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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. klinika : samkurnalo
(a) saministro : diplomatiuri
(b) poligoni : gamocdili
(g) laboratoria : kvleviTi
(d) observatoria : optikuri
2. mezRvauri : mfrinavi
(a) qoreografi : mocekvave
(b) cirkis msaxiobi : klouni
(g) Jiuris wevri : Semsrulebeli
(d) kompozitori : reJisori
3. udabno : gaudabnoeba
(a) zRva : mozRvaveba
(b) riye : gamoriyva
(g) myinvari : gamyinvareba
(d) Waobi : daWaobeba
4. avtomaturi mowyobiloba : roboti
(a) SeniRbva : kamuflaJi
(b) mimarTuleba : isari
(g) SemosazRvra : fargali
(d) eqskursia : marSruti
5. saTave : saTauri
(a) zedapiri : ekrani
(b) mwvervali : kulminacia
(g) Suaguli : centri
(d) kuTxe : kide
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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) poetisTvis saintereso ar
Zebnas
(b) poetisTvis saintereso ar
da asaxavs
(g) Rirebul masalas gvaZlevs
wyaros povnas
(d) Rirebul masalas gvaZlevs
mxareebs
aris / imiT rodia / daiwyebs STagonebis wyaros
aris / swored imiTaa / saintereso mxares SeamCnevs
poeziisTvis / imiT rodia / ver SeZlebs STagonebis
poeziisTvis / swored imiTaa / eZebs saintereso
7. gasaocaria, rom politologebi _____ gavlenas, romelsac memkvidreobis
kanonebi axdens adamianTa urTierTobebze. marTalia, xsenebuli kanonebi _____
ganekuTvneba, magram isini _____ mniSvnelovania, radgan _____ ama Tu im xalxis
socialur wyobaze.
(a) ar aRiareben im udides / samoqalaqo kanonmdeblobis sferos / yvela
politikur institutze ufro / warmoudgenlad Zlier zemoqmedebas axdens
(b) esoden azviadeben im / politikuri institutebis sferos / sxva politikur
institutebze ufro naklebad / warmoudgenlad Zlier zemoqmedebas axdens
(g) esoden azviadeben im / politikuri institutebis sferos ar / politikur
institutebze ufro / mxolod mcired Tu zemoqmedebs
(d) ar aRiareben im udides / samoqalaqo kanonmdeblobis sferos / yvela
politikur institutze ufro naklebad / mxolod mcired Tu zemoqmedebs
8. komediaSi Sesasruleblad
asrulebs, _____ iyos.
(a)
(b)
(g)
(d)
yvelaze
yvelaze
yvelaze
yvelaze
Zneli /
advili
Zneli /
advili
_____
masxaras
rolia,
_____
is,
vinc
mas
miuxedavad imisa, rom / TviTonac gonebamaxvili unda
/ miuxedavad imisa, rom / TviTon gonebamaxvili rodi unda
radgan / ar SeiZleba, TviTonac gonebamaxvili ar
/ radgan / ar SeiZleba, TviTon gonebamaxvili ar
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9. adamianebSi arsebobs raRac dauokebeli da kanonieri Jini _____ , romelic
imdenad Zlieria, rom adamianebi mzad arian, umal daTanxmdnen _____ , vidre
_____ .
(a) Tavisuflebisa
monobaSi
(b) Tavisuflebisa
(g) Tanasworobisa
(d) Tanasworobisa
monobaSi
/ Tavisuflebas Tanasworobis pirobebSi / uTanasworobas
/ monobaSi Tanasworobas / TavisuflebaSi uTanasworobas
/ Tanasworobas monobaSi / uTanasworobas TavisuflebaSi
/ uTanasworobas Tavisuflebis pirobebSi / Tanasworobas
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 keTili adamiani emociuria.
• yvela Cemi megobari keTili adamiania.
qvemoT CamoTvlilTagan romeli daskvna gamomdinareobs mocemuli debulebebidan?
(a)
(b)
(g)
(d)
yvela emociuri adamiani keTilia
yvela emociuri adamiani Cemi megobaria
mxolod keTili adamianebi arian emociurebi
yvela Cemi megobari emociuria
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11. qalaqis centraluri moedani garSemortymulia oTxi SenobiT, romelTaganac
erTSi qalaqis meriaa, erTSi _ banki, erTSi _ muzeumi da erTSic _ sastumro.
Senobebi sxvadasxva masaliTaa mopirkeTebuli: erTi _ bazaltiT, erTi _ tufiT,
erTi _ granitiT da erTic _ marmariloTi. bazaltiT mopirkeTebuli Senoba,
romelSic arc meriaa da arc banki, tufiT mopirkeTebul Senobasa da sastumros
Sorisaa, xolo granitiT mopirkeTebuli _ marmariloTi mopirkeTebulsa da banks
Soris.
qvemoT mocemulia SenobaTa sxvadasxva masaliT mopirkeTebis ori SesaZlo varianti:
1. meria _ marmarilo, banki _ graniti, muzeumi _ bazalti, sastumro _ tufi.
2. meria _ graniti, banki _ tufi, muzeumi _ bazalti, sastumro _ marmarilo.
miTiTebuli variantebidan romeli akmayofilebs amocanis pirobebs?
(a)
(b)
(g)
(d)
pirveli
meore
arc erTi
SeuZlebelia amis dadgena
12. cxovelebSi TviTcnobierebis fenomens mecnierebi ikvleven e. w. `sarkis
testis~ gamoyenebiT: sxvadasxva situaciaSi amowmeben, amoicnobs Tu ara cxoveli
sarkeSi danaxul gamosaxulebaSi sakuTar Tavs.
qvemoT CamoTvlilTagan romeli eqsperimentis Sedegebi amyarebs yvelaze metad
Sesabamis cxovelSi TviTcnobierebis arsebobis varauds?
(a) eqsperimentSi, romelic goWebze Caatares, saWmliT savse Tasi kedlis ukan iyo
damaluli da goWebi mas iqve mdgar sarkeSi xedavdnen. rva goWidan Svidma
SeZlo Tasis povna sarkeSi danaxuli anareklis meSveobiT. erTma ki saWmels
sarkis ukan dauwyo Zebna
(b) ori mdedri da ori mamri Simpanze ramdenime dRiT izolaciaSi hyavdaT,
Semdeg ki maT galiaSi sarke dadges. oTxive Simpanze Tavidan agresiuli
JestebiT Sexvda sarkeSi danaxul gamosaxulebas, garkveuli xnis Semdeg ki
eWyaneboda da enas uyofda _ Taviseburad eTamaSeboda _ mas
(g) daZinebul spilos usuno wiTeli saRebaviT ori laqa miaxates: erTi _
Sublze, meore _ mucelze iseT adgilas, romelsac verc uSualod da verc
sarkeSi ver xedavda. msgavsi laqebi daxates galiis kedlebzec. gaRviZebis
Semdeg spilo arc erT laqas ar aqcevda yuradRebas, magram rogorc ki win
sarke daudges, daiwyo Tavis Sublze wiTeli laqis xorTumiT mosinjva
(d) mtredi jer gawvrTnes sarkis gamoyenebiT im nivTebis povnaSi, romelTac
uSualod ver xedavda, Semdeg _ sakuTar da sxva mtredebis frTebze mixatuli
laqebis niskartiT moSorebaSi. Semdeg mkerdze miaxates msgavsi laqa, romelsac
mxolod sarkeSi xedavda, uSualod ki _ vera. sarkeSi Tavisi gamosaxulebis
danaxvisTanave mtredma laqis niskartiT moSoreba scada
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13. SejibrSi sami saprizo adgili daikaves kaxam, sandrom da levanma (ara
aucileblad am TanmimdevrobiT). maT Soris saprizo adgilebis ganawilebis
Sesaxeb ori cnoba movida:
•
•
pirveli adgili daikava sandrom, kaxam _ meore.
pirveli adgili daikava levanma, sandrom _ meore.
mogvianebiT gairkva, rom TiToeul cnobaSi mxolod erTi nawili iyo marTali,
xolo meore _ ara.
vin daikava mesame adgili?
(a)
(b)
(g)
(d)
kaxam
sandrom
levanma
mocemuli informacia ar aris sakmarisi pasuxis dasadgenad
14. mocemulia:
•
Tu xval qariani amindi iqneba, qalaqis quCebi xmeli foTlebiT gaivseba.
•
Tu xval qariani amindi ar iqneba, nino botanikur baRSi gaiseirnebs an
qalaqgareT gaatarebs mTel dRes.
•
nino xval mniSvnelovan zars elodeba da, amitom, qalaqidan ar gava.
qvemoT CamoTvlilTagan romeli debulebaa aucileblad WeSmariti, Tu davuSvebT,
rom mocemuli wanamZRvrebi WeSmaritia?
(a)
(b)
(g)
(d)
xval qariani amindi iqneba an qalaqis quCebi xmeli foTlebiT gaivseba
xval qariani amindi ar iqneba an nino qalaqgareT gaatarebs dRes
xval nino botanikur baRSi gaiseirnebs an qalaqgareT gaatarebs dRes
xval qalaqis quCebi xmeli foTlebiT gaivseba an nino botanikur baRSi
gaiseirnebs
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wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
antikuri xanis avtorebi berZnebs (elinebs) uwodebdnen aqavelebs. swored
aqavelebma daangries da gadawves troa. Tumca, mecnierebs miTebi troas omze
didxans mxolod berZnuli fantaziis nayofi egonaT. am tradiciuli poziciis
arsebiTi gadasinjva XIX saukunis 70-iani wlebidan daiwyo, rac hainrix Slimanis
saxels ukavSirdeba. Slimans, homerosis poemebiT gatacebul poliglotsa da
warmatebul komersants, mtkiced swamda, rom troas Sesaxeb berZnuli eposis
cnobebi istoriul realobas Seesabameboda. miuxedavad samecniero sazogadoebis
skeptikuri damokidebulebisa, Slimani gaemgzavra TurqeTSi da daiwyo im
adgilis Zebna, sadac, antikur wyaroTa mixedviT, troa unda arsebuliyo.
im dros mecnierTa umravlesobas miaCnda, rom Tuki troa marTlac
arsebobda, is unda yofiliyo im adgilas, sadac axla patara sofeli bunarbaSia.
iqve ori wyaroa, ramac yvelaze gabedul arqeologebs afiqrebina, rom swored am
adgilas unda yofiliyo Zveli troa. `iliadas~ XXII simReraSi xom saubaria or
_ civsa da cxel _ wyaroze. SlimanisTvis pirveli SexedvisTanave cxadi gaxda,
rom troa ar SeiZleboda yofiliyo aq, zRvidan sami saaTis savalze. homerosis
gmirebi xom dReSi ramdenjerme Cadiodnen gemebidan qalaqSi. Slimanma daaTvaliera
wyaroebi da mxolod 500 kvadratuli metris farTobze 2 ki ara, 34 wyaro
daiTvala. megzuri ki arwmunebda, SegeSalaT, 34-ze metiao.
homerosis wigniT xelSi man gaiara gza im borcvidan, troas rom icavda,
koncxamde, sadac aqavelTa gemebi unda mdgariyo. homerosis aRweras SlimanisTvis
topografiuli rukis Zala hqonda. `iliadis~ II-VII simRerebis mixedviT man
zustad aRadgina brZolis msvleloba da im daskvnamde mivida, rom Tu troa
marTlac bunarbaSis adgilas mdebareobda, aqavelebs 9 saaTSi 84 km mainc unda
gaevloT. amasTan, SeuZlebeli iyo troas uzarmazari kedlebi ukvalod
gamqraliyo. garda amisa, sruliad zerele daTvalierebisas zRudis naSTebi Canda
hisarliyis nangrevebTan, romelic zRvidan mxolod 1 saaTis savalze mdebareobs.
Slimani varaudobda, rom troa hisarliyis borcvis qveS unda yofiliyo.
is male daeWvda Tavisi azris sisworeSi, radgan am adgilebSi arc erTi wyaro
ar Canda. Tumca, kalvertma, amerikelma konsulma, romelsac ekuTvnoda
hisarliyis borcvis nawili, SeniSna, rom hisarliyis vulkanur miwaSi SedarebiT
mokle xanSi gaCnda da isev gaqra ramdenime cxeli wyaro.
Slimanma gaTxara hisarliyis borcvis mwvervali da iq kedeli naxa, magram
nangrevebis qveS sxva nangrevebic aRmoaCina, maT qveS _ kidev sxva. borcvi
waagavda uzarmazar bolqvs, romelic fena-fena unda gawmendiliyo. advili
misaxvedri iyo, rom yoveli fena calke epoqas ekuTvnoda. Slimanma gaTxrebi
daiwyo homerosis troas sapovnelad, magram Svidi qalaqi aRmoaCina. SemdgomSi
kidev ori aRmoCnda. es iyo warsulis cxra sarkmeli, romelTa Sesaxeb manamde
araferi icodnen. magram am cxra qalaqidan romeli iyo homerosis troa?
Slimanma qvemodan II fenaSi aRmoaCina xanZris nakvalevi, uzarmazari zRudisa da
WiSkris naSTebi da gadawyvita, rom es zRude troas mefis, priamosis, sasaxles
uvlida gars. didi cixis kedlis qveS aRmoCnda Zvirfaseuloba. Slimani erTi
wuTiTac ar daeWvebula, rom troelTa mefis _ priamosis _ ganZi ipova. mxolod
mis sikvdilamde cota xniT adre damtkicda: homerosis troa qvemodan II fena ki
ar iyo, aramed _ VI an VII, xolo napovni ganZi ekuTvnoda mefes, romelic
priamosze, sul mcire, 1000 wliT adre cxovrobda.
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15. troas omi:
(a) miTebis Tanaxmad, berZnuli fantaziis nayofia, rasac homerosis poemebic
adasturebs
(b) antikur wyaroTa Tanaxmad, berZnuli fantaziis nayofia; miTiurma aqavelebma
daangries da gadawves troa
(g) hainrix Slimanis azriT, realurad unda momxdariyo; misi rwmena homerosis
poemebs emyareboda
(d) mecnierTa azriT, realurad unda momxdariyo; skepticizmisTvis safuZveli ar
arsebobda
16. Slimani ar eTanxmeboda im azrs, rom troa
bunarbaSis teritoriaze. ra iyo misi eWvis safuZveli?
mdebareobda
dRevandeli
(a) homerosis `iliadaSi~ iyo miniSneba, rom troa iq unda yofiliyo, sadac
gverdigverdaa civi da cxeli wyaroebi, aseTi adgili ki bunarbaSia
(b) arqeologTa gamokvlevebi adasturebda, rom troa sami saaTis savalze unda
yofiliyo zRvis sanapirodan, rogorc patara sofeli bunarbaSia
(g) bunarbaSTan megzuris daxmarebiT 34-ze meti wyaro aRmoaCines, garda amisa, am
soflis teritoriaze didi qalaqis kedlis nangrevebic Canda
(d) sanapirodan bunarbaSi sakmaod moSorebulia, troas asaRebad gemebiT mosuli
aqavelebi ki ver SeZlebdnen dRis manZilze qalaqSi ramdenjerme amosvlas da
kvlav gemebTan dabrunebas
17. qvemoT CamoTvlilTagan Slimanis romeli qmedebis safuZvlad ar SeiZleba
gamoviyenoT III abzacSi aRniSnuli informacia _ `homerosis aRweras
SlimanisTvis topografiuli rukis Zala hqonda~?
(a) `iliadis~ II-VII simRerebis mixedviT, Slimanma daadgina is adgilebi, sadac
brZola mimdinareobda
(b) sruliad zerele daTvalierebisas Slimanma aRmoaCina zRudis naSTebi
hisarliyis nangrevebTan
(g) Slimanma daaskvna, rom Tu troa marTlac bunarbaSis adgilas mdebareobda,
aqavelebs 9 saaTSi 84 km mainc unda gaevloT
(d) homerosis wigniT xelSi Slimanma gaiara gza im borcvidan, troas rom
icavda, koncxamde, sadac aqavelTa gemebi unda mdgariyo
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18. kalvertis SeniSvna Slimanis kvlevisTvis gadamwyveti aRmoCnda, radgan:
(a) wyaroTa raodenoba, rac mecnierebs manamde mniSvnelovnad eCvenebodaT,
araarsebiTi yofila, amis gaazrebam ki xeli Seuwyo hisarliyis midamoebSi
troas Ziebas
(b) vulkanur miwaSi SeiZleba moulodnelad gaCndes da aseve gauCinardes cxeli
wyaroebi, Sesabamisad, wyaroTa raodenoba unda gamxdariyo ZiriTadi
orientiri troas adgilmdebareobis dasadgenad
(g) hisarliyi zRvidan 1 saaTis, xolo bunarbaSi 3 saaTis savalze mdebareobs,
Sesabamisad, troas omis gmirebi ver SeZlebdnen cxra saaTSi 84 kilometris
gavlas
(d) qalaqis zRudis naSTebi iyo hisarliyTan, Sesabamisad, am borcvis qveS unda
yofiliyo homerosis troa, bunarbaSTan ki troas kedlebis kvalic ar Canda
19. im adgils, sadac Slimanma 34 wyaro daiTvala, megzuris TqmiT, Turqulad
`kirk giozs~ eZaxian, rac `ormoc Tvals~ niSnavs. adgilobrivebi irwmunebodnen,
es saxeli 40 wyaroze migvaniSnebso.
teqstisa da am informaciis safuZvelze SeiZleba vivaraudoT:
(a) ricxvi 40 simravles gulisxmobs da am adgilebSi marTlac mravali civi da
cxeli wyaro iyo, amasve gvamcnobs homerosis `iliada~
(b) homerosis cnobebma civsa da cxel wyaroze xeli SeuSala mecnierebs, epovaT
troa, vulkanuri miwis specifikurobam ki cxadi gaxada 40 wyaros arseboba
(g) im droisTvis, rodesac am adgils saxeli Seerqva, SesaZloa aq 40 wyaroc
yofiliyo, radgan droTa ganmavlobaSi maTi raodenoba icvleboda
(d) Slimanma arasworad daiTvala 34 wyaro, megzuri marTali iyo, iq yovelTvis
40 wyaro iyo
20. bolo abzacSi gvxvdeba fraza `warsulis cxra sarkmeli~.
CamoTvlilTagan am sityvebis romeli interpretaciaa marTebuli?
qvemoT
(a) Slimanis mier gamovlenili cxrave qalaqi iyo troa, Tumca, calkeuli fena
misi ganviTarebis sxvadasxva etaps cxadyofda
(b) cxra fenidan mxolod II-Si Canda xanZrisa da ngrevis nakvalevi, Sesabamisad,
mxolod es fena warmoadgenda homerosis troas
(g) Slimanma cxra sxvadasxva qalaqi aRmoaCina, maTgan mxolod erTs hqonda
SemorCenili didi WiSkari, da, cxadia, es unda yofiliyo priamosis qalaqi
(d) borcvis cxrave fena sxvadasxva epoqas ekuTvnoda, da, TiToeuli fenis
SeswavliT cxra sxvadasxva qalaqis `gacnoba~ SeiZleboda
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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. acra : daavadeba
(a) sistema : qaosi
(b) Semoqmedeba : fantazia
(g) anonsi : premiera
(d) kompania : koordinacia
22. wonasworobas kargavs : simSvides inarCunebs
(a) ileTs asrulebs : xerxs iyenebs
(b) beds emorCileba : Tavs icavs
(g) angariSs uwevs : xels uSlis
(d) niRabs ixsnis : anonimurad moqmedebs
23. aSeneba : simaRle
(a) kvleva : meTodi
(b) cekva : ritmi
(g) xazva : forma
(d) gazomva : sidide
24. safuZveli : fundamenti
(a) Sre : fena
(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
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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. inglisis konstituciiT, TemTa palata mefes akontrolebs, rac ori
faqtoriTaa gamarTlebuli: erTi, rom _____ , sazogadoeba _____ endos mefes,
radgan absoluturi Zalauflebisken swrafva _____ ; meorec, rom TemTa palata,
romelic swored monarqis kontrolis mizniTaa arCeuli, _____ imsaxurebs.
