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 !

I

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. Txzavs : moTxroba (a) baZavs : nimuSi

(b) ikvlevs : kvali

(g) agrovebs : koleqcia

(d) amravlebs : mamravli

2. waaxalisa : waaqeza (a) miimxro : gadaibira

(b) moiTmina : gajiutda

(g) endo : daimsaxura

(d) SeigrZno : mixvda

3. siurprizi : moulodneli (a) sarkazmi : ironiuli

(b) komplimenti : Sesaferisi

(g) fsevdonimi : sakuTari

(d) paradoqsi : uCveulo

4. oranJerea : oazisi (a) herbariumi : baRi

(b) zooparki : nakrZali

(g) limonariumi : sanerge

(d) akvariumi : akvaparki

5. wertili : polusebi (a) adamiani : antipodebi

(b) disertanti : oponentebi

(g) ucxoeli : emigrantebi

(d) lideri : pretendentebi

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. radgan _____ da radgan yovelTvis _____ sruli codna warsulis Sesaxeb, _____ viyoT darwmunebulni, rom swori gadawyvetileba miviReT.

(a) momavali SegviZlia sakmaod zustad viwinaswarmetyveloT / gvaqvs / Znelia (b) momavalTan dakavSirebiT mxolod varaudi SegviZlia gamovTqvaT / ar gvaqvs /

Znelia

(g) momavalTan dakavSirebiT mxolod varaudi SegviZlia gamovTqvaT / gvaqvs /

SeuZlebelia

(d) momavali SegviZlia sakmaod zustad viwinaswarmetyveloT / ar gvaqvs /

SeuZlebelia

8. _____ adamianebi _____ socialur normebs, isini, ZiriTadad, _____ arian, _____ cdiloben daicvan samarTlebrivad dadgenili normebi.

(a) marTalia, / iSviaTad arRveven / kanonmorCilni / Tumca, yovelTvis

(b) radgan / xSirad arRveven / kanonmorCilni ar / Tumca, yovelTvis

(g) miuxedavad imisa, rom / xSirad arRveven / kanonmorCilni / da, Sesabamisad,

(d) imis gamo, rom / iSviaTad arRveven / kanonmorCilni ar / da, Sesabamisad,

9. Sua saukuneebis teqstebSi warmodgenilia ideali, romelTan miaxloebac

_____ , magram ganxorcieleba _ _____ . albaT, amaSia don-kixotis yvela

warumateblobis saidumlo _ imas, _____ , igi _____ miiCnevs.

(a) SeuZlebelia / SesaZlebeli / rac adamianisTvis Cveuli qcevis nimuSia /

idealad

(b) SesaZlebelia / SeuZlebeli / rac yoveldRiuri qcevis normaa / adamianisTvis

Cveuli qcevis nimuSad

(g) SeuZlebelia / SesaZlebeli / riskenac adamiani SeiZleba mxolod iswrafodes /

idealad

(d) SesaZlebelia / SeuZlebeli / riskenac adamiani SeiZleba mxolod iswrafodes /

yoveldRiuri qcevis normad

4

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. frangi, italieli da espaneli alpinistebis jgufi sam karavSi ise ganawilda, rom TiToeul karavSi ori alpinisti aRmoCnda.

• pirvel karavSi erTi da imave erovnebis alpinistebi arian, xolo danarCen

orSi _ sxvadasxva erovnebisa

• meore karavSi arc erTi alpinisti ar aris frangi

qvemoT CamoTvlilTagan alpinistTa karvebSi ganawilebis romeli varianti

akmayofilebs am pirobebs?

I karavi II karavi III karavi

(a) espaneli, espaneli frangi, italieli italieli, espaneli

(b) espaneli, frangi italieli, espaneli frangi, italieli

(g) italieli, italieli espaneli, frangi frangi, frangi

(d) frangi, frangi espaneli, italieli espaneli, italieli

11. mocemulia: • odesme aucileblad dadasturdeba marsze sicocxlis arseboba

Semdegi winadadebebidan romelia mocemulis tolfasi?

(a) SeuZlebelia, odesme marsze sicocxlis arseboba dadasturdes

(b) SesaZlebelia, odesme marsze sicocxlis arseboba dadasturdes

(g) SeuZlebelia, marsze sicocxlis arseboba arasodes dadasturdes

(d) SesaZlebelia, marsze sicocxlis arseboba arasodes dadasturdes

5

12. mocemulia: • me ar myavs iseTi megobari, romelic ar aris saqmiani adamiani

• me bevri megobari myavs da yvela Cemi megobari modurad icvams

qvemoT CamoTvlilTagan romeli gamomdinareobs am ori debulebidan?

(a) yvela saqmiani adamiani icvams modurad

(b) zogierTi adamiani saqmiania da moduradac icvams

(g) yvela, vinc modurad icvams, aris saqmiani adamiani

(d) ar arsebobs adamiani, romelic saqmiania da, amave dros, modurad ar icvams

13. veSapebis masobrivi gamoriyvis mizezebis Sesaxeb mecnierTa Soris azrTa

sxvadasxvaobaa. biologTa erTi jgufi am fenomens ase xsnis: veSapebi TavianTi

eqolokaciis unaris meSveobiT, Cveulebriv, Tavs arideben sanapiroebs. magram es

unari ar aris imdenad ganviTarebuli, rom veSapebma igrZnon wyalsa da xmeleTs

Soris gansxvaveba iseT adgilebSi, sadac wylis siRrme napirisken TandaTan,

SeumCnevlad mcirdeba.

qvemoT CamoTvlilTagan romeli viTareba ganamtkicebs biologTa am mosazrebas?

