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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
analogiuria. pasuxis arCevisas gaiTvaliswineT sityvaTa Tanmimdevroba wyvilebSi.
1. ia : mcenare (a) moTxroba : wigni
(b) funji : fanqari
(g) Wiqa : WurWeli
(d) CarCo : suraTi
2. konfliqti : sawinaaRmdegod (a) ganrigi : Tanmimdevrulad
(b) meTodika : eqsperimentulad
(g) praqtika : Teoriulad
(d) testi : standartulad
3. presa : televizia (a) droSa : gerbi
(b) saxazavi : naxazi
(g) formula : ricxvi
(d) melodia : simfonia
4. sinaTle : gaumWvirvale (a) cecxli : aalebadi
(b) haeri : dagmanuli
(g) wyali : gaJRenTili
(d) miwa : fxvieri
5. CayvinTa : CaiZira (a) Seyovnda : Seferxda
(b) Caimuxla : Camojda
(g) Caifiqra : moifiqra
(d) mousmina : moesma
3
6. odesRac : odesme (a) garSemo : irgvliv
(b) odnav : nawilobriv
(g) Tvalwin : miRma
(d) SemTxveviT : uneburad
7. akvareli : plastilini (a) Ruza : ialqani
(b) gemi : TviTmfrinavi
(g) sateliti : kosmosi
(d) porti : akvatoria
4
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.
8. adamianis ori umTavresi movaleobaa iyos gonieri da samarTliani. gonieria is, vinc icis gansxvaveba ______ Soris, xolo samarTliania is, ______ im
sakiTxebis Sesaxeb, romlebic ______ icis.
(a) codnasa da arcodnas / visac ar SeuZlia azris gamoTqma / kargad
(b) samarTlianobasa da usamarTlobas / visac SeuZlia azris gamoTqma / ar
(g) codnasa da arcodnas / vinc ar gamoTqvams sakuTar mosazrebas / ar
(d) samarTlianobasa da usamarTlobas / visac ar aqvs sakuTari mosazreba /
kargad
9. Cvens saukuneSi saxelmwifoebi uzarmazar valebs iReben omebis sawarmoeblad, magram _____ didi sesxi ganaTlebisTvis. rogorc Cans, arc erTi saxelmwifo ar
aris _____ , rom _____ . arCevani unda gavakeToT _ orive ver gveqneba.
(a) yovel maTgans aRebuli aqvs kidev ufro / imdenad Raribi / ver SeZlos
xarjebis gaReba rogorc omis, ise civilizaciisTvis
(b) is, rac maT marTla sWirdebaT, aris / sakmarisad mdidari imisTvis /
gauWirdes saxsrebis moZieba omisTvisac da civilizaciisTvisac
(g) arc erT saxelmwifos arasodes auRia / sakmarisad mdidari imisTvis / SeZlos
xarjebis gaReba omisTvisac da civilizaciisTvisac
(d) warmoudgenelia, rom saxelmwifom aiRos / imdenad Raribi / SeZlos xarjebis
gaReba rogorc omis, ise civilizaciisTvis
10. rac ufro Rrmad vswavlobT mecnierebas, miT ufro ______ , rom samyaros yvela saidumlo ______ kanoniT aixsneba. es kanonebi isea ______ , rom ueWveli
xdeba yoveli maTganis ukan erTi da imave uzenaesi wesrigis arseboba.
(a) aSkara xdeba / mravali erTmaneTisgan damoukidebeli / urTierTdakavSirebuli
da urTierTdamokidebuli
(b) naTlad vxedavT / sul ramdenime martivi / erTmaneTTan dakavSirebuli da
erTmaneTze gadajaWvuli
(g) ucnaurad gveCveneba / sul ramdenime martivi / garTulebuli gadauWreli
problemebiTa da paradoqsebiT
(d) aSkarad vxedavT / erTi-ori fundamenturi / mowyvetili da gamijnuli
erTmaneTisgan
5
logika
am saxis davalebebi gansxvavdeba erTmaneTisgan monacemebisa da gamosatani
daskvnebis TvalsazrisiT. amitom gansakuTrebuli yuradReba miaqcieT SekiTxvas,
romelic axlavs TiToeul davalebas, da mocemuli variantebidan airCieT
Sesabamisi pasuxi.
zogierT SekiTxvaze pasuxis gacemas gagiadvilebT monacemebis gamosaxva
naxazis formiT.
11. samSabaTs moswavleebs oTxi gakveTili aqvT: qarTuli, maTematika, buneba da xatva. gakveTilebis cxrili Semdegi moTxovnebis mixedviTaa Sedgenili:
• qarTulis gakveTili ufro adrea, vidre maTematikisa.
• bunebis gakveTili ufro adrea, vidre maTematikisa.
• xatvis gakveTili ufro gvianaa, vidre qarTulisa.
qvemoT CamoTvlilTagan gakveTilebis romeli Tanmimdevroba Seesabameba am
monacemebs?
I gakveTili II gakveTili III gakveTili IV gakveTili
(a) buneba maTematika qarTuli xatva
(b) maTematika qarTuli xatva buneba
(g) xatva buneba qarTuli maTematika
(d) buneba qarTuli maTematika xatva
12. Team gadawyvita, SabaT saRamos an TeatrSi wavides, an Tavis Zvel megobars, makas estumros. amasTan, cnobilia:
• Tu Tea SabaT saRamos TeatrSi wava, iq Tavis Tanajgufelebs Sexvdeba.
• Tea makas mxolod im SemTxvevaSi estumreba, Tu makasTan maTi saerTo
megobari ninoc wava.
qvemoT CamoTvlilTagan romeli daskvnis gamotana SegviZlia, Tu viciT, rom Team
Tavisi gadawyvetileba Seasrula, miuxedavad imisa, rom ninom SabaT saRamos
makasTan stumrad wasvla ver SeZlo?
SabaT saRamos Tea:
(a) makas estumra
(b) TeatrSic iyo da makasac estumra
(g) Tavis Tanajgufelebs Sexvda
(d) ninos ver Sexvda
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13. sxvadasxva feris oTxi burTi _ wiTeli, mwvane, yviTeli da lurji _
dalagebulia mwkrivad.
• wiTeli burTi devs mwvane burTis gverdiT.
• lurji burTis gverdiT ar devs arc yviTeli da arc wiTeli burTi.
romeli burTi devs yviTeli burTis gverdiT?
(a) wiTeli
(b) mwvane
(g) wiTeli da mwvane
(d) mocemuli informacia ar aris sakmarisi kiTxvaze pasuxis gasacemad
14. biologma SeamCnia, rom beRurebi Tavs arideben sakvebis gamo konfliqtis dawyebas im TanagundelebTan, romelTac yelze maTze ufro muqi feris bumbuli
aqvT. mkvlevarma amis safuZvelze ivarauda, rom beRuras yelze bumbulis muqi
Seferiloba e. w. `statusis signalis~ rols asrulebs _ Tanagundelebs amcnobs,
rom am niSnis mqone individs brZolis gansakuTrebuli unari aqvs da amiT
gundis wevrebs usargeblo Setakebebisgan icavs.
qvemoT CamoTvlilTagan romeli argumenti ayenebs eWvqveS mkvlevris varauds?
