verbaluri nawili 1. wyali : zrva (a) varskvlavi : ca (b) qvisa : udabno (g) yvavili : mindori (d) fotoli : tye

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2 verbaluri nawili analogiebi am saxis davalebebsi mocemulia muqi SriftiT gamokvetili ori sityva (sawyisi wyvili), romelta mnisvnelobebs Soris arsebobs garkveuli mimarteba. daadginet, ra saxisaa es mimarteba. savaraudo pasuxta yovel variantsi mocemulia, aseve, mnisvnelobit urtiertdakavsirebuli sityvebis wyvili. airciet matgan is wyvili, romelsic sityvata mnisvnelobebs Soris mimarteba sawyis wyvilsi arsebuli mimartebis msgavsia (analogiuria). pasuxis arcevisas gaitvaliswinet wyvilebsi sityvata Tanmimdevroba. 1. wyali : zrva (a) varskvlavi : ca (b) qvisa : udabno (g) yvavili : mindori (d) fotoli : tye 2. rikulebiani : qongurebiani (a) mrvrie : gazavebuli (b) teniani : wvimiani (g) gamwvirvale : gamwoli (d) ujredebiani : calxaziani 3. reklama : interesi (a) acra : imuniteti (b) matiane : istoria (g) amocana : minisneba (d) qaragma : saidumlo 4. marsruti : winaswar dasaxuli gza (a) manevri : strategia (b) traeqtoria : mozraoba (g) gezi : mimartuleba (d) orientiri : tendencia 5. burji : qvakutxedi (a) cixe : koski (b) gumbati : saxuravi (g) jebiri : moajiri (d) fuze : sazirkveli a

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. 6. nuravin ityvis, rom sinamdvile. aramc da aramc! Zlieri poeti, rom Cveulebriv, yoveldriur ambavsi, ubralo sagansi. (a) ar aris saintereso poetistvis / imit rodia / daiwyebs STagonebis wyaros Zebnas (b) ar aris saintereso poetistvis / swored imitaa / saintereso mxares SeamCnevs da asaxavs (g) Rirebul masalas gvazlevs poeziistvis / imit rodia / ver SeZlebs STagonebis wyaros povnas (d) Rirebul masalas gvazlevs poeziistvis / swored imitaa / ezebs saintereso mxareebs 7. qveynis ar gvazlevs safuzvels fiqristvis, rom, raki qveyana, aketos yvelaferi, rac moesurveba., mas, rogorc moqalaqes,, vidre hqonda manamde, sanam qveynis moqalaqe gaxdeboda. (a) dapyroba / Tavisuflebas kargavs, adamians arar aqvs ufleba / martlac / moqmedebistvis ufro farto asparezi ezleva / dapyrobili (b) gatavisufleba / Tavisufalia, adamians aqvs ufleba / piriqit / kidev ufro meti sapasuxismgeblo movaleoba ucndeba / damoukidebeli da Tavisufali (g) gatavisufleba / Tavisufalia, adamians arar ezleva ufleba / martlac / kidev ufro meti sapasuxismgeblo movaleoba ucndeba / dapyrobili (d) dapyroba / Tavisuflebas kargavs, adamians ezleva ufleba / piriqit / moqmedebistvis naklebad farto asparezi rceba / damoukidebeli da Tavisufali a

4 8. Zalauflebis centralizaciis amtkiceben, rom mtavroba ganagebs sxvadasxva tipis dasaxlebul adgilebs, mati mkvidrni Tavad SeZlebdnen amas. es SeiZleba martalic iyos, Tuki ganatlebita da aqtiurobit gamoircevian, xolo uswavleli, inertuli, morcilebas Cveulia. (a) momxreebi / uket / vidre / centraluri xelisuflebis warmomadgenlebi / mosaxleoba (b) mowinaarmdegeni / ise kargad ver / rogorc / centraluri xelisuflebis warmomadgenlebi / mosaxleoba (g) momxreebi / iseve kargad / rogorc / dasaxlebata mkvidrni / centraluri xelisuflebis TanamSromelTa umravlesoba (d) mowinaarmdegeni / uket / vidre / dasaxlebata mkvidrni / centraluri xelisuflebis TanamSromelTa umravlesoba 9., adamianebi daarwmuno, rom mat ufro iolad daainteresebt, vidre. (a) ar aris Zneli / sakutari saqme Tavad aketon / politikuri dapirebebit / TavianTive saxlis SekeTebiT (b) ar aris Zneli / mat gasaketebels axali da kargi mtavroba gaaketebs / TavianTi saqmis Tavad gaketebis perspeqtivit / politikuri dapirebebit (g) ertob rtuli amocanaa / sakutari saqme Tavad aketon / samefo karis etiketis wvrilmanebit / TavianTive saxlis SekeTebiT (d) ertob rtuli amocanaa / mat gasaketebels axali da kargi xelisufleba gaaketebs / samefo karis etiketis wvrilmanebit / TavianTi saqmis Tavad gaketebis perspeqtivit a

5 logika am saxis davalebebi gansxvavdeba ertmanetisgan 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. 10. mocemulia: yvela satavgadasavlo romani sainteresoa. am avtoris yvela romani satavgadasavlo Janrisaa. qvemot CamoTvlilTagan romeli daskvna gamomdinareobs mocemuli debulebebidan? (a) yvela saintereso romani satavgadasavlo Janrisaa (b) yvela saintereso romani am avtorisaa (g) mxolod satavgadasavlo romanebia saintereso (d) am avtoris yvela romani sainteresoa 11. ana, mari, sofo da nino mrgvali magidis irgvliv sxedan. mwvanekabiani, romelic arc anaa da arc _ mari, cisferkabiansa da ninos Soris zis. TeTrkabiani ki zis vardisferkabiansa da maris Soris. qvemot mocemulia gogonebis kabebis ferebis ori SesaZlo ganawileba: 1. ana _ vardisferi, mari _ TeTri, sofo _ mwvane, nino _ cisferi 2. ana _ TeTri, mari _ cisferi, sofo _ mwvane, nino _ vardisferi romeli matgania SesaZlebeli amocanis pirobebis Tanaxmad? (a) pirveli (b) meore (g) arc erti (d) SeuZlebelia dadgena 12. mocemulia sami winadadeba: I. arc ert niangs ar SeuZlia frena. II. yvela niangi zarmacia. III. arc ert zarmac cxovels ar SeuZlia frena. qvemot CamoTvlilTagan romeli debuleba arwers sworad am winadadebebs Soris mimartebas? (a) I da II winadadebebidan gamomdinareobs III (b) I da III winadadebebidan gamomdinareobs II (g) II da III winadadebebidan gamomdinareobs I (d) am sami winadadebidan arc erti ar gamomdinareobs danarceni oridan a

