zogadi unarebis testizogadiunarebis testi

testi Sedgeba ori _ da _ nawilisagan.

TiToeuli nawili 50 davalebas Seicavs. yovel davalebas axlavs oTxi

an xuTi savaraudo pasuxi, romelTagan mxolod erTia swori.

yuradRebiT waikiTxeT davalebaTa instruqciebi, kargad gaiazreT,

ra mogeTxovebaT TiToeul davalebaSi, da Semdeg airCieT pasuxi.

drois amowurvis Sesaxeb gacnobebT meTvalyure.

Tu ar gaqvT romelime davalebis pasuxi, dros nu dakargavT da

gadadiT Semdeg davalebaze.

Canawerebis an naxazebisaTvis gamoiyeneT mxolod da mxolod testis

furclebze arsebuli carieli adgilebi.

verbaluri maTematikuri

arCeuli pasuxi aucileblad moniSneT pasuxebis furcelze,

romelic axlavs tests (Sesabamisi instruqcia ixileT pasuxebis

furcelze).

testis furclebze moniSnuli pasuxebi ar Semowmdeba. zogadi

unarebis testirebis Sedegi dadgindeba mxolod da mxolod pasuxebis

furclis safuZvelze.

testis TiToeul nawilze samuSaod geZlevaT 1 saaTi da 30 wuTi.

Tu gaTvaliswinebulze meti droiT SeyovndebiT testis ama Tu im

nawilze, Tqveni naSromi ar Semowmdeba.

instruqcia

gisurvebT warmatebas !

instruqcia



furcelze).



furclis safuZvelze.





zogadi unarebis testizogadi unarebis testi

I

2

verbaluri nawili

analogiebi

am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva,

romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. daadgineT, ra

saxisaa es mimarTeba.

savaraudo pasuxTa yovel variantSi aseve mocemulia mniSvnelobiT

urTierTdakavSirebuli sityvebis wyvili. airCieT maTgan is wyvili, romelSic

sityvaTa mniSvnelobebs Soris mimarTeba gamuqebul sityvaTa urTierTmimarTebis

msgavsia (analogiuria). pasuxis arCevisas gaiTvaliswineT wyvilebSi sityvaTa

Tanmimdevroba.

magaliTad: kenWi : qva

(a) velosipedi : manqana

(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi

swori pasuxia (b), radgan mimarTeba _ "biliki aris momcro gza" _ msgavsia mimarTebisa _ "kenWi aris momcro qva".

1. cxvari : batkani

(a) Wuki : wiwila

(b) ZaRli : nagazi

(g) rema : kvici (d) vefxvi : bokveri

2. gaTamamda : morcxvi

(a) gaisarja : mSromeli

(b) gamoaSkaravda : cru

(g) ganawyenda : gulnatkeni

(d) gamococxlda : zanti

3. leqsi : krebuli

(a) girCa : naZvi

(b) jejili : yana

(g) yvavili : Taiguli

(d) atami : baRi

4. kerZi : momzadeba

(a) informacia : gavrceleba

(b) zRapari : SeTxzva

(g) tradicia : SenarCuneba

(d) lxini : gamaspinZleba

3

5. xe : tye

(a) ujra : magida

(b) wigni : biblioTeka

(g) xorbali : wisqvili

(d) ekali : vardi

6. mxatvari : funji

(a) mzareuli : TefSi

(b) mwerali : wigni

(g) durgali : CaquCi

(d) mepure : Tone

7. saxelmwifo : sazRvari

(a) okeane : napiri

(b) konstitucia : himni

(g) dedamiwa : ca

(d) globusi : ruka

8. qaRaldi : daqucmaceba

(a) liToni : gadnoba

(b) SeSa : gapoba

(g) brinji : dabneva

(d) mina : damsxvreva

4

winadadebis Sevseba

am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa

gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiTaa aRniSnuli. erTi

xazi zogjer erT sityvas gulisxmobs, zogjer ki _ ramdenimes.

savaraudo pasuxTa yovel variantSi mocemulia sityvaTa jgufi, romlis

nawilebi erTmaneTisgan daxrili xazebiTaa (/) gamijnuli. airCieT pasuxis is

varianti, romlis TiToeuli nawilis Tanmimdevrulad Casma Sesabamis

gamotovebul adgilebSi azrobrivad gamarTul winadadebas mogvcems.

9. ufrosklaselebma gamravlebis cxrili _____ , miuxedavad amisa angariSis dros xandaxan _____ .

(a) cudad ar ician \ Secdomas ar uSveben

(b) cudad ician \ Secdomas uSveben

(g) kargad ician \ Secdomas ar uSveben

(d) kargad ician \ Secdomas uSveben

10. sadReisod egvipturi damwerloba _____ . samagierod, maias tomis damwerloba _____ , vinaidan misi _____ yvela cda _____ .

(a) gaSifrulia / srulad aris amokiTxuli / Seswavlis / warumatebeli aRmoCnda

(b) srulad aris Seswavlili / gamocanad rCeba / gaSifvris / marcxiT damTavrda

(g) jer kidev ar aris Seswavlili / gauSifravia / amokiTxvis / warmatebiT

dasrulda

(d) gauSifravia / gamoucnobia / wakiTxvis / nayofieri aRmoCnda

11. im dros gazeTebi sul ufro _____ , vinaidan _____ Sinaarsis statiebs aqveynebdnen.

(a) metad gansxvavdebodnen urTierTisgan / analogiuri

(b) naklebad gansxvavdebodnen erTmaneTisgan / erTmaneTis sapirispiro

(g) metad emsgavsebodnen erTmaneTs / standartuli

(d) emsgavsebodnen urTierTs / erTmaneTisagan gansxvavebuli

5

12. avtori _____ , ama Tu im SexedulebisaTvis _____ , raTa mkiTxveli _____ , avtori am hopoTezis momxrea, Tu misi _____ .

(a) cdilobda / upiratesoba ar mieniWebina / ver mimxvdariyo / mowinaaRmdege

(b) miznad ar isaxavda / upiratesoba mieniWebina / garkveuliyo / mimdevari

(g) ar cdilobda / upiratesoba mieniWebina / ver mimxvdariyo / gulSematkivari

(d) miznad isaxavda / upiratesoba ar mieniWebina / darwmunebuliyo /

uarmyofeli

13. mudam unda gvaxsovdes, rom _____ Cveni saTqmelis mitana xalxTan _____ da, ufro metad ki, _____ , radgan kiTxvis dros glexsa da muSas ucxo

sityvaTa leqsikoni ar uWiravs xelSi, da mgoni, inteligentic _____ am wignSi.

(a) SeuZlebelia / damaxinjebuli sintaqsiT / advilad gasagebi leqsikiT / ar

ixedeba

(b) SesaZlebelia /gamarTuli sintaqsiT / Warbad datvirTuli ucxo sityvebiT /

iSviaTad ixedeba

(g) SeuZlebelia / damaxinjebuli sintaqsiT / Warbad datvirTuli ucxo sityvebiT /

iSviaTad ixedeba

(d) SesaZlebelia / gamarTuli sintaqsiT / advilad gasagebi leqsikiT / xSirad

ixedeba

6

logika

am saxis davalebebi gansxvavdeba erTmaneTisgan winaswari monacemebisa da

gamosatani daskvnebis TvalsazrisiT. amitom gansakuTrebuli yuradReba miaqcieT

SekiTxvas, romelic axlavs TiToeul davalebas da mocemuli variantebidan

airCieT Sesabamisi pasuxi.

zogierT SekiTxvaze pasuxis gacemas gagiadvilebT monacemebis gamosaxva

naxazis formiT.

14. cnobili zRapris _ "sami goWis" gmirebis _ nafnafis, nifnifisa da nufnufis saxlebi mwkrivSia ganlagebuli. erT-erTs aqvs Calis saxli, meores _ wnelis,

mesames ki – aguris. nufnufis saxli SuaSi dgas. mis marcxniv dgas aguris saxli,

xolo nafnafis saxli wnelisaa.

ra masalisaa nufnufis saxli?

(a) wnelis an aguris

(b) wnelis

(g) Calis

(d) aguris

15. anam gadawyvita, ardadegebze waekiTxa ori wigni (es wignebi mas ukve SerCeuli hqonda) da erTxel mainc wasuliyo TeatrSi an koncertze.

qvemoT CamoTvlilTagan romel SemTxvevaSi ar Seasrula man Tavisi

gadawyvetileba?

(a) iyo simfoniur koncertze da waikiTxa orive wigni

(b) iyo Tojinebis TeatrSi da waikiTxa orive wigni

(g) iyo TeatrSic da koncertzec, magram ver waikiTxa orive wigni

(d) iyo TeatrSic, koncertzec da waikiTxa orive wigni

16. A qalaqSi mcxovreb musikis moyvarulTa saSualo asakis dasadgenad am qalaqis erT-erT musikalur maRaziaSi audiokasetebis myidvelebs akvirdebodnen.

aRmoCnda, rom maRaziaSi ZiriTadad Semodiodnen axalgazrda qalbatonebi

bavSvebTan erTad. Sesabamisad, damkvirveblebma ivaraudes, rom:

A qalaqSi musikas ZiriTadad axalgazrda qalbatonebi usmenen.

qvemoT CamoTvlilTagan romeli faqti ayenebs eWvqveS am varauds?

(a) A qalaqSi mcxovreb axalgazrda qalbatonebs ZiriTadad musikaluri ganaTleba aqvT miRebuli

(b) A qalaqSi bevri sxva musikaluri maRaziac aris, es maRazia ki sabavSvo baRis gverdiT mdebareobs

(g) A qalaqSi kidev ramdenime musikaluri maRaziaa, magram isini gamokvlevis dros droebiT daketili iyo

(d) A qalaqSi mcxovrebi axalgazrda qalbatonebi gansakuTrebul mniSvnelobas aniWeben Svilebis musikalur aRzrdas

7

17. davuSvaT, rom: • arc erTi Zunwi ar aris qvelmoqmedi

• zogierTi Zunwi Zalian mdidaria

qvemoT CamoTvlilTagan romeli gamomdinareobs am debulebebidan aucileblad?

(a) arc erTi Zalian mdidari ar aris qvelmoqmedi

(b) zogierTi Zalian mdidari ar aris qvelmoqmedi

(g) zogierTi Zalian mdidari ar aris Zunwi

(d) yvela qvelmoqmedi aris mdidari

18. nini, TaTa, levani da rezo megobrebi arian. TiToeulma maTganma varskvlavi dauxata danarCeni samidan erT-erTs.

cnobilia, rom:

• rezom varskvlavi dauxata ninis

• levans ori varskvlavi dauxates

qvemoT CamoTvlilTagan romeli SemTxveva ar SeiZleboda momxdariyo?

(a) TaTam varskvlavi dauxata levans

(b) ninim varskvlavi dauxata levans

(g) ninim varskvlavi dauxata TaTas

(d) levanma varskvlavi dauxata rezos

8

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis

mixedviT.

antikur samyaroSi ori "iberia" iyo cnobili: erTi dasavleTisa _ pireneis naxevarkunZulze, xolo meore _ kavkasiisa, dRevandel aRmosavleT saqarTvelos

miwa-wyalze. am ukanasknelis moxseniebisas berZeni mwerlebi daumatebdnen xolme:

"aRmosavleT iberia", "iberTa aRmosavleli tomi", "aziis iberni" da amiT

ganasxvavebdnen maT baskebis, imave espaneTis iberTagan, romelTa mimarT ityodnen:

"evropeli iberni", "dasavleTis iberia". II saukunis berZeni mwerali apiane wers: "iberebs, romlebic aziaSi arian,

zogi evropeli iberebis winaprebad miiCnevs, zogi _ evropelTa moaxalSeneebad,

sxvebi ki mxolod Tanamosaxeleebad, radgan maT arc zne aqvT arafriT msgavsi da

arc ena". sainteresoa, rom azri espaneTis iberebTan qarTvelTa naTesaobis Sesaxeb Sua

saukuneebSi qarTvelTa Sorisac iyo gavrcelebuli. jer kidev X saukunis

dasasruls ioane mTawmindeli (aToneli) apirebda Tavis mowafeebTan erTad

espaneTSi gamgzavrebas, rom gascnoboda "dasavleTis qarTvelTa cxovrebas". X-XI saukuneebSi berZnulidan qarTul enaze Targmnil TxzulebebSi ki xSirad gvxdeba

gamoTqma _ "espaneTis qarTvelni". arsebobs azri qarTveluri da baskuri enebis SesaZlo genetikuri kavSiris

(naTesaobis) Sesaxeb. magram es genetikuri kavSiri, romelic enebs Soris

arsebuli regularuli fonetikuri Sesatyvisobebis safuZvelze unda dadgindes,

jer damtkicebuli araa. aseTi kavSiri, Tuki is marTlac arsebobda, Zalian

Soreul xanaSi unda vivaraudoT. Zalze saeWvoa, rom dRes lingvisturma

mecnierebam, Tundac arqeologiuri monacemebis gaTvaliswinebiT, SeZlos iseTi

fuZeenis rekonstruqcia, romlisganac unda warmoqmniliyo qarTuli da baskuri

enebi.

ZvelqarTul saistorio mwerlobaSi saxelwodebani "iberia" da "iberni" ar gvxvdeba. maT nacvlad ixmareba "qarTli". terminebi "iberia" da "iberebi" ki

mxolod berZnul-romaulsa da bizantiur wyaroebSi dasturdeba. am

saxelwodebis ("iberia") etimologia* naTeli ar aris da mis Sesaxeb azrTa

sxvadasxvaobaa.

erT-erTi mosazrebis Tanaxmad, sityva "iberia" modis semituri Ziridan "ybr", "hbr", rac niSnavs "imiers", "mTis gadaRma mxares" Tu "mTis iqiT mcxovrebs". kolxeTSi Semosuli Zveli berZenisa Tu romaelisTvis qarTli, marTlac, mTis

gadaRma mxarea. ase rom, semituri Ziridan momdinare berZnul-romaul saxels _

"iberias" da mis qarTul Sesatyviss _ "qarTls" (Tavdapirvelad "qarTli" erqva dRevandeli mcxeTis pirdapir md. mtkvris marjvena napirze mdebare borcvs)

ufro politikuri an geografiuli mniSvneloba unda hqonoda, vidre eTnikuri.

* etimologia _ (aq) sityvis warmomavloba, Sedgeniloba da Tavdapirveli

mniSvneloba

9

19. ras uwodebdnen Zveli berZeni mwerlebi pireneis naxevarkunZulze mcxovrebT?

(a) aziis iberebs

(b) dasavleTis iberebs

(g) aRmosavleTis iberebs

(d) kavkasiis iberebs

20. qvemoT CamoTvlilTagan romel mosazrebas ar Seicavs Zveli berZeni mwerlis _ apianes cnoba kavkasiis iberTa Sesaxeb?

(a) aziis iberni evropeli iberebis winaprebi arian

(b) pireneis iberni aRmosavleTis iberTa winaprebi arian

(g) aRmosavleTisa da dasavleTis iberebs mxolod saxeli aqvT saerTo, ena da

Tvisebebi ki _ sxvadasxva

(d) kavkasiis iberebi espaneTis iberTa moaxalSeneebi arian

21. romeli faqti migvaniSnebs imas, rom Sua saukuneebis qarTvelni

interesdebodnen dasavleTisa da aRmosavleTis iberTa naTesaobis sakiTxiT?

(a) qarTulidan berZnulad naTargmn TxzulebebSi xSirad gvxvdeba gamoTqma _

"espaneTis qarTvelni" (b) berZnulidan qarTul enaze iTargmneboda "espaneTis qarTvelTa" Txzulebebi (g) apianes surda pireneis naxevarkunZulze gamgzavreba "dasavleTis qarTvelTa

cxovrebis" gasacnobad (d) Zvel qarTvel moRvaweebs surdaT espaneTSi gamgzavreba "dasavleTis

qarTvelTa cxovrebis" gasacnobad

22. romeli winadadeba gamoxatavs amomwuravad meoTxe abzacis ZiriTad azrs?

(a) qarTvelur da baskur enebs Soris genetikuri kavSiri regularuli

fonetikuri Sesatyvisobebis safuZvelze ar dasturdeba, Sesabamisad,

yuradRebiT unda SeviswavloT arqeologiuri monacemebi

(b) qarTveluri da baskuri enebis SesaZlo genetikuri kavSiris Sesaxeb

arqeologiuri monacemebi arasakmarisia am kavSiris dasadastureblad, saWiroa

enaTa fonetikuri Sesatyvisobis kvleva

(g) Tanamedrove qarTveluri da baskuri enebis arc ukve ganxorcielebuli kvleva

da arc kvlevis samomavlo perspeqtivebi ar gvaZlevs maT Soris genetikuri

kavSiris dadasturebis imeds

(d) qarTveluri da baskuri enebis genetikuri kavSiris dadastureba SesaZlebelia

Tanamedrove enaTmecnieruli da arqeologiuri kvlevebis Sedegebis Sejerebis

safuZvelze

10

23. "iberiis" semituri etimologia aseTi varaudis safuZvels gvaZlevs:

(a) "iberiis" semituri mniSvneloba emTxveva misi qarTuli Sesatyvisis _ "qarTlis"_ etimologias

(b) "iberia" saqarTvelosa da espaneTSi eTnosis saxelwodebaa (g) Tavdapirvelad "iberia" geografiuli an politikuri mniSvnelobis saxeli iyo (d) mtkvarTan mdebare borcvis saxeli "qarTli" genetikurad ukavSirdeba semitur

"iberias"

24. romeli debulebaa marTebuli teqstis mixedviT?

(a) SesaZloa kavkasiisa da espaneTis iberebi berZnebs enaTesavebodnen

(b) kvlevis Sedegad dadginda, rom iberebi semituri warmomavlobis xalxia, erTi

Sto espaneTSi dasaxlebula, meore _ qarTlSi

(g) kvlevis Sedegad dadginda espaneTis iberebisa da aRmosavleT saqarTvelos

mcxovrebTa eTnikuri warmomavloba

(d) SeiZleba visaubroT espaneTisa da kavkasiis iberTa ara eTnikur, aramed

mxolod saxelwodebis saerTo warmomavlobaze

25. ra aris mocemuli teqstis ZiriTadi mizani?

(a) dasavleTisa da aRmosavleTis iberTa Soris SesaZlo naTesaobis sakiTxis

mimoxilva

(b) qarTveluri da baskuri enebis SesaZlo genetikuri kavSiris dadgena

(g) berZen mweralTa mosazrebebis gacnoba dasavleTisa da aRmosavleTis iberTa

naTesaobis Sesaxeb

(d) ZvelqarTuli saistorio mwerlobis mixedviT terminebis _ "iberia" da "qarTli" _ etimologiis Seswavla

11

analogiebi








Tanmimdevroba.



(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi


26. niavi : grigali

(a) Rame : wyvdiadi

(b) elva : quxili

(g) nakaduli : niaRvari

(d) gvalva : warRvna

27. klaviSi : roiali

(a) asfalti : gza

(b) layuCi : Tevzi

(g) Rili : tansacmeli

(d) bolqvi : mcenare

28. dardi : gaqarveba

(a) Rirseba : Selaxva

(b) ndoba : damsaxureba

(g) Ralati : patieba

(d) Secdoma : gamosworeba

29. reJisori : Teatris scena

(a) msaji : ringi

(b) mwvrTneli : fexburTis moedani

(g) jambazi : cirkis arena

(d) mayurebeli : darbazi

12

30. omi : zavi

(a) muSaoba : Svebuleba

(b) naTeba : bindi

(g) siZulvili : siyvaruli

(d) kamaTi : ganxeTqileba

31. abreSumi : qsovili

(a) sazrdo : sakvebi

(b) yda : wigni

(g) ludi : sasmeli

(d) taxti : sawoli

32. xnavs : xnuli

(a) rwyavs : sarwyavi

(b) texs : natexi

(g) rgavs : nergi

(d) tivtivebs : tivi

33. Wreli : mxedveloba

(a) gamarTuli : metyveleba

(b) mxiaruli : grZnoba

(g) maxvili : smena

(d) surnelovani : ynosva

13

winadadebis Sevseba








34. _____ , visi azriTac, Sav zRvaSi Tevzis raodenobis Semcireba mxolod aqtiuri TevzWeris damRupvel zegavlenas _____ . Sav zRvaSi garemos

dabinZurebis Sedegad _____ im Tevzebis ricxvic, romlebic TevzWeris obieqts

ar warmoadgens.

(a) sworad msjelobs is / mowmobs / mcirdeba

(b) cdeba is / ar mowmobs / izrdeba

(g) sworad msjelobs is / ar mowmobs / izrdeba

(d) cdeba is / mowmobs / mcirdeba

35. xSirad vcdilobT, _____ CvenTvis nacnobi meTodebiT gavumklavdeT. es meTodebi _____ , radgan _____ gansxvavdeba _____ .

(a) sirTuleebs / umetesad warumatebelia / realoba ar / imisgan, rac CvenTvis

ukve nacnobia

(b) gaurkvevel situaciebs / ZiriTadad warmatebulia / sinamdvile / imisgan,

rasac Cven moveliT

(g) axal situaciebs / zogjer warumatebelia / arsebuli realoba / warsulisagan

(d) rTul amocanebs / ZiriTadad warmatebulia / yoveli axali amocana / wina

amocanisgan

14

36. gelaTis mxatvroba saocrad hgavs italiuri renesansis pirvel nawarmoebebs, magram yoveli msgavseba _____ . arsebobs ideaTa da formaTa _____ , romelsac

kulturul garemoebaTa analogia badebs. _____ , rom saqarTveloSi

aRmaSeneblisa da Tamaris epoqaSi Tavi iCina zogierTma esTetikurma

mimarTulebam, romelic _____ .

(a) gavleniT rodi aixsneba / sxvaoba / amiTaa ganpirobebuli / srulad mxolod

italiaSi gamovlinda

(b) mxolod gavleniT aixsneba / paralelizmi / Tumca ucnauria / mravalmxriv

gamovlinda saqarTveloSi

(g) gavleniT rodi aixsneba / paralelizmi / amiT aixsneba is / srulad mxolod

italiaSi gamovlinda

(d) mxolod gavleniT aixsneba / sxvaoba / amitom gasakviri araa / mravalmxriv


37. ucnauria, magram kognituri disonansis Teoriis Tanaxmad, fsiqologiuri eqsperimentis monawilisaTvis raime movlenisadmi _____ SesaZlebelia ______ ,

da ara am Tanxis _____ .

(a) dadebiTi ganwyobis Seqmna / misTvis gadaxdili gasamrjelos SemcirebiT /

gazrdiT

(b) dadebiTi ganwyobis Secvla / gaweuli Sromis anazRaurebis gazrdiT / aSkara

matebiT

(g) uaryofiTi ganwyobis Secvla / gaweuli Sromis anazRaurebis ganaxevrebiT /

SemcirebiT (d) uaryofiTi ganwyobis Seqmna / misTvis gadaxdili gasamrjelos gaormagebiT /

gazrdiT

15

logika






naxazis formiT.

38. sabavSvo baRSi sami studenti-praqtikanti akvirdeboda erTi da imave bavSvis qcevas da akeTebda Canawerebs.

nikas Canaweri: "is jer TamaSobda manqaniT, Semdeg matarebliT. isauzma, dalia vaSlis wveni, mere daxata saxli".

lias Canaweri: "bavSvma iTamaSa asawyobi saTamaSoTi, Semdeg gaerTo sabavSvo kompiuteriT, SeWama xaWapuri, dalia wveni, plasteliniT

raRacas Zerwavda". Tamunas Canaweri: "igi jer gaerTo dasaqoqi manqaniT, Semdeg gaagor-gamoagora

matarebeli. sauzmis dros SeWama vaSlis Rvezeli, romelsac

daayola rZe. didxans xatavda".

gaiTvaliswineT, rom:

• erT-erTma praqtikantma mxolod erTi faqti aRniSna sworad, yvela sxva

faqti SecdomiT CainiSna;

• erTma _ yvelaferi zustad asaxa;

• erTma ki _ mxolod erTi faqti CainiSna SecdomiT.

am praqtikantebidan romelma dauSva mxolod erTi uzustoba? (a) liam

(b) Tamunam

(g) nikam

(d) amis dadgena SeuZlebelia

39. viciT, rom arseboben gawvrTnili ZaRlebi da, amasTanave, mocemulia: • yvela gawvrTnil ZaRls aqvs cisferi Tvalebi

• yvela gawvrTnili ZaRli aris cnobismoyvare

Tu es debulebebi WeSmaritia, maSin Semdegi oTxi debulebidan romelia

aucileblad mcdari?

(a) zogierTi cisferTvaleba arseba aris cnobismoyvare

(b) zogierT cnobismoyvare arsebas aqvs cisferi Tvalebi

(g) arc erTi cisferTvaleba arseba ar aris cnobismoyvare

(d) yvela, visac cisferi Tvalebi aqvs, aris cnobismoyvare

16

40. kvlevis monawileebs dasamaxsovreblad aZlevdnen ori saxis masalas: jer sityvebs da Semdeg _ winadadebebs. Sedegebma aCvena, rom monawileTa ufro didi

nawili winadadebebs ukeT imaxsovrebda, vidre sityvebs. amis safuZvelze

ivaraudes, rom:

sazogadod, winadadebebis damaxsovreba ufro advilia, vidre sityvebis.


(a) kvlevis monawileebs dasamaxsovreblad aZlevdnen 20 sityvas da mxolod 4 winadadebas

(b) kvlevis monawileebs dasamaxsovreblad aZlevdnen 20 sityvasa da 20 winadadebas

(g) kvlevis monawileebs sityvebis dasamaxsovreblad maTi mravaljer gameorebis

ufleba hqondaT, winadadebebis dasamaxsovreblad ki _ ara

(d) kvlevis monawileebs rogorc sityvebis, ise winadadebebis xuT-xuTjer

gameorebis ufleba hqondaT

41. davuSvaT, rom: • yvela adamiani, romelic am qalaqSi cxovrobs, mxiarulia

• yvela mxiaruli adamiani axalgazrdaa


(a) yvela axalgazrda adamiani mxiarulia

(b) yvela mxiaruli adamiani am qalaqSi cxovrobs

(g) yvela axalgazrda adamiani am qalaqSi cxovrobs

(d) am qalaqSi mcxovrebi yvela adamiani axalgazrdaa

17



pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

bavSvis fsiqologiis, rogorc mecnierebis amocanas adamianis cxovrebis im

periodis Seswavla warmoadgens, rodesac arsebiTad is jer kidev moklebulia e.w.

