare periodTan SedarebiT, naklebad Seicvala / werilobiTi komunikaciis

farTod gavrcelebas / sakmaod swrafi cvlilebebi / ar gaaCniaT

(g) momdevno periodTan SedarebiT, naklebad Seicvala / werilobiTi komunikaciis

gavrcelebis dabal dones / umniSvnelo cvlilebebi / ar gaaCniaT

(d) momdevno periodTan SedarebiT, mniSvnelovnad Seicvala / werilobiTi

komunikaciis farTod gavrcelebas / umniSvnelo cvlilebebi / Seqmnes

13

logika

am saxis davalebebi gansxvavdeba erTmaneTisgan winaswari monacemebisa da

gamosatani daskvnebis TvalsazrisiT. amitom gansakuTrebuli yuradReba miaqcieT

SekiTxvas, romelic axlavs TiToeul davalebas da mocemuli variantebidan

airCieT Sesabamisi pasuxi.

zogierT SekiTxvaze pasuxis gacemas gagiadvilebT monacemebis gamosaxva

naxazis formiT.

38. mocemulia:

• Tu sandro tyuis, maSin tyuis qeTic

Semdegi oTxi viTarebidan romeli SeiZleba gamoviyenoT imis sabuTad, rom es

mocemuloba mcdaria (gaiTvaliswineT, rom TeZami namdvilad aris mdinare)?

(a) sandro ambobs: TeZami ar aris mdinare

qeTi ambobs: marTalia, rom TeZami ar aris mdinare

(b) sandro ambobs: marTalia, rom TeZami ar aris mdinare

qeTi ambobs: tyuilia, rom marTalia, rom TeZami aris mdinare

(g) sandro ambobs: tyuilia, rom marTalia, rom TeZami aris mdinare

qeTi ambobs: marTalia, rom TeZami aris mdinare

(d) sandro ambobs: marTalia, rom tyuilia, rom TeZami aris mdinare

qeTi ambobs: TeZami ar aris mdinare

39. xuTi bavSvi magidis irgvliv (erTmaneTis pirispir) dgas.

qvemoT CamoTvlilTagan romeli SemTxvevaa SesaZlebeli?

(a) yoveli bavSvi maRalia mis marjvniv mdgomze

(b) yoveli gogona dgas or biWs Soris, xolo yoveli biWi or gogonas Soris

(g) yoveli ori gverdi-gverd mdgomi bavSvis asakTa jami tolia

(d) yovel bavSvs uWiravs ufro didi vaSli, vidre mis marcxniv mdgoms

14

40. umaRles saswavlebelSi pirvelkurselTa Soris Catarda konkursi, romlis Sedegadac gamovlinda:

• pirvelkurselTa umravlesobam kargad icis ucxouri ena

• pirvelkurselTa umravlesobas Tavisuflad SeuZlia kompiuteriT sargebloba

• yvelam, vinc konkursze gamoavlina rogorc ucxouri enis kargad codna,

aseve _ kompiuteriT Tavisuflad sargeblobis unari, miiRo jildo.

qvemoT CamoTvlilTagan romeli debuleba gamomdinareobs aucileblad am

monacemebidan?

(a) TiTqmis yvela pirvelkurselma miiRo jildo

(b) pirvelkurselTa mxolod umciresobam miiRo jildo

(g) zogierTma pirvelkurselma namdvilad miiRo jildo

(d) verc erTma pirvelkurselma jildo ver miiRo

41. A da B firmebi Tixisa da faifuris WurWels amzadeben. wels maT Tavisi produqciis mxolod mcire nawili gayides. gaiyida A firmis mier damzadebuli gacilebiT meti Tixis WurWeli, vidre _ B firmis faifuris WurWeli.

am informaciis safuZvelze gamoiTqva varaudi, rom:

wels Tixis WurWeli meti popularobiT sargeblobs, vidre _ faifuris.

qvemoT CamoTvlilTagan romeli faqti matebs damajereblobas am varauds?

(a) wels gaiyida A firmis ufro meti Tixis WurWeli, vidre B firmis Tixis WurWeli

(b) wels gaiyida A firmis ufro meti faifuris WurWeli, vidre misive Tixis WurWeli

(g) A firmis WurWeli zogadad meti popularobiT sargeblobs, vidre B firmis WurWeli

(d) B firmis WurWeli zogadad meti popularobiT sargeblobs, vidre A firmis WurWeli

15

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT

(saWiroebis SemTxvevaSi SegiZliaT danomroT abzacebi).