6 13. evoluciuri biologiis zogierti mkvlevari spilos gansakutrebit didi yurebis Camoyalibebas xsnis imit, rom didi yurebi spilos sxeulis temperaturis regulirebasi exmareba _ yurebis mozraobis Sedegad matsi sisxli grildeba, rac sxeulis temperaturis Semcirebasac iwvevs. qvemot CamoTvlilTagan romeli faqtis dadastureba ganamtkicebda am varauds? (a) spilos afrikuli da aziuri saxeobebi mnisvnelovnad gansxvavdeba ertmanetisagan sxeulisa da yurebis zomit, Tumca, yurebisa da sxeulis zomis Tanafardoba orive saxeobasi ertnairia. (b) spilos afrikuli saxeoba gacilebit ufro socialuria da ufro aqtiurad iyenebs komunikaciistvis bgerit signalebs, vidre aziuri saxeoba, romelsac ufro patara yurebi da naklebad ganvitarebuli smenis aparati aqvs. (g) spilos afrikuli da aziuri saxeobebi daaxloebit ertnair klimatur pirobebsi arseboben, Tumca, isini mravali garegnuli nisnit gansxvavdebian ertmanetisgan, magalitad, bewvis sixsirit, esvebisa da yurebis zomit da sxva. (d) spilos afrikuli saxeobis saarsebo garemo ufro cxeli klimatit xasiatdeba, vidre aziuri saxeobisa, romelsac, mraval sxva nisantan ertad, bevrad ufro mcire zomis yurebic ganasxvavebs afrikeli `TanamoZmisgan~. 14. mocemulia winadadebata wyvilebi: I. TbilisSi arc erti sanayine ar aris `cisartyelaze~ uketesi. `cisartyelaze~ uketesi sanayine ar arsebobs. II. ar SeiZleba manqanis dazvra, rodesac SuqniSanze witeli antia. Tu SuqniSanze witeli ar antia, SeiZleba manqanis dazvra. III. yoveltvis scade, ar gaanawyeno sxva adamianebi. yoveltvis scade, asiamovno sxva adamianebs. IV. ar aris martali, rom gusin ar iwvima. cdeba is, visac hgonia, rom gusin ar iwvima. romeli wyvili Sedgeba erti da imave Sinaarsis mqone winadadebebisgan? (a) (b) (g) (d) I II III IV a

7 wakitxuli teqstis gaazreba yuradrebit waikitxet da gaiazret teqsti. TiToeuli SekiTxvis savaraudo pasuxebidan airciet is varianti, romelic martebulia mocemuli teqstis mixedvit. arqaikis* epoqasi berzenta ganfenam mtel xmeltasua zrvis auzsi, mravalricxovani koloniebis daarsebam bizgi misca elinta mier armosavluri kulturuli tradiciebis aqtiurad atvisebas. armosavluri, pirvel rigsi ki egvipturi skulpturis gavlenit, TandaTan iwyebs Camoyalibebas sakutriv elinuri qandakeba. saberznetsi popularuli xdeba rogorc skulpturuli bareliefebi, aseve, e. w. mrgvali qandakebebi. am periodis xelovnebis ZeglebSi gamosaxul adamianebs saxeze Rimili arbewdviat, arqauli Rimili, romelsac Seumcdarad SeuZlia gvikarnaxos, Tu romeli epoqis nawarmoebia Cven Tvalwin. arqaikis epoqis qandakebistvis yvelaze nisandoblivi gaxda WabukTa anu kurosebis da qalwulta anu koreebis mtliani qandakebebis Seqmna. arqauli** qandakebis orive tipisatvis damaxasiatebeli iyo mkacri frontaluroba _ arqauli figura absoluturad umoqmedoa da gamosaxulia anfassi. qandakebis centralur aresi warmosaxviti RerZi rom gavavlot, igi figuras or simetriul nawilad gayofs. sxeulis formebi anatomiuri TvalsazrisiT sworad aris agebuli, magram xazebis ertgvari kutxovaneba, sxeulis nawilebis, agretve, varcxnilobis `gaqvavebuloba~ moqandakes jer kidev ar azlevs sasualebas, `suli STaberos Tavis qmnilebas~. SesaZloa, am miznis misarwevad uzrav sxeulsi mas Semoaqvs erti arsebiti Strixi _ Rimili, romelic aris Zv. w. VIII-VI saukuneebis plastikasi adamianis gamosaxulebis ert-erti yvelaze ufro tipuri nisani. amgvari pirobiti Rimili qandakebas TiTqos sicocxles aniwebs. arqaikis epoqis qandakebis ert-ert sayuradrebo nimusad unda mivicniot momrimari `kore broweulit~. aq jer kidev didia armosavluri sqemebis gavlena, magram SeiniSneba gamosaxulebis simetriuli uzraobis darrvevis cdebic _ kores odnav moxril xelsi uwiravs broweuli. Zv. w. VI saukunidan skulptori ukve cdilobs, gamosaxos mozraoba, rac TandaTan atavisuflebs mas frontalurobis dacvisgan da gamoqandakebul sxeuls naklebad SeboWils xdis. gvian arqaul periodsi moqandake ukve savsebit bunebriv formebs aniwebs adamianis figuras. Zv. w. 500 wlistvis koreta saxidan nel-nela qreba Rimili, rac imis mauwyebelia, rom arqauli stili TandaTan adgils utmobs klasikurs. kunzul eginaze afaias tazris frontonebs*** amkobs skulpturuli kompoziciebi, romlebic gadmoscems troas omis epizodebs. ori Zveli frontoni daaxloebit Zv. w. 510 wlit TariRdeba, xolo mesame, romlitac Zveli armosavlet frontoni SeucvliaT, daaxloebit oci wlit ufro gviandelia. dasavletis frontonze gamosaxuli qalrmert atenas msvidi, frontaluri figura kontrasts qmnis brzolis SedarebiT dinamikur scenebtan. axal, armosavletis frontonzec troas brzolebia gamokvetili, centrsi kvlav atena Cans. TiTqos oci weli, romelic afaias tazris qandakebata armosavletis jgufs asorebs dasavletis frontonis skulpturebisgan, ar aris didi dro, magram gansxvaveba mat Soris stilsa da teqnikasi mnisvnelovania. armosavletis frontonis skulpturebsi meti Tavisufleba da dinamizmia, sxeulta modelireba gvicvenebs adamianis gamoqandakebis axal koncefcias, romelic esoden damaxasiatebeli gaxdeba klasikuri epoqis monumenturi skulpturisatvis. arqauli Rimili odnavra Tu gaikiafebs zogierti figuris bageze. *arqaika _ berznuli civilizaciis ganvitarebis periodi _ Zv. w. VII-VI saukuneebi. **arqauli _ aq: igulisxmeba _ arqaikis epoqis. ***frontoni _ Senobis fasadis zeda, Cveulebriv, samkutxa nawili a

