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zogadi unarebis testizogadi unarebis testi
20102010instruqcia
testi Sedgeba ori _ verbaluri da maTematikuri _ nawilisgan.TiToeuli nawili 40 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.
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.drois amowurvis Sesaxeb gacnobebT meTvalyure.
Tu gaTvaliswinebulze meti droiT SeyovndebiT testis ama Tu im nawilze, Tqveni naSromi ar Semowmdeba.
Tu ar gaqvT romelime davalebis pasuxi, dros nu dakargavT da gadadiT Semdeg davalebaze.
Canawerebis an naxazebisTvis gamoiyeneT mxolod da mxolod testis furclebze arsebuli carieli adgilebi.
gisurvebT warmatebas !
III
2
verbaluri nawili analogiebi
am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva (sawyisi
wyvili), romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. daadgineT, ra
saxisaa es mimarTeba.
savaraudo pasuxTa yovel variantSi mocemulia, aseve, mniSvnelobiT
urTierTdakavSirebuli sityvebis wyvili. airCieT maTgan is wyvili, romelSic
sityvaTa mniSvnelobebs Soris mimarTeba sawyis wyvilSi arsebuli mimarTebis
msgavsia (analogiuria). pasuxis arCevisas gaiTvaliswineT wyvilebSi sityvaTa
Tanmimdevroba.
1. scenaristi : msaxiobi (a) arqiteqtori : mSenebeli
(b) kompozitori : msmeneli
(g) mxatvari : dizaineri
(d) iuristi : braldebuli
2. waaxalisa : waaqeza (a) SeigrZno : mixvda
(b) moiTmina : gajiutda
(g) endo : daimsaxura
(d) miimxro : gadaibira
3. brtyeli : reliefuri (a) lakonuri : sxarti
(b) harmoniuli : SeTanxmebuli
(g) absurduli : kanonzomieri
(d) adaptirebuli : Seguebuli
4. lambaqi : langari (a) lifti : eskalatori
(b) ruka : atlasi
(g) gvirabi : borani
(d) kedeli : tixari
5. hangi : musikaluri (a) variacia : ucvleli
(b) energia : birTvuli
(g) klimati : polaruli
(d) eqsperimenti : dagegmili
6. winapiroba : sawindari (a) mizani : strategia
(b) Sefaseba : kriteriumi
(g) Sedegi : produqti
(d) daskvna : analizi
3
winadadebebis Sevseba
am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa
gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiT aris aRniSnuli.
erTi xazi zogjer erT sityvas gulisxmobs, zogjer ki _ ramdenimes.
savaraudo pasuxTa yovel variantSi mocemulia sityvaTa jgufi, romlis
nawilebi erTmaneTisgan daxrili xazebiTaa (/) gamijnuli. airCieT pasuxis is
varianti, romlis TiToeuli nawilis Tanmimdevrulad Casma Sesabamis
gamotovebul adgilebSi azrobrivad gamarTul winadadebas mogvcems.
7. _____ islandielma xalxma Seqmna mravali saga, romlebSic mTavari personaJebi Tavisuflebismoyvare gmirebi arian. sagaSi xalxi ayalibebda mxatvrul samyaros,
romelic _____ garemomcvel sinamdviles. _____ , rom es gamogonili samyaro
_____ man gansazRvra islandielTa xasiaTi.
(a) damonebulma / ar hgavda / amitom, bunebrivia / garkveuli azriT, sinamdviled
iqca, Tumca,
(b) damonebulma / ar hgavda / Tumca, gasaocari isaa / garkveuli azriT,
sinamdviled iqca, radgan
(g) gamarjvebulma / asaxavda / amitom, bunebrivia / sruliad gansxvavdeboda
sinamdvilisgan. Sesabamisad,
(d) gamarjvebulma / asaxavda / Tumca, gasaocari isaa / sruliad gansxvavdeboda
sinamdvilisgan. miuxedavad amisa,
8. `gameoreba swavlis dedaa~ _ es Sexeduleba ______ SeZenis process:
dasaswavli masalis ______ ufro mniSvnelovania, vidre ______ . magram es
Sexeduleba ______ SeZenas exeba: sistematuri varjiSi ______ .
(a) zedmiwevniT miesadageba codnis / Rrmad gaazreba / mudmivi gameoreba /
WeSmaritia, roca saqme Cvevis / ar aris informaciis mopovebis erTaderTi
xerxi
(b) Zalian kargad miesadageba Cvevis / xSirad gameoreba am SemTxvevaSi / codnis
SeZenisas / mcdaria, Tu saqme codnis / xom informaciis mopovebis erTaderTi
gzaa
(g) zustad rodi miesadageba codnis / Rrmad gaazreba / ubralo gameoreba /
WeSmaritia, Tu saqme Cvevis / Cvevis Camoyalibebis aucilebeli pirobaa
(d) zustad miesadageba Cvevis / xSirad gameoreba am SemTxvevaSi / swavlisas /
mcdaria, roca saqme codnis / ar aris Cvevis Camoyalibebis saukeTeso xerxi
4
9. arcTu kargis mauwyebelia erebisa da, Tundac, pirovnebebisTvis, ______ rom gansakuTrebul mniSvnelobas ______ – bednieri adamianebi xom ______ , radgan ______ uxvi saCuqrebi.
(a) winaswarmetyvelebas / aniWeben / awmyoTi cxovroben / sruliad akmayofilebT
misi
(b) winaswarmetyvelebas / ar aniWeben / awmyoTi cxovroben / sruliad
akmayofilebT misi
(g) awmyos / aniWeben / momavalze arian orientirebulni / akmayofilebT awmyos
(d) awmyos / ar aniWeben / momavalze arian orientirebulni / ar akmayofilebT
awmyos
5
logika
am saxis davalebebi gansxvavdeba erTmaneTisgan monacemebisa da gamosatani
daskvnebis TvalsazrisiT. amitom gansakuTrebuli yuradReba miaqcieT SekiTxvas,
romelic axlavs TiToeul davalebas, da mocemuli variantebidan airCieT
Sesabamisi pasuxi.
zogierT SekiTxvaze pasuxis gacemas gagiadvilebT monacemebis gamosaxva
naxazis formiT.
10. mocemulia: • Walis binadari yvela SaSvi kargad galobs
• arc erTma Wrelma SaSvma ar icis galoba
qvemoT CamoTvlilTagan romeli debuleba gamomdinareobs am wanamZRvrebidan?
(a) yvela mgalobeli SaSvi binadrobs WalaSi
(b) WalaSi ar binadrobs arc erTi Wreli SaSvi
(g) Walis gareT mobinadre arc erTi SaSvi ar aris Wreli
(d) zogierTi Wreli SaSvi WalaSi binadrobs
11. mocemulia: • mecnierebi odesme aucileblad aRmoaCenen axal galaqtikas
Semdegi winadadebebidan romelia mocemulis tolfasi?