italieli mxatvari da mecnieri _ leonardo da vinCi _ dakvirvebiT

swavlobda frinvelTa frenis Taviseburebas. Cvenamde moaRwia misma Canaxatebma da

SeniSvnebma, romlebic safren aparats exeba. man pirvelma mogvca frenis

Teoriuli dasabuTeba, haerze mZime aparatebis (helikopteri, paraSuti) Seqmnis

idea. leonardos aqvs aseTi gamonaTqvami: “frinveli erTgvari aparatia, romlis moZraoba eqvemdebareba maTematikis kanonebs. Sesabamisad, adamianma unda SeZlos

aseTi aparatis Seqmna”. masve ekuTvnis Canaweri: “wadi milanis simagris maxlobel TxrilebSi, raTa daakvirde nemsiylapiebis frenas”. am sityvebidan ramdenime

saukunis Semdeg nemsiylapiebis safreni aparatis Seswavlam gaxsna erTi iseTi

saidumlo, romelic metad mniSvnelovani aRmoCnda aviaciis Semdgomi

ganviTarebisTvis.

cnobilia, rom buneba frinvelisa Tu mweris safren aparats xangrZlivi

drois manZilze “agebda”. arsebobs garkveuli Tanafardoba frinvelis sxeulis wonasa da frTebis Slils Soris. sxvadasxva frinvelisTvis gansazRvrulia

frTebis moqnevis sixSirec. magaliTad, svavi, romlis frTebis Slili sxeulis

sigrZes TiTqmis 3-jer aRemateba, erTi wamis ganmavlobaSi frTebs erTxel

moiqnevs, xolo xoxobi, kakabi, mwyeri, romelTa gaSlili frTebi 1,5-jer aRemateba

sxeulis sigrZes, wamSi frTebs 5-jer moiqneven.

frinvelTa ganviTarebis istoria gviCvenebs, rom sxeulis giganturi zoma

maTTvis “araekonomiuria”. sxeulis zomis metismeti zrda ganapirobebda masiuri

kunTovani sistemisa da ConCxis ganviTarebas, Sesabamisad ki saWiroebda Warb sakvebs,

rac, TavisTavad, arcTu ioli mosapovebeli iyo. unda aRiniSnos is naklic,

romelic zogierT didi zomis frinvels axasiaTebs. weroebs ar SeuZliaT

adgilidan afrena. isini “starts” iReben mxolod mas Semdeg, rac ramdenime aTeul nabijs gairbenen miwaze. zogierTi frinveli afrenas iwyebs xeebis totebidan an

kldeebidan. miuxedavad amisa, frTosnebi wonasTan SefardebiT gacilebiT ufro

nakleb energias xarjaven, vidre adamianis mier Seqmnili aparatebi.

gasuli saukunis 30-ian wlebSi xSiri iyo sahaero katastrofebi.

mecnierebma Seiswavles aviakatastrofis Sedegad daSlili TviTmfrinavis

nawilebi, romlebsac xanZris an afeTqebis kvali ar aCnda. gamoirkva, rom

aviakatastrofa TviTmfrinavis araswori konstruirebis Sedegi iyo.

TviTmfrinavis mier garkveuli siCqaris gadalaxvis Semdeg aerodinamikuri Zalebis

moqmedebiT iwyeboda frTis rxeviTi moZraoba, tkacuni da daSla. am movlenas

“flateri” (ing. _ TrTolva) uwodes. ucnauria, magram faqtia, rom Tanamedrove TviTmfrinavebs ufro meti aqvT

saerTo mwerebTan, vidre frinvelebTan. nemsiylapiebis safreni aparatis Seswavlis

Sedegad gairkva, rom am mwerebs frTebis kideebze aqvT gamsxvileba, romlis

daniSnuleba, rogorc Cans, unda iyos mweris frTis damZimeba da vibraciis

Tavidan acileba. aviakonstruqtorebma isargebles aRmoCeniT da TviTmfrinavis

frTebic daamZimes, riTac aRkveTes flateris saSiSroeba.

Tanamedrove reaqtiuli safreni aparatebis siCqare nebismieri cocxali

arsebis siCqares mniSvnelovnad aRemateba. samgzavro TviTmfrinavi 25-jer ufro

swrafad dafrinavs, vidre _ nemsiylapia, da 90-jer ufro swrafad, vidre _

pepela. magram gairkva, rom TviTmfrinavi saaTSi gadis manZils, romelic 15 000-jer

aRemateba mis sigrZes, xolo, vTqvaT, bazi (erTgvari mweri) _ manZils, romelic

milionjer metia mis sigrZeze.

16

42. leonardo da vinCis damsaxurebaa is, rom man:

(a) pirvelma mogvca frenis Teoriuli dasabuTeba da Seqmna haerze mZime

aparatebi: helikopteri, paraSuti

(b) Seiswavla frinvelTa frenis Tavisebureba da frinvelis safreni aparati

maTematikur kanonebs dauqvemdebara

(g) migviTiTa cocxali bunebis Sesaxeb arsebuli codnis gamoyenebiT sainJinro

amocanaTa gadawyvetis SesaZleblobaze

(d) gaxsna erTi iseTi saidumlo, romelic Zalze mniSvnelovani aRmoCnda aviaciis

Semdgomi ganviTarebisTvis

43. ra Tanafardobazea saubari II abzacSi?

