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