8 15. ram Seuwyo xeli arqaikis periodis berznuli qandakebis formirebas? (a) skulpturuli bareliefebis popularobam xmeltasua zrvis qveynebsi (b) armosavluri kulturuli tradiciebis intensiurad atvisebam (g) egvipturi e. w. mrgvali qandakebebis gavrcelebam saberznetsi (d) xmeltasua zrvis auzsi mravalricxovani berznuli koloniebis arsebobam 16. ris sailustraciod aris SemoTavazebuli teqstsi qandakebis centralur aresi warmosaxviti RerZis gavleba? rata TvalsaCino gaxdes, rom: (a) absoluturad umoqmedo arqauli figuris sxeulis formebis simetria darrveulia (b) arqaul figuras axasiatebs xazebis ertgvari kutxovaneba da sxeulis nawilebis, magalitad, varcxnilobis `gaqvavebuloba~ (g) arqauli qandakeba, ZiriTadad, warmodgenilia anfassi, ar gamosaxavs mozraobas, statikuria (d) frontaluri figurebis gamosaxva sasualebas azlevs arqaikis periodis moqandakes, Seqmnas dinamikuri kompoziciebi 17. arqauli periodis xelovnebis ZeglebSi gamosaxul adamianebs saxeze Rimili arbewdviat, radgan: (a) es aris arsebiti Strixi kurosebisa Tu koreebis mkacri frontalurobis xazgasasmelad (b) es aris tipuri nisani, romelmac unda Seumcdarad gvikarnaxos ama Tu im qandakebis Seqmnis dro (g) moqandake, savaraudod, cdilobs, am StrixiT `suli STaberos Tavis qmnilebas~ (d) moqandake cdilobs, gamoiyenos am periodis plastikur xelovnebasi damkvidrebuli ertgvari pirobiti gamomsaxvelobiti sasualebebi 18. ra funqcia aqvs teqstsi epizods _ `kore broweulit~? (a) gamokvets tendencias, gatavisufldes moqandake simetriuli uzraobis dacvisgan da gamosaxos figura anatomiuri sizustit (b) gamokvets tendencias, SeinarCunos moqandakem armosavluri sqemebis ertguleba da daicvas figuris tradiciuli frontaluroba (g) gamokvets or mnisvnelovan faqtors: Zveli armosavluri sqemebis radikalurad Secvlis mcdelobas da kores saxidan Rimilis gaqrobas (d) gamokvets or mnisvnelovan faqtors: tradiciuli sqemebis gavlenas arqauli qandakebis gamokvetisas da axal nisans _ moxrili xeli `acocxlebs~ kores a

9 19. afaias tazris frontonebze gamosaxulia troas omis epizodebi. dasavletis frontonze gamosaxulia brzolasi dacemuli meomari, romelic irimeba, armosavletis frontonzec aris gamosaxuli brzolasi dacemuli meomari, magram is ar irimeba. misi dazabuli sxeuli tkivils, gancdas gamoxatavs. rit SeiZleba avxsnat es gansxvaveba? (a) dasavletis frontonze gamosaxuli meomari brzolasi daeca, Tumca is Zlier metoqeze imarjvebs da irimeba, armosavletis meomari ki _ damarcxebulia (b) dasavletis frontonze gamosaxuli dacemuli meomris Rimili am epoqistvis nisandoblivi Strixia, armosavletis meomari ki ukve gardamaval epoqas ekutvnis (g) dasavletis frontonze gamosaxuli dacemuli meomari brzolasi marcxdeba da es simwris sicilia, armosavletis meomari ki ver malavs tkivils (d) dasavletis frontonze gamosaxuli dacemuli meomris Rimili ucveulo detalia arqaikisatvis, armosavletis frontonis meomari ki zustad migvanisnebs klasikuri skulpturis principebze 20. raze migvanisnebs teqstis bolo fraza: `arqauli Rimili odnavra Tu gaikiafebs zogierti figuris bageze~? (a) brzolis epizodebis gadmocemisas moqandake arar gamosaxavs momrimar meomrebs, radgan upiratesobas aniwebs qandakebis Sinaarsis Sesabamisi emociis gamosaxvas (b) sxeulta modelireba gvicvenebs adamianis gamoqandakebis axal koncefcias, rac gulisxmobs frontalurobis SenarCunebas (g) arqaul epoqasi Camoyalibebuli xelovnebis stili da teqnika kidev ufro ixveweba klasikuri epoqis monumentur skulpturasi (d) arqauli epoqa adgils utmobs klasikurs, xelovnebasi adamianis statikur gamosaxulebas cvlis _ bunebrivi, plastikuri a

10 analogiebi am saxis davalebebsi mocemulia muqi SriftiT gamokvetili ori sityva (sawyisi wyvili), romelta mnisvnelobebs Soris arsebobs garkveuli mimarteba. daadginet, ra saxisaa es mimarteba. savaraudo pasuxta yovel variantsi mocemulia, aseve, mnisvnelobit urtiertdakavsirebuli sityvebis wyvili. airciet matgan is wyvili, romelsic sityvata mnisvnelobebs Soris mimarteba sawyis wyvilsi arsebuli mimartebis msgavsia (analogiuria). pasuxis arcevisas gaitvaliswinet wyvilebsi sityvata Tanmimdevroba. 21. akrobati : wonasworobas icavs (a) arlekini : nirabs iketebs (b) komedianti : politikoss dascinis (g) jambazi : arenaze gamodis (d) iluzionisti : STabeWdilebas qmnis 22. apatia : interesi (a) sasowarkveta : imedi (b) SiSi : riski (g) warmateba : sixaruli (d) eiforia : diskomforti 23. sinjara : kolba (a) gemi : kaiuta (b) akvani : hamaki (g) anbani : bgera (d) TariRi : ricxvi 24. safuzveli : fundamenti (a) fena : Sre (b) dedamiwa : qanebi (g) kvali : nafexuri (d) xmeleti : miwa 25. jawvi : jawvuri reaqcia (a) TaRi : TaRovani gadaxurva (b) kenwi : kenwovani daavadeba (g) vertikali : vertikaluri RerZi (d) sazrvari : zrvruli sicqare a