(a) rac ufro xangrZlivi drois manZilze “agebda” buneba frinvelis safren aparats, miT metia misi frTebis Slili da naklebia frTebis moqnevis sixSire

(b) rac ufro metia frinvelis sxeulis wona, miT ufro metia misi frTebis

Slili da metia frTebis moqnevis sixSire

(g) rac ufro metia frinvelis sxeulis sigrZe, miT ufro mcirea misi frTebis

Slili, magram didia frTebis moqnevis sixSire

(d) rac ufro metjer aRemateba frTebis Slili frinvelis sxeulis sigrZes, miT

ufro mcirea misi frTebis moqnevis sixSire drois garkveul monakveTSi

44. teqstSi yuradReba gamaxvilebulia didi zomis frinvelebisTvis damaxasiaTebel naklze. CamoTvlilTagan romeli winadadeba gamoxatavs mas?

(a) didi zomis frinvelebi wonasTan SedarebiT gacilebiT nakleb energias

xarjaven, vidre _ adamianis mier Seqmnili aparatebi

(b) didi zomis zogierT frinvels afrena SeuZlia mxolod mas Semdeg, rac

miwaze ramdenime nabijs gairbens

(g) weroebi afrenas iwyeben xis totebidan, maSin, rodesac zogierT samxedro

TviTmfrinavs SeuZlia adgilidan afrena

(d) Warbi sakvebis mosapoveblad didi zomis frinvelebs sWirdebaT masiuri

kunTovani sistema

45. romeli safreni aparatebis aviakatastrofazea saubari teqstSi?

(a) arasworad konstruirebuli safreni aparatebisa, romelTac zedmetad mZime

frTebi hqondaT

(b) Tanamedrove reaqtiuli safreni aparatebisa, romlebic 90-jer ufro swrafad

dafrinaven, vidre _ peplebi

(g) TviTmfrinavebisa, romlebic xanZris Sedegad xSirad feTqdeboda gasuli

saukunis 30-ian wlebSi

(d) safreni aparatebisa, romelTa frTebis vibracia iwvevda mTeli aparatis

daSlas

17

46. rogor aRikveTa flateris saSiSroeba?

(a) xanZarsawinaaRmdego mowyobilobis rekonstruirebis Sedegad

(b) frTebis damZimebis gziT, risi konstruirebac erT-erTi mweris agebulebis

analogiiT moxerxda

(g) aerodinamikuri Zalebis moqmedebis Sedegad

(d) nemsiylapiebisa da bazis safreni aparatebis Seswavlis meSveobiT

47. teqstis mixedviT, ra mimarTebaa samgzavro TviTmfrinavisa da erT-erTi

mweris frenis garkveul maxasiaTebels Soris?

(a) nemsiylapia 25-jer nela dafrinavs, vidre _ TviTmfrinavi da 90-jer ufro

swrafad, vidre _ pepela

(b) bazi saaTSi gadis manZils, romelic milionjer aRemateba missave sigrZes,

xolo TviTmfrinavi saaTSi gadis manZils, romelic mxolod 15 000-jer metia

missave sigrZeze

(g) pepela saaTSi gadis manZils, romelic milionjer aRemateba missave sigrZes,

xolo TviTmfrinavi amave droSi gadis manZils, romelic 90-jer metia missave

sigrZeze

(d) TviTmfrinavis siCqare mniSvnelovnad aRemateba nebismieri mweris siCqares,

Tumca bazi milionjer met manZils gadis saaTSi, vidre _ TviTmfrinavi

48. pirvel abzacSi ori citataa leonardos Canawerebidan: 1. “frinveli erTgvari aparatia, romlis moZraoba eqvemdebareba maTematikis

kanonebs. Sesabamisad, adamianma unda SeZlos aseTi aparatis Seqmna”; 2. “wadi milanis simagris maxlobel TxrilebSi, raTa daakvirde nemsiylapiebis

frenas”.

romel abzacebs miemarTeba uSualod es citatebi?

(a) pirveli citata _ II da III abzacebs, meore citata ki _ IV, V, VI abzacebs

(b) pirveli citata _ III, IV, V abzacebs, meore citata ki _ II da VI abzacebs

(g) pirveli citata _ IV da VI abzacebs, meore citata ki _ II, III, V abzacebs

(d) pirveli citata _ II, V, VI abzacebs, meore citata ki _ III da IV abzacebs

18

49. teqstis dasawyisSi naxsenebia _ “saidumlos gaxsna”. romel saidumlozea

saubari?