(a) dauSvebelia / brmad / adre Tu gvian TemTa palatis wevrebsac ki uCndebaT /
ndobas kidev ufro naklebad
(b) sasurvelia / brmad ar / monarqis mimarT undoblobas warmoSobs / ndobas
kidev ufro naklebad
(g) sasurvelia / brmad ar / iSviaTad aris damaxasiaTebeli monarqisaTvis / met
ndobas
(d) dauSvebelia / brmad / monarqis Tandayolili avadmyofobaa / met ndobas
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)
(b)
(g)
(d)
simetriuli / TiToeul saxelmwifos meore / araefeqturia
asimetriuli / TiToeul saxelmwifos meore / efeqturia
asimetriuli / donor saxelmwifos daxmarebis mimReb / Zlieria
simetriuli / donor saxelmwifos daxmarebis mimReb / Zlieria
11
653008a
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. bolo dros saqarTvelos N regionSi SeiniSneba niadagis eroziuli (daSlis,
rRvevis) procesebis gamwvaveba. garemos damcvelebma ivaraudes, rom amis mizezi,
upirveles yovlisa, aRniSnuli teritoriis zamTris saZovrebad gamoyenebaa.
qvemoT CamoTvlilTagan romeli mosazreba ganamtkicebs am varauds?
(a) miwaTsargeblobis tradiciuli sistema iTvaliswinebda zamTrisa da
sazafxulo saZovrebis monacvleobas, Tumca karga xania saqarTvelodan
zamTarSi cxvari aRar gadahyavT mezobeli qveynis saZovrebze
(b) Semodgomis miwuruls mwyemsebi iwyeben gamxmari balaxis gadawvas zafxulis
saZovrebze, ris Sedegadac nadgurdeba mcenareulobis fesvTa sistema, niadagis
struqtura da sxv.
(g) niadagis Sedgenilobis gansazRvris mizniT N regionSi axlaxan Catarda
monitoringi, romlis Sedegebis Sedarebisas niadagis qimiuri Sedgenilobis
Zvel monacemebTan sxvaoba ar dadasturda
(d) N regionSi axali wyalsacavis aSenebis Sedegad dairRva regionis yvelaze
didi mdinaris auzis bunebrivi balansi, ramac teritoriis didi nawilis
gaudabnoeba ganapiroba
12
653008a
31. mocemulia winadadebaTa wyvilebi:
I. TbilisSi arc erTi sanayine ar aris `cisartyelaze~ ukeTesi.
`cisartyelaze~ ukeTesi sanayine ar arsebobs.
II. ar SeiZleba manqanis daZvra, Tu SuqniSanze wiTeli anTia.
rodesac SuqniSanze wiTeli ar anTia, mxolod maSin 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 iwvima.
romeli wyvili Sedgeba erTi da imave Sinaarsis mqone winadadebebisgan?
(a)
(b)
(g)
(d)
I
II
III
IV
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 dawinaurebis gziT
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
13
653008a
33. kolofSi devs erTi nivTi _ liTonisgan an xisgan damzadebuli kubi an
burTi. kolofs aweria ori winadadeba:
•
aq devs liTonis nivTi.
•
aq devs burTi.
cnobilia, rom Tu kolofSi devs liTonis kubi an xis burTi, yvelaferi,
rac kolofs aweria, marTalia. winaaRmdeg SemTxvevaSi ki, yvelaferi, rac mas
aweria, tyuilia.
ra devs kolofSi?
(a)
(b)
(g)
(d)
liTonis kubi
liTonis burTi
xis kubi
xis burTi
34. mocemulia:
•
Tu iaponia gazrdis avtomobilebis eqsports, maSin koreis an laosis
ekonomika safrTxis winaSe aRmoCndeba.
•
koreis ekonomikas safrTxe ar emuqreba.
qvemoT CamoTvlilTagan romeli debulebaa aucileblad WeSmariti, Tu davuSvebT,
rom mocemuli wanamZRvrebi WeSmaritia?
(a) iaponia aRar gazrdis avtomobilebis eqsports
(b) laosis ekonomika safrTxis winaSe aRmoCndeba
(g) Tu laosis ekonomika safrTxis winaSe aRmoCndeba, iaponias avtomobilebis
eqsporti gauzrdia
(d) iaponia avtomobilebis eqsports aRar gazrdis an laosis ekonomika safrTxis
winaSe aRmoCndeba
14
653008a
wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
planetebi da yvela is sxeuli, romelic mzis sistemaSia, im mimarTulebiT
moZraobs, saiTac brunavs mze Tavisi RerZis garSemo. mzis mizidulobas
`CaWerili hyavs~ mis maxloblad mdebare yvela ciuri sxeuli, 8 planetisa da
maTi 60-ze meti Tanamgzavris CaTvliT. mzis masa aTasjer da ufro metad
aRemateba TviT yvelaze didi planetis masas da, Sesabamisad, misi mizidulobis
Zala yvela danarCeni axlomyofi sxeulis mizidulobaze gacilebiT ufro didia.
planetebi mzis irgvliv moZraoben da, amave dros, sakuTari RerZis garSemoc
brunaven, ris Sedegadac viRebT suraTs, romelic SeiZleba SevadaroT
Cveulebrivi wylis morevs.
Tu mze planetebs aseTi ZaliT izidavs, maSin ratom ar cviva isini masze?
sistemis formirebis adreul etapebze mze izidavda axlomdebare kosmosuri
materiis* grovebs da Tavisken mimarTul aCqarebasac aniWebda, rac am grovebis
masze dacemiT unda dasrulebuliyo. magram zogierTi maTgani aseT katastrofas
gadaurCa im sawyisi siCqaris gamo, romelic maT sistemis Camoyalibebisas SeiZines.
am siCqaris wyalobiT isini `ewinaaRmdegebodnen~ mimzidvel gravitaciul vels da
`cdilobdnen, gaqceodnen~ mas. garkveuli drois Semdeg, mzisgan garkveul
manZilze am or sapirispiro process Soris myardeboda wonasworoba da axlad
Camoyalibebuli planeta mzis garSemo sakuTar orbitaze iwyebda moZraobas. is
obieqtebi, romlebmac aseTi wonasworoba ver SeinarCunes, gansakuTrebiT, Tu
isini mzis siaxloves yalibdebodnen, masze Camocvivdnen. mzisgan Zalze Sors
myofi materiis grovebis nawili planetad ver Camoyalibda isev da isev
gravitaciis gamo. SesaZloa, amis magaliTia asteroidTa sartyeli marssa da
iupiters Soris. am ori planetis gravitaciuli Zalebi mzesTan erTad TavTavisken izidavdnen materiis grovebs da ar aZlevdnen maT SeerTebis
saSualebas. Sedegad, planetis nacvlad gaCnda sakuTar orbitebze moZravi
asteroidebis rgoli.
marTebuli iqneba, Tu vityviT, rom dedamiwa gamudmebiT `vardeba~ mzeze,
magram vera da ver ,,axerxebs~ amas. ukve 5 miliardi welia is Tavis orbitaze
moZraobs da am moZraobaSi erTmaneTTanaa Serwymuli mzisken ganuwyveteli
,,swrafva~ da, aseve, gamudmebuli ,,mcdeloba~, daSordes mas. am ori
urTierTsapirispiro procesis Sedegia is, rom saSualo manZili dedamiwidan
mzemde TiTqmis ar icvleba.
is, rom dedamiwis moZraobis siCqare da misgan mzemde manZili ar icvleba,
ramdenime mizeziT aixsneba, maT Soris imiT, rom: 1. mzis masa da, Sesabamisad, misi
mizidulobis Zala TiTqmis ar Secvlila; 2. sistemis sxva planetebma, romelTac
mzesTan SedarebiT Zalze mcire masa aqvT, ver SeZles TavianTi mizidulobis
ZaliT dedamiwis `gadagdeba~ misi orbitidan; 3. dedamiwa moZraobs vakuumSi,
amitom ar arsebobs garemo, romelTan xaxunic gamoiwvevda misi brunvis siCqaris
Semcirebas.
aRsaniSnavia agreTve im giganti planetebis (magaliTad, iupiteris an
saturnis) roli, romlebic Cvens planetas xSirad `icaven~ mzis sistemaSi
SemoWrili ciuri sxeulebis dajaxebisgan, radgan Tavad izidaven maT an ucvlian
moZraobis mimarTulebas.
*kosmosuri materia _ erT-erTi Tanamedrove hipoTezis Tanaxmad, mzis sistema
sxvadasxva qimiuri elementis Semcveli airmtvrovani Rrublis SekumSvis Sedegad.
15
Camoyalibda
653008a
35. wylis morevTan mzis sistemis Sedareba avtors mohyavs im mizniT, rom:
(a) konkretuli movlenis magaliTze naTlad aRweros da axsnas mzis sistemaSi
mimdinare rTuli procesebis buneba
(b) TvalsaCinod warmoadginos mzis sistemaSi moxvedrili ciuri sxeulebis
moZraobis Tavisebureba
(g) naTlad dagvanaxos, ramdenad didia msgavseba im procesebs Soris, romlebic
mzis mizidulobis zegavleniT mimdinareobs dedamiwaze da kosmosSi
(d) konkretuli bunebrivi movlenis magaliTze dagvanaxos, ra kanonzomierebebi
vlindeba mzis sistemaSi ciur sxeulTa urTierTqmedebisas
36. qvemoT CamoTvlilTagan romelSia sworad gadmocemuli im movlenis arsi,
romelic II abzacSia aRwerili?
(a) Camoyalibebis stadiaze myof planetebs mzeze Camocvenisgan icavda Tavad
mnaTobis mizidulobis Zala
(b) mzis garSemo arsebuli materiis grovebi mxolod im SemTxvevaSi SeZlebdnen
mzis mizidulobisagan `Tavis daRwevas~, Tu isini planetad Camoyalibdebodnen
(g) planetebis Camoyalibebis sawyis etapze maTi gadarCenis winapirobas
warmoadgenda ori sapirispirod moqmedi procesis urTierTdabalanseba
(d) mzisgan Tavis aridebis ZiriTadi faqtori iyo kosmosuri materiis grovebad
SekavSireba da, Sedegad, mizidulobis Zalebs Soris wonasworobis Seqmna
37. mizidulobis movlenasTan dakavSirebiT Camoyalibebuli romeli debuleba ar
aris marTebuli?
(a) rac ufro didia kosmosuri sxeulis masa, miT ufro didia misi mizidulobis
Zala
(b) rac ufro axlos aRmoCndeba ciuri sxeuli mzesTan, miT ufro
mosalodnelia, rom is ver gaeqceva misi mizidulobis Zalas da masze
Camovardeba
(g) rac ufro Zlieri gravitaciuli velis mqone planetebs Soris moeqceva
mzisgan daSorebuli kosmosuri materia, miT ufro savaraudoa, rom is
planetad ver Camoyalibdeba
(d) rac ufro naklebia planetebis mizidulobis Zala, miT ufro mosalodnelia,
rom maT orbitaze warmoiqmneba asteroiduli sartyeli
16
653008a
38. ra mimarTebaa II da III abzacebs Soris?
(a) II abzacSi mocemuli informacia mxolod nawilobrivaa dadasturebuli III
abzacSi, radgan es ukanaskneli moicavs iseT masalasac, romelic Semdgom
abzacSi eWvis qveSaa dayenebuli
(b) III abzacSi konkretul planetasTan mimarTebaSi mokled aris warmodgenili II
abzacis ZiriTadi Tema da, amasTan, miniSnebulia Semdgom abzacSi gaSuqebuli
sakiTxi
(g) II da III abzacebSi ganxilulia erTi da imave movlenis sruliad
gansxvavebuli aspeqtebi da maTTan dakavSirebuli procesebi
(d) III abzacSi konkretuli planetis Sesaxeb mopovebuli informaciis WrilSi
sruliad axleburadaa gaazrebuli II abzacSi gaSuqebuli Tema
39. ratomaa Casmuli brWyalebSi sityvebi: I. `CaWerili hyavs~, II. `cdilobda,
gaqceoda~, III. `gadagdeba~?
(a) samive SemTxvevaSi es sityvebi gamoyenebulia erTgvari komikuri efeqtis
Sesaqmnelad
(b) samive SemTxvevaSi es sityvebi uCveulo konteqstSia gamoyenebuli – usulo
obieqtebis moqmedebis aRsaniSnavad
(g) I da II SemTxvevaSi gamoyenebuli sityvebi kosmosSi mimdinare movlenebis
uCveulobis xazgasmas emsaxureba, xolo III-Si – mzis rolis Cvenebas
(d) I da III SemTxvevaSi gamoyenebuli sityvebi emsaxureba iluziis Seqmnas, TiTqos
kosmosSi mimdinare procesebi dedamiwaze arsebulis analogiuria, xolo II-Si
– komikuri efeqtis Seqmnas
40. teqstis romel abzacebs ukavSirdeba qvemoT mocemuli faqtebi?
1. 1994 wels iupiterma Tavis Tavze miiRo Sumeiker-levis kometis dartyma,
romelic planetaze dacemamde ramdenime nawilad daiSala. TiToeul am nawils
dedamiwis mospoba SeeZlo.
2. zogierTi kometa Tavis arsebobas mzesTan an planetebTan SejaxebiT amTavrebs
_ giganti planetebis Tu maxlobeli varskvlavebis gravitaciuli SeSfoTebis
gamo, is mimarTulebas icvlis da maT saxifaTod uaxlovdeba.
3. mTvare dedamiwis garSemo brunavs 1km/wm siCqariT, anu sakmarisad nela, rom
ar gascdes Tavis orbitas da `ar gafrindes~ kosmosSi, magram sakmarisad
swrafad, raTa ar daeces dedamiwas.
(a)
(b)
(g)
(d)
2 _ II abzacs, 3 – II-III abzacebs, 1 da 2 – V abzacs
1 da 2 _ I-II abzacebs, 3 _ III abzacs, 1 – V abzacs
2 da 3 _ III abzacs, 2 – IV-V abzacebs, 1 – V abzacs
2 _ II abzacs, 3 – I da III abzacebs, 1 da 3 – IV abzacs
17
653008a
Savi samuSaosTvis
18
653008a
Savi samuSaosTvis
19
653008a
maTematikuri nawili
2013
II
testis maTematikur nawilze muSaobisas gaiTvaliswineT:



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
.
n
3. xarisxi: a = a · a · a · ...· a (n-jer)
an · am = an + m
n
m
a :a =a
n–m
m
(a n ) = a n · m
4. proporcia: Tu
5. siCqare:
siCqare
, maSin ad = bc.

manZili
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:
AB2 = AC2 + BC2
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 elementa-
ruli xdomilobebi Tanabrad mosalodnelia.
8. Semoklebuli gamravlebis formulebi:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2
9. naxazze kuTxe SeiZleba
moniSnuli iyos kuTxis
gverdebs Soris Casmuli
patara rkaliT, marTi kuTxe
ki _ patara kvadratiT.
A aRniSnavs A kuTxis sidides.
 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 = r2.
14. marTkuTxa paralelepipedi:
 marTkuTxa paralelepipedis
moculoba misi sigrZis, siganisa da
simaRlis namravlis tolia: V = abc;
 kubis SemTxvevaSi: a = b = c.
21
653008b
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
41.
B
7
3
2,114
(a)
(b)
(g)
(d)
2
n 1
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
n naturaluri ricxvia.
42.
43.
3
n 3
kubis yvela waxnagis perimetrTa jamia 48 sm.
2 sm
kubis wibos sigrZe
22
653008b
44.
umciresi samniSna
ricxvi, romlis cifrTa
jami 21-is tolia
400
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
funTuSa 30 TeTri Rirs. xaWapuri 50 TeTriT Zviria
Rvezelze.
45.
2 xaWapuris da
2 Rvezelis Rirebuleba
marTkuTxedis mcire
46. diagonalisa _ d.
a
1 xaWapuris,
3 Rvezelisa da
2 funTuSis Rirebuleba
gverdis
sigrZea
d
2
23
a,
xolo
653008b
amocanebi
47. 7
(a)
(b)
(g)
(d)
(e)
milion 600 aTasze 2 milion 500 aTasiT metia:
9 milion 100 aTasi
9 milion 500 aTasi
9 milion 600 aTasi
10 milion 100 aTasi
10 milion 600 aTasi
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 arasruli saSualo ganaTleba?
(a)
(b)
(g)
(d)
(e)
49. 8
(a)
(b)
(g)
(d)
(e)
9,8%
10,2%
11,6%
12,4%
13,5%
wlis win arCili 24 wlis iyo. ramdeni wlis iyo arCili x wlis win?
x  32
x  16
32  x
16  x
16  x
24
653008b
50. ABCD marTkuTxedis AB gverdis sigrZea 6 sm,
xolo A wverosa da BC gverdis M Suawertilis
SemaerTebeli monakveTisa _ 10 sm. ris tolia
marTkuTxedis AD gverdis sigrZe?
(a) 12 sm
(b) 13 sm
(g) 14 sm
(d) 15 sm
(e) 16 sm
51. maRaziaSi 1 kilogrami atami 1,5 lari Rirda, vaSli _ 2-jer meti. daviTma
am maRaziaSi atami da vaSli iyida, romelTa saerTo wona 8 kilogrami iyo.
atmis wona nayidi xilis wonis meoTxeds Seadgenda. sul ramdeni laris xili
uyidia daviTs?
(a) 11,5
(b) 12
(g) 17,5
(d) 21
(e) 24
25
653008b
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
naklebad kmayofili sakuTari profesiuli warmatebiT?
(a) soflis meurneoba
(b) ekonomika
(g) jandacva
(d) ganaTleba
(e) arc erTi
26
653008b
53. ramdenjer aRemateba jandacvis sferoSi dasaqmebul
menejerTa raodenoba,
romlebic sakuTari profesiuli warmatebiT kmayofilni arian, imave sferoSi
dasaqmebul im menejerTa raodenobas, romlebic sakuTari profesiuli warmatebiT
Zalian ukmayofiloni arian?
(a) 2-jer
(b) 2,4-jer
(g) 2,8-jer
(d) 3,2-jer
(e) 3,6-jer
54. kmayofilebis romeli xarisxobrivi kategoriis SemTxvevaSia
menejer mamakacTa raodenoba 7-iT meti menejer qalTa raodenobaze?
(a) Zalian ukmayofilo
(b) naklebad kmayofili
(g) kmayofili
(d) Zalian kmayofili
(e) arc erTi kategoriis SemTxvevaSi
dasaqmebul
55. gamokiTxul menejer qalTagan sakuTari profesiuli warmatebiT Zalian
kmayofilni aRmoCndnen ekonomikis sferoSi dasaqmebuli 6 menejeri da ganaTlebis
sferoSi dasaqmebuli 4 menejeri. ris tolia soflis meurneobis sferoSi
dasaqmebul
menejer
qalTa
raodenoba,
romlebic
sakuTari
profesiuli
warmatebiT Zalian kmayofilni arian?
(a) 16
(b) 14
(g) 12
(d) 10
(e) 8
amocanebi
56. b  27 ·43 ·34 ·356 ·701 .
Canaweri?
(a) 0
(b) 2
(g) 4
(d) 6
(e) 8
romeli
cifriT
27
bolovdeba
b
ricxvis
cifruli
653008b
57. kvadratis farTobia 81 sm2. misi TiToeuli gverdi
dayofilia sam tol nawilad da dayofis wertilebi
SeerTebulia monakveTebiT (ix. naxazi). ris tolia
miRebuli rvakuTxedis farTobi?
(a) 48 sm2
(b) 54 sm2
(g) 57 sm2
(d) 63 sm2
(e) 72 sm2
3 nawilis mosapirkeTeblad 12 saaTia saWiro. ramdeni saaTia saWiro
10
imave kedlis 1 nawilis mosapirkeTeblad?