Segnebuli cxovrebis unars da misi qceva jer kidev uSualo moTxovnilebebiT

ganisazRvreba. es ki sakmao xans grZeldeba: jer 6-7 wlamde, e.i. skolaSi

Sesvlamde da Semdeg skolaSi, sadac bavSvi ganviTarebis rTul safexurebs

gaivlis.

mozrdili adamiani, bavSvisagan gansxvavebiT, rogorc ki igrZnobs raime

moTxovnilebas, imwamsve, uSualod rodi cdilobs mis dakmayofilebas. mas ukve

sagangebo unari aqvs gamomuSavebuli, Tavi Seikavos da ama Tu im qcevas mas

Semdeg mimarTos, rac gadawyvets, Tu ra qceva iqneba misTvis xelsayreli. swored

es aris Segnebuli cxovrebis unari.

ra meTodebs mivmarTavT imisTvis, rom bavSvis ganviTarebis safexurebi

SeviswavloT? bavSvis fsiqologiis mTavar meTods dakvirveba warmoadgens. mecniereba orgvar dakvirvebas ganasxvavebs: dakvirvebas bunebriv pirobebSi da dakvirvebas

xelovnur pirobebSi. rodesac dakvirvebis sagnad raime movlenaa dasaxuli, romelic

mkvlevaris monawileobis gareSe Cndeba da icvleba, maSin dakvirvebis pirvel

saxesTan gvaqvs saqme. magram rodesac mkvlevari TviTon qmnis an cvlis pirobebs,

romelSic esa Tu is movlena Cndeba da viTardeba, Cvens winaSe xelovnuri

dakvirveba _ cda, igive eqsperimenti dgas (pirvels martivad dakvirvebas uwodeben,

xolo meores _ cdas an eqsperiments).

cnobili mkvlevari uiliam Sterni aRniSnavda: "zogierTi mniSvnelovani Sedegis miuxedavad, Znelia vifiqroT, rom eqsperimenti adreuli bavSvobis xanis Sesaswavlad

odesme iseTsave mniSvnelobas moipovebs, rogoric mas saskolo asakis bavSvobisaTvis

aqvs..." amas, Sternis azriT, ramdenime mizezi ganapirobebs: adreul asakSi bavSvis swrafi daRliloba, interesis sisuste; aseve, eqsperimentatorsa da mcirewlovan

bavSvs Soris urTierTgagebisa da mWidro kontaqtis damyarebis siZnele... Sesabamisad,

adreul asakSi bavSvis qcevis Sesaswavlad upiratesoba eniWeba bunebriv pirobebSi

dakvirvebas. kerZod ki, warsulSi da dResac, gansakuTrebiT didi mniSvneloba e.w.

dRiuris warmoebis meTods aqvs. bavSvis pirveli mkvlevarni, maT Soris, vilhelm

praieri _ fuZemdebeli mecnierebis am dargisa, TavianT gamokvlevebSi gansakuTrebiT

dRiuris masalas eyrdnobian.

xSirad xdeba, rom damkvirvebeli imas ki ar adevnebs interesiT Tvalyurs,

rac bavSvisaTvis Cveulebriv, damaxasiaTebel movlenas warmoadgens, aramed

piriqiT, meti xalisiT swored araCveulebrivsa da iSviaT SemTxvevebs aRniSnavs,

e.i. imas, rac ufrosi asakisaTvis ufroa damaxasiaTebeli. ra Tqma unda, aseTi

masala SeiZleba saintereso iyos Tavisi iSviaTobis mxriv romelime konkretuli

bavSvis individualur TaviseburebaTa Sesaswavlad, magram imis gasagebad, Tu ras

warmoadgens bavSvobis xanis mocemuli periodi sazogadod, is mkvlevars

daxmarebas TiTqmis ver gauwevs.

amrigad, bavSvis fsiqologiis mizans yvelaze ufro is masala Seesabameba,

romelic am asakisaTvis damaxasiaTebeli, Cveulebrivi garemoebis, e.i. asakobrivi

situaciis pirobebSi gvxvdeba. maSasadame, bavSvis fsiqologiis, rogorc mecnie-

rebis, mTavar meTods swored asakobrivi situaciis pirobebSi dakvirveba

warmoadgens.

18

42. CamoTvlilTagan romeli asaxavs marTebulad teqstis pirveli da meore

abzacebis ZiriTad azrs, daniSnulebas?

(a) pirvel abzacSi aRniSnulia skolamdeli asakis bavSvis qcevis Tavisebureba,

meoreSi ki daxasiaTebulia skolis moswavlis qceva

(b) pirvel abzacSi aRniSnulia, rom bavSvi ganviTarebis rTul safexurebs

gaivlis, meoreSi ki aRwerilia bavSvis fsiqologiis, rogorc mecnierebis

mTavari meTodi

(g) pirvel abzacSi aRniSnulia bavSvis qcevis ZiriTadi Tavisebureba, meoreSi ki

aRwerilia bavSvis mier Segnebuli cxovrebis unaris TandaTanobiT

gamomuSaveba

(d) pirvel abzacSi aRniSnulia bavSvis qcevis ZiriTadi Tavisebureba, meoreSi ki

aRwerilia mozrdil adamianTa erT-erTi arsebiTi maxasiaTebeli

43. ra aris "Segnebuli cxovrebis unari" (upasuxeT meore abzacis mixedviT)? esaa adamianis unari:

(a) winaswar ganWvritos qcevis dadebiTi da uaryofiTi Sedegebi da

ganaxorcielos misTvis xelsayreli qceva

(b) igrZnos moTxovnileba da uSualod, maSinve daikmayofilos igi

(g) Tavi Seikavos misTvis xelsayreli qcevis ganxorcielebisgan

(d) winaswar igrZnos, Tu ra dadebiTi da uaryofiTi mxareebi aqvs ama Tu im

moTxovnilebas

44. ra gansxvavebaa bunebrivsa da xelovnur pirobebSi warmoebul dakvirvebaTa Soris?

(a) bunebriv pirobebSi dakvirveba SedarebiT xanmoklea da martivad

gansaxorcielebeli, xelovnur pirobebSi dakvirveba ki ufro xangrZlivi da

rTulia

(b) bunebriv pirobebSi dakvirvebis masala mkvlevarisTvis gacilebiT sando da

mniSvnelovania, vidre xelovnur pirobebSi warmoebuli dakvirvebis masala

(g) bunebriv pirobebSi warmoebuli dakvirvebis masala mecnierul kvlevas

naklebad exmareba, xelovnur pirobebSi dakvirvebis masala ki gacilebiT

sando da mniSvnelovania

(d) bunebriv pirobebSi mkvlevari pasiurad adevnebs Tvalyurs movlenebs,

xelovnuri dakvirvebis dros ki TviTon ganapirobebs Sesaswavli movlenis

aRmocenebas da ganviTarebas

45. CamoTvlilTagan romeli asaxavs marTebulad da amomwuravad Sternis mier eqsperimentis rolis Sesaxeb gamoTqmul azrs?

(a) eqsperimenti adreuli bavSvobis xanis Sesaswavlad gamousadegari meTodia,

radgan am meTodiT kvlevas Sedegi arasodes mohyolia

(b) skolamdeli asakis bavSvobis Sesaswavlad eqsperimenti Zalian mniSvnelovania,

radgan 6-7 wlis bavSvTan eqsperimentatori kontaqts advilad amyarebs (g) adreuli bavSvobis Sesaswavlad eqsperimenti iseTive mniSvnelobis mqonea,

rogoric is saskolo asakis bavSvobisTvisaa

(d) eqsperimenti albaT yovelTvis gacilebiT mniSvnelovani iqneba saskolo

asakis bavSvobis sakvlevad, vidre _ adreuli bavSvobis Sesaswavlad

19

46. umcrosi asakis bavSvTan eqsperimentis ganxorcielebisas mkvlevars sirTules ar uqmnis:

(a) mcirewlovani bavSvisaTvis damaxasiaTebeli interesis sisuste

(b) mcirewlovani bavSvis individualuri Taviseburebani

(g) am asakobriv periodSi bavSvis swrafi daRla

(d) am asakobriv periodSi bavSvTan kontaqtis damyarebis Tavisebureba

47. teqstis mixedviT, dRiuris warmoebis meTodi aris:

(a) bunebrivi dakvirvebis meTodis konkretuli saxe

(b) eqsperimentuli kvlevis aucilebeli komponenti

(g) eqsperimentis Sedegebis aRnusxvis erT-erTi saSualeba

(d) bunebrivi dakvirvebis danergvamde arsebuli meTodi

48. rogori masala gagviwevs daxmarebas bavSvis individualur TaviseburebaTa Sesaswavlad?

(a) mxolod is masala, romelic asakobrivi situaciis pirobebSi dakvirvebiT

Segrovda

(b) mxolod iseTi masala, romelsac mkvlevari cdis, eqsperimentis Sedegad

moipovebs

(g) dakvirvebis masala, romelic bavSvis qcevis gansakuTrebul, iSviaT SemTxvevebs

aRwers

(d) dakvirvebis masala, romelic adasturebs, rom bavSvi uSualod cdilobs

Tavisi moTxovnilebis dakmayofilebas

49. ra aris bavSvis fsiqologiis, rogorc mecnierebis mTavari amocana?

(a) bavSvobis xanisTvis damaxasiaTebeli, asakobrivi situaciis pirobebSi

gamovlenili qcevis Seswavla

(b) im asakobrivi periodis kvleva, roca Segnebuli cxovrebis unari sakmaodaa

ganviTarebuli

(g) adreuli bavSvobis xanis Sesaswavlad cdis, eqsperimentis meTodis Sedegianad

gamoyeneba

(d) bavSvobis xanis ama Tu im periodSi gamovlenili gansakuTrebuli, iSviaTi

qcevis SemTxvevaTa Seswavla

50. ras isaxavs ZiriTad miznad es teqsti?

(a) gagvacnos bavSvisa da mozrdili adamianis qcevaTa ganmasxvavebeli niSnebi

(b) gagvacnos bavSvis fsiqologiis cnobil mkvlevarTa ZiriTadi mosazrebebi

(g) gagvacnos bavSvis fsiqologiis, rogorc mecnierebis kvlevis sagani da

ZiriTadi meTodi

(d) gagvacnos samecniero Tvalsazrisi bunebrivsa da xelovnur pirobebSi

dakvirvebis meTodTa Sesaxeb

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)

an · am = an + m

an : am = an – m

(an)m = an · m

4. proporcia: Tu , maSin ad = bc.

5. siCqare: dro

manZilisiCqare =

6. saSualo ariTmetikuli:

raodenoba monacemTa

jami monacemTasaSualo monacemTa =

7. Semoklebuli gamravlebis formulebi: (a+b)2 = a2 + 2ab + b2

(a - b)2 = a2 – 2ab + b2

(a + b)(a – b) = a2 – b2 8. naxazze kuTxe SeiZleba kuTxis gverdebs Soris

Casmuli patara rkaliT

iyos moniSnuli, marTi

kuTxe ki _ patara

kvadratiT.

∠A aRniSnavs A kuTxis sidides. 9. paraleluri wrfeebi:

• ori paraleluri

wrfis mesame wrfiT

gadakveTisas Siga jvaredina

kuTxeebi tolia: α = β.

10. 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: .

11. 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.

12. wre, wrewiri: • wrewiris sigrZe L misi

radiusis mixedviT gamoiTvleba

formuliT: L = 2πr; π ricxvi, measedis sizustiT, 3,14-is tolia;.

• r radiusiani wris farTobi gamoiTvleba formuliT: L = πr2.

13. 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

51.

(a) (b) (g) (d)

52.

(a) (b) (g) (d)

53.

x < y

(a) (b) (g) (d)

54.

(a) (b) (g) (d)

55.

ABC samkuTxedSi AB = BC da ∠A = ∠B.

(a) (b) (g) (d)

( )242 − 24 −

15733 : 17 + 1 15748 : 16 + 1

4 – x 4 – y

61 2,0

60° ∠C

23

56.

(a) (b) (g) (d)

57.

(a) (b) (g) (d)

58.

(a) (b) (g) (d)

amocanebi

59. ramdeniTaa naklebi udidesi samniSna ricxvi udides xuTniSna ricxvze? (a) 99000-iT (b) 80100-iT (g) 900-iT

(d) 100-iT (e) 99-iT

60. ricxvTa RerZi masze moniSnuli wertilebiT dayofilia tol monakveTebad

(ix. naxazi). moniSnuli wertilebidan A da C wertilebis koordinatebi miTiTebulia naxazze. B wertilis koordinatia:

(a) 400 (b) 420 (g) 430 (d) 440 (e) 460

25-is naturaluri gamyofebis

raodenoba


raodenoba

( )21 y+ 2y

eqvskuTxa pira-

midis wveroebis

raodenoba

kubis wveroebis

raodenoba

24

61. A klasSi 11-iT meti moswavlea, vidre B klasSi. ramdeniT meti iqneba A klasSi moswavleTa raodenoba B klasSi moswavleTa raodenobaze, Tu A klasidan B-Si 3 moswavle gadava?

(a) 3-iT (b) 4-iT (g) 5-iT (d) 6-iT (e) 7-iT

62. laSam 8 saaTi da 30 wuTi iZina da diliT 8-is 20 wT-ze gaiRviZa. romel saaTze dauZinia laSas?

(a) 22 sT 10 wT (b) 22 sT 50 wT (g) 23 sT 10 wT (d) 23 sT 50 wT (e) 00 sT 10 wT

monacemTa analizi

cxrilSi Tveebis mixedviT warmodgenilia monacemebi axalSobili gogonebisa da

vaJebis raodenobaTa Sesaxeb.

Tve I II III IV V VI VII VIII IX X XI XII weliwadSi

gogonebi 3537 3407 3866 3711 3775 3665 3621 3596 3491 3391 3160 3371 42591 vaJebi 3743 3550 4017 4173 4117 3944 3964 3797 3712 3512 3392 3761 45682 erTad 7280 6957 7883 7884 7892 7609 7585 7393 7203 6903 6552 7132 88273

mocemuli cxrilis mixedviT upasuxeT Semdeg oTx SekiTxvas:

63. ramdeni gogona daibada maisSi? (a) 3407 (b) 3621 (g) 3711 (d) 3775 (e) 4117

64. Tu mTeli wlis ganmavlobaSi axalSobili vaJebis raodenoba gogonebis raodenobaze x-iTaa meti, maSin:

(a) x > 6000 (b) 5000 < x < 6000 (g) 4000 < x < 5000 (d) 3000 < x < 4000 (e) x < 3000

25

65. romel TveSi iyo axalSobil vaJTa raodenoba yvelaze mcire? (a) XII

(b) XI

(g) IX

(d) VII

(e) IV 66. ramdeni Tvea iseTi, romelSic axalSobilTa saerTo raodenoba 7800-ze metia?

(a) 3 (b) 4 (g) 5 (d) 6 (e) 7

amocanebi

67. Tu x + 3y = 11 da 3x + y = 9 , maSin x + y = (a) 1 (b) 5 (g) 10 (d) 15 (e) 20

68. sibrtyeze mocemulia marTkuTxa koordinatTa sistema. ABC samkuTxedis erTi gverdi x RerZis paraleluria, meore _ y RerZis. samkuTxedis B da C wveroebis koordinatebi miTiTebulia naxazze.

A wveros koordinatebi (a; b) = (a) (3; 1) (b) (1; 3) (g) (1; 5) (d) (5; 1) (e) (1; 7)

26

69. mgzavrs gasavleli hqonda garkveuli manZili. 24 kilometris gavlis Semdeg

mas gasavleli darCa mTeli gzis 51 nawili. sul ra manZili hqonia gasavleli

mgzavrs? (a) 28 km (b) 29 km (g) 30 km (d) 32 km (e) 35 km

70. Semodgomaze qurTuki 160 lari Rirda, zamTris dasawyisSi ki misma fasma 25%-iT moimata. ramdeni lari eRireboda qurTuki fasis momatebis Semdeg?

(a) 170 (b) 180 (g) 185 (d) 200 (e) 225

71. marTkuTxedis sami wvero tolgverda samkuTxedis gverdebze mdebareobs (ix. naxazi). x° =

(a) 35° (b) 45° (g) 50° (d) 55° (e) 60°

72. ricxvebi 6, a, 5, b, 2, c, 1 klebis mixedviTaa dalagebuli, amasTan a = b + c. CamoTvlili ricxvebidan romlis toli ar SeiZleba iyos b ricxvi?

(a) 2,8 (b) 3,2 (g) 3,8 (d) 4,2 (e) 4,8

27

73. maRaziaSi 1 kg atami 4 lari Rirda, 1 kg msxali _ 3 lari, 1 kg vaSli _ 2 lari, 1 kg qliavi _ 1,5 lari. ninos, daTos, gias da lias eqvs-eqvsi lari hqondaT. ninom eqvsive lariT atami iyida, daTom _ msxali, giam _ vaSli, liam _

qliavi. sul ramdeni kilogrami xili uyidiaT ninos, daTos, gias da lias?

(a) 12 (b) 11 (g) 10,5 (d) 10 (e) 9,5

74. MNKD marTkuTxedi, romlis farTobi 48 sm2

-ia,

dayofilia tol marTkuTxedebad. ramdeni kvadratuli

santimetria gamuqebuli mravalkuTxedis farTobi (ix.

naxazi), Tu misi wveroebi dayofis Sedegad miRebuli marTkuTxedebis wveroebs emTxveva?

(a) 12 (b) 15 (g) 18 (d) 20 (e) 22

75. vTqvaT, im oTaxis kedlebis SesaRebad, romlis sigrZea a metri, sigane _ b metri, xolo simaRle _ h metri, saWiroa p kilogrami saRebavi. p SeiZleba gamovTvaloT formuliT: p = 0,4(a+b)h.

ramdeni kilogrami saRebavi iqneba saWiro, mocemuli formulis mixedviT, im

oTaxis kedlebis SesaRebad, romlis sigrZea 6 m, sigane _ 4 m, simaRle ki _ 3 m? (a) 6 (b) 7,6 (g) 9 (d) 10,8 (e) 12

28







meti, airCieT (d).

A B

76.

tyeSi mxolod wiflis, muxis da

naZvis xeebia. wiflis xeebis raodenoba

300-ze metia. wriul diagramaze miTiTebulia, tyeSi xeebis saerTo

raodenobis ramdeni procentia

wiflisa da muxis xeebis raodenoba.

(a) (b) (g) (d)

77.

mimdevrobis pirveli wevria 5, yoveli momdevno wevri ki mis wina wevrze 3-iT metia. am mimdevrobis mexuTe wevri p-s tolia.

(a) (b) (g) (d)

78.

Saqris Warxlidan miRebuli Saqris wona Warxlis

wonis 13%-ia, xolo Saqris lerwmidan miRebuli

Saqris wona _ lerwmis wonis 15%.

(a) (b) (g) (d)

am tyeSi naZvebis

raodenoba 110

p 17

Saqris wona, rome-

lic miiReba 50 kg Saqris Warxlisgan

Saqris wona, rome-

lic miiReba 40 kg Saqris lerwmisgan

29

79.

wris diametris sigrZe 6 metria.

(a) (b) (g) (d)

80.

kaxam daxarjuli eleqtroenergiis safasuri _ 45 lari gadaixada. es Tanxa kaxas xelfasis mecxredze

metia, magram mervedze naklebi.

(a) (b) (g) (d)

81.

nebismieri x ricxvisaTvis ( )∗x -iT aRniSnulia

umciresi mTeli ricxvi, romelic metia x ricxvze.

(a) (b) (g) (d)

82.

MNKE marTkuTxedis farTobia 40 sm2.

ABCD marTkuTxedis farTobia 30 sm2.

(a) (b) (g) (d)

am wris farTobi 30 m2

( ) ( )** 4,3+x ( )*4,3+x

MNKE marTkuT-xedis perimetri

ABCD marTkuT-xedis perimetri

kaxas xelfasi 345 lari

30

amocanebi

83. romelia is ricxvi, romlis 350% udris 70-s? (a) 10 (b) 15 (g) 20 (d) 25 (e) 30

84. miwis nakveTs didi da patara traqtorebiT xnaven. TiToeuli didi traq-tori yoveldRe imave farTobis miwis nakveTs xnavs, rasac am nakveTze momuSave

nebismieri sxva didi traqtori. aseve, TiToeuli patara traqtori yoveldRe

imave farTobis miwis nakveTs xnavs, rasac am nakveTze momuSave nebismieri sxva

patara traqtori (traqtorebi muSaobisas erTmaneTs xels ar uSlian).

miwis nakveTis moxvnas 2 didi traqtori 6 dRes andomebs. amave nakveTis moxvna 6 dReSi 3 patara traqtorsac SeuZlia. ramden dReSi moxnavs am nakveTs 6 didi da 9 patara traqtori erTad muSaobiT?

(a) 1 (b) 2 (g) 3 (d) 4 (e) 5

85. beqam, vaJam da nikam sul 45 cali Tevzi daiWires. vaJam daiWira 2-jer naklebi raodenobis Tevzi, vidre beqam, xolo nikam _ 3 TevziT meti, vidre beqam da vaJam erTad. ramdeni cali Tevzi dauWeria beqas?

(a) 8 (b) 12 (g) 14 (d) 15 (e) 21

86. ras udris tolferda samkuTxedis fuZis sigrZis Sefardeba am samkuTxedis perimetrTan, Tu fuZis sigrZe 2-jer naklebia ferdis sigrZeze?

(a) 61

(b) 51

(g) 31

(d) 32

(e) 54

31

monacemTa analizi

fsiqologis Txovnaze, daesaxelebinaT Tavisufali drois gatarebis mxolod

erTi, maTTvis yvelaze sayvareli forma, studentebma daasaxeles: megobrebTan

urTierToba, televizoris yureba, musikis mosmena, wignis kiTxva, seirnoba.

svetovan diagramaze warmodgenilia im studentTa raodenobebi, romlebsac

Tavisufali drois ama Tu im formiT gatareba uyvarT.

mocemuli diagramis mixedviT upasuxeT Semdeg oTx SekiTxvas:

87. Tavisufali drois gatarebis romeli forma daasaxela studentTa yvelaze mcire nawilma?

(a) megobrebTan urTierToba

(b) televizoris yureba

(g) musikis mosmena

(d) wignis kiTxva

(e) seirnoba

88. ramdenjer metia im studentTa raodenoba, romlebmac daasaxeles televizo-ris yureba, im studentTa raodenobaze, romlebmac daasaxeles musikis mosmena?

(a) 1,5-jer (b) 2-jer (g) 2,5-jer (d) 3-jer (e) 3,5-jer

89. studentTa ramdenma procentma daasaxela wignis kiTxva?

(a) 15%

(b) 20%

(g) 25%

(d) 30%

(e) 35%

32

90. im studentebis raodenobaTa jami, romlebmac daasaxeles megobrebTan urTierToba da seirnoba, gamokiTxulTa saerTo raodenobis:

(a) naxevarze metia

(b) naxevaria

(g) naxevarze naklebia, magram mesamedze metia

(d) mesamedia

(e) mesamedze naklebia, magram meoTxedze metia

amocanebi

91. axal mxatvrul films 4 dRis ganmavlobaSi uCvenebdnen. filmis Cvenebas

yvelaze meti mayurebeli pirvel dRes daeswro. yovel momdevno dRes ki

mayurebelTa raodenoba wina dResTan SedarebiT 50-iT mcirdeboda. bolo dRes es filmi naxa 200-ma mayurebelma. sul ramden mayurebels unaxavs es filmi am oTxi dRis ganmavlobaSi?

(a) 850

(b) 900

(g) 950 (d) 1000

(e) 1100 92. marTkuTxedis erTi gverdis sigrZea 12 sm, diagonalisa _ 13 sm. ramdeni santimetria am marTkuTxedis perimetri?

(a) 28 (b) 30 (g) 32 (d) 34 (e) 36

93. sami ricxvidan erTi ricxvi meoreze 5-iT naklebia, mesameze ki _ 9-iT meti. am ricxvebs Soris udidesia n + 6. qvemoT CamoTvlilTagan romeli gamosaxule-biT Caiwereba am sami ricxvis jami?

(a) 3n – 1

(b) 3n – 4

(g) 3n + 2

(d) 3n + 14 (e) 3n + 20

33

94. gundSi, romelSic Tinas CaTvliT 8 momReralia, momReralTa saSualo asaki 12 welia. ramdeni wlisaa Tina, Tu misi gundidan wasvlis SemTxvevaSi gundSi momReralTa saSualo asaki 11 weli gaxdeba?

(a) 11 (b) 12 (g) 17 (d) 19 (e) 21

95. marTkuTxa paralelepipedi, romlis fuZis wiboebis sigrZeebia 7 sm da 3 sm, dayves a da b marTkuTxa parale-lepipedebad, romelTagan b kubia (ix. naxazi). ramdeni kuburi santimetria a marTkuTxa paralelepipedis moculoba?

(a) 9 (b) 10 (g) 21 (d) 36 (e) 63

96. b = 4 · 5 · 6 · 7 · 8 – 7. risi tolia b ricxvis 6-ze gayofisas miRebuli naSTi?

(a) 1 (b) 2 (g) 3 (d) 4 (e) 5

97. seifis gasaRebad 5-cifriani kodis akrefaa saWiro. molares daaviwyda asa-krefi kodis bolo 3 cifri, magram mas axsovda, rom am kodis bolo 2 cifri erTnairi iyo, xolo bolodan mesame _ 8-iani an 9-iani iyo. minimum ramdeni 5-cifriani kodis akrefa mouwevs molares, raTa man aucileblad gaxsnas seifi?

(a) 10 (b) 20 (g) 25 (d) 30 (e) 35

34

98. Tu a, b da c mTeli dadebiTi ricxvebia, romelTagan TiToeuli 11-ze

naklebia, maSin c

ba + gamosaxulebis udidesi mniSvnelobaa:

(a) 0,1 (b) 2 (g) 10 (d) 15 (e) 20

99. xeivanSi 160 xea, romelTa 65% naZvia. am xeivanSi xeebis 55% xuTi wlis winaa darguli. xeivanSi darguli naZvebidan minimum ramdeni darges xuTi wlis win?

(a) 10 (b) 16 (g) 28 (d) 32 (e) 40

100. manZili or figuras Soris, romlebsac saerTo wertili ar aqvT, ewodeba umciresi monakveTis sigrZes im monakveTebidan, romlebic erTi figuris

wertilebs meore figuris wertilebTan aerTebs.

sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 2 sm. man-Zili pirvel da meore wreebs Soris 25 sm-ia, xolo meore da mesame wreebs Soris _ 1 sm. qvemoT CamoTvlilTagan romlis toli ar SeiZleba iyos manZili pirvel da mesame wreebs Soris?

(a) 21 sm (b) 22 sm (g) 23 sm (d) 25 sm (e) 28 sm

21

maTematikuri nawili













an · am = an + m

an : am = an – m

(an)m = an · m


5. siCqare: dro

manZilisiCqare =


raodenoba monacemTa



(a - b)2 = a2 – 2ab + b2




kuTxe ki _ patara

kvadratiT.


• ori paraleluri

wrfis mesame wrfiT






hipotenuzis sigrZis



AB2 = AC2 + BC2
















22







meti, airCieT (d).

A B

51.

(a) (b) (g) (d)

52.

(a) (b) (g) (d)

53.

x < y

(a) (b) (g) (d)

54.

(a) (b) (g) (d)

55.

ABC samkuTxedSi AB = BC da ∠A = ∠B.

(a) (b) (g) (d)

( )242 − 24 −

15733 : 17 + 1 15748 : 16 + 1

4 – x 4 – y

61 2,0

60° ∠C

23

56.

(a) (b) (g) (d)

57.

(a) (b) (g) (d)

58.

(a) (b) (g) (d)

amocanebi

59. ramdeniTaa naklebi udidesi samniSna ricxvi udides xuTniSna ricxvze? (a) 99000-iT (b) 80100-iT (g) 900-iT

(d) 100-iT (e) 99-iT


(ix. naxazi). moniSnuli wertilebidan A da C wertilebis koordinatebi miTiTebulia naxazze. B wertilis koordinatia:

(a) 400 (b) 420 (g) 430 (d) 440 (e) 460


raodenoba


raodenoba

( )21 y+ 2y

eqvskuTxa pira-

midis wveroebis

raodenoba

kubis wveroebis

raodenoba

24

61. A klasSi 11-iT meti moswavlea, vidre B klasSi. ramdeniT meti iqneba A klasSi moswavleTa raodenoba B klasSi moswavleTa raodenobaze, Tu A klasidan B-Si 3 moswavle gadava?

(a) 3-iT (b) 4-iT (g) 5-iT (d) 6-iT (e) 7-iT

62. laSam 8 saaTi da 30 wuTi iZina da diliT 8-is 20 wT-ze gaiRviZa. romel saaTze dauZinia laSas?


monacemTa analizi






63. ramdeni gogona daibada maisSi? (a) 3407 (b) 3621 (g) 3711 (d) 3775 (e) 4117

64. Tu mTeli wlis ganmavlobaSi axalSobili vaJebis raodenoba gogonebis raodenobaze x-iTaa meti, maSin:

(a) x > 6000 (b) 5000 < x < 6000 (g) 4000 < x < 5000 (d) 3000 < x < 4000 (e) x < 3000

25

65. romel TveSi iyo axalSobil vaJTa raodenoba yvelaze mcire? (a) XII

(b) XI

(g) IX

(d) VII

(e) IV 66. ramdeni Tvea iseTi, romelSic axalSobilTa saerTo raodenoba 7800-ze metia?

(a) 3 (b) 4 (g) 5 (d) 6 (e) 7

amocanebi

67. Tu x + 3y = 11 da 3x + y = 9 , maSin x + y = (a) 1 (b) 5 (g) 10 (d) 15 (e) 20

68. sibrtyeze mocemulia marTkuTxa koordinatTa sistema. ABC samkuTxedis erTi gverdi x RerZis paraleluria, meore _ y RerZis. samkuTxedis B da C wveroebis koordinatebi miTiTebulia naxazze.

A wveros koordinatebi (a; b) = (a) (3; 1) (b) (1; 3) (g) (1; 5) (d) (5; 1) (e) (1; 7)

26

69. mgzavrs gasavleli hqonda garkveuli manZili. 24 kilometris gavlis Semdeg

mas gasavleli darCa mTeli gzis 51 nawili. sul ra manZili hqonia gasavleli

mgzavrs? (a) 28 km (b) 29 km (g) 30 km (d) 32 km (e) 35 km

70. Semodgomaze qurTuki 160 lari Rirda, zamTris dasawyisSi ki misma fasma 25%-iT moimata. ramdeni lari eRireboda qurTuki fasis momatebis Semdeg?