(a) ratom eqvemdebareba frinvelTa moZraoba maTematikis kanonebs

(b) ratom aqvT Tanamedrove TviTmfrinavebs ufro meti saerTo mwerebTan, vidre

_ frinvelebTan

(g) ra ganapirobebs imas, rom mwerebi erT saaTSi sakuTar sigrZesTan SedarebiT

gacilebiT met manZils gadian, vidre _ TviTmfrinavebi

(d) ra gziTaa SesaZlebeli safren aparatTa frTebis vibraciis Tavidan acileba

50. qvemoT CamoTvlilTagan romeli daskvnis gamotana SeiZleba teqstis safuZvelze?

(a) aviakonstruqtorebma SeiZleba isargeblon aRmoCeniT, romelic exeba

nemsiylapiebis frTebis agebulebas da aRkveTon aerodinamikuri Zalebis moqmedeba

(b) miuxedavad imisa, rom frTosnebi wonasTan SefardebiT gacilebiT ufro

nakleb energias xarjaven, vidre adamianis mier Seqmnili aparatebi, isini bevrad

ufro “araekonomiurni” arian (g) miuxedavad imisa, rom Tanamedrove safreni aparatebis SesaZleblobebi mravali

parametriT aRemateba frinvelebisa da mwerebisas, am ukanasknelT aqvT

safrenosno unarebi, romlebic jerjerobiT miuRwevelia aviaciisTvis

(d) aviaciis Semdgomi ganviTareba SeuZlebelia cocxal arsebaTa safreni

aparatebis Seswavlisa da konstruirebis gareSe

19

Savi samuSaosaTvis

20

maTematikuri nawili

testis maTematikur nawilze muSaobisas gaiTvaliswineT:

• naxazebi, romlebic erTvis zogierT davalebas, araa Sesrulebuli davalebis

pirobaSi miTiTebuli zomebis zusti dacviT. amitom monakveTebis sigrZis an sxva

sidideebis Sesaxeb daskvnis gamotanisas nu daeyrdnobiT naxazis zomebs. yuradReba

gaamaxvileT davalebis pirobaze;

• Tu naxazze mocemuli swori xazis Sesaxeb amocanis pirobaSi damatebiT araferia

naTqvami, maSin unda CaTvaloT, rom es swori xazi _ wrfea an misi nawili;

• testSi gamoyenebulia ricxvTa Caweris mxolod aTobiTi poziciuri sistema.

maTematikuri aRniSvnebi da formulebi:

10. samkuTxedi: • samkuTxedis kuTxeebis sidideTa

jami 180°-is tolia. • piTagoras Teorema:

marTkuTxa samkuTxedis

hipotenuzis sigrZis

kvadrati tolia kaTetebis

sigrZeTa kvadratebis jamis:

AB2 = AC2 + BC2 (ix. naxazi).

• samkuTxedis farTobi

samkuTxedis gverdis sigrZisa da Sesabamisi

simaRlis namravlis naxevaris toli .

11. oTxkuTxedi: • oTxkuTxedis kuTxeebis sidideTa

jamia 360°. • marTkuTxedis farTobi misi sigrZisa

da siganis namravlis tolia: S = ab. • paralelogramis farTobi misi

gverdis sigrZisa da am gverdis Sesabamisi

simaRlis namravlis tolia: S = ah.

12. wre, wrewiri: • wrewiris sigrZe L misi

radiusis mixedviT gamoiTvleba

formuliT: L = 2πr. π ricxvi measedis sizustiT 3,14-is tolia.

• r radiusiani wris farTobi gamoiTvleba formuliT: S = πr2.

13. marTkuTxa paralelepipedi: • marTkuTxa paralelepipedis

moculoba misi sigrZis, siganisa da

simaRlis namravlis tolia: V = abc; • kubis SemTxvevaSi: a = b = c.

1. nuli arc dadebiTia da arc uaryofiTi; 1 ar aris martivi ricxvi.

2. procenti: a ricxvis k% aris ;

3. xarisxi: an = a · a · a · ...· a (n-jer)

an · am = an + m

an : am = an – m

(an)m = an · m

4. proporcia: Tu , maSin ad = bc.

5. siCqare: dro

siCqare =manZili

6. saSualo ariTmetikuli:

raodenoba monacemTa

jami monacemTasaSualo monacemTa =

7. Semoklebuli gamravlebis formulebi: (a+b)2 = a2 + 2ab + b2;

(a - b)2 = a2 – 2ab + b2;

(a + b)(a – b) = a2 – b2 . 8. naxazze kuTxe SeiZleba kuTxis gverdebs Soris

Casmuli patara rkaliT

iyos moniSnuli, marTi

kuTxe ki _ patara

kvadratiT.

Canaweri: ∠A aRniSnavs A kuTxis sidides.