5
(a) 6
(b) 7
(g) 8
(d) 9
(e) 10
58. kedlis
59. m, n da k erTmaneTis momdevno naturaluri ricxvebia, amasTan m  n  k .
CamoTvlilTagan romeli winadadebaa mcdari?
I. k  m kentia
II. m  n luwia
III. n · k kentia
(a)
(b)
(g)
(d)
(e)
mxolod I
mxolod II
mxolod I da II
mxolod II da III
I, II da III
60. ori qalaqidan erTmaneTis Sesaxvedrad ori matarebeli erTdroulad gamovida.
orive maTgani Tanabari siCqariT, Seferxebebis gareSe moZraobda. pirvelma
matarebelma, romlis siCqare 60 km/sT iyo, Sexvedramde 1,2-jer meti manZili gaiara,
vidre meorem. ris toli iyo meore matareblis siCqare?
(a) 48 km/sT
(b) 50 km/sT
(g) 56 km/sT
(d) 64 km/sT
(e) 72 km/sT
28
653008b
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
n naturaluri ricxvia.
61.
n-is 4-ze gayofisas
miRebuli naSTi
2n-is 4-ze gayofisas
miRebuli naSTi
5, 10, 6, ... mimdevrobis wevrebs nika da Tamari rigrigobiT werdnen _ jer nika, Semdeg _ Tamari.
62. Tamaris mier Cawerili yoveli wevri mimdevrobis
wina wevrze 2-jer meti iyo, xolo nikas mier
Cawerili _ wina wevrze 4-iT naklebi.
mimdevrobis me-4 wevri
(b)
(g)
(d)
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
mimdevrobis me-7 wevri
wris centri im marTkuTxedis erTerT wveros emTxveva, romlis erTi
gverdi wris radiusis tolia,
63. xolo meore _ diametrisa.
marTkuTxedis farTobi
(a)
wris farTobis
naxevari
29
653008b
64.
bostneuliT savse 7 erTnairi yuTis gadatanas
3 urika dasWirda. TiToeuli urikiT 120 kilogramamde tvirTis gadatanaa SesaZlebeli.
(b)
(g)
(d)
350 kg
gadatanili bostneulis wona
65.
(a)
ujridan, romelSic 4 TeTri da ramdenime wiTeli
burTulaa,
unda
amoiRon
erTi
burTula.
albaToba
imisa,
rom
ujridan
amoRebuli
3
burTula wiTeli iqneba, metia
-ze.
5
wiTeli burTulebis
raodenoba
(a)
(b)
(g)
(d)
5
amocanebi
66. saklebi 8-iT metia maklebze, xolo maklebi 8-iT metia sxvaobaze. ris tolia
maklebi?
(a) 8-is
(b) 12-is
(g) 16-is
(d) 24-is
(e) 32-is
30
653008b
67. sarben biliks wesieri xuTkuTxedis forma aqvs
(ix. naxazi). bilikis sigrZe 350 metria. sportsmenma
sirbili daiwyo A wverodan isriT miTiTebuli
mimarTulebiT. bilikis romel monakveTze aRmoCndeba
sportsmeni 800 metris garbenis Semdeg?
(a) AB -ze
(b) BC -ze
(g) CD -ze
(d) DE -ze
(e) EA -ze
68. im naturaluri ricxvebidan, romlebic metia 12-ze, magram naklebia 82-ze,
ramdenia iseTi, romlis 4-ze gayofisas miRebuli naSTi 1-is toli iqneba?
(a) 15
(b) 16
(g) 17
(d) 18
(e) 20
69. baRSi mxolod alvisa da Wadris xeebia. Wadris xeebis raodenobis Sefardeba
alvis xeebis raodenobasTan
2 -is tolia. baRSi xeebis saerTo raodenobis ra
7
nawilia alvis xeebis raodenoba?
(a) 1
(b)
(g)
(d)
(e)
5
3
5
5
7
5
6
7
9
31
653008b
70. a da b iseTi ricxvebia, rom 2a  3  4b  3 . qvemoT CamoTvlilTagan romeli
mimarTeba ar SeiZleba iyos marTebuli?
(a) a  2b  1
(b) a  4b
(g) 2b  a 1
(d) a  2b  1
(e) b  a
6
71. pirveli marTkuTxedis sigrZe 8-jer metia meore marTkuTxedis sigrZeze, xolo
farTobi 2-jer metia meore marTkuTxedis farTobze. ramdenjer naklebia pirveli
marTkuTxedis sigane meore marTkuTxedis siganeze?
(a) 2-jer
(b) 4-jer
(g) 6-jer
(d) 10-jer
(e) 16-jer
monacemTa sakmarisoba
72. fakultetze sul 300 studenti swavlobs.
mocemulia ori piroba:
I. student gogonaTa
1 nawili ucxoelia.
20
II. student vaJTa 1
nawili ucxoelia.
10
imis gasarkvevad, Tu ramdeni ucxoeli studenti swavlobs fakultetze:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
32
653008b
73. ABCD oTxkuTxedia.
mocemulia ori piroba:
I. A  B  100 .
II. B  C  200 .
imis gasarkvevad, Tu ris tolia C  D :
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
74. ori ricxvidan erTi x-is tolia, meore _ y-is.
mocemulia ori piroba:
I. x-isa da y-is jami 10-is tolia.
II. x-isa da y-is sxvaoba 4-is tolia.
imis gasarkvevad, Tu ris tolia 2 x  3 y :
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
75. turistuli saagentos TanamSromlebidan yvelaze umcrosia 25 wlis lia,
xolo yvelaze ufrosi _ ana. maT garda saagentoSi muSaobs 3 mamakaci, romelTa
saSualo asaki 30 welia.
mocemulia Semdegi ori piroba:
I. qalTa saSualo asaki mamakacTa saSualo asakze 1,5-jer metia.
II. saagentos TanamSromlebis saSualo asaki 36 welia.
imis gasarkvevad, Tu ramdeni wlisaa ana:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
33
653008b
amocanebi
76. Tornikes gasuli wlis ganmavlobaSi Tavisi xelfasis 9% bankSi Sehqonda.
wels Tornikes xelfasi 10%-iT Seumcirda, ris gamoc man bankSi Tavisi xelfasis
mxolod 6%-is Setana daiwyo. gasuli wlis ganmavlobaSi bankSi Setanili Tanxis
ramdeni procenti iqneba Tornikes mier am wlis ganmavlobaSi Setanili Tanxis
raodenoba?
(a) 50%
(b) 55%
(g) 60%
(d) 75%
(e) 90%
77. nebismieri naturaluri x
ricxvisaTvis x -iT aRniSnulia
ricxvi, romelic miiReba Semdegi
sqemis mixedviT:
magaliTad, sqemis mixedviT 5  5 · 3 · 2  4  26 .
ris tolia 8  7 ?
(a) 48
(b) 54
(g) 62
(d) 78
(e) 86
78. 3 m siRrmis mqone kubis formis auzi avsebulia wyliT. ris tolia aseve
kubis formis mqone ufro didi auzis siRrme, Tu mcire auzSi arsebuli wyliT
didi auzis mxolod 1 nawili ivseba?
8
(a) 4 m
(b) 4,5 m
(g) 5 m
(d) 5,5 m
(e) 6 m
34
653008b
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 d  c ?
ca
(a) 1
4
(b) 1
3
(g) 4
3
(d) 3
(e) 4
80. Teatris dasis wevrTa 25%-s mamakaci msaxiobebi Seadgendnen. roca dasis
6 wevri samuSaod sxva TeatrSi gadavida, mamakac msaxiobTa raodenoba Semcirda,
procentuli wili ki gaizarda. ramdeni qali msaxiobi gamoaklda Teatris dass?
(a) 6
(b) 5
(g) 4
(d) 3
(e) 2
35
653008b
2013
653009a
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. Secdoma : gasworeba
(a) saSleli : waSla
(b) naRmi : ganaRmva
(g) riye : gariyva
(d) qari : gaqarveba
2. guli aicrua : Tavi daaneba
(a) lagami miuSva : lagami amosdo
(b) gza uCvena : gza gaukafa
(g) sityva Seubruna : sityva gatexa
(d) niadagi moumzada : niadagi gamoacala
3. acra : imuniteti
(a) reklama : interesi
(b) matiane : istoria
(g) amocana : miniSneba
(d) qaragma : saidumlo
4. ekonomika : ekonomikuri bumi
(a) kultura : renesansi
(b) medicina : epidemia
(g) politikuri asparezi : arCevnebi
(d) sportuli Sejibri : finiSi
5. msaxiobi : dubliori
(a) oficeri : jariskaci
(b) mcveli : guSagi
(g) samxedro mosamsaxure : rezervisti
(d) omis veterani : axalwveuli
2
653009a
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. goeTe axalgazrda poetebs urCevda, mcire moculobis _____ did Txzulebebs
_____ : did poetur qmnilebaze muSaoba _____ , xolo axalgazrdebs _____ .
(a) nawarmoebebze dro ar daexarjaT da pirdapir / SesWidebodnen / calmxrivobas
ver itans / jer kidev ar aqvT mravalmxrivi codna movlenaTa Sesaxeb
(b) nawarmoebebze muSaobiT daewyoT da / ar SesWidebodnen / mravalmxriv codnas
moiTxovs / jer kidev calmxrivi warmodgena aqvT movlenaTa Sesaxeb
(g) nawarmoebebze muSaobiT daewyoT da / ar SesWidebodnen / calmxrivobisgan
Tavis daRwevis saukeTeso gzaa / swored mravalmxrivi codna akliaT
(d) nawarmoebebze dro ar daexarjaT da pirdapir / SesWidebodnen / xels uwyobs
mravalmxrivi codnis SeZenas / yvelaze naklebad swored calmxrivoba
axasiaTebT
7. komediaSi Sesasruleblad _____ masxaras rolia, _____ is, vinc mas asrulebs,
_____ iyos.
(a)
(b)
(g)
(d)
yvelaze
yvelaze
yvelaze
yvelaze
Zneli /
advili
Zneli /
advili
miuxedavad imisa, rom / TviTonac gonebamaxvili unda
/ miuxedavad imisa, rom / TviTon gonebamaxvili rodi unda
radgan / ar SeiZleba, TviTonac gonebamaxvili ar
/ radgan / ar SeiZleba, TviTon gonebamaxvili ar
8. _____ xelisuflebis upirvelesi daniSnuleba da mizani _____ , aSkaraa, rom
xelisuflebis nebismieri forma, romelic _____ uqmnis usafrTxo garemos
moqalaqeebs, _____ sasurvelia.
(a) miuxedavad imisa, rom / usafrTxoebis uzrunvelyofaze ar daiyvaneba / Tavisi
sxva movaleobebis ugulebelyofis xarjze / sxva formebze naklebad
(b) radgan / usafrTxoebis uzrunvelyofaa / minimaluri danaxarjebiTa da
maqsimaluri efeqturobiT / yvela sxva formaze ufro
(g) radgan / usafrTxoebis uzrunvelyofaze ar daiyvaneba / Tundac yvela sxva
movaleobis ugulebelyofis xarjze / yvela sxva formaze ufro
(d) miuxedavad imisa, rom / usafrTxoebis uzrunvelyofaa / minimaluri
danaxarjebiTa da maqsimaluri efeqturobiT / sxva formebze naklebad
3
653009a
9. imis aRsawerad, risi arsebobac _____ , rom _____ , yvelaze _____
gamoviyenoT, _____ miviRebT _ aseTma sityvebma, SesaZloa, smena daatkbon, magram
isini verafers SesZenen gonebas.
(a) SeuZlebelia an rac imdenad gaugebaria / aRweras ar eqvemdebareba /
keTilxmovani frazebi romc / Sedegad mainc mxolod cariel sityvebs
(b) ukve damtkicebulia da rac imdenad cxadia / aRweras arc saWiroebs /
damajerebeli argumentebic rom / Sedegad mainc misi iluzorulobis kidev
erT dasabuTebas
(g) SeuZlebelia an rac imdenad gaugebaria / aRweras arc saWiroebs /
damajerebeli argumentebi unda / magram Sedegad mxolod cariel sityvebs
(d) ukve damtkicebulia da rac imdenad cxadia / damajerebel dasabuTebas arc
eqvemdebareba / keTilxmovani frazebi unda / Sedegad ki misi iluzorulobis
STabeWdilebas rodi
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. turistulma kompaniam Caatara kvleva, raTa gaerkvia, Tu romels aniWebs
mosaxleoba upiratesobas Semdegi oTxi kategoriidan: sazRvao kurortze
dasveneba,
samTo
kurortze
dasveneba,
istoriuli
Zeglebis
monaxuleba,
egzotikur bunebaSi mogzauroba. Sedegebi aseTi iyo:
• egzotikur bunebaSi mogzaurobas ufro meti adamiani aniWebs
upiratesobas, vidre samTo kurortze dasvenebas.
• istoriuli Zeglebis monaxulebas ufro meti adamiani aniWebs
upiratesobas, vidre samTo kurortze dasvenebas.
• sazRvao kurortze dasvenebas ufro naklebi adamiani aniWebs upiratesobas,
vidre egzotikur bunebaSi mogzaurobas.
qvemoT CamoTvlilTagan prioritetebis romeli ganawileba (I _ yvelaze
sasurveli, IV _ yvelaze naklebad sasurveli) Seesabameba am monacemebs?
(a)
(b)
(g)
(d)
I
istoriuli Zeglebi
samTo kurorti
sazRvao kurorti
istoriuli Zeglebi
II
samTo kurorti
egzotikuri buneba
istoriuli Zeglebi
egzotikuri buneba
4
III
egzotikuri buneba
sazRvao kurorti
egzotikuri buneba
samTo kurorti
IV
sazRvao kurorti
istoriuli Zeglebi
samTo kurorti
sazRvao kurorti
653009a
11. mocemulia ori debuleba:
• Tu wvima male ar Sewydeba, nana diliT saseirnod ar wava.
• Tu nana diliT saseirnod wava, is samsaxurSi daigvianebs.
maSasadame, Tu nana diliT saseirnod wavida, wvima male Sewyvetila.
es daskvna:
(a)
(b)
(g)
(d)
gamomdinareobs mxolod orive debulebidan erToblivad
gamomdinareobs TiToeuli debulebidan meorisgan damoukideblad
gamomdinareobs mxolod erT-erTi debulebidan meorisgan damoukideblad
ar gamomdinareobs mocemuli debulebebidan
12. qalaqis centralur quCaze erT mxares oTxi didi Senobaa ganlagebuli:
eklesia,
universiteti,
biblioTeka
da
saavadmyofo.
TiToeuli
Senoba
gansxvavebuli masaliTaa mopirkeTebuli _ tufiT, granitiT, marmariloTi an
bazaltiT. amasTan cnobilia:
• saavadmyofo da eklesia ar aris tufiT mopirkeTebuli.
• bazaltiT ar aris mopirkeTebuli arc universiteti da arc saavadmyofo.
• universitetis Senoba mdebareobs uSualod marmariloTi mopirkeTebul
Senobasa da biblioTekas Soris.
• granitiT da marmariloTi mopirkeTebul Senobebs Soris mxolod erTi
Senobaa.
romeli Senobaa mopirkeTebuli marmariloTi?
(a)
(b)
(g)
(d)
eklesia
universiteti
biblioTeka
saavadmyofo
13. evoluciuri biologiis zogierTi mkvlevari spilos gansakuTrebiT didi
yurebis Camoyalibebas xsnis imiT, rom didi yurebi am cxovels sxeulis
temperaturis regulirebaSi exmareba. TavianT varauds isini afuZneben im faqtze,
rom afrikul spilos, romlis saarsebo garemoc ufro cxeli klimatiT
xasiaTdeba, bevrad ufro didi yurebi aqvs, vidre aziur spilos.
qvemoT CamoTvlilTagan romeli faqtebis dadastureba ganamtkicebda am varauds?
(a) spilos afrikuli da aziuri saxeobebi mniSvnelovnad gansxvavdeba
erTmaneTisagan sxeulis zomiT _ afrikuli spilo aziurze ufro didia.
(b) spilos afrikuli saxeoba ufro aqtiurad iyenebs komunikaciisTvis bgeriT
signalebs, vidre aziuri, romelsac naklebad aqvs ganviTarebuli smenis aparati.
(g) afrikuli spilos qvesaxeobebSi miT ufro mcirea yurisa da sxeulis zomebis
Sefardeba, rac ufro Sorsaa ekvatoridan qvesaxeobis saarsebo garemo.
(d) aziuri spilos qvesaxeobebi TiTqmis ar gansxvavdeba erTmaneTisgan garegnuli
niSnebiT, Tumca, maTi saarsebo garemo Zalian mravalferovania.
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14. qvemoT mocemul msjelobaSi daSvebulia Secdoma logikis TvalsazrisiT:
yvela frinveli frTosania da yvela mtredi frTosania. maSasadame, yvela
mtredi frinvelia.
qvemoT CamoTvlilTagan romeli msjeloba Seicavs imave tipis Secdomas?
(a) yvela studenti swavlobs inglisur enas da maikos yvela megobari studentia.
maSasadame, maikos yvela megobari swavlobs inglisur enas.
(b) yvela planeta elifsur orbitaze moZraobs da iupiteris yvela Tanamgzavri
elifsur orbitaze moZraobs. maSasadame, iupiteris yvela Tanamgzavri
planetaa.
(g) mTis yvela mdinare Cqaria da mTis zogierTi mdinaris wyali yinuliviT civia.
maSasadame, yvela Cqari mdinaris wyali yinuliviT civia.
(d) yvela meocnebe adamiani gulubryviloa da zogierTi meocnebe adamiani
idealistia. maSasadame, zogierTi gulubryvilo adamiani idealistia.
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wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
Zv. w. II aTaswleulis dasabamidan WeSmariti revolucia daiwyo egeosis
zRvis auzis kulturebSi. centraluri kunZuli iyo kreta, romelmac auwereli
naxtomi gaakeTa adrebrinjaos kulturidan Suabrinjaos xanis saocrad daxvewil
da TviTmyofad minosur* civilizaciamde. minosuri kreta mWidro ZafebiT iyo
dakavSirebuli xmelTaSua zRvis auzis mraval qveyanasTan. Zlieri da swrafi
flotis wyalobiT sakmaod farTo arealze gavrcelda kretuli kulturis
gavlena. kretis irgvliv ganlagebuli mravali kunZuli Tavad warmoadgenda
minosuri kulturis erTgvar filials da, amave dros, am kulturis
gamavrcelebels xmelTaSuazRvispireTis bevr regionSi. erT-erTi aseTi kunZuli
iyo Tera _ minosuri kretis umniSvnelovanesi dasayrdeni.
1967 wels berZeni arqeologis _ spiridon marinatosis _ gaTxrebis Sedegad
gamovlinda egeosuri kulturis mniSvnelovani kera kunZul Teraze, romlis
arsebobac Seuwyvetia udidesi Zalis vulkanur amofrqvevas. wriuli formis
kunZulis didi nawili wyliT daifara. Teram naxevarmTvaris forma miiRo. Teras
katastrofas ukavSireben berZnul miTs devkalionis warRvnis Sesaxeb. es miTi
Zalian hgavs noes mier adamianTa modgmis gadarCenis ambavs, romelic bibliaSia
aRwerili. devkalioni, miTis Tanaxmad, mama yofila helenosis, elinTa eponimis.
helenosi ki, Tavis mxriv, yvela ZiriTadi berZnuli tomis winaprad aris
miCneuli. devkalionis warRvna daaxloebiT Zv. w. XV saukuneSi unda momxdariyo.
kunZuli Tera aSkarad minosuri kretis filials warmoadgenda daRupvis
momentisaTvis.
umniSvnelo
lokaluri
Taviseburebebis
miuxedavad,
Teraze
aRmoCenili
freskebis
stili
imgvarivea,
rogoric
kretul
mxatvrobaSi.
sayuradReboa Teraze aRmoCenili sami freska: 1. TerelTa
ganebivrebaze unda
migviTiTebdes cisferi maimunebis freska, radgan es cxovelebi fufunebis
moyvarul Terelebs mxolod afrikidan SeeZloT SemoeyvanaT. 2. erTi freska
warmogvidgens scenas libiis an romeliRac afrikuli qveynis cxovrebidan,
rogorc amas masze gamosaxuli adamianebis Tmis varcxniloba da lomisgan
devnili antilopebis detali miuTiTebs. 3. aseve sainteresoa freska, romelzec
gamosaxulia, Tu rogor mierekebian mwyemsebi naxirs. amave freskaze qvemoT Cans
grZeli SubebiT da uzarmazari farebiT SeiaraRebul, afrikul tunikebSi
gamowyobil mamakacTa razmi, romelic aSkarad sabrZolvelad miemarTeba.
