zogadi unarebis testizogadiunarebis testi · • yvela biWs uyvars fexburTi • zogierT biWs uyvars...
Transcript of zogadi unarebis testizogadiunarebis testi · • yvela biWs uyvars fexburTi • zogierT biWs uyvars...
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
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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. 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
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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
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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. 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
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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
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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. 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
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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
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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
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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
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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
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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. 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
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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
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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. 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
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
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