9. paraleluri wrfeebi: • ori paraleluri

wrfis mesame wrfiT

gadakveTisas Siga jvaredina

kuTxeebi tolia: α = β.

21

raodenobrivi Sedareba

SeadareT erTmaneTs A da B svetebis ujrebSi mocemuli raodenobebi. Tu A svetis ujraSi mocemuli raodenoba metia B svetis Sesabamis ujraSi

mocemul raodenobaze, airCieT (a);

Tu B svetis ujraSi mocemuli raodenoba metia A svetis Sesabamis ujraSi mocemul raodenobaze, airCieT (b);

Tu ujrebSi mocemuli raodenobebi tolia, airCieT (g);

Tu mocemuli informacia sakmarisi araa imis dasadgenad, romeli raodenobaa

meti, airCieT (d).

A B

51.

(a) (b) (g) (d)( )42 −·( )413 −−−

52.

(a) (b) (g) (d)2718

2114

53.

(a) (b) (g) (d) 1>> ab2a 3b

54.

(a) (b) (g) (d) 09,3·28,2 2,10:60

55.

ABC samkuTxedis AB da BC gverdebi tolia.

(a) (b) (g) (d) 150° B kuTxis sidide

22

56.

a da b uaryofiTi ricxvebia.

(a) (b) (g) (d) ba + ba −

57.

(a) (b) (g) (d) 5,0>> ba22 ba − ba −

58.

a piramidas sul 12 wibo aqvs, b piramidas sul 12waxnagi aqvs.

(a) (b) (g) (d)

a piramidis wveroebis raodenoba

b piramidis wveroebis raodenoba

amocanebi

59. qvemoT mocemul gamosaxulebaTagan romlis mniSvnelobaa umciresi? (a) 8,5 + 1 + 1 + 6,5 (b) 8,5 · 1 · 1 · 6,5 (g) (8,5 + 1) · (1 + 6,5) (d) (8,5 + 1) · (1 · 6,5) (e) 8,5 · 1 + 1 · 6,5

60. sandros plastilinisgan gamoZerwili 20 patara burTula hqonda. 4 patara burTulisgan man erTi didi burTula gamoZerwa, 5 patara burTulisgan ki _ meore didi burTula.

sul ramdeni burTula eqneba amis Semdeg sandros? (a) 11 (b) 12 (g) 13 (d) 14 (e) 15

23

61. saaTnaxevris meramdenedi nawilia 1 wuTi?

(a) 151

(b) 301

(g) 451

(d) 601

(e) 901

62. marTkuTxedidan, romlis sigrZea 7 sm, xolo sigane _ 5 sm, amokveTilia kvadrati, romlis gverdis sigrZea 2 sm (ix. naxazi). ramdeni kvadratuli santimetria marTkuTxedis darCenili nawilis farTobi?

(a) 33 (b) 31 (g) 28 (d) 21 (e) 10

monacemTa analizi

cxrilSi mocemulia, ramdeni studenti swavlobda 2000-2005 wlebSi erT-erTi umaRlesi saswavleblis humanitarul da sabunebismetyvelo mecnierebaTa

fakultetebis specialobebze.

humanitaruli fakulteti sabunebismetyvelo mecnierebaTa fakulteti

filologia istoria fsiqologia fizika qimia biologia geologia

2000 160 120 90 80 30 45 40 2001 180 100 85 75 25 40 35 2002 190 110 80 85 20 35 25 2003 180 105 90 80 25 30 20 2004 175 110 95 70 30 45 35 2005 170 100 95 65 35 40 25

cxrilis mixedviT upasuxeT Semdeg 4 SekiTxvas: 63. ramdeni studenti swavlobda humanitarul fakultetze 2004 wels?

(a) 360 (b) 370 (g) 380 (d) 390 (e) 400

24

64. romel wlebSi iyo im studentTa raodenoba, romlebic sabunebismetyvelo fakultetis fizikis specialobaze swavlobdnen, ufro meti, vidre maTi saerTo

raodenoba, vinc imave fakultetis biologiis an geologiis specialobebze

swavlobda? (a) 2000 da 2001 wlebSi (b) 2001 da 2002 wlebSi (g) 2002 da 2003 wlebSi (d) 2003 da 2004 wlebSi (e) 2004 da 2005 wlebSi

65. ramdenjer meti iyo im studentTa raodenoba, romlebic 2001 wels humanita-ruli fakultetis istoriis specialobaze swavlobdnen, maT raodenobaze, vinc

imave wels sabunebismetyvelo fakultetis biologiis specialobaze swavlobda? (a) 3,5-jer (b) 3-jer (g) 2,5-jer (d) 2-jer (e) 1,5-jer

66. qvemoT CamoTvlilTagan romeli daskvnaa marTebuli cxrilis mixedviT?