(a) 170 (b) 180 (g) 185 (d) 200 (e) 225

71. marTkuTxedis sami wvero tolgverda samkuTxedis gverdebze mdebareobs (ix. naxazi). x° =

(a) 35° (b) 45° (g) 50° (d) 55° (e) 60°

72. ricxvebi 6, a, 5, b, 2, c, 1 klebis mixedviTaa dalagebuli, amasTan a = b + c. CamoTvlili ricxvebidan romlis toli ar SeiZleba iyos b ricxvi?

(a) 2,8 (b) 3,2 (g) 3,8 (d) 4,2 (e) 4,8

27

73. maRaziaSi 1 kg atami 4 lari Rirda, 1 kg msxali _ 3 lari, 1 kg vaSli _ 2 lari, 1 kg qliavi _ 1,5 lari. ninos, daTos, gias da lias eqvs-eqvsi lari hqondaT. ninom eqvsive lariT atami iyida, daTom _ msxali, giam _ vaSli, liam _

qliavi. sul ramdeni kilogrami xili uyidiaT ninos, daTos, gias da lias?

(a) 12 (b) 11 (g) 10,5 (d) 10 (e) 9,5

74. MNKD marTkuTxedi, romlis farTobi 48 sm2

-ia,

dayofilia tol marTkuTxedebad. ramdeni kvadratuli

santimetria gamuqebuli mravalkuTxedis farTobi (ix.

naxazi), Tu misi wveroebi dayofis Sedegad miRebuli marTkuTxedebis wveroebs emTxveva?

(a) 12 (b) 15 (g) 18 (d) 20 (e) 22

75. vTqvaT, im oTaxis kedlebis SesaRebad, romlis sigrZea a metri, sigane _ b metri, xolo simaRle _ h metri, saWiroa p kilogrami saRebavi. p SeiZleba gamovTvaloT formuliT: p = 0,4(a+b)h.

ramdeni kilogrami saRebavi iqneba saWiro, mocemuli formulis mixedviT, im

oTaxis kedlebis SesaRebad, romlis sigrZea 6 m, sigane _ 4 m, simaRle ki _ 3 m? (a) 6 (b) 7,6 (g) 9 (d) 10,8 (e) 12

28







meti, airCieT (d).

A B

76.

tyeSi mxolod wiflis, muxis da

naZvis xeebia. wiflis xeebis raodenoba

300-ze metia. wriul diagramaze miTiTebulia, tyeSi xeebis saerTo

raodenobis ramdeni procentia

wiflisa da muxis xeebis raodenoba.

(a) (b) (g) (d)

77.

mimdevrobis pirveli wevria 5, yoveli momdevno wevri ki mis wina wevrze 3-iT metia. am mimdevrobis mexuTe wevri p-s tolia.

(a) (b) (g) (d)

78.

Saqris Warxlidan miRebuli Saqris wona Warxlis

wonis 13%-ia, xolo Saqris lerwmidan miRebuli

Saqris wona _ lerwmis wonis 15%.

(a) (b) (g) (d)

am tyeSi naZvebis

raodenoba 110

p 17

Saqris wona, rome-

lic miiReba 50 kg Saqris Warxlisgan

Saqris wona, rome-

lic miiReba 40 kg Saqris lerwmisgan

29

79.

wris diametris sigrZe 6 metria.

(a) (b) (g) (d)

80.

kaxam daxarjuli eleqtroenergiis safasuri _ 45 lari gadaixada. es Tanxa kaxas xelfasis mecxredze

metia, magram mervedze naklebi.

(a) (b) (g) (d)

81.



(a) (b) (g) (d)

82.

MNKE marTkuTxedis farTobia 40 sm2.

ABCD marTkuTxedis farTobia 30 sm2.

(a) (b) (g) (d)

am wris farTobi 30 m2

( ) ( )** 4,3+x ( )*4,3+x

MNKE marTkuT-xedis perimetri

ABCD marTkuT-xedis perimetri

kaxas xelfasi 345 lari

30

amocanebi

83. romelia is ricxvi, romlis 350% udris 70-s? (a) 10 (b) 15 (g) 20 (d) 25 (e) 30

84. miwis nakveTs didi da patara traqtorebiT xnaven. TiToeuli didi traq-tori yoveldRe imave farTobis miwis nakveTs xnavs, rasac am nakveTze momuSave

nebismieri sxva didi traqtori. aseve, TiToeuli patara traqtori yoveldRe

imave farTobis miwis nakveTs xnavs, rasac am nakveTze momuSave nebismieri sxva

patara traqtori (traqtorebi muSaobisas erTmaneTs xels ar uSlian).

miwis nakveTis moxvnas 2 didi traqtori 6 dRes andomebs. amave nakveTis moxvna 6 dReSi 3 patara traqtorsac SeuZlia. ramden dReSi moxnavs am nakveTs 6 didi da 9 patara traqtori erTad muSaobiT?

(a) 1 (b) 2 (g) 3 (d) 4 (e) 5

85. beqam, vaJam da nikam sul 45 cali Tevzi daiWires. vaJam daiWira 2-jer naklebi raodenobis Tevzi, vidre beqam, xolo nikam _ 3 TevziT meti, vidre beqam da vaJam erTad. ramdeni cali Tevzi dauWeria beqas?

(a) 8 (b) 12 (g) 14 (d) 15 (e) 21

86. ras udris tolferda samkuTxedis fuZis sigrZis Sefardeba am samkuTxedis perimetrTan, Tu fuZis sigrZe 2-jer naklebia ferdis sigrZeze?

(a) 61

(b) 51

(g) 31

(d) 32

(e) 54

31

monacemTa analizi







87. Tavisufali drois gatarebis romeli forma daasaxela studentTa yvelaze mcire nawilma?

(a) megobrebTan urTierToba

(b) televizoris yureba

(g) musikis mosmena

(d) wignis kiTxva

(e) seirnoba

88. ramdenjer metia im studentTa raodenoba, romlebmac daasaxeles televizo-ris yureba, im studentTa raodenobaze, romlebmac daasaxeles musikis mosmena?


89. studentTa ramdenma procentma daasaxela wignis kiTxva?

(a) 15%

(b) 20%

(g) 25%

(d) 30%

(e) 35%

32

90. im studentebis raodenobaTa jami, romlebmac daasaxeles megobrebTan urTierToba da seirnoba, gamokiTxulTa saerTo raodenobis:

(a) naxevarze metia

(b) naxevaria

(g) naxevarze naklebia, magram mesamedze metia

(d) mesamedia

(e) mesamedze naklebia, magram meoTxedze metia

amocanebi

91. axal mxatvrul films 4 dRis ganmavlobaSi uCvenebdnen. filmis Cvenebas

yvelaze meti mayurebeli pirvel dRes daeswro. yovel momdevno dRes ki

mayurebelTa raodenoba wina dResTan SedarebiT 50-iT mcirdeboda. bolo dRes es filmi naxa 200-ma mayurebelma. sul ramden mayurebels unaxavs es filmi am oTxi dRis ganmavlobaSi?

(a) 850

(b) 900

(g) 950 (d) 1000

(e) 1100 92. marTkuTxedis erTi gverdis sigrZea 12 sm, diagonalisa _ 13 sm. ramdeni santimetria am marTkuTxedis perimetri?

(a) 28 (b) 30 (g) 32 (d) 34 (e) 36

93. sami ricxvidan erTi ricxvi meoreze 5-iT naklebia, mesameze ki _ 9-iT meti. am ricxvebs Soris udidesia n + 6. qvemoT CamoTvlilTagan romeli gamosaxule-biT Caiwereba am sami ricxvis jami?

(a) 3n – 1

(b) 3n – 4

(g) 3n + 2

(d) 3n + 14 (e) 3n + 20

33

94. gundSi, romelSic Tinas CaTvliT 8 momReralia, momReralTa saSualo asaki 12 welia. ramdeni wlisaa Tina, Tu misi gundidan wasvlis SemTxvevaSi gundSi momReralTa saSualo asaki 11 weli gaxdeba?

(a) 11 (b) 12 (g) 17 (d) 19 (e) 21

95. marTkuTxa paralelepipedi, romlis fuZis wiboebis sigrZeebia 7 sm da 3 sm, dayves a da b marTkuTxa parale-lepipedebad, romelTagan b kubia (ix. naxazi). ramdeni kuburi santimetria a marTkuTxa paralelepipedis moculoba?

(a) 9 (b) 10 (g) 21 (d) 36 (e) 63

96. b = 4 · 5 · 6 · 7 · 8 – 7. risi tolia b ricxvis 6-ze gayofisas miRebuli naSTi?

(a) 1 (b) 2 (g) 3 (d) 4 (e) 5

97. seifis gasaRebad 5-cifriani kodis akrefaa saWiro. molares daaviwyda asa-krefi kodis bolo 3 cifri, magram mas axsovda, rom am kodis bolo 2 cifri erTnairi iyo, xolo bolodan mesame _ 8-iani an 9-iani iyo. minimum ramdeni 5-cifriani kodis akrefa mouwevs molares, raTa man aucileblad gaxsnas seifi?

(a) 10 (b) 20 (g) 25 (d) 30 (e) 35

34

98. Tu a, b da c mTeli dadebiTi ricxvebia, romelTagan TiToeuli 11-ze

naklebia, maSin c

ba + gamosaxulebis udidesi mniSvnelobaa:

(a) 0,1 (b) 2 (g) 10 (d) 15 (e) 20

99. xeivanSi 160 xea, romelTa 65% naZvia. am xeivanSi xeebis 55% xuTi wlis winaa darguli. xeivanSi darguli naZvebidan minimum ramdeni darges xuTi wlis win?

(a) 10 (b) 16 (g) 28 (d) 32 (e) 40

100. manZili or figuras Soris, romlebsac saerTo wertili ar aqvT, ewodeba umciresi monakveTis sigrZes im monakveTebidan, romlebic erTi figuris

wertilebs meore figuris wertilebTan aerTebs.

sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 2 sm. man-Zili pirvel da meore wreebs Soris 25 sm-ia, xolo meore da mesame wreebs Soris _ 1 sm. qvemoT CamoTvlilTagan romlis toli ar SeiZleba iyos manZili pirvel da mesame wreebs Soris?


kiTxvebi

N varianti 1 varianti 1

(rusuli varianti)

varianti 2 varianti 3 varianti 4

1 d d b d d

2 d g g b a

3 g g d g g

4 b b b a d

5 b b g g g

6 g g g b a

7 a a g a b

8 d d a g d

9 d d d d d

10 b b d g a

11 g g b d d

12 a a d d d

13 g b g g a

14 g g b b d

15 g g g b d

16 b b b g a

17 b b a a g

18 g g a g d

19 b b b g g

20 b b a g a

21 d d g b b

22 g g d a d

23 g g g b d

24 d d d d g

25 a a g a g

26 g g d b g

27 b b a b b

28 d d b d g

29 b b d g d

30 a a d b b

31 g g g a a

32 b b d g b

33 d d g b b

34 d d d b b

35 g g g b b

36 g g g d d

37 a a b a a

38 b b a a g

39 g g b b d

40 a a b b d

41 d d b a a

42 d d a g d

43 a a g g a

44 d d g g g

45 d d d d b

46 b b g b d

47 a a b b a

48 g g b d d

49 a a d g a

50 g g b b d

ver

bal

ur

i n

awil

i

kiTxvebi


(rusuli

varianti)


51 a a b g b

52 b b b a a

53 a a b b d

54 b b a b b

55 g g a d b

56 b b b a g

57 d d g b d

58 b b d g a

59 a a g g d

60 d d d b g

61 g g a b d

62 b d g g d

63 d d g e a

64 d d b d d

65 b b a e g

66 a a d g g

67 b b e b a

68 a a e e b

69 g g b d e

70 d d d g d

71 g g d d a

72 a a g e d

73 g g d e e

74 d d g b a

75 e e b d b

76 d d a a g

77 g g a b d

78 a a b g d

79 b b d b a

80 a a a d a

81 d d a d g

82 d d d a b

83 g g e d b

84 a a d b g

85 g g d e b

86 b b g g a

87 e e e e d

88 b b d g a

89 g g b b a

90 g g d e e

91 e e b a d

92 d b a g

93 a a e g e

94 d d d g a

95 d d a e b

96 e e g b d

97 b b b d e

98 e e b g b

99 d d d e g

100 a a e e g

maT

emat

ikur

i

naw

il

i














furcelze).



furclis safuZvelze.




instruqcia


instruqcia



furcelze).



furclis safuZvelze.






II

2

verbaluri nawili

analogiebi








Tanmimdevroba.



(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi


1. gaxexva : jagrisi

(a) gacurva : auzi

(b) kerva : nemsi

(g) gauToeba : deni

(d) wera : leqsi

2. lodi : mZime

(a) funji : feradi

(b) wyali : mRvrie

(g) mina : gamWvirvale

(d) Rumeli : umi

3. mosamarTle : ganaCeni

(a) parlamentari : arCevnebi

(b) mwvrTneli : warmateba

(g) maswavlebeli : atestati

(d) eqimi : diagnozi

4. SekeTeba : dazianebuli

(a) datuqsva : mousvenari

(b) swavleba : ucodinari

(g) daTmoba : braziani

(d) mosmena : xmauriani

3

5. Tavdadeba : Tavganwirva

(a) Tavdasxma : Tavdacva

(b) Tavxedoba : Tavmdabloba

(g) TavdaWera : TavSekaveba

(d) Tavmoyvareoba : Tavgasuloba

6. morwyva : sveli

(a) davarcxna : aqoCrili

(b) ciliswameba : mliqvneli

(g) axsna : gasagebi

(d) Semokleba : zusti

7. guTnisdeda : puri

(a) monadire : tye

(b) meTevze : bade

(g) mevenaxe : Rvino

(d) mzareuli : kerZi

8. yayaCo : mindori

(a) jixvi : klde

(b) soko : wvima

(g) ru : tba

(d) ferdobi : mTa

4

winadadebis Sevseba








9. am iSviaTi daavadebis gansakurneblad samkurnalo mcenareebis upiratesobas _____ eqimi _____ , mxolod zogierTs _____ maTi miReba Sedegis momtanad.

(a) arc erTi / ar aRiarebs / ar miaCnia

(b) erTaderTi / aRiarebs / ar miaCnia

(g) yvela / aRiarebs / miaCnia

(d) yvela / ar aRiarebs / miaCnia

10. kunZulze _____ iseTi masala, romliTac iq arsebuli nagebobebia aSenebuli, _____ , rom samSeneblo masala uaxloesi kunZulidan _____ .

(a) arsad moipoveboda / amitom daujerebelia/ SemohqondaT

(b) yvelgan moipoveboda / Sesabamisad, savaraudoa / SemohqondaT

(g) yvelgan moipoveboda/ amitom daujerebelia / ar SemohqondaT

(d) arsad moipoveboda / amitom savaraudoa / SemohqondaT

11. sayovelTao aRiarebiT, miTebi uZveles xalxTa _____, magram argonavtebis miTi _____ cnobebs Zveli kolxeTis Sesaxeb.

(a) warmosaxvis nayofia / Seicavs ararealur

(b) fantaziis nayofia / gvawvdis sarwmuno

(g) utyuar istorias asaxavs / gvawvdis WeSmarit

(d) wes-Cveulebebs aRwers / Seicavs realur

5

12. Zlier mters SeuZlia _____ ers Tavmoyvareoba, _____ mas miwa-wyali da uflebani, magram ar SeuZlia _____ gulistkivili da survili imisa, rom

daibrunos _____.

(a) Seulaxos / Tumca ar waarTvas / daacxros am eris / SenarCunebuli

(b) ar Seulaxos / SeunarCunos / gaiTvaliswinos am eris / kuTvnili

(g) ar Seulaxos / nebayoflobiT daaTmobinos / aRkveTos am eris / mopovebuli

(d) Seulaxos / waarTvas / mospos am eris / dakarguli

13. mudam unda gvaxsovdes, rom _____ Cveni saTqmelis mitana xalxTan _____ da, ufro metad ki, _____, radgan kiTxvis dros glexsa da muSas ucxo

sityvaTa leqsikoni ar uWiravs xelSi, da mgoni, inteligentic _____ am wignSi.

(a) SeuZlebelia / damaxinjebuli sintaqsiT / advilad gasagebi leqsikiT / ar

ixedeba

(b) SesaZlebelia /gamarTuli sintaqsiT / Warbad datvirTuli ucxo sityvebiT /

iSviaTad ixedeba

(g) SeuZlebelia / damaxinjebuli sintaqsiT / Warbad datvirTuli ucxo sityvebiT /

iSviaTad ixedeba

(d) SesaZlebelia / gamarTuli sintaqsiT / advilad gasagebi leqsikiT / xSirad

ixedeba

6

logika






naxazis formiT.

14. Temuri, lali da kote mwkrivSi dganan (ara aucileblad am TanmimdevrobiT). cnobilia, rom erT-erT maTgans axuravs lurji qudi, meores _ Savi, mesames ki _

wiTeli.

• mas, vinc Temuris marjvena mxares dgas, lurji qudi axuravs

• mwkrivSi marcxnidan pirveli adamiani kotea

qvemoT CamoTvlilTagan romeli gamomdinareobs am mocemulobidan aucileblad?

(a) kotes axuravs wiTeli qudi

(b) kotes axuravs wiTeli an Savi

(g) kotes axuravs Savi qudi

(d) kotes axuravs lurji an wiTeli qudi

15. mocemulia: • yvelaferi, rac brwyinavs, oqro ar aris

qvemoT CamoTvlilTagan romel debulebas aqvs igive Sinaarsi, rac mocemuls?

(a) arsebobs iseTi oqro, romelic ar brwyinavs

(b) rac oqro ar aris, ar brwyinavs

(g) zogierTi ram, rac brwyinavs, ar aris oqro

(d) rac brwyinavs, ar aris oqro

7

16. A qalaqSi mcxovreb musikis moyvarulTa saSualo asakis dasadgenad am qalaqis erT-erT musikalur maRaziaSi audiokasetebis myidvelebs akvirdebodnen.

aRmoCnda, rom maRaziaSi ZiriTadad Semodiodnen axalgazrda qalbatonebi

bavSvebTan erTad. Sesabamisad, damkvirveblebma ivaraudes, rom:

A qalaqSi musikas ZiriTadad axalgazrda qalbatonebi usmenen.


(a) A qalaqSi mcxovreb axalgazrda qalbatonebs ZiriTadad musikaluri ganaTleba aqvT miRebuli

(b) A qalaqSi bevri sxva musikaluri maRaziac aris, es maRazia ki sabavSvo baRis gverdiT mdebareobs

(g) A qalaqSi kidev ramdenime musikaluri maRaziaa, magram isini gamokvlevis dros droebiT daketili iyo

(d) A qalaqSi mcxovrebi axalgazrda qalbatonebi gansakuTrebul mniSvnelobas aniWeben Svilebis musikalur aRzrdas

17. davuSvaT, rom:

• yvela biWs uyvars fexburTi

• zogierT biWs uyvars Wadraki


(a) yvela biWs, romelsac uyvars Wadraki, uyvars fexburTi

(b) Wadrakis moyvarul arc erT biWs ar uyvars fexburTi

(g) yvela biWs, romelsac uyvars fexburTi, uyvars Wadraki

(d) fexburTis moyvarul arc erT biWs ar uyvars Wadraki

18. kodala, SoSia, guguli da Cxikvi simindis marcvals Semousxdnen (ara

aucileblad am TanmimdevrobiT). am marcvals isini niskartiT ugorebdnen

erTmaneTs im wesis dacviT, rom marcvlis gagoreba mxolod marcxniv mjdomisTvis

SeiZleboda. simindis marcvali Cxikvisgan axla SoSiam miiRo.

romeli frinveli miiRebs simindis marcvals kidev oTxi gagorebis Sedegad?

(a) SoSia

(b) guguli

(g) kodala

(d) Cxikvi

8




kosmosis aTviseba, msoflio okeanis Seswavla, gamomTvleli manqanebis Seqmna

da mravali sxva miRweva adamianis saqmianobis sxvadasxva sferoSi _ xSirad

ukavSirdeba cocxal organizmTa: futkris, Ramuris, delfinis da a.S.

fiziologiuri da anatomiuri Taviseburebebis Seswavlas. es arcaa gasakviri.

yvelaferi, rac ki dRemde Seuqmnia adamians, uferuldeba im efeqturi da

kompaqturi "mowyobilobebis" winaSe, romlebiTac aRWurvilia frinvelis frTebi, Tevzis farflebi da a.S. mecnierebas, romelic sainJinro amocanebis

gadasawyvetad biologiur sistemebsa da procesebs swavlobs, bionika ewodeba.

bionikis devizia: "cocxali prototipebi* axali teqnikis gasaRebia". cocxali bunebis Sesaxeb arsebuli codnis sainJinro amocanaTa

gadasawyvetad gamoyenebis idea ekuTvnis italiel mxatvars _ leonardo da vinCis,

romelic cdilobda, frinvelTa frenis meqanizmis Seswavlis safuZvelze Seeqmna

safreni aparati _ orniTopteri.

cnobilia, rom delfini Zalian swrafad curavs da gigantur naxtomebs

akeTebs. hidrodinamikosTa** gamoangariSebiT, delfins ar unda SeeZlos curva

saaTSi 20 kilometrze meti siCqariT. sinamdvileSi ki igi or-samjer aWarbebs am siCqares. amerikelma mecnierma jeims greim am movlenas jer kidev 1936 wels

miaqcia yuradReba. igi werda: "delfins an nebismier ZuZumwovarze Svidjer ufro meti Zala aqvs, rac SeuZlebelia, anda igi raRac saswaulebrivi ZaliT axerxebs

wylis winaaRmdegobis Semcirebas". am auxsnelma movlenam _ imoZrao Sens

SesaZleblobebze ufro swrafad _ "greis paradoqsis" saxelwodeba miiRo. ufro gviandelma dakvirvebebma cxadyo, rom delfinis hidrodinamikuri

Tvisebebi gacilebiT ufro srulyofilia, vidre wyalqveSa navebis konstruqciebi.

am faqtiT dainteresdnen mecnierebi. maT Seiswavles delfinis gluvi, mkvrivi kani

da misi analogiiT Seqmnes wyalqveSa navis korpusis "Casacmeli" (garsafari).

saaTSi 70 kilometri siCqaris ganviTarebisas wyalSi aseTi modeli 60 procentiT nakleb winaaRmdegobas xvdeboda, vidre "Caucmeli" navebi. magram es modeli

delfinis kanis mxolod yvelaze uxeS mibaZvas warmoadgens.

amJamad dadgenilia, rom curvis procesSi, kanis garegani Sris

Taviseburebebis garda, wylis winaaRmdegobis daZlevis saqmeSi did rols

asrulebs delfinis Tavis tvini. igi specialuri biodenebis saSualebiT

aregulirebs sxeulis im nawilis kanqveSa kunTovani sistemis funqcionirebas,

sadac garkveul momentSi wylis yvelaze meti winaaRmdegoba igrZnoba.

* prototipi _ risame pirveladi nimuSi, pirvelsaxe

** hidrodinamikosi _ mecnieri, romelic Seiswavlis myari sxeulebis moZraobas

siTxeSi

9

19. ras swavlobs bionika?

(a) adamianis sainJinro saqmianobis ganviTarebis kanonzomierebas, teqnikuri

progresis daCqarebis mizniT

(b) cocxal organizmTa fiziologiur da anatomiur Taviseburebebs, teqnikis

ama Tu im amocanis gadaWris mizniT

(g) zogierTi cxovelis kompaqtur "mowyobilobebs", gare samyarosTan misi urTierTobis asaxsnelad

(d) cocxal organizmTa biologiur sistemebs, maTi funqcionirebis zogadi

kanonzomierebebis dasadgenad

20. im epizodis saSualebiT, romelSic leonardo da vinCis Sesaxebaa saubari, avtori:

(a) gvacnobs cocxali bunebis Sesaxeb arsebuli codnis gamoyenebiT sainJinro

amocanis gadawyvetis pirvel mcdelobas

(b) gamokveTs frinvelTa frenis meqanizmis srulyofilebas safren aparatTan _

orniTopterTan SedarebiT

(g) gvacnobs bionikis, rogorc mecnierebis, Tanamedrove meTodebsa da miRwevebs

(d) gamokveTs italieli mxatvris moRvaweobis sferoTa mravalferovnebas

21. teqstis mixedviT, hidrodinamikosebisTvis auxsneli iyo is, rom:

(a) delfinis curvis siCqare aRemateba orniTopteris frenis siCqares

(b) delfins ar SeuZlia saaTSi 20 – 30 km-ze meti siCqariT curva

(g) delfins aqvs unari, mniSvnelovnad Seamciros wylis winaaRmdegoba

(d) delfins nebismier ZuZumwovarze Svidjer ufro meti Zala aqvs

22. ra Sedegi mohyva delfinis kanis struqturis Seswavlas?

(a) gaumjobesda Tanamedrove safreni aparatebis konstruqcia

(b) dadginda navis moZraobisas wylis winaaRmdegobis gazrdis meqanizmi

(g) gamoicada leonardo da vinCis mier Seqmnili xomaldis konstruqciebi

(d) daixvewa zogierTi tipis xomaldis hidrodinamikuri Tvisebebi

10

23. kanis gansakuTrebuli Tvisebebis garda, ra exmareba delfins swraf curvaSi?

(a) kanis garegani Sre, romelic ganapirobebs specialuri biodenebis

funqcionirebas

(b) Tavis tvini, romelic biodenebiT aregulirebs wylis dinebaTa mimarTulebebs

(g) Tavis tvini, romelic biodenebis meSveobiT awesrigebs kanqveSa kunTovani

sistemis funqcionirebas

(d) specialuri biodenebi, romlebic uzrunvelyofs Tavis tvinis funqcionirebas

curvis procesSi

24. ra mimarTebaa bolo abzacsa da mTel teqsts Soris?

(a) bolo abzacSi Sejamebulia teqstSi mimoxiluli sakiTxi

(b) bolo abzacSi ganzogadebulia teqstSi moyvanili konkretuli faqtebi

(g) bolo abzacSi gamoTqmuli daskvna ewinaaRmdegeba teqstSi warmodgenil

debulebebs

(d) bolo abzacSi mocemulia teqstSi ganxiluli mniSvnelovani movlenis kidev

erTi mizezi

25. romeli winadadeba gamoxatavs amomwuravad am teqstis mTavar saTqmels?

(a) greis paradoqsia _ "imoZrave Sens SesaZleblobebze ufro swrafad"

(b) delfinis hidrodinamikuri Tvisebebi ufro srulyofilia, vidre wyalqveSa

navebis konstruqciebi

(g) "cocxali prototipebi axali teqnikis gasaRebia"

(d) bionika biologiuri sistemebis kanonzomierebebs arRvevs

11

analogiebi





urTierTdakavSirebuli sityvebis wyvili. SearCieT maTgan is wyvili, romelSic



Tanmimdevroba.



(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi


26. Zafi : Toki

(a) kokori : kvirti

(b) Txili : kakali

(g) cikani : Txa

(d) nakaduli : mdinare

27. Tevzi : layuCi

(a) roiali : klaviSi

(b) xe : wiwvi

(g) gza : asfalti

(d) tansacmeli : Rili

28. kinostudia : reJisori

(a) qveyana : turisti

(b) klasi : maswavlebeli

(g) matarebeli : mgzavri

(d) gundi : momRerali

29. devi : devgmiri

(a) qari : qariSxali

(b) gveli : gveleSapi

(g) kaci : kacobrioba

(d) lomi : lomguli

12

30. varskvlavi : Tanavarskvlavedi

(a) qari : qarbuqi

(b) Rrubeli : wvima

(g) naxazi : naxati

(d) bgera : melodia

31. sasmeli : Rvino

(a) nadimi : kerZi

(b) wigni : yda

(g) qsovili : abreSumi

(d) sawoli : taxti

32. natexi : texs

(a) tivi : tivtivebs

(b) nergi : rgavs

(g) sarwyavi : rwyavs

(d) xnuli : xnavs

33. ynosva : surnelovani

(a) smena : maxvili

(b) grZnoba : sevdiani

(g) Sexeba : myari

(d) metyveleba : mkafio

13

winadadebis Sevseba








34. _____ , visi azriTac, Sav zRvaSi Tevzis raodenobis Semcireba mxolod aqtiuri TevzWeris damRupvel zegavlenas _____. Sav zRvaSi garemos

dabinZurebis Sedegad _____ im Tevzebis ricxvic, romlebic TevzWeris obieqts

ar warmoadgens.