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. 26. rodesac dapyrobili xalxi, dampyrobi ki, gamarjveba imas, rom adre Tu gvian igi da miicnevs. (a) ganatlebulia / naxevrad veluri / barbarosistvis uzrunvelyofs / civilizebulis doneze amarldeba / dapyrobil xalxs Tavis tol-sworad (b) naxevrad veluria / ganatlebuli / dampyroblisatvis sulac ar gulisxmobs / dapyrobili xalxis ganvitarebis dones miarwevs / mas Tavis tol-sworad (g) ganatlebulia / naxevrad veluri / barbarosistvis uzrunvelyofs / dapyrobili xalxis ganvitarebis dones daswevs / mas Tavisze ufro marla mdgomad (d) naxevrad veluria / ganatlebuli / dampyroblisatvis sulac ar gulisxmobs / civilizebulis doneze amarldeba / dapyrobil xalxs Tavisze ufro marla mdgomad 27. iqneboda, adamianta morvaweobis sxvadasxva sferosi arsebuli Tanasworoba politikis gavrcelebuliyo., mravali TvalsazrisiT darceniliyvnen da mierwiat yvela sferosi TanasworobisaTvis. (a) gaugebari / sferosic rom ar / warmoudgenelia / Tanaswori adamianebi ert romelime sferosi rom aratanasworni / adre Tu gvian ar (b) gasakviri / sferosic rom / ufro ioli warmosadgenia / Tanasworobis miuxedavad, adamianebi politikasi aratanasworni / odesme mainc (g) gasakviri sul ar / sferosic rom / ufro warmoudgenelia / utanasworobis miuxedavad, adamianebi utanasworoni politikasi mainc ar / odesme mainc (d) gaugebari sul ar / sferosi rom ar / ioli warmosadgenia / utanasworobas SeCveuli adamianebi politikasic aratanasworni / adre Tu gvian mainc 28. zogjer ucxouri daxmarebis Sedegad warmoqmnili kavsiri irebs urtiertdamokidebulebis saxes, romelsic saxelmwifoze zemoqmedebis mnisvnelovani berketebi moepoveba. es berketebi kidev ufro, roca donori saxelmwifo avtoritaruli an totalitarulia. (a) simetriuli / TiToeul saxelmwifos meore / araefeqturia (b) asimetriuli / TiToeul saxelmwifos meore / efeqturia (g) asimetriuli / donor saxelmwifos daxmarebis mimreb / Zlieria (d) simetriuli / donor saxelmwifos daxmarebis mimreb / Zlieria a

12 29. platoni sokrates miawerda poeziis Sesaxeb Semdeg azrs: is, rac poetebs leqsebis weris unars azlevs, aris instinqti an STagoneba,, rasac winaswarmetyvelebsa Tu misnebtan vxvdebit xom TavianT satqmels ise gvamcnoben, rom esmit misi mnisvneloba. (a) ara sibrzne, aramed Taviseburi / rarac imis msgavsi / es ukanasknelni / odnavadac ar (b) Taviseburi sibrzne, da ara _ / rarac imis msgavsi / matgan gansxvavebit, poetebi / odnavadac ar (g) ara sibrzne, aramed Taviseburi / Zalian gansxvavebuli imisgan / matgan gansxvavebit, poetebi / Zalian kargad (d) Taviseburi sibrzne, da ara _ / Zalian gansxvavebuli imisgan / es ukanasknelni / Zalian kargad logika am saxis davalebebi gansxvavdeba ertmanetisgan 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. 30. saqartvelosi nazvis xeebis dazianebisa da gaxmobis procesma sakmaod didi masstabebi miiro. specialistebis erti jgufis azrit, amis ZiriTad mizezad unda mivicniot lafniwamia xowos gavrceleba, romelic ucxoetidan Semotanil kedris morebs Semohyva. Tumca, zogierti ekologi varaudobs, rom nazvebis intensiuri dazianeba ganpirobebulia xowoebis bunebrivi mtrebis mkvetri SemcirebiT. qvemot CamoTvlilTagan romeli faqti ganamtkicebs am varauds? (a) ucxoetidan Semoyvanilma ciyvis ert-ertma saxeobam gandevna adgilobrivi jisis ciyvebi, romlebic, pirvelisgan gansxvavebit, ar emterebodnen kodalebs da sxva frinvelebs (b) ucxoetidan mravlad Semoitanes sxvadasxva jisis xis morebi, romlebsac, lafniwamias garda, xis mavnebeli mwerebis sxva saxeobebic Semohyva (g) nazvnaris intensiuri dazianebis periods daemtxva sxva regionebidan rogorc lafniwamias, iseve kaliebis SemoWra, romlebic seriozul safrtxes uqmnis mcenareul safars (d) xis mavneblebis gavrcelebis ert-ert mnisvnelovan faqtorad miicneva e. w. monokulturis, anu erti saxeobis xeebisgan Semdgari tyeebis gaseneba, nazvnari swored monokulturuli tyis kategorias miekutvneba a

13 31. qvemot mocemul msjelobasi dasvebulia Secdoma logikis TvalsazrisiT: arc erti ketili adamiani ar aris egoisti da yvela egoisti adamiani ubeduria, masasadame, arc erti ketili adamiani ar aris ubeduri. qvemot CamoTvlilTagan romeli msjeloba Seicavs imave tipis Secdomas? (a) arc erti ciuri sxeuli ar mozraobs sinatlis sicqarit da zogierti ciuri sxeulis orbita elifsuria, masasadame, sinatlis sicqarit mozravi arc erti sxeulis orbita ar aris elifsuri. (b) arc erti reptilia ar aris Tbilsisxliani da yvela reptilia xerxemliania, masasadame, zogierti Tbilsisxliani cxoveli ar aris xerxemliani. (g) zogiert balaxs samkurnalo Tvisebebi aqvs da tradiciuli medicina samkurnalo Tvisebebis mqone yvela balaxs iyenebs, masasadame, tradiciuli medicina ar iyenebs arc ert balaxs, romelsac samkurnalo Tvisebebi ar aqvs. (d) arc erti kargi mecnieruli Teoria ar aris absoluturad utyuari da yvela absoluturad utyuari Teoria trivialuria, masasadame, arc erti kargi mecnieruli Teoria ar aris trivialuri. 32. statistikuri monacemebis mixedvit, kerzo seqtorsi dasaqmebuli specialistis Semosavali sasualod 50%-iT aremateba imave kvalifikaciis mqone specialistis Semosavals sajaro samsaxursi. amis miuxedavad, sajaro samsaxursi marali kvalifikaciis specialistebis nakleboba ar aris. amis safuzvelze eqspertma ivarauda, rom sajaro moxeleebis musaobis ZiriTadi motivi ar aris finansuri daintereseba. qvemot CamoTvlilTagan romeli vitareba ganamtkicebs am varauds? (a) kerzo seqtorsi dasaqmebuli specialistebistvis Tanamdebobrivi dawinaurebis da, Sesabamisad, anazraurebis gazrdis albatoba ufro mcirea, vidre _ sajaro samsaxursi dasaqmebultatvis (b) sajaro samsaxursi specialistebis kvalifikaciis mimart ar aris imdenad marali motxovnebi, rogoric _ kerzo seqtorsi (g) kerzo seqtorsi dasaqmebuli specialistebis samusao, sazogadod, ufro stresulia, vidre sajaro samsaxursi dasaqmebul specialistta samusao (d) sajaro mosamsaxureebi damatebiti SeRavaTebiT sargebloben, rac SedarebiT dabali xelfasebis ertgvari kompensaciaa a