(a) SeuZlebelia, mecnierebma odesme aRmoaCinon axali galaqtika
(b) SesaZlebelia, mecnierebma odesme aRmoaCinon axali galaqtika
(g) SesaZlebelia, mecnierebma verasodes aRmoaCinon axali galaqtika
(d) SeuZlebelia, mecnierebma verasodes aRmoaCinon axali galaqtika
12. mocemulia:
arseboben mamaci adamianebi, da arian iseTi adamianebic, romelTac ar
aviwydebaT keTilgoniereba. Tumca, mamaci adamianebi arasodes iCenen
keTilgonierebas.
qvemoT CamoTvlilTagan romeli debuleba ar gamomdinareobs am mocemulobidan?
(a) vinc keTilgonierebas iCens, mamaci ar aris
(b) Tu adamiani keTilgonierebas iCens, is mamacia
(g) Tu adamiani mamaci ar aris, SesaZlebelia, is keTilgonieri iyos
(d) zogierTi adamiani ar aris keTilgonieri
6
13. romis imperiis zogierT regionSi wyals intensiurad iyenebdnen energiis
wyarod. Tumca, did qalaqebSi wylis energia ar gamoiyeneboda. zogierTi
istorikosi am faqts ase xsnis: mWidrod dasaxlebul adgilebSi mmarTveli elita
amjobinebda energiis tradiciuli wyaroebis gamoyenebas, rac moiTxovda didi
raodenobis muSaxelis dasaqmebas; wylis energiis gamoyenebis danergva ki samuSaos
gareSe datovebda bevr adamians da socialur areulobas gamoiwvevda.
qvemoT CamoTvlilTagan romeli faqti ayenebs eWvqveS am axsnas?
(a) romaelebi didi ostatobiT aSenebdnen akvedukebs – Tavisebur arxebs, romelTa saSualebiTac wyali Soridan miewodeboda did qalaqebs
(b) romis imperiis yvela im regionSi, sadac wylis energia ar gamoiyeneboda,
wlis ganmavlobaSi mdinareebSi wylis nakadi Zalian arastabiluri iyo
(g) romis imperiis did qalaqebSi wylis energiis gamoyenebis danergva SesaZlebeli
iyo sakmaod mokle droSi, Tanac, didi danaxarjebis gareSe
(d) romis imperiis yvela im regionSi, sadac wyali ar gamoiyeneboda energiis
wyarod, upiratesobas aniWebdnen energiis sxva, ufro tradiciul wyaroebs
7
wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
Zveli berZnebis rwmeniT, maTi kulturis aRmavlobamde egeosis zRvis
auzSi wamyvani adgili winaberZnul tomebs ekavaT. berZnuli enis
araindoevropuli elementebis, egeosuri toponimebis* Seswavlam naTeli gaxada,
rom amgvari winare mosaxleoba marTlac unda arsebuliyo. am TvalsazrisiT
mniSvnelovania kunZul kretaze aRmoCenili damwerlobis sistemebis Seswavla.
maTgan yvelaze Zvelia e. w. kretuli _ ieroglifur-piqtografiuli (xatovani)
damwerloba. am sistemis nimuSebi, ZiriTadad, qvis, spilos Zvlisa da liTonis
beWdebze SemogvrCa. zogi mecnieri varaudobs, rom es niSnebi ideogramebs
(damoukidebeli azris mqone simboloebs) warmoadgens, sxvebi ki am sistemas
marcvlovani damwerlobis adreul safexurad miiCneven.
sruliad originaluria kretaze festos sasaxlis nangrevebSi aRmoCenili
Tixis disko, romlis orive mxares spiraluradaa amotvifruli piqtografiuli
niSnebi. isini erTmaneTisgan vertikaluri xazebiT gamoyofil jgufebs qmnis.
gansakuTrebiT saintereso isaa, rom diskoze niSnebi amokawruli an daxatuli ki
ar aris, aramed liTonis specialuri, winaswar Camosxmuli formebiT (figuruli
niSnebiT) aris amotvifruli. es msoflio kulturis istoriaSi moZravi anbanis
gamoyenebis pirveli SemTxvevaa. festos diskos suraTovan niSnebs arc kunZul
kretaze da arc, zogadad, damwerlobis istoriaSi sarwmuno paralelebi ar
moepoveba. isic araa garkveuli, disko adgilobrivi warmoSobisaa, Tu romelime
sxva regionidan aris aq moxvedrili, rogoria damwerlobis sistemis xasiaTi da a. S.
kretuli damwerlobis ganviTarebis Sedegi unda yofiliyo minosuri**
xazovani damwerloba, romelsac A-xazovans uwodeben. A-xazovaniT Sesrulebuli teqstebi gvxvdeba keramikaze, qvis nivTebze, Tixis firfitebze. A-xazovani warwerebi jerjerobiT ar aris gaSifruli. dRes mxolod is SegviZlia vTqvaT,
rom damwerlobis es sistema marcvlovania.
kretaze aRmoaCines pirveli berZnuli damwerlobis, e. w. B-xazovanis nimuSebic. es damwerloba A-xazovanis ganviTarebis Sedegs warmoadgens. B-xazovani warwerebi gaSifra ingliselma mkvlevarma ventrisma. misi Teoriis
dadasturebas xeli Seuwyo cnobili arqeologis, blegenis mier mopovebulma
epigrafikulma masalam. erT axladaRmoCenil firfitaze yovel warweras Tan
axlda sxvadasxva tipis keramikuli WurWlis gamosaxuleba. ventrisis mier
dadgenili B-xazovanis bgeriTi mniSvnelobebiT TiToeul warweraSi ikiTxeboda Sesabamisi WurWlis berZnuli saxelwodeba, magaliTad, `samfexa~, `oTxyura~.
B-xazovani iyenebs silabogramebs (marcvlovan niSnebs), romlebic aRniSnavs
xmovans an xmovnisa da Tanxmovnis kompleqss, agreTve, ideogramebs. rogorc Cans,
berZnebs minosuri damwerlobis sistema mourgiaT TavianTi enisTvis. maT, erTi
mxriv, ar gamouyenebiaT A-xazovanis zogierTi niSani, xolo, meore mxriv,
daumatebiaT ramdenime axali grafema, romelTac minosuri damwerloba ar icnobs.
B-xazovani gavrcelebula kontinentur saberZneTSic. Tumca, sistemis sirTulem,
rogorc Cans, ganapiroba am damwerlobis SezRudulad gamoyeneba. kreta-mikenis
civilizaciis dacemis Semdeg B-xazovani sistema anbanurma damwerlobam Secvala, romelic, Tavis mxriv, finikiuri damwerlobis safuZvelze Camoyalibda.
*toponimi _ geografiuli adgilis (mTis, soflis, tyis, mindvris da a. S.) saxelwodeba.
**minosi _ kretis miTiuri mefe; kretis winaberZnul kulturas minosursac uwodeben.
8
14. qvemoT CamoTvlilTagan romeli mosazreba SeiZleba miviCnioT imis
argumentad, rom egeosis zRvis auzSi berZnuli civilizaciis warmoSobamde
araberZnuli warmomavlobis tomebi saxlobdnen?
