zogadi unarebis testizogadiunarebis testi · 2018. 6. 10. · (b) biliki : gza (g) otaxi : bina (d)...

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

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.

gisurvebT warmatebas !

zogadi unarebis testizogadi unarebis testi

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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".

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

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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

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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.

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

gamovlinda saqarTveloSi

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

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.

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.

qvemoT CamoTvlilTagan romeli faqti ayenebs eWvqveS am varauds?

(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

qvemoT CamoTvlilTagan romeli gamomdinareobs am debulebebidan aucileblad?

(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

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

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

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







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


raodenoba


raodenoba

( )21 y+ 2y

eqvskuTxa pira-

midis wveroebis

raodenoba

kubis wveroebis

raodenoba