14 33. dabadebis dreze salomes megobarma lamazad SefuTuli kolofit sacuqari miutana da stxova, gamoecno, Tu ra ido massi. salomem icis, rom sacuqari oridan ert-ertia _ xeltatmanebis wyvili an qudi; amastan, sacuqari an lurjia an yviteli. kolofs aweria ori winadadeba: es xeltatmanebia. es yviteli nivtia. damatebit, megobarma salomes miawoda Semdegi cnoba: Tu sacuqari lurji xeltatmanebi an yviteli qudia, masin yvelaferi, rac kolofs aweria, martalia. winaarmdeg SemTxvevaSi ki yvelaferi, rac mas aweria, tyuilia. ra acuqa megobarma salomes? (a) lurji xeltatmanebi (b) yviteli xeltatmanebi (g) lurji qudi (d) yviteli qudi 34. mocemulia: Tu CineTi gazrdis kompiuteruli teqnikis eqsports, masin taivanis an koreis ekonomika safrtxis winase armocndeba. taivanis ekonomikas safrtxe ar emuqreba. qvemot CamoTvlilTagan romeli debulebaa aucileblad WeSmariti, Tu davusvebt, rom mocemuli wanamzrvrebi WeSmaritia? (a) CineTi arar gazrdis kompiuteruli teqnikis eqsports (b) koreis ekonomika safrtxis winase armocndeba (g) CineTi kompiuteruli teqnikis eqsports arar gazrdis an koreis ekonomika safrtxis winase armocndeba (d) Tu koreis ekonomika safrtxis winase armocndeba, CineTs kompiuteruli teqnikis eqsporti gauzrdia a

15 wakitxuli teqstis gaazreba yuradrebit waikitxet da gaiazret teqsti. TiToeuli SekiTxvis savaraudo pasuxebidan airciet is varianti, romelic martebulia mocemuli teqstis mixedvit. ciur sxeulta ert-erti yvelaze lamazi da STambeWdavi nairsaxeobaa kometebi. Zvelad mat `kudian varskvlavebs~ uwodebdnen da xan mosalodneli ubedurebis, xanac siketis mauwyeblad miicnevdnen. grzeli mnati kudis mqone ciuri sxeulebi zogjer gamocndebian xolme caze da Semdeg isev gaucinardebian. kometebi, asteroidebis msgavsad, ertgvari kosmosuri narcenebia. asteroidebi im obieqtebis narcenebia, romlebic planetebad ver Camoyalibdnen. zogierti kometac SeiZleba Camoyalibdes asteroidad, Tu is dakargavs yinulis garss da misgan mxolod myari birtvi darceba. mzisgan mosorebit kometebi vizualurad ar ganircevian asteroidebisgan. magram zogjer, rodesac isini giganti planetebis Tu maxlobeli varskvlavebis gravitaciuli SeSfoTebis gamo mimartulebas icvlian da mzes uaxlovdebian, mati zedapiri xurdeba, massi Cayinuli msubuqi airebi ortqldeba da myari birtvis garsemo qmnis Rrubels e. w. komas (rac berznulad Tmas nisnavs aqedanaa saxelwodeba `kometa~). mzis gamosxivebis wneva da mzis qari misgan momdinare damuxtuli nawilakebis nakadi moqmedeben am airze, ase vtqvat, `uberaven~,,tmas~ da warmoiqmneba e. w. kudi, romelic, Cveulebriv, mzisgan sawinaarmdego mxaresaa mimartuli. kometebi, rogorc wesi, mozraoben metad gawelil orbitebze, romelta garsemo ert bruns sxvadasxva (ramdenime wlidan ramdenime milion wlamde) dros andomeben. ert-erti kometa, romelic dedamiwidan SeuiaraRebeli TvaliTac Cans da romelsac haleis kometa ewoda, yovel weliwadsi ertxel gamocndeba caze. zogierti kometa Tavis arsebobas mzestan an planetebtan SejaxebiT amtavrebs. ase moxda 1994 wels, rodesac iupiters Sumeiker-levis kometa daeca. es iyo pirveli SemTxveva kacobriobis istoriasi, rodesac adamianma Tavisi TvaliT ixila ori ciuri sxeulis Sejaxeba kosmossi. is, rac dres esoden isviatia, daaxloebit 4 miliardi wlis win, mzis sistemis Camoyalibebis dros, Cveulebrivi movlena iyo. Semdgom planetebi TandaTanobiT Camoyalibdnen da mdgomareoba stabiluri gaxda. axla Sejaxebebi, sabednierod, uarresad isviatad xdeba. dedamiwaze aseti ram ukanasknelad 1908 wels moxda, rodesac cimbirsi `tunguskis meteoriti~ Camovarda (ufro sworad, haersive afetqda) da 2 atasi kvadratuli kilometris fartobze mteli tye miwastan gaaswora. itvleba, rom es iyo mcire zomis kometa an misi natexi wels haleis kometis mtvris nawilakebis analizma acvena, rom is iyo organuli naertebit ert-erti yvelaze mdidari sxeuli mzis sistemasi. amitomac gacnda mosazreba, rom dedamiwastan Sejaxebisas kometebma wyali da organuli nivtierebebi yovel SemTxvevaSi, mati didi nawili mzis sistemis ganapira regionebidan Semoitanes. radgan kometebi yinulis, Cayinuli airisa da myari nawilisgan Sedgeba, dedamiwaze mati dacemisas da yinulis dnobisas gamotavisuflebulma wyalma da airebma xeli Seuwyo sicocxlis warmosobas Cvens planetaze. mtvaris zedapiric daserilia kometebisgan miyenebuli `WrilobebiT~. astronomebi didi xania, varaudobdnen iq wylis arsebobas, rac ass-s kosmosuri sivrcis kvlevis saagentos ert-ertma misiam martlac daadastura. kometebis mier sicocxlis Semotanis Teorias yvela mecnieri ar iziarebs. skeptikosebi miicneven, rom kometebi ver `mozidavdnen~ im raodenobis wyals, ramdenic dedamiwazea. momavali kvlevebi gvicvenebs, unda vumadlodet Tu ara Cvens arsebobas im ciur sxeulebs, romelta gamocenisac adamians mravali saukunis ganmavlobasi panikurad esinoda a