(a) kunZul kretaze aRmoCenil warweraTa Sinaarsobrivi mravalferovneba
cxadyofs, rom egeosis zRvis auzSi saxlobdnen sxvadasxva enaze molaparake
tomebi
(b) Zveli berZnebis rwmeniT, maTi kulturis Camoyalibebamde egeosis zRvis auzSi
wamyvan rols winaberZnuli tomebi asrulebdnen
(g) berZnuli indoevropul enaTa jgufs ganekuTvneba, Tumca, am enaSi da
saberZneTis geografiuli adgilebis bevr saxelwodebaSi araindoevropuli
elementebia SemorCenili
(d) berZnulenovan samyaroSi uZvelesia e. w. kretuli damwerloba, romelsac
bevri paraleli SeiZleba movuZebnoT sxva civilizaciebSi Seqmnil
damwerlobaTa sistemebTan
15. ra saerTo aqvT e. w. kretul damwerlobasa da festos diskos warwerebs?
(a) orive tipis warwerebi spiralurad aris amotvifruli qvaze, spilos Zvalsa
da Tixis firfitebze
(b) orive damwerlobis niSnebi vertikaluri xazebiT gamoyofil jgufebs qmnis
(g) orive damwerlobis niSnebi damoukidebeli azris mqone simboloebs
warmoadgens
(d) orive tipis werilobiTi niSnebi piqtografiulia _ xatovani damwerlobis
nimuSebs warmoadgens
16. ratom miiCneven festos diskos warwerebs moZravi anbanis gamoyenebis pirvel nimuSad?
(a) moZravi anbanis calkeuli asoebiT SeiZleba `avawyoT~ sityva, festos diskoze
warwera winaswar Camosxmuli werilobiTi niSnebiTaa amotvifruli
(b) Tanamedrove pedagogikaSi moZrav anbans iyeneben wera-kiTxvis swavlebis sawyis
etapze, kunZul kretazec festos diskos swored amgvari daniSnuleba unda
hqonoda
(g) festos diskoze piqtografiuli niSnebi spiralurad aris amotvifruli,
moZravi anbaniTac SeiZleba spiralurad `davweroT~ sityvebi
(d) kretaze aRmoCenil yvela damwerlobas safuZvlad udevs moZravi anbanis
principi, Tumca, festos diskos warweris Sesrulebis teqnika yvelaze
daxvewilia
9
17. qvemoT CamoTvlilTagan romeli ar iyo mniSvnelovani imis dasadastureblad, rom ventrisma sworad gaSifra B-xazovani damwerloba?
(a) keramikul nakeTobaTa gamosaxulebani axladaRmoCenil firfitaze
(b) keramikuli WurWlis saxeobani
(g) warwerebi axladaRmoCenil firfitaze
(d) WurWlis berZnuli saxelwodebani
18. minosurs uwodeben:
(a) mTel berZnul kulturas, radgan minosi iyo Zveli saberZneTis miTiuri mefe
(b) A-xazovan da B-xazovan damwerlobebs, radgan orive kretaze Seiqmna minosis mefobis dros
(g) A-xazovan damwerlobas, radgan es sistema winaberZnul civilizaciaSi unda Seqmniliyo
(d) B-xazovan damwerlobas, radgan es damwerloba berZnulia, minosi ki winaberZnuli mosaxleobis miTologiuri gmiria
19. cnobilia, rom kunZul kviprosze aRmoCnda e. w. kviprominosuri, anu C-xazovani damwerloba, romelic ganviTarebis istoriiTa da xasiaTiT B-xazovani damwerlobis analogiuria. adgilobrivi mosaxleobis garda, C-xazovan damwerlobas iyenebdnen kviprosze gadmosaxlebuli berZnebic.
Tu am informacias teqstSi mocemul cnobebs davukavSirebT, davaskvniT:
(a) C-xazovani damwerloba xatovania, rogorc e. w. kretuli; aqac gaurkvevelia, C-xazovanis niSnebi ideogramebs warmoadgens Tu marcvlovani damwerlobis adreuli safexuria
(b) C-xazovani damwerloba piqtografiulia, rogorc festos diskos warwera, Tumca, C-xazovanis nimuSebi winaswar damzadebuli specialuri matricebiT ar aris amotvifruli
(g) C-xazovani damwerloba A-xazovanis ganviTarebis Sedegs warmoadgens, amasTan, isic iyenebs marcvlovan niSnebs da ideogramebs _ cnebis aRmniSvnel pirobiT
werilobiT niSnebs
(d) C-xazovani damwerloba B-xazovanis ganviTarebis Sedegs warmoadgens, amasTan, isic marcvlovani sistemaa da isic kontinentur saberZneTSi gavrcelebula
10
20. teqstis safuZvelze unda vivaraudoT, rom:
(a) B-xazovani damwerloba Seiqmna minosur kretaze, Tumca, sistemis sirTulis gamo igi ver gavrcelda kontinentur saberZneTSi
(b) berZnebma racionaluri midgoma gamoiCines minosuri werilobiTi tradiciebis
mimarT: gamoiyenes A-xazovanis yvela niSani da mas daumates ramdenime axali grafema anbanuri damwerlobidan
(g) winaberZnuli tomebis mier Seqmnili B-xazovani damwerloba safuZvlad daedo anbanuri damwerlobis ganviTarebas
(d) minosuri damwerlobis (kretulis da A-xazovanis) gaSifvram SesaZloa gadaWras egeosis zRvis auzSi berZnebamde mosaxle araindoevropuli
warmomavlobis xalxis eTnikuri vinaobis sakiTxi
11
analogiebi
am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva (sawyisi
wyvili), romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. maT gaswvriv
mocemulia sityva, romelsac savaraudo pasuxebidan unda SeusabamoT erT-erTi
varianti, ise, rom sityvaTa mniSvnelobebs Soris mimarTeba sawyis wyvilSi
arsebuli mimarTebis msgavsi (analogiuri) iyos.
21. cxeli : temperatura msubuqi :
(a) wona
(b) saswori
(g) grami
(d) moculoba
22. elva : sinaTle miwisZvra :
(a) stiqia
(b) epicentri
(g) ngreva
(d) ryeva
23. nebarTva : aTavisuflebs xelSekruleba :
(a) aRkveTs
(b) azustebs
(g) adasturebs
(d) avaldebulebs
24. monadire : brakonieri mwerali :
(a) diletanti
(b) plagiatori
(g) cenzori
(d) kritikosi
25. erTdrouli : sinqronuloba mikerZoebuli :
(a) subieqturoba
(b) indiferentuloba
(g) radikaluroba
(d) samarTlianoba 26. energia : aqtiurad epidemia :
(a) vrclad
(b) swrafad
(g) operatiulad
(d) moulodnelad
12
winadadebebis Sevseba
am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa
gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiT aris aRniSnuli.
erTi xazi zogjer erT sityvas gulisxmobs, zogjer ki _ ramdenimes.
savaraudo pasuxTa yovel variantSi mocemulia sityvaTa jgufi, romlis
nawilebi erTmaneTisgan daxrili xazebiTaa (/) gamijnuli. airCieT pasuxis is
varianti, romlis TiToeuli nawilis Tanmimdevrulad Casma Sesabamis
gamotovebul adgilebSi azrobrivad gamarTul winadadebas mogvcems.
