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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
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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
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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
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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
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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
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