16 35. kometebisa da asteroidebis Sedarebidan irkveva, rom: (a) asteroidebi, kometebisgan gansxvavebit, mzes, rogorc wesi, ar uaxlovdebian da matze ar moqmedebs maxlobeli varskvlavebis mizidulobis Zala (b) asteroidebi da kometebi garegnulad ar gansxvavdebian ertmanetisgan, miuxedavad imisa, rom kometebi kosmosuri narcenebia, xolo asteroidebi arsemdgari planetebi (g) asteroidebs da kometebs gansxvavebuli struqtura aqvt, Tumca, garegnulad SeiZleba ertnairad gamoiyurebodnen da msgavsi warmosobisac iyvnen (d) asteroidebs, kometebisgan gansxvavebit, myari birtvi aqvt, masin rodesac kometebi mzestan miaxloebisas ortqldebian da Rrublad iqcevian 36. qvemot CamoTvlilTagan romeli ar aris martebuli? iupitertan Sumeiker-levis kometis Sejaxebis SemTxveva moyvanilia: (a) imis sailustraciod, Tu rogori SeiZleba iyos kometis sicocxlis dasasruli (b) rogorc magaliti imisa, ramdenad isviatad xdeba kometis Sejaxeba planetebtan mas Semdeg, rac sabolood Camoyalibda Cveni mzis sistema (g) imis sacveneblad, Tu ra procesebi mimdinareobda planetebis Camoyalibebis adreul etapebze (d) im rolis xazgasasmelad, romelsac kometebi da asteroidebi asrulebdnen mzis sistemis formirebisas 37. teqstsi ramdenime sityva brwyalebsia Casmuli: I _ `uberaven~, II _ `Tma~, III _ `Wrilobebi~, IV _ `tunguskis meteoriti~, V _ `mozidavdnen~. qvemot CamoTvlilTagan romelsia sworad mititebuli, Tu ratomaa TiToeuli matgani Casmuli brwyalebsi? (a) II da III sityvebi gadataniti mnisvnelobitaa gamoyenebuli, xolo I, IV da V kometebtan dakavsirebuli procesis xatovan arweras emsaxureba (b) I, III da V sityvebis mesveobit daxasiatebulia kosmossi mimdinare procesebi, xolo II da IV _ kometis arsanisnavadaa gamoyenebuli (g) I, II, III da V sityvebi ucveulo konteqstsi _ usulo obieqtebis mimartaa gamoyenebuli, xolo IV _ ert-erti kometis saxelia (d) IV im adgilis saxelia, sadac kometa Camovarda, xolo yvela danarceni sityva kometebis specifikuri nisnebis arsaweradaa gamoyenebuli a

17 38. ra mimartebaa bolo or abzacs Soris? (a) IV abzacsi xazgasmulia kometebis roli planetebze sicocxlis warmosobasi, xolo V abzacsi am sakitxis Sesaxeb gamotqmuli mosazrebebis dadasturebis imedia gamotqmuli (b) IV abzacsi warmocenilia kometebis struqturis is Taviseburebebi, romlebic garkveul hipotezas daedo safuzvlad, V abzacsi ki am hipotezis mimart gamotqmul ewvtan ertad sakitxi Riad aris datovebuli (g) IV da V abzacebsi arsebitad ertsa da imave problemazea saubari, Tumca, pirvelsi es sakitxi dadebitadaa gadawyvetili, xolo meoresi _ uaryofitad (d) orive abzacsi kometebisa da planetebis urtiertkavsirzea saubari, Tumca, IV abzacsi am kavsiris arseboba axsnilia kometebis struqturuli TaviseburebebiT, V-Si ki mxolod Teoriuli mosazrebebis mosveliebit 39. ra mizans emsaxureba IV abzacsi moyvanili mtvaris epizodi? (a) im varaudis uaryofas, rom kometebs SeeZloT dadamiwaze sicocxlis Semotana (b) im varaudis gamyarebas, rom kometebs SeeZloT dadamiwaze sicocxlis warmosobisatvis ert-erti umnisvnelovanesi pirobis Seqmna (g) imis Cvenebas, Tu ramdenad ufro xsirad stumrobdnen kometebi mtvares, dedamiwisgan gansxvavebit (d) kvlevis im metodebis Cvenebas, romelta mesveobit SesaZlebelia planetebze sicocxlis warmosobis xelsemwyobi faqtorebis Seswavla 40. teqstis danisnulebaa: (a) gagvacnos ert-erti tipis ciur sxeulta buneba da mis Sesaxeb arsebuli varaudebi (b) warmoacinos kosmosuri sxeulebis gansxvavebuli arsi da mati urtiertqmedebis SesaZlo Sedegebi (g) ciuri sxeulebis ert-erti uisviatesi warmomadgenlis magalitze dagvanaxos, ra procesebi uzroda win mzis sistemis Camoyalibebas (d) dagvanaxos ert-erti kosmosuri sxeulis SesaZlo roli dedamiwaze sicocxlis warmosobasi a

18 Savi samusaostvis a

19 Savi samusaostvis a

20 matematikuri nawili 2013 testis matematikur nawilze musaobisas gaitvaliswinet: I naxazebi, romlebic Tan ertvis zogiert davalebas, ar aris 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: 1. nuli arc dadebitia da arc uaryofiti; 1 ar aris martivi ricxvi. 2. procenti: a ricxvis k% aris. 3. xarisxi: a n = a a a... a (n-jer) a n a m = a n + m a n : a m = a n m (a n ) m = a n m 4. proporcia: Tu, masin ad = bc. manzili 5. sicqare: sicqare dro 6. sasualo aritmetikuli: monacemta sasualo monacemta jami monacemta raodenoba 7. albatoba: Tu yvela elementaruli xdomiloba Tanabrad mosalodnelia, masin xdomilobis albatoba tolia am xdomilobis xelsemwyob elementarul xdomilobata raodenobis Sefardebisa elementarul xdomilobata saerto raodenobastan. Tu amocanis pirobasi sawinaarmdego araa natqvami, yoveltvis igulisxmeba, rom elementaruli xdomilobebi Tanabrad mosalodnelia. 8. Semoklebuli gamravlebis formulebi: (a + b) 2 = a 2 + 2ab + b 2 (a b) 2 = a 2 2ab + b 2 (a + b)(a b) = a 2 b 2 9. naxazze kutxe SeiZleba monisnuli iyos kutxis gverdebs Soris Casmuli patara rkalit, marti kutxe ki _ patara kvadratit. A arnisnavs A kutxis sidides. 10. paraleluri wrfeebi: ori paraleluri wrfis mesame wrfit gadakvetisas Siga jvaredina kutxeebi tolia: α = β. 11. samkutxedi: samkutxedis kutxeebis sidideta jami 180 -is tolia; pitagoras Teorema: martkutxa samkutxedis hipotenuzis sigrzis kvadrati katetebis sigrzeta kvadratebis jamis tolia: AB 2 = AC 2 + BC 2 samkutxedis fartobi samkutxedis gverdis sigrzisa da Sesabamisi simarlis namravlis naxevris tolia:. 12. otxkutxedi: otxkutxedis kutxeebis sidideta jami 360 -is tolia; martkutxedis fartobi misi sigrzisa da siganis namravlis tolia: S = ab; paralelogramis fartobi misi gverdis sigrzisa da am gverdis Sesabamisi simarlis namravlis tolia: S = ah. 13. wre, wrewiri: wrewiris sigrze misi radiusis mixedvit gamoitvleba formulit: L = 2 r; ricxvi, measedis sizustit, 3,14-is tolia; r radiusiani wris fartobi gamoitvleba formulit: S = r martkutxa paralelepipedi: martkutxa paralelepipedis moculoba misi sigrzis, siganisa da simarlis namravlis tolia: V = abc; kubis SemTxvevaSi: a = b = c b

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 , 68 (a) (b) (g) (d) n naturaluri ricxvia n 2 6 n 1 (a) (b) (g) (d) 43. kubis yvela wibos sigrzeta jamia 42 sm. kubis erti waxnagis perimetri 14 sm (a) (b) (g) (d) b