Teras katastrofa gamanadgurebeli aRmoCnda egeosis zRvis kunZulebisTvis,
pirvel rigSi ki kretisTvis. marTalia, am katastrofas minosuri kreta mTlianad
ar waulekavs, magram erTbaSad ganadgurda kretelTa cnobili floti, maTi
xmelTaSua zRvaSi pirvelobis erT-erTi mZlavri sayrdeni, daqveiTda vulkanuri
ferfliT mofenili vrceli teritoriebis nayofiereba da, rac mTavaria, am
katastrofam moralurad dasca minoselebi, daarRvia maTi civilizaciis
harmoniuloba, romelic mniSvnelovanwilad emyareboda egeosis zRvis sxvadasxva
regionis kretasTan urTierTkavSirs.
Zv. w. XV saukunidan kretaze dafuZnebas iwyeben berZnebi. rogorc Cans,
ufro maRali donis minosur kulturasTan uSualo Sexeba kretis berZen
dampyroblebze Zlier gavlenas axdens. marTalia, kretaze kvlav grZeldeba
cxovreba, magram kunZuli sabolood kargavs wamyvan poziciebs da TandaTan
aRmavali berZnuli samyaros periferiad gadaiqceva.
* winaberZnuli civilizacia; ewoda kretis legendaruli mefis – minosis – saxelis mixedviT.
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15. qvemoT CamoTvlilTagan romeli ar iyo mniSvnelovani faqtori imisaTvis,
rom kunZuli kreta minosuri civilizaciis centri gamxdariyo?
(a) minosuri kreta mWidro ZafebiT iyo dakavSirebuli xmelTaSua zRvis auzis
mraval qveyanasTan
(b) minosuri kretis filiali da misTvis erT-erTi mniSvnelovani dasayrdeni iyo
kunZuli Tera
(g) Zlieri da swrafi flotis wyalobiT sakmaod farTo arealze gavrcelda
kretuli kulturis gavlena
(d) kretis irgvliv ganlagebuli mravali kunZuli Tavad warmoadgenda minosuri
kulturis gamavrcelebels xmelTaSuazRvispireTis bevr regionSi
16. ras niSnavs sityva eponimi (upasuxeT konteqstis mixedviT)?
(a)
(b)
(g)
(d)
pirs, romlis saxelisganac warmosdgeba xalxis saxelwodeba (helenosi _ elini)
bibliur personaJs, romlis saxelic ukavSirdeba warRvnas (noe _ devkalioni)
bibliuri noes analogiur miTologiur personaJs (noe _ devkalioni)
berZnuli tomebis winapris saxels (helenosi _ elini)
17. gTavazobT Teraze aRmoCenili freskebis interpretaciebs:
I cisferi maimunebis freska _ es egzotikuri cxovelebi migvaniSnebs TerelTa
garTobasa da siamovnebaze orientirebul cxovrebaze, agreTve, TerelTa
urTierTobebze afrikis qveynebTan.
II antilopebis freska _ gagvacnobs TerelTa cxovrebis wess, maTs yofas;
antilopebis gamosaxuleba ki mxolod detalia da daskvnis gamotanis
saSualebas ar gvaZlevs.
III mwyemsebis freska _ TerelTa yofis mSvidobian xasiaTzec migvaniSnebs da
romeliRac brZolis istoriazec mogviTxrobs, Tumca, es SeiZleba afrikuli
ambavic iyos.
romeli interpretaciaa marTebuli?
(a)
(b)
(g)
(d)
mxolod I
mxolod II
I da III
II da III
8
653009a
18. minosuri kultura Zvel samyaroSi gamorCeuli iyo Tavisi mSvidobiani
xasiaTiT, harmoniulobiT. kretaze ar yofila arc erTi cixesimagre, araviTari
niSani imisa, rom kunZulis mosaxleobas minosur periodSi vinmesTan omi
ewarmoebinos. am viTarebis aRsaniSnad mecnierebaSi damkvidrda termini `minosuri
mSvidoba~ (Pax Minoica).
teqstisa da am informaciis safuZvelze kretasa da Teras urTierTmimarTebis
Sesaxeb SeiZleba vivaraudoT:
(a) Tera zustad, lokaluri Taviseburebebis gareSe, icavs minosuri kretis
kulturul, sazogadoebrivsa Tu mxatvrul principebs
(b) Teras cxovreba radikalurad gansxvavdeba kretulisgan, radgan Teras
freskebidan Cans am kunZulis sabrZolo ganwyoba ucxotomelTa mimarT
(g) Teras intensiuri kontaqtebi unda hqonoda afrikis qveynebTan, rasac samive
aRniSnuli freskac mowmobs, kretas ki kulturuli urTierTobebi ar hqonia
ucxo qveynebTan
(d) Teras freskaze gamosaxuli iaraRi Cans mxolod afrikul konteqstSi,
amdenad, am kunZulTa cxovrebis wesi urTierTsapirispiro ar unda iyos _
`minosuri mSvidoba~ SeiZleba Terazec gavavrceloT
19. devkalionis warRvnis
ZiriTadi momenti:
miTis
gacnobis
Semdeg
SeiZleba
gamovyoT
ori
(a) marinatosis
gaTxrebma,
ZiriTadad,
daadastura
devkalionis
warRvnis
realuroba; minosuri kulturis centri unda yofiliyo kunZuli Tera da
ara _ kreta
(b) berZnebis aRmavlobamde kreta da misi maxlobeli kunZulebi dasaxlebuli
yofila
araelinuri
tomebiT;
did
katastrofas
gamouwvevia
ZalTa
Tanafardobis Secvla egeosis zRvis auzSi, ris Semdegac asparezze
gamosulan sakuTriv berZnebi
(g) arqeologiuri kvlevis Sedegad gamovlinda minosuri kulturis kvali
kunZul Teraze; warRvnis Sesaxeb berZnul miTs ar SeiZleba paraleli
movuZebnoT bibliur istoriaSi
(d) dasturdeba bibliuri warRvnisa da devkalionis warRvnis identuroba;
devkalionis Svili, helenosi, yofila im xalxis winapari, romelmac Seqmna
winaberZnuli civilizacia
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20.
qvemoT CamoTvlilTagan
mixedviT?
romeli
daskvna
ar
aris
marTebuli
teqstis
(a) kreta minosuri kulturis centri iyo, kargadac aris Seswavlili, magram
Teras freskebs egeosuri kulturis mTliani suraTis aRsadgenad uTuod
didi mniSvneloba aqvT
(b) egeosis zRvis auzSi marTlac momxdara geologiuri katastrofa, romlis
masStabebi warRvnis Sesaxeb devkalionis miTis warmoqmnas savsebiT realur
safuZvels uqmnida
(g) egeosuri kultura gavlenas axdenda xmelTaSua zRvis auzis qveynebze, Teras
freskebidan ki sapirispiro procesi Cans: afrikis qveynebi uaryofiT gavlenas
axdendnen berZnuli kulturis TviTmyofadobaze
(d) Teras katastrofam daarRvia minosuri kulturis harmoniuloba, kretam
dakarga kulturuli centris funqciebi, rasac mohyva elinuri poziciebis
gamyareba da berZnuli civilizaciis aRmavloba
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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. apaTia : interesi
(a) sasowarkveTa : imedi
(b) SiSi : riski
(g) warmateba : sixaruli
(d) eiforia : diskomforti
22. Waobi : wyali
(a) udabno : oazisi
(b) jungli : tropikuli klimati
(g) tramali : stepi
(d) taiga : wiwvovani tye
23. konkurencia : metoqeoba
(a) koleqcia : SerCeva
(b) kombinacia : dakavSireba
(g) kolonizacia : gadasaxleba
(d) komunikacia : gadacema
24. jaWvi : jaWvuri reaqcia
(a) wertili : wertilovani xazi
(b) ornamenti : ornamentuli dekori
(g) kenWi : kenWovani daavadeba
(d) horizonti : horizontaluri mdgomareoba
25. sinaTle : siTbo
(a) wyali : talRa
(b) ali : nakverCxali
(g) feri : surneli
(d) gemo : sitkbo
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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. sazogadoebrivi simSvide didi sikeTea, _____ , xalxebi tiraniamde swored
_____ . cxadia, es imas ar niSnavs, rom _____ sazogadoebrivi wesrigi; _____ .
nebismieri xalxi, romelic Tavis mTavrobas _____ , gulis siRrmeSi ukve monaa
_ mona sakuTari keTildReobisa, da _____ mas borkilebs daadebs.
(a) Tumca, / sazogadoebrivi wesrigis naklebobas mihyavs / unda gvsurdes mxolod /
magaliTad, Tavisufleba aranakleb mniSvnelovania / wesrigis SenarCunebaze
mets sTxovs / male gamoCndeba vinme, vinc
(b) Sesabamisad, / sazogadoebrivi wesrigis naklebobas mihyavs / yvelafers unda
gverCivnos / magram is namdvilad ufro mniSvnelovania, vidre Tavisufleba /
wesrigis SenarCunebaze mets sTxovs / nuravis eqneba imedi, rom
(g) magram / sanimuSo sazogadoebrivi wesrigiT midian / araferia ufro
mniSvnelovani, vidre / magaliTad, Tavisufleba masze ufro mniSvnelovania /
mxolod wesrigis SenarCunebas sTxovs / nuravis eqneba imedi, rom
(d) magram / sanimuSo sazogadoebrivi wesrigiT midian / ar unda gvsurdes /
Tumca, marto wesrigi sakmarisi ar aris / mxolod wesrigis SenarCunebas
sTxovs / male gamoCndeba vinme, vinc
27.
erTi
adamianis
Zala
_____
misi
sasicocxlo
moTxovnilebebis
dasakmayofileblad, _____ adamianis suli da goneba _____ adamianebi _____
sxvebTan urTierTobas, _____ saWiroeben sxvebis Tanadgomasa da daxmarebas.
(a) SeiZleba sruliad sakmarisi iyos / xolo / kargad eguebodes maradiul
martoobas, magram / mainc gaurbian / Tuki aucileblad ar
(b) SeiZleba sruliad sakmarisi iyos / magram / ver egueba maradiul martoobas
_ marTlac, / imdenad aucileblobad ar miiCneven / ramdenadac
(g) imdenad arasakmarisia / xolo / imdenad ver egueba maradiul martoobas, rom /
bunebrivad eswrafvian / aucileblad
(d) imdenad arasakmarisia / da / imdenad kargad egueba maradiul martoobas, rom /
xSirad gaurbian / Tumca, iSviaTad
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28. vagneri
werda:
,,tristanisa
da
izoldas“ werisas
grZnoba
Cemi
Seyvarebulisadmi _____ gaxldaT, _____ is martooden sawyisi wertilis rols
_____ , vinaidan Cemi mizani _____ piradi gancdebis gamomJRavneba musikalur
TanaxmianobaSi.
(a)
(b)
(g)
(d)
mravalTa Soris erT-erTi motivi / maSasadame, / asrulebda / iyo mxolod
gadamwyveti stimuli / maSasadame, / ar asrulebda / ufro didi iyo, vidre
mravalTa Soris erT-erTi motivi / magram / ar asrulebda / ar iyo mxolod
gadamwyveti stimuli / magram / asrulebda / ufro didi iyo, vidre
29. bolo aTwleulebis ganmavlobaSi biologebis nayofieri muSaobis _____
organizmebis materialuri struqturisa da maTi funqcionirebis Sesaxeb, _____ ,
ratom _____ dRevandeli fizika da qimia cocxal organizmSi mimdinare
movlenebs.
(a) miuxedavad, kidev didxans imdenad mcire gvecodineba / rom imis Tqmas mainc
SevZlebT / ver xsnis
(b) wyalobiT male sakmaod bevri gvecodineba / Tumca, imis Tqmas mainc ver
SevZlebT / xsnis ase warmatebiT
(g) miuxedavad, jer kidev imdenad mcirea cnobili / rom Znelia Tundac imis Tqma /
xsnis ase warmatebiT
(d) wyalobiT dRes sakmaod bevria cnobili / raTa imis Tqma mainc SevZloT /
ver xsnis
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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. 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 ayenebs eWvqveS am varauds?
(a) kerZo seqtorSi dasaqmebuli specialistebisTvis Tanamdebobrivi dawinaurebis
da, Sesabamisad, anazRaurebis gazrdis albaToba ufro mcirea, vidre _
sajaro samsaxurSi dasaqmebulTaTvis
(b) sajaro samsaxurebSi specialistebis kvalifikaciis mimarT bevrad ufro
maRali moTxovnebia, vidre _ kerZo seqtorSi
(g) kerZo seqtorSi mosamsaxureebs samuSaos SenarCunebis TvalsazrisiT ufro
meti stabilurobis gancda aqvT, vidre _ sajaro seqtorSi dasaqmebul
specialistebs
(d) kerZo seqtorSi didi moTxovnaa kvalificiur specialistebze, Sesabamisad,
kerZo kompaniebi cdiloben, saukeTeso pirobebi SesTavazon TanamSromlebs
31. mebaRem vaSlis, atmis, msxlisa da blis TiTo nergi SeiZina da erT mwkrivad
daawyo. erTmaneTisgan gasarCevad maT sxvadasxva feris _ wiTeli, yviTeli, lurji da
TeTri _ niSnebi gaukeTa (ara aucileblad am TanmimdevrobiT). mocemulia:
•
•
•
•
lurjniSniani nergi atmisa da blis nergebze ufro maRalia.
TeTrniSniani nergis marcxniv blis nergi devs, xolo marjvniv _ atmis nergi.
blis nergs wiTeli niSani ar ukeTia.
vaSlis nergi da wiTelniSniani nergi erTmaneTis gverdiT ar awyvia.
ra feris niSani ukeTia TiToeul nergs?
(a)
(b)
(g)
(d)
vaSls
TeTri
lurji
yviTeli
lurji
atams
wiTeli
yviTeli
TeTri
wiTeli
msxals
lurji
wiTeli
lurji
TeTri
14
bals
yviTeli
TeTri
wiTeli
yviTeli
653009a
32. mocemulia:
• yvela mdinare, romelic maRal mTebSi iRebs saTaves, didi siswrafiT
moedineba da Zalian civi wyliT gamoirCeva.
• yvela mdinare, romlis saTavec maRal mTebSi ar aris, mravali cocxali
organizmis saarsebo garemoa da mniSvnelovania soflis meurneobisaTvis.
qvemoT CamoTvlilTagan romlis arsebobaa SeuZlebeli am wanamZRvrebis mixedviT?
(a) mdinarisa, romelic maRal mTebSi iRebs saTaves, didi siswrafiT moedineba da
ar aris mravali cocxali organizmis saarsebo garemo
(b) mdinarisa, romelic Zalian civi wyliT ar gamoirCeva da ar aris
mniSvnelovani soflis meurneobisaTvis
(g) mdinarisa, romelic Zalian civi wyliT ar gamoirCeva da cocxali
organizmebis saarsebo garemoa
(d) mdinarisa, romlis saTavec maRal mTebSi ar aris da Zalian civi wyliT
gamoirCeva
33. sami megobari gegmavs erTad mogzaurobas evropaSi. isini msjeloben imaze, Tu
romeli qalaqebi moinaxulon. maT gadawyvetili aqvT, rom aucileblad
daaTvaliereben erT-erTs mainc _ prados muzeums madridSi an uficis galereas
florenciaSi. amasTan, TiToeuli maTgani TiTo mosazrebas gamoTqvams:
A: Tu parizSi CavalT, madridSi wasvlas veRar movaswrebT.
B: Tu florenciaSi wavalT, maSin romSic aucileblad unda CavideT.
C: Tu romSi wavalT, arc madridSi wasvlaze unda vTqvaT uari.
Tu davuSvebT, rom megobrebma erTmaneTis yvela mosazreba gaiTvaliswines da
sawyisi gadawyvetilebac Seasrules, qvemoT CamoTvlilTagan romeli SemTxveva
ganxorcielda?
(a)
(b)
(g)
(d)
megobrebi iyvnen
megobrebi iyvnen
megobrebma uari
megobrebma uari
parizsa da florenciaSi
parizSi da uari Tqves romSi wasvlaze
Tqves rogorc parizSi, ise madridSi wasvlaze
Tqves parizSi wasvlaze, Tumca, iyvnen florenciaSi
15
653009a
34. sapatrulo policiis monacemebiT, manqanis marTvisas qalebi ufro xSirad
iyeneben usafrTxoebis Rvedebs, vidre mamakacebi. erT-erTi policielis varaudiT,
es imiT aixsneba, rom qalebi naklebad gamocdili mZRolebi arian da amitom
ufro xSirad icaven usafrTxoebis wesebs.
qvemoT CamoTvlilTagan romeli ayenebs eWvqveS am varauds?
(a) mamakaci mZRolebi, qalebTan SedarebiT, ufro xSirad arRveven sagzao wesebs,
Tumca, iseve xSirad qmnian saavario situaciebs, rogorc qalebi
(b) qali mZRolebis umravlesoba, mamakacebTan SedarebiT, gacilebiT ufro gvian
miujda saWes, Tumca, aranaklebi ostatobiT marTavs manqanas
(g) im markis manqanebis salonis dizainis Seqmnisas, romlebsac mamakacebi aniWeben
upiratesobas, naklebi yuradReba eqceva Rvedebis komfortulobas
(d) im markis manqanebi, romlebsac qalebi aniWeben upiratesobas, rogorc wesi,
Zravis simZlavriT ar gamoirCeva da did siCqares ver aviTarebs
16
653009a
wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
mravali saukunis ganmavlobaSi miaCndaT, rom varskvlavebi calke arsebul,
erTmaneTisgan izolirebul mnaTobebs warmoadgenen. marTalia, zog adgilas isini
Zalze axlomyof varskvlavTa erTobliobas qmnian, magram amis axsna advilad
SeiZleboda: xeebi da cocxali arsebebic xom xSirad mWidro jgufebis saxiT
gvxvdebian da, miuxedavad amisa, TiToeuli damoukidebel, calke arsebul
obieqtad rCeba. Tumca, teleskopis gamogonebis Semdeg gairkva, rom zogjer
varskvlavebs Soris gacilebiT ufro mcire manZilia, vidre adre varaudobdnen.
uiliam herSeli, romelic galaqtikis modelze muSaobda, XVIII saukunis
bolos
Seiswavlida
varskvlavebs,
romlebic
caze
erTmaneTTan
Zalze
axlomyofebad
aRiqmebodnen. herSeli varaudobda, rom sinamdvileSi erT-erTi
maTgani ufro axlos iqneboda CvenTan, xolo meore _ gacilebiT Sors.
Sesabamisad, is SeZlebda, ganesazRvra manZili axlomdebare varskvlavamde da am
ukanasknelis paralaqsi* daSorebulis mimarT. magram paralaqsis gansazRvris
nacvlad man aRmoaCina, rom xSirad varskvlavebi erTmaneTis irgvliv brunaven.
herSeli mixvda, rom mis winaSe `binaruli~ (ormagi) varskvlavebia, romelTa
Soris manZili imdenad mcirea, rom maT magnituri velic ki saerTo aqvT.