(a) muqi feris bumbuli, zogadad, gundebad mcxovrebi frinvelebis bevr
saxeobaSi asrulebs statusis signalis rols, vinaidan is ar aris
damokidebuli individebs Soris asakobriv an sqesobriv gansxvavebebze
(b) cnobilia, rom patara Citis _ wiwkanas _ SemTxvevaSi statusis signalis
rols asrulebs mkerdze muqi zolis sigane: rac ufro ganieri zoli aqvs
individs, miT ufro naklebad savaraudoa TanagundelTa mxridan masze
Tavdasxma, misi asakisa da sqesis miuxedavad
(g) zrdasrul beRurebs yelze ufro muqi feris bumbuli aqvT, vidre
axalgazrdebs; statusis signali ki iseT niSans ewodeba, romelic individs
gamoarCevs ara mxolod asakis an sqesis mixedviT, aramed ganasxvavebs mas imave
asakisa Tu sqesis sxva individTaganac
(d) beRurebis kvlevam aCvena, rom rac ufro kargad aqvs individs ganviTarebuli
kunTovani sistema da rac ufro swrafad SeuZlia reagireba garemodan
miRebul stimulebze, miT ufro muqi bumbuli aqvs mas yelze, misi asakisa da
sqesis miuxedavad
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wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
maTematikis sferoSi piTagoramde (Zv. w. VI-V s.s.) sakmaod mniSvnelovani
codna iyo dagrovebuli, arsebobda Sexedulebebi calkeul ricxvTa simbolur
mniSvnelobebzec, magram arqaul saberZneTSi piTagora iyo pirveli, vinc ricxvi
da ricxviTi mimarTebebi daudo safuZvlad kosmosis kanonzomierebaTa axsnas.
piTagorasTvis ricxvi iyo ara mxolod raodenobis gamomxatveli, aramed samyaros
pirvelsawyisi. amgvari Tvalsazrisi gvxvdeba ricxvTa mistikis adreul
warmodgenebSic. sakmarisia gavecnoT piTagoras cxovrebis wesisa da moZRvrebis
Sesaxeb arsebul cnobebs, rom Cvens yuradRebas uTuod miipyrobs mistikurisa da
mecnierul-racionaluris ara marto ubralo Tanaarseboba, aramed maTi erT
sistemad gaerTianebis cda.
aristotele werda: `piTagorelebi fiqrobdnen, rom maTematikis sawyisi
yvelafris sawyisia, yvelaferi ricxvebs emsgavseba Tavisi bunebiT, da ricxvebi
mTel bunebas uswrebs win.~ piTagorelTa moZRvrebis amosavali unda yofiliyo
is dakvirveba, rom musikaluri harmonia ricxviT mimarTebebs efuZneba. isini
musikalur bgeraTa Soris intervalebs ariTmetikulad gamosaxavdnen ricxvebis _
1, 2, 3 da 4 _ urTierTmimarTebebiT. am ricxvebis jami _ 10 _ piTagorelebma
srulyofil ricxvad gamoacxades, xolo Canaweri 1+2+3+4=10 kosmosis harmonias
warmogvidgenda. ricxvTa Taviseburi gaazrebis safuZvelze Camoyalibda
piTagoruli e. w. planetebis Teoria, romlis Tanaxmad, sferoseburi samyaros
(kosmosis) centrs warmoadgens `wminda cecxli~. mas ekvris aTi ciuri sxeuli. am
harmonias, piTagorelTa azriT, musikaluri proporciebi udevs safuZvlad.
sainteresoa is gadmocemac, romlis Tanaxmad, piTagoram pirvelma daadgina mimarTeba
simis sigrZesa da tonis simaRles Soris _ erTnairi daWimulobisas tonis simaRle
ukuproporciul damokidebulebaSia simis sigrZesTan.
piTagorelebma pirvelebma warmoaCines ricxviTi mimarTebebis mniSvneloba
zogadi kanonzomierebebis dasadgenad. SesaZloa, maT pirvelebma dauSves, rom
dedamiwa sferos formis planetaa. piTagorelTa mignebebi Semdegdroindel
filosofiasa da mecnierebaSi poulobs ganviTarebas, zogjer ki Tanamedrove
mecnierTa uTamames hipoTezebs exmianeba. dRes arc ise advilia piTagorizmSi
mkveTri zRvris gavleba racionalizmsa da iracionalizms, logikursa da
alogikurs Soris. Tanamedrove mecnierebis TvalTaxedviT, piTagorelTa ltolva
samyaros struqturaSi maTematikuri simetriisa Tu harmoniis aRmoCenisken
erTgvarad gamarTlebulicaa.
tiran polikratesgan Seviwroebulma piTagoram miatova mSobliuri kunZuli
samosi da samxreT italiaSi gadasaxlda, sadac daaarsa mistikur-filosofiuri
wre. piTagorelebma SeimuSaves cxovrebis garkveuli wesi, romelic elinTaTvis
manamde uCveulo saxiT _ miwier keTildReobaze uaris TqmiT _ gamoixata.
piTagorelebs SezRuduli hqondaT sakvebi, uaryofdnen sisxlian msxverplSewirvas
da a. S. maTTvis ZiriTadi avtoriteti iyo maswavlebeli (anu piTagora) da misive
zepiri gziT gadacemuli dadgenilebani, e. w. akusmebi (`mosmenilni~). piTagorelTa
wre Tavisi gansakuTrebulobiTa da cxovrebis uCveulo wesiT daupirispirda
sazogadoebrivi cxovrebis Cveul praqtikas. Tumca piTagorelTa umTavresi
wvlili elinuri mecnierebis ganviTarebaSi iyo is, rom maT adamianis azrovnebas
gza gauxsnes ricxviT mimarTebaTa samyarosken.
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15. aristoteles citatis romeli perifrazi ar aris marTebuli?
piTagorelTa azriT:
(a) ricxvi da ricxviTi mimarTebebi safuZvlad udevs samyaros nebismier
gamovlinebas
(b) kosmosSi yvelafers, samyaros yovel gamovlinebas ricxvTa analogiuri buneba
aqvs
(g) bunebaSi Tavdapirvelad Seiqmna ricxvebi da Semdeg Camoyalibda ricxviTi
mimarTebebi
(d) ricxvebi da ricxviTi mimarTebebi samyaros kanonzomierebaTa formirebamde
arsebobda
16. qvemoT CamoTvlilTagan romel winadadebaSia sworad asaxuli piTagoras
wvlili musikis kvlevaSi?