(a) sworad msjelobs is / mowmobs / mcirdeba

(b) cdeba is / ar mowmobs / izrdeba

(g) sworad msjelobs is / ar mowmobs / izrdeba

(d) cdeba is / mowmobs / mcirdeba

35. radgan uxucesi veziri mefis aRmzrdeli iyo da samefo karis saTaTbiros _____, mas _____ mefisTvis rCevis micema, _____ dakisrebuli hqonda mefis

mrCevlis movaleoba.

(a) saTaveSi edga / ara Tu evaleboda / aramed

(b) wevri ar iyo / SeeZlo mxolod / magram

(g) saTaveSi edga / ara Tu SeeZlo / aramed

(d) wevric iyo / mxolod evaleboda / magram

36. gelaTis mxatvroba saocrad hgavs italiuri renesansis pirvel nawarmoebebs, magram yoveli msgavseba _____. arsebobs ideaTa da formaTa _____, romelsac

kulturul garemoebaTa analogia badebs. _____, rom saqarTveloSi

aRmaSeneblisa da Tamaris epoqaSi Tavi iCina zogierTma esTetikurma

mimarTulebam, romelic _____ .

(a) gavleniT rodi aixsneba / sxvaoba / amiTaa ganpirobebuli / srulad mxolod

italiaSi gamovlinda

(b) mxolod gavleniT aixsneba / paralelizmi / Tumca ucnauria / mravalmxriv


(g) gavleniT rodi aixsneba / paralelizmi / amiT aixsneba is / srulad mxolod

italiaSi gamovlinda

(d) mxolod gavleniT aixsneba / sxvaoba / amitom gasakviri araa / mravalmxriv


14

37. ucnauria, magram kognituri disonansis Teoriis Tanaxmad, fsiqologiuri eqsperimentis monawilisaTvis raime movlenisadmi _____ SesaZlebelia _____ , da

ara am Tanxis _____ .

(a) uaryofiTi ganwyobis Seqmna / misTvis gadaxdili gasamrjelos gaormagebiT /

gazrdiT

(b) dadebiTi ganwyobis Seqmna / misTvis gadaxdili gasamrjelos SemcirebiT /

gazrdiT

(g) uaryofiTi ganwyobis Secvla / gaweuli Sromis anazRaurebis ganaxevrebiT /

SemcirebiT

(d) dadebiTi ganwyobis Secvla / gaweuli Sromis anazRaurebis gazrdiT / aSkara

matebiT

logika






naxazis formiT.

38. turisti A qalaqs estumra da aRfrTovanda qalaqis quCebis sisufTaviT, maRali xarisxis gzis safariT da usafrTxo garemoTi. amis sapirispirod,

informaciis masobrivi saSualebebidan mas xSirad smenia A qalaqSi arsebuli rTuli kriminogenuli situaciis, areulobisa da dazianebuli gzebis Sesaxeb.

turistma ivarauda, rom:

informaciis masobrivi saSualebebi mcdar cnobebs avrceleben A qalaqis Sesaxeb.


(a) turisti A qalaqis centralur ubanSi moxvda, romelic, periferiuli ubnebisgan gansxvavebiT, qalaqisTvis aratipurad mowesrigebulia

(b) A qalaqis meria uzrunvelyofs sanimuSo wesrigsa da sisufTaves qalaqis rogorc centralur, aseve periferiul ubnebSi

(g) A qalaqis policiis samsaxuri srulad akontrolebs qalaqis yvela quCas da, Sesabamisad, aq Tavdasxmebi adamianebze arasodes xdeba

(d) informaciis masobrivi saSualebebi, ZiriTadad, eyrdnobian arasarwmuno

wyaroebs, da, Sesabamisad, avrceleben mcdar cnobebs

15

39. davuSvaT:

• tyuilia, rom yvela ofofs Tavze savarcxeli aqvs

• mxolod savarcxlian ofofebs uyvarT sarkeSi yureba


(a) visac sarkeSi yureba ar uyvars, ofofi ar aris

(b) yvela ofofs rodi uyvars sarkeSi yureba

(g) arc erTi, visac sarkeSi yureba uyvars, araa ofofi

(d) yvela, visac Tavze savarcxeli aqvs, rodia ofofi

40. mocemulia debuleba, romelSic daSvebulia Secdoma logikis TvalsazrisiT:

mxolod cisferTvala adamiani SeiZleba iyos qeraTmiani, saidanac gamomdinareobs,

rom ar arsebobs qeraTmiani adamiani, romelsac aqvs cisferi Tvalebi.

qvemoT CamoTvlilTagan romeli Sesworeba unda gamoviyenoT, rom mocemuli

debuleba gaxdes logikurad gamarTuli?

(a) Seicvalos sityva "mxolod" sityviT "yvela" (b) Seicvalos sityva "aqvs" sityviT "ar aqvs" (g) Seicvalos sityva "mxolod" sityviT "zogierTi" (d) SevunacvloT adgili sityvebs "qeraTmiani" da "cisferTvala"

41. megobrebi ana, veriko, Tina da lia magidas irgvliv usxedan (ara aucileblad am TanmimdevrobiT). cnobilia, rom erTi maT Soris yvelaze

maRalia, erTi _ yvelaze Wkviani, erTi _ yvelaze xalisiani, erTi ki – yvelaze

dinji.

aseve mocemulia, rom:

• Tinas erT mxares uzis yvelaze Wkviani megobari, meore mxares _ veriko

• yvelaze xalisianis pirdapir zis ana

• veriko araa yvelaze xalisiani

aRniSnuli oTxi Tvisebidan romeli axasiaTebs lias?

(a) yvelaze maRali

(b) yvelaze Wkviani

(g) yvelaze xalisiani

(d) yvelaze dinji

16




1940 wels mcxeTa-armazSi arqeologiuri gaTxrebis Sedegad aRmoaCines antiku-ri xanis damwerlobis Zeglebi. isini Sesrulebulia qarTulad, qarTuli anbaniT.

kerZod, armazis sapitiaxSo nekropolSi aRmoCenil iqna vercxlis langari,

didi zomis WurWeli (diametri – 48 santimetri). masze Sesrulebulia sami

warwera: maT Soris ori aris berZnuli, xolo erTi Sesrulebulia qarTulad.

qronologiurad jer Sesrulebula pirveli berZnuli warwera, Semdeg _

qarTuli. orive warwera moTavsebulia langris fskerze. berZnuli warwera

gvatyobinebs, rom es nivTi mefe flavios-dades uwyalobebia bercum

pitiaxSisaTvis ("flavios-dade" iberiis mefis sapatio saxelia; es saxelwodeba

iberTa mefes miuRia Tavisi Tanamedrove romis imperatorebis _ flaviosis

sagvareulos pativsacemad). meore, qarTuli warwera ki Seicavs or asos da

moTavsebulia fskeris Suagul adgilas.

im epoqaSi, romelsac ekuTvnis es Zegli (Cveni welTaRricxvis dasawyisi

saukuneebi), qarTul Zeglebze warweris Sesruleba mosalodnelia Semdegi

damwerlobiT: berZnuli, arameuli, qarTuli. magram es asoebi ar aris arc

berZnuli da arc arameuli, udavod qarTulia. pirveli asoa ZvelqarTuli

damwerlobis _ b, xolo meore – q.

ras aRniSnavs es asoebi? radgan asoebi moTavsebulia niSneul adgilas,

safuZveli gvaqvs davaskvnaT, rom es langris patronis inicialebi unda iyos.

Tavdapirvelad saWiroa gaviTvaliswinoT, Tu rogor aRiniSneboda vinaoba uZvelesi

xanis qarTul ZeglebSi. CvenTvis cnobilia vinaobis aRniSvnis sami variacia:

1) saxeli + 2) mamis saxeli; 1) saxeli + 2) Tanamdeboba (tituli); 1) saxeli + 2) Tanamdeboba (tituli) + 3) mamis saxeli. amrigad, safiqrebelia, rom langris inicialebidan pirveli aso "b" pitiaxSis saxels aRniSnavs. berZnuli warweris Tanaxmad, langari bercum pitiaxSs

uwyalobes. maSasadame, qarTuli warweris viTareba ase warmogvidgeba: rodesac

langari, nawyalobevi mefis mier, Semosula bercumis ojaxSi, mas Semdeg fskerze

amouWdeviaT TviT patronis inicialebic.

raki inicialebis pirveli asos mniSvneloba amoxsnilia da warweris

qarTuloba saeWvo aRar aris, ganvagrZoT Zieba meore nawilis amosacnobad.

savaraudod, es aris titulTan dakavSirebuli aso: qarTlisa pitiaxSi. magram

amgvari axsna mainc saTuod unda CaiTvalos. saqme is aris, rom im epoqis yvela

Zeglze armazeli pitiaxSebis tituli aRniSnulia mxolod rogorc "pitiaxSi", "qarTlis" daurTvelad. qarTuli matianeebis Seswavlidan irkveva, rom I _ II saukuneebSi armazeli

pitiaxSebi iberiis mefis TanammarTvelni – moadgileni yofilan; armazeli pitiaxSi

_ uzenaesi xelisufali mefis Semdeg _ iniSneboda TviT mefis uaxloes mkvidrTagan.

isini, pirvel rigSi, mefis Zeni, ufliswulebi iyvnen. da bolos, qarTuli saxeli

iberiis im mefisa, romelic flaviosTa sagvareulos Tanamedrove iyo, aris qarZami.

17

42. qvemoT CamoTvlilTagan romeli asaxavs marTebulad pirveli da meore

abzacebis Sinaarss?

(a) pirvel abzacSi saubaria movlenaze, romlis erT-erT konkretul faqts

gvacnobs teqstis meore abzaci

(b) pirvel abzacSi saubaria konkretul faqtze, romelic ganzogadebulia meore

abzacSi

(g) pirvel abzacSi saubaria Zveli berZnuli, xolo meoreSi _ Zveli qarTuli

damwerlobis Zeglebis Sesaxeb

(d) pirvel abzacSi saubaria qarTuli anbaniT, xolo meoreSi _ berZnuli

anbaniT Sesrulebuli warwerebis Sesaxeb

43. CamoTvlilTagan ra ar aRmoCnda mniSvnelovani qarTuli warweris amosakiTxad?

(a) langarze warweraTa Sesrulebis dro, epoqa

(b) is faqti, rom nekropoli armazeli pitiaxSebis samarxi iyo

(g) pitiaxSis samarxSi aRmoCenili langris aRweriloba: masala, zoma

(d) langarze amotvifruli qarTuli asoebis adgilmdebareoba

44. qvemoT CamoTvlilTagan romeli faqti dasturdeba teqstSi?

(a) langarze pirveli warwera ZvelqarTuli damwerlobiT aris Sesrulebuli

(b) langarze Sesrulebulia sami warwera: berZnuli, arameuli, qarTuli

(g) berZnuli warweris Tanaxmad, bercum pitiaxSs langari mefe flavios-dadesagan

miuRia

(d) langarze inicialebiT aRniSnulia armazeli pitiaxSis saxeli da tituli

45. qarTuli warweris amokiTxvisas teqstis avtori Tavdapirvelad:

(a) yuradRebas amaxvilebs matianeebSi aRniSnul faqtze, rom armazeli pitiaxSebi

mefis mkvidrTagan iniSnebodnen

(b) yuradRebas aqcevs im faqts, rom aRmoCenil Zeglebze armazeli pitiaxSebis

tituls ar erTvis sityva "qarTli" (g) adgens "flavios-dades" Sesabamis qarTul saxels (d) ganixilavs inicialebiT vinaobis aRniSvnis variantebs

18

46. imis dasadgenad, Tu ras aRniSnavs langarze qarTuli warweris (inicialebis) pirveli aso, avtori iTvaliswinebs mxolod:

(a) langarze arsebul berZnul warweras

(b) vinaobis aRniSvnis variaciebs uZvelesi xanis qarTul ZeglebSi

(g) langarze arsebul berZnul warweras da vinaobis aRniSvnis variaciebs

(d) berZnuli da qarTuli warwerebis adgilmdebareobas langarze

47. teqstSi vkiTxulobT:

I _ safiqrebelia, rom langris inicialebidan pirveli aso "b" pitiaxSis saxels aRniSnavs

II _ berZnuli warweris Tanaxmad, langari bercum pitiaxSs uwyalobes

III _ maSasadame, qarTuli warweris viTareba ase warmogvidgeba: rodesac langari,

nawyalobevi mefis mier, Semosula bercumis ojaxSi, mas Semdeg fskerze

amouWdeviaT TviT patronis inicialebic

qvemoT CamoTvlilTagan romeli asaxavs sworad imas, Tu ras warmoadgens

mocemuli winadadebebi?

(a) I _ faqts, II _ varauds, III _ daskvnas

(b) I _ varauds, II _ faqts, III _ daskvnas

(g) I _ faqts, II _ daskvnas, III _ varauds

(d) I _ varauds, II _ daskvnas, III _ faqts

48. warweris kvlevis romel etapze gaCnda sxvadasxva varaudi, sxvadasxva SesaZlo axsna?

(a) roca dasadgeni iyo, Tu romeli damwerlobiT aris Sesrulebuli warwerebi

langarze

(b) rodesac dasadgeni iyo, Tu ras aRniSnavda langarze amotvifruli

inicialebis meore aso

(g) roca zustdeboda qarTuli da berZnuli warwerebis urTierTkavSiri

(d) rodesac daisva sakiTxi, ra saxis warwerasTan gvaqvs saqme _ aris Tu ara

qarTuli asoebi inicialebi

19

49. inicialebis meore nawilis amosacnobad gadamwyveti mniSvnelobis mqone aRmoCnda is faqti, rom:

(a) uZvelesi xanis qarTul Zeglebze inicialebiT aRiniSneboda maTi patronis

vinaoba

(b) im epoqaSi iberiis mefes sapatio saxeli miuRia romis imperatorTa

pativsacemad

(g) langarze qarTuli warwera moTavsebulia fskeris Suagul adgilas

(d) im epoqaSi armazeli pitiaxSebi, umTavresad, ufliswulebi iyvnen

50. romeli daskvnaa marTebuli teqstis mixedviT?

(a) radgan berZnuli warwera bercumis tituls aRniSnavs, SesaZloa, iniciali "q" gamonaklisis saxiT, aqac tituls aRniSnavdes

(b) armazeli pitiaxSi bercumi mefe flavios-dades – igive _ qarZamis Ze unda

iyos

(g) langarze Sesrulebuli berZnuli warwera sakmarisi aRmoCnda qarTuli warweris amosakiTxad

(d) flaviosTa sagvareulos Tanamedrove qarTvel mefeTa saxelebis dadgena

berZnuli saistorio wyaroebis daxmarebiT yofila SesaZlebeli

21

maTematikuri nawili













an · am = an + m

an : am = an – m

(an)m = an · m


5. siCqare: dro

manZilisiCqare =


raodenoba monacemTa



(a - b)2 = a2 – 2ab + b2




kuTxe ki _ patara

kvadratiT.


• ori paraleluri

wrfis mesame wrfiT






hipotenuzis sigrZis



AB2 = AC2 + BC2
















22







meti, airCieT (d).

A B

51. (a) (b) (g) (d)

52. (a) (b) (g) (d)

53. a > 0

(a) (b) (g) (d)

54. (a) (b) (g) (d)

55. ABC samkuTxedSi AB = BC.

(a) (b) (g) (d)

56. (a) (b) (g) (d)

( )257 − 2·3

9,5·48 7,102,327 +

a4− a3−

6,0 7

3

90° ∠A

9-is naturalur gamyofTa jami


23

57.

(a) (b) (g) (d)

58.

(a) (b) (g) (d)

amocanebi

59. ramdeniTaa meti udidesi oTxniSna ricxvi umcires samniSna ricxvze?

(a) 1999-iT (b) 4899-iT

(g) 9899-iT (d) 9900-iT

(e) 9990-iT


(ix. naxazi). moniSnuli wertilebidan A da C wertilebis koordinatebi miTiTebulia naxazze. B wertilis koordinatia: (a) 45 000

(b) 48 000 (g) 50 000 (d) 52 000 (e) 56 000

61. pirvel ujraSi 15-iT naklebi rveulia, vidre meoreSi. ramdeniT naklebi

iqneba pirvel ujraSi rveulebis raodenoba meore ujraSi rveulebis raode-

nobaze, Tu meore ujridan 4 rveuls pirvel ujraSi gadavawyobT? (a) 7-iT (b) 8-iT (g) 9-iT (d) 10-iT (e) 12-iT

62. romel saaTze dawyebula leqcia, Tu is 75 wuTs gagrZelda da 15 saaTze damTavrda?


22aab − ( )aba 2−

piramidis wveroebis

raodenoba

kubis wveroebis

raodenoba

24

monacemTa analizi






63. ramdeni vaJi daibada seqtemberSi? (a) 4173 (b) 3964 (g) 3712 (d) 3392 (e) 3761

64. Tu mTeli wlis ganmavlobaSi axalSobili gogonebis raodenoba vaJebis raodenobaze x-iTaa naklebi, maSin:

(a) x > 4000 (b) 3000 < x < 4000 (g) 2000 < x < 3000 (d) 1000 < x < 2000 (e) x < 1000

65. romel TveSi iyo axalSobil gogonaTa raodenoba yvelaze meti?

(a) III

(b) IV

(g) V

(d) VI

(e) VII

66. ramdeni Tvea iseTi, romelSic axalSobilTa saerTo raodenoba 7200-ze naklebia?

(a) 1 (b) 2 (g) 3 (d) 4 (e) 5

25

amocanebi

67. Tu x – 2y = 6 da 2x – y = 18 , maSin x – y = (a) 24 (b) 12 (g) 11 (d) 9 (e) 8

68. sibrtyeze mocemulia marTkuTxa koordinatTa sistema. ABC tolferda marTkuTxa samkuTxedis A da B wveroebis koordinatebi miTiTebulia naxazze. C wveros koordinatebi (m; n) =

(a) (3; 2) (b) (3; 5)

(g) (6; 1) (d) (8; 3) (e) (8; 1)

69. vaxtangma Tavisi xelfasis

61 nawili gadasaxadebze daxarja. amis Semdeg mas

200 lari darCa. ramdeni lari hqonia vaxtangs xelfasi? (a) 210 (b) 240 (g) 250 (d) 270 (e) 300

70. mevenaxem SarSan 5 tona yurZeni dakrifa, wels ki _ 5,5 tona. ramdeni

procentiT meti yurZeni daukrefia mevenaxes wels SarSandelTan SedarebiT? (a) 5 %-iT

(b) 8 %-iT

(g) 9 %-iT

(d) 10 %-iT

(e) 12 %-iT

71. tolgverda samkuTxedi da ori kvadrati sibrtyeze isea ganlagebuli, rom TiToeul kvadrats am samkuT-

xedTan erTi gverdi saerTo aqvs (ix. naxazi).

ramdeni gradusia β kuTxis sidide? (a) 60° (b) 90° (g) 100° (d) 120° (e) 150°

26

72. ricxvebi 2, x, 3, y, 7, z, 8 zrdis mixedviTaa dalagebuli, amasTan z = x + y. CamoTvlili ricxvebidan romeli SeiZleba iyos y-is toli?

(a) 3,1 (b) 3,8 (g) 5,4 (d) 6,2 (e) 6,9

73. daTos, vaJas da gias or-ori kilogrami Tixa hqondaT. maT sxvadasxva zomis doqebi gamoZerwes. daTom am TixiT gamoZerwa doqebi, romelTagan TiToeulisTvis

0,2 kg Tixa gamoiyena, vaJam TiToeulisTvis _ 0,5 kg, xolo giam TiToeulisTvis _ 1 kg. arc erT maTgans Tixa ar darCenia. sul ramdeni doqi gamouZerwavT bavSvebs?

(a) 12 (b) 14 (g) 15 (d) 16 (e) 18

74. ABCD marTkuTxedi dayofilia 9 tol marTkuT-xedad. M da N wertilebi dayofis Sedegad miRebuli marTkuTxedebis wveroebs emTxveva (ix. naxazi). MNBD oTxkuTxedis farTobia 10 m2

. ramdeni kvadratuli

metria ABCD marTkuTxedis farTobi? (a) 54 (b) 45 (g) 36 (d) 27 (e) 18

75. kasris moculoba miaxloebiT gamoiTvleba formuliT:

sadac V _ kasris moculobaa, D _ kasris diametris sigrZe yvelaze farTo adgilas, d _ kasris fuZis (fskeris) diametris sigrZe, xolo h _ kasris simaRle. risi tolia, am formulis mixedviT, kasris moculoba, Tu

yvelaze farTo adgilas kasris diametris sigrZea 1,1 m, fuZis diametris sigrZe _ 0,8 m, xolo kasris simaRle _ 1 m?

(a) 2,14 m3

(b) 3,14 m3

(g) 4,28 m3

(d) 6,28 m3

(e) 9,42 m3

hdDV ·3

2·14,32⎟⎠⎞

⎜⎝⎛ +

=

27







meti, airCieT (d).

A B

76.

fermerma simindis, xorblisa da

qeris mosavali aiRo. qeris mosavali

3 t iyo. wriul diagramaze miTiTe-bulia, aRebuli mosavlis wonis ra

nawilia xorblisa da simindis wona.

(a) (b) (g) (d)

77.

mimdevrobis pirveli wevria 20, yoveli momdevno wevri ki mis wina wevrze 4-iT naklebia. am mimdevrobis meoTxe wevri a-s tolia.

(a) (b) (g) (d)

78.

Savi zRvis wyalSi marilis wona wylis wonis 2,5%-ia, mkvdari zRvis wyalSi _ 24%.

(a) (b) (g) (d)

simindis mosavlis wona 5 t

a 7

marilis wona, romel-

sac Seicavs 230 kg Savi zRvis wyali


sac Seicavs 25 kg mkvdari zRvis wyali

28

79.

wris radiusis sigrZe 10 decimetrze metia.

(a) (b) (g) (d)

80.

maRaziaSi erTi kviris ganmavlobaSi 260 kg vaSli gaiyida. es am maRaziaSi imave kviraSi gayiduli

xilis mexuTedze metia, magram meoTxedze _ naklebi.

(a) (b) (g) (d)

81.



(a) (b) (g) (d)

82.

ABCD paralelogramis perimetri 20 sm-ia;

MNPQ kvadratis perimetri 8 sm-ia.

(a) (b) (g) (d)

am wris farTobi 320 dm2

900 kg imave kviris ganmavlo-

baSi maRaziaSi gayi-

duli xilis wona

( ) ( )** 12+x ( )*12+x

ABCD parale-logramis farTobi

MNPQ kvadratis farTobi

29

amocanebi

83. 40-is ramdeni procentia 26 ?

(a) 45%

(b) 54%

(g) 56%

(d) 60%

(e) 65% 84. qviSis karieridan qviSa erTnairi satvirTo manqanebiT gaaqvT. TiToeul manqanas yovel dRe imdeni qviSa gaaqvs, ramdenic am karierSi momuSave nebismier

sxva satvirTo manqanas (manqanebi muSaobisas erTmaneTs xels ar uSlian).

3 dRis ganmavlobaSi 4 satvirTo manqanis erTad muSaobiT karieridan 150 tona qviSa gamoitanes. ramden tona qviSas gamoitandnen karieridan 9 dRis ganmavlobaSi 8 satvirTo manqanis erTad muSaobiT?

(a) 450 (b) 600 (g) 750 (d) 900 (e) 1050

85. giam, sandrom da Tornikem kalaTburTis TamaSisas sul 60 qula daagroves. giam 4-jer meti qula daagrova, vidre sandrom, xolo Tornikem _ 30 quliT naklebi, vidre giam da sandrom erTad. ramdeni qula daugrovebia Tornikes?

(a) 30 (b) 25 (g) 20 (d) 15 (e) 10

86. risi tolia tolferda samkuTxedis ferdis sigrZis Sefardeba am samkuTxedis fuZis sigrZesTan, Tu am samkuTxedis perimetri fuZis sigrZeze 5-jer metia?

(a) 52

(b) 56

(g) 2 (d)

25

(e) 3

30

monacemTa analizi







87. Tavisufali drois gatarebis romeli forma daasaxela studentTa yvelaze didma nawilma?

(a) musikis mosmena

(b) wignis kiTxva

(g) seirnoba

(d) televizoris yureba

(e) megobrebTan urTierToba

88. ramdenjer metia im studentTa raodenoba, romlebmac daasaxeles televizo-ris yureba, im studentTa raodenobaze, romlebmac daasaxeles seirnoba?


31

89. gamokiTxuli pirvelkurselebis ramden procents uyvars Tavisufal dros musikis mosmena?

(a) 15%

(b) 20%

(g) 25%

(d) 30%

(e) 35%

90. im gamokiTxul studentTa raodenobebis jami, romlebmac daasaxeles musikis mosmena da wignis wakiTxva, gamokiTxulTa saerTo raodenobis:

(a) naxevarze metia

(b) naxevarze naklebia, magram mesamedze metia

(g) mesamedia

(d) mesamedze naklebia, magram meoTxedze metia

(e) mexuTedia

amocanebi

91. 2000-2004 wlebSi qveyanaSi Semosul turistTa raodenoba yovel wels, wina welTan SedarebiT, 5 aTasiT matulobda. bolo, 2004 wels am qveyanas 45 aTasi turisti estumra. sul ramdeni turisti estumra qveyanas 2000-2004 wlebis

ganmavlobaSi?

(a) 165 aTasi

(b) 175 aTasi

(g) 180 aTasi (d) 195 aTasi

(e) 200 aTasi 92. rombis gverdis sigrZea 25 m, xolo erTi diagonalisa _ 48 m. ramdeni metria am rombis meore diagonalis sigrZe?

(a) 10 (b) 14 (g) 15 (d) 16 (e) 17

32

93. kolofSi mxolod lurji, wiTeli da yviTeli feris burTulebia. lurji burTulebis raodenoba 4-iT naklebia wiTeli burTulebis raodenobaze da 3-jer metia yviTeli burTulebis raodenobaze.

Tu am kolofSi yviTeli burTulebis raodenobas aRvniSnavT m-iT, maSin qvemoT CamoTvlilTagan romeli gamosaxulebiT Caiwereba kolofSi moTavsebuli

samive feris burTulebis raodenoba? (a) 3m + 7 (b) 6m – 7 (g) 6m – 12 (d) 7m – 4 (e) 7m + 4

94. ansamblSi, romelSic 5 mocekvavea, mocekvaveTa saSualo asaki 20 welia. rodesac ansamblSi axali mocekvave _ gurami miiRes, ansamblis mocekvaveTa

saSualo asaki 21 weli gaxda. ramdeni wlis yofila gurami, rodesac igi ansamblSi miiRes?

(a) 21 (b) 22 (g) 24 (d) 26 (e) 28

95. marTkuTxa paralelepipedi, romlis wiboebis sigrZeebia 9 sm, 4 sm da 2 sm, dayves a, b da c marTkuTxa paralelepipedebad, romelTagan b da c kubebia (ix. naxazi). ramdeni kuburi santimetria a marTkuTxa paralelepipedis moculoba?

(a) 56 (b) 60 (g) 64 (d) 68 (e) 72

33

96. a = 6 · 7 · 8 · 9 + 18. risi tolia a ricxvis 7-ze gayofisas miRebuli naSTi?

(a) 2 (b) 3 (g) 4 (d) 5 (e) 6

97. daTos daaviwyda nacnobis telefonis nomris bolo sami cifri, Tumca

axsovda, rom daviwyebuli cifrebidan pirveli cifri kenti iyo, xolo meore

cifri 6-iT meti iyo mesameze. minimum ramdeni sxvadasxva nomeri unda akrifos daTom, raTa man aucileblad SeZlos nacnobTan dakavSireba?