Tavdapirvelad fiqrobdnen, rom binaruli varskvlavebi iSviaTi movlenaa. Tumca,
Semdgomi kvlevebidan gairkva, rom bevri varskvlavi binaruli, zogjer ki ufro
rTuli sistemis nawilia.
germanelma astronomma fridrix beselma, romelic siriusamde manZilis
dasadgenad akvirdeboda mis gadaadgilebas caze, aRmoaCina, rom mnaTobi Tavis
traeqtoriaze, sworxazovanis nacvlad, talRiseburad moZraobs. varskvlavis
amgvari gadaadgileba, beselis azriT, romeliRac axlo obieqtiT unda yofiliyo
ganpirobebuli. Tu siriusis sididis varskvlavi iZulebulia, talRiseburad
imoZraos, es niSnavs, rom meore obieqtis mizidulobis Zala uzarmazaria. meore
obieqti ki mxolod varskvlavi SeiZleboda yofiliyo. beselma ivarauda, rom
siriusi binaruli varskvlavia, romelsac Tavisi uxilavi, `bneli kompanioni~
hyavs. imdroindeli samecniero sazogadoeba skeptikurad Sexvda beselis
hipoTezas, romlis mixedviTac siriusis mewyvilis masa daaxloebiT mzis toli unda
yofiliyo. Tavad siriusi mzeze 20-jer ufro elvarea da orjer ufro masiuri.
1862 wels amerikelma elvin klarkma siriusze gamoscada Tavisi axali
teleskopiT miRebuli gamosaxulebis simkveTre. siriusis maxloblad – iq, sadac,
beselis varaudiT, varskvlavis `bneli kompanioni~ unda yofiliyo, man susti
naTeba dainaxa. am naTebis yuradRebiT daTvalierebis Sedegad klarkma daaskvna,
rom es namdvilad siriusis mewyvile iyo, romelic mis talRisebur moZraobaSia
`damnaSave~. amJamad Tavad siriuss uwodeben А siriuss, xolo mis `megobars~– B
siriuss.
B siriusi gavarvarebuli, udidesi simkvrivisa da mcire zomis varskvlavia,
romelic varskvlavTa e. w. TeTri jujebis jgufs miekuTvneba. roca varskvlavi
Tavisi sicocxlis dasasruls uaxlovdeba, is TeTr jujad – evoluciis bolo
stadiaze myof Zalze SekumSul varskvlavad gadaiqceva. cnobilia, rom
varskvlavis SigniT TermobirTvuli reaqciebi mimdinareobs. TermobirTvuli
sawvavis amowurvasTan erTad varskvlavis siRrmeebi `civdeba~ da misi Termuli
wneviT warmoqmnili Zala veRar uwevs winaaRmdegobas gravitaciul SekumSvas.
Tumca, Zalze didi dro gaivlis, vidre is energiis mTel Tavis marags gaxarjavs.
* paralaqsis, paralaqsuri gadaadgilebis gansazRvra ciur mnaTobamde manZilis dadgenis erTerTi ZiriTadi meTodia astronomiaSi.
17
653009a
35. ra mizniT mohyavs avtors xeebTan da cocxal arsebebTan varskvlavebis
Sedarebis magaliTi?
(a) ciur sxeulTa urTierTganlagebis kanonzomierebaTa naTelsayofad
(b) teleskopis gamogonebamde arsebuli Sexedulebis gasamyarebel argumentad
(g) teleskopiT warmoebuli dakvirvebebis Sedegebis safuZvlianobis
dasadastureblad
(d) varskvlavTa sivrculi ganawilebis Sesaxeb arsebuli hipoTezebis
mravalferovnebis xazgasasmelad
36. herSelma Tavisi dakvirvebebis safuZvelze aRmoaCina, rom:
(a) binaruli varskvlavebidan erT-erTi ufro axlosaa CvenTan, xolo meore _
gacilebiT Sors, miuxedavad amisa, maT saerTo magnituri veli aqvT
(b) erTmaneTTan Zalze axlomyofi varskvlavebis paralaqsis dadgena SeuZlebelia
(g) xSirad varskvlavebi ara marto aRiqmebian erTmaneTTan axlomyof obieqtebad,
aramed realuradac amgvarad arian ganlagebulni
(d) varskvlavebis umravlesoba binaruli, zogjer ki ufro rTuli sistemis
nawilia
37. ratomaa brWyalebSi Casmuli B siriusis aRsaniSnavad gamoyenebuli sityvebi
(`bneli kompanioni~, `damnaSave~ da ,,megobari~)?
(a) es sityvebi uCveulo konteqstSia gamoyenebuli – usulo obieqtebis
maxasiaTeblebad
(b) am xerxiT SesaZlebeli iyo e. w. TeTri jujebis mimarT ironiuli
damokidebulebis gamoxatva
(g) am gziT avtorma e. w. TeTri jujebis urTierTkavSiris TvalsaCino suraTi
Seqmna
(d) am sityvebis meSveobiT avtori aRwers binaruli varskvlavebis WeSmarit
bunebas
38. moyvanilia ramdenime winadadeba III abzacidan:
• Tu siriusis sididis varskvlavi iZulebulia, talRiseburad imoZraos, es
niSnavs, rom meore obieqtis mizidulobis Zala uzarmazaria.
• siriusi Tavis traeqtoriaze, sworxazovanis nacvlad, talRiseburad
moZraobs.
• varskvlavis amgvari gadaadgileba romeliRac axlo obieqtiT unda
yofiliyo ganpirobebuli.
• meore obieqti mxolod varskvlavi SeiZleboda yofiliyo.
qvemoT CamoTvlilTagan romelSia marTebulad warmodgenili am winadadebaTa
Tanmimdevroba maTi daniSnulebis mixedviT?
(a)
(b)
(g)
(d)
faqti da varaudi – varaudi – daskvna – varaudi
varaudi da mizezi – faqti _ mizezi – daskvna
faqti da daskvna – faqti – varaudi – varaudi
mizezi da Sedegi – varaudi – daskvna – faqti
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653009a
39. ra mimarTebaa fridrix beselisa da elvin klarkis mier gakeTebul aRmoCenebs
Soris?
(a) beselma aRmoaCina, rom siriuss hyavs Tavisi mewyvile, xolo klarkma es
varskvlavi e. w. TeTri jujebis kategorias miakuTvna
(b) klarkma uSualo dakvirvebis Sedegebis safuZvelze daadastura beselis
hipoTezis marTebuloba
(g) beselma maTematikuri formulebis gamoyenebiT daadgina, rom siriusi
binaruli varskvlavia, xolo klarkma teleskopiT dakvirvebis safuZvelze
gamoitana daskvna
(d) klarkma gaimeora beselis kvleva, raTa daezustebina A siriusis mdebareoba B
siriusis mimarT
40. teqstis romel abzacebs ukavSirdeba qvemoT mocemuli damatebiTi cnobebi?
1. varskvlavi gigantur Rumels hgavs, romelic sawvavis gamolevasTan erTad
gacivebas iwyebs. Tu gavigebT, ramdenad civia es Rumeli, maSin isic
gvecodineba, ra xnis ganmavlobaSi ganicdida is sawvavis ukmarisobas.
2. alfa centavra an gedi 61, romlebic erT varskvlavad iyvnen miCneulni,
sinamdvileSi binaruli varskvlavebi aRmoCndnen.
3. В siriusis diametri ufro mcirea, vidre dedamiwisa. Tumca, is mxolod
zomiTaa patara da ara masiT, rac beselisTvis imTaviTve cxadi iyo. Semdgomi
kvlevebiT dadginda, rom В siriusis masa mzis masis tolia; anu TiTqos mzis
mTeli masa erT pawawina moculobis varskvlavSia Cawnexili.
(a)
(b)
(g)
(d)
2
2
2
2
_
_
_
_
II abzacs, 1 – III abzacs, 3 – IV-V abzacebs
I-II abzacebs, 3 – III abzacs, 1 – V abzacs
I abzacs, 1 – III-IV abzacebs, 3 – V abzacs
I abzacs, 3 – III da V abzacebs, 1 – V abzacs
19
653009a
maTematikuri nawili
2013
III
testis maTematikur nawilze muSaobisas gaiTvaliswineT:



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:
10. paraleluri wrfeebi:
ori paraleluri wrfis mesame
wrfiT gadakveTisas Siga jvaredina
kuTxeebi tolia: α = β.
11. samkuTxedi:
1. nuli arc dadebiTia da arc uaryofiTi;
1 ar aris martivi ricxvi.
2. procenti:
a ricxvis k% aris
.
n
3. xarisxi: a = a · a · a · ...· a (n-jer)
 samkuTxedis kuTxeebis sidideTa jami
180°-is tolia;
 piTagoras Teorema:
marTkuTxa samkuTxedis
hipotenuzis sigrZis
kvadrati kaTetebis sigrZeTa
kvadratebis jamis tolia:
an · am = an + m
n
m
a :a =a
n–m
m
(a n ) = a n · m
4. proporcia: Tu
5. siCqare:
, maSin ad = bc.
siCqare 
manZili
AB2 = AC2 + BC2
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 elementa-
ruli xdomilobebi Tanabrad mosalodnelia.
 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 = r2.
8. Semoklebuli gamravlebis formulebi:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2
9. naxazze kuTxe SeiZleba
moniSnuli iyos kuTxis
gverdebs Soris Casmuli
patara rkaliT, marTi kuTxe
ki _ patara kvadratiT.
14. marTkuTxa paralelepipedi:
 marTkuTxa paralelepipedis
moculoba misi sigrZis, siganisa da
simaRlis namravlis tolia: V = abc;
 kubis SemTxvevaSi: a = b = c.
A aRniSnavs A kuTxis sidides.
21
653009b
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
41.
B
11
4
2,750
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
m naturaluri ricxvia.
42.
m 1
2
m2
3
xuTkuTxa piramidis yvela wibo erTmaneTis tolia,
maTi sigrZeTa jami ki 25 sm-ia.
43.
am piramidis gverdiTi
waxnagis perimetri
6 sm
22
653009b
44.
samniSna ricxvi,
romlis cifrTa jami
19-is tolia
samniSna ricxvi,
romlis cifrTa jami
15-is tolia
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
funTuSa 30 TeTri Rirs. xaWapuri 80 TeTriT Zviria
Rvezelze.
45.
2 xaWapuris da
1 Rvezelis
Rirebuleba
1 xaWapuris,
3 Rvezelisa da
1 funTuSis Rirebuleba
kvadratis gverdis sigrZea a, xolo diagonalisa _ d.
46.
d
2
a
23
653009b
amocanebi
47. 4
(a)
(b)
(g)
(d)
(e)
milion 700 aTasze 3-jer metia:
6 milion 100 aTasi
7 milion 700 aTasi
12 milion 700 aTasi
14 milion 100 aTasi
15 milion 200 aTasi
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 ar
aqvs ganaTleba?
(a)
(b)
(g)
(d)
(e)
10,2%
11,3%
11,8%
12,1%
12,6%
49. 9 wlis Semdeg giorgi 25 wlis gaxdeba. ramdeni wlis gaxdeba giorgi y wlis
Semdeg?
(a) 34  y
(b) 15  y
(g) 15  y
(d) y  34
(e) y  16
24
653009b
50. MNEF marTkuTxedis MN gverdis sigrZea 4 sm,
MF gverdisa _ 9 sm, xolo M wverosa da NE
gverdis A wertilis SemaerTebeli MA monakveTisa _
5 sm. ris tolia AE monakveTis sigrZe?
(a) 4 sm
(b) 5 sm
(g) 6 sm
(d) 7 sm
(e) 8 sm
51. moTxrobebis krebulis fasi iyo 6 lari. magram gayiduli 250 krebulidan am
fasad mxolod 60% gaiyida, danarCeni ki fasdaklebiT _ naxevarfasad. sul
ramden larad gaiyida es krebulebi?
(a) 1000
(b) 1150
(g) 1200
(d) 1350
(e) 1500
25
653009b
monacemTa analizi
erT-erTma sadazRvevo kompaniam Caatara gamokiTxva klientebis sxvadasxva
sadazRvevo
produqtiT
kmayofilebis
xarisxis
dasadgenad.
gamokiTxvaSi
monawileoba miiRes pirebma, romlebic sargeblobdnen janmrTelobis, avtomanqanis,
uZravi qonebis an samogzauro dazRveviT (sul 160 respondenti), maT Soris
80 respondenti miekuTvneboda 31-dan 40 wlamde asakobriv jgufs, xolo
danarCeni _ 41-dan 50 wlamde asakobriv jgufs.
pirvel
diagramaze
warmodgenilia
respondentTa
ganawileba
sxvadasxva
sadazRvevo produqtiT kmayofilebis xarisxis mixedviT.
meore diagramaze ki warmodgenilia 31-dan 40 wlamde da 41-dan 50 wlamde
asakobrivi
jgufebis
respondentTa
ganawileba
sadazRvevo
produqtebiT
kmayofilebis xarisxis mixedviT.
diagramebis mixedviT upasuxeT Semdeg 4 SekiTxvas:
26
653009b
52. ramdenjer aRemateba im klientTa raodenoba, romlebic uZravi qonebis
dazRveviT sargebloben da momsaxurebiT kmayofilni arian, im klientTa
raodenobas, romlebic dazRvevis imave produqtiT sargebloben da momsaxurebiT
naklebad kmayofilni arian?
(a) 3-jer
(b) 3,2-jer
(g) 3,6-jer
(d) 4-jer
(e) 4,4-jer
53. kmayofilebis romeli xarisxobrivi kategoriis SemTxvevaSia 41-dan 50 wlamde
respondentTa raodenoba 6-iT meti 31-dan 40 wlamde respondentTa raodenobaze?
(a) Zalian ukmayofilo
(b) naklebad kmayofili
(g) kmayofili
(d) Zalian kmayofili
(e) arc erTi kategoriis SemTxvevaSi
54. sadazRvevo produqtebidan romliT ar aris arc erTi klienti Zalian
kmayofili momsaxurebis xarisxiT?
(a) avtodazRveviT
(b) janmrTelobis dazRveviT
(g) samogzauro dazRveviT
(d) uZravi qonebis dazRveviT
(e) arc erTiT
55. 41-dan 50 wlamde respondentebidan janmrTelobis dazRveviT
naklebad
kmayofili aRmoCnda 5 klienti, xolo avtodazRveviT _ 11 klienti. am asakobrivi
jgufis respondentebidan ramdeni aRmoCnda naklebad kmayofili uZravi qonebis
dazRveviT?
(a) 7
(b) 6
(g) 5
(d) 4
(e) 3
amocanebi
56. b  28 ·49 ·31 ·357 ·703 . ris tolia b ricxvis 10-ze gayofisas miRebuli naSTi?
(a) 0
(b) 2
(g) 4
(d) 6
(e) 8
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653009b
57. kvadratis farTobia 9 sm2. misi ori mopirdapire
gverdis Suawertilebis SemaerTebeli monakveTi dayofilia
sam tol nawilad da dayofis wertilebi SeerTebulia
monakveTebiT kvadratis wveroebTan (ix. naxazi). ris tolia
miRebuli eqvskuTxedis farTobi?
(a) 5 sm2
(b) 5,5 sm2
(g) 6 sm2
(d) 6,5 sm2
(e) 7 sm2
58. kedlis ra nawilis mopirkeTebaa SesaZlebeli 3 saaTsa da 20 wuTSi, Tu amave
kedlis 2 nawilis mosapirkeTeblad 2 saaTi da 40 wuTia saWiro?
(a)
(b)
(g)
(d)
(e)
5
1
2
3
5
2
3
3
4
5
6
59. a, b da c kenti naturaluri ricxvebia, amasTan a  b  c . CamoTvlilTagan
romeli winadadebaa marTebuli?
I. a  b  c luwia
II. ab  c luwia
III. a ·b ·c kentia
(a)
(b)
(g)
(d)
(e)
mxolod I
mxolod II
mxolod I da II
mxolod II da III
I, II da III
60. velosipedisti 3 saaTis ganmavlobaSi Tanabrad, 20 km/sT siCqariT moZraobda,
xolo momdevno 2 saaTis ganmavlobaSi _ 30 km/sT siCqariT. ukan dabrunebisas
velosipedistma igive manZili Tanabari siCqariT 5 saaTis ganmavlobaSi gaiara. ra
siCqariT moZraobda velosipedisti ukan dabrunebisas?
(a) 18 km/sT
(b) 20 km/sT
(g) 22 km/sT
(d) 24 km/sT
(e) 26 km/sT
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653009b
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
m naturaluri ricxvia.
61.
m-is 6-ze gayofisas
miRebuli naSTi
(m + 72)-is 6-ze gayofisas
miRebuli naSTi
 3,  2,  4, ... mimdevrobis wevrebs lia
rigrigobiT werdnen _ jer lia, Semdeg
sandros mier Cawerili yoveli wevri
62. wina wevrze 5-iT meti iyo, xolo
Cawerili _ wina wevrze 6-iT naklebi.
mimdevrobis ori
mezobeli wevris jami
da sandro
_ sandro.
mimdevrobis
lias mier
(b)
(g)
(d)
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
0
wris centri kvadratis erTerT wveros emTxveva, xolo
diametri kvadratis
63. diagonalis tolia.
wris farTobis naxevari
(a)
kvadratis farTobi
29
653009b
9 tona tvirTi, romelic 10 yuTSi Tanabradaa
ganawilebuli,
erTdroulad
unda
gadaitanon
satvirTo
avtomanqanebiT
yuTebis
gauxsnelad.
64. TiToeul avtomanqanas 2,5 tonamde tvirTis waReba
SeuZlia.
tvirTis gadasatanad saWiro
avtomanqanebis raodenoba
(a)
(b)
(g)
(d)
5
ujraSi 10 TeTri da ramdenime wiTeli burTulaa.
albaToba imisa, rom ujridan amoRebuli burTula
wiTeli iqneba, 2 -is tolia.
7
65.
ujridan amoiRes ori burTula, romelTagan erTi
TeTri iyo, meore _ wiTeli.
albaToba imisa, rom ujridan
amoRebuli kidev erTi
burTula iqneba wiTeli
(a)
(b)
(g)
(d)
2
7
amocanebi
66. gasayofi 4-jer metia gamyofze, xolo gamyofi 4-jer metia ganayofze. ris
tolia gamyofi?
(a) 4-is
(b) 8-is
(g) 12-is
(d) 16-is
(e) 20-is
30
653009b
67. sarben biliks wesieri eqvskuTxedis forma aqvs (ix.
naxazi). bilikis sigrZe 240 metria. sportsmenma sirbili
daiwyo A wverodan isriT miTiTebuli mimarTulebiT da
ramdenime xnis Semdeg gaCerda bilikis B wverosTan.
CamoTvlilTagan romlis toli SeiZleba iyos sportsmenis
mier gavlili manZili?
(a) 300 m
(b) 440 m
(g) 520 m
(d) 660 m
(e) 880 m
68. im naturaluri ricxvebidan, romlebic metia 16-ze, magram naklebia 122-ze,
ramdenia 6-is jeradi?
(a) 15
(b) 16
(g) 17
(d) 18
(e) 19
69. organizaciis TanamSromelTa 80% qalebi arian. TanamSromel
raodenobis ramdeni procentia TanamSromel mamakacTa raodenoba?
(a) 20%
(b) 25%
(g) 40%
(d) 45%
(e) 60%
31
qalTa
653009b
70. p da q iseTi naturaluri ricxvebia, rom
1  1 . qvemoT CamoTvlilTagan
p q
romeli mimarTeba SeiZleba iyos marTebuli?