(a) humanitaruli fakultetis studentTa naxevarze meti filologiis

specialobaze swavlobs

(b) im studentTa raodenoba, romlebic humanitaruli fakultetis istoriis

specialobaze swavlobdnen, yovelwliurad iklebda, xolo maTi, vinc

fsiqologiis specialobaze swavlobda _ imatebda

(g) im studentTa raodenoba, romlebic sabunebismetyvelo fakultetis

geologiis specialobaze swavlobdnen, 2000-2002 wlebSi yovelwliurad iklebda, xolo 2003-2005 wlebSi _ imatebda

(d) sabunebismetyvelo fakultetis fizikis specialobaze yovel wels ufro

meti studenti swavlobda, vidre imave fakultetis sxva danarCen

specialobebze (erTad)

(e) humanitaruli fakultetis fsiqologiis specialobaze yovel wels

studentTa ufro naklebi raodenoba swavlobda, vidre sabunebismetyvelo

fakultetis fizikis an qimiis specialobebze (erTad)

amocanebi

67. aTwiladebis Sekrebisas sandrom erT-erT Sesakrebad 4,82-is nacvlad Secdo-miT 4,87 Cawera da Sekreba ise Seasrula. qvemoT CamoTvlil moqmedebaTagan rome-li unda Seasrulos sandrom amis Semdeg, raTa SeZlos Secdomis gamosworeba?

(a) miRebul jams gamoaklos 0,05 (b) miRebul jams miumatos 0,05 (g) miRebul jams gamoaklos 0,5 (d) miRebul jams miumatos 0,5 (e) miRebul jams miumatos 5

25

68. Tu ( ) ( 64·6· 231

231 −=+ xx ) , maSin 2x =

(a) 2 (b) 4 (g) 6 (d) 8 (e) 10

69. ABCD oTxkuTxedi BK monakveTiT dayofilia samkuTxedad da marTkuTxedad (ix. naxazi). am oTxkuT-

xedis BC gverdis sigrZea 7 sm, CD gverdisa _ 3 sm, xolo AD gverdisa _ 11 sm. ramdeni santimetria AB gverdis sigrZe?

(a) 4 (b) 5 (g) 6 (d) 7 (e) 8

70. erT-erTi wlis 1 maisi samSabaTi iyo. ra ricxvi iqneba am Tvis bolo SabaTi?

(a) 26 (b) 28 (g) 29 (d) 30 (e) 31

71. giorgim Sekriba ori naturaluri ricxvis kvadratebi. CamoTvlilTagan romeli SeiZleba iyos giorgis mier Sekrebis Sedegad miRebuli ricxvi?

(a) 3 (b) 6 (g) 9 (d) 12 (e) 17

26

72. M qalaqidan N qalaqisaken ori avtomobili gamovida. pirveli avtomobilis siCqarea 70 km/sT, xolo meoresi _ 80 km/sT. avtomobilebi Tanabari siCqariT, Seuferxeblad moZraobdnen. pirveli avtomobili N qalaqSi 4 saaTSi Cavida.

ramden saaTSi Cavidoda meore manqana imave gziT N qalaqSi? (a) 2 sT (b) 2,5 sT (g) 3 sT (d) 3,5 sT (e) 4 sT

73. marTkuTxedis mcire gverdi tolgverda samkuTxedis gverdze mdebareobs. tolgverda samkuTxedisa da marTkuTxedis

gverdebiT Sedgenili blagvi kuTxe α-s tolia (ix. naxazi). ramdeni gradusia α kuTxis sidide? (a) 120° (b) 135° (g) 140° (d) 145° (e) 150°

74. erToblivi firmis dasafuZneblad daTom 3 aTasi lari daxarja, giorgim _ 5 aTasi lari. firmis yovelTviur mogebas isini am danaxarjebis proporciulad inawileben. ramden lars miiRebs giorgi firmisgan ianvarSi, Tu firmis mogeba am

TveSi 1600 laria? (a) 1250 (b) 1200 (g) 1100 (d) 1000 (e) 900

75. rgolebSi iseTi ricxvebia Cawerili, rom did rgolSi Cawerili ricxvebis jami 2-jer metia patara rgolSi Cawerili ricxvebis

jamze (ix. naxazi). risi tolia n ? (a) 6 (b) 5 (g) 4 (d) 3 (e) 2

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raodenobrivi Sedareba

SeadareT erTmaneTs A da B svetebis ujrebSi mocemuli raodenobebi. Tu A svetis ujraSi mocemuli raodenoba metia B svetis Sesabamis ujraSi

mocemul raodenobaze, airCieT (a);

Tu B svetis ujraSi mocemuli raodenoba metia A svetis Sesabamis ujraSi mocemul raodenobaze, airCieT (b);

Tu ujrebSi mocemuli raodenobebi tolia, airCieT (g);

Tu mocemuli informacia sakmarisi araa imis dasadgenad, romeli raodenobaa

meti, airCieT (d).