(a) 14

(b) 20

(g) 22 (d) 24

(e) 30

98. Tu a, b, c da d erTmaneTisagan gansxvavebuli 20-ze naklebi naturaluri ricxvebia, maSin a : b – c · d gamosaxulebis udidesi mniSvnelobaa:

(a) 14 (b) 13 (g) 12 (d) 11 (e) 10

34

99. skolaSi 200 moswavlea. im moswavleTa raodenoba, romlebsac hyavT Zma, moswavleTa saerTo raodenobis

53 nawils Seadgens, xolo im moswavleTa

raodenoba, romlebsac hyavT da _ 54 nawils. am skolis moswavleTagan minimum

ramdens hyavs Zmac da dac? (a) 40 (b) 60 (g) 75 (d) 80 (e) 90

100. nbo[jmj or figuras Soris, romlebsac saerTo wertili ar aqvT, ewodeba

umciresi monakveTis sigrZes im monakveTebidan, romlebic erTi figuris werti-

lebs meore figuris wertilebTan aerTebs.

sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 1 sm.

manZili pirvel da meore wreebs Soris 50 sm-ia, xolo meore da mesame wreebs Soris _ 6 sm. qvemoT CamoTvlilTagan romlis toli bs!Tfj[mfcb iyos manZili

pirvel da mesame wreebs Soris?


21

maTematikuri nawili













an · am = an + m

an : am = an – m

(an)m = an · m


5. siCqare: dro

manZilisiCqare =


raodenoba monacemTa



(a - b)2 = a2 – 2ab + b2




kuTxe ki _ patara

kvadratiT.


• ori paraleluri

wrfis mesame wrfiT






hipotenuzis sigrZis



AB2 = AC2 + BC2
















22







meti, airCieT (d).

A B

51. (a) (b) (g) (d)

52. (a) (b) (g) (d)

53. a > 0

(a) (b) (g) (d)

54. (a) (b) (g) (d)

55. ABC samkuTxedSi AB = BC.

(a) (b) (g) (d)

56. (a) (b) (g) (d)

( )257 − 2·3

9,5·48 7,102,327 +

a4− a3−

6,0 7

3

90° ∠A



23

57.

(a) (b) (g) (d)

58.

(a) (b) (g) (d)

amocanebi

59. ramdeniTaa meti udidesi oTxniSna ricxvi umcires samniSna ricxvze?

(a) 1999-iT (b) 4899-iT

(g) 9899-iT (d) 9900-iT

(e) 9990-iT


(ix. naxazi). moniSnuli wertilebidan A da C wertilebis koordinatebi miTiTebulia naxazze. B wertilis koordinatia: (a) 45 000

(b) 48 000 (g) 50 000 (d) 52 000 (e) 56 000

61. pirvel ujraSi 15-iT naklebi rveulia, vidre meoreSi. ramdeniT naklebi

iqneba pirvel ujraSi rveulebis raodenoba meore ujraSi rveulebis raode-

nobaze, Tu meore ujridan 4 rveuls pirvel ujraSi gadavawyobT? (a) 7-iT (b) 8-iT (g) 9-iT (d) 10-iT (e) 12-iT

62. romel saaTze dawyebula leqcia, Tu is 75 wuTs gagrZelda da 15 saaTze damTavrda?


22aab − ( )aba 2−

piramidis wveroebis

raodenoba

kubis wveroebis

raodenoba

24

monacemTa analizi






63. ramdeni vaJi daibada seqtemberSi? (a) 4173 (b) 3964 (g) 3712 (d) 3392 (e) 3761

64. Tu mTeli wlis ganmavlobaSi axalSobili gogonebis raodenoba vaJebis raodenobaze x-iTaa naklebi, maSin:

(a) x > 4000 (b) 3000 < x < 4000 (g) 2000 < x < 3000 (d) 1000 < x < 2000 (e) x < 1000

65. romel TveSi iyo axalSobil gogonaTa raodenoba yvelaze meti?

(a) III

(b) IV

(g) V

(d) VI

(e) VII

66. ramdeni Tvea iseTi, romelSic axalSobilTa saerTo raodenoba 7200-ze naklebia?

(a) 1 (b) 2 (g) 3 (d) 4 (e) 5

25

amocanebi

67. Tu x – 2y = 6 da 2x – y = 18 , maSin x – y = (a) 24 (b) 12 (g) 11 (d) 9 (e) 8

68. sibrtyeze mocemulia marTkuTxa koordinatTa sistema. ABC tolferda marTkuTxa samkuTxedis A da B wveroebis koordinatebi miTiTebulia naxazze. C wveros koordinatebi (m; n) =

(a) (3; 2) (b) (3; 5)

(g) (6; 1) (d) (8; 3) (e) (8; 1)

69. vaxtangma Tavisi xelfasis

61 nawili gadasaxadebze daxarja. amis Semdeg mas

200 lari darCa. ramdeni lari hqonia vaxtangs xelfasi? (a) 210 (b) 240 (g) 250 (d) 270 (e) 300

70. mevenaxem SarSan 5 tona yurZeni dakrifa, wels ki _ 5,5 tona. ramdeni

procentiT meti yurZeni daukrefia mevenaxes wels SarSandelTan SedarebiT? (a) 5 %-iT

(b) 8 %-iT

(g) 9 %-iT

(d) 10 %-iT

(e) 12 %-iT

71. tolgverda samkuTxedi da ori kvadrati sibrtyeze isea ganlagebuli, rom TiToeul kvadrats am samkuT-

xedTan erTi gverdi saerTo aqvs (ix. naxazi).

ramdeni gradusia β kuTxis sidide? (a) 60° (b) 90° (g) 100° (d) 120° (e) 150°

26

72. ricxvebi 2, x, 3, y, 7, z, 8 zrdis mixedviTaa dalagebuli, amasTan z = x + y. CamoTvlili ricxvebidan romeli SeiZleba iyos y-is toli?

(a) 3,1 (b) 3,8 (g) 5,4 (d) 6,2 (e) 6,9

73. daTos, vaJas da gias or-ori kilogrami Tixa hqondaT. maT sxvadasxva zomis doqebi gamoZerwes. daTom am TixiT gamoZerwa doqebi, romelTagan TiToeulisTvis

0,2 kg Tixa gamoiyena, vaJam TiToeulisTvis _ 0,5 kg, xolo giam TiToeulisTvis _ 1 kg. arc erT maTgans Tixa ar darCenia. sul ramdeni doqi gamouZerwavT bavSvebs?

(a) 12 (b) 14 (g) 15 (d) 16 (e) 18

74. ABCD marTkuTxedi dayofilia 9 tol marTkuT-xedad. M da N wertilebi dayofis Sedegad miRebuli marTkuTxedebis wveroebs emTxveva (ix. naxazi). MNBD oTxkuTxedis farTobia 10 m2

. ramdeni kvadratuli

metria ABCD marTkuTxedis farTobi? (a) 54 (b) 45 (g) 36 (d) 27 (e) 18

75. kasris moculoba miaxloebiT gamoiTvleba formuliT:

sadac V _ kasris moculobaa, D _ kasris diametris sigrZe yvelaze farTo adgilas, d _ kasris fuZis (fskeris) diametris sigrZe, xolo h _ kasris simaRle. risi tolia, am formulis mixedviT, kasris moculoba, Tu

yvelaze farTo adgilas kasris diametris sigrZea 1,1 m, fuZis diametris sigrZe _ 0,8 m, xolo kasris simaRle _ 1 m?

(a) 2,14 m3

(b) 3,14 m3

(g) 4,28 m3

(d) 6,28 m3

(e) 9,42 m3

hdDV ·3

2·14,32⎟⎠⎞

⎜⎝⎛ +

=

27







meti, airCieT (d).

A B

76.

fermerma simindis, xorblisa da

qeris mosavali aiRo. qeris mosavali

3 t iyo. wriul diagramaze miTiTe-bulia, aRebuli mosavlis wonis ra

nawilia xorblisa da simindis wona.

(a) (b) (g) (d)

77.

mimdevrobis pirveli wevria 20, yoveli momdevno wevri ki mis wina wevrze 4-iT naklebia. am mimdevrobis meoTxe wevri a-s tolia.

(a) (b) (g) (d)

78.

Savi zRvis wyalSi marilis wona wylis wonis 2,5%-ia, mkvdari zRvis wyalSi _ 24%.

(a) (b) (g) (d)

simindis mosavlis wona 5 t

a 7


sac Seicavs 230 kg Savi zRvis wyali


sac Seicavs 25 kg mkvdari zRvis wyali

28

79.

wris radiusis sigrZe 10 decimetrze metia.

(a) (b) (g) (d)

80.

maRaziaSi erTi kviris ganmavlobaSi 260 kg vaSli gaiyida. es am maRaziaSi imave kviraSi gayiduli

xilis mexuTedze metia, magram meoTxedze _ naklebi.

(a) (b) (g) (d)

81.



(a) (b) (g) (d)

82.

ABCD paralelogramis perimetri 20 sm-ia;

MNPQ kvadratis perimetri 8 sm-ia.

(a) (b) (g) (d)

am wris farTobi 320 dm2

900 kg imave kviris ganmavlo-

baSi maRaziaSi gayi-

duli xilis wona

( ) ( )** 12+x ( )*12+x

ABCD parale-logramis farTobi

MNPQ kvadratis farTobi

29

amocanebi

83. 40-is ramdeni procentia 26 ?

(a) 45%

(b) 54%

(g) 56%

(d) 60%

(e) 65% 84. qviSis karieridan qviSa erTnairi satvirTo manqanebiT gaaqvT. TiToeul manqanas yovel dRe imdeni qviSa gaaqvs, ramdenic am karierSi momuSave nebismier

sxva satvirTo manqanas (manqanebi muSaobisas erTmaneTs xels ar uSlian).

3 dRis ganmavlobaSi 4 satvirTo manqanis erTad muSaobiT karieridan 150 tona qviSa gamoitanes. ramden tona qviSas gamoitandnen karieridan 9 dRis ganmavlobaSi 8 satvirTo manqanis erTad muSaobiT?

(a) 450 (b) 600 (g) 750 (d) 900 (e) 1050

85. giam, sandrom da Tornikem kalaTburTis TamaSisas sul 60 qula daagroves. giam 4-jer meti qula daagrova, vidre sandrom, xolo Tornikem _ 30 quliT naklebi, vidre giam da sandrom erTad. ramdeni qula daugrovebia Tornikes?

(a) 30 (b) 25 (g) 20 (d) 15 (e) 10

86. risi tolia tolferda samkuTxedis ferdis sigrZis Sefardeba am samkuTxedis fuZis sigrZesTan, Tu am samkuTxedis perimetri fuZis sigrZeze 5-jer metia?

(a) 52

(b) 56

(g) 2 (d)

25

(e) 3

30

monacemTa analizi







87. Tavisufali drois gatarebis romeli forma daasaxela studentTa yvelaze didma nawilma?

(a) musikis mosmena

(b) wignis kiTxva

(g) seirnoba

(d) televizoris yureba

(e) megobrebTan urTierToba

88. ramdenjer metia im studentTa raodenoba, romlebmac daasaxeles televizo-ris yureba, im studentTa raodenobaze, romlebmac daasaxeles seirnoba?


31

89. gamokiTxuli pirvelkurselebis ramden procents uyvars Tavisufal dros musikis mosmena?

(a) 15%

(b) 20%

(g) 25%

(d) 30%

(e) 35%

90. im gamokiTxul studentTa raodenobebis jami, romlebmac daasaxeles musikis mosmena da wignis wakiTxva, gamokiTxulTa saerTo raodenobis:

(a) naxevarze metia

(b) naxevarze naklebia, magram mesamedze metia

(g) mesamedia

(d) mesamedze naklebia, magram meoTxedze metia

(e) mexuTedia

amocanebi

91. 2000-2004 wlebSi qveyanaSi Semosul turistTa raodenoba yovel wels, wina welTan SedarebiT, 5 aTasiT matulobda. bolo, 2004 wels am qveyanas 45 aTasi turisti estumra. sul ramdeni turisti estumra qveyanas 2000-2004 wlebis

ganmavlobaSi?

(a) 165 aTasi

(b) 175 aTasi

(g) 180 aTasi (d) 195 aTasi

(e) 200 aTasi 92. rombis gverdis sigrZea 25 m, xolo erTi diagonalisa _ 48 m. ramdeni metria am rombis meore diagonalis sigrZe?

(a) 10 (b) 14 (g) 15 (d) 16 (e) 17

32

93. kolofSi mxolod lurji, wiTeli da yviTeli feris burTulebia. lurji burTulebis raodenoba 4-iT naklebia wiTeli burTulebis raodenobaze da 3-jer metia yviTeli burTulebis raodenobaze.

Tu am kolofSi yviTeli burTulebis raodenobas aRvniSnavT m-iT, maSin qvemoT CamoTvlilTagan romeli gamosaxulebiT Caiwereba kolofSi moTavsebuli

samive feris burTulebis raodenoba? (a) 3m + 7 (b) 6m – 7 (g) 6m – 12 (d) 7m – 4 (e) 7m + 4

94. ansamblSi, romelSic 5 mocekvavea, mocekvaveTa saSualo asaki 20 welia. rodesac ansamblSi axali mocekvave _ gurami miiRes, ansamblis mocekvaveTa

saSualo asaki 21 weli gaxda. ramdeni wlis yofila gurami, rodesac igi ansamblSi miiRes?

(a) 21 (b) 22 (g) 24 (d) 26 (e) 28

95. marTkuTxa paralelepipedi, romlis wiboebis sigrZeebia 9 sm, 4 sm da 2 sm, dayves a, b da c marTkuTxa paralelepipedebad, romelTagan b da c kubebia (ix. naxazi). ramdeni kuburi santimetria a marTkuTxa paralelepipedis moculoba?

(a) 56 (b) 60 (g) 64 (d) 68 (e) 72

33

96. a = 6 · 7 · 8 · 9 + 18. risi tolia a ricxvis 7-ze gayofisas miRebuli naSTi?

(a) 2 (b) 3 (g) 4 (d) 5 (e) 6

97. daTos daaviwyda nacnobis telefonis nomris bolo sami cifri, Tumca

axsovda, rom daviwyebuli cifrebidan pirveli cifri kenti iyo, xolo meore

cifri 6-iT meti iyo mesameze. minimum ramdeni sxvadasxva nomeri unda akrifos daTom, raTa man aucileblad SeZlos nacnobTan dakavSireba?

(a) 14

(b) 20

(g) 22 (d) 24

(e) 30

98. Tu a, b, c da d erTmaneTisagan gansxvavebuli 20-ze naklebi naturaluri ricxvebia, maSin a : b – c · d gamosaxulebis udidesi mniSvnelobaa:

(a) 14 (b) 13 (g) 12 (d) 11 (e) 10

34

99. skolaSi 200 moswavlea. im moswavleTa raodenoba, romlebsac hyavT Zma, moswavleTa saerTo raodenobis

53 nawils Seadgens, xolo im moswavleTa

raodenoba, romlebsac hyavT da _ 54 nawils. am skolis moswavleTagan minimum

ramdens hyavs Zmac da dac? (a) 40 (b) 60 (g) 75 (d) 80 (e) 90

100. nbo[jmj or figuras Soris, romlebsac saerTo wertili ar aqvT, ewodeba

umciresi monakveTis sigrZes im monakveTebidan, romlebic erTi figuris werti-

lebs meore figuris wertilebTan aerTebs.

sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 1 sm.

manZili pirvel da meore wreebs Soris 50 sm-ia, xolo meore da mesame wreebs Soris _ 6 sm. qvemoT CamoTvlilTagan romlis toli bs!Tfj[mfcb iyos manZili

pirvel da mesame wreebs Soris?


kiTxvebi


(rusuli varianti)


1 d d b d d

2 d g g b a

3 g g d g g

4 b b b a d

5 b b g g g

6 g g g b a

7 a a g a b

8 d d a g d

9 d d d d d

10 b b d g a

11 g g b d d

12 a a d d d

13 g b g g a

14 g g b b d

15 g g g b d

16 b b b g a

17 b b a a g

18 g g a g d

19 b b b g g

20 b b a g a

21 d d g b b

22 g g d a d

23 g g g b d

24 d d d d g

25 a a g a g

26 g g d b g

27 b b a b b

28 d d b d g

29 b b d g d

30 a a d b b

31 g g g a a

32 b b d g b

33 d d g b b

34 d d d b b

35 g g g b b

36 g g g d d

37 a a b a a

38 b b a a g

39 g g b b d

40 a a b b d

41 d d b a a

42 d d a g d

43 a a g g a

44 d d g g g

45 d d d d b

46 b b g b d

47 a a b b a

48 g g b d d

49 a a d g a

50 g g b b d

ver

bal

ur

i n

awil

i

kiTxvebi


(rusuli

varianti)


51 a a b g b

52 b b b a a

53 a a b b d

54 b b a b b

55 g g a d b

56 b b b a g

57 d d g b d

58 b b d g a

59 a a g g d

60 d d d b g

61 g g a b d

62 b d g g d

63 d d g e a

64 d d b d d

65 b b a e g

66 a a d g g

67 b b e b a

68 a a e e b

69 g g b d e

70 d d d g d

71 g g d d a

72 a a g e d

73 g g d e e

74 d d g b a

75 e e b d b

76 d d a a g

77 g g a b d

78 a a b g d

79 b b d b a

80 a a a d a

81 d d a d g

82 d d d a b

83 g g e d b

84 a a d b g

85 g g d e b

86 b b g g a

87 e e e e d

88 b b d g a

89 g g b b a

90 g g d e e

91 e e b a d

92 d b a g

93 a a e g e

94 d d d g a

95 d d a e b

96 e e g b d

97 b b b d e

98 e e b g b

99 d d d e g

100 a a e e g

maT

emat

ikur

i

naw

il

i














furcelze).



furclis safuZvelze.




instruqcia


instruqcia



furcelze).



furclis safuZvelze.






III

2

verbaluri nawili

analogiebi








Tanmimdevroba.



(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi


1. kaqtusi : qoTani

(a) Citi : bude

(b) Zroxa : boseli

(g) mela : soro

(d) Tevzi : akvariumi

2. cixesimagre : galavani

(a) mdinare : xidi

(b) suraTi : CarCo

(g) veli : arxi

(d) wigni : furceli

3. sityvamoswrebuli : enamaxvili

(a) Zunwi : xelmokle

(b) erTguli : orpiri

(g) natifi : daxvewili

(d) Tamami : Tavxedi

4. saaTi : isari

(a) kari : saxeluri

(b) dafa : carci

(g) savarZeli : skami

(d) Taro : wigni

3

5. metyveleba : sityva

(a) cekva : ritmi

(b) zRapari : legenda

(g) Tvla : ricxvi

(d) anbani : ieroglifi

6. klde : gamoqvabuli

(a) wyali : Wa

(b) xe : fuRuro

(g) fskeri : ormo

(d) mdinare : kalapoti

7. ganaTeba : naTura

(a) gamocxoba : qura

(b) gaxureba : uTo

(g) gasrola : samizne

(d) gadnoba : yinuli

8. mZivi : samkauli

(a) cxeni : gaxednili

(b) bati : gareuli

(g) vefxvi : mtacebeli

(d) xoWo : mfrinavi

4

winadadebis Sevseba








9. es zamTari, sinoptikosebis informaciiT, _____ unda yofiliyo, Tumca sinamdvileSi is _____ aRmoCnda.

(a) naleqiani \ sakmaod wvimiani

(b) Tbili da mziani \ sakmaod Tbili

(g) civi da susxiani \ sakmaod civi

(d) civi da susxiani \ sakmaod mziani

10. ar SeiZleba iTqvas, rom qarTvelebs _____ gamogveCinos politikur asparezze, _____ , SeiZleba iTqvas, erT dros didi da Zlieri saxelmwifo _____ , da ara

Tu sakuTar qveyanas, _____ ganvagebdiT.

(a) ugunureba / Sesabamisad / dagvisustebia / sakuTar teritoriebsac ki

ugulisyurod

(b) niWiereba / Sesabamisad / aRgvidgenia / dapyrobil teritoriebsac ki

gonivrulad

(g) sruli uniWoba / piriqiT / gvqonia / dapyrobil teritoriebsac ki brZnulad

(d) didi sibrZne / piriqiT / agviyvavebia / sakuTar teritoriebsac ki

gonivrulad

11. TamaSi, rogorc aRzrdis saSualeba, pedagogikis erT-erTi _____ sakiTxia, miuxedavad amisa, dRes mecnierebi da pedagogebi mas _____ .

(a) umniSvnelo / saTanado yuradRebas ar uTmoben

(b) mniSvnelovani / yuradRebiT ikvleven

(g) araaqtualuri / saTanadod ar ikvleven

(d) aqtualuri / saTanado yuradRebas ar uTmoben

5

12. arseboben adamianebi, romlebic _____ . Sesabamisad, isini _____ arian im sferoebSi, sadac SemoqmedebiTi fantaziaa saWiro. _____ , im sferoSi, sadac

gadamwyveti mniSvneloba realistur alRosa da dakvirvebas aqvs, _____ raime

mniSvnelovans.

(a) ar gamoirCevian fantaziis sicxoveliT da siZlieriT / warumatebelni / amis

sapirispirod / ver qmnian

(b) gamoirCevian fantaziis erTferovnebiTa da simwiriT / warmatebulni / swored

amitom / qmnian

(g) ar gamoirCevian fantaziis sicxoveliT da siZlieriT / warmatebulni / Tumca /

qmnian

(d) gamoirCevian fantaziis sicxoveliT da siZlieriT / Seudarebelni / Tumca /

ver qmnian

13. esa Tu is eri, rogori _____ unda iyos is ekonomikurad, _____ , rodesac _____ .

(a) ganviTarebulic / Waobidan iwyebs amosvlas / maradiul Rirebulebebs iviwyebs

(b) warmatebulic / mainc aRwevs mizans / maradiul Rirebulebebs ar aRiarebs

(g) Zlieric / ufskrulisken iwyebs svlas / maradiul Rirebulebebs iviwyebs

(d) uZluric / mainc sastikad marcxdeba / maradiul Rirebulebebs aRiarebs

6

logika






naxazis formiT.

14. gazafxulobiT qalaqis erT-erT sayvavileSi lamazi Taigulebi iyideba. • Taigulebs konaven mxolod iebisgan, enZelebisgan da yoCivardebisgan –

cal-calke an maTi SereviT

• Tu TaigulSi aris enZelebi, aris yoCivardebic

qvemoT CamoTvlilTagan romeli Semadgenlobis Taiguls ver viyidiT am

sayvavileSi?

(a) Taiguls, romelSic samive saxis yvavilia

(b) Taiguls, romelSic mxolod iebi da enZelebia

(g) Taiguls, romelic mxolod iebisgan aris Sekonili

(d) Taiguls, romelSic mxolod enZelebi da yoCivardebia

15. sawarmos xelmZRvanelobam gadawyvita, sakuTari produqciis Sesaxeb

informaciis ukeT gavrcelebis mizniT, saqarTvelos regionebSi am produqciis

satelevizio reklama sagazeTo reklamiT Seecvala.

qvemoT CamoTvlilTagan romeli faqti metyvelebs am gadawyvetilebis

marTebulobaze?

(a) regionebSi Zalze xSirad uyureben televizors, magram gazeTebs iSviaTad

kiTxuloben

(b) regionebs eleqtroenergia Zalze SezRudulad miewodeba, xolo gazeTebs

regularulad iReben

(g) wlis sxvadasxva periodSi sareklamo momsaxurebis fasi icvleba

(d) regionis mosaxleobis naxevari informacias iRebs gazeTiT, naxevari ki – televiziiT

16. davuSvaT, rom: • TuTiyuSebi mxolod tropikul tyeSi cxovroben

qvemoT CamoTvlilTagan romeli ewinaaRmdegeba am debulebas?

(a) Jako tropikul tyeSi cxovrobs da is TuTiyuSia

(b) Jako tropikul tyeSi cxovrobs da is ar aris TuTiyuSi

(g) Jako ar cxovrobs tropikul tyeSi da is TuTiyuSia

(d) Jako ar cxovrobs tropikul tyeSi da is ar aris TuTiyuSi

7

17. sportuli klubis wevrTa Soris arian mxiaruli, Savgvremani da warmosadegi adamianebi. yovelwliurad klubis wevrebi irCeven klubis prezidents amgvari

pirobebis dacviT:

• prezidenti unda iyos mxiaruli

• prezidenti unda iyos an Savgvremani, an warmosadegi, magram ara

orive erTad

qvemoT CamoTvlilTagan romeli debulebidan gamomdinareobs aucileblad, rom

prezidentis arCeva klubis wevrTaganaa SesaZlebeli?

(a) klubis yvela mxiaruli wevri Savgvremania, magram arc erTi maTgani araa

warmosadegi

(b) klubis yvela mxiaruli wevri Savgvremanicaa da warmosadegic

(g) klubis yvela warmosadegi wevri Savgvremania, magram arc erTi ar aris

mxiaruli

(d) klubis arc erTi Savgvremani wevri ar aris arc warmosadegi da arc

mxiaruli

18. ninom, katom, mziam da elenem zafxulis ardadegebze zRvis piras saxli iqiraves. yoveli maTgani sxvadasxva oTaxSi cxovrobs. elenes oTaxs saerTo kari

aqvs katos oTaxTan, aseve saerTo kari aqvs mzias oTaxTan. mzias oTaxs ki ninos

oTaxTan aqvs saerTo kari. oTaxebs Soris sxva damakavSirebeli gza ar arsebobs. vis oTaxSi unda gaiaros katom, rom ninos oTaxSi aRmoCndes?

(a) mxolod elenes oTaxSi

(b) jer mzias, Semdeg ki elenes oTaxSi

(g) jer elenes, Semdeg ki mzias oTaxSi

(d) mxolod mzias oTaxSi

8




kometebi didi zomis ciuri sxeulebia, romlebic iSviaTad gamoCndebian da

moulodneli SemoWriT arRveven cis Cveulebriv, sayovelTaod cnobil suraTs.

isini adamianma uxsovari droidan SeniSna. kometebi periodulad gamoCndebian,

uaxlovdebian mzes da, Sesabamisad, dedamiwasac, da isev uCinardebian Soreul

sivrceSi.

1577 w. tixo brahem (dania) Teoriulad daaskvna, rom kometebi mTvareze

ufro Sors arian. haleim (inglisi) ki daamtkica, rom kometebi gawelil elifsur

orbitebze* moZraoben mzis garSemo. amitom erTi da igive kometa ramdenjerme

SeiZleba mogviaxlovdes. kerZod, man daadgina, rom 1531, 1607 da 1682 wlebSi gamoCenili kometebi erTi da igive obieqtia, romlis mzis irgvliv garemoqcevis

periodi daaxloebiT 76 welia. haleim amave kometis xelaxali gamoCenis weli

iwinaswarmetyvela, rac dadasturda kidec. amis gamo am kometas haleis saxeli

uwodes. ukanasknelad haleis kometam mzis siaxloves 1986 wels gaiara. mzis siaxloves gavlisas mzis sinaTlis wnevis ZaliT kometebidan

amoityorcneba mtvris nawilakebi da Cndeba e.w. kudi, romelic mzis

sawinaaRmdego mxaresaa mimarTuli. Sesabamisad, kometebs kudian varskvlavebs

uwodeben. zogierTi kometis kudi aseulobiT kilometris sigrZisaa. arsebobs

orkudiani da samkudiani kometebic, aseve, anomaliurkudiani kometebi, romelTa

mokle kudi mziskenaa mimarTuli. es imaze metyvelebs, rom kudebis warmoqmnis

meqanizmi sxvadasxvagvari SeiZleba iyos.

kometebis birTvi Sedgeba gayinuli CH4, NH3, H2O da CO2-sagan. kometebi

varskvlavTSorisi sivrcidan SemoiWrebian da periheliumSi** gavlis Semdeg kvlav

uCinardebian. zogjer didi planetebis zemoqmedebiT ama Tu im kometis orbita

sagrZnoblad icvleba. rogorc Cans, ase Seiqmna kometaTa e. w. iupiteris jgufi,

saturnis jgufi da sxva.

zogi kometa mzis zemoqmedebiT TandaTan kargavs masas da iSleba. magaliTad,

bielas kometa or kometad daiSala, Semdeg erT-erTi maTgani daikarga,

samagierod gamoCnda meteoruli nakadi imave orbitaze. axlaxan wamoayenes

hipoTeza, rom 1908 w. tunguskaSi Camovardnili meteoriti erT-erTi kometis _ enkes namsxvrevi iyo.

zogierTi kometa mzes Sordeba plutonis orbitaze aTasjer meti manZiliT.

am kometebis garemoqcevis periodebi milion wels aRwevs. magaliTad, vestis

kometis garemoqcevis periodi daaxloebiT erTi milioni welia, delavanis

kometisa ki _ daaxloebiT ocdaoTxi milioni weli. es sxeulebi mzis sistemis

sazRvrebamde aRweven, zogi ki tovebs kidec mas da varskvlavTSorisSi gadis.