(a) veSapebis gamoriyva SeiZleba iyos Sedegi maTi mcdelobisa, Tavi daaRwion ama

Tu im mtaceblis Tavdasxmas

(b) arsebobs imis sabuTebi, rom samxedro sazRvao wvrTnebis dros gamoyenebuli

intensiuri bgeriTi signalebi azianebs veSapebis eqolokaciis organoebs

(g) veSapebi specialuri bgeriTi signalebiT uxmoben Tanagundelebs saSvelad;

erTi gariyuli veSapis aseT signalze sapasuxod SeiZleba mTeli gundi misken

gaeSuros da zogierTma maTganma Tavadac veRar SeZlos wyalSi dabruneba

(d) veSapebis gamoriyvis SemTxvevebis statistikam aCvena, rom sanapiro zolze

arsebobs e. w. `cxeli wertilebi~, sadac gansakuTrebiT xSirad xdeba

masobrivi gamoriyva. am adgilebSi okeanis fskeris daxra mxolod naxevari

gradusia

6

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

msoflios uZvelesi civilizaciebis SemoqmedTa umravlesoba didi xnis win

gadaSenda. maias xalxi* ki dResac arsebobs, misi STamomavlebi garegnulad arc

gamocvlilan. maias tomebma enac SeinarCunes, Tumca, maTi warsulis Seswavla

bevrad ufro rTulia, vidre didi xnis win dangreuli sxva romelime

civilizaciisa. axali welTaRricxvis dasawyisSi maiam Seqmna Zlieri imperia,

romelic qalaqebis mSeneblobasa da ganviTarebaze iyo orientirebuli. VIII Tu

IX saukuneSi ki maias tomebma uceb miatoves TavianTi qalaqebi, uceb Sewyda

didmasStabiani mSeneblobebi. am civilizaciis dacemis savaraudo mizezebs or

kategoriad yofen: araekologiurad (mosaxleobis siWarbe, mtris Tavdasxma,

mniSvnelovani savaWro gzebis ganadgureba) da ekologiurad (ekologiuri

katastrofa, epidemiebi, klimatis mkveTri cvlileba).

centraluri amerikis mkvlevrebs sami siZnele eRobebodaT win: am kulturis

TaviseburebiT gamowveuli sruliad axali problemebi; mravalferovani masalis

uqonloba; adgilobriv landSaftsa da havasTan dakavSirebuli siZneleebi. maias

enaze SemorCenili ramdenime sabuTisa Tu warweris wakiTxva SesaZlebeli gaxda

mxolod diego de landas wignis daxmarebiT. diego de landam maias tomis erT-erTi

ukanaskneli mefisgan Caiwera cnobebi maias xalxis cxovrebis wesze, mis RmerTebze,

mezobel tomebTan urTierTobebze. wigns darTuli aqvs suraTebi, romlebic

gviCvenebs, Tu ra niSnebiT aRniSnavda maia Tveebsa da dReebs. maias mier qvis

iaraRiT amokveTili yoveli reliefi, ornamenti Tu cxovelis gamosaxuleba

dakavSirebuli iyo raime TariRTan. yoveli ucnauri saxe aRniSnavda romelime

ricxvs, an mTel kalendarul sqemasac ki. magaliTad, ornamenti, romelic

TxuTmetjer meordeboda ieroglifTa kibeze qalaq kopanSi, aRniSnavda gasuli

drois ciklebs. SeiZleba iTqvas, rom maias yoveli nageboba gaqvavebuli kalendaria.

Tanamedrove kalendari zedmiwevniT zusti ar aris _ igi mxolod ramdenadme

ukeTesia winamorbedebze. Zv. w. 238 wels ptolemeos III-m odnav gaaumjobesa

Zvelegvipturi kalendari. iulius keisris saxelTanaa dakavSirebuli e. w. iuliusis

kalendari, romelic gamoiyeneboda 1582 wlamde, rodesac igi axali, e. w.

grigorianuli kalendriT Secvala papma grigol XIII-m. Tu wlis xangrZlivobis

Sesaxeb sxvadasxva kalendrisa da astronomiuli gamoTvlebiT miRebul Tanamedrove

monacemebs erTmaneTs SevadarebT, aseT suraTs miviRebT:

wlis xangrZlivoba _ iuliusis kalendriT 365,250000 dRe

grigorianuli kalendriT 365,242000 dRe

maias kalendriT 365,242129 dRe

astronomiuli gamoTvlebiT 365,242198 dRe

ucnauria, magram xalxi, romelic uzustes astronomiul dakvirvebebsa da

maTematikur gamoTvlebs awarmoebda, yvelafers mistikur mniSvnelobas aniWebda. maias

warmodgenebSi konkretuli TariRebi, ciklebi `zebunebriv~ Zalebs ukavSirdeboda.

maias tomebi Tavis didebul Senobebs maSin ki ar agebdnen, roca es maT

sWirdebodaT, aramed maSin, roca kalendari `ubrZanebda~. isini aSenebdnen yovel

xuT, aT, oc weliwadSi erTxel da usaTuod miuTiTebdnen aSenebis TariRs. Tu

axali kalendaruli cikli moiTxovda, ukve aSenebul piramidas meores daaSenebdnen.

msoflioSi yvelaze zusti kalendris Semqmneli xalxi imave dros misi mona gaxda.

*maias xalxi _ centraluri amerikis mkvidrni, ax. w. dasawyisSi Seqmnes didi civilizacia.

7

14. qvemoT dawyvilebulia pirveli abzacis winadadebebi. CamoTvlilTagan romeli ori winadadebis dasakavSireblad ar iqneboda swori kavSiris _ `Tumca~ _

gamoyeneba?

(a) msoflios uZvelesi civilizaciebis SemoqmedTa umravlesoba didi xnis win

gadaSenda _ maias xalxi dResac arsebobs

(b) maias tomebma enac SeinarCunes _ maTi warsulis Seswavla bevrad ufro

rTulia, vidre didi xnis win dangreuli sxva romelime civilizaciisa

(g) axali welTaRricxvis dasawyisSi maiam Seqmna Zlieri imperia, romelic

qalaqebis ganviTarebaze iyo orientirebuli _ maias tomebma uceb miatoves

TavianTi qalaqebi, uceb Sewyda didmasStabiani mSeneblobebi

(d) maias tomebma uceb miatoves TavianTi qalaqebi, uceb Sewyda didmasStabiani

mSeneblobebi _ am civilizaciis dacemis savaraudo mizezebs or kategoriad

yofen

15. ra sirTules ukavSirdeba maias civilizaciis kvleva?