27. qali da mamakaci ______ privilegiebis mopovebisa da SenarCunebis
moTxovnilebis TvalsazrisiT; Tumca, maTi socialuri mdgomareoba ______ qals
mamakacze ______ da motivacia aqvs, rom sakuTari mdgomareobis
gasaumjobeseblad ibrZolos.
(a) mniSvnelovnad gansxvavdebian erTmaneTisgan / metwilad erTnairia; amitom /
bevrad naklebi resursebi
(b) ar gansxvavdebian erTmaneTisgan / xSirad imdenad gansxvavebulia, rom / bevrad
naklebi SesaZlebloba
(g) sakmaod gansxvavdebian erTmaneTisgan / xSirad gansxvavebulia; amitom /
aranaklebi resursebi
(d) mcired Tu gansxvavdebian erTmaneTisgan / metwilad erTnairia, da /
aranaklebi SesaZlebloba 28. uiliam terneri xSirad xatavda nislian londons, nawvimar quCebs. oskar uaildi amtkicebda, rom londonis _____ . am _____ gamosWvivis xelovnebis
qmediTobis idea. _____ , is _____ .
(a) nislma Seqmna terneris ferwera / SefasebaSi / xelovnebis qmediTobas
ganapirobebs samyaros mravalferovneba / ver qmnis samyaros xedvis wess
(b) nisli terneris ferweram Seqmna / paradoqsul mtkicebaSi / xelovnebis
qmediTobas ganapirobebs samyaros mravalferovneba / qmnis Tvals, romelic
aRiqvams silamazes, yurs, romelic swvdeba bgeraTa harmonias
(g) nislma Seqmna terneris ferwera / SefasebaSi / xelovneba ayalibebs samyaros
xedvis wess / srulyofilad ver asaxavs samyaros feradovnebas
(d) nisli terneris ferweram Seqmna / paradoqsul mtkicebaSi / xelovneba
ayalibebs samyaros xedvis wess / qmnis Tvals, romelic aRiqvams silamazes,
yurs, romelic swvdeba bgeraTa harmonias
13
29. didi moazrovne _____ , vinc _____ , rom misi, rogorc moazrovnis,
upirvelesi movaleobaa, _____ sakuTar gonebas, _____ .
(a) ver iqneba is / ar aRiarebs / misdios / ra daskvnebamdec ar unda miiyvanos
man
(b) mxolod is SeiZleba iyos / acnobierebs / ar endos / Tu misi daskvnebi
gabatonebul Sexedulebebs upirispirdeba
(g) mxolod is SeiZleba iyos / ar fiqrobs / misdios / Tundac aman
avtoritetebTan dapirispirebamde miiyvanos
(d) ver iqneba is / darwmunebulia / ar endos / ra daskvnebamdec ar unda
miiyvanos man
30. sityva `martivi~ gulisxmobs nawilTa ararsebobas. _____ , martivi _____ sazogadoebas, romelic _____ sazogadoebebs, vidre Tavadaa; romelic ara
mxolod amJamadaa dayvanili _____ segmentamde, aramed _____ manamde arsebuli
segmentaciisa.
(a) maSasadame / unda davarqvaT yovel / ar Seicavs sxva, imaze martiv /
erTaderT / arc Seicavs araviTar niSans
(b) miuxedavad amisa / SesaZlebelia vuwodoT / ar Seicavs sxva, imaze martiv /
erTaderT / arc Seicavs araviTar niSans
(g) miuxedavad amisa / SeuZlebelia davarqvaT yovel / Seicavs sxva, imaze martiv /
ramdenime / Seicavs kidec utyuar niSnebs
(d) maSasadame / unda davarqvaT / Seicavs sxva, imaze martiv / ramdenime / Seicavs
kidec utyuar niSnebs
14
logika
am saxis davalebebi gansxvavdeba erTmaneTisgan monacemebisa da gamosatani
daskvnebis TvalsazrisiT. amitom gansakuTrebuli yuradReba miaqcieT SekiTxvas,
romelic axlavs TiToeul davalebas, da mocemuli variantebidan airCieT
Sesabamisi pasuxi.
zogierT SekiTxvaze pasuxis gacemas gagiadvilebT monacemebis gamosaxva
naxazis formiT.
31. mocemulia: • arc erTi wyalburTeli ar aris gulCaTxrobili
• yvela wyalburTeli kargi mocuravea
qvemoT CamoTvlilTagan romeli debuleba gamomdinareobs am wanamZRvrebidan?
(a) arc erTi kargi mocurave ar aris gulCaTxrobili
(b) ar arsebobs adamiani, romelic gulCaTxrobilic aris da kargi mocuravec
(g) zogierTi kargi mocurave gulCaTxrobilia
(d) zogierTi kargi mocurave ar aris gulCaTxrobili
32. oTxi yuTidan TiToeulSi devs erTi wiTeli da erTi mwvane burTi. oTxive yuTi, oTxive wiTeli da oTxive mwvane burTi danomrilia ricxvebiT 1, 2, 3 da 4. TiToeuli yuTisa da masSi moTavsebuli ori burTis nomrebi (e. i. samive
nomeri) gansxvavdeba erTmaneTisgan. garda amisa, mocemulia:
• #1 yuTSi moTavsebuli wiTeli burTis nomeri emTxveva #2 yuTSi
moTavsebuli mwvane burTis nomers
• #2 wiTeli da #1 mwvane burTebi erTsa da imave yuTSi awyvia
• #3 yuTSi devs #4 mwvane burTi
yuTebSi wiTeli burTebis romeli ganawileba akmayofilebs amocanis pirobebs?
yuTebi #1 #2 #3 #4
(a) 3 4 2 1
(b) 3 4 1 2
(g) 2 1 4 3
(d) 4 3 1 2
15
33. 19 wels gadacilebuli moqalaqeebis gamokiTxvam imis Sesaxeb, hqondaT Tu ara damTavrebuli saSualo skola, aCvena, rom A qalaqis mcxovrebTa Soris
procentulad gansakuTrebiT didia maTi raodenoba, vinc skola swavlis
damTavrebamde miatova. am SedegTan Seusabamo aRmoCnda A qalaqis skolebis
arqivebidan miRebuli informacia, romlis mixedviTac moswavleTa mier skolis
mitovebis procentuli maCvenebeli qalaqis yvela skolaSi sakmaod dabali iyo.
qvemoT CamoTvlilTagan romeli viTarebiT SeiZleba aixsnas gansxvaveba gamokiTxvis
Sedegebsa da A qalaqis skolebis monacemebs Soris?