* orbita _ ciuri sxeulis samoZrao gza

** periheliumi _ ciuri sxeulis orbitis wertili, romelic yvelaze ufro

axlosaa mzesTan

9

19. qvemoT CamoTvlilTagan romeli gadmoscems pirveli abzacis ZiriTad azrs?

(a) kometebi moulodnelad SemoiWrebian caze da uaxlovdebian dedamiwas

(b) adamianma uxsovari droidan SeniSna, rom kometebi caze periodulad Cndeba

(g) kometebi ciuri obieqtebia, romlebic periodulad gamoCndebian, uaxlovdebian

mzes da uCinardebian

(d) adamianma uxsovari droidan SeniSna, Tu rogor icvleba cis suraTi

kometebis gamoCeniT

20. ingliseli mecnieris, haleis mosazrebis Tanaxmad:

(a) kometebi mzisgan dedamiwaze ufro Sors arian

(b) zogierTi kometa wrfiv orbitaze moZraobs

(g) kometa SeiZleba orjer an metjer miuaxlovdes mzes

(d) erT-erTi kometa dedamiwis irgvliv moZraobs

21. romel welsaa mosalodneli haleis kometis gamoCena mzis siaxloves?

(a) 2010 wels (b) 2062 wels (g) 2167 wels (d) 2276 wels

22. kometebs kudian varskvlavebsac uwodeben, radgan:

(a) mzis zemoqmedebiT kometebidan erTi mimarTulebiT amoityorcneba mtvris

nawilakebi

(b) mzis sinaTlis wnevis ZaliT kometebis orbita sagrZnoblad icvleba

(g) zogierT kometas ori an sami kudi aqvs, zogs _ arc erTi

(d) zogierTi kometis kudi mziskenaa mimarTuli, zogis ki _ mzis sawinaaRmdego

mxares

10

23. rogor Seiqmna kometaTa e.w. iupiterisa da saturnis jgufebi?

(a) kometebis periheliumSi gavliT

(b) didi planetebis zemoqmedebiT

(g) mzis sinaTlis wnevis ZaliT

(d) meteoruli nakadis zemoqmedebiT

24. qvemoT CamoTvlilTagan romeli movlena araa ganxiluli teqstSi, rogorc mzis zemoqmedebis Sedegi?

(a) enkes namsxvrevis Camovardna

(b) kometebis masis Semcireba

(g) bielas kometis daSla

(d) kometebis birTvis warmoqmna

25. ra aris teqstis ZiriTadi mizani?

(a) kometebis arsebiTi niSnebis mimoxilva

(b) kometebis garemoqcevis periodis gansazRvra

(g) kometebis qimiuri Semadgenlobis dadgena

(d) kometebis Sesaxeb ZiriTadi Teoriebis ganxilva

11

analogiebi








Tanmimdevroba.



(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi


26. urduli : WiSkari

(a) karmidamo : miwa

(b) balTa : qamari

(g) xmali : fari

(d) perangi : sayelo

27. cecxli : naperwkali

(a) grigali : niavi

(b) wyali : Sxefi

(g) miwa : qviSa

(d) xe : kvirti

28. galia : sakani

(a) ezo : Robe

(b) soro : bude

(g) koSki : sarkmeli

(d) bunagi : saxli

29. ankesi : bade

(a) yvavili : Taiguli

(b) zurgCanTa : karavi

(g) motocikli : avtobusi

(d) isari : mSvildi

12

30. rTveli : mevenaxe

(a) doRi : mayurebeli

(b) koncerti : momRerali

(g) qorwili : mzareuli

(d) konkursi : Jiuri

31. talRa : zvirTi

(a) Zewkvi : jaWvi

(b) Rori : taxi

(g) marTve : arwivi

(d) wigni : wignaki

32. sasaxle : Senoba

(a) bgera : musika

(b) speqtakli : piesa

(g) samaia : cekva

(d) saTamaSo : TamaSi

33. gemos SegrZneba : tkbili

(a) ynosva : gamZafrebuli

(b) mxedveloba : vardisferi

(g) smena : daxSuli

(d) Sexeba : faqizi

13

winadadebis Sevseba








34. gamocdaze _____ is sakiTxi Semxvda, romelic _____ , magram mainc _____ friadze.

(a) SemTxveviT \ saerTod ar vicodi \ ver vupasuxe

(b) swored \ wina dRes gavimeore \ ver vupasuxe

(g) samwuxarod \ kargad vicodi \ vupasuxe

(d) sabednierod \ wina dRes gavimeore \ vupasuxe

35. warumatebeli adamianebi _____ cxovroben arsebuli realobiT. _____ , isini orientirebulni arian _____ .

(a) yovelTvis / miuxedavad amisa / realur gancdebsa da awmyo situaciebze

(b) iSviaTad / Sesabamisad / warsulis mogonebebze an momavlis lodinze

(g) arasodes / swored amitom / realur gancdebsa da awmyo situaciebze

(d) xSirad / Sesabamisad / warsulis mogonebebze an momavlis lodinze

36. sascenod gadakeTebisas moTxrobis arsi daumaxinjebiaT: moTxrobis mTavari personaJi - _____ dedakaci scenaze gadaiqca _____ qalad. mizezi amisa is aris,

rom moTxrobaSi misi xasiaTi gamoxatulia _____ scenaze ki - _____ .

(a) sentimentaluri, ybedi / Zlier, Seudrekel / moqmedebiT, saqcieliT / mxolod

sityvebiTa da replikebiT

(b) Zlieri, Seudrekeli / ybed, sentimentalur / mxolod sityvebiTa da

replikebiT / moqmedebiT, saqcieliT

(g) sentimentaluri, ybedi / Zlier, Seudrekel / mozomili sityviTa da

moqmedebiT / mxolod replikebiTa da qceviT

(d) Zlieri, Seudrekeli / ybed, sentimentalur / moqmedebiT, saqcieliT / mxolod


14

37. sakuTari damwerlobisadmi erebis erTgulebas yvelaze kargad espaneTis

ebraelebsa da arabebze dakvirveba gvidasturebs. pirvelni espaneTSi arabTa

batonobis dros _____ Seqmnili mniSvnelovani literatura dagvitoves, magram

igi _____ iyo dawerili. aseve, arabebma mSobliur enad _____ da am enaze

Seqmnes brwyinvale literatura, romelic _____ iyo Sesrulebuli.

(a) arabulad laparakobdnen da arabul enaze / maTive sakuTari ebrauli anbaniT /

espanuri SeiTvises / arabuli damwerlobiT

(b) arabulad laparakobdnen da espanur enaze / maTive sakuTari ebrauli anbaniT /

espanuri SeiTvises / espanuri anbanis gamoyenebiT

(g) ebraul enaze laparakobdnen da ebraul enaze / arabuli anbaniT / espanuri

ver SeiTvises / ebrauli damwerlobiT

(d) ebraul enaze laparakobdnen da espanur enaze / arabuli anbaniT / arabuli

SeiTvises / espanuri anbanis gamoyenebiT

logika






naxazis formiT.

38. giorgi, levani da sandro erTi saxlis pirvel, meore da mesame sarTulebze cxovroben (ara aucileblad am TanmimdevrobiT). maTgan erT-erTma icis mxolod

fexburTis TamaSi, meorem _ mxolod Wadrakis, mesamem ki _ mxolod kalaTburTis.

• is, vinc pirvel sarTulze cxovrobs, TamaSobs kalaTburTs

• is, vinc giorgis binis zemoT cxovrobs, TamaSobs fexburTs

• is, vinc levanis binis qvemoT cxovrobs, TamaSobs Wadraks

qvemoT CamoTvlilTagan romeli debuleba ar SeiZleba iyos WeSmariti am

mocemulobis pirobebSi?

(a) levani TamaSobs kalaTburTs

(b) giorgi TamaSobs Wadraks

(g) sandro TamaSobs kalaTburTs

(d) levani TamaSobs fexburTs

15

39. viciT, rom arsebobs mdinareebi, romlebic tbaSi Caedineba. mocemulia:

• yvela mdinare, romelic tbaSi Caedineba, civia

• wyalmcenare mxolod im mdinareSia, romelic tbaSi Caedineba


(a) yvela civi mdinare tbaSi Caedineba

(b) mdinare, romelSic aris wyalmcenare, civia

(g) mdinare, romelSic ar aris wyalmcenare, ar aris civi

(d) yvela civ mdinareSi aris wyalmcenare

40. davuSvaT, rom arseboben wiTeli lomebi da amasTanave mocemulia:

• yvela wiTel loms aqvs Savi fafari

Tu es debuleba WeSmaritia, maSin qvemoT CamoTvlilTagan romeli SeiZleba iyos

mcdari?

(a) ar arsebobs wiTeli lomi, romelsac ar aqvs Savi fafari

(b) yvela Savfafriani arseba aris wiTeli lomi

(g) arc erTi arseba, romelsac Savi fafari ara aqvs, ar aris wiTeli lomi

(d) arseboben Savfafriani wiTeli lomebi

41. qalaqis A ubani ufro SemaRlebul adgilas mdebareobs, vidre B ubani. binebi A ubanSi ufro Zviria, vidre B ubanSi. ninom amis safuZvelze ivarauda, rom:

A ubanSi binebis siZvires swored am ubnis adgilmdebareoba ganapirobebs.

qvemoT CamoTvlilTagan romelma faqtma SeiZleba ganamtkicos es varaudi?

(a) A ubanTan SedarebiT, B ubanSi binebi ukeTesi proeqtis mixedviTaa aSenebuli (b) B ubanSi gacilebiT uaresi eleqtromomaragebaa, vidre A ubanSi (g) A ubanSi binebi ufro prestiJuli samSeneblo firmis mieraa aSenebuli,

vidre B ubanSi (d) B ubanTan SedarebiT, A ubanSi quCebi gacilebiT ufro keTilmowyobilia

16




tim severins _ inglisel mkvlevar-mogzaurs _ miznad dausaxavs Zvelad

ganxorcielebul mogzaurobaTa rekonstruqcia werilobiT wyaroebSi Semonaxuli

cnobebis safuZvelze, imave wesiTa da xerxebiT, romlebic aRweril epoqas

Seesatyviseboda.

1984 wels man eqsperimenti ganaxorciela: gaimeora argonavtebis laSqroba. mecnierTa erTi nawili amtkicebda, rom Zalian Zlieri da swrafi dinebis gamo

SeuZlebeli iqneboda dardanelisa da bosforis sruteebis gacurva da Sav

zRvaSi Sesvla Zv. w. VII saukunemde, e. i. manam, sanam berZnebi gamoigonebdnen e.

w. pentakonters, anu ormocdaaTniCbian xomalds. radgan mikenur epoqaSi (Zv. w. II

aTaswleulis II naxevarSi) berZnuli xomaldebi gacilebiT patara zomis iyo, tim

severinma gadawyvita eqsperimentis Catareba _ ocniCbiani naviT Sav zRvaSi

Semosvla da rionze (Zvel fazisze) aRmasvla.

Seiqmna axali "argo", ocniCbiani galeri _ berZnuli sabrZolo xomaldis zusti asli. xomaldis mSenebloba naxevar welze met xans grZeldeboda. maisis

pirvel ricxvebSi saberZneTis qalaq volosidan (Zveli iolkosidan) axalma "argom" gezi Savi zRvis sanapiroebisken aiRo. tim severinma megzurad apolonios

rodoselis poema "argonavtika" airCia. "argo" zustad imeorebda Zveli argonavtebis ara mxolod marSruts, aramed

curvis wessac. xomaldi micuravda napir-napir, iseve, rogorc es Zvel mwerlebs

aqvT aRwerili. mxolod 16 ivniss SeZlo "argom" Sav zRvaSi Semosvla. tim

severinis ekipaJs mravali faTeraki gadaxda Tavs. miuxedavad didi gansacdelisa,

mas arc kompasi gamouyenebia, arc raciisTvis miumarTavs. tim severinma Zveli

mogzaurebis msgavsad, talRebis moyvanilobisa da qaris mimarTulebis mixedviT

zustad gansazRvra xmeleTis adgilmdebareoba da xomaldi sanapiros miayena.

eqsperimenti warmatebiT dasrulda. axalma "argom" zustad gaimeora

apolonios rodoselis mier aRwerili gza argonavtebisa, daZlia yvela siZnele,

bosforis srutiT Semovida Sav zRvaSi, moadga Zveli kolxeTis sanapiroze qalaq

foTs da ganaxorciela TiTqmis rvasaaTiani aRmasvla mdinare rionze. tim

severinis eqspediciam saboloo banaki Tanamedrove WyviSTan, vanis naqalaqarTan

axlos daido. eqspediciis mecnieruli Sedegebi aqve Seajames. tim severinma

eqsperimentulad daamtkica, rom berZenTa pirveli mogzauroba Zvel kolxeTSi

namdvilad SesaZlebeli iyo jer kidev Zv. w. XIII saukuneSi, e. i. gvianbrinjaos

epoqaSi.

antikuri xanis kolxuri civilizacia md. rionis gayolebaze jerjerobiT

yvelaze ufro TvalsaCinod vanSia gamovlenili, Tumca gvianbrinjaos xanis

mikenuri arqeologiuri Zeglebi jer ar aRmoCenila. Zveli argonavtebis laSqroba

arsebiTad pirveli eqspedicia iyo mamaci zRvaosnebisa, Soreuli qveynebisken rom

miiltvodnen saxelisa da simdidris mosaxveWad. safiqrebelia, rom aseTi

mogzauroba kolxeTSi ver datovebda nivTier kvals.

17

42. ra daisaxa miznad ingliselma mecnierma-mogzaurma tim severinma?

(a) Zvelad ganxorcielebul mogzaurobaTa gameoreba Tanamedrove teqnikuri

saSualebebis gamoyenebiT

(b) dausaxlebeli miwebis aRmoCena werilobiT wyaroebSi Semonaxuli cnobebis

safuZvelze

(g) Zvelad ganxorcielebul mogzaurobaTa gameoreba Sesabamis epoqaSi (warsulSi)

arsebuli saSualebebis gamoyenebiT

(d) werilobiT wyaroebSi Semonaxuli cnobebis safuZvelze Zveli kolxeTis

migneba

43. tim severinma mogzaurobisaTvis ocniCbiani xomaldi airCia, radgan:

(a) ingliseli mecnierebi ZiriTadad ocniCbiani xomaldebiT mogzauroben

(b) Zv. w. VII saukunemde Zveli berZnebi mxolod pentakonteriT mogzaurobdnen

(g) mikenur epoqaSi berZnebi ocniCbiani xomaldebiT mogzaurobdnen

(d) mikenur epoqaSi bosforis da dardanelis sruteebis gacurva mxolod

pentakonteriT iyo SesaZlebeli

44. axalma "argom" daicva Zveli berZeni mwerlebis mier aRwerili curvis wesic, anu:

(a) gezi Savi zRvis sanapiroebisken aiRo

(b) megzurad apolonios rodoselis "argonavtika" airCia (g) napir-napir micuravda

(d) rionze rvasaaTiani aRmasvla ganaxorciela

45. tim severinma xmeleTis adgilmdebareoba zustad gansazRvra:

(a) Zveli berZnuli kompasis saSualebiT

(b) berZnuli istoriuli rukebis daxmarebiT

(g) Zveli kolxuri wyaroebis daxmarebiT

(d) talRebis moyvanilobisa da qaris mimarTulebis mixedviT

18

46. qvemoT CamoTvlilTagan romelia tim severinis marSruti?

(a) volosi _ dardaneli _ bosfori _ Savi zRva _ WyviSi _ fazisi _ foTi

(b) volosi _ dardaneli _ bosfori _ Savi zRva _ foTi _ fazisi _ WyviSi

(g) iolkosi _ Savi zRva _ foTi _ fazisi _ dardaneli _ bosfori _ WyviSi

(d) iolkosi _ Savi zRva _ dardaneli _ bosfori _ WyviSi _ foTi _ fazisi

47. tim severinma eqsperimentulad daamtkica, rom:

(a) antikuri xanis kolxuri civilizacia Zveli argonavtebis mogzaurobis

gavlenas ganicdida

(b) berZenTa pirveli mogzauroba kolxeTSi jer kidev mikenur epoqaSi iyo

SesaZlebeli

(g) mdinare rionze aRmasvla pentakonteriT SeuZlebeli iyo

(d) axali " argo" berZnuli sabrZolo xomaldis zusti aslia

48. CamoTvlilTagan romeli informacia ar dasturdeba teqstSi?

(a) vanSi SemorCenilia antikuri xanis kolxuri civilizaciis kvali

(b) tim severinis eqspediciam Tavisi Sedegebi vanis naqalaqarTan, WyviSSi Seajama

(g) vanSi jerjerobiT ar aRmoCenila gvianbrinjaos xanis mikenuri kulturis

Zeglebi

(d) tim severinis eqspedicias Sedegad mohyva argonavtebis mogzaurobis

damadasturebeli arqeologiuri masalis aRmoCena

19

49. SeavseT Semdegi winadadeba ise, rom igi marTebuli iyos teqstis mixedviT:

argonavtebis mier _____ ganxorcielebuli mogzauroba simdidrisa da saxelis

moxveWas isaxavda miznad da, savaraudod, _____ . albaT amiT aixsneba is, rom

rionis napirebze _____ .

(a) mikenur epoqaSi \ mniSvnelovan kvals daaCnevda kolxur kulturas \ gvxvdeba

antikuri xanis kolxuri civilizaciis Zeglebi

(b) Zv. w. VII saukuneSi \ mniSvnelovan kvals daaCnevda kolxur kulturas \ am

periodis mravali arqeologiuri Zeglia aRmoCenili

(g) mikenur epoqaSi \ ver datovebda nivTier kvals \ mikenuri arqeologiuri

Zeglebi araa aRmoCenili

(d) Zv. w. II aTaswleulSi \ ver datovebda nivTier kvals \ xSirad gvxvdeba

mikenuri arqeologiuri Zeglebi

50. ra aris mocemuli teqstis ZiriTadi mizani?

(a) sazRvaosno eqspediciaTa mecnieruli Sedegebis Sejameba

(b) ingliseli mkvlevris mier ganxorcielebuli eqsperimentis aRwera

(g) Zvel argonavtTa mier ganxorcielebuli eqspediciis aRwera

(d) mikenur epoqaSi ganxorcielebuli mogzaurobis Sedegebis Sejameba

21

maTematikuri nawili













an · am = an + m

an : am = an – m

(an)m = an · m


5. siCqare: dro

manZilisiCqare =


raodenoba monacemTa



(a - b)2 = a2 – 2ab + b2




kuTxe ki _ patara

kvadratiT.


• ori paraleluri wrfis mesame wrfiT






hipotenuzis sigrZis



AB2 = AC2 + BC2

• samkuTxedis farTobi samkuTxedis gverdis sigrZisa da Sesabamisi simaRlis




da siganis namravlis tolia: S = ab; • paralelogramis farTobi misi gverdis

sigrZisa da am gverdis Sesabamisi simaRlis

namravlis tolia: S = ah.








22







meti, airCieT (d).

A B

51.

(a) (b) (g) (d)

52.

(a) (b) (g) (d)

53.

x < 0, y > 0

(a) (b) (g) (d)

54.

(a) (b) (g) (d)

55.

ABC marTkuTxa samkuTxedSi ∠C = 90° da ∠A > ∠B.

(a) (b) (g) (d)

( )367− 67 −

(675 – 179) · 87 (673 – 188) · 87

1 xy

74 8,0

∠B 40°

23

56.

(a) (b) (g) (d)

57.

(a) (b) (g) (d)

58.

xuTkuTxa piramidas

sul 10 wibo aqvs.

(a) (b) (g) (d)

amocanebi

59. ramdenjeraa meti udidesi samniSna ricxvi umcires orniSna ricxvze? (a) 10-jer

(b) 9,9-jer (g) 99,9-jer

(d) 10,1-jer

(e) 10,9-jer

60. ricxvTa RerZi masze moniSnuli wertilebiT dayofilia tol

monakveTebad (ix. naxazi). moniSnuli

wertilebidan B da C wertilebis koordinatebi miTiTebulia naxazze.

A wertilis koordinatia: (a) 800 (b) 810 (g) 820 (d) 830 (e) 840

15-isa da 25-is umciresi saerTo

jeradi


jeradi

( ) xx 63 2 +− 102 +x

eqvskuTxa piramidis

wiboebis raodenoba

kubis wiboebis

raodenoba

24

61. mas Semdeg, rac gaCerebaze avtobusidan 4 mgzavri Cavida, xolo 9 mgzavri amovida, avtobusSi 32 mgzavri aRmoCnda. ramdeni mgzavri yofila avtobusSi am gaCerebamde?

(a) 22 (b) 27 (g) 28 (d) 36 (e) 41

62. koncerti dagvianebiT daiwyo. is 85 wuTs gagrZelda da 22 saaTze

damTavrda. romel saaTze dawyebula koncerti? (a) 19 sT 35 wT (b) 20 sT 25 wT (g) 20 sT 35 wT (d) 21 sT 25 wT (e) 21 sT 35 wT

monacemTa analizi

cxrilSi miTiTebulia, Tu ramdeni lari iyo zogierTi sakvebi produqtis

saSualo fasi sxvadasxva wels (1995 wlidan 1998 wlis CaTvliT)

1995 1996 1997 1998 saqonlis xorci (1 kg) 3.72 3.30 3.80 4.10

Roris xorci (1 kg) 3.88 3.70 4.00 4.20

qaTami (1 kg) 4.62 4.50 4.00 3.62

kvercxi (10 cali) 1.30 1.40 1.50 1.60

karaqi (1 kg) 5.20 5.00 5.00 6.20

yveli (1 kg) 4.90 3.80 3.80 3.80

Saqris fxvnili (1 kg) 0.80 0.91 0.84 0.97

xorblis fqvili (1 kg) 0.85 1.00 0.94 1.00

Rvino (0.7 litri) 1.13 1.37 1.37 1.37


63. ramdeni lari iyo 1 kg yvelis saSualo fasi 1995 wels? (a) 3.60 (b) 3.80 (g) 4.50 (d) 4.62 (e) 4.90

25

64. qvemoT CamoTvlilTagan romeli produqtis saSualo fasi Semcirda 1997 wels wina welTan SedarebiT?

(a) saqonlis xorcis

(b) Roris xorcis

(g) yvelis

(d) xorblis fqvilis

(e) Rvinis

65. romeli produqtis saSualo fasi imatebda yovelwliurad 1995-1998 wlebSi?

(a) Roris xorcis

(b) qaTmis

(g) Saqris fxvnilis

(d) xorblis fqvilis

(e) kvercxis

66. ra farglebSi meryeobda (icvleboda) Roris xorcis saSualo fasi 1995-1998 wlebSi?

(a) 3.70-sa da 4.00 lars Soris (b) 3.88-sa da 4.00 lars Soris (g) 3.70-sa da 4.20 lars Soris (d) 4.00-sa da 4.20 lars Soris (e) 3.88-sa da 4.20 lars Soris

amocanebi

67. Tu x – 2y = 1 da – x + 6y = 7 , maSin 5y = (a) 5 (b) 10 (g) 15 (d) 20 (e) 25

68. sibrtyeze mocemulia marTkuTxa koor-dinatTa sistema. ABC tolferda samkuTxedis AC fuZe x-RerZis paraleluria. samkuTxedis A da B wveroebis koordinatebi miTiTebulia naxazze. C wveros koordinatebi (a; b) =

(a) (5; 7) (b) (7; 8) (g) (2; 7) (d) (8; 2) (e) (9; 2)

26

69. kolofSi mxolod Savi da wiTeli feris fanqrebia. Savi fanqrebis raode-noba fanqrebis saerTo raodenobis

87 nawilia, xolo wiTelia 4 cali fanqari.

sul ramdeni cali fanqaria am kolofSi? (a) 24 (b) 28 (g) 30 (d) 32 (e) 36

70. mariamis xelfasi 10%-iT momatebis Semdeg 132 lari gaxda. ramdeni lari iyo mariamis xelfasi momatebamde?

(a) 108 (b) 110 (g) 120 (d) 122 (e) 130

71. erT sibrtyeze mdebare a, b, c da d wrfeebidan a wrfe paraleluria b wrfis, xolo c wrfe _ d-si. a da c wrfeebiT Seqmnili blagvi kuTxis sididea 115° (ix. naxazi). risi tolia b da d wrfeebiT Seqmnili maxvili kuTxis sidide?

(a) 35° (b) 45° (g) 55° (d) 65° (e) 75°

72. ricxvebi m, 7, 9, 13, n, 17 zrdis mixedviTaa dalagebuli da cnobilia, rom m = n – 11. CamoTvlili ricxvebidan romeli ar SeiZleba iyos m-is toli?

(a) 3,2 (b) 4,6 (g) 5 (d) 5,8 (e) 6,3

27

73. dedam zamTrisTvis sami saxis xilis wveni moimaraga: vaSlis, qliavis da

alublis, TiToeuli _ 4 litri. vaSlis wveni mTlianad Seinaxa 0,5 l tevadobis qilebSi, qliavis _ 0,8 l tevadobis qilebSi, xolo alublis _ 1 l tevadobis qilebSi (dedam yvela qila bolomde Seavso). sul ramdeni qila gamouyenebia

dedas xilis wvenis Sesanaxad? (a) 12 (b) 14 (g) 15 (d) 16 (e) 17

74. ABCD marTkuTxedi dayofilia tol marTkuT-xedebad. M da N wertilebi dayofis Sedegad miRe-buli marTkuTxedebis wveroebs emTxveva (ix. naxazi).

MNCD oTxkuTxedis farTobia 18 dm2. ramdeni

kvadratuli decimetria ABCD marTkuTxedis farTobi?

(a) 20 (b) 24 (g) 26 (d) 28 (e) 30

75. Tu klienti bankSi Seitans x lars, k wlis Semdeg mis angariSze bankSi iqneba p lari. p gamoiTvleba formuliT: p = x(1 + 0,2k). Tanxis Setanidan 5 wlis Semdeg klientis angariSze iyo 7000 lari. ramdeni lari Seutania klients bankSi?

(a) 1400 (b) 2200 (g) 3000 (d) 3500 (e) 3800

28







meti, airCieT (d).

A B

76.

glexma vaSli, msxali da qliavi ga-

yida. gayiduli vaSlis wona 80 kg-ia. wriul diagramaze miTiTebulia,

gayiduli xilis wonis ra nawilia

msxlisa da vaSlis wona.

(a) (b) (g) (d)

77.

mimdevrobis yoveli wevri mis momdevno wevrze 2-iT naklebia. am mimdevrobis meaTe wevria 17, xolo meeqvse wevria b.

(a) (b) (g) (d)

78.

soia Seicavs cxims, romlis wona soias wonis 20%-ia.

rZe Seicavs cxims, romlis wona rZis wonis 4%-ia.

(a) (b) (g) (d)

gayiduli qliavis

wona 35 kg

b 10

cximis wona, romel-

sac Seicavs 12 kg soia

cximis wona,

romelsac Seicavs

60 kg rZe

29

79.

kvadratis gverdis sigrZea 8 sm, wris diametris sigrZec 8 sm-ia.

(a) (b) (g) (d)

80.

biznesmeni, romlis wliuri Semosavali 75 aTas larze metia da 85 aTas larze naklebi, yovelwli-urad Semosavlis mexuTeds qvelmoqmedebaze xarjavs.

(a) (b) (g) (d)

81.

nebismieri a ricxvisaTvis ( )∗a -iT aRniSnulia

udidesi mTeli ricxvi, romelic naklebia a ricxvze.

(a) (b) (g) (d)

82. rombis farTobia 36 sm2

.

(a) (b) (g) (d)

biznesmenis mier qvelmo-

qmedebaze yovelwliurad

daxarjuli Tanxa

16 aTasi lari

( ) ( )** 3,8−a ( )*3,8−a

am rombis perimetri 22 sm

kvadratis farTobs gamok-

lebuli wris farTobi 16 sm2

30

amocanebi

83. 36-is meramdenedi nawilia 27?

(a) 31

(b) 32

(g) 42

(d) 43

(e) 276

84. auzSi wyali ori miliT Caedineba. erTi milis gaxsnisas yovel saaTSi auzSi erTi da imave raodenobis wyali Caedineba. meore milis gaxsnis SemTxvevaSic

auzSi yovel saaTSi erTi da imave raodenobis wyali Caedineba. marto pirveli

miliT carieli auzi 4 saaTSi ivseba, marto meoreTi _ 6 saaTSi. ramden saaTSi aivseba carieli auzi, Tu orive mils erTdroulad gaxsnian?