22 44. samnisna ricxvi, romlis cifrta jami 25-is tolia 700 (a) (b) (g) (d) funtusa 40 TeTri Rirs. xawapuri 80 TeTriT Zviria Rvezelze xawapuris da 2 Rvezelis Rirebuleba 1 xawapuris, 3 Rvezelisa da 2 funtusis Rirebuleba (a) (b) (g) (d) 46. martkutxedis didi gverdis sigrzea a, xolo diagonalisa _ d. (a) (b) (g) (d) a d b

23 amocanebi milioni metia 4 milion 700 atasze: (a) 6 milion 700 atasit (b) 7 milion 300 atasit (g) 7 milion 700 atasit (d) 8 milion 300 atasit (e) 8 milion 700 atasit 48. wriul diagramaze mocemulia, qalaqis mcxovrebta ramden procents ar aqvs ganatleba da ramden procents aqvs dawyebiti, arasruli sasualo, sasualo zogadi, sasualo profesiuli Tu umarlesi ganatleba. qalaqis mcxovrebta ramden procents aqvs umarlesi ganatleba? (a) 22,5% (b) 22,8% (g) 23,2% (d) 23,5% (e) 24,3% wlis win ana 28 wlis iyo. ramdeni wlis iyo ana x wlis win? (a) x 34 (b) x 22 (g) 34 x (d) 22 x (e) 22 x b

24 50. ABCD martkutxedis AD gverdis sigrzea 12 sm, xolo AB-si _ 8 sm. M wertili BC gverdis Suawertilia. ris tolia AM monakvetis sigrze? (a) 8 sm (b) 9 sm (g) 10 sm (d) 11 sm (e) 12 sm 51. maraziasi 1 kilogrami vasli 5 lari Rirda, gargari _ 2-jer naklebi. ninom am maraziasi vasli da gargari iyida, romelta saerto wona 6 kilogrami iyo. vaslis wona nayidi xilis wonis mesameds Seadgenda. sul ramdeni laris xili uyidia ninos? (a) 12,5 (b) 14 (g) 16,5 (d) 18 (e) b

25 monacemta analizi ert-ert evropul qveyanasi Catarda gamokitxva, romlis mizani iyo sxvadasxva sferosi dasaqmebul menejerta sakutari profesiuli warmatebit kmayofilebis xarisxis dadgena. gamokitxvasi monawileobdnen ganatlebis, jandacvis, ekonomikisa da soflis meurneobis sferosi dasaqmebuli menejerebi _ sul 150 respondenti. gamokitxulta naxevari qali iyo, naxevari _ mamakaci. pirvel diagramaze warmodgenilia sxvadasxva sferosi dasaqmebul respondentta ganawileba profesiuli warmatebit kmayofilebis xarisxis mixedvit. meore diagramaze ki warmodgenilia sxvadasxva sqesis respondentta ganawileba profesiuli warmatebit kmayofilebis xarisxis mixedvit. diagramebis mixedvit upasuxet Semdeg 4 SekiTxvas: 52. romeli sferoa iseti, romelsic dasaqmebul menejertagan arc erti araa Zalian kmayofili sakutari profesiuli warmatebit? (a) ganatleba (b) jandacva (g) ekonomika (d) soflis meurneoba (e) arc erti b

26 53. ramdenit aremateba menejerta raodenoba, romlebic sakutari profesiuli warmatebit naklebad kmayofilni arian, im menejerta raodenobas, romlebic sakutari profesiuli warmatebit Zalian ukmayofiloni arian? (a) 8-iT (b) 10-iT (g) 12-iT (d) 14-iT (e) 16-iT 54. kmayofilebis romeli xarisxobrivi kategoriis SemTxvevaSia dasaqmebul menejer qalta raodenoba 5-iT meti menejer mamakacta raodenobaze? (a) Zalian ukmayofilo (b) naklebad kmayofili (g) kmayofili (d) Zalian kmayofili (e) arc erti kategoriis SemTxvevaSi 55. gamokitxul menejer mamakactagan sakutari profesiuli warmatebit Zalian kmayofilni armocndnen soflis meurneobis sferosi dasaqmebuli 6 menejeri da ekonomikis sferosi dasaqmebuli 15 menejeri. ris tolia ganatlebis sferosi dasaqmebul menejer mamakacta raodenoba, romlebic sakutari profesiuli warmatebit Zalian kmayofilni arian? (a) 1 (b) 2 (g) 3 (d) 4 (e) 5 amocanebi 56. c romeli cifrit bolovdeba c ricxvis cifruli Canaweri? (a) 0 (b) 2 (g) 4 (d) 6 (e) b

27 57. kvadratis fartobia 36 sm 2. misi TiToeuli gverdi dayofilia sam tol nawilad da dayofis wertilebi SeerTebulia monakvetebit (ix. naxazi). ris tolia mirebuli rvakutxedis fartobi? (a) 24 sm 2 (b) 26 sm 2 (g) 28 sm 2 (d) 30 sm 2 (e) 32 sm traqtorit miwis nakvetis 5 nawilis moxvnas 2,5 saati swirdeba. ramdeni 12 saatia sawiro am traqtorit imave nakvetis 2 nawilis mosaxnavad? 3 (a) 3 (b) 3,5 (g) 4 (d) 4,5 (e) m, n da k ertmanetis momdevno naturaluri ricxvebia, amastan m n k. CamoTvlilTagan romeli winadadebaa martebuli? I. m k luwia II. n k kentia III. n k luwia (a) mxolod I (b) mxolod II (g) mxolod I da II (d) mxolod II da III (e) I, II da III 60. ori qalaqidan ertmanetis Sesaxvedrad ori avtobusi ertdroulad gamovida. orive avtobusi Tanabari sicqarit, Seferxebebis garese mozraobda. pirvelma avtobusma, romlis sicqare 70 km/st iyo, Sexvedramde 1,4-jer meti manzili gaiara, vidre meorem. ris toli iyo meore avtobusis sicqare? (a) 50 km/st (b) 60 km/st (g) 65 km/st (d) 80 km/st (e) 98 km/st b

28 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 61. m-is 4-ze gayofisas mirebuli nasti m naturaluri ricxvia. m-is 8-ze gayofisas mirebuli nasti (a) (b) (g) (d) 62. 6, 12, 7,... mimdevrobis wevrebs nika da Tamari rigrigobit werdnen. pirveli wevri Cawera nikam, meore _ Tamarma da ase Semdeg. Tamaris mier Cawerili yoveli wevri mimdevrobis wina wevrze 2-jer meti iyo, xolo nikas mier Cawerili _ wina wevrze 5-iT naklebi. (a) (b) (g) (d) mimdevrobis me-4 wevri mimdevrobis me-7 wevri 63. wris centri im martkutxedis ertert wveros emtxveva, romlis erti gverdi wris radiusis tolia, xolo meore _ diametrisa. (a) (b) (g) (d) wris fartobi martkutxedis fartobi b