(a) piTagoram aRmoaCina instrumentisa da musikaluri bgeris urTierTmimarTebis
specifika _ rac ufro moklea simi, miT ufro maRalia toni
(b) piTagoram daadgina, rom musikaluri harmonia kosmosis kanonzomierebaTa
safuZvelze unda aixsnas
(g) musika piTagorasTvis mistikis sfero iyo, Sesabamisad, is cdilobda
maTematikisa da musikis saerTo sawyisebis amocnobas
(d) piTagoram musikaluri harmoniis safuZvelze Camoayaliba `planetebis Teoria~,
romelic, Tavis mxriv, gansazRvravs kosmosur harmonias
17. ra funqcia aqvs teqstSi Canawers 1+2+3+4=10?
(a) es Canaweri adasturebs im faqts, rom yovel ricxvs miesadageba samyaros esa
Tu is konkretuli gamovlineba
(b) es aris piTagoruli e. w. planetebis Teoriis amosavali formula, romelic
cxadyofs, rom samyaros centrs gars ekvris aTi ciuri sxeuli
(g) piTagorelTaTvis es Canaweri samyaros wesrigis simboluri gamoxatulebaa
(d) es Canaweri musikalur bgeraTa Soris intervalebs aRniSnavs
18. qvemoT CamoTvlilTagan romeli mosazrebaa warmodgenili teqstSi varaudis saxiT?
(a) piTagorelTa ideebma ganviTareba pova filosofiasa da mecnierebaSi, isini
Tanamedrove mecnierebis zogierT hipoTezasac exmianeba
(b) piTagorelebma ricxviTi mimarTebebi universaluri principis rangSi aiyvanes,
es mimarTebebi miusadages musikas, planetebs Tu, zogadad, mTel kosmoss
(g) piTagorelebi Seecadnen racionalizmisa da iracionalizmis, logikurisa da
alogikuris erT sistemad gaerTianebas
(d) piTagorelebma pirvelebma gamoTqves mosazreba, rom dedamiwa sferos
moyvanilobis planetaa
9
19. qvemoT mocemulia cnobebi ramdenime subkulturis Sesaxeb:
I. bitnikebi _ 1950-iani wlebis axalgazrduli moZraobis warmomadgenlebi
dasavleTSi, mwerlebi, mxatvrebi, musikosebi; maTTvis damaxasiaTebeli iyo
subieqtivizmi, anarqistuli ganwyoba; gatacebulni iyvnen jaziT,
ikribebodnen yavis saxlebSi, TiTqos dakarguli hqondaT cxovrebisadmi
interesi.
II. hipebi _ axalgazrduli moZraobis warmomadgenlebi; gamodiodnen
sazogadoebis mier dawesebuli zneobrivi normebis, aseve fufunebis,
Zaladobis, omis winaaRmdeg; iaraRs upirispirebdnen yvavilebs; xSirad
meditirebdnen, gatacebulni iyvnen rokmusikiT, aseve, aRmosavluri mistikiT.
III. emoebi _ XXI saukunis axalgazrduli moZraobis warmomadgenlebi;
gamoiyurebian da iqcevian, rogorc bavSvebi, maTi garToba celqobas hgavs,
weren dRiurebs, Canaxatebs, leqsebs, sadac Zlier emociur gancdebzea
saubari, Tumca TviTgamoxatvis ZiriTadi saSualeba mainc musikaa.
romel subkulturaSi aRmovaCenT piTagorelTaTvis damaxasiaTebel yvelaze met
niSans?
(a) bitnikebTan
(b) hipebTan
(g) emoebTan
(d) piTagorelebsa da romelime aq warmodgenil subkulturas Soris paralelis
gavleba SeuZlebelia 20. ra aris teqstis mTavari saTqmeli?
(a) piTagorelTa moZRvreba, aseve, maTi cxovrebis wesi mistikurisa da mecnierul-
racionaluris Serwymis saintereso magaliTs warmoadgens
(b) piTagorizmSi Tavs iCens arqauli berZnuli kulturisTvis damaxasiaTebeli
swrafva maTematikuri simetriisken
(g) piTagorelebi aRiarebdnen misticizms, Tumca maT moZRvrebaSi arsebobs
mkveTri zRvari logikursa da alogikurs Soris
(d) piTagorelTa swrafva, musikaluri harmoniis kanonzomierebebi maTematikuri
formulebiT gamoesaxaT, gamoxmaurebas povebs Tanamedrove mecnierebaSi
10
analogiebi
am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva (sawyisi
wyvili), romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. maT gaswvriv
mocemulia sityva, romelsac savaraudo pasuxebidan unda SeusabamoT erT-erTi
varianti, ise, rom sityvaTa mniSvnelobebs Soris mimarTeba sawyis wyvilSi
arsebuli mimarTebis analogiuri iyos.
21. Tavisufali : mZevali unikaluri :
(a) Sedevri
(b) asli
(g) dedani
(d) foto
22. vulkani : Sadrevani naperwkali :
(a) namceci
(b) ali
(g) Sxefi
(d) mtveri
23. Sefaseba : kriteriumi dadanaSauleba :
(a) niuansi
(b) sasjeli
(g) incidenti
(d) samxili
24. kuriozi : uCveulo eqspromti :
(a) saxeldaxelo
(b) sagangebo
(g) sasacilo
(d) sasceno
25. kinofiri : gamosaxuleba mexsiereba :
(a) mogoneba
(b) fantazia
(g) cnobiereba
(d) STabeWdileba
11
winadadebebis Sevseba
am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa
gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiT aris aRniSnuli.
erTi xazi zogjer erT sityvas gulisxmobs, zogjer ki _ ramdenimes.
savaraudo pasuxTa yovel variantSi mocemulia sityvaTa jgufi, romlis
nawilebi erTmaneTisgan daxrili xazebiTaa (/) gamijnuli. airCieT pasuxis is
varianti, romlis TiToeuli nawilis Tanmimdevrulad Casma Sesabamis
gamotovebul adgilebSi azrobrivad gamarTul winadadebas mogvcems.
26. elinuri keramika berZenTa mxatvruli kulturis erT-erT umniSvnelovanes sferod aris miCneuli, _____ man _____ informacia elinuri ferweris Sesaxeb.
_____ , dRes Cven gacilebiT _____ vicnobT Zv. w. II aTaswleulis minosursa
Tu mikenur freskul ferweras, vidre klasikur berZnuls. _____ moxatuli
keramikuli nawarmi CvenTvis am xarvezis Sevsebis marTlac erTaderT wyaros
warmoadgens.
(a) Tumca / Semogvinaxa mxolod mcire / raoden paradoqsuladac unda
mogveCvenos / ufro cudad / uxvad SemorCenili
(b) miuxedavad imisa, rom / Semogvinaxa didi / bunebrivia / ufro cudad /
umniSvnelo raodenobiT SemorCenili
(g) radgan / Semogvinaxa, faqtobrivad, mTeli / raoden paradoqsuladac unda
mogveCvenos / ukeT / uxvad SemorCenili
(d) vinaidan / faqtobrivad ver Semogvinaxa / bunebrivia / ukeT / umniSvnelo
raodenobiT SemorCenili
27. Cven vcxovrobT samyaroSi, romelsac yvela juris fiqcia marTavs: masobrivi marketingi, reklama, mecnierebis da teqnologiis miRwevebis uxarisxo `Targmanebi~
popularul enaze. mokled, Cven ______ vcxovrobT. ______ Tavisi romanis
_____ . fiqcia ukve yoveldRiurobis nawilia, mwerlis amocanad ki ______
qceula.