(a) p  q  1
(b) q  2 p
(g) p 
q
3
(d) p  2q
(e) q  2 p
71. pirveli marTkuTxa samkuTxedis didi kaTetis sigrZe 6-jer metia meore
marTkuTxa samkuTxedis mcire kaTetis sigrZeze, xolo farTobi 3-jer metia meore
marTkuTxa samkuTxedis farTobze. ramdenjer naklebia pirveli marTkuTxa
samkuTxedis mcire kaTetis sigrZe meore marTkuTxa samkuTxedis didi kaTetis
sigrZeze?
(a) 2-jer
(b) 3-jer
(g) 6-jer
(d) 9-jer
(e) 12-jer
monacemTa sakmarisoba
72. fakultetze sul 60 ucxoeli studenti swavlobs, romelTagan 40 gogonaa.
mocemulia ori piroba:
I. ucxoel student gogonaTa raodenoba am fakultetis studentTa saerTo
raodenobis 10%-s Seadgens.
II. ucxoel student vaJTa raodenoba am fakultetis studentTa saerTo
raodenobis 5%-s Seadgens.
imis gasarkvevad, Tu sul ramdeni studenti swavlobs am fakultetze:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
32
653009b
73. ABC samkuTxedis AB gverdis M wertili
da BC gverdis N wertili monakveTiTaa
SeerTebuli.
mocemulia ori piroba:
I.  BMN   MNB  130  .
II.  B   C  160  .
imis gasarkvevad, Tu ris tolia  A   B :
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
74. ori ricxvidan erTi a-s tolia, meore _ b-si.
mocemulia ori piroba:
I. a-s da b-s jami am ori ricxvidan erT-erTis tolia.
II. a ricxvi 3-iT metia b-ze.
imis gasarkvevad, Tu ris tolia a-s da b-s namravli:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
75. turistuli saagentos TanamSromlebidan yvelaze umcrosia elene, xolo
yvelaze ufrosi _ merabi. maT garda saagentoSi muSaobs 2 mamakaci da 1 qali,
romelTa saSualo asaki 40 welia.
mocemulia ori piroba:
I. mamakacTa saSualo asaki 45 welia.
II. qalTa saSualo asaki 35 welia.
imis gasarkvevad, Tu ramdeni wlisaa merabi:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
33
653009b
amocanebi
76. Tornikes gasuli wlis ganmavlobaSi Tavisi xelfasis 10% bankSi Sehqonda.
wels Tornikes xelfasi 20%-iT Seumcirda, ris gamoc man bankSi Tavisi xelfasis
mxolod 5%-is Setana daiwyo. ramdenjer nakleb Tanxas Seitans Tornike am wels
bankSi wina welTan SedarebiT?
(a) 1,5-jer
(b) 2-jer
(g) 2,5-jer
(d) 3-jer
(e) 3,5-jer
77. nebismieri a ricxvisaTvis a -iT
aRniSnulia ricxvi, romelic miiReba
Semdegi sqemis mixedviT:
magaliTad, am sqemis mixedviT
 2   2  4· 3  6  0 .
risi tolia
(a)
(b)
(g)
(d)
(e)
 6  ?
6
10
18
25
27
78. 3 m siRrmis mqone kubis formis wyliT savse rezervuaridan wyali mTlianad
gadatumbes marTkuTxa paralelepipedis formis sacurao auzSi, romlis fskeris
sigrZea 9 m, sigane _ 3 m. ris toli iqneba sacurao auzSi wylis simaRle?
(a) 0,5 m
(b) 1 m
(g) 1,5 m
(d) 2 m
(e) 2,5 m
34
653009b
79. M, N, K da D ricxvTa RerZis sxvadasxva wertilebia, xolo m, n, k da d,
Sesabamisad, maTi koordinatebia. K wertili Tanabradaa daSorebuli M da D
wertilebidan, xolo N wertili _ K da D wertilebidan. ris tolia k  n ?
nm
(a)
(b)
(g)
(d)
(e)
1
4
1
3
2

3
1
4
1
3
80. skolaSi moswavleTa 40%-s biWebi Seadgendnen. roca skolaSi ramdenime axali
moswavle gadmovida, biWebis raodenoba 5-iT gaizarda, Tumca maTi procentuli
wili Semcirda. CamoTvlilTagan romlis toli SeiZleba iyos skolaSi gadmosul
moswavleTa raodenoba?
(a) 9
(b) 10
(g) 11
(d) 12
(e) 13
35
653009b
2013
653010a
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. Zieba : aRmoCena
(a) msjeloba : azrovneba
(b) qmedeba : Semoqmedeba
(g) damuSaveba : mopirkeTeba
(d) Sejibri : gamarjveba
2. koreqtori : koreqturuli Secdoma
(a) Jurnalisti : Jurnali
(b) monarqi : monarqia
(g) mexanZre : xanZari
(d) mewisqvile : wisqvili
3. acra : imuniteti
(a) reklama : interesi
(b) matiane : istoria
(g) amocana : miniSneba
(d) qaragma : saidumlo
4. morevi : qarborbala
(a) zvavi : mewyeri
(b) vulkani : lava
(g) Stormi : Sxefi
(d) gamyinvareba : yinuli
5. niRabi : fariseveli
(a) saTvale : dakvirvebuli
(b) airwinaRi : momwamlavi
(g) javSani : SeSinebuli
(d) naWuWi : gulCaTxrobili
2
653010a
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. goeTe axalgazrda poetebs urCevda, mcire moculobis _____ did Txzulebebs
_____ : did poetur qmnilebaze muSaoba _____ , xolo axalgazrdebs _____ .
(a) nawarmoebebze dro ar daexarjaT da pirdapir / SesWidebodnen / calmxrivobas
ver itans / jer kidev ar aqvT mravalmxrivi codna movlenaTa Sesaxeb
(b) nawarmoebebze muSaobiT daewyoT da / ar SesWidebodnen / mravalmxriv codnas
moiTxovs / jer kidev calmxrivi warmodgena aqvT movlenaTa Sesaxeb
(g) nawarmoebebze muSaobiT daewyoT da / ar SesWidebodnen / calmxrivobisgan
Tavis daRwevis saukeTeso gzaa / swored mravalmxrivi codna akliaT
(d) nawarmoebebze dro ar daexarjaT da pirdapir / SesWidebodnen / xels uwyobs
mravalmxrivi codnis SeZenas / yvelaze naklebad swored calmxrivoba
axasiaTebT
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 eZleva ufleba / piriqiT /
moqmedebisTvis naklebad farTo asparezi rCeba / damoukidebeli da
Tavisufali
(b) dapyroba / Tavisuflebas kargavs, adamians aRar aqvs ufleba / marTlac /
moqmedebisTvis ufro farTo asparezi eZleva / dapyrobili
(g) gaTavisufleba / Tavisufalia, adamians aRar eZleva ufleba / marTlac /
kidev ufro meti sapasuxismgeblo movaleoba uCndeba / dapyrobili
(d) gaTavisufleba / Tavisufalia, adamians aqvs ufleba / piriqiT / kidev ufro
meti sapasuxismgeblo movaleoba uCndeba / damoukidebeli da Tavisufali
3
653010a
8. amerikis SeerTebul StatebSi revolucia iyo Tavisuflebisken _____
swrafvis Sedegi da ara _ _____ nayofi. _____
igi warimarTa ara _____ ,
aramed, piriqiT, _____ .
(a) kargad gaazrebuli / raRac bundovani, gaurkveveli impulsebis / amitomac /
uwesrigobisaken ltolviT / wesrigisa da kanonebisadmi pativiscemiT
(b) instinqturi, gaucnobierebeli / kargad gaazrebuli politikis / amis
miuxedavad, / wesrigisa da kanonebisadmi pativiscemiT / yovelgvari wesrigis
darRvevisken ltolviT
(g) kargad gaazrebuli / raRac bundovani, gaurkveveli impulsebis / amis
miuxedavad, / wesrigisa da kanonebisadmi pativiscemiT / uwesrigobis Tavidan
acilebis motiviT
(d) instinqturi, gaucnobierebeli / kargad gaazrebuli politikis / amitomac /
uwesrigobisaken ltolviT / wesrigisa da kanonebisadmi pativiscemiT
9. inglisis konstituciiT, TemTa palata mefes akontrolebs, rac ori
faqtoriTaa gamarTlebuli: erTi, rom _____ , sazogadoeba ______ endos mefes,
radgan absoluturi Zalauflebisken swrafva _____ ; meorec, rom TemTa palata,
romelic swored monarqis kontrolis mizniTaa arCeuli, _____ imsaxurebs.
(a) dauSvebelia / brmad / adre Tu gvian TemTa palatis wevrebsac ki uCndebaT /
ndobas kidev ufro naklebad
(b) dauSvebelia / brmad / monarqis Tandayolili avadmyofobaa / met ndobas
(g) sasurvelia / brmad ar / iSviaTad aris damaxasiaTebeli monarqisaTvis / met
ndobas
(d) sasurvelia / brmad ar / monarqis mimarT undoblobas warmoSobs / ndobas
kidev ufro naklebad
4
653010a
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. Sua saukuneebis qalaqs oTxi karibWe aqvs _ aRmosavleTiT, dasavleTiT,
CrdiloeTiT da samxreTiT. TiToeul karibWesTan maRali saguSago koSki dgas.
amasTan cnobilia:
• aRmosavleTis koSki ufro maRalia, vidre dasavleTisa.
• samxreTis koSki ufro maRalia, vidre dasavleTisa.
• CrdiloeTis koSki ufro dabalia, vidre aRmosavleTisa.
qvemoT CamoTvlilTagan, simaRlis mixedviT koSkebis romeli ganawileba (I _
yvelaze maRali, IV _ yvelaze dabali) Seesabameba am monacemebs?
I
(a) samxreTis
(b) dasavleTis
(g) CrdiloeTis
(d) samxreTis
II
dasavleTis
aRmosavleTis
samxreTis
aRmosavleTis
III
aRmosavleTis
CrdiloeTis
aRmosavleTis
dasavleTis
IV
CrdiloeTis
samxreTis
dasavleTis
CrdiloeTis
11. mocemulia ori debuleba:
• Tu zRvispireTSi wvima male ar Sewydeba, iq turistuli sezoni ar
gaixsneba.
• Tu zRvispireTSi turistuli sezoni gaixsneba, mTis kurortebze
damsvenebelTa raodenoba Semcirdeba.
maSasadame, Tu zRvispireTSi turistuli sezoni gaixsna, iq wvima male
Sewyvetila.
es daskvna:
(a)
(b)
(g)
(d)
gamomdinareobs mxolod orive debulebidan erToblivad
gamomdinareobs TiToeuli debulebidan meorisgan damoukideblad
gamomdinareobs mxolod erT-erTi debulebidan meorisgan damoukideblad
ar gamomdinareobs mocemuli debulebebidan
5
653010a
12. erT mwkrivad awyvia oTxi sxvadasxva feris kolofi: wiTeli, yviTeli, mwvane
da TeTri. TiToeulSi devs Semdegi oTxi sagnidan erT-erTi: beWedi, samajuri,
mZivi an werili.
amasTan, cnobilia:
•
werili da beWedi ar devs wiTel kolofSi.
•
TeTr kolofSi ar devs arc samajuri da arc werili.
•
kolofi samajuriT moTavsebulia uSualod mwvane kolofsa da im kolofs
Soris, romelSic mZivia.
•
yviTelsa da mwvane kolofebs Soris erTi kolofi devs.
ra devs mwvane kolofSi?
(a)
(b)
(g)
(d)
beWedi
samajuri
mZivi
werili
13. mocemulia sami winadadeba:
I. amfibiebi arseboben da yvela amfibia civsisxliania.
II. arc erTi cxoveli, romelmac curva ar icis, ar aris amfibia.
III. arc erTma cxovelma, romelic civsisxliania, ar icis curva.
qvemoT CamoTvlilTagan romeli debuleba aRwers sworad am winadadebebs Soris
mimarTebas?
(a)
(b)
(g)
(d)
I da II winadadebebidan gamomdinareobs III
II da III winadadebebidan gamomdinareobs I
Tu I da III winadadebebi WeSmaritia, maSin II winadadebac WeSmaritia
Tu I da II winadadebebi WeSmaritia, maSin III winadadeba mcdaria
14. gamomcemlobam, romelsac gadawyvetili hqonda axalgazrda poetis leqsebis
krebulis gamoqveyneba, Caatara kvleva imis gasarkvevad, Seuwyobda Tu ara xels
krebulis gamocema avtoris popularobis zrdas. gamohkiTxes adamianTa jgufi
krebulis gamocemamde da mis Semdeg. meore gamokiTxvis Sedegebis mixedviT, poeti
bevrad ufro popularuli aRmoCnda, vidre pirveli gamokiTxvis mixedviT. amis
safuZvelze ivaraudes, rom krebulis gamocemam xeli Seuwyo avtoris
popularobis gazrdas.
qvemoT CamoTvlilTagan romeli faqti ganamtkicebs am varaudis marTebulobas?
(a) axalgazrda poetis Sesaxeb pirvelma gamokiTxvam ganapiroba mkiTxvelTa
interesis gazrda mis mimarT
(b) axalgazrda poetis nawarmoebebi gamokiTxvamde arasodes gamoqveynebula sxva
gamomcemlobebis mier
(g) meore gamokiTxva Caatares gamoucdelma interviuerebma, romlebmac ver
uzrunvelyves gamokiTxvis obieqturoba
(d) im periodSi, rodesac kvleva tardeboda, poeti monawileobda telegadacemaTa
ciklSi, romelic Tanamedrove literaturis problemebs Seexeboda
6
653010a
wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
Zv. w. II aTaswleulis kreta elinTaTvis iyo winaberZnuli kulturis
Zlierebisa da simaRlis simbolo. swored II aTaswleulis dasabamidan daiwyo
WeSmariti revolucia egeosis zRvis auzis kulturebSi, rodesac kunZul
kretaze e. w. didi sasaxleebis epoqa dadga. kretam TiTqos auwereli naxtomi
gaakeTa adrebrinjaos kulturidan Suabrinjaos xanis saocrad daxvewil da
TviTmyofad minosur* civilizaciamde. am kunZulis politikuri da kulturuli
cxovrebis centri iyo knosos sasaxle, romelic rTuli konstruqciis nagebobaTa
mTel
sistemas
qmnida.
kretis
irgvliv
ganlagebuli
mravali
kunZuli
warmoadgenda kretuli kulturis gamavrcelebels egeosis zRvis auzSi.
pirveli, rac kretaze TvalSi xvdeba adamians, es aris civilizaciis
Tanabrad maRali done kunZulis TiTqmis yovel nawilSi, stilis erTianoba, da,
rac mTavaria, dRemde auxsneli mSvidobiani xasiaTi minosuri kulturisa. cneba
Pax Minoica _ `minosuri mSvidoba~ _ damkvidrda mecnierebaSi im sruliad
gansakuTrebuli viTarebis aRsaniSnavad, romelic kunZulze sufevda daaxloebiT
xuTi saukunis ganmavlobaSi. aq ar yofila arc erTi cixesimagre, araviTari
niSani imisa, rom kretis mosaxleobas minosur periodSi vinmesTan omi
ewarmoebinos, xelovnebaSi arsad Cans aramcTu omis Tema, aramed ubralo saomari
iaraRic ki. riT unda avxsnaT es? mecnierebs damajerebeli pasuxi jer ar aqvT.
kretaze ar Cans erTi pirovnebis, mefis Tu mmarTvelis, sruli dominirebis
kvali. sainteresoa, rom TviT berZnuli miTebic ki, Tu ar CavTvliT legendarul
minoss, romelic kretis xelisufalTa ufro ganmazogadebeli saxeli unda iyos,
ver asaxelebs cnobil kretel mefeebs, ver iZleva maT genealogiur siebs. es ki,
SesaZloa, imiT aixsnas, rom minosur kretaze ar arsebobda mefis kulti. Tavis
mxriv, amgvari garemoeba uTuod xels uwyobda pirovnuli iniciativis
ganviTarebas, rac sakmaod ucxoa ZvelaRmosavluri kulturebisTvis.
unda aRvniSnoT kretuli xelovnebis e. w. impresionistuli xasiaTi. Zveli
aRmosavleTis xelovanTagan gansxvavebiT, minosuri epoqis mxatvars ainteresebs ara
imdenad istoriuli Tu miTologiuri piris ukvdavyofa, ramdenadac erTi
STabeWdilebiT miRebul gancdaTa gadmotana xazisa Tu ferebis meSveobiT.
kretaze xataven yvavilebs, frinvelebs, ufliswulebs, meTevzeebsa da akrobatebs.
XX saukunis dasawyisis evropuli xelovnebis principebTan (da parizul
modasTan) siaxlovis gamo erT-erT freskaze gamosaxul qals `parizeli qalic~ ki
Searqves. kreteli mxatvari cdilobs, sasiamovno ganwyoba Seqmnas feris, xazis,
ornamentis, gamosaxulebis monacvleobiT.
kretuli mxatvruli kultura mimarTulia ara masStaburobiTa da
grandiozulobiT TanamoqalaqeTa gancvifrebisa Tu daTrgunvisken, aramed Tavisi
uaRresad adamianuri formebiT, uSualo emociebiT sasiamovno da myudro
atmosferos Seqmnisken. igi swrafad icvleba adamianis gemovnebis, moTxovnilebebis
Sesabamisad. yovelive es da kidev mravali ram, rac minosuri kulturisaTvis
aseve niSandoblivia, miiRes memkvidreobiT berZnebma da maTTvis damaxasiaTebeli
mizanswrafulobiT SeZles, egeosuri stimulebis safuZvelze SeeqmnaT sakuTriv
elinuri civilizacia, romelic amosavali gaxda evropuli civilizaciis
ganviTarebisTvis.
* winaberZnuli civilizacia; minosuri ewoda kretis legendaruli mefis _ minosis _ saxelis
mixedviT.
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15. I abzacSi warmodgenilia zogadi xasiaTis cnobebi erT-erTi civilizaciis
Sesaxeb. qvemoT CamoTvlilTagan am civilizaciis romeli daxasiaTebaa marTebuli?
(a) kretuli civilizacia _ am kulturis centri iyo kunZuli kreta; es iyo
tipuri elinuri civilizacia
(b) winaberZnuli civilizacia _ is araelinur samyaroSi Caisaxa da araferi
aqvs saerTo berZnul civilizaciasTan
(g) minosuri civilizacia _ am kulturis umniSvnelovanesi centri iyo kretis
legendaruli mefis minosis didi sasaxle
(d) egeosuri civilizacia _ is winaberZnul kretaze Caisaxa da egeosis zRvis
mraval kunZulze gavrcelda
16. gamoTqmis _
Pax Minoica _ romeli interpretacia ar aris marTebuli?
(a) xuTi saukunis ganmavlobaSi kunZul kretaze sruliad gansakuTrebuli
viTareba Seiqmna _ am kunZulis xelovnebaSi ar Cans omis Tema
(b) minosuri kulturisaTvis ucnobia Zaladoba, kretaze ar aRmoCenila arc
erTi cixesimagre, ar Cans saomari iaraRic ki
(g) daaxloebiT xuTi saukunis ganmavlobaSi kunZul kretaze SenarCunda
civilizaciis Tanabrad maRali done
(d) kretul xelovnebaSi ar Cans antagonizmis gamovlenis araviTari kvali, ar
Cans arc erTi TavdacviTi nageboba
17. egeosis zRvis ramdenime kunZuli warmoadgenda minosuri kretis erTgvar
filials. erT-erTi aseTi kunZuli iyo Tera, kretuli kulturis dasayrdeni
da gamavrcelebeli mTel regionSi. Teraze mogvianebiT aRmoaCines freska,
romelic gamonaklisad unda miviCnioT: masze gamosaxulia pastoraluri suraTi
_ mwyemsebi mierekebian naxirs; aqve Cans grZeli SubebiTa da uzarmazari
farebiT SeiaraRebul, afrikul tunikebSi gamowyobil mamakacTa razmi,
romelic aSkarad sabrZolvelad miemarTeba.
teqstisa da am informaciis Sejerebis safuZvelze SeiZleba vivaraudoT:
(a) es freska Tavisi SinaarsiT mTlianad amovardnilia kretuli xelovnebis
Tematikidan, radgan Teras xelovneba radikalurad gansxvavdeboda Tavisi
xasiaTiT kretulisgan
(b) minosur mxatvrobaSi gamosaxulni arian SeiaraRebuli adamianebic, Tumca,
es gasakviri ar aris, radgan freskaze gamosaxuli meomrebi Terelebi arian,
romlebic ebrZodnen kretelebs
(g) omis Tema SeiZleba iSviaTad gamoCndes minosuri civilizaciis konteqstSi,
Tumca, TerelTa freska SesaZloa afrikul ambavs gadmogvcemdes, amitom es
informacia ar ewinaaRmdegeba teqstis paToss
(d) es informacia ewinaaRmdegeba teqstSi aRweril viTarebas, radgan kretul
kulturaSi ar Cans Zaladobis araviTari niSani, Teraze ki mravlad iyo
omis Temaze Seqmnili freskebi
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18. ra funqcia aqvs teqstSi `parizeli qalis~ epizods?