29 64. bostneulit savse 10 ertnairi yutis gadatanas 4 urika daswirda. TiToeuli urikit 150 kilogramamde tvirtis gadatanaa SesaZlebeli. (a) (b) (g) (d) gadatanili bostneulis wona 400 kg 65. ujridan, romelsic 3 TeTri da ramdenime witeli burtulaa, unda amoiron erti burtula. albatoba imisa, rom ujridan amorebuli burtula witeli iqneba, metia 2 -ze. 3 (a) (b) (g) (d) witeli burtulebis raodenoba 8 amocanebi 66. saklebi 9-iT metia maklebze, xolo maklebi 9-iT metia sxvaobaze. ris tolia saklebi? (a) 18-is (b) 24-is (g) 27-is (d) 30-is (e) 36-is b

30 67. sarben biliks wesieri xutkutxedis forma aqvs (ix. naxazi). bilikis sigrze 250 metria. sportsmenma sirbili daiwyo A wverodan isrit mititebuli mimartulebit. bilikis romel monakvetze armocndeba sportsmeni 680 metris garbenis Semdeg? (a) AB -ze (b) BC -ze (g) CD -ze (d) DE -ze (e) EA -ze 68. im naturaluri ricxvebidan, romlebic metia 22-ze, magram naklebia 84-ze, ramdenia iseti, romlis 5-ze gayofisas mirebuli nasti 3-is toli iqneba? (a) 13 (b) 12 (g) 11 (d) 10 (e) nakrzalsi mxolod nazvis da fiwvis xeebia. fiwvis xeebis raodenobis Sefardeba nazvis xeebis raodenobastan 2 -is tolia. nakrzalsi xeebis saerto 5 raodenobis ra nawilia nazvis xeebis raodenoba? (a) 1 3 (b) 3 5 (g) 3 4 (d) 5 7 (e) b

31 70. m da n iseti ricxvebia, rom 2n 1 2m 1. qvemot CamoTvlilTagan romeli mimarteba ar SeiZleba iyos martebuli? (a) m n 1 (b) n m 3 (g) n m 1 (d) n m 1 (e) m 4n 71. pirveli martkutxedis sigrze 2-jer metia meore martkutxedis sigrzeze, xolo fartobi 6-jer naklebia meore martkutxedis fartobze. ramdenjer naklebia pirveli martkutxedis sigane meore martkutxedis siganeze? (a) 12-jer (b) 8-jer (g) 4-jer (d) 3-jer (e) 2-jer monacemta sakmarisoba 72. fakultetze sul 600 studenti swavlobs. mocemulia ori piroba: I. studentta 15 1 nawili ucxoelia. II. ucxoeli studentebis 4 1 nawili gogonebia. imis gasarkvevad, Tu ramdeni ucxoeli studenti vaji swavlobs fakultetze: (a) I piroba sakmarisia, II ki _ ara (b) II piroba sakmarisia, I ki _ ara (g) I da II piroba ertad sakmarisia, cal-calke arc erti ar aris sakmarisi (d) sakmarisia cal-calke rogorc I, aseve, II piroba (e) mocemuli pirobebi ar aris sakmarisi b

32 73. ABCD otxkutxedia. mocemulia ori piroba: I. A B 100. II. B C 200. imis gasarkvevad, Tu ris tolia A C : (a) I piroba sakmarisia, II ki _ ara (b) II piroba sakmarisia, I ki _ ara (g) I da II piroba ertad sakmarisia, cal-calke arc erti ar aris sakmarisi (d) sakmarisia cal-calke rogorc I, aseve, II piroba (e) mocemuli pirobebi ar aris sakmarisi 74. x da y ricxvebis jami 8-is tolia. mocemulia ori piroba: I. x-is Sefardeba y-tan 3-is tolia. II. x-isa da y-is sxvaoba 4-is tolia. imis gasarkvevad, Tu ris tolia x 2 y : (a) I piroba sakmarisia, II ki _ ara (b) II piroba sakmarisia, I ki _ ara (g) I da II piroba ertad sakmarisia, cal-calke arc erti ar aris sakmarisi (d) sakmarisia cal-calke rogorc I, aseve, II piroba (e) mocemuli pirobebi ar aris sakmarisi 75. ninos Svilebidan yvelaze umcrosia eka, romelic 3 wlisaa, yvelaze ufrosi ki _ sandro. mat garda ninos kidev hyavs 2 gogona da 1 vaji, romelta sasualo asaki 13 welia. mocemulia Semdegi ori piroba: I. vajebs Soris asaksi gansxvaveba 5 welia. II. ninos Svilebis sasualo asaki 12 welia. imis gasarkvevad, Tu ramdeni wlisaa sandro: (a) I piroba sakmarisia, II ki _ ara (b) II piroba sakmarisia, I ki _ ara (g) I da II piroba ertad sakmarisia, cal-calke arc erti ar aris sakmarisi (d) sakmarisia cal-calke rogorc I, aseve, II piroba (e) mocemuli pirobebi ar aris sakmarisi b

33 amocanebi 76. Tornikes gasuli wlis ganmavlobasi Tavisi xelfasis 6% banksi Sehqonda. wels Tornikes xelfasi 20%-iT gaezarda, ris gamoc man banksi Tavisi xelfasis 9%-is Setana daiwyo. gasuli wlis ganmavlobasi banksi Setanili Tanxis ramdeni procenti iqneba Tornikes mier am wlis ganmavlobasi Setanili Tanxis raodenoba? (a) 120% (b) 135% (g) 150% (d) 165% (e) 180% 77. nebismieri naturaluri x ricxvisatvis x -it arnisnulia ricxvi, romelic miireba Semdegi sqemis mixedvit: magalitad, sqemis mixedvit ris tolia 9 4? (a) 26 (b) 32 (g) 35 (d) 40 (e) m sirrmis mqone kubis formis auzis 8 1 nawili avsebulia wylit. ris tolia aseve kubis formis mqone ufro mcire auzis sirrme, Tu did auzsi arsebuli wylit mcire auzi bolomde ivseba? (a) 1 m 2 (b) 1 m (g) 11 m 2 (d) 2 m (e) 2 1 m b

34 79. A, B, C da D ricxvta RerZis sxvadasxva wertilebia, xolo a, b, c da d, Sesabamisad, mati koordinatebia. B wertili Tanabradaa dasorebuli A da D wertilebidan, xolo C wertili _ A da B wertilebidan. ris tolia c d? a b (a) 1 3 (b) 2 3 (g) 4 3 (d) 3 4 (e) ansamblis wevrta 15%-s biwebi Seadgendnen. roca ansambls 12 axali wevri daemata, biwebis raodenoba gaizarda, procentuli wili ki Semcirda. ramdeni gogona daemata ansambls? (a) 11 (b) 10 (g) 9 (d) 8 (e) b

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