(a) realistur romanSi / mwerlisTvis sul ufro ioli xdeba / realisturi
SinaarsiT Sevseba / sinamdvilisgan distancireba
(b) realobis da fiqciis zRvarze / mwerlisTvis sul ufro Znelia /
realisturi SinaarsiT Sevseba / sinamdvilisgan distancireba
(g) ukve, realobis nacvlad, fiqciaSi / mwerals sul ufro metad sWirdeba /
fiqciuri Sinaarsis gamogoneba / sinamdvilis gamogoneba
(d) erT did romanSi / mwerals sul ufro naklebad sWirdeba / fiqciuri
Sinaarsis gamogoneba / sinamdvilis gamogoneba
12
28. yoveli adamiani fiqrobs, rom Tanasworoba samarTlianobis moTxovnaa, _____ iq, sadac, misi azriT, sazogadoebisTvis _____ . is, vinc fiqrobs, rom
wodebrivi gansxvavebebi _____ miiCnevs simdidrisa da socialuri privilegiebis
_____ ganawilebas; xolo visac aseTi _____ miaCnia, fiqrobs, rom is _____
aris.
(a) Tumca mxolod / mavnebelia uTanasworoba / sasargebloa, usamarTlobad ar /
Tanabrad / Tanasworoba sasargeblod / samarTlianic
(b) magram ara / sasargebloa uTanasworoba / sasargebloa, usamarTlobad ar /
araTanabrad / uTanasworoba sasargeblod ar / usamarTlobac
(g) Tumca mxolod / sasargebloa Tanasworoba / mavnebelia, samarTlianad ar /
araTanabrad / uTanasworoba sasargeblod ar / samarTlianic
(d) magram ara / mavnebelia Tanasworoba / mavnebelia, samarTlianad / Tanabrad /
Tanasworoba sasargeblod / usamarTlobac
29. _____ , rom vaJam _____ mouxmo _____ saCveneblad, aramed, piriqiT, _____ .
(a) bunebrivi rodia / eTnosur samyarosa da dialeqts / ara universaluris /
provinciulis gamosaxatavad
(b) bunebrivia / eTnosur samyarosa da dialeqts ki ar / provinciulis /
sazogadosa da universalurs
(g) paradoqsia / eTnosur samyarosa da dialeqts ki ar / universaluris /
sazogadosa da araspecifikurs
(d) paradoqsia / eTnosur samyarosa da dialeqts / ara provinciulis /
universaluris gamosaxatavad
30. cnobilia jon raskinis fraza Tvalis `umankoebis~ Sesaxeb: `sinamdvilis
amsaxveli WeSmariti xedva _____ , sagnis _____ Cveni Semecnebis, gamocdilebis
da swavlis Sedegia.~ amgvari gamonaTqvamebi aqvT XIX saukunis sxva
Teoretikosebsac. maTSi _____ , rom yovelgvari cnebisa da codnis ukugdeba
_____ mxatvars, Caswvdes xiluli samyaros WeSmarit arss.
(a) aris mxolod sibrtyeze ferebis monacvleobis aRqma / Sesaxeb yoveli sxva
warmodgena ki / ikveTeba is azri / SesaZleblobas aZlevs
(b) mxolod sibrtyeze ferebis monacvleobis aRqmas rodi gulisxmobs / namdvili
arsis wvdoma / ikveTeba is azri / SesaZleblobas aZlevs
(g) aris mxolod sibrtyeze ferebis monacvleobis aRqma / namdvili arsis wvdoma
swored / uaryofilia mosazreba / xels uSlis
(d) mxolod sibrtyeze ferebis monacvleobis aRqmas rodi gulisxmobs / Sesaxeb
yoveli warmodgena / uaryofilia mosazreba / xels uSlis
13
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.
31. mocemulia wanamZRvrebi:
• yvela Jirafi binadrobs afrikaSi.
• zogierT Jirafs aqvs susti mxedveloba.
• Jirafi ar aris mtacebeli cxoveli.
qvemoT CamoTvlilTagan romeli debuleba gamomdinareobs mocemuli
wanamZRvrebidan?
I. yvela Jirafi, romelsac aqvs susti mxedveloba, binadrobs afrikaSi.
II. afrikaSi binadar zogierT aramtacebel cxovels aqvs susti mxedveloba.
(a) orive
(b) mxolod pirveli
(g) mxolod meore
(d) arc erTi
32. Serlok holmsi msjelobs: saxlSi ori oTaxi iyo. mZarcvelebi sul samni iyvnen _ A, B da C. erTi cdilobda seifis gaxsnas, erTi mas exmareboda, erTic meore oTaxSi saidumlo dokumentebs eZebda. garda amisa:
• Tu A xsnida seifs, maSin B meore oTaxSi unda yofiliyo. • Tu B meore oTaxSi iyo, C damxmare ar iqneboda. • Tu C meore oTaxSi ar iyo, seifs xsnida B.
vin xsnida seifs?
(a) A (b) B (g) C (d) mocemuli informacia ar aris sakmarisi amis dasadgenad
14
33. zogierT sadazRvevo kompaniaSi avtosagzao SemTxvevebisgan dazRvevis tarifi wiTeli manqanebisTvis ufro maRalia, vidre sxva feris manqanebisTvis. am
informaciis safuZvelze ivaraudes, rom procentulad wiTeli manqanebi yvela
sxva feris manqanaze ufro xSirad xvdeba avtosagzao SemTxvevebSi.
qvemoT CamoTvlilTagan romeli viTareba ayenebs eWvqveS am varauds?
(a) mZRolebi, romlebic xSirad arRveven avtosagzao moZraobis wesebs, wiTel
manqanebs aniWeben upiratesobas
(b) qveynebSi, sadac aRniSnuli sadazRvevo kompaniebi muSaobs, wiTeli manqanebi
nebismieri sxva feris manqanebze ufro popularulia
(g) rogorc wesi, wiTeli manqanebis SekeTeba imave modelis nebismieri sxva feris
manqanis SekeTebaze ufro Zviri Rirs
(d) qveynebSi, sadac aRniSnuli sadazRvevo kompaniebi muSaobs, wlis ganmavlobaSi
sxva feris manqanebze naklebi wiTeli manqana iyideba
34. mocemulia ori debuleba: • holivudis zogierTi filmi literaturuli nawarmoebis ekranizacias
warmoadgens.