(a) 2 (b) 2,4 (g) 5 (d) 6,5 (e) 10

85. sastumroSi mxolod 1-adgiliani, 2-adgiliani da 4-adgiliani nomrebia, sul _ 44 nomeri. 2-adgiliani nomrebi imdenia, ramdenic 1-adgiliani da 4-adgiliani nomrebi erTad. sastumroSi sul 84 adgilia. ramdeni 1-adgiliani nomeria sastumroSi?

(a) 12 (b) 13 (g) 14 (d) 15 (e) 16

86. marTkuTxedi dayofilia 3 tol kvadratad. risi tolia am marTkuTxedis perimetris Sefardeba dayofis Sedegad miRebuli kvadratis perimetrTan?

(a) 4 (b) 2,5 (g) 2 (d) 1,5 (e) 1

31

monacemTa analizi

saTamaSoebis maRaziaSi mxolod manqanebi, Tojinebi, burTebi, konstruqtorebi da

naZvis xis saTamaSoebi iyideboda. svetovan diagramaze warmodgenilia am maRaziaSi

erTi Tvis ganmavlobaSi gayiduli sxvadasxva saxis saTamaSoTa raodenobebi:


87. ra saxis saTamaSoebi gayidula yvelaze didi raodenobiT? (a) manqanebi

(b) konstruqtorebi

(g) burTebi

(d) naZvis xis saTamaSoebi

(e) Tojinebi

88. ramdenjer naklebia gayiduli konstruqtorebis raodenoba gayiduli manqanebis raodenobaze?

(a) 2-jer (b) 2,5-jer (g) 3-jer (d) 3,5-jer (e) 4-jer

89. gayiduli saTamaSoebis saerTo raodenobis ramdeni procentia gayiduli naZvis xis saTamaSoebis raodenoba?

(a) 12%

(b) 15%

(g) 18%

(d) 20%

(e) 25%

32

90. gayidul saTamaSoTa saerTo raodenobis meoTxedze metia, magram mesamedze naklebi:

(a) manqanebisa da konstruqtorebis raodenobaTa jami

(b) Tojinebisa da naZvis xis saTamaSoebis raodenobaTa jami

(g) burTebisa da konstruqtorebis raodenobaTa jami

(d) burTebisa da Tojinebis raodenobaTa jami

(e) naZvis xis saTamaSoebisa da burTebis raodenobaTa jami

amocanebi

91. mewarmis Semosavali ianvarSi 1000 lari iyo. TebervalSi misi Tviuri Semosavali 100 lariT gaizarda, martSi _ kidev 100 lariT. aprilidan moyolebuli sami Tvis ganmavlobaSi mewarmis Semosavali yovelTviurad 200 lariT mcirdeboda. sul ramdeni lari iyo mewarmis Semosavali am 6 Tvis ganmavlobaSi?

(a) 5700 (b) 5900 (g) 6000 (d) 6100 (e) 6300

92. ABCD paralelogramis AB gverdi BD diagonalis tolia. B wverodan AD gverdze daSvebuli marTobis sigrZea 5 sm. ramdeni santimetria AB gverdis sigrZe, Tu AD gverdis sigrZe 24 sm-ia?

(a) 13 (b) 14 (g) 15 (d) 16 (e) 18

93. ninom, vaJam da sandrom wignebi SeiZines. ninom 3-iT meti wigni SeiZina, vidre vaJam, xolo sandrom orjer meti, vidre vaJam. ninos mier SeZenili

wignebis raodenobaa n. qvemoT CamoTvlilTagan romeli gamosaxulebiT Caiwereba ninos, vaJas da sandros mier SeZenili wignebis saerTo raodenoba?

(a) 2n + 12 (b) 3n – 9 (g) 4n – 9 (d) 4n – 6 (e) 4n – 3

33

94. sareklamo saagentoSi 7 vaJi da 3 gogona muSaobs. Tu saagentos TanamSromelTa saSualo asaki 27 welia, xolo TanamSromel gogonaTa saSualo asaki _ 20 weli, maSin am saagentos TanamSromel vaJTa saSualo asakia:

(a) 23 weli (b) 24 weli (g) 30 weli (d) 32 weli (e) 34 weli

95. kubi dayves 3 tol marTkuTxa paralelepipedad, romelTagan TiToeulis fuZis wiboebis sigrZeebia 2 sm da 6 sm. ramdeni kuburi santimetria am dayofis Sedegad miRebuli TiToeuli

marTkuTxa paralelepipedis moculoba? (a) 8 (b) 12 (g) 24 (d) 36 (e) 72

96. naturaluri n ricxvis 9-ze gayofisas miRebuli naSTia 7. risi toli iqneba (n + 14)-is 9-ze gayofisas miRebuli naSTi?

(a) 2 (b) 3 (g) 5 (d) 6 (e) 7

97. kolofSi mxolod 8 Savi da 6 wiTeli fanqari awyvia. ilia kolofidan (masSi Cauxedavad) iRebs TiTo fanqars da magidaze debs. minimum ramdeni fanqari

unda amoiRos iliam, rom amoRebul fanqrebs Soris aucileblad iyos orive

feris fanqari? (a) 3 (b) 5 (g) 7 (d) 9 (e) 11

34

98. Tu a, b da c iseTi naturaluri ricxvebia, rom a < 5, b < 3 , c > 20 , maSin

bac − gamosaxulebis umciresi mniSvnelobaa: (a) 3 (b) 4 (g) 5 (d) 6 (e) 7

99. turistTa jgufis yvela wevrma icis germanuli an inglisuri ena. im turistTa raodenoba, romlebmac ician germanuli ena, turistTa saerTo

raodenobis 83 nawilia, xolo im turistTa raodenoba, romlebmac ician

inglisuri ena _ 87 nawili. jgufidan 24-ma turistma icis germanuli enac da

inglisuri enac. sul ramdeni turistia am jgufSi? (a) 64 (b) 72 (g) 80 (d) 88 (e) 96

100. maqsimaluri daSoreba ori figuris wertilebs Soris! vuwodoT udidesi monakveTis sigrZes im monakveTebidan, romlebic erTi figuris wertilebs meore

figuris wertilebTan aerTebs.

sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 1 dm. maqsi-maluri daSoreba pirveli da meore wreebis wertilebs Soris 50 dm-ia, xolo meore da mesame wreebis wertilebs Soris _ 4 dm. qvemoT CamoTvlilTagan romlis toli ar SeiZleba iyos maqsimaluri daSoreba pirveli da mesame wreebis

wertilebs Soris? (a) 47 dm (b) 49 dm (g) 50 dm (d) 53 dm (e) 54 dm

21

maTematikuri nawili













an · am = an + m

an : am = an – m

(an)m = an · m


5. siCqare: dro

manZilisiCqare =


raodenoba monacemTa



(a - b)2 = a2 – 2ab + b2




kuTxe ki _ patara

kvadratiT.








hipotenuzis sigrZis



AB2 = AC2 + BC2















22







meti, airCieT (d).

A B

51.

(a) (b) (g) (d)

52.

(a) (b) (g) (d)

53.

x < 0, y > 0

(a) (b) (g) (d)

54.

(a) (b) (g) (d)

55.


(a) (b) (g) (d)

( )367− 67 −

(675 – 179) · 87 (673 – 188) · 87

1 xy

74 8,0

∠B 40°

23

56.

(a) (b) (g) (d)

57.

(a) (b) (g) (d)

58.

xuTkuTxa piramidas

sul 10 wibo aqvs.

(a) (b) (g) (d)

amocanebi


(b) 9,9-jer (g) 99,9-jer

(d) 10,1-jer

(e) 10,9-jer






jeradi


jeradi

( ) xx 63 2 +− 102 +x

eqvskuTxa piramidis

wiboebis raodenoba

kubis wiboebis

raodenoba

24


(a) 22 (b) 27 (g) 28 (d) 36 (e) 41



monacemTa analizi




Roris xorci (1 kg) 3.88 3.70 4.00 4.20

qaTami (1 kg) 4.62 4.50 4.00 3.62

kvercxi (10 cali) 1.30 1.40 1.50 1.60

karaqi (1 kg) 5.20 5.00 5.00 6.20

yveli (1 kg) 4.90 3.80 3.80 3.80



Rvino (0.7 litri) 1.13 1.37 1.37 1.37



25


(a) saqonlis xorcis

(b) Roris xorcis

(g) yvelis

(d) xorblis fqvilis

(e) Rvinis


(a) Roris xorcis

(b) qaTmis

(g) Saqris fxvnilis

(d) xorblis fqvilis

(e) kvercxis



amocanebi



(a) (5; 7) (b) (7; 8) (g) (2; 7) (d) (8; 2) (e) (9; 2)

26





(a) 108 (b) 110 (g) 120 (d) 122 (e) 130


(a) 35° (b) 45° (g) 55° (d) 65° (e) 75°


(a) 3,2 (b) 4,6 (g) 5 (d) 5,8 (e) 6,3

27







(a) 20 (b) 24 (g) 26 (d) 28 (e) 30


(a) 1400 (b) 2200 (g) 3000 (d) 3500 (e) 3800

28







meti, airCieT (d).

A B

76.





(a) (b) (g) (d)

77.


(a) (b) (g) (d)

78.



(a) (b) (g) (d)

gayiduli qliavis

wona 35 kg

b 10

cximis wona, romel-


cximis wona,

romelsac Seicavs

60 kg rZe

29

79.


(a) (b) (g) (d)

80.


(a) (b) (g) (d)

81.



(a) (b) (g) (d)


.

(a) (b) (g) (d)



daxarjuli Tanxa

16 aTasi lari

( ) ( )** 3,8−a ( )*3,8−a




30

amocanebi


(a) 31

(b) 32

(g) 42

(d) 43

(e) 276




(a) 2 (b) 2,4 (g) 5 (d) 6,5 (e) 10


(a) 12 (b) 13 (g) 14 (d) 15 (e) 16


(a) 4 (b) 2,5 (g) 2 (d) 1,5 (e) 1

31

monacemTa analizi






(b) konstruqtorebi

(g) burTebi


(e) Tojinebi




(a) 12%

(b) 15%

(g) 18%

(d) 20%

(e) 25%

32







amocanebi


(a) 5700 (b) 5900 (g) 6000 (d) 6100 (e) 6300


(a) 13 (b) 14 (g) 15 (d) 16 (e) 18



(a) 2n + 12 (b) 3n – 9 (g) 4n – 9 (d) 4n – 6 (e) 4n – 3

33






(a) 2 (b) 3 (g) 5 (d) 6 (e) 7




34











kiTxvebi


(rusuli varianti)


1 d d b d d

2 d g g b a

3 g g d g g

4 b b b a d

5 b b g g g

6 g g g b a

7 a a g a b

8 d d a g d

9 d d d d d

10 b b d g a

11 g g b d d

12 a a d d d

13 g b g g a

14 g g b b d

15 g g g b d

16 b b b g a

17 b b a a g

18 g g a g d

19 b b b g g

20 b b a g a

21 d d g b b

22 g g d a d

23 g g g b d

24 d d d d g

25 a a g a g

26 g g d b g

27 b b a b b

28 d d b d g

29 b b d g d

30 a a d b b

31 g g g a a

32 b b d g b

33 d d g b b

34 d d d b b

35 g g g b b

36 g g g d d

37 a a b a a

38 b b a a g

39 g g b b d

40 a a b b d

41 d d b a a

42 d d a g d

43 a a g g a

44 d d g g g

45 d d d d b

46 b b g b d

47 a a b b a

48 g g b d d

49 a a d g a

50 g g b b d

ver

bal

ur

i n

awil

i

kiTxvebi


(rusuli

varianti)


51 a a b g b

52 b b b a a

53 a a b b d

54 b b a b b

55 g g a d b

56 b b b a g

57 d d g b d

58 b b d g a

59 a a g g d

60 d d d b g

61 g g a b d

62 b d g g d

63 d d g e a

64 d d b d d

65 b b a e g

66 a a d g g

67 b b e b a

68 a a e e b

69 g g b d e

70 d d d g d

71 g g d d a

72 a a g e d

73 g g d e e

74 d d g b a

75 e e b d b

76 d d a a g

77 g g a b d

78 a a b g d

79 b b d b a

80 a a a d a

81 d d a d g

82 d d d a b

83 g g e d b

84 a a d b g

85 g g d e b

86 b b g g a

87 e e e e d

88 b b d g a

89 g g b b a

90 g g d e e

91 e e b a d

92 d b a g

93 a a e g e

94 d d d g a

95 d d a e b

96 e e g b d

97 b b b d e

98 e e b g b

99 d d d e g

100 a a e e g

maT

emat

ikur

i

naw

il

i














furcelze).



furclis safuZvelze.




instruqcia


instruqcia



furcelze).



furclis safuZvelze.






IV

2

verbaluri nawili

analogiebi








Tanmimdevroba.



(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi


1. cxvari : fara

(a) simRera : misamReri

(b) nabadi : menabde

(g) uremi : urmuli

(d) buCqi : buCqnari

2. magida : skami

(a) dana : Cangali

(b) sufra : qsovili

(g) lambaqi : WurWeli

(d) doqi : sasmeli

3. koconi : fiCxis Segroveba

(a) urika : tvirTis dadeba

(b) Wa : wylis amoxapva

(g) Rvino : yurZnis dawurva

(d) xili : gemos gasinjva

4. burTi : mrgvali

(a) balaxi : norCi

(b) rZe : aWrili

(g) miwa : nayofieri

(d) Tafli : tkbili

3

5. mexsiereba : gulmaviwyi

(a) fantazia : realuri

(b) emocia : naRvliani

(g) yuradReba : dabneuli

(d) azrovneba : sxarti

6. kompasi : mogzauri

(a) maTraxi : mxedari

(b) gakveTili : maswavlebeli

(g) wamali : eqimi

(d) moTxroba : mwerali

7. qaRaldi : wigni

(a) limoni : citrusi

(b) fqvili : namcxvari

(g) yveli : karaqi

(d) vazi : mtevani

8. cxoveli : fafari

(a) fesvi : rto

(b) Tevzi : qviriTi

(g) cxeni : nali

(d) yvavili : ekali

4

winadadebis Sevseba








9. saswavlebelSi sabunebismetyvelo saganTa swavleba ori mimarTulebiT

mimdinareobs: Teoriuli kursis _____ praqtikuli mecadineoba _____ tardeba.

(a) gaxangrZlivebis gamo / aRar

(b) nacvlad / sistematurad

(g) dasrulebis gamo / yoveldRiurad

(d) paralelurad / aucileblad

10. bevri sxva _____, romlebic marto nadiroben, mgeli warmatebuli monadire mxolod _____ nadirobis wyalobiT xdeba, rac nadirobis dros _____

gulisxmobs.

(a) mtaceblisgan gansxvavebiT / jgufuri / funqciebis ganawilebas

(b) mtaceblis msgavsad / jgufuri / damoukideblad moqmedebas

(g) mtaceblis msgavsad / marto / erTobliv moqmedebas

(d) mtaceblisgan gansxvavebiT / marto / TanamoZmeebis aqtiurobas

11. mozardi, patarasTan SedarebiT, xSirad Tavs aridebs Tematur naxats, radgan SiSobs, rom _____ , rogorc Caifiqra. miuxedavad amisa, mozardebis naxatebis

Tematika gacilebiT mravalferovania. es _____ isini xatvis teqnikas _____ .

(a) ise ver daxatavs / gasakviria, miT ufro, rom / mkveTrad aumjobeseben

(b) ise daxatavs / arcaa gasakviri, radgan / kargad ver floben

(g) ise daxatavs / gaugebaria imitom, rom / mudmivad xvewen

(d) ise ver daxatavs / bunebrivia, vinaidan / ukeT floben

5

12. TavisTavad ucxo kapitalis SeWra _____ ama Tu im qveynisTvis, Tu mas win ganviTarebuli Segneba da politikuri Zala _____ . magram roca qveyana erovnul

Segnebasa da saxelmwifo Zalas _____ , ucxo kapitalis gavlena _____ .

(a) sruliad ar warmoadgens safrTxes / ar egebeba / moklebulia /

ganmaviTarebel faqtorad iqceva

(b) seriozul safrTxes warmoadgens / ar egebeba / ar aris moklebuli / Zalze

saxifaTo faqtorad iqceva

(g) seriozul safrTxes warmoadgens / egebeba / ar aris moklebuli / pirdapir

gamanadgurebeli xdeba

(d) sruliad ar warmoadgens safrTxes / egebeba / moklebulia / pirdapir

gamanadgurebeli xdeba

13. damwerlobis ZiriTadi daniSnulebaa raime _____ da ara _____ miRweva. _____ damwerloba yovelTvis _____ zemoqmedebis elements.

(a) cnobis Cawera da gadacema / mxatvruli efeqtis / miuxedavad amisa, / Seicavda

esTetikuri

(b) informaciisadmi SemoqmedebiTi midgoma / esTetikuri zemoqmedebis / swored

amitom / gulisxmobda esTetikuri

(g) informaciis esTetikurad gadmocema / mxatvruli efeqtis / Sesabamisad, /

rodi gulisxmobda esTetikuri

(d) informaciis zustad gadacema / fsiqologiuri zemoqmedebis / miuxedavad

amisa, / ar Seicavda esTetikuri

6

logika






naxazis formiT.

14. dilaadrian mgelma akelam Tvali mohkra msuqan kurdRels nenis da gaekida mas.

• Tu akela nenis daeweva, neni akelas cocxali ver gadaurCeba

• Tu neni akelas cocxali ver gadaurCeba, SuadRisas akela maZRari

daiZinebs

• SuadRisas akelas SimSilisgan ar daeZina


(a) akela daewia nenis da neni akelas cocxali ver gadaurCa

(b) akela daewia nenis, magram neni akelas cocxali gadaurCa

(g) akela ver daewia nenis da neni akelas cocxali ver gadaurCa

(d) akela ver daewia nenis da neni akelas cocxali gadaurCa

15. zafxulis erT dRes sofom axal saparikmaxeroSi wasvla gadawyvita. SesasvlelSi mas am saparikmaxeros damlagebeli gamoelaparaka, romelsac qudi

exura. sofos SekiTxvaze: "ratom gaxuravT qudi am sicxeSi?", damlagebelma upasuxa: "parikmaxerma zedmetad mokled SemWra Tma". sofo saswrafod gamovida saparikmaxerodan, radgan damlageblis naTqvamis safuZvelze ivarauda, rom:

am saparikmaxeroSi araprofesionalebi muSaoben.


(a) saparikmaxeroSi damlagebels, rogorc sakuTar TanamSromels, gansakuTrebuli

mondomebiT SeWres Tma

(b) miuxedavad imisa, rom damlagebeli am saparikmaxeros TanamSromelia, misTvis

momsaxureba aq ufaso araa

(g) saparikmaxero ar sargeblobs didi popularobiT

(d) damlagebelma Tma sxva saparikmaxeroSi SeiWra

7

16. davuSvaT, rom:

• arc erT meTevzes ar hyavs kata

• yvelas, visac ar hyavs kata, axuravs qudi


(a) yvela meTevzes axuravs qudi

(b) yvela, visac axuravs qudi, meTevzea

(g) mxolod zogierT meTevzes axuravs qudi

(d) arc erT meTevzes ar axuravs qudi

17. magidaze oTxi yuTi devs Semdegi TanmimdevrobiT: wiTeli, yviTeli, mwvane da lurji.

TiToeul yuTSi sabam TiTo burTi Cado: erTSi _ wiTeli, erTSi _ yviTeli,

erTSi _ mwvane da erTSi _ lurji, magram ise, rom:

• arc erT yuTSi ar devs amave yuTis feris burTi

• arc wiTel da arc yviTel yuTSi ar devs lurji burTi

yuTebSi burTebis ganlagebis mocemuli variantebidan romelia SeuZlebeli?

(a) yviTeli, wiTeli, lurji, mwvane

(b) mwvane, wiTeli, lurji, yviTeli

(g) mwvane, lurji, wiTeli, yviTeli

(d) yviTeli, mwvane, lurji, wiTeli

18. davuSvaT, rom: • brZolaSi imarjveben is meomrebi, romlebsac mtkice xasiaTi aqvT, an

gonieri sardali hyavT, anda mokavSireebi

• meomrebma brZolaSi ver gaimarjves

Semdegi debulebebidan romliT aixsneba maTi damarcxeba?

(a) meomrebs mtkice xasiaTi hqondaT

(b) meomrebs ar hqondaT mtkice xasiaTi, Tumca maT hyavdaT mokavSireebi

(g) meomrebs ar hyavdaT mokavSireebi, magram hyavdaT gonieri sardali

(d) meomrebs ar hqondaT mtkice xasiaTi, maT arc gonieri sardali da arc

mokavSireebi hyavdaT

8




dedamiwaze arsebuli mtacebeli frinvelebis 62 procenti sezonur

gadafrenas (migracias) axorcielebs sabudar da sazamTro adgilebs Soris.

sazogadod, am movlenis ZiriTadi mamoZravebeli Zala sakvebis raodenobis

sezonuri cvlilebaa. mtacebelTa umravlesoba, sxva mravali frinvelisgan (mag.

weroebisa da batebisgan) gansxvavebiT, gundurad ki ar migrirebs, aramed cal-

calke, anu farTo "frontiT", romelic moicavs mraval samigracio gzas

(saSemodgomo da sagazafxulo samigracio gzebi yovelTvis ar emTxveva erTmaneTs).

isini gadafrenisas sakmaod moxerxebulad zogaven energias _ iyeneben mziT

gamTbari miwis zedapiridan haeris zeamaval siTbur nakadebs, e.w. Termalebs, da

qaris zeamaval nakadebs. haeris zeamaval nakadze "damjdari" frinveli asrulebs iraos, igi nel-nela adis maRla manam, sanam amwevi nakadi TandaTan ar gacivdeba

da Sesustdeba. amis Semdeg frinveli livlivis meSveobiT "gadaxteba" maxlobel axalwarmoqmnil Tbil nakadze da iraos meSveobiT isev zemoT adis. ase irao-

livlivis monacvleobiT SeuZlia dafaros 600 km dReSi. aseTi samigracio strategiis gamo mtacebeli frinvelebi eridebian zRvisa

da tbebis gadafrenas im adgilebSi, sadac wylis zedapiris sigane 25 km-ze metia, radgan wylis zedapirze Termalebi da sxva zeamavali haeris nakadebi ar

warmoiqmneba. amaze naTlad metyvelebs amerikisa da evropa-afrikis samigracio

sistema. mravali mtacebeli frinveli gadafrenisas Tavs iyris iseT adgilebSi,

sadac wylis zedapiris sigane mcirea, rogoricaa panamis arxi centralur

amerikaSi, gibraltaris, mesinisa da bosforis sruteebi evropaSi. ramdenime

samigracio gzis Tavmoyris adgils samigracio derefans an "Zabrs" uwodeben. mtacebeli frinvelebi maRali qedebis gadalaxvasac eridebian da maT

Semovlas cdiloben. Rrubliani amindis dros, rodesac Termalebi sustdeba,

gadamfreni mtaceblebi frenas wyveten. unda aRiniSnos, rom SavardnisebrT da

Zelqorebs gadafrenisas ufro aqtiuri frena sCveviaT da amitom Termalebze

naklebad arian damokidebulni. Sesabamisad, maTi samigracio gzebi aSkara Zabrs

ar qmnis.

evropa-afrikis samigracio sistemis erT-erTi mniSvnelovani Zabri mdebareobs

saqarTveloSi, baTumis maxloblad. baTumis Zabri saSemodgomo gadafrenisas ase

iqmneba: mtacebeli frinvelebi didi kavkasionis centralur da dasavleT nawils

gadmolaxaven da eSvebian kolxeTis dablobze. energiis dazogvis mizniT isini

eridebian Savi zRvis zedapirs, lixisa (suramis) da mesxeTis qedebs. amitom maTi

umetesi nawili Tavs iyris baTumis midamoebSi, Semdeg saqarTvelo-TurqeTis

sazRvars gadakveTen, TandaTan isev dascildebian erTmaneTs da ganagrZoben

frenas Tbili qveynebisken.

9

19. ra Tavisebureba axasiaTebs mtacebeli frinvelebis migracias?

(a) maTi migraciis saSemodgomo da sagazafxulo gzebi erTmaneTs emTxveva

(b) isini sabudar da sazamTro adgilebs Soris migrireben

(g) sabudari adgilebidan Tbili qveynebisken isini mifrinaven cal-calke

(d) isini sabudar adgilebs toveben sakvebi bazis sezonur cvlilebebTan

dakavSirebiT

20. ra aris Termalebi?

(a) haeris zeamavali nakadebi

(b) qaris zeamavali nakadebi

(g) miwis mziT gamTbari monakveTebi

(d) wylis sxvadasxva Tbili dineba

21. "irao-livlivis monacvleobis" meSveobiT:

(a) frinvelebi irCeven saSemodgomo da sagazafxulo samigracio gzebs

(b) frinvelebi frenisas inarCuneben simaRles da amasTanave, zogaven energias

(g) frinvelebi advilad pouloben axalwarmoqmnil Termalebs

(d) frinvelebi aregulireben Termalebsa da qaris zeamaval nakadebs

22. amerikisa da evropa-afrikis samigracio gzebze dakvirvebis Semdeg SeiZleba davaskvnaT:

(a) wylis zedapirze warmoiqmneba Termalebi da haeris sxva zeamavali nakadebi

(b) mtacebeli frinvelebi wylis zedapirze gadafrenisas iseTive samigracio gzebs

irCeven, rogorsac weroebi da batebi

(g) zRvis zedapirze warmoqmnili Termalebi exmareba frinvelebs iraos

SesrulebaSi

(d) mtacebeli frinvelebi eridebian gadafrenas iq, sadac wylis zedapiri Zalze

farToa

10

23. ratom wyveten frenas Rrubliani amindis dros gadamfreni mtaceblebi?

(a) am dros wylis zedapiri civdeba

(b) am dros qaris zeamavali nakadebi Zlierdeba

(g) Rrubliani amindis dros samigracio gza ar Cans

(d) Rrubliani amindis dros Termalebi sustdeba

24. Zelqorebisa da SavardnisebrTa samigracio gzebi aSkara "Zabrs" ar qmnis, radgan:

(a) maT migrirebisas gundad frena sCveviaT

(b) gadafrenisas isini moxerxebulad zogaven energias

(g) isini naklebad arian damokidebuli haeris siTbur nakadebze

(d) isini eridebian qedebis gadalaxvas

25. ra mimarTeba aqvs bolo abzacs teqstTan?

(a) bolo abzacSi Sejamebulia teqstSi gamoTqmuli mosazrebani

(b) bolo abzacSi ganzogadebulia teqstSi dawyebuli msjeloba

(g) bolo abzacSi warmodgenilia teqstSi ganxiluli sakiTxis erTi konkretuli

nimuSi

(d) bolo abzacSi ganxilulia teqstSi gamoTqmul mosazrebaTa sawinaaRmdego

argumentebi

11

analogiebi








Tanmimdevroba.



(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi


26. mindori : yvavilebi

(a) winadadeba : sityvebi

(b) mze : sxivebi

(g) ca : varskvlavebi

(d) rveuli : furclebi

27. qamari : balTa

(a) karmidamo : miwa

(b) WiSkari : urduli

(g) fari : xmali

(d) sayelo : perangi

28. ankesi : bade

(a) yvavili : Taiguli

(b) zurgCanTa : karavi

(g) motocikli : avtobusi

(d) isari : mSvildi

29. meTauri : winamZRoli

(a) xelyumbara : xelSubi

(b) xelsawyo : xelsafqvavi

(g) xelwerili : xelnaweri

(d) xelsaxoci : xelsawmendi

12

30. Senoba : sasaxle

(a) cekva : ritmi

(b) simRera : iavnana

(g) piesa : speqtakli

(d) TamaSi : saTamaSo

31. Teatris scena : reJisori

(a) fexburTis moedani : mwvrTneli

(b) cirkis arena : jambazi

(g) darbazi : mayurebeli

(d) ringi : msaji

32. wyali : CanCqeri

(a) comi : puri

(b) cecxli : koconi

(g) Tiva : Cala

(d) maWari : Rvino

33. fafuki : Sexeba

(a) mZafri : grZnoba

(b) Wreli : mxedveloba

(g) daxSuli : smena

(d) ucnauri : warmosaxva

13

winadadebis Sevseba








34. gamocdaze _____ is sakiTxi Semxvda, romelic _____ , magram mainc _____ friadze.