(a) es civilizacia uZvelesia da man didi xnis win Sewyvita arseboba; Sesabamisad,

maias civilizaciidan mxolod ramdenime werilobiTi sabuTi SemogvrCa

(b) centraluri amerikis civilizaciebs savaWro gzebi akavSirebda erTmaneTTan,

am sasicocxlo gzebis ganadgurebam ki SeuZlebeli gaxada komunikaciebi

(g) maias civilizaciis dacema ekologiurma katastrofam ganapiroba, Sesabamisad,

ganadgurda nivTieri kulturis uamravi nimuSi

(d) maias kulturis specifikuroba sruliad axal problemebs badebs, mwiri

masala ki Sedarebebisa da ganzogadebis saSualebas ar iZleva

16. ras gulisxmobs gamoTqma: `maias yoveli nageboba gaqvavebuli kalendaria~?

(a) maias xalxis mier qvis iaraRiT amokveTil reliefebze asaxulia Zveli

qalaqebis cxovrebisa da omis epizodebi

(b) taZrebze, piramidebze amokveTili yoveli ornamenti Tu ucnauri saxe

aRniSnavda romelime TariRs, SesaZloa, mTel kalendarul sqemasac

(g) cnobebi, romlebic diego de landam maias tomis erT-erTi ukanaskneli

mefisgan Caiwera, ZiriTadad, qvis nagebobebsa da kalendars ukavSirdeboda

(d) qvis ornamenti, romelic TxuTmetjer meordeboda ieroglifTa kibeze qalaq

kopanSi, warmoadgens maias xalxis mier Seqmnili kalendris fragments

8

17. ra mizniT aris moyvanili teqstSi sxvadasxva epoqis kalendris monacemebi?

isini naTels xdis, rom:

(a) maias kalendris monacemebi naklebad zustia astronomiuli gamoTvlebiT

miRebul Tanamedrove monacemebTan SedarebiT

(b) droTa ganmavlobaSi sxvadasxva kalendris monacemebi sul ufro metad

uaxlovdeboda astronomiuli gamoTvlebiT miRebul Tanamedrove monacemebs

(g) sxva kalendrebis monacemebTan SedarebiT, maias kalendris monacemebi yvelaze

axlos aris Tanamedrove samecniero kvlevebiT miRebul SedegebTan

(d) maias kalendaruli sqema Zvelegvipturi, iuliusis, ptolemeosisa da

grigorianuli kalendaruli sqemebis msgavsia

18. teqstis Tanaxmad, maias xalxis swrafva mistikurobisken ucnauria, radgan:

(a) maias xalxi uzustes astronomiul dakvirvebebsa da maTematikur gamoTvlebs

awarmoebda, rac am xalxis azrovnebis racionalurobaze unda metyvelebdes

(b) diego de landa maias xalxs sxvagvarad axasiaTebs: isini winaswar

SemuSavebuli gegmis Sesabamisad aSenebdnen uzarmazar qalaqebs, taZrebs,

piramidebs

(g) maias miTebSi asaxuli warmodgenebi RmerTze, samyaroze, civilizaciaze

gansazRvrulia zebunebrivi Zalebis rwmeniT

(d) ekologiur katastrofebs, klimatis mkveTr cvlilebebs maias xalxi bunebis

kanonebiT xsnida da yovel konkretul movlenas ieroglifTa kibeze

aRnusxavda

19. `yvelaze zusti kalendris Semqmneli xalxi imave dros misi mona gaxda~. qvemoT CamoTvlilTagan romeli gamoxatavs am winadadebis azrs?

(a) maias civilizaciaSi xSirad gvxvdeba piramida, romelzec meore piramidaa

daSenebuli da masze miTiTebulia axali TariRi

(b) ornamentebiT, sxvadasxva gamosaxulebiT maias xalxi aRniSnavda gasuli drois

ciklebs

(g) nebismier did mSeneblobas maias xalxi gegmavda dReebis, Tveebis, wlebis

aRnusxvis garkveuli sistemis `karnaxiT~

(d) maias xalxi aSenebda did qalaqebs, taZrebs, sasaxleebs da yvela nagebobas

zustad aTariRebda

9

20. ucnobi avtoris mier XX saukuneSi gadaRebul erT fotosuraTze

aRbeWdilia indieli Wabuki profilSi. indieli dgas aTas xuTasi wlis win

agebuli taZris fonze. taZris kedelze amokveTilia reliefi, romelzec

gamosaxulia maias tomis mamakacis profili, aseve, varskvlavebi, ieroglifebi,

ornamentebi.

teqstis romeli abzacis sailustraciod SeiZleba gamoviyenoT es

fotosuraTi?

(a) I abzacis, radgan aq saubaria centraluri amerikis erT-erTi civilizaciis

SemoqmedTa da Tanamedrove indielTa anTropologiur (garegnul) msgavsebaze

(b) II abzacis, radgan aq saubaria kopanis ieroglifTa kibeze drois ciklebis

aRniSvnis principis Sesaxeb, reliefze ki ieroglifebiT weria maias

ukanaskneli mefis saxeli

(g) III abzacis, radgan aq saubaria sxvadasxva epoqis kalendarze, reliefze

gamosaxuli ornamentebi ki, SesaZloa, grigorianuli kalendris fragmentebi

iyos

(d) IV abzacis, radgan aq saubaria maias xalxis miRwevebze astronomiaSi,

fotoze gamosaxuli Wabuki ki reliefze gamosaxul varskvlavebs uyurebs

10

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. monarqia : memkvidreobiToba respublika :