A B

76.

svetovan diagramebze miTiTebulia, B da Cqveynebis moqalaqeTa ramdenma procentma icis

franguli, germanuli an inglisuri enebi.

(a) (b) (g) (d)

inglisuri enis

mcodne moqalaqeTa

raodenoba B qveyanaSi

franguli enis mcodne

moqalaqeTa

raodenoba C qveyanaSi

77.

Taroze sul 40 wigni awyvia. wignebis 54 nawilze

meti qarTulia, xolo qarTuli wignebis 41

nawilze meti _ sabavSvo.

(a) (b) (g) (d)

6

28

am Taroze dawyobili

qarTuli sabavSvo

wignebis raodenoba

78.

dadebiTwevrebiani mimdevrobis yoveli wevri, dawye-

buli meore wevridan, mis wina wevrze 2-jer metia. a8 am mimdevrobis me-8 wevria, a5 _ me-5 wevri.

(a) (b) (g) (d)

858 aa :

79.

gamuqebuli

oTxkuTxedisa da

samkuTxedis yvela

wvero toluj-

redebiani badis

kvanZebs emTxveva.

(a) (b) (g) (d)

ABCD oTxkuTxedis farTobi

EFK samkuTxedis farTobi

80.

29 litri badagiT ramdenime 3-litriani da

ramdenime 7-litriani qila gaavses.

(a) (b) (g) (d)

badagiT savse qilebis

saerTo raodenoba 7

81.

nebismieri a da b ricxvebisaTvis baba −=∗ 2 .

(a) (b) (g) (d) ( ) aa ∗∗1 ( ) aa ∗∗2

82.

wrewirze mdebare M da N wertilebis SemaerTebeli monakveTis sigrZea c.

(a) (b) (g) (d)

am wris farTobi 221 c

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amocanebi

83. xaWapuris 8 naWridan ramdenime oTxad daWres. ramdeni naWeri dauWriaT oTxad, Tu sul 23 naWeri miiRes?

(a) 2 (b) 3 (g) 4 (d) 5 (e) 6

84. marTkuTxa sakoordinato sibrtyeze mocemuli wre-wiris centri koordinatTa saTaves emTxveva. A da C wer-tilebi am wrewirze mdebareobs. C wertilis orive ko-ordinati da A wertilis meore koordinati miTiTe-bulia naxazze. A wertilis pirveli koordinati a =

(a) 3 (b) 4 (g) 5 (d) 6 (e) 7

85. karadaSi mxolod TeTri, Savi da lurji maisurebi awyvia. maTi 75 nawili

TeTria, 71 nawili _ Savi, 4 maisuri ki _ lurji. sul ramdeni maisuria

karadaSi?

(a) 7 (b) 14 (g) 21 (d) 28 (e) 35

86. tyviis msrolelma turnirisaTvis mosamzadeblad garkveuli raodenobis vaznebi iyida. igi savarjiSod yoveldRiurad erTi da imave raodenobis vaznebs

xarjavda. varjiSis dawyebidan 12 dRis Semdeg mas darCenili hqonda 2600 vazna, 17 dRis Semdeg ki _ 1600 vazna. kidev ramden dRes eyofoda savarjiSod vaznebi tyviis msrolels?

(a) 4 (b) 5 (g) 6 (d) 7 (e) 8

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monacemTa analizi

firmis mogeba da zarali mis Semosavlebsa da xarjebzea damokidebuli. Tu

firmis Semosavlebi metia xarjebze, maSin firmis mogeba Semosavlebisa da xarjebis

sxvaobis tolia. Tuki Semosavlebi naklebia xarjebze, maSin firma zaralobs da

zarali xarjebisa da Semosavlebis sxvaobis tolia.

diagramaze mocemulia, ramden aTas lars Seadgens turistuli firmis

Semosavlebi da xarjebi Tveebis mixedviT mTeli wlis ganmavlobaSi.

diagramis mixedviT upasuxeT Semdeg 4 SekiTxvas:

87. romel TveSi iyo firmis xarjebi 20 aTasi laris toli? (a) aprilSi

(b) maisSi

(g) ivnisSi

(d) oqtomberSi

(e) noemberSi

88. moigo Tu izarala firmam noemberSi da ramdeni? (a) izarala 10 aTasi lari (b) izarala 15 aTasi lari (g) arc mougia, arc uzaralia

(d) moigo 5 aTasi lari (e) moigo 10 aTasi lari

89. sul ramdeni aTasi lari moigo firmam wlis meore meoTxedSi (aprilis, maisis da ivnisis Tveebis ganmavlobaSi)? (a) 5 aTasi lari (b) 10 aTasi lari (g) 15 aTasi lari (d) 20 aTasi lari (e) 25 aTasi lari