(a) SemTxveviT \ saerTod ar vicodi \ ver vupasuxe

(b) swored \ wina dRes gavimeore \ ver vupasuxe

(g) samwuxarod \ kargad vicodi \ vupasuxe

(d) sabednierod \ wina dRes gavimeore \ vupasuxe

35. warumatebeli adamianebi _____ cxovroben arsebuli realobiT. _____ , isini Sinaganad mimarTulni arian _____ .

(a) yovelTvis /miuxedavad amisa / realur gancdebsa da awmyo situaciebze

(b) iSviaTad / Sesabamisad / warsulis mogonebebze an momavlis lodinze

(g) arasodes / aqedan gamomdinare / realur gancdebsa da awmyo situaciebze

(d) xSirad / Sesabamisad / warsulis mogonebebze an momavlis lodinze

36. sascenod gadakeTebisas moTxrobis arsi daumaxinjebiaT: moTxrobis mTavari personaJi - _____ dedakaci scenaze gadaiqca _____ qalad. mizezi amisa is aris,

rom moTxrobaSi misi xasiaTi gamoxatulia _____ , scenaze ki - _____ .

(a) sentimentaluri, ybedi / Zlier, Seudrekel / moqmedebiT, saqcieliT / mxolod


(b) Zlieri, Seudrekeli / ybed, sentimentalur / mxolod sityvebiTa da

replikebiT / moqmedebiT, saqcieliT

(g) sentimentaluri, ybedi / Zlier, Seudrekel / mozomili sityviTa da

moqmedebiT / mxolod replikebiTa da qceviT

(d) Zlieri, Seudrekeli / ybed, sentimentalur / moqmedebiT, saqcieliT / mxolod


14

37. sakuTari damwerlobisadmi erebis erTgulebas yvelaze kargad espaneTis

ebraelebsa da arabebze dakvirveba gvidasturebs. pirvelni espaneTSi arabTa

batonobis dros _____ Seqmnili mniSvnelovani literatura dagvitoves, magram

igi _____ iyo dawerili. aseve, arabebma mSobliur enad _____ da am enaze

Seqmnes brwyinvale literatura, romelic _____ iyo Sesrulebuli.

(a) arabulad laparakobdnen da arabul enaze / maTive sakuTari ebrauli anbaniT /

espanuri SeiTvises / arabuli damwerlobiT

(b) arabulad laparakobdnen da espanur enaze / maTive sakuTari ebrauli anbaniT /

espanuri SeiTvises / espanuri anbanis gamoyenebiT

(g) ebraul enaze laparakobdnen da ebraul enaze / arabuli anbaniT / espanuri

ver SeiTvises / ebrauli damwerlobiT

(d) ebraul enaze laparakobdnen da espanur enaze / arabuli anbaniT / arabuli

SeiTvises / espanuri anbanis gamoyenebiT

logika






naxazis formiT.

38. kodala, SoSia, guguli da Cxikvi simindis marcvals Semousxdnen (ara

aucileblad am TanmimdevrobiT). am marcvals isini niskartiT ugorebdnen

erTmaneTs im wesis dacviT, rom marcvlis gagoreba mxolod marcxniv mjdomisTvis

SeiZleboda. simindis marcvali Cxikvisgan axla SoSiam miiRo.

romeli frinveli miiRebs simindis marcvals kidev oTxi gagorebis Sedegad?

(a) kodala

(b) guguli

(g) SoSia

(d) Cxikvi

15

39. davuSvaT rom: • yvela meviolines uyvars poezia

• orkestris zogierT musikoss ar uyvars poezia

Tu es debulebebi WeSmaritia, maSin qvemoT CamoTvlilTagan romeli debuleba

ar SeiZleba iyos WeSmariti?

(a) poeziis moyvaruli zogierTi musikosi ar aris mevioline

(b) mxolod meviolineebs uyvarT poezia

(g) meviolineebi orkestris musikosebi arian

(d) mxolod meviolineebi arian orkestris musikosebi

40. naZvis xis irgvliv xuTi bavSvi dgas xelCakidebuli. kaxas iasTvis aqvs xeli Cakidebuli, sosos – makasTvis, makas ki _ TedosTvis.

qvemoT CamoTvlilTagan romeli SemTxvevaa SeuZlebeli?

(a) ias xeli aqvs Cakidebuli TedosTvis

(b) Tedos xeli aqvs Cakidebuli kaxasTvis

(g) sosos xeli aqvs Cakidebuli iasTvis

(d) kaxas xeli aqvs Cakidebuli makasTvis

41. qalaqis A ubani ufro SemaRlebul adgilas mdebareobs, vidre B ubani. binebi A ubanSi ufro Zviria, vidre B ubanSi. ninom amis safuZvelze ivarauda, rom:

A ubanSi binebis siZvires swored am ubnis adgilmdebareoba ganapirobebs.

qvemoT CamoTvlTagan romelma faqtma SeiZleba ganamtkicos es varaudi?

(a) A ubanTan SedarebiT, B ubanSi binebi ukeTesi proeqtis mixedviTaa aSenebuli (b) B ubanSi gacilebiT uaresi eleqtromomaragebaa, vidre A ubanSi (g) A ubanSi binebi ufro prestiJuli samSeneblo firmis mieraa aSenebuli,

vidre B ubanSi (d) B ubanTan SedarebiT, A ubanSi quCebi gacilebiT ufro keTilmowyobilia

16




kavkasionis qedis gaswvriv uZvelesi droidan gavrcelda koSkura sacxovreblebi,

romelTa naSTebi dResac SeiniSneba Savi zRvidan kaspiis zRvamde maRalmTian

regionebSi. bunebrivia, saqarTveloSi koSkebis simravlem warmoSva uamravi legenda

da fsevdomecnieruli hipoTeza _ mTebSi koSkebi Sua saukuneebSi gamoCnda da

warmoadgenda an glexebis mier feodalTa cixesimagreebis mibaZviT agebul nagebobebs,

an gaRaribebuli feodalebis sacxovrebels.

arsebuli koSkura ansamblebis didi nawili agebulia XIV-XVI saukuneebSi,

ganviTarebuli feodalizmis periodSi. magram es garemoeba imis safuZvels ar

gvaZlevs, rom maTi warmoSoba Sua saukuneebs mivakuTvnoT. koSkura sacxovreblebi

mTebSi unda warmoSobiliyo bevrad ufro adreul istoriul epoqaSi _ Temur-

gvarovnuli wyobis stadiaze. garda amisa, antikuri xanis avtorebi aRweren msgavs

nagebobebs amierkavkasiis da, kerZod, kolxeTis teritoriaze. magaliTad, romaeli

moRvawe vitruviusi Tavis traqtatSi "arqiteqturis Sesaxeb" aRwers kolxuri

koSkura saxlebis xis konstruqcias da kolxeTis koSkebs sacxovrebelTa uZveles

tips miakuTvnebs. svaneTSi, sofel xaiSSi, napovnia koSkura saxlis oqros modeli _

amuleti, romelic daTariRebulia I saukunis miwuruliT Cv. w. aR.-mde. svaneTis

sofel xaiSSi napovni sacxovrebeli koSkis modeli TariRdeba periodiT, rodesac

vitruviusma kolxeTis sacxovrebeli koSkebi aRwera, da imaze miuTiTebs, rom

saqarTvelo koSkura sacxovreblis gavrcelebis erT-erTi mniSvnelovani kera iyo.

antikuri wyaroebis didi umravlesoba qarTvelTa sacxovrebeli koSkebis arsebobas

ukavSirebs rogorc gareSe mtris Semosevebs, aseve Sida konfliqtebs qveynis dablob

da mTian regionebs Soris.

CrdiloeT SuamdinareTSi aRmoaCines Tixis miniaturuli amuleti xis koSkis

gamosaxulebiT, romelic saocrad hgavs saqarTveloSi napovn oqros amulets.

Tumca am or models oTxi aTaswleuli aSorebs erTmaneTs, isini gamosaxaven

formiTa da tipiT identur koSkura saxlebs. Zvel egviptesa da SuamdinareTSi

koSkura sacxovreblis farTo gavrcelebaze miuTiTebs adreuli periodis

ieroglifuri niSnebic, romlebic garkveviT aRniSnaven TavdacviT koSkura saxls.

Tu rukaze sagangebod movniSnavT yvela regions, sadac aRmoCenilia saxli-

simagreebi, TvalSi mogvxvdeba erTi kanonzomiereba: Zvel samyaroSi isini

Tavmoyrilia iq, sadac mdebareobs didi samTo masivebi _ himalai, kavkasioni,

balkaneTi da apeninebi, amerikaSi _ kordilierebi da andebi. mTel msoflioSi

koSkura sacxovreblebis aseTi ganawileba am saxis nagebobebis erTi wyarodan

gavrcelebis Teoriis umweobaze miuTiTebs. safiqrebelia, rom msgavsma

geografiulma pirobebma sazogadoebrivi struqturis da, Sesabamisad,

sacxovreblebis struqturis msgavsebac ganapiroba.

mTiani saqarTvelos koSkura sacxovreblebs didi mniSvneloba eniWeba, rogorc

erT-erT wyaros msoflio kulturis istoriisaTvis, radgan am masalis safuZvelze

SesaZlebeli xdeba ara mxolod aTaswleulebiT daSorebul am ZeglTa aRdgena,

aramed im sazogadoebrivi struqturis Seswavlac, romelmac maTi warmoSoba

ganapiroba.

17

42. qvemoT CamoTvlilTagan romeli mosazrebaa marTebuli? (upasuxeT I-II abzacis mixedviT)

(a) adreul istoriul epoqaSi mTielni feodalTa cixesimagreebis mibaZviT

agebdnen koSkebs

(b) arsebuli koSkura ansamblebi warmoadgens Sua saukuneebSi gaRaribebul

feodalTa sacxovreblebs

(g) Savi zRvidan kaspiis zRvamde maRalmTian regionebSi koSkura nagebobebi XIV-

XVI saukuneebSi unda warmoSobiliyo

(d) kavkasionis qedis gaswvriv gavrcelebuli koSkura sacxovreblebis warmoSoba

Temur-gvarovnuli wyobis stadias unda mivakuTvnoT

43. teqstidan vigebT, rom: I. antikuri xanis avtorebi aRweren amierkavkasiis da, kerZod, kolxeTis

teritoriaze arsebul koSkura ansamblebs.

II. vitruviusi Tavis traqtatSi "arqiteqturis Sesaxeb" aRwers kolxuri koSkura saxlebis xis konstruqcias.

III. dRes arsebuli koSkura ansamblebis didi nawili agebulia ganviTarebuli

feodalizmis periodSi.

IV. svaneTis erT-erT sofelSi napovnia koSkura saxlis oqros modeli, romelic

TariRdeba I saukunis miwuruliT Cv. w. aR.-mde.

romeli sami argumenti ganamtkicebs im mosazrebas, rom saqarTvelos mTebSi

koSkura saxlebi Sua saukuneebamde gacilebiT adre warmoiSva? (a) I, II da IV

(b) I, II da III

(g) II, III da IV

(d) III, IV da I

44. rodis moRvaweobda vitruviusi?

(a) XVI saukunis I naxevarSi

(b) XIV saukunis II naxevarSi

(g) I saukunis II naxevarSi Cv. w. aR.-mde

(d) Cv. w. aR-is II saukunis I naxevarSi

18

45. saqarTvelos mTian regionebSi koSkura nagebobebis gavrceleba ukavSirdeba:

(a) mTielTa Soris gacxovelebul urTierTobas, romelsac maTi kulturis

msgavseba ganapirobebda

(b) qveynis dablob da mTian regionebs Soris konfliqtebs, aseve gareSe mtris

Semosevebs

(g) kavkasionis, kordilierebisa da andebis koSkura sacxovreblebis gavrcelebis

saerTo wyaros

(d) antikuri xanis werilobiTi wyaroebis gavlenas kolxur arqiteqturaze

46. romeli qveynis damwerlobaSi aisaxa koSkis forma?

(a) antikuri saberZneTis

(b) Zveli romis

(g) kolxeTis

(d) Zveli egviptis

47. teqstis mixedviT, romeli debuleba araa marTebuli?

(a) koSkebi sazogadoebrivi struqturis aRdgenas emsaxureba

(b) koSkebi sacxovreblis funqcias asrulebda

(g) koSkebs Tavdacvis mizniT agebdnen

(d) koSkura nagebobebi ZiriTadad mTian regionebSi gvxvdeba

48. CamoTvlilTagan romeli faqti ayenebs eWvqveS sxvadasxva qveyanaSi arsebuli koSkura nagebobebis erTi wyarodan gavrcelebis Teorias?

(a) ieroglifur niSnebSi TavdacviTi koSkura saxlis gamosaxva

(b) antikuri xanis avtorTa mier koSkura saxlebis konstruqciebis aRwera

(g) koSkura nagebobebis Tixisa da oqros modelebis aRmoCena

(d) koSkura nagebobebis ganlageba sxvadasxva geografiul adgilas

19

49. ratom aris mniSvnelovani saqarTvelos mTian regionebSi gavrcelebuli

koSkura sacxovreblebis Seswavla?

(a) is erT-erTi wyaroa msoflio kulturis istoriis kvlevisaTvis

(b) is gvexmareba Zvelegvipturi da Suamdinaruli ieroglifebis gaSifrvaSi

(g) ufro gasagebi xdeba vitruviusis traqtati ,,arqiteqturis Sesaxeb”

(d) SegviZlia warmovidginoT XIV-XVI saukuneebis qarTvel feodalTa yofa

50. ra aris am teqstis mTavari saTqmeli?

(a) kavkasionis qedis gaswvriv SemorCenili koSkebis naSTebi uamravi legendis

warmoSobis safuZvelia

(b) aTaswleulebiT daSorebul ZeglTa aRdgena SesaZlebelia mxolod koSkura

sacxovreblebis Sesaxeb istoriuli masalis safuZvelze

(g) saqarTvelo koSkura sacxovreblebis gavrcelebis erTaderTi mniSvnelovani

keraa

(d) TavdacviTi koSkebis warmoSoba sxvadasxva samTo masivebSi msgavsma

sazogadoebrivma struqturam ganapiroba

21

maTematikuri nawili













an · am = an + m

an : am = an – m

(an)m = an · m


5. siCqare: dro

manZilisiCqare =


raodenoba monacemTa



(a - b)2 = a2 – 2ab + b2




kuTxe ki _ patara

kvadratiT.


• ori paraleluri

wrfis mesame wrfiT






hipotenuzis sigrZis



AB2 = AC2 + BC2
















22







meti, airCieT (d).

A B

51.

(a) (b) (g) (d)

52.

(a) (b) (g) (d)

53. a > 0, b > 0

(a) (b) (g) (d)

54.

(a) (b) (g) (d)

55.

ABC marTkuTxa samkuTxedSi ∠C = 90° da ∠A < ∠B.

(a) (b) (g) (d)

56.

(a) (b) (g) (d)

( )334− ( )213−

75648 · 256 – 1 75643 · 253 + 1

a – b 0

94 5,0

∠A 45°

16-is da 20-is udidesi saerTo

gamyofi

12-is da 28-is udi-desi saerTo

gamyofi

23

57.

(a) (b) (g) (d)

58.

oTxkuTxa piramidas

sul 5 waxnagi aqvs.

(a) (b) (g) (d)

amocanebi

59. ramdenjeraa naklebi udidesi orniSna ricxvi udides oTxniSna ricxvze?

(a) 2-jer (b) 99-jer (g) 100-jer (d) 101-jer

(e) 900-jer



wertilebidan A da B wertilebis koordinatebi miTiTebulia naxazze. C wertilis koordinatia:

(a) 1,9 (b) 2,9 (g) 3,3 (d) 3,5 (e) 3,7

( ) aa 32 2 +−aa 34 2 +−

SvidkuTxa pira-

midis waxnagebis

raodenoba

marTkuTxa parale-

lepipedis waxnagebis

raodenoba

24

61. mas Semdeg, rac gaCerebaze troleibusidan 11 mgzavri Cavida, xolo 7 mgzavri amovida, troleibusSi 29 mgzavri aRmoCnda. ramdeni mgzavri yofila

troleibusSi am gaCerebamde? (a) 18 (b) 22 (g) 26 (d) 33 (e) 36

62. kinoseansi 18 saaTze daiwyo. romel saaTze dasruldeba seansi, Tu is 95 wuTs grZeldeba?


monacemTa analizi




Roris xorci (1 kg) 3.88 3.70 4.00 4.20

qaTami (1 kg) 4.62 4.50 4.00 3.62

kvercxi (10 cali) 1.30 1.30 1.50 1.60

karaqi (1 kg) 5.20 5.00 5.00 6.20

yveli (1 kg) 4.90 3.80 3.80 3.80



Rvino (0.7 litri) 1.13 1.37 1.37 1.37

mocemuli cxrilis mixedviT upasuxeT Semdeg 4 SekiTxvas:

63. ramdeni lari iyo 1 kg Roris xorcis saSualo fasi 1996 wels? (a) 3.70 (b) 3.88 (g) 4.00 (d) 4.20 (e) 5.20

25

64. qvemoT CamoTvlilTagan romeli produqtis saSualo fasi ar Semcirebula 1996 wels wina welTan SedarebiT?

(a) saqonlis xorcis

(b) qaTmis

(g) karaqis

(d) Saqris fxvnilis

(e) yvelis

65. romeli produqtis saSualo fasi mcirdeboda yovelwliurad 1995-1998 wlebSi?

(a) Roris xorcis

(b) kvercxis

(g) qaTmis

(d) Saqris fxvnilis

(e) Rvinis

66. ra farglebSi meryeobda (icvleboda) saqonlis xorcis saSualo fasi 1995-1998 wlebSi?


amocanebi

67. Tu 3x + y = 3 da 2x – y = 2 , maSin 3x = (a) 3 (b) 5 (g) 6 (d) 9 (e) 15

68. sibrtyeze mocemulia marTkuTxa koordinatTa sistema. ABC tolferda samkuTxedis AC fuZe y-RerZis paraleluria. A da B wveroebis koordinatebi miTiTebulia naxazze. C wveros koordinatebi (a; b) =

(a) (4; 6) (b) (4; 8) (g) (5; 2) (d) (5: 6) (e) (6: 7)

26

69. maRaziaSi feradi da Sav-TeTri televizorebi gaiyida. gayiduli televizo-

rebis 65 nawili feradi iyo, xolo 8 televizori _ Sav-TeTri. sul ramdeni

televizori gaiyida maRaziaSi? (a) 18 (b) 24 (g) 36 (d) 42 (e) 48

70. mas Semdeg, rac perangis fasi 20%-iT Semcirda, perangi 72 larad iyideboda. ramdeni lari Rirda perangi fasis Semcirebamde?

(a) 100 (b) 96 (g) 92 (d) 90 (e) 80

71. ABCD paralelogramis B wverodan AD gverdze daSvebulia BE marTobi, romelic AB gverdTan 58°-ian kuTxes qmnis (ix. naxazi). ramdeni gradusia am

paralelogramis C kuTxis sidide?

(a) 32°

(b) 38° (g) 42° (d) 58°

(e) 62° 72. ricxvebi 17, b, 16, 10, a, 6 klebis mixedviTaa dalagebuli da cnobilia, rom a = b – 9. CamoTvlili ricxvebidan romeli SeiZleba iyos a-s toli?

(a) 5,8 (b) 6,4 (g) 6,9 (d) 7,5 (e) 8,2

27

73. Tinam TeTri, lurji da wiTeli feris Zafi iyida, TiToeuli _ 1,5 kg. TeTri Zafi Tinam mTlianad gamoiyena mokle Sarfebis mosaqsovad, TiTo Sarfs

dasWirda 0,1 kg; lurji Zafi _ saSualo sigrZis Sarfebis mosaqsovad, TiTo Sarfs dasWirda 0,15 kg; xolo wiTeli Zafi _ grZeli Sarfebis mosaqsovad, TiTo Sarfs dasWirda 0,3 kg. sul ramdeni Sarfi mouqsovia Tinas am ZafebiT?

(a) 10 (b) 18 (g) 25 (d) 28 (e) 30

74. MNKL marTkuTxedi, romlis farTobia 72 sm2,

dayofilia tol marTkuTxedebad (ix. naxazi). ramdeni

kvadratuli santimetria gamuqebuli mravalkuTxedis

farTobi, Tu misi wveroebi dayofis Sedegad miRebuli marTkuTxedebis wveroebs emTxveva?

(a) 48 (b) 50 (g) 52 (d) 56 (e) 60

75. Tu klienti bankSi Seitans x lars, t Tvis Semdeg mis angariSze bankSi iqneba p lari. p gamoiTvleba formuliT: p = x + 0,02xt. ramdeni lari iqneba klientis angariSze 5000 laris Setanidan 5 Tvis Semdeg?

(a) 5300 (b) 5500 (g) 5600 (d) 5800 (e) 6000

28







meti, airCieT (d).

A B

76.

mevenaxem ojaleSis, colikaurisa da

cicqas jiSis yurZeni dakrifa.

dakrefili cicqas wona 2 t iyo. wriul diagramaze miTiTebulia, dak-

refili yurZnis wonis ramdeni procen-

ti iyo ojaleSisa da colikauris wona.

(a) (b) (g) (d)

77.

mimdevrobis yoveli wevri mis momdevno wevrze 3-iT naklebia.

am mimdevrobis mesame wevri y-is tolia.

(a) (b) (g) (d)

78.

gaxmobis Sedegad miRebuli sokos wona nedli sokos

wonis 25%-ze naklebia.

(a) (b) (g) (d)

ojaleSis wona 5 t

y 12

gamxmari sokos wona,

romelic miiReba 16 kg nedli sokosagan

3,8 kg

29

79.

wris radiusis sigrZea 10 sm. kvadratis yvela wvero am

wrewirze mdebareobs.

(a) (b) (g) (d)

80.

ofisis gasaremonteblad daixarja organizaciis mier

bolo Tvis ganmavlobaSi miRebuli Semosavlis meoT-

xedze meti da mesamedze naklebi. organizaciis

Semosavali bolo TveSi 7200 lari iyo.

(a) (b) (g) (d)

81.


udidesi mTeli ricxvi, romelic naklebia x ricxvze. a da b mTeli ricxvebia.

(a) (b) (g) (d)

82.

rombis perimetria 24 sm.

(a) (b) (g) (d)

2500 lari ofisis gasaremon-

teblad daxarjuli

Tanxa

( ) ( )** ba − ba −

am rombis farTobi 38 sm2

wris farTobs

gamoklebuli

kvadratis farTobi

110 sm2

30

amocanebi

83. romelia is ricxvi, romlis 47 nawili udris 35-s?

(a) 18 (b) 20 (g) 21 (d) 25 (e) 27

84. Teatris ganaTebisaTvis erTnairi naTurebi SeiZines. TiToeuli anTebuli naTura yovel saaTSi erTi da imave Rirebulebis eleqtroenergias xarjavs.

10 erTdroulad anTebuli naTura 5 saaTSi 30 TeTri Rirebulebis eleqtro-energias xarjavs. ramdeni TeTri Rirebulebis eleqtroenergias daxarjavs 40 erT-droulad anTebuli naTura 3 saaTSi?

(a) 48 (b) 70 (g) 72 (d) 90 (e) 120

85. ofisSi mxolod erTujriani, orujriani an samujriani magidebi dgas, sul _ 24 cali. am magidebSi 41 ujraa. erTujriani magidebi imdenia, ramdenic

orujriani da samujriani magidebi erTad. ramdeni orujriani magidaa am ofisSi? (a) 6 (b) 7 (g) 8 (d) 9 (e) 11

86. marTkuTxedi dayofilia or kvadratad. TiToeuli kvadratis perimetria 40 sm. ramdeni santimetria am marTkuTxedis perimetri?

(a) 60 (b) 64 (g) 70 (d) 76 (e) 80

31

monacemTa analizi





87. ra saxis saTamaSoebi gayidula yvelaze mcire raodenobiT?

(a) Tojinebi

(b) naZvis xis saTamaSoebi

(g) konstruqtorebi

(d) manqanebi

(e) burTebi

88. ramdenjer metia gayiduli Tojinebis raodenoba gayiduli naZvis xis saTamaSoebis raodenobaze?


89. gayiduli saTamaSoebis saerTo raodenobis ramdeni procentia gayiduli konstruqtorebis raodenoba?

(a) 10%

(b) 15%

(g) 18%

(d) 20%

(e) 25%

32

90. gayiduli saTamaSoebis saerTo raodenobis meoTxedze metia, magram mesamedze naklebi:

(a) gayiduli manqanebisa da konstruqtorebis raodenobaTa jami

(b) gayiduli manqanebisa da naZvis xis saTamaSoebis raodenobaTa jami

(g) gayiduli naZvis xis saTamaSoebisa da Tojinebis raodenobaTa jami

(d) gayiduli burTebisa da Tojinebis raodenobaTa jami

(e) gayiduli burTebis da konstruqtorebis raodenobaTa jami

amocanebi

91. maRaziaSi qurTukebi ramdenime dRis ganmavlobaSi iyideboda. pirvel dRes gaiyida 60 qurTuki. yovel momdevno dRes iyideboda 10 qurTukiT naklebi, vidre wina dRes. bolo dRes ukanaskneli 10 qurTuki gaiyida. sul ramdeni qurTuki gayidula maRaziaSi am dReebis ganmavlobaSi?

(a) 70 (b) 80 (g) 120 (d) 210 (e) 600

92. tolferda samkuTxedis fuZis sigrZea 12 dm, xolo fuZeze daSvebuli simaRle _ 8 dm. ramdeni decimetria am tolferda samkuTxedis ferdis sigrZe?

(a) 8 (b) 9 (g) 10 (d) 11 (e) 13

93. mimdevrobis pirveli wevric da meore wevric aris a + 3 , mesame wevri 4-iT metia meore wevrze da 7-iT naklebia meoTxe wevrze. qvemoT CamoTvlilTagan romeli gamosaxulebiT Caiwereba am mimdevrobis pirveli oTxi wevris jami?

(a) 4a + 9

(b) 4a + 12 (g) 4a + 15 (d) 4a + 21 (e) 4a + 27

33

94. mTargmnelTa biuroSi sul 10 TanamSromelia, maTgan 6 inglisur enaze Targmnis, danarCeni 4 _ germanul enaze. inglisur enaze mTargmnelTa saSualo xelfasi 400 laria, germanul enaze mTargmnelTa saSualo xelfasi ki _ 500 lari. ramdeni laria biuros TanamSromelTa saSualo xelfasi ?

(a) 440 (b) 445 (g) 455 (d) 460 (e) 465

95. marTkuTxa paralelepipedi, romlis fuZis wiboebis sigrZeebia 10 sm da 2 sm, dayves 5 tol kubad. ramdeni kuburi santimetri iyo am marTkuTxa paralelepipedis

moculoba? (a) 20 (b) 40 (g) 50 (d) 100 (e) 200

96. naturaluri m ricxvis 8-ze gayofisas miRebuli naSTia 7. risi toli iqneba 2m-is 8-ze gayofisas miRebuli naSTi?

(a) 1 (b) 3 (g) 4 (d) 6 (e) 7

97. kalaTSi 9 wiTeli, 8 yviTeli da 6 mwvane feris vaSlia. minimum ramdeni vaSli unda amoiRos liam kalaTidan (masSi Cauxedavad), rom amoRebul vaSlebs

Soris aucileblad iyos samive feris vaSli? (a) 14 (b) 15 (g) 16 (d) 17 (e) 18

34

98. Tu x, y da z iseTi mTeli dadebiTi ricxvebia, rom 8 < x < 11, 4 < y < 9, 1 < z < 4 , maSin ( )zyx −: gamosaxulebis umciresi mniSvnelobaa:

(a) 1 (b)

23

(g) 49

(d) 67

(e) 2

99. sofelSi TiToeul ojaxs hyavs ZaRli an kata. ZaRli hyavs ojaxebis 85%-s, xolo kata _ 40%-s. sofelSi mcxovreb 50 ojaxs hyavs ZaRlic da katac. sul ramdeni ojaxia am sofelSi?

(a) 150 (b) 180 (g) 200 (d) 250 (e) 300



sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 1 sm. maqsima-luri daSoreba pirveli da meore wreebis wertilebs Soris 40 sm-ia, xolo meo-re da mesame wreebis wertilebs Soris _ 3 sm. qvemoT CamoTvlilTagan romlis toli SeiZleba iyos maqsimaluri daSoreba pirveli da mesame wreebis wertilebs

Soris?