(a) gamokiTxvisas ar iyo gaTvaliswinebuli, rom zogierTi axalgazrda 17 wlisa
amTavrebs saSualo skolas
(b) gamokiTxvis Sedegebis mixedviT, qalaqis mosaxleobis did nawils saSualo
skola warCinebiT aqvs damTavrebuli
(g) A qalaqis zrdasruli mosaxleobis didi nawili sxva qalaqebidan aris sacxovreblad gadmosuli dasaqmebis mizniT
(d) A qalaqis saSualo skolebSi moswavleTa mimarT moTxovnebi Zalian maRalia, ris gamoc bevri moswavle ver iRebs atestats
34. sofom da Teonam axalgazrda pianistis sakoncerto programa waikiTxes. programis SinaarsiT giorgic dainteresda.
sofo: Tu pianisti Seasrulebs baxis fugas, maSin is ar Seasrulebs
mocartis sonatas. Teona: Tu pianisti Seasrulebs baxis fugas, maSin is Seasrulebs mocartis
sonatasac.
qvemoT CamoTvlilTagan romeli gamomdinareobs gogonebis saubridan, Tu
cnobilia, rom orive gogonam simarTle Tqva?
(a) pianisti ar Seasrulebs baxis fugas
(b) pianisti ar Seasrulebs mocartis sonatas (g) pianisti Seasrulebs baxis fugasac da mocartis sonatasac (d) zemoT mocemuli pasuxebidan arc erTi ar aris swori
16
wakiTxuli teqstis gaazreba
yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo
pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.
saerTaSoriso urTierTobaTa sistemaSi zogierTi saxelmwifo buferis rols
asrulebs. buferuls, rogorc wesi, uwodeben or an met Zlier qveyanas Soris
moqceul patara, sust saxelmwifos, romelsac ar aqvs aqtiuri saxelmwifo
politika da romlis upirvelesi funqciaa dapirispirebulTa gamijvna da
konfliqtis SesaZleblobis minimumamde dayvana. buferi SeiZleba iyos, aseve,
dapirispirebul saxelmwifoebs, blokebsa da maTi gavlenis sferoebs Soris
moqceuli mTeli regioni an zona.
termini `buferuli saxelmwifo~ pirvelad XIX saukunis bolos gamoiyenes.
es sulac ar niSnavs imas, rom buferuli teritoriis an qveynis koncefcia
saerTaSoriso urTierTobebis praqtikaSi adre ar arsebobda. Zveli egviptis
politika saSiS mezoblebTan mimarTebaSi buferuli teritoriebis arsebobas
iTvaliswinebda. Zveli romis xelisufleba sparseTisgan Tavis dasacavad buferul
zonad sirias iyenebda.
saxelmwifos buferulobis erT-erTi mniSvnelovani ganmsazRvrelia wminda
geografiuli faqtori. jer kidev uZvelesi civilizaciebi cdilobdnen, fizikur-
geografiuli zRudeebi (mTebi, udabnoebi, Waobebi) erTmaneTisgan gasamijnad
gamoeyenebinaT. dRes, roca ganviTarebuli samxedro teqnika (TviTmfrinavebi,
raketebi) buferuli teritoriis reliefis mniSvnelobas TiTqos unda
amcirebdes, is usafrTxoebis TvalsazrisiT mainc mniSvnelovania _ samxedro
moqmedebebi dResac, ZiriTadad, teritoriis dakavebas gulisxmobs. buferuli
qveynis reliefi gansazRvravs buferis xasiaTs _ Tu reliefi satransporto
komunikaciisTvis araxelsayrelia, maSin qveyanam SeiZleba gammijvnelis funqcia
Seasrulos, xolo Tu reliefi xelsayrelia gadaadgilebisTvis, is agresorma
SeiZleba metoqeze TavdasxmisTvis gamoiyenos.
m. uaiTi gamoyofs buferuli saxelmwifoebis sam tips: trimerebs, neitralebsa
da satelitebs. trimeri iseTi buferia, romelic erTmaneTTan dapirispirebul
Zlier mezoblebze garkveuli gavlenis moxdenas, maT `wakidebas~, maT Soris
manevrirebas axerxebs. neitrali iseTi saxelmwifoa, romelsac aqtiuri sagareo
politika ar aqvs. amis karg magaliTad SeiZleba safrangeT-germaniisa da safrangeT-
italiis sazRvrebis gaswvriv ganlagebuli patara qveynebi – Sveicaria, luqsemburgi,
niderlandebi da belgia _ miviCnioT. sateliti ki iseTi qveyanaa, romelsac sagareo
politikas sxva ukontrolebs. aRniSnuli tipis buferebs Soris zRvris gavleba
xSirad Wirs. ZalTa Tanafardobis cvalebadobam erTsa da imave buferul
saxelmwifos SeiZleba mokle istoriul periodSi samive roli Seasrulebinos.
buferuli zonisa Tu saxelmwifos `Tandayolili~ Tavisebureba is aris,
rom igi Tavad SeiZleba iqces dapirispirebul mezobelTa interesebis obieqtad
da konfliqtis mizezad. metoqisgan buferuli qveyniT gamoyofili yoveli Zlieri
saxelmwifo dainteresebulia, ar dauSvas metoqis mier buferis gakontroleba. is
Seecdeba, Tavad gaakontrolos buferuli saxelmwifo, an SeunarCunos mas
neitraluroba da suverenuloba. Tumca, dRes saxelmwifoebi amjobineben,
buferuli qveyana maT Soris Seqmnil stabilur neitralur zonas warmoadgendes.
amrigad, buferuli saxelmwifos sicocxlisunarianoba damokidebulia mezoblebis
survilze, SeinarCunon igi, rogorc buferi, aseve imaze, Tu ramdenad uwyobs is
xels Zlier mezoblebs Soris mSvidobis SenarCunebas.
17
35. buferad yofnis aucilebeli pirobaa, rom qveyana:
(a) patara da susti iyos
(b) garemoculi iyos Zlieri qveynebiT
(g) ar atarebdes aqtiur sagareo politikas
(d) mdebareobdes dapirispirebul saxelmwifoTa Soris
36. III abzacis safuZvelze SeiZleba davaskvnaT, rom:
(a) Zvel drosTan SedarebiT, Tanamedrove epoqaSi buferis ZiriTadi daniSnuleba
radikalurad Seicvala
(b) droTa ganmavlobaSi buferuli qveynis reliefis xasiaTma meti mniSvneloba
SeiZina
(g) buferul qveyanaSi fizikur-geografiuli zRudeebis arseboba-ararseboba
dResac gansazRvravs mis funqciebs
(d) samxedro moqmedebebi Tanamedrove epoqaSi mxolod teritoriis dakavebas
gulisxmobs
37. ra aris is ZiriTadi kriteriumi, rac m. uaiTis mier gamoyofil sami tipis buferul qveynebs erTmaneTisgan ganasxvavebs:
(a) maTTvis damaxasiaTebeli sagareo politika
(b) mezobel qveynebze maTi gavlenis Sedegebi
(g) sxva saxelmwifoTa Soris manevrirebis mcdeloba
(d) geografiuli adgilmdebareobis xasiaTi
38. ratom SeiZleba iqces buferi dapirispirebul mezobelTa interesebis
obieqtad?