• literaturuli nawarmoebis zogierTi ekranizacia kinoxelovnebis
mniSvnelovani miRwevaa.
maSasadame, holivudis zogierTi filmi kinoxelovnebis mniSvnelovani miRwevaa.
es daskvna:
(a) gamomdinareobs mxolod pirveli debulebidan
(b) gamomdinareobs mxolod meore debulebidan
(g) gamomdinareobs orive debulebidan erTad
(d) ar gamomdinareobs mocemuli debulebebidan
15
wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
adamiani didwilad aRqmis meSveobiT iRebs informacias gare sinamdvilis
Sesaxeb. garedan Semosul stimulebze adamianis saTanado reaqcia damokidebulia
sagnebisa Tu movlenebis zust aRqmaze. cvalebad da aramdgrad samyaroSi aRqma,
uwinares yovlisa ki, adamianis mxedvelobis sistema, emsaxureba mdgradobisa da
stabilurobis moTxovnilebis dakmayofilebas. miuxedavad amisa, aRqma ar aris
sagnis `sarkiseburi~, ucvleli da sruliad obieqturi asaxva. aRqmaze gavlenas
axdens aRmqmelis mdgomareoba da individualuri Taviseburebebi, aseve, garemo
pirobebi. swored amitom aRqmam SesaZlebelia adamians erTgvari siurprizi
mouwyos iluziebis saxiT.
gansakuTrebiT xSiria e. w. mxedvelobiTi iluziebi, romlebic mxedvelobis
sistemaSi informaciis gadamuSavebis zogierT SezRudvasa da cdomilebas
ukavSirdeba. specifikur garemoSi garkveuli obieqtebis aRqmisas adamiani arcTu
zustad afasebs obieqtebis zomas, formas, maTi moZraobis xasiaTs da a. S.
magaliTad, TeTri feris sagani, Cveulebriv, ufro didi gveCveneba, vidre amave
zomis muqi sagani. sagnis sididis gazomviT Cven SegviZlia aRqmis mcdaroba
gamovavlinoT, Tumca, rogorc wesi, ar SegviZlia amgvari `mcdari~ xatebis
`koreqtireba~. am SemTxvevaSi sagani uSualod aRiqmeba arasworad _ arasworia
sagnis suraTi da ara codna, ara azri sagnis Sesaxeb. amgvar iluziebs fizikuri
iluziebi ewodeba. maT iwvevs sagnis mocemulobis fizikuri pirobebi, magaliTad:
wyalSi CaSvebuli joxi gadatexilad aRiqmeba, risi mizezic wylis zedapirze
sinaTlis sxivebis gardatexaa.
arsebobs iseTi mxedvelobiTi iluziebi, romlebic ufro subieqturi,
fsiqikuri faqtorebiTaa ganpirobebuli. erTsa da imave movlenas adamiani
gansxvavebulad aRiqvams imis mixedviT, Tu rogoria misi gamocdileba am
movlenasTan dakavSirebiT, rogor aris is am momentSi ganwyobili. pirovnebis
Sinagani mdgomareobisa da misi warsuli gamocdilebis Sesatyvisad aRqmis
damaxinjeba xSirad iCens Tavs adamianis yoveldRiur cxovrebaSi. misi Tavidan
acileba SeuZlebelia. magaliTad, mZime sagnebis awevis Semdeg msubuqi sagani
ufro msubuqi gveCveneba, vidre is sinamdvileSia, da piriqiT. adamianis am
tendencias ewodeba percefciuli mzaobis, anu ganwyobis fenomeni.
magaliTad, ra simboloa warmodgenili naxatis centrSi _ aso-niSani
Tu ricxvi? Tu asoebisgan Sedgenil horizontalur rigs mivyvebiT,
centrSi aso B-s davinaxavT. mis aRsaqmelad Cven asoebis rigiT viqnebiT
Semzadebuli. magram Tu vertikalur rigs CamovyvebiT, aRmoCndeba, rom centrSi
ricxvi 13-ia, ris dasanaxadac ricxvebis rigma gangvawyo.
xSirad adamiani samyaros aRiqvams ara iseTad, rogoric is sinamdvileSia,
aramed rogoradac misi danaxva unda. is `eZebs~ obieqtis sasurvel formas, fers
Tu sxva niSans. amas aRqmis seleqciurobas (SerCeviTobas) uwodeben. aRqmis
seleqciuroba mkafiod vlindeba maSin, rodesac saqme exeba CvenTvis mniSvnelovan
movlenebs an obieqtebs. Tu adamians vetyviT, rom am wignSi misi gvaria, is
wignis gadafurcvlisas Tvalis erTi gadavlebiT aRmoaCens Tavis gvars mraval
sityvas Soris. amgvarad, iluzia erTgvari sakvlevi instrumentia _ daakvirdiT
Tqvens iluziebs da mets SeityobT sakuTari Tavis Sesaxeb.
16
35. aRqma ar warmoadgens ama Tu im sagnis `sarkisebur~ asaxvas, radgan:
(a) garemo, romelSic adamiani cxovrobs, aramdgradi da cvalebadia, Sesabamisad,
SeuZlebelia misi obieqturi xatis Seqmna
(b) adamianis aRqmaze gavlenas axdens subieqturi Tu obieqturi xasiaTis uamravi
faqtori
(g) adamianis mxedvelobis sistemaze moqmedebs garedan Semosuli uamravi stimuli
(d) adamiani nebismier informacias specifikur garemoSi da, Sesabamisad,
damaxinjebulad aRiqvams
36. CamoTvlilTagan romel movlenebs Sorisaa mizezSedegobrivi kavSiri?
(a) sagnis mocemulobis fizikuri pirobebi iwvevs mcdar aRqmas _ garkveuli
obieqtebis aRqmisas adamiani arcTu zustad afasebs maT zomas
(b) Cven SegviZlia aRqmis mcdaroba gamovavlinoT _ Cven ar SegviZlia `mcdari~
xatebis `koreqtireba~
(g) arasworia sagnis suraTi da ara codna sagnis Sesaxeb _ wyalSi CaSvebuli
joxi gadatexilad aRiqmeba
(d) iluziebi mxedvelobis sistemaSi informaciis gadamuSavebis zogierT
SezRudvas ukavSirdeba _ amgvar iluziebs fizikuri iluziebi ewodeba
37. qvemoT mocemulia ramdenime debuleba:
I. rogorc fizikuri, ise fsiqikuri bunebis iluziebis aRmocenebas erTi
ZiriTadi faqtori ganapirobebs _ adamianis warsuli gamocdileba
II. rogorc fizikuri, ise fsiqikuri bunebis iluziebi adamians misdauneburad
uCndeba
III. fizikuri da fsiqikuri bunebis iluziebis ZiriTadi mizezia is, rom gare
samyaro adamianis mier pasiurad ar aRiqmeba
mocemuli debulebebidan sworia:
(a) mxolod I
(b) mxolod II
(g) mxolod I da III
(d) mxolod II da III
17
38. qvemoT CamoTvlilTagan romeli iluziaa ganpirobebuli percefciuli mzaobiT?
