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

II

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. 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

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. 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

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. 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.

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

17. davuSvaT, rom:

• yvela biWs uyvars fexburTi

• zogierT biWs uyvars Wadraki

qvemoT CamoTvlilTagan romeli gamomdinareobs am debulebebidan aucileblad?

(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

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

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

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. SearCieT 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. 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

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. 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

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

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

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. 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.

qvemoT CamoTvlilTagan romeli faqti ayenebs eWvqveS am varauds?

(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

qvemoT CamoTvlilTagan romeli gamomdinareobs am debulebebidan aucileblad?

(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

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

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

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. 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

8-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

60. ricxvTa RerZi masze moniSnuli wertilebiT dayofilia tol monakveTebad

(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?

(a) 12 sT 55 wT (b) 13 sT 15 wT (g) 13 sT 45 wT (d) 14 sT 15 wT (e) 14 sT 45 wT

22aab − ( )aba 2−

piramidis wveroebis

raodenoba

kubis wveroebis

raodenoba

24

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 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

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

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

marilis wona, romel-

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.

nebismieri x ricxvisaTvis ( )∗x -iT aRniSnulia

umciresi mTeli ricxvi, romelic metia x ricxvze.

(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

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 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?

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

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?

(a) 43 sm (b) 44 sm (g) 50 sm (d) 57 sm (e) 58 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

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. 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

8-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

60. ricxvTa RerZi masze moniSnuli wertilebiT dayofilia tol monakveTebad

(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?

(a) 12 sT 55 wT (b) 13 sT 15 wT (g) 13 sT 45 wT (d) 14 sT 15 wT (e) 14 sT 45 wT

22aab − ( )aba 2−

piramidis wveroebis

raodenoba

kubis wveroebis

raodenoba

24

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 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

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

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

marilis wona, romel-

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.

nebismieri x ricxvisaTvis ( )∗x -iT aRniSnulia

umciresi mTeli ricxvi, romelic metia x ricxvze.

(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

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 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?

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

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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

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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

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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

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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?

(a) 43 sm (b) 44 sm (g) 50 sm (d) 57 sm (e) 58 sm

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

N varianti 1 varianti 1

(rusuli

varianti)

varianti 2 varianti 3 varianti 4

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