(a) warmoaCens minosuri periodis istoriuli da miTologiuri personaJebis
damaxasiaTebel Tvisebebs
(b) xazs usvams minosuri xelovnebis Taviseburebas _ wuTieri STabeWdilebiT
miRebuli gancdis gadmocemiT sasiamovno ganwyobis Seqmnas
(g) kargad gviCvenebs kretuli xelovnebis gansxvavebas aRmosavleTis qveynebis
xelovnebisgan
(d) cxadyofs msgavsebasa da gansxvavebas kretuli xelovnebisa da parizuli
modis principebs Soris
19. qvemoT CamoTvlilTagan romelSia asaxuli aRmosavluri civilizaciebisgan
minosuri kulturis arsebiTi ganmasxvavebeli Tavisebureba?
(a) kretis legendaruli mefis magaliTze aSkarad Cans kunZulze erTi
pirovnebis _ mefe minosis dominirebis kvali
(b) kretuli mxatvruli kultura masStaburi da grandiozulia, es garemoeba
ki xels uwyobda pirovnuli iniciativebis ignorirebas
(g) mTeli minosuri civilizacia impresionistuli xasiaTisaa; kretel xelovanTa
ZiriTadi Temebia: yvavilebi da frinvelebi, ufliswulebis cxovreba
(d) kretaze arsebuli viTareba xels uwyobda pirovnuli iniciativis
ganviTarebas; kretuli kultura icvleboda adamianis moTxovnilebebis
Sesabamisad
20. qvemoT CamoTvlilTagan romel mosazrebaze migvaniSnebs gamoTqma `egeosuri
stimulebi~?
(a) winaberZnul-egeosuri kulturis tradiciebi, romlebic ganviTarebis mraval
kods Seicavda, berZnebma Seisisxlxorces da Seqmnes axali, sakuTriv
elinuri civilizacia
(b) kulturis egeosur-berZnuli modeli bevrad aris ganpirobebuli xmelTaSua
zRvis auzis qveynebisa da aRmosavluri kulturis specifikiT
(g) adamianis moTxovnilebebis dakmayofilebaze orientirebuli berZnuli
kultura ganviTarda egeosuri civilizaciis gverdis avliT
(d) winaberZnul-kretuli kulturis impresionistuli xasiaTi gaxda gadamwyveti
faqtori egeosuri civilizaciis aRmavlobisa da Semdgom evropuli
civilizaciis CamoyalibebisTvis
9
653010a
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. areali : sazRvari
(a) xma : toni
(b) aromati : ingredienti
(g) manZili : distancia
(d) gamosaxuleba : konturi
22. derefani : srute
(a) xidi : uReltexili
(b) delta : Senakadi
(g) marjani : rifi
(d) mTa : mRvime
23. bilingva : binokli
(a) martorqa : ciklopi
(b) dekada : kvartali
(g) rvafexa : meduza
(d) biosfero : naxevarsfero
24. jaWvi : jaWvuri reaqcia
(a) wertili : wertilovani xazi
(b) ornamenti : ornamentuli dekori
(g) kenWi : kenWovani daavadeba
(d) horizonti : horizontaluri mdgomareoba
25. sinaTle : siTbo
(a) wyali : talRa
(b) ali : nakverCxali
(g) feri : surneli
(d) gemo : sitkbo
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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. adamians, _____ , raime axlis gakeTeba _____ . swored Secdomis _____
adamianTa umravlesoba, raime axali gaakeTos. isini ver xvdebian, rom
warmatebisaken _____ .
(a) romelic arasodes Semcdara / arasodes ucdia / daSvebis SiSis gamo ar
cdilobs / mimavali gza sakuTar Secdomebze swavlaze gadis
(b) romelic xSirad cdeba / ar unda mivandoT / araRiarebis gamo ver axerxebs /
swrafva zogjer Secdomebze Tvalis daxuWvas moiTxovs
(g) romelsac Secdomebis eSinia / arasodes gamouva / Tavidan aridebis imediT
cdilobs / mimaval gzaze udidesi sifrTxilea saWiro
(d) romelsac Secdomebi ar aSinebs / ar gauWirdeba / gamosworebis imediT Tu
ecdeba / svlisas warsuli Secdomebi sul unda gvaxsovdes
27. vagneri
werda:
,,tristanisa
da
izoldas“
werisas
grZnoba
Cemi
Seyvarebulisadmi _____ gaxldaT, _____ is martooden sawyisi wertilis rols
_____ , vinaidan Cemi mizani _____ piradi gancdebis gamomJRavneba musikalur
TanaxmianobaSi.
(a)
(b)
(g)
(d)
mravalTa Soris erT-erTi motivi / maSasadame, / asrulebda / iyo mxolod
gadamwyveti stimuli / maSasadame / ar asrulebda / ufro didi iyo, vidre
mravalTa Soris erT-erTi motivi / magram / ar asrulebda / ar iyo mxolod
gadamwyveti stimuli / magram / asrulebda / ufro didi iyo, vidre
28.
erTi
adamianis
Zala
_____
misi
sasicocxlo
moTxovnilebebis
dasakmayofileblad, _____ adamianis suli da goneba _____ adamianebi _____
sxvebTan urTierTobas, _____ saWiroeben sxvebis Tanadgomasa da daxmarebas.
(a) SeiZleba sruliad sakmarisi iyos / xolo / kargad eguebodes maradiul
martoobas, magram / mainc gaurbian / Tuki aucileblad ar
(b) SeiZleba sruliad sakmarisi iyos / magram / ver egueba maradiul martoobas
_ marTlac, / imdenad aucileblobad ar miiCneven / ramdenadac
(g) imdenad arasakmarisia / xolo / imdenad ver egueba maradiul martoobas, rom /
bunebrivad eswrafvian / aucileblad
(d) imdenad arasakmarisia / da / imdenad kargad egueba maradiul martoobas, rom /
xSirad gaurbian / Tumca, iSviaTad
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29. bolo aTwleulebis ganmavlobaSi biologebis nayofieri muSaobis _____
organizmebis materialuri struqturisa da maTi funqcionirebis Sesaxeb, _____ ,
ratom _____ dRevandeli fizika da qimia cocxal organizmSi mimdinare
movlenebs.
(a) miuxedavad, kidev did xans imdenad mcire gvecodineba / rom imis Tqmas mainc
SevZlebT / ver xsnis
(b) wyalobiT male sakmaod bevri gvecodineba / Tumca, imis Tqmas mainc ver
SevZlebT / xsnis ase warmatebiT
(g) miuxedavad, jer kidev imdenad mcirea cnobili / rom Znelia Tundac imis Tqma /
xsnis ase warmatebiT
(d) wyalobiT dRes sakmaod bevria cnobili / raTa imis Tqma mainc SevZloT /
ver xsnis
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. evoluciuri biologiis zogierTi mkvlevari spilos gansakuTrebiT didi
yurebis Camoyalibebas xsnis imiT, rom didi yurebi am cxovels sxeulis
temperaturis regulirebaSi exmareba. TavianT varauds isini afuZneben im faqtze,
rom spilos afrikul saxeobas, romlis saarsebo garemoc ufro cxeli klimatiT
xasiaTdeba, bevrad ufro didi yurebi aqvs, vidre aziur spilos.
qvemoT CamoTvlilTagan romeli faqtis dadastureba Seasustebda am varauds?
(a) spilos afrikuli da aziuri saxeobebi mxolod umniSvnelod gansxvavdeba
erTmaneTisagan sxeulis zomiT
(b) spilos afrikuli saxeoba ufro aqtiurad iyenebs komunikaciisTvis bgeriT
signalebs, vidre aziuri, romelsac nakleb ganviTarebuli smenis aparati aqvs
(g) afrikuli spilos qvesaxeobebSi yurisa da sxeulis zomebis Sefardeba miT
ufro mcirea, rac ufro Sorsaa ekvatoridan qvesaxeobis saarsebo garemo
(d) aziuri spilos qvesaxeobebi mniSvnelovnad gansxvavdeba erTmaneTisgan
garegnuli niSnebiT, Tumca, isini erTi da imave tipis garemoSi arseboben
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31. giorgi, nana, levani da elene mezobel saxlebSi cxovroben da TiToeuli
maTganis saxlis karze mikrulia dafa, romelzec mcxovrebis saxeli weria. erT
saRamos daviTi maT gaexumra da zogierT dafas adgili Seucvala. meore diliT
sxva saerTo megobris kiTxvebze daviTma aseTi pasuxebi gasca:
• nanas saxlis karze mivakari dafa levanis saxeliT.
• Tu giorgis saxlze mikruli dafa ucvleli davtove, maSin elenes da
levanis saxlebis dafebs namdvilad Sevcvlidi.
• Tu giorgis saxlis karze mikruli dafa Sevcvale, maSin ar Semicvlia
levanis saxlis karze mikruli dafa.
Tu samive pasuxi simarTlea, visi dafa miakra daviTma levanis saxlis kars?
(a)
(b)
(g)
(d)
giorgis
nanas
elenes
levanis saxlze dafa ar Seucvlia
32. mocemulia:
• yvela gulisxmieri adamiani ufrTxildeba bunebas da kargad epyroba
cxovelebs.
• yvela aragulisxmieri adamiani mxolod sakuTar interesebze fiqrobs da ar
TanaugrZnobs sxva adamianebs.
qvemoT CamoTvlilTagan romlis arsebobaa SeuZlebeli am wanamZRvrebis mixedviT?
(a) gulisxmieri adamianisa, romelic bunebas ufrTxildeba da ar fiqrobs
mxolod sakuTar interesebze
(b) adamianisa, romelic cxovelebs kargad ar epyroba da sxva adamianebs
TanaugrZnobs
(g) adamianisa, romelic cxovelebs kargad ar epyroba da sxva adamianebs ar
TanaugrZnobs
(d) aragulisxmieri adamianisa, romelic kargad epyroba cxovelebs
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33. vanos kargi samsaxiobo monacemebi aqvs da fiqrobs, ra profesia airCios. mas
gadawyvetili aqvs, rom nebismieri profesiis arCevis SemTxvevaSi sportis ori
sayvareli saxeobidan erT-erTs mainc gaagrZelebs _ CogburTis an wyalburTis
TamaSs. is arCevanis gakeTebas Semdegi mosazrebebis gaTvaliswinebiT cdilobs:
•
•
•
Tu msaxiobobas gadawyvets, CogburTis TamaSs veRar gaagrZelebs.
Tu wyalburTis TamaSs gaagrZelebs, xSirad mouwevs bavSvobis megobrebTan
Sexvedra.
bavSvobis megobrebTan Sexvedris SemTxvevaSi uars ver ityvis maTTan erTad
CogburTis TamaSzec.
Tu davuSvebT, rom vano zemoT mocemul arc erT msjelobaSi ar cdeboda da
Tavisi gadawyvetilebac Seasrula, qvemoT CamoTvlilTagan romeli SemTxveva
ganxorcielda?
(a)
(b)
(g)
(d)
vano gaxda msaxiobi da gaagrZela wyalburTis TamaSi
vano gaxda msaxiobi da uari Tqva bavSvobis megobrebTan Sexvedrebze
vanom uari Tqva msaxiobis profesiazec da CogburTis TamaSzec
vanom uari Tqva msaxiobis profesiaze da gaagrZela wyalburTis TamaSi
34. sapatrulo policiis monacemebiT, manqanis marTvisas qalebi ufro xSirad
iyeneben usafrTxoebis Rvedebs, vidre mamakacebi. erT-erTi policielis varaudiT,
es imiT aixsneba, rom qalebi naklebad gamocdili mZRolebi arian da amitom
ufro xSirad icaven usafrTxoebis wesebs.
qvemoT CamoTvlilTagan romeli ayenebs eWvqveS am varauds?
(a) mamakaci mZRolebi, qalebTan SedarebiT, ufro xSirad arRveven sagzao wesebs,
Tumca, iseve xSirad qmnian saavario situaciebs, rogorc qalebi
(b) qali mZRolebis umravlesoba, mamakacebTan SedarebiT, gacilebiT ufro gvian
miujda saWes, Tumca aranaklebi ostatobiT marTavs manqanas
(g) im markis manqanebis salonis dizainis Seqmnisas, romlebsac mamakacebi aniWeben
upiratesobas, naklebi yuradReba eqceva Rvedebis komfortulobas
(d) im markis manqanebi, romlebsac qalebi aniWeben upiratesobas, rogorc wesi,
Zravis simZlavriT ar gamoirCeva da did siCqares ver aviTarebs
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wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
planeta marsis arseboba aTasobiT wlis winaT iyo adamianebisaTvis
cnobili. jer kidev babilonSi, Semdeg ki Zvel saberZneTsa da romSi mas omis
RmerTTan aigivebdnen, albaT, misi wiTeli feris gamo. saxeli marsi mas romaelTa
omis RmerTis pativsacemad uwodes. gansakuTrebuli interesi marsisadmi
teleskopis gamogonebis Semdeg gaCnda, Tumca, misi realuri kvleva 1877 wlidan
iwyeba. agvistos miwuruls, marsisa da dedamiwis morigi pirispir dgomisas, roca
planetebi maqsimalurad uaxlovdebian erTmaneTs, aSS-s sazRvao observatoriis
TanamSromelma asaf holma erTi meoris miyolebiT marsis orive Tanamgzavri aRmoaCina.
paralelurad marss msoflios mravali sxva mecnieric Seiswavlida. maT
Soris iyo italieli jovani skiapareli, romelmac marsze dakvirveba kidev
mravali wlis ganmavlobaSi ganagrZo, sanam planeta did manZilze ar daSorda
dedamiwas. swored am garemoebis wyalobiT SeZlo skiaparelim Tavisi aRmoCenis
gakeTeba. man dainaxa is, rac manamde aravis SeumCnevia: mkafio xazebi, romlebic
marsis zedapirs aseulobiT da aTaseulobiT kilometrze gasdevs.
Tavad skiapareli Zalze frTxilad moekida Tavis aRmoCenas. am xazebs man
uwoda `canali~, rac italiurad mdinaris bunebriv kalapots niSnavs. mecnieris
mignebis Sesaxeb informacia statiis saxiT inglisur enaze gamoqveynda. magram
Targmnisas Secdoma dauSves _ sityva `canali~ naTargmni iyo, rogorc `arxi~, anu
rogorc xelovnuri nageboba. es ki arsebiTad cvlida mis pirvelad Sinaarss.
statiam sensacia gamoiwvia: bevrma miiCnia, rom arxebi sarwyavi sistemis nawilia,
romlis meSveobiT marselebi uwylobas ebrZvian TavianT planetaze. am droidan
moyolebuli
marsis
mkvlevrebis
erT-erTi
amocana
masze
sicocxlis
damadasturebeli niSnebis aRmoCena iyo. gamoqveynda uamravi wigni, romlebSic
avtorebi marsze sicocxlis arsebobaze mianiSnebdnen. viTareba kidev ufro
gamwvavda, rodesac amerikelma p. louelma marsze erTwliani dakvirvebis Semdeg
Seadgina planetis arxebis ruka da gamoaqveyna wignebi, romlebSic amtkicebda,
rom arxebi gonieri arsebebis mieraa gayvanili. wignebma im astronomTa
moTminebis fiala aavso, romelTac marselebis arsebobis ar sjerodaT.
ingliselma astronomma e. maunderma imis gasarkvevad, Tu sinamdvileSi ras
warmoadgenda marsis arxebi, 1903 wels eqspertebad skolis moswavleebi miiwvia.
maT Soridan aCvenes marsis suraTebi, romlebzec arxebi wertilTa rigis saxiT
iyo
warmodgenili. bavSvebis
umetesobam
am
gamosaxulebaTa
gadaxatvisas
wertilebis nacvlad xazebi gaavlo, ramac maunders afiqrebina, rom arxebi
marsze, SeiZleboda, optikuri iluzia yofiliyo. Tavis mxriv, frangma
astronomma antoniadim marsze dakvirvebis Sedegad daaskvna, rom `arxebi~ aris
uswormasworo muqi zolebi, romelTac sxvadasxva zomis calkeuli laqebi qmnis.
amrigad, rogorc amerikelma mecnierma u. korlisma aRniSna, `imisaTvis, rom
marsze arxebi davinaxoT, saWiroa, gvqondes kargi teleskopi, kargi mxedveloba da
... kargi warmosaxva~. zogjer Tvali da tvini TiTqos ganazogadebs aRqmuls da
calkeuli detalebidan qmnis mTlian suraTs. Tanamedrove mecnierTa azriT,
obieqtebs, romlebic marsze sicocxlis arsebobis Sesaxeb varaudebs daedo
safuZvlad, warmoadgens marsis zedapirze arsebuli napralebi, mTis qedebi da a. S.
Tumca, amerikis kosmosuri saagentos sul axali aRmoCenis Tanaxmad, marsis
zedapiruli qanebi didi raodenobiT Seicavs wyals, ZiriTadad yinulis saxiT. es
Zalze mniSvnelovani aRmoCenaa, romelic mecnierebs daexmareba marsis saidumlos
amoxsnaSi.
15
653010a
35. ratom gamoiwvia skiaparelis statiis gamoqveynebam sensacia sazogadoebSi?
(a) statiaSi sityva `canali~ gamoyenebuli iyo planetaze arsebuli mdinareebis
aRsaniSnavad
(b) statiidan gamomdinareobda, rom marsze aRmoCenili iyo xelovnuri nagebobebi
(g) statiis safuZvelze daiwera uamravi wigni, romlebSic aRwerili iyo marsze
wylis mopovebis gzebi da saSualebebi
(d) statiaSi skiapareli Zalze frTxilad, magram savsebiT argumentirebulad
asabuTebda, rom planetis zedapiri daserili iyo sarwyavi arxebiT
36. ra mimarTebaa skiaparelis mier marsze dakvirvebis processa da ingliseli
astronomis maunderis mier Catarebul eqsperiments Soris?
(a) skiaparelim da maunderma Seqmnes dakvirvebis msgavsi pirobebi, ris Sedegad
ingliselma astronomma SeZlo daesabuTebina skiaparelis mier gamoyenebuli
dakvirvebis meTodis efeqturoba
(b) maunderi da skiapareli sxvadasxva gziT – erTi bunebriv pirobebSi
dakvirvebiT, meore ki saeqsperto gamokiTxviT – Seiswavlidnen planeta marsis
agebulebas
(g) miuxedavad imisa, rom skiaparelis dakvirvebis meTodsa da maunderis
eqsperiments Soris Zalze didi gansxvaveba iyo, orive astronomma marsis
zedapiris msgavs Taviseburebas miakvlia
(d) maunderma eqsperimentulad Seqmna dakvirvebis iseTive pirobebi, rogoric
bunebrivad Seiqmna dedamiwidan marsis did manZilze daSorebisas, ris Sedegad
man SeZlo, eWvqveS daeyenebina skiaparelis hipoTeza
37. qvemoT CamoTvlilTagan romelia marTebuli?
antoniadis dakvirvebis Sedegebma:
(a) daadastura, rom marsis zedapirs sulac ar gasdevs xazebi Tu zolebi
(b) sxva, ufro dazustebuli monacemebiT ganamtkica skiaparelis hipoTezis
marTebuloba
(g) axali mtkicebulebebiT gaamyara maunderis varaudi
(d) gansxvavebuli kuTxiT warmoaCina marsze mdinareTa kalapotebis ganlagebis
suraTi
16
653010a
38. `imisaTvis, rom marsze arxebi davinaxoT, saWiroa gvqondes kargi teleskopi,
kargi mxedveloba da ... kargi warmosaxva”.
qvemoT CamoTvlilTagan romeli damatebiTi cnoba gamogvadgeba amerikeli
mecnieris u. korlisis am ironiuli gamonaTqvamis erTgvar ilustraciad?