(a) `metoqisgan buferuli qveyniT gamoyofili yoveli Zlieri saxelmwifo
dainteresebulia, ar dauSvas metoqis mier buferis gakontroleba~
(b) `buferuli saxelmwifos sicocxlisunarianoba damokidebulia imaze, Tu
ramdenad uwyobs is xels Zlier mezoblebs Soris mSvidobis SenarCunebas~
(g) `Zlieri saxelmwifo ... Seecdeba Tavad gaakontrolos buferuli saxelmwifo,
an SeunarCunos mas neitraluroba da suverenuloba~
(d) `saxelmwifoebi amjobineben, buferuli qveyana maT Soris Seqmnil stabilur
neitralur zonas warmoadgendes~
18
39. qvemoT CamoTvlilTagan romeli funqcia ar aqvs buferul qveyanas?
(a) dapirispirebul qveynebs Soris satransporto derefnis
(b) konfliqtSi CarTul saxelmwifoTa Soris Suamavlis
(g) dapirispirebul mxareTa erTmaneTisgan daSorebis
(d) konfliqtis warmoqmnis SesaZleblobis maqsimalurad Semcirebis
40. qvemoT dasaxelebulia sami Tema, romlebic mimoxilulia teqstSi:
1. garkveuli politikuri movlenis ZiriTadi niSnebi da funqciebi
2. garkveuli politikuri movlenis saxeobaTa aRwera
3. eqskursi garkveuli politikuri movlenis istoriidan
romel abzacSi viTardeba TiToeuli Tema, anu pasuxis variantebidan romelia
marTebuli?
(a) 1 _ I, II, IV abzacebi; 2 _ III, IV abzacebi; 3 _ II, III abzacebi
(b) 1 _ I, II, IV abzacebi; 2 _ IV abzaci; 3 _ I, II, IV abzacebi
(g) 1 _ I, III, V abzacebi; 2 _ IV abzaci; 3 _ II, III abzacebi
(d) 1 _ I, III, V abzacebi; 2 _ II, III abzacebi; 3 _ II, IV abzacebi
19
Savi samuSaosTvis
20
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. albaToba: Tu yvela elementaruli xdomiloba Tanabrad mosalodnelia, maSin
xdomilobis albaToba tolia am xdomilobis
xelSemwyob elementarul xdomilobaTa
raodenobis Sefardebisa elementarul
xdomilobaTa saerTo raodenobasTan.
Tu amocanis pirobaSi sawinaaRmdego araa
naTqvami, yovelTvis igulisxmeba, rom elementa-
ruli xdomilobebi Tanabrad mosalodnelia.
8. Semoklebuli gamravlebis formulebi:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2 9. naxazze kuTxe SeiZleba moniSnuli iyos kuTxis
gverdebs Soris Casmuli
patara rkaliT, marTi kuTxe
ki _ patara kvadratiT.
∠A aRniSnavs A kuTxis sidides.
10. paraleluri wrfeebi: ori paraleluri wrfis mesame
wrfiT gadakveTisas Siga jvaredina
kuTxeebi tolia: α = β. 11. samkuTxedi:
• samkuTxedis kuTxeebis sidideTa jami
180°-is tolia; • piTagoras Teorema:
marTkuTxa samkuTxedis
hipotenuzis sigrZis
kvadrati kaTetebis sigrZeTa
kvadratebis jamis tolia:
AB2 = AC2 + BC2
• samkuTxedis farTobi samkuTxedis
gverdis sigrZisa da Sesabamisi simaRlis
namravlis naxevris tolia: . 12. oTxkuTxedi:
• oTxkuTxedis kuTxeebis sidideTa jami
360°-is tolia; • marTkuTxedis farTobi misi sigrZisa da
siganis namravlis tolia: S = ab; • paralelogramis farTobi misi gverdis
sigrZisa da am gverdis Sesabamisi simaRlis
namravlis tolia: S = ah.
13. wre, wrewiri: • wrewiris sigrZe L misi
radiusis mixedviT gamoiTvleba
formuliT: L = 2πr; π ricxvi, measedis sizustiT, 3,14-is tolia;
• r radiusiani wris farTobi gamoiTvleba formuliT: S = πr2.
14. marTkuTxa paralelepipedi: • marTkuTxa paralelepipedis
moculoba misi sigrZis, siganisa da
simaRlis namravlis tolia: V = abc; • kubis SemTxvevaSi: a = b = c.
22
raodenobrivi Sedareba
SeadareT erTmaneTs A da B svetebis ujrebSi mocemuli raodenobebi. Tu A svetis ujraSi mocemuli raodenoba metia B svetis Sesabamis ujraSi
mocemul raodenobaze, airCieT (a);
Tu B svetis ujraSi mocemuli raodenoba metia A svetis Sesabamis ujraSi mocemul raodenobaze, airCieT (b);
Tu ujrebSi mocemuli raodenobebi tolia, airCieT (g);
Tu mocemuli informacia sakmarisi araa imis dasadgenad, romeli raodenobaa
meti, airCieT (d).
A B
41.
(a) (b) (g) (d)
42.
Tornikem, sandrom, sofom da anam soko Seagroves.
gogonebma imdenive soko Seagroves, ramdenic _
biWebma. anam Seagrova yvelaze meti soko.
(a) (b) (g) (d)
43.
rombis gverdis sigrZea a, didi diagonalisa _ d.
(a) (b) (g) (d)
93,0:27 09,228,24 +
sofos mier
Segrovebuli sokos
raodenoba
Tornikes mier
Segrovebuli sokos
raodenoba
d a
23
44.
a da b iseTi ricxvebia, rom 0>a da 0<+ ba .
(a) (b) (g) (d)
45.
ori toli wrewiri erTmaneTs ar kveTs. C wertili erT-erT wrewirze mdebareobs, D _ meoreze. am wertilebisa da wrewirTa centrebis SeerTebiT
miRebuli oTxkuTxedis perimetria 24 sm.
(a) (b) (g) (d)
46.
x da y ricxvebis saSualo ariTmetikuli y da z ricxvebis saSualo ariTmetikulis tolia.
(a) (b) (g) (d)
manZili ricxvTa
RerZze b-s Sesabamisi wertilidan saTavemde
manZili ricxvTa
RerZze a-s Sesabamisi wertilidan saTavemde
6 sm wrewiris radiusis sigrZe
zx-is da z-is saSualo
ariTmetikuli
24
amocanebi
47. 41-isa da 56-is erT-erT naturalur ricxvze gayofisas miRebuli naSTebi erTmaneTis tolia. CamoTvlilTagan romlis toli SeiZleba iyos es naturaluri
ricxvi? (a) 2
(b) 4
(g) 5
(d) 6
(e) 7
48. Tu 1−=x , maSin ( )( )=+−− 32 2331 xxx
(a) –12
(b) –8
(g) 0
(d) 8
(e) 12
49. TamTam 42 cali fanqari ramdenime kolofSi Caawyo: zogSi _ 2 cali, zogSi _ 3. CamoTvlilTagan romlis toli SeiZleba iyos im kolofTa raodenoba, romlebSic 3 fanqaria?