(a) matareblis daZvrisas adamians eCveneba, rom moZraobs liandagis gaswvriv
mdgari xeebi da ara matarebeli, romliTac is mgzavrobs
(b) Tu cdispiri uyurebs sinaTlis laqas, romelic TandaTan farTovdeba, mas
moeCveneba, rom laqis zoma ki ar izrdeba, aramed laqa mas uaxlovdeba
(g) Tu cdispirs vTxovT, garkveuli sigrZis xazebi ramdenjerme gaavlos, Semdeg ki
maTze orjer ufro naklebi sigrZis xazebi daxazos, is mainc ufro grZel
xazebs gaavlebs
(d) damkvirvebels ufro didi zomisa eCveneba mTvare, rodesac is horizontzea,
vidre maSin, rodesac is zenitSia
39. qvemoT CamoTvlilTagan romeli faqtori ar aris ganxiluli teqstSi, rogorc iluziis gamomwvevi mizezi?
(a) sagnis fizikuri maxasiaTeblebi
(b) obieqtis cvalebadoba
(g) adamianis gamocdileba
(d) adamianis molodinebi
40. winadadeba, romliTac sruldeba teqsti, gulisxmobs, rom:
(a) iluziebis meSveobiT Cven ukeT vaxerxebT garemosTan Seguebas
(b) iluziebSi vlindeba Cveni gaucnobierebeli survilebi da molodinebi
(g) iluziebi Cvens Tavze dakvirvebis erTaderTi sando saSualebaa
(d) iluziebis gareSe Cven ver SevZlebT sakuTari Tavis Secnobas
21
maTematikuri nawili
testis maTematikur nawilze muSaobisas gaiTvaliswineT:
• naxazebi, romlebic erTvis zogierT davalebas, araa Sesrulebuli davalebis
pirobaSi miTiTebuli zomebis zusti dacviT. amitom monakveTebis sigrZis an sxva
sidideebis Sesaxeb daskvnis gamotanisas nu daeyrdnobiT naxazis zomebs. yuradReba
gaamaxvileT davalebis pirobaze;
• Tu naxazze mocemuli swori xazis Sesaxeb amocanis pirobaSi damatebiT araferia
naTqvami, maSin unda CaTvaloT, rom es swori xazi wrfea an misi nawili;
• testSi gamoyenebulia ricxvTa Caweris mxolod aTobiTi poziciuri sistema.
maTematikuri aRniSvnebi da formulebi:
1. nuli arc dadebiTia da arc uaryofiTi; 1 ar aris martivi ricxvi.
2. procenti: a ricxvis k% aris .
3. xarisxi: an = a · a · a · ...· a (n-jer)
mnmn aaa +=⋅
mnmn aaa −=:
mnmn aa ⋅=)(
4. proporcia: Tu , maSin ad = bc.
5. siCqare: dro
manZilisiCqare =
6. saSualo ariTmetikuli:
raodenoba monacemTa
jami monacemTasaSualo monacemTa =
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:
( ) 222 2 bababa ++=+
( ) 222 2 bababa +−=−
( )( ) 22 bababa −=−+ 9. naxazze kuTxe SeiZleba moniSnuli iyos kuTxis
gverdebs Soris Casmuli
patara rkaliT, marTi kuTxe
ki _ patara kvadratiT.
∠A aRniSnavs A kuTxis sidides.
10. paraleluri wrfeebi: ori paraleluri wrfis mesame
wrfiT gadakveTisas Siga jvaredina
kuTxeebi tolia: βα = .
11. samkuTxedi: • samkuTxedis kuTxeebis sidideTa jami
180°-is tolia; • piTagoras Teorema:
marTkuTxa samkuTxedis
hipotenuzis sigrZis
kvadrati kaTetebis sigrZeTa
kvadratebis jamis tolia:
AB2 = AC2 + BC2
• 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 L misi
radiusis mixedviT gamoiTvleba
formuliT: L = 2πr; π ricxvi, measedis sizustiT, 3,14-is tolia;
• r radiusiani wris farTobi gamoiTvleba formuliT: S = πr2.
14. marTkuTxa paralelepipedi: • marTkuTxa paralelepipedis
moculoba misi sigrZis, siganisa da
simaRlis namravlis tolia: V = abc; • kubis SemTxvevaSi: a = b = c.
22
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
41. (a) (b) (g) (d)
42.
iardi sigrZis erTeulia. davuSvaT, rom 1 iardi 90 metris tolia.
(a) (b) (g) (d)
43.
marTkuTxedis mcire gverdis
sigrZea x, didi gverdisa _ y. did gverdze mdebare K wertili marTkuTxedis A da B wveroebTan monakveTebiTaa SeerTebuli (ix. naxazi).
(a) (b) (g) (d)
911131517 +−+− 1112131415 +−+−
16 m/wT12 iardi/sT
AKB texilis sigrZe 4x
23
44.
daxlze awyvia sazamTro, nesvi, gogra da Talgami.
sazamTro da nesvi erTad 9,5 kg-s iwonis, xolo
sazamTro da Talgami _ 8,5 kg-s.
(a) (b) (g) (d)
45.
ramdenime Tanamamravlis namravli 5148-is tolia.
TiToeuli Tanamamravli araa naklebi 10-ze.
(a) (b) (g) (d)
46.
ori samkuTxedidan erTi maxvilkuTxaa, meore _
blagvkuTxa.
(a) (b) (g) (d)
Talgamisa da
gogris wona
gogrisa da nesvis
wona
4TanamamravlTa raodenoba
blagvkuTxa
samkuTxedis umciresi
kuTxis sidide
maxvilkuTxa
samkuTxedis umciresi
kuTxis sidide
24
amocanebi
47. pirvel gaCerebaze avtobusidan 10 mgzavri Cavida, 8 ki _ amovida. meore
gaCerebaze Cavida 7 mgzavri, amovida _ 3. mesame gaCerebaze Cavida 1 mgzavri, amovida _ 5. amis Semdeg avtobusSi 13 mgzavri aRmoCnda. ramdeni mgzavri yofila avtobusSi Tavdapirvelad?
(a) 12 (b) 15 (g) 18 (d) 21 (e) 24
48. pirvel kedelze xuTjer meti suraTi kidia, vidre meoreze, xolo mesameze _ samjer naklebi, vidre pirvel da meore kedlebze erTad. ramdenjer naklebi
suraTi kidia meore kedelze mesamesTan SedarebiT?
(a) 6-jer (b) 5-jer (g) 4-jer (d) 3-jer (e) 2-jer
49. oTxkuTxa piramidas 5 waxnagi da 8 wibo aqvs. ramdeni waxnagi aqvs piramidas, romelsac 18 wibo aqvs?
(a) 8 (b) 9 (g) 10 (d) 12 (e) 13
25
50. vanos mxolod 1-TeTriani, 2-TeTriani, 5-TeTriani, 10-TeTriani da 20-TeTriani monetebi aqvs. man Tavis 6 megobars TiTo moneta aCuqa. aRmoCnda, rom or
maTgans erTnairi monetebi Sexvda, xolo danarCenebs _ sxvadasxvanairi.
CamoTvlilTagan romlis toli SeiZleba iyos vanos mier gaCuqebuli Tanxis
raodenoba?