(a) marsze arsebuli Camqrali vulkani olimpi yvelaze maRali mTaa mzis
sistemaSi, xolo marineras xeoba – yvelaze msxvili kanioni
(b) axlo manZilidan gadaRebulma suraTebma Zireulad Secvala marsis zedapiris
Sesaxeb arsebuli warmodgenebi. ase, magaliTad, e. w. zRvebis laqiseburi
gamosaxulebebi planetaze arsebuli kraterebiT aixsneba
(g) marsi uamravi wriuli mTebi-kraterebiTaa dafaruli. rogorc Cans, amgvari
reliefi yvela im planetisTvisaa damaxasiaTebeli, romlebsac gaiSviaTebuli
atmosfero da ufro mcire farTobi aqvT, vidre dedamiwas
(d) marsze arsebuli e.w. polaruli qudebi, romlebic yinulisa da Cayinuli
airisgan Sedgeba, weliwadis drois mixedviT cvlilebas ganicdis: maTi sisqe 1
metridan 3.5 km. aRwevs.
39. teqstis Tanaxmad, ra aris marsis is saidumlo, romlis amoxsnas dRemde
cdiloben mecnierebi?
(a) SesaZlebelia Tu ara sicocxlis raime gamovlinebis arseboba marsze
(b) SemorCa Tu ara marss sarwyavi sistemebisa Tu sxva xelovnuri nagebobebis
kvali
(g) rogor warmoiSva marsze wyali da, ZiriTadad, ra formiTaa is warmodgenili
am planetaze
(d) ram ganapiroba marsis zedapiruli qanebis is agebuleba, romlis Sesaxeb
gvamcnobs Tanamedrove kvlevebi
40. teqstis struqtura gamoiyureba Semdegnairad:
A.
B.
G.
D.
zogadi informacia planeta marsis Sesaxeb
marsis zedapiris TaviseburebasTan dakavSirebiT gamoTqmuli varaudebi
marsze dakvirvebisas gakeTebuli aRmoCenebi
marsis saidumlos amosaxsnelad Catarebuli kvlevebis Sedegebi
(a)
(b)
(g)
(d)
I
I
I
I
abzaci _ G; II
da II abzacebi
abzaci – G; II
abzaci _ A; I
da III abzacebi _ B; IV abzaci _ D; V abzaci _ A
_ A; II da III abzacebi _ G; IV abzaci _ B; V abzaci _ D
abzaci – B; IV abzaci – D; V abzaci – A
da II abzacebi _ G; III abzaci _ B; IV da V abzacebi _ D
17
653010a
Savi samuSaosTvis
18
653010a
Savi samuSaosTvis
19
653010a
maTematikuri nawili
2013
IV
testis maTematikur nawilze muSaobisas gaiTvaliswineT:



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:
10. paraleluri wrfeebi:
ori paraleluri wrfis mesame
wrfiT gadakveTisas Siga jvaredina
kuTxeebi tolia: α = β.
11. samkuTxedi:
1. nuli arc dadebiTia da arc uaryofiTi;
1 ar aris martivi ricxvi.
2. procenti:
a ricxvis k% aris
.
n
3. xarisxi: a = a · a · a · ...· a (n-jer)
 samkuTxedis kuTxeebis sidideTa jami
180°-is tolia;
 piTagoras Teorema:
marTkuTxa samkuTxedis
hipotenuzis sigrZis
kvadrati kaTetebis sigrZeTa
kvadratebis jamis tolia:
an · am = an + m
n
m
a :a =a
n–m
m
(a n ) = a n · m
4. proporcia: Tu
5. siCqare:
siCqare
, maSin ad = bc.

manZili
AB2 = AC2 + BC2
dro
6. saSualo ariTmetikuli:
monacemTa saSualo
 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.
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 elementa-
ruli xdomilobebi Tanabrad mosalodnelia.
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 = r2.
8. Semoklebuli gamravlebis formulebi:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2
9. naxazze kuTxe SeiZleba
moniSnuli iyos kuTxis
gverdebs Soris Casmuli
patara rkaliT, marTi kuTxe
ki _ patara kvadratiT.
14. marTkuTxa paralelepipedi:
 marTkuTxa paralelepipedis
moculoba misi sigrZis, siganisa da
simaRlis namravlis tolia: V = abc;
 kubis SemTxvevaSi: a = b = c.
A aRniSnavs A kuTxis sidides.
21
653010b
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
41.
B
0,08
1
9
(a)
(b)
(g)
(d)
m4
2
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
m 5.
42.
43.
m 5
3
oTxkuTxa piramidis yvela wibo erTmaneTis tolia,
maT sigrZeTa jami ki 40 sm-ia.
15 sm
am piramidis fuZis perimetri
22
653010b
44.
samniSna ricxvi,
romlis cifrTa jami
17-is tolia
samniSna ricxvi,
romlis cifrTa jami
14-is tolia
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
funTuSa 40 TeTri Rirs. 1 xaWapuri 80 TeTriT
meti Rirs, vidre _ 2 Rvezeli.
45.
2 xaWapuris da
1 Rvezelis Rirebuleba
1 xaWapuris, 3 Rvezelisa
da 2 funTuSis
Rirebuleba
rombis gverdis sigrZea a, xolo didi
46. diagonalisa _ d.
d
2
a
23
653010b
amocanebi
47. 13 milion 800 aTasze 6-jer naklebia:
(a) 2 milion 100 aTasi
(b) 2 milion 200 aTasi
(g) 2 milion 300 aTasi
(d) 2 milion 400 aTasi
(e) 2 milion 800 aTasi
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 ramdeni procentia
saSualo profesiuli ganaTlebis mqone?
(a)
(b)
(g)
(d)
(e)
11,9%
12,3%
13,8%
14,2%
15,6%
49. 7 wlis Semdeg vaJa 26 wlis gaxdeba. ramdeni wlis gaxdeba vaJa y wlis
Semdeg?
(a) 18  y
(b) 33  y
(g) y  33
(d) 18  y
(e) y  19
24
653010b
50. MNEF marTkuTxedis MN gverdis sigrZea 11 sm,
MF gverdisa _ 6 sm, xolo M wverosa da EF gverdis
A wertilis SemaerTebeli MA monakveTisa _ 10 sm.
ris tolia AE monakveTis sigrZe?
(a) 1 sm
(b) 2 sm
(g) 3 sm
(d) 4 sm
(e) 5 sm
51. moTxrobebis krebulis fasi iyo 8 lari. magram gayiduli 150 krebulidan am
fasad mxolod 80% gaiyida, danarCeni ki fasdaklebiT _ naxevarfasad. sul
ramden larad gaiyida es krebulebi?
(a) 1000
(b) 1080
(g) 1140
(d) 1200
(e) 1360
25
653010b
monacemTa analizi
erT-erTma sadazRvevo kompaniam Caatara gamokiTxva klientebis sxvadasxva
sadazRvevo
produqtiT
kmayofilebis
xarisxis
dasadgenad.
gamokiTxvaSi
monawileoba miiRes pirebma, romlebic sargeblobdnen janmrTelobis, avtomanqanis,
uZravi qonebis an samogzauro dazRveviT (sul 160 respondenti), maT Soris
80 respondenti miekuTvneboda 31-dan 40 wlamde asakobriv jgufs, xolo
danarCeni _ 41-dan 50 wlamde asakobriv jgufs.
pirvel
diagramaze
warmodgenilia
respondentTa
ganawileba
sxvadasxva
sadazRvevo produqtiT kmayofilebis xarisxis mixedviT.
meore diagramaze ki warmodgenilia 31-dan 40 wlamde da 41-dan 50 wlamde
asakobrivi
jgufebis
respondentTa
ganawileba
sadazRvevo
produqtebiT
kmayofilebis xarisxis mixedviT.
diagramebis mixedviT upasuxeT Semdeg 4 SekiTxvas:
26
653010b
52. ramdenjer aRemateba im klientTa raodenoba, romlebic avtodazRveviT
sargebloben da momsaxurebiT kmayofilni arian, im klientTa raodenobas,
romlebic dazRvevis imave produqtiT sargebloben da momsaxurebiT Zalian
ukmayofiloni arian?
(a) 2-jer
(b) 2,5-jer
(g) 3-jer
(d) 3,5-jer
(e) 4-jer
53. kmayofilebis romeli xarisxobrivi kategoriis SemTxvevaSia 41-dan 50 wlamde
respondentTa raodenoba 4-iT meti 31-dan 40 wlamde respondentTa raodenobaze?
(a) Zalian ukmayofilo
(b) naklebad kmayofili
(g) kmayofili
(d) Zalian kmayofili
(e) arc erTi kategoriis SemTxvevaSi
54. ramdeniT metia sadazRvevo produqtebiT kmayofil klientTa
sadazRvevo produqtebiT Zalian ukmayofilo klientTa raodenobaze?
(a) 21-iT
(b) 35-iT
(g) 42-iT
(d) 46-iT
(e) 52-iT
raodenoba
55. 31-dan 40 wlamde respondentebidan samogzauro dazRveviT Zalian kmayofili
aRmoCnda 12 klienti, xolo uZravi qonebis dazRveviT _ 14 klienti. am
asakobrivi jgufis respondentebidan ramdeni aRmoCnda Zalian kmayofili
janmrTelobis dazRveviT?
(a) 2
(b) 4
(g) 6
(d) 8
(e) 10
amocanebi
56.
mocemuli
naturaluri
ricxvi
unaSTod
iyofa
214-ze.
qvemoT
CamoTvlilTagan romeli cifriT ar SeiZleba dabolovdes mocemuli ricxvis
Canaweri?
(a) 0
(b) 2
(g) 4
(d) 7
(e) 8
27
653010b
57. marTkuTxedis farTobia 18 sm2. misi ori mopirdapire
gverdis Suawertilebis SemaerTebeli monakveTi dayofilia
sam tol nawilad da dayofis wertilebi monakveTebiTaa
SeerTebuli marTkuTxedis wveroebTan (ix. naxazi). ris tolia
miRebuli eqvskuTxedis farTobi?
(a) 15 sm2
(b) 14 sm2
(g) 13 sm2
(d) 12 sm2
(e) 11 sm2
58. nakveTis ra nawils moxnavs traqtori 1 saaTsa da 20 wuTSi, Tu nakveTis
5 nawilis mosaxnavad 1 saaTi da 40 wuTia saWiro?
6
(a) 1
3
(b) 1
2
4
(g)
5
(d) 3
4
2
(e)
3
59. a, b da c kenti naturaluri ricxvebia, amasTan a  b  c . CamoTvlilTagan
romeli winadadebaa mcdari?
I. a  b  c luwia
II. ab  c kentia
III. a ·b ·c kentia
(a)
(b)
(g)
(d)
(e)
mxolod I
mxolod II
mxolod I da II
mxolod II da III
I, II da III
60. velosipedisti 2 saaTis ganmavlobaSi Tanabrad, 25 km/sT siCqariT moZraobda,
xolo momdevno 3 saaTis ganmavlobaSi _ 20 km/sT siCqariT. ukan dabrunebisas
velosipedistma igive manZili Tanabari siCqariT 5 saaTis ganmavlobaSi gaiara. ra
siCqariT moZraobda velosipedisti ukan dabrunebisas?
(a) 21 km/sT
(b) 22 km/sT
(g) 23 km/sT
(d) 24 km/sT
(e) 25 km/sT
28
653010b
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
n naturaluri ricxvia.
61.
n-is 12-ze gayofisas
miRebuli naSTi
(n + 48)-is 12-ze gayofisas miRebuli naSTi
7, 9, 4, ... mimdevrobis wevrebs lia da sandro rigrigobiT werdnen _ jer lia, Semdeg _ sandro.
sandros mier Cawerili yoveli wevri mimdevrobis
62. wina wevrze 2-iT meti iyo, xolo lias mier
Cawerili _ wina wevrze 5-iT naklebi.
mimdevrobis ori mezobeli
wevris namravli
(b)
(g)
(d)
(a)
(b)
(g)
(d)
(a)
(b)
(g)
(d)
0
kvadratis erT-erTi wvero
wris centrs emTxveva, xolo
gverdi wris diametris
63. tolia.
wris farTobi
(a)
kvadratis farTobi
29
653010b
16 tona tvirTi, romelic 20 yuTSi Tanabradaa
ganawilebuli,
erTdroulad
unda
gadaitanon
satvirTo
avtomanqanebiT
yuTebis
gauxsnelad.
64. TiToeul avtomanqanas 3 tonamde tvirTis waReba
SeuZlia.
tvirTis gadasatanad saWiro
avtomanqanebis raodenoba
65.
(a)
(b)
(g)
(b)
(g)
(d)
6
ujraSi 15 TeTri da ramdenime wiTeli burTulaa.
albaToba imisa, rom ujridan amoRebuli burTula
wiTeli iqneba, 2 -is tolia.
7
wiTeli burTulebis
raodenoba
(a)
(d)
6
amocanebi
66. gasayofi 3-jer metia gamyofze, xolo gamyofi 3-jer metia ganayofze. ris
tolia gasayofi?
(a) 27-is
(b) 24-is
(g) 18-is
(d) 15-is
(e) 9-is
30
653010b
67. sarben biliks wesieri eqvskuTxedis forma aqvs (ix. naxazi).
bilikis sigrZe 300 metria. sportsmenma sirbili daiwyo
A wverodan isriT miTiTebuli mimarTulebiT da ramdenime
xnis Semdeg gaCerda bilikis B wverosTan. CamoTvlilTagan
romlis toli SeiZleba iyos sportsmenis mier gavlili
manZili?
(a) 700 m
(b) 750 m
(g) 800 m
(d) 850 m
(e) 900 m
68. im naturaluri ricxvebidan, romlebic metia 20-ze, magram naklebia 128-ze,
ramdeni iyofa 6-ze unaSTod?
(a) 16
(b) 17
(g) 18
(d) 19
(e) 20
69. dawesebulebaSi TanamSromelTa 40% qalebi arian. TanamSromel
raodenobis ramdeni procentia TanamSromel mamakacTa raodenoba?
(a) 60%
(b) 80%
(g) 120%
(d) 140%
(e) 150%
31
qalTa
653010b
70. x da y iseTi naturaluri ricxvebia, rom
2  2 . qvemoT CamoTvlilTagan
x y
romeli mimarTeba SeiZleba iyos marTebuli?
(a) y  x  1
(b) x  2 y
(g) y  x
3
(d) y  2 x
(e) x  2 y
71. pirveli marTkuTxa samkuTxedis didi kaTetis sigrZe 6-jer metia meore
marTkuTxa samkuTxedis didi kaTetis sigrZeze, xolo farTobi 3-jer naklebia
meore marTkuTxa samkuTxedis farTobze. ramdenjer naklebia pirveli marTkuTxa
samkuTxedis mcire kaTetis sigrZe meore marTkuTxa samkuTxedis mcire kaTetis
sigrZeze?
(a) 2-jer
(b) 3-jer
(g) 9-jer
(d) 15-jer
(e) 18-jer
monacemTa sakmarisoba
72. fakultetze sul 80 ucxoeli studenti swavlobs, romelTagan 50 gogonaa.
mocemulia ori piroba:
I. ucxoel student gogonaTa raodenoba am fakultetis studentTa saerTo
raodenobis 10%-s Seadgens.
II. ucxoel student vaJTa raodenoba am fakultetis student vaJTa saerTo
raodenobis 15%-s Seadgens.
imis gasarkvevad, Tu sul ramdeni studenti swavlobs am fakultetze:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
32
653010b
73. ABC samkuTxedis AB gverdis M wertili
da BC gverdis N wertili monakveTiTaa
SeerTebuli.
mocemulia ori piroba:
I. BMN  MNB  130 .
II. A  C  130 .
imis gasarkvevad, Tu ris tolia B :
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
74. ori ricxvidan erTi a-s tolia, meore _ b-si.
mocemulia ori piroba:
I. a-s Sefardeba b-sTan 3-is tolia.
II. a-s da b-s jami 4-jer metia b-ze.
imis gasarkvevad, Tu ris tolia a da b ricxvebis namravli:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
75. ninos Svilebidan yvelaze umcrosia giorgi, xolo yvelaze ufrosi
arCili. maT garda ninos hyavs 3 gogona, romelTa saSualo asaki 13 welia.
_
mocemulia ori piroba:
I. vaJebs Soris asakSi gansxvaveba 15 welia.
II. ninos Svilebis saSualo asaki 12 welia.
imis gasarkvevad, Tu ramdeni wlisaa arCili:
(a)
(b)
(g)
(d)
(e)
I piroba sakmarisia, II ki _ ara
II piroba sakmarisia, I ki _ ara
I da II piroba erTad sakmarisia, cal-calke arc erTi ar aris sakmarisi
sakmarisia cal-calke rogorc I, aseve, II piroba
mocemuli pirobebi ar aris sakmarisi
33
653010b
amocanebi
76. Tornikes gasuli wlis ganmavlobaSi yovelTviurad Tavisi xelfasis 10%
bankSi Sehqonda. wels Tornikes xelfasi 20%-iT gaezarda, ris gamoc man bankSi
Tavisi xelfasis 15%-is Setana daiwyo. ramdenjer met Tanxas Seitans Tornike am
wels bankSi wina welTan SedarebiT?
(a) 1,5-jer
(b) 1,8-jer
(g) 2-jer
(d) 2,4-jer
(e) 3-jer
77. nebismieri a ricxvisaTvis a -iT
aRniSnulia ricxvi, romelic miiReba
Semdegi sqemis mixedviT:
magaliTad, am sqemis mixedviT
 2   2  4· 3  6  0 .
ris tolia
(a)
(b)
(g)
(d)
(e)
 8  ?
8
16
24
32
40
78. 4 m siRrmis mqone kubis formis wyliT savse rezervuaridan wyali mTlianad
gadatumbes marTkuTxa paralelepipedis formis sacurao auzSi, romlis fskeris
sigrZea 8 m, sigane _ 4 m. ris toli iqneba sacurao auzSi wylis siRrme?
(a) 0,5 m
(b) 1 m
(g) 1,5 m
(d) 2 m
(e) 2,5 m
34
653010b
79. M, N, K da D ricxvTa RerZis sxvadasxva wertilebia, xolo m, n, k da d,
Sesabamisad, maTi koordinatebia. K wertili Tanabradaa daSorebuli M da D
wertilebidan, xolo N wertili _ K da D wertilebidan. ris tolia k  d ?
nm
(a)
(b)
(g)
(d)
(e)
1
3
2
3
3

4
1
3
3
4
80. cekvisa da simReris ansamblis wevrTa 60%-s mocekvaveebi Seadgendnen. roca
ansamblis ramdenime wevri sxva ansamblSi gadavida, mocekvaveTa raodenoba 7-iT
Semcirda, Tumca, maTi procentuli wili gaizarda. CamoTvlilTagan romlis
toli SeiZleba iyos sxva ansamblSi gadasul wevrTa raodenoba?
(a) 8
(b) 9
(g) 10
(d) 11
(e) 12
35
653010b