(a) 9
(b) 10
(g) 11
(d) 13
(e) 14
25
50. marTkuTxa samkuTxedisa da marTkuTxedis wveroebi tolujredebiani
badis kvanZebs emTxveva (ix. naxazi). risi
tolia marTkuTxa samkuTxedis farTobis
Sefardeba marTkuTxedis farTobTan? (a) 4
1
(b) 31
(g) 21
(d) 32
(e) 43
51. ramdeniT metia udidesi samniSna ricxvi, romlis cifrTa jami 15-is tolia, umcires orniSna ricxvze, romlis cifrTa jamic, aseve, 15-is tolia?
(a) 784-iT
(b) 791-iT
(g) 832-iT
(d) 879-iT
(e) 891-iT
26
monacemTa analizi
cxrilSi warmodgenilia monacemebi imis Sesaxeb, Tu ramdeni aTasi
srulwlovani adamiani iyo dasaqmebuli Tbilissa da aRmosavleT saqarTvelos
sxvadasxva regionSi 2004-2008 wlebSi, amasTan, 2008 wlis monacemebi moyvanilia kvartalTa mixedviT.
weli da kvartali Tbilisi kaxeTi mcxeTa-mTianeTi qvemo qarTli Sida qarTli
2004 w 149,0 10,8 5,6 23,5 9,8 2005 w 189,0 13,6 6,8 29,4 12,8 2006 w 189,6 15,9 7,2 26,2 12,0 2007 w 196,0 14,2 5,5 23,6 11,8 2008 w I kv. 181,0 10,7 4,8 23,7 11,4
II kv. 184,6 11,9 5,1 24,3 11,3 III kv. 180,8 12,2 4,8 24,6 10,1 IV kv. 189,0 11,8 5,0 24,7 11,3
cxrilis mixedviT upasuxeT Semdeg 2 SekiTxvas: 52. romel regionSi aRiniSna dasaqmebul adamianTa raodenobis zrda yovel
kvartalSi 2008 wlis ganmavlobaSi? (a) TbilisSi
(b) kaxeTSi
(g) mcxeTa-mTianeTSi
(d) Sida qarTlSi
(e) qvemo qarTlSi
53. davuSvaT, rom Sida qarTlSi 2006 wels 150 aTasi srulwlovani adamiani cxovrobda. am regionis srulwlovan adamianTa raodenobis ramdeni procenti
yofila dasaqmebuli 2006 wels? (a) 7%
(b) 8%
(g) 9%
(d) 10%
(e) 12%
27
amocanebi
54. gasayofis (romelic naturaluri ricxvia), gamyofisa da maTi ganayofis
namravli 400-is tolia. risi tolia gasayofi? (a) 20-is
(b) 25-is
(g) 40-is
(d) 50-is
(e) 100-is
55. CamoTvlilTagan romeli SeiZleba iyos im samkuTxedis wveroebis koordinatebi, romelic naxazze
mocemuli samkuTxedis simetriulia y-RerZis mimarT?
(a) (–1; 1), (–3; 4), (–5; 0)
(b) (–3; 3), (–4; 0), (–21; 3)
(g) (1; –2), (3; –4), (7; –4)
(d) (2; 2), (6; 10), (12; 2)
(e) (–2; 2), (–6; 8), (–14; 2)
56. gamomcemlobam sabavSvo literaturis gamofena-gayidva moawyo. dRis pirvel naxevarSi gasayidad gamotanili wignebis raodenoba jer ganaxevrda, Semdeg _ 6-iT Semcirda. dRis meore naxevarSi ki darCenili wignebis raodenoba jer isev
ganaxevrda, Semdeg ki _ 5-iT Semcirda; amis Semdeg gamofenaze arc erTi wigni aRar darCa. sul ramdeni wigni gamoutania gamomcemlobas gasayidad?
(a) 22
(b) 28
(g) 30
(d) 32
(e) 36
57. daviTma 2-jer meti fotosuraTi gadaiRo, vidre _ levanma da 3-jer meti, vidre _ Tornikem. samivem erTad 80-ze naklebi fotosuraTi gadaiRo. maqsimum ramdeni fotosuraTi SeiZleba gadaeRo daviTs?
(a) 36
(b) 42
(g) 48
(d) 54
(e) 60
28
58. wrewiri, romlis diametris sigrZea 2 sm, mdebareobs im wrewiris SigniT, romlis diametris sigrZea 4 sm. ramdeni kvadratuli santimetria am wrewirebiT SemosazRvruli
gamuqebuli figuris farTobi? (a) π
(b) π2
(g) π3
(d) π4
(e) π5
59. mimdevrobis mesame wevria 4, mexuTe wevri ki 1-is tolia. ras udris
mimdevrobis pirveli wevri, Tu cnobilia, rom am mimdevrobis nebismieri wevrisa
da misi momdevno ori wevris namravli 24-is tolia? (a) 24
(b) 6
(g) 5
(d) 4
(e) 1
60. sastumroSi mxolod erTadgiliani da oradgiliani nomrebia. menejerma
Seityo, rom sastumroSi unda ganaTavsos 4 universitetis 10 studenti gogona ise, rom sxvadasxva universitetis studentebi erT nomerSi ar moxvdnen. minimum
ramdeni nomeria saWiro, raTa menejerma aucileblad SeZlos studentebis
sastumroSi ganTavseba? (a) 5
(b) 6
(g) 7
(d) 8
(e) 9
29
raodenobrivi Sedareba
SeadareT erTmaneTs A da B svetebis ujrebSi mocemuli raodenobebi.
Tu A svetis ujraSi mocemuli raodenoba metia B svetis Sesabamis ujraSi mocemul raodenobaze, airCieT (a);
Tu B svetis ujraSi mocemuli raodenoba metia A svetis Sesabamis ujraSi mocemul raodenobaze, airCieT (b);
Tu ujrebSi mocemuli raodenobebi tolia, airCieT (g);
Tu mocemuli informacia sakmarisi araa imis dasadgenad, romeli raodenobaa
meti, airCieT (d).
A B
61.
elenem SabaTs mTeli Tanxis 20% daxarja, xolo
kviras _ darCenili Tanxis 25%.
(a) (b) (g) (d)
62. x > y
(a) (b) (g) (d)
63.
nikam kibis safexurebi gadanomra. pirvel safexurs
man daawera ricxvi 1, meores _ 2 da ase Semdeg.yvela safexuris dasanomrad, sxva cifrebTan erTad,
mas sul 5 cali 3-ianis dawera dasWirda.
(a) (b) (g) (d)
elenes mier SabaTs
daxarjuli Tanxa elenes mier kviras
daxarjuli Tanxa
kibis safexurebis
raodenoba 31
– 2x – 5y
30
64.
gias xelfasi nikas xelfasis naxevarze 250 lariT metia.
(a) (b) (g) (d)
65.
nebismieri a ricxvisTvis ∗a -iT aRniSnulia a-ze
meti umciresi mTeli ricxvi, xolo a#-iT _ a-ze naklebi udidesi mTeli ricxvi.
(a) (b) (g) (d)
66.