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90. qvemoT CamoTvlilTagan romeli daskvnaa marTebuli? (a) firmis yovelTviuri Semosavlebi aRemateboda yovelTviur xarjebs

(b) firmis yovelTviuri Semosavlebi wlis ganmavlobaSi TandaTan izrdeboda,

xarjebi ki _ TandaTan mcirdeboda

(g) zafxulis TveebSi firmis Semosavlebi yovelTvis aRemateboda xarjebs,

Semodgomis TveebSi ki _ ara

(d) zamTris TveebSi firmis Semosavlebi yovelTvis aRemateboda xarjebs,

gazafxulis TveebSi ki _ ara

(e) firmis Semosavlebi gazafxulis TveebSi ufro meti iyo, vidre _ zafxulis

TveebSi

amocanebi

91. raRac ricxvis 8-ze gayofisas miRebuli naSTi 5-is tolia. qvemoT Camo-TvlilTagan romlis toli SeiZleba iyos naSTi imave ricxvis 24-ze gayofisas? (a) 3

(b) 12 (g) 16 (d) 19 (e) 21

92. sandro yoveldRe jiriTobs ipodromze, nika ki _ dRegamoSvebiT. jiriTis yovel dRes TiToeuli ymawvili mejinibes uxdis 8 lars. maqsimum ramdeni lari SeiZleba miiRos mejinibem maTgan zedized Svidi dRis ganmavlobaSi?

(a) 72 (b) 80 (g) 84 (d) 88 (e) 96

93. marTkuTxedi dayofilia oTx marTkuTxedad, romelTagan erTis perimetri 12 m-ia, meoris _ 18 m, mesamisa ki _ 20 m (ix. naxazi). ramdeni metria meoTxe marTkuTxedis perimetri?

(a) 22 (b) 24 (g) 26 (d) 28 (e) 30

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94. gundSi, romelSic arCili TamaSobs, arCilze maRalia 12 moTamaSe. roca SearCies am gundis 10 yvelaze dabali moTamaSe, maT Soris moxvda arCilic. SerCeulTagan arCilze maRali aRmoCnda 4 moTamaSe. sul ramdeni moTamaSe yofila arCilis gundSi?

(a) 14 (b) 16 (g) 18 (d) 20 (e) 22

95. x da y iseTi naturaluri ricxvebia, rom yx 2+ luwia. qvemoT

CamoTvlilTagan romeli SeiZleba iyos kenti? (a) 4+xy(b) yx 4+(g) xyx +(d) yx 23 +(e) yx +2

96. nikas erTnairi xis kubebi hqonda, ramdenime maTgani man Suaze gaxerxa. am naxevrebisa da kubebisagan nikam mTliani

sveti aago (ix. naxazi), ise, rom araferi darCenia.

sul ramdeni kubi hqonia nikas Tavdapirvelad? (a) 7 (b) 10 (g) 12 (d) 14 (e) 16

97. maRaziaSi 4 kg vaSli da 2 kg msxali erTad imdenive Rirs, ramdenic _ 1 kg vaSli da 4 kg msxali erTad. ninom am maRaziaSi 4,5 kg vaSli iyida. ramdeni kilogrami msxlis yidva SeeZlo ninos imave TanxiT?

(a) 3 (b) 2,5 (g) 2 (d) 1,5 (e) 1

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98. daxlze 4 nesvi devs. maT wonaTa saSualo 8 kilogramia. am nesvebidan sami iseTia, rom TiToeulis wona 9 kg-ze metia da 10 kg-ze naklebi. qvemoT CamoTvlilTagan romlis toli SeiZleba iyos meoTxe nesvis wona?

(a) 2 kg (b) 3 kg (g) 5 kg (d) 6 kg (e) 7 kg

99. ramdeni procentiT gadiddeba marTkuTxedis farTobi, Tu marTkuTxedis

sigrZes gavadidebT 60%-iT, xolo siganes SevamcirebT 20%-iT? (a) gadiddeba 12%-iT

(b) gadiddeba 20%-iT

(g) gadiddeba 28%-iT

(d) gadiddeba 40%-iT

(e) gadiddeba 42%-iT

100. Tu wrewirze moniSnulia 5 sxvadasxva wertili: A, B, C, D da E, maSin sul 6 samkuTxedia iseTi, romelTa erTi wvero A wertilSia, xolo danarCeni ori wvero B, C, D an E wertilebSia (ix. naxazi).

vTqvaT, wrewirze moniSnes kidev erTi wertili K. sul ramdeni iqneba iseTi samkuTxedi, romelTa erTi

wvero A wertilSia, xolo danarCeni ori wvero B, C, D, E an K wertilebSia?

(a) 9 (b) 10 (g) 11 (d) 12 (e) 13

34