(a) rigiToba

(b) arCeviToba

(g) cvalebadoba

(d) Tanasworoba

22. leqsika : sityva biosfero :

(a) anatomiuri agebuleba

(b) cocxali organizmi

(g) sicocxlis gavrceleba

(d) ekologiuri sistema

23. nebarTva : aTavisuflebs xelSekruleba :

(a) aRkveTs

(b) azustebs

(g) adasturebs

(d) avaldebulebs

24. vefxvi : pantera ia :

(a) buCqi

(b) bolqvi

(g) vardi

(d) yoCivarda

25. individualizmi : pirovneba skepticizmi :

(a) eWvi

(b) kritika

(g) pozicia

(d) ndoba

26. artileristi : kavaleristi freska :

(a) bareliefi

(b) ornamenti

(g) palitra

(d) ferwera

11

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. xelovneba _____ sinamdviles, _____ , rac aris sinamdvile. xelovani _____ da cdilobs, esTetikuri xilviT dagvanaxos is, rac _____ .

(a) marTlac asaxavs / radgan yovelTvis imas gamoxatavs / scildeba realur

movlenaTa farglebs / sinamdvileSia

(b) fotografiulad ar asaxavs / Tumca, arasdrosaa mxolod is / zustad aRwers

realur movlenebs / sinamdvileSia

(g) marTlac asaxavs / magram arasdrosaa mxolod is / scildeba aRqmad movlenaTa

farglebs / sinamdvileSi ar aris

(d) fotografiulad ar asaxavs / radgan yovelTvis imas gamoxatavs / zustad

aRwers aRqmad movlenebs / sinamdvileSi ar aris

28. udavod ______ , rom ______ adamians velur mxecTan aaxloebs, ______ , rom ______ RvTaebriobis niSniT aris aRbeWdili.

(a) mcdari azria / martoobis siyvaruli / Sesabamisad, arc is aris marTali / martoobis siyvaruli

(b) marTalia / sazogadoebisgan gandgoma / Sesabamisad, sicruea / martoobis

siyvaruli

(g) marTalia / martoobis siyvaruli / Tumca, isic sicruea / adamianebTan

urTierTobis survili

(d) mcdari azria / sazogadoebisgan gandgoma / miuxedavad amisa, marTalia /

adamianebTan urTierTobis survili

12

29. epoqisTvis, romelSic Cven vcxovrobT, ganmsazRvrelia rusos sentencia:

`bunebam adamiani bednieri da keTili Seqmna, da Tu is sxvagvaria, amaSi _____ ~.

es TvalTaxedva or Secdomas emyareba: erTi, rom adamiani _____ bednieri da

keTili iyo, _____ is _____ .

(a) TviTon mas miuZRvis brali / sazogadoebis warmoSobamde / da rom,

Sesabamisad, / sakuTari nebiT xdeba sazogadoebis wevri

(b) bunebis xeli ar urevia / Tavisi bunebiT / xolo sazogadoebasTan

urTierTobiT / iZens am Tvisebebs (g) sazogadoebaa damnaSave / Tavdapirvel, bunebriv mdgomareobaSi / da, meore,

rom Tavidan / sazogadoebis gareSe arsebobda

(d) veravis davdebT brals / sazogadoebis wiaRSi / xolo sazogadoebisgan

gandgomis Sedegad / ubeduri da boroti xdeba

30. miTis ZiriTadi struqtura sxvadasxva civilizaciis xalxebTan _____ ,

radgan miTi Tavisufali _____ _ igi _____ . amitom miTosis mkvlevarTaTvis

_____ .

(a) xSirad msgavsia, zogjer identuric / gamonagoni ar aris / dawuruli

formiT mocemuli msoflios suraTia / siuJeturi sqemis identuroba

advilad asaxsnelia

(b) yovelTvis sxvadasxvagvaria / gamonagoni ar aris / msoflios

mravalferovnebis ilustrirebas warmoadgens / siuJeturi sqemis identuroba

advilad asaxsnelia

(g) xSirad msgavsia, zogjer identuric / gamonagonia / dawuruli formiT

mocemuli msoflios suraTia / siuJetTa nairgvaroba Znelad asaxsneli araa

(d) yovelTvis sxvadasxvagvaria / gamonagonia / msoflios mravalferovnebis

ilustrirebas warmoadgens / siuJetTa nairgvaroba Znelad asaxsnelia

13

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. magidaze erT rigad awyvia xuTi firfita. iqvea saRebavebi da funjebi.

sandrom TiToeul firfitas unda gaukeTos erTi zoli _ wiTeli an lurji,

Tanac ise, rom Sesruldes Semdegi ori piroba:

• wiTelzoliani firfitebi lurjzolian firfitebze meti iyos

• erTmaneTis miyolebiT mdebare sami firfitidan erTi mainc iyos lurjzoliani

sandros amis gakeTeba bevrnairad SeuZlia. qvemoT CamoTvlilTagan romeli

viTareba ganxorcieldeba yvela SemTxvevaSi?

(a) meore firfitas aqvs wiTeli zoli

(b) pirvel an mexuTe firfitas (an orives) aqvs wiTeli zoli

(g) mesame an meoTxe firfitas (an orives) aqvs wiTeli zoli

(d) meoTxe firfitas aqvs lurji zoli

32. viciT, rom arseboben cnobili moWadrakeebi. amasTan, mocemulia:

• arc erTi cnobili moWadrake ar aris kosmonavti

• yvela cnobili moWadrake fexburTis gulSematkivaria

qvemoT CamoTvlilTagan romeli debuleba gamomdinareobs am wanamZRvrebidan?