(a) 41 TeTri (b) 43 TeTri (g) 45 TeTri (d) 47 TeTri (e) 49 TeTri
51. =30102,0
(a) 1000002
10001
103 ++
(b) 1000002
10001
1003 ++
(g) 10002
1001
103 ++
(d) 10002
10001
103 ++
(e) 100002
10001
103 ++
26
monacemTa analizi
diagramaze mocemulia, qalTa da mamakacTa ramdeni procenti iyo dasaqmebuli
saqarTveloSi 2005 wels (asakobrivi jgufebis mixedviT).
cxrilSi ki mocemulia, Tu ramdeni aTasi qali da mamakaci iyo dasaqmebuli
saqarTveloSi 2003-2005 wlebSi (asakobrivi jgufebis mixedviT).
2003 2004 2005 qali mamakaci qali mamakaci qali mamakaci
15-24 wlis 59,7 96,6 49,4 81,8 50,7 89,5 25-34 wlis 140,5 190,4 129,7 174,0 135,0 160,0 35-49 wlis 300,2 320,4 314,8 327,2 286,6 313,8 50-59 wlis 148,9 146,7 156,9 150,7 165,4 156,0
60 an meti wlis 207,7 203,3 210,6 192,8 204,2 188,8
diagramisa da cxrilis mixedviT upasuxeT Semdeg 4 SekiTxvas:
52. romel wels da romel asakobriv jgufSi iyo dasaqmebul qalTa raodenoba yvelaze meti?
(a) 2003 wels, 25-34 wlis asakobriv jgufSi (b) 2003 wels, 50-59 wlis asakobriv jgufSi (g) 2004 wels, 15-24 wlis asakobriv jgufSi (d) 2004 wels, 35-49 wlis asakobriv jgufSi (e) 2005 wels, 60 an meti wlis asakobriv jgufSi
53. romeli asakobrivi jgufis SemTxvevaSia 2005 wels dasaqmebul mamakacTa da qalTa procentul maCveneblebs Soris sxvaoba yvelaze didi?
(a) 15-24 wlis (b) 25-34 wlis (g) 35-49 wlis (d) 50-59 wlis (e) 60 an meti wlis
27
54. 25-34 wlis ramdeni qali cxovrobda saqarTveloSi 2005 wels?
(a) 240 aTasi (b) 260 aTasi (g) 280 aTasi (d) 300 aTasi (e) 320 aTasi
55. romeli asakobrivi jgufis SemTxvevaSi ar iyo dasaqmebuli 2005 wels mamakacTa ara umetes 50%-isa, xolo qalTa _ aranakleb 60%-isa?
(a) 15-24 wlis (b) 25-34 wlis (g) 35-49 wlis (d) 50-59 wlis (e) 60 an meti wlis
amocanebi
56. da niSnebiT cifrebia aRniSnuli. risi tolia sxvaoba − , Tuki
78 + 134 = 9 1 ?
(a) 2 (b) 3 (g) 4 (d) 5 (e) 6
57. m da n iseTi naturaluri ricxvebia, rom nm 23 =+ . CamoTvlilTagan
romlis toli ar SeiZleba iyos m ?
(a) 61 (b) 31 (g) 13 (d) 5
(e) 1
28
58. ABCD marTkuTxedi dayofilia tol
kvadratebad, romelTagan zogierTi araa
gamuqebuli (ix. naxazi). minimum ramdeni kvadrati
unda gavamuqoT kidev, rom miRebuli gaumuqebeli
figura iyos simetriuli AD da BC gverdebis
Suawertilebze gavlebuli RerZis mimarT?
(a) 1 (b) 2 (g) 3 (d) 4 (e) 5
59. ramdenjer gadiddeba dadebiTi ricxvi, Tu mas amave ricxvis 250%-s mivumatebT?
(a) 1,5-jer (b) 2-jer (g) 2,5-jer (d) 3-jer (e) 3,5-jer
60. erTmaneTis momdevno 8 naturaluri ricxvisgan Sedgenili mimdevrobis
pirveli 4 wevris jami 38-is tolia. risi tolia am mimdevrobis yvela wevris jami? (a) 76
(b) 80 (g) 84 (d) 88 (e) 92
29
raodenobrivi Sedareba
SeadareT erTmaneTs A da B svetebis ujrebSi mocemuli raodenobebi.
Tu A svetis ujraSi mocemuli raodenoba metia B svetis Sesabamis ujraSi mocemul raodenobaze, airCieT (a);
Tu B svetis ujraSi mocemuli raodenoba metia A svetis Sesabamis ujraSi mocemul raodenobaze, airCieT (b);
Tu ujrebSi mocemuli raodenobebi tolia, airCieT (g);
Tu mocemuli informacia sakmarisi araa imis dasadgenad, romeli raodenobaa
meti, airCieT (d).
A B
61.
maRaziaSi feradi furclebi iyideba. 60-furcliani Sekvra 5 lari Rirs, 40-furcliani _ 4 lari, xolo calobiT TiTo feradi furceli _ 15 TeTri. giam sul 90 feradi furceli SeiZina.
(a) (b) (g) (d)
62.
nebismieri k naturaluri ricxvisaTvis *k aRniSnavs
1-dan k-s CaTvliT yvela naturaluri ricxvis jams. magaliTad, 6321*3 =++= .
(a) (b) (g) (d)
63.
kvadratidan, romlis gverdis sigrZea
4 sm, amoWrilia wre, romlis radiusis sigrZea 1 sm; wridan, romlis radiusis sigrZea
3 sm, amoWrilia kvadrati, romlis gverdis sigrZea 4 sm.
(a) (b) (g) (d)
gias mier gadaxdili
Tanxis raodenoba 9 lari
( )*4+k kk 4*4* ++
kvadratis darCenili
nawilis farTobi
wris darCenili
nawilis farTobi
30
64.
akvariumSi mxolod 10 sm-dan 12 sm-mde sigrZis
wiTeli da 18 sm-dan 20 sm-mde sigrZis vercxlisferi Tevzebia. vercxlisferi Tevzebis raodenoba 2-jer aRemateba wiTeli Tevzebis raodenobas.
(a) (b) (g) (d)
65.
CogburTelma mogebiT daasrula wlis I naxevarSi
gamarTuli Sexvedrebis 60% da wlis II naxevarSi
gamarTuli Sexvedrebis 30%.
(a) (b) (g) (d)
amocanebi
66. Tu m naturaluri ricxvia, maSin ( )12 +mm :
(a) aucileblad luwia
(b) aucileblad kentia
(g) luwia mxolod maSin, roca m luwia (d) kentia mxolod maSin, roca m luwia (e) kentia, roca m luwia
67. ABCD oTxkuTxedis A da C wertilebi y RerZze mdebareobs, xolo B da D wertilebis koordinatebia, Sesabamisad,
( )4,5;9− da ( )3;6 − (ix. naxazi).
risi tolia ABC samkuTxedis farTobis Sefardeba ACD samkuTxedis farTobTan?
