2

verbaluri nawili analogiebi

am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva (sawyisi

wyvili), romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. daadgineT, ra

saxisaa es mimarTeba.

savaraudo pasuxTa yovel variantSi mocemulia, aseve, mniSvnelobiT

urTierTdakavSirebuli sityvebis wyvili. airCieT maTgan is wyvili, romelSic

sityvaTa mniSvnelobebs Soris mimarTeba sawyis wyvilSi arsebuli mimarTebis

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

6

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

7

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.

8

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

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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

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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

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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

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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