AMND marTkuTxedis farTobis Sefardeba ABCD
kvadratis farTobTan 21-ze
naklebia.
(a) (b) (g) (d)
gias xelfasi nikas xelfasi
AMND marTkuTxedis perimetris Sefardeba ABCD
kvadratis perimetrTan 32
( )#17 ∗∗ − ( )∗− ## 17
31
amocanebi
67. kubSi 12 erTnairi marTkuTxa paralelepipedi isea ganlagebuli, rom yovel or mezobel
marTkuTxa paralelepipeds erTi waxnagi saerTo
aqvs (ix. naxazi). kidev ramdeni aseTi marTkuTxa
paralelepipedi Caeteva am kubSi? (a) 54
(b) 60
(g) 66
(d) 72
(e) 78
68. mocemulia namravli 35·30·15·12·4 . CamoTvlilTagan romel namravlze bs!
jzpgb es namravli unaSTod? (a) 40·21·8
(b) 50·21·24
(g) 25·21·16
(d) 50·9·8
(e) 75·14·9
69. ricxvebi x, 2x, y, 7,7 zrdis mixedviTaa dalagebuli. gansxvaveba yovel or mezobel ricxvs Soris 2-ze naklebia. CamoTvlilTagan romlis toli SeiZleba iyos y?
(a) 5,4
(b) 5,5
(g) 5,7
(d) 5,8
(e) 6
70. ujraSi oTxi erTnairi baraTia, romlebic danomrilia ricxvebiT: 1, 2, 3 da 4. ujridan, masSi Cauxedavad, unda amoiRon ori baraTi. risi tolia imis
albaToba, rom amoRebuli baraTebis nomrebis jami luwi ricxvi iqneba? (a) 4
3
(b) 32
(g) 21
(d) 31
(e) 41
32
monacemTa analizi
grafikze warmodgenilia monacemebi imis Sesaxeb, Tu zogadsaganmanaTleblo
skolis TiToeuli safexuris (dawyebiTi, sabazo, saSualo) moswavleTa raodenobis ramden procents Seadgenda amave safexuris im moswavleTa raodenoba, romlebic
sportiT iyvnen dakavebulni 2001/2002 _ 2005/2006 saswavlo wlebSi. magaliTad, grafikis mixedviT varkvevT, rom 2001/2002 saswavlo wels sportiT dakavebuli yofila saSualo skolis moswavleTa 14% .
diagramaze ki warmodgenilia monacemebi imis Sesaxeb, Tu
zogadsaganmanaTleblo skolis TiToeul safexurze sportiT dakavebul
moswavleTa saerTo raodenobis ramden procents Seadgenda fexburTiT, ragbiT,
WidaobiT Tu sportis romelime sxva saxeobiT dakavebul moswavleTa
raodenobebi 2005/2006 saswavlo wels. magaliTad, diagramis mixedviT varkvevT, rom 2005/2006 saswavlo wels dawyebiT skolaSi fexburTiT dakavebuli yofila dawyebiT skolaSi sportiT dakavebul moswavleTa 20%.
grafikisa da diagramis mixedviT upasuxeT Semdeg 4 SekiTxvas:
33
71. romel saswavlo wels iyo sportiT dakavebul moswavleTa wili dawyebiT skolaSi 1,5-jer meti, vidre _ saSualo skolaSi?
(a) 2001/2002 saswavlo wels
(b) 2002/2003 saswavlo wels
(g) 2003/2004 saswavlo wels
(d) 2004/2005 saswavlo wels
(e) 2005/2006 saswavlo wels
72. ramdeniT aRemateboda 2003/2004 saswavlo wels sabazo skolaSi sportiT dakavebul moswavleTa procentuli maCvenebeli wina saswavlo wlis Sesabamis
maCvenebels? (a) 2-iT
(b) 3-iT
(g) 4-iT
(d) 5-iT
(e) 6-iT
73. sportiT dakavebul moswavleTa ramdeni procenti yofila dakavebuli
WidaobiT saSualo skolaSi 2005/2006 saswavlo wels? (a) 20%
(b) 30%
(g) 40%
(d) 50%
(e) 70%
74. dawyebiTi skolis moswavleTa raodenobis ramden procents Seadgenda
ragbiTa Tu fexburTiT dakavebul moswavleTa raodenoba 2005/2006 saswavlo
wels? (a) 6%
(b) 8%
(g) 12%
(d) 14%
(e) 16%
34
amocanebi
75. figuris diametri vuwodoT am figuris wertilebis
SemaerTebeli monakveTebidan udidesi sigrZis mqone monakveTs.
tolgverda samkuTxedis gverdis sigrZea 12 sm.
risi tolia am samkuTxedis diametris sigrZe? (a) 4 sm
(b) 6 sm
(g) 12 sm
(d) 24 sm
(e) 36 sm
76. Tamarma, naTiam da elenem zRvis napiras sul 27 niJara Seagroves. Tamarma naTias misca 4 niJara, naTiam elenes _ 1 niJara. Tavis mxriv, elenem Tamars ramdenime niJara misca. amis Semdeg samives toli raodenobis niJarebi
aRmoaCndaT. ramdeni niJara Seugrovebia naTias? (a) 9
(b) 8
(g) 7
(d) 6
(e) 5
77. ramdeni fiala gaawonasworebs rZian
kolofsa da mawvnis qilas
marjvena sasworze? (a) 8
(b) 9
(g) 10
(d) 11
(e) 12
35
78. erT sibrtyeze mdebare ori araTanamkveTi wris centrebs Soris manZilia 7 sm, xolo erT-erTi wris radiusis sigrZea 5 sm. qvemoT CamoTvlilTagan
romlis toli SeiZleba iyos meore wris radiusis sigrZe? (a) 1,2 sm
(b) 2,1 sm
(g) 2,3 sm
(d) 3,4 sm
(e) 4,5 sm
79. saaTebis qarxana wlis I naxevarSi
uSvebda rogorc meqanikur, ise _
eleqtronul saaTebs, xolo wlis II
naxevarSi _ mxolod eleqtronul saaTebs.
diagramebze warmodgenilia monacemebi imis
Sesaxeb, Tu qarxnis mier gamoSvebuli
saaTebis raodenobis ramden procents
Seadgenda meqanikuri da eleqtronuli
saaTebis raodenoba rogorc wlis I
naxevarSi, ise mTeli wlis ganmavlobaSi.
ramdenjer meti eleqtronuli saaTi gamouSvia qarxanas wlis I naxevarSi wlis
II naxevarTan SedarebiT? (a) 1,2-jer
(b) 1,6-jer
(g) 2-jer
(d) 2,4-jer
(e) 3-jer
80. xexilis baRSi msxlis xeebis raodenoba 15-iT naklebia vaSlis xeebis
raodenobaze. CamoTvlilTagan romlis toli SeiZleba iyos msxlis xeebis
raodenobis Sefardeba vaSlis xeebis raodenobasTan? (a) 3
1
(b) 53
(g) 72
(d) 73
(e) 95
36
Savi samuSaosTvis