(a) fexburTis arc erTi gulSematkivari ar aris kosmonavti

(b) ar arsebobs adamiani, romelic kosmonavticaa da fexburTis gulSematkivaric

(g) fexburTis zogierTi gulSematkivari kosmonavtia

(d) fexburTis zogierTi gulSematkivari ar aris kosmonavti

14

33. A regioni bolo aTi wlis ganmavlobaSi grili klimatiT gamoirCeoda,

magram im wlebSi, romlebSic aq haeris saSualo dRiuri temperatura da

tenianoba normaze ufro maRali iyo, mniSvnelovnad izrdeboda yvela saxis

sasoflo-sameurneo kulturis mosavali. mosalodnelia, rom globaluri

daTbobis procesebis Sedegad ramdenime wlis Semdeg A regionisTvis normad

iqces haeris dRiuri temperaturisa da tenianobis maRali maCveneblebi, romlebic

aRniSnul wlebSi dafiqsirda. am informaciis safuZvelze fermerma ivarauda,

rom momaval aTwleulebSi A regionSi mosavali gaizrdeba.

qvemoT CamoTvlilTagan romeli faqti ayenebs eWvqveS am varauds?

(a) haeris temperaturisa da tenianobis zrdasTan erTad gaizrdeba atmosferoSi

iseTi airebis Semcveloba, romlebic aCqarebs mcenareTa zrdas

(b) A regionSi bolo wlebSi zogadad grili da mSrali klimatis gamo regionis savargulebze mniSvnelovnad Semcirda parazitebis raodenoba

(g) haeris temperaturisa da tenianobis zrdasTan erTad gaizrdeba wliuri

naleqebis raodenobac, rac xelsayrelia mcenareTa mravali saxeobisTvis

(d) bolo wlebSi zogadad grili da mSrali klimatis gamo A regionSi zogierTi kulturis moyvana SeuZlebeli gaxda

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

15

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

saxelmwifos neitralitetis cneba da masTan dakavSirebuli praqtika

istoriis manZilze icvleboda da axal-axal Taviseburebebs iZenda. metic, yvela

neitralurma saxelmwifom am cnebas da mis praqtikul mxares raRac sakuTari,

gansakuTrebuli SesZina. fineTis yofilma prezidentma urho kekonenma erTxel

SeniSna, ramdeni neitraluri saxelmwifoc aris, imdeni saxis neitraliteti

arsebobso. neitralitetis uZvelesi saxea neitraliteti omSi _ gansakuTrebuli

uflebrivi statusi saxelmwifosi, romelic ar erTveba or qveyanas Soris

SeiaraRebul konfliqtSi da maT mimarT miukerZoebel pozicias inarCunebs.

neitralitetis cneba jer kidev Zvel samyaroSi iyo cnobili. geografiuli,

politikuri, ekonomikuri da sxva faqtorebi saSualebas aZlevda calkeul

saxelmwifoebs, samxedro konfliqtebis miRma darCeniliyvnen. Zveli berZnuli da

romauli istoriuli wyaroebi saintereso cnobebs gvawvdis neitralitetis

Sesaxeb, romelic aRiniSneboda, rogorc `ganze dgoma~, `dapirispirebul mxareebTan

megobrobis SenarCuneba~. Tumca, realurad neitraliteti niSnavda qveynis

valdebulebas, ar daxmareboda im mxares, romelic `usamarTlo~ oms awarmoebda.

`agresoris~ dadgenisas didi mniSvneloba eniWeboda imas, iyo Tu ara daculi

yvela saWiro rituali omis gamocxadebisas, da ara imas, Tu vin daiwyo omi.

gansakuTrebiT mkafiod iyo gansazRvruli omis gamocxadebisa da dasrulebis

wesebi Zvel romSi. Tu agresoris dadgena ver xerxdeboda, maSin qveyana valdebuli

iyo, konfliqtis orive mxaris mimarT erTnairi pozicia daekavebina iseT

sakiTxebTan dakavSirebiT, rogorebicaa jarisTvis teritoriis gadakveTis uflebis

micema, jaris sursaTiT momarageba, alyaSemortymulTa daxmarebaze uaris Tqma.

neitralitetis valdebulebebi xelSekrulebebSic aisaxeboda.

feodalizmis epoqaSi neitraluri saxelmwifos valdebuleba, ar mieRo

monawileoba sxva qveynebis omebSi, naklebad mkacri gaxda. garda imisa, rom saomar

moqmedebebSi monawile jarebs neitraluri teritoriis mSvidobianad gadakveTis

ufleba hqondaT, nebadarTuli iyo, agreTve, neitraluri qveynis mkvidrTa gamoyeneba

daqiravebul jariskacebad. dasaSvebi iyo omSi CarTul mxareTa daxmareba jariT,

fuladi saxsrebiT an iaraRiT. es, ZiriTadad, maSin xdeboda, roca neitraluri

qveyana omSi amgvari iribi monawileobis Sedegad garkveul sargebels moeloda.

meore mxriv, neitralitetis saerTaSoriso garantiebi TiTqmis ar arsebobda. xSiri

iyo neitraluri saxelmwifos teritoriaze samxedro moqmedebaTa akrZalvis

ugulebelyofa, Tu am saxelmwifos teritoriaze iyo iseTi obieqtebi (magaliTad,

cixesimagre), romelTa xelSi CagdebiT dapirispirebul mxareTagan erT-erTi

upiratesobas moipovebda. neitralur saxelmwifos sakuTari ZalebiT uxdeboda

`neitralitetis~ SenarCuneba.

Tanamedrove epoqaSi neitralitetis statusi saxelmwifosTvis aris

damoukideblobis garanti, sxva saxelmwifoebisTvis ki _ imis garanti, rom

neitraluri qveyana konfliqtSi ar CaerTveba. Tumca, Tanamedrove konfliqtebis

umravlesoba gansxvavdeba klasikuri omebisgan da axali tipis problemebs wamoWris:

rogor unda moiqces neitraluri saxelmwifo, Tu mas sTxoven, gaxsnas sahaero an

sazRvao sazRvrebi, raTa xeli Seuwyos konfliqtis prevencias, antiteroristul Tu

humanitarul aqciebs? am SekiTxvaze pasuxi neitralurobis Teorias jerjerobiT ar

aqvs.