(a) 1,2 (b) 1,5 (g) 1,8 (d) 2 (e) 2,5
akvariumSi Tevzebis
saSualo sigrZe 15 sm
50%CogburTelis mier mogebuli
Sexvedrebis procentuli wili
mTeli wlis ganmavlobaSi
31
68. Tu ( )( ) 0921 2 =−+ yy , maSin =y4
(a) 18 (b) 14 (g) 10 (d) 18− (e) 14−
69. wriul diagramaze warmodgenilia monacemebi Rvinis qarxanaSi dawuruli sxvadasxva jiSis
yurZnis (colikauris, cicqas, kraxunas da
ojaleSis) raodenobaTa Sesaxeb.
ramdeni tona kraxuna dauwuravT qarxanaSi, Tu
cnobilia, rom am qarxanaSi 180 tona ojaleSi dawures?
(a) 100 (b) 110 (g) 120 (d) 130 (e) 140
70. wyliT savse auzis dacla erTi miliT SesaZlebelia 3 saaTSi, meoriT _ 4 saaTSi, xolo mesamiT _ 5 saaTSi. auzis maqsimum ra nawili iqneba wyliT Sevsebuli 1 saaTis Semdeg, Tu savse auzis dasaclelad am sami milidan mxolod ors gaxsnian?
(a) 2011
(b) 125
(g) 157
(d) 158
(e) 107
71. 20 decimetri sigrZis Zeli wiTeli xazebiT dayves 4 tol nawilad, xolo lurji xazebiT _ 5 tol nawilad. Semdeg dayofis yvela xazze Zeli gadaxerxes. gaxerxvis Sedegad miiReba Zelis:
(a) 1 dm, 2 dm, 4 dm da 5 dm sigrZis naWrebi (b) 1 dm, 2 dm, 3 dm da 4 dm sigrZis naWrebi (g) mxolod 4 dm da 5 dm sigrZis naWrebi (d) mxolod 1 dm da 4 dm sigrZis naWrebi (e) mxolod 2 dm, 3 dm da 4 dm sigrZis naWrebi
32
monacemTa sakmarisoba
72. ABCD marTkuTxedi dayofilia ABMN marTkuTxedad da MCDN kvadratad.
mocemulia Semdegi ori piroba:
I. ABCD marTkuTxedis perimetria 56 sm. II. MCDN kvadratis perimetria 40 sm.
imis gasarkvevad, Tu risi tolia ABMN marTkuTxedis farTobi:
(a) I piroba sakmarisia, II ki _ ara
(b) II piroba sakmarisia, I ki _ ara
(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi
(d) sakmarisia cal-calke rogorc I, aseve II piroba
(e) mocemuli pirobebi araa sakmarisi
73. ianvris ganmavlobaSi benzini 1 lari da 80 TeTri Rirda. TebervalSi
benzini gaZvirda, martSi ki isev gaiafda da imdenive Rirda, rac _ ianvarSi.
mocemulia Semdegi ori piroba:
I. TebervalSi benzini ianvarTan SedarebiT 20 TeTriT gaZvirda. II. martSi benzini TebervalTan SedarebiT 10%-iT gaiafda.
imis gasarkvevad, Tu ramdeni procentiT gaZvirda benzini TebervalSi
ianvarTan SedarebiT:
(a) I piroba sakmarisia, II ki _ ara
(b) II piroba sakmarisia, I ki _ ara
(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi
(d) sakmarisia cal-calke rogorc I, aseve II piroba
(e) mocemuli pirobebi araa sakmarisi
33
74. mTargmnelTa biuroSi sul 20 TanamSromeli muSaobs.
mocemulia Semdegi ori piroba:
I. inglisuri enis mcodne TanamSromelTa raodenoba 8-is tolia. II. germanuli enis mcodne TanamSromelTa raodenoba 10-is tolia.
imis gasarkvevad, Tu risi tolia im TanamSromelTa raodenoba, romlebmac
inglisuri enac ician da germanuli enac:
(a) I piroba sakmarisia, II ki _ ara
(b) II piroba sakmarisia, I ki _ ara
(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi
(d) sakmarisia cal-calke rogorc I, aseve II piroba
(e) mocemuli pirobebi araa sakmarisi
75. x da y erTmaneTisgan gansxvavebuli iseTi ricxvebia, rom 0>xy .
mocemulia Semdegi ori piroba:
I. 0<+ yx .
II. 0<− yx .
imis gasarkvevad, uaryofiTia Tu ara ricxvi x:
(a) I piroba sakmarisia, II ki _ ara
(b) II piroba sakmarisia, I ki _ ara
(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi
(d) sakmarisia cal-calke rogorc I, aseve II piroba
(e) mocemuli pirobebi araa sakmarisi
34
amocanebi
76. marTkuTxa paralelepipedi, romlis siganea 10 sm, xolo simaRle _ 9 sm, dayofilia 6 tol marTkuTxa paralelepipedad (ix. naxazi). risi tolia dayofis
Sedegad miRebuli TiToeuli marTkuTxa
paralelepipedis moculoba? (a) 90 sm3
(b) 110 sm3
(g) 120 sm3
(d) 150 sm3
(e) 180 sm3 77. m da n martivi ricxvebia. CamoTvlilTagan romlis toli ar SeiZleba iyos
nm ⋅ ?
(a) 35 (b) 28 (g) 22 (d) 14 (e) 10
78. kolofSi mxolod wiTeli da TeTri feris burTulebi awyvia. wiTeli
burTulebis raodenoba a-s tolia, xolo TeTri burTulebisa _ b-si. nikam
kolofidan amoiRo 4 wiTeli da 2 TeTri burTula. risi tolia imis albaToba, rom amis Semdeg nikas mier kolofidan amoRebuli kidev erTi burTula TeTri
feris iqneba?
(a) ab
(b) bab+
(g) 62−+
−ba
b
(d) 22−+
−ba
b
(e) 42
−−
ab
35
79. yoveli kvadrati misi gadamkveTi wrfeebiT
SeiZleba daiyos tol marTkuTxedebad. magaliTad,
ABCD kvadrati misi gadamkveTi 3 wrfiT
dayofilia 6 tol marTkuTxedad (ix. naxazi). kvadrati misi gadamkveTi 10 wrfiT dayofilia
tol marTkuTxedebad. CamoTvlilTagan romlis
toli SeiZleba iyos dayofis Sedegad miRebuli
marTkuTxedebis raodenoba?
(a) 22 (b) 25 (g) 28 (d) 30 (e) 35
80. eqskursiaze moswavleebi ori avtobusiT gaemgzavrnen. pirvel avtobusSi
myofi moswavleebis raodenoba meore avtobusSi myof moswavleTa raodenobis
naxevari iyo. mas Semdeg, rac pirveli avtobusidan meoreSi 6 moswavle gadavida, pirvel avtobusSi moswavleTa raodenoba meore avtobusSi myofi moswavleebis
raodenobis mesamedi gaxda. sul ramdeni moswavle gamgzavrebula eqskursiaze?
(a) 60 (b) 63 (g) 69 (d) 72 (e) 75
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