16

35. ra mizans emsaxureba urho kekonenis mosazrebis citireba?

(a) ganmartavs neitralitetis cnebis arss yoveli calkeuli saxelmwifos konteqstSi

(b) xazs usvams neitralitetis specifikurobas ama Tu im qveyanasTan mimarTebaSi

(g) warmoaCens neitraluri saxelmwifoebis mravalferovnebis ganmapirobebel

faqtorebs

(d) asabuTebs neitraluri qveynebis Taviseburebasa da cvalebad bunebas

36. ratom aris II abzacSi sityva agresori Casmuli brWyalebSi?

(a) am sityvis `usamarTlobis~ sinonimad gamoyenebis aRsaniSnavad

(b) teqstis avtoris ironiuli damokidebulebis gamosaxatavad

(g) teqstis avtorisTvis am sityvis gansakuTrebuli mniSvnelobis xazgasasmelad

(d) realur viTarebasTan am sityvis mniSvnelobis SesaZlo Seusabamobis

aRsaniSnavad

37. III abzacis mixedviT, romel winadadebebs Soris aris mizezSedegobrivi kavSiri?

(a) neitraluri qveyana omSi iribi monawileobis Sedegad garkveul sargebels

moeloda _ dasaSvebi iyo omSi CarTul mxareTa daxmareba

(b) neitralitetis saerTaSoriso garantiebi TiTqmis ar arsebobda _ xSiri iyo

neitraluri saxelmwifos teritoriaze samxedro moqmedebaTa akrZalvis

ugulebelyofa

(g) neitralitetis saerTaSoriso garantiebi TiTqmis ar arsebobda _ neitraluri

saxelmwifos valdebuleba, ar mieRo monawileoba sxva qveynebis omebSi, naklebad

mkacri gaxda

(d) neitraluri qveyana omSi iribi monawileobis Sedegad garkveul sargebels

moeloda _ nebadarTuli iyo neitraluri qveynis mkvidrTa gamoyeneba

daqiravebul jariskacebad

17

38. Zveli samyarosa da feodalizmis periodSi arsebuli neitralitetis principebis urTierTSedarebis safuZvelze SeiZleba davaskvnaT, rom:

(a) neitraluri saxelmwifo orive epoqaSi Tanabar SesaZleblobebs sTavazobda

dapirispirebul mxareebs, Tumca, pirvel SemTxvevaSi es yovelTvis

savaldebulo iyo, xolo meoreSi _ ara

(b) neitraluri saxelmwifosTvis orive epoqaSi dasaSvebi iyo dapirispirebul

mxareTagan erT-erTis daxmareba, Tumca, pirvel SemTxvevaSi amas winaswar

dadgenili wesebi gansazRvravda, xolo meoreSi _ sargeblis miRebis SesaZlebloba

(g) Zvel epoqaSi neitraliteti krZalavda dapirispirebul mxareTa jarebis mier

neitraluri qveynis sazRvrebis gadakveTas, xolo feodalizmis periodSi es

nebadarTuli iyo

(d) Zvel epoqaSi neitralitetis SenarCuneba damokidebuli iyo saxelmwifoTa

Soris gaformebul xelSekrulebebze, xolo feodalizmis epoqaSi _

neitraluri qveynis teritoriaze samxedro moqmedebaTa akrZalvaze

39. bolo abzacSi dasmuli SekiTxva imaze miuTiTebs, rom:

(a) neitraluri qveynis valdebulebebi ar Seesabameba omis warmoebis Tanamedrove

principebs

(b) neitralitetis statusi uzrunvelyofs qveynis usafrTxoebas Tanamedrove

konfliqtebis saxecvlilebis pirobebSi

(g) neitralitetis principebi ver iTvaliswinebs konfliqturi situaciis yvela

SesaZlo variants

(d) qveynis neitraluroba gamoricxavs mis monawileobas konfliqtebis prevenciasa

da humanitaruli aqciebis ganxorcielebaSi

40. ra mimarTebaa teqstis I abzacsa da danarCen sam abzacs Soris?

(a) I abzacSi saubaria erT-erTi politikuri movlenis damaxasiaTebel niSnebze,

romlebic ganxilulia II-III abzacebSi, xolo bolo abzacSi warmodgenilia am

movlenis Sesaxeb arsebuli Teoriis ZiriTadi principebi

(b) I abzacSi ganxilulia konkretuli politikuri fenomeni, xolo Semdgom

abzacebSi mocemulia misi arsebobis damadasturebeli magaliTebi

(g) I abzacSi gamokveTilia erT-erTi politikuri movlenis mniSvnelovani

Tavisebureba, romelic ilustrirebulia danarCen sam abzacSi

(d) I abzacSi daxasiaTebulia erT-erTi politikuri movlenis buneba, II-III

abzacebSi istoriuli faqtebis safuZvelze gaanalizebulia misi gamomwvevi

mizezebi, romlebic SekiTxvis saxiTaa warmodgenili bolo abzacSi

18

Savi samuSaosTvis

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.

anam Seagrova yvelaze meti soko, xolo sofom _

yvelaze naklebi.

(a) (b) (g) (d)

43.

rombis gverdis sigrZea a, didi diagonalisa _ d.

(a) (b) (g) (d)

03,1·28 29,1–12,29

gogonebis mier

Segrovebuli sokos

raodenoba

biWebis mier

Segrovebuli sokos

raodenoba

a 2d

23

44.

x da y iseTi ricxvebia, rom 0>x da 0=+ yx .

(a) (b) (g) (d)

45.

ori wrewiri, romelTagan erTis radiusis sigrZea 5 sm,meorisa _ 8 sm, erTmaneTs M da N wertilebSi kveTs.

am wertilebisa da wrewirTa centrebis SeerTebiT

miRebuli oTxkuTxedis perimetri p-s tolia.

(a) (b) (g) (d)

46.

a naklebia 5-ze. a da b ricxvebis saSualo

ariTmetikuli metia 8-ze.

(a) (b) (g) (d)

manZili ricxvTa

RerZze y-is Sesabamisi wertilidan saTavemde

manZili ricxvTa

RerZze x-is Sesabamisi wertilidan saTavemde

26 sm p

13b

24

amocanebi

47. 41-isa da 34-is erT-erT naturalur ricxvze gayofisas miRebuli naSTebi, Sesabamisad, 5-is da 4-is tolia. romelia es naturaluri ricxvi?

(a) 10

(b) 9

(g) 8

(d) 7

(e) 6

48. Tu 2−=x , maSin ( )( )=+−− 32 33 xxx

(a) –9

(b) –6

(g) –3

(d) 3

(e) 6

49. eqspediciis xelmZRvanelma eqspediciis wevrebi 5 jgufad gayo. TiToeul

jgufSi kenti raodenobis wevri aRmoCnda. CamoTvlilTagan romlis toli ar

SeiZleboda yofiliyo eqspediciis wevrTa raodenoba? (a) 51

(b) 43

(g) 37

(d) 25

(e) 22

25

50. a da b marTkuTxa samkuTxedebis wveroebi tolujredebiani badis kvanZebs

emTxveva (ix. naxazi). risi tolia a-s farTobis Sefardeba b-s farTobTan?

(a) 32

(b) 97

(g) 21

(d) 31

(e) 43

51. ramdeniT naklebia udidesi orniSna ricxvi im samniSna ricxvebidan

umciresze, romelTa cifrebis jami 21-is tolia? (a) 200-iT

(b) 250-iT

(g) 300-iT

(d) 350-iT

(e) 400-iT

26

monacemTa analizi

cxrilSi warmodgenilia monacemebi imis Sesaxeb, Tu ramdeni aTasi

srulwlovani adamiani iyo dasaqmebuli dasavleT saqarTvelos sxvadasxva

regionSi 2004-2008 wlebSi, amasTan, 2008 wlis monacemebi moyvanilia kvartalTa mixedviT.

weli da kvartali

aWara imereTi guria samegrelo-zemo svaneTi

raWa-leCxumi da qvemo svaneTi

2004 w 32,00 33,6 4,4 18,3 2,3 2005 w 38,89 39,6 4,9 21,7 2,5 2006 w 36,10 37,4 5,0 20,9 3,3 2007 w 36,12 34,2 5,2 21,9 2,6 2008 w I kv. 32,26 34,6 3,4 20,1 1,3 II kv. 33,14 35,6 3,5 20,6 1,6 III kv. 32,97 36,0 3,9 20,7 1,6 IV kv. 33,83 36,6 3,9 20,3 1,8

cxrilis mixedviT upasuxeT Semdeg 2 SekiTxvas: 52. romel regionSi aRiniSna dasaqmebul adamianTa raodenobis zrda yovel

kvartalSi 2008 wlis ganmavlobaSi? (a) raWa-leCxumsa da qvemo svaneTSi

(b) samegrelo-zemo svaneTSi

(g) guriaSi

(d) imereTSi

(e) aWaraSi

53. davuSvaT, rom aWaraSi 2004 wels 160 aTasi srulwlovani adamiani

cxovrobda. am regionis srulwlovan adamianTa raodenobis ramdeni procenti

yofila dasaqmebuli 2004 wels? (a) 15%

(b) 20%

(g) 25%

(d) 30%

(e) 35%

27

amocanebi

54. saklebis, maklebisa da maTi sxvaobis jami 48-is tolia. risi tolia saklebi? (a) 12-is

(b) 16-is

(g) 20-is

(d) 24-is

(e) 28-is

55. CamoTvlilTagan romeli SeiZleba iyos im samkuTxedis wveroebis koordinatebi, romelic naxazze mocemuli

samkuTxedis simetriulia y-RerZis mimarT?

(a) (2; 1), (4; 3), (2; 7)

(b) (4; 1), (2; 3), (4; 7)

(g) (2; 1), (0; 3), (1; 7)

(d) (–4; –2), (–8; –6), (–4; –14)

(e) (3; –1), (3; –6), (5; –3)

56. kolofSi asanTis Rerebi ewyo. maTi raodenoba jer gaaormages, Semdeg ki 8-iT Seamcires. amis Semdeg kolofSi darCenili asanTis Rerebis raodenoba isev gaaormages, Semdeg ki 8-iT Seamcires. ase moiqcnen mesamedac. amis Sedegad

kolofSi asanTis arc erTi Reri aRar darCa. asanTis ramdeni Reri ewyo

kolofSi Tavdapirvelad? (a) 4

(b) 5

(g) 6

(d) 7

(e) 8

57. daviTs 4-jer naklebi wigni aqvs, vidre _ levans da 2-jer meti, vidre _ Tornikes. samives erTad 70-ze meti wigni aqvs. CamoTvlilTagan romlis toli SeiZleba iyos levanis wignebis raodenoba?

(a) 48

(b) 58

(g) 64

(d) 68

(e) 74

28

58. saerTo centris mqone ori wrewiridan erTis radiusis sigrZea 2 sm, meorisa _ 3 sm. ramdeni kvadratuli santimetria am wrewirebiT SemosazRvruli gamuqebuli

figuris farTobi? (a) π

(b) π2

(g) π3

(d) π4

(e) π5

59. mimdevrobis pirveli wevria 3, xolo meore wevria 6. ras udris am

mimdevrobis me-11 wevri, Tu cnobilia, rom am mimdevrobis nebismieri wevrisa da misi momdevno ori wevris jami erTi da imave ricxvis tolia?

(a) 1

(b) 3

(g) 6

(d) 9

(e) 12

60. yuTSi mxolod wiTeli da TeTri feris windebia. minimum ramdeni winda unda amoviRoT yuTidan, masSi Cauxedavad, rom maTgan aucileblad Sedges 3 wyvili? (wyvils Seadgens ori erTnairi feris winda)

(a) 6

(b) 7

(g) 8

(d) 9

(e) 10

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 41 nawili daxarja,

xolo kviras _ darCenili Tanxis 31.

(a) (b) (g) (d)

62. a > b, b > c

(a) (b) (g) (d)

63.

12-gverdiani gazeTis gverdebis dasanomrad, sxva

cifrebTan erTad, saWiroa xuTi 1-iani.

(a) (b) (g) (d)

elenes mier SabaTs

daxarjuli Tanxa elenes mier kviras

daxarjuli Tanxa

200-gverdiani wignis gverdebis dasanomrad

saWiro 1-ianebis raodenoba

300-gverdiani wignis gverdebis dasanomrad

saWiro 5-ianebis raodenoba

a – 3 c – 4

30

64.

kotes xelfasis mesamedi Tengos xelfasis mesamedze

150 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.

ABCD marTkuTxedia.

(a) (b) (g) (d)

kotes da Tengos xelfasebis sxvaoba

400 lari

ABCD marTkuTxedis perimetris Sefardeba

ABD samkuTxedis perimetrTan

ABCD marTkuTxedis farTobis Sefardeba

ABD samkuTxedis farTobTan

#7·∗a ∗7·#a

31

amocanebi

67. marTkuTxa paralelepipedSi 10 erTnairi kubi isea ganlagebuli, rom yovel or mezobel kubs erTi waxnagi

saerTo aqvs (ix. naxazi). sul ramdeni aseTi kubi Caeteva

am marTkuTxa paralelepipedSi? (a) 75

(b) 60

(g) 55

(d) 45

(e) 30

68. mocemulia namravli 28·15·6·4·2 . CamoTvlilTagan romel ricxvze bs! jzpgb

unaSTod es namravli? (a) 18

(b) 20

(g) 21

(d) 25

(e) 45

69. ricxvebi 2,1, x, y, z, 5,8 zrdis mixedviTaa dalagebuli. gansxvaveba yovel or mezobel ricxvs Soris 1-ze naklebia. CamoTvlilTagan romlis toli SeiZleba iyos y ?

(a) 3,6

(b) 3,7

(g) 3,8

(d) 3,9

(e) 4,1 70. lias 2 gogona hyavs. saaxalwlod liam gogonebs saCuqrad erTnairad

SefuTuli 5 wigni SesTavaza, romelTagan sami leqsebis krebuli iyo, xolo

danarCeni _ moTxrobebisa. TiToeul gogonas TiTo wigni unda aeRo. risi

tolia imis albaToba, rom orive gogonas leqsebis krebuli Sexvdeba? (a) 5

1

(b) 103

(g) 41

(d) 32

(e) 85

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, romlebsac

xelovnebasac aswavlidnen 2003/2004 _ 2007/2008 saswavlo wlebSi. magaliTad,

grafikis mixedviT varkvevT, rom 2003/2004 saswavlo wels xelovnebas dawyebiTi skolis moswavleTa 16% Seiswavlida.

diagramaze ki warmodgenilia monacemebi imis Sesaxeb, Tu

zogadsaganmanaTleblo skolis TiToeul safexurze xelovnebis Semswavlel

moswavleTa saerTo raodenobis ramden procents Seadgenda cekvis, musikis, xatvis

Tu xelovnebis sxva dargebis Semswavlel moswavleTa raodenobebi 2007/2008 saswavlo wels. magaliTad, diagramis mixedviT varkvevT, rom 2007/2008 saswavlo wels dawyebiT skolaSi cekvas Seiswavlida dawyebiT skolaSi xelovnebis

Semswavlel moswavleTa 40%.

grafikisa da diagramis mixedviT upasuxeT Semdeg 4 SekiTxvas:

33

71. romel saswavlo wels iyo xelovnebis Semswavlel moswavleTa wili dawyebiT skolaSi 2,2-jer meti, vidre _ saSualo skolaSi?

(a) 2003/2004 saswavlo wels

(b) 2004/2005 saswavlo wels

(g) 2005/2006 saswavlo wels

(d) 2006/2007 saswavlo wels

(e) 2007/2008 saswavlo wels

72. ramdeniT aRemateboda 2006/2007 saswavlo wels sabazo skolaSi xelovnebis Semswavlel moswavleTa procentuli maCvenebeli 2003/2004 saswavlo wlis

Sesabamis maCvenebels? (a) 1-iT

(b) 2-iT

(g) 3-iT

(d) 4-iT

(e) 5-iT

73. ramdenjer aRemateboda 2007/2008 saswavlo wels saSualo skolaSi musikis Semswavlel moswavleTa raodenoba cekvis Semswavlel moswavleTa raodenobas?

(a) 1,5-jer

(b) 2-jer

(g) 2,5-jer

(d) 3-jer

(e) 3,5-jer

74. dawyebiTi skolis moswavleTa raodenobis ramden procents Seadgenda xatvis Semswavlel moswavleTa raodenoba 2007/2008 saswavlo wels?

(a) 2%

(b) 2,5%

(g) 3%

(d) 3,5%

(e) 4%

34

amocanebi

75. figuris radiusis sigrZe vuwodoT am figuris momcvel wreebs Soris umciresis radiusis sigrZes.

marTkuTxedis gverdebis sigrZeebia 3 sm da 4 sm.

risi tolia am marTkuTxedis radiusis sigrZe?

(a) 1,5 sm

(b) 2 sm

(g) 2,5 sm

(d) 3 sm

(e) 3,5 sm

76. Tamarma, naTiam da elenem zRvis napiras sul 36 niJara Seagroves. Tamarma naTias misca 5 niJara, naTiam elenes _ 2 niJara, xolo elenem Tamars _ 7 niJara. amis Semdeg samives toli raodenobis niJarebi aRmoaCndaT. ramdeni niJara

Seugrovebia elenes?

(a) 12

(b) 14

(g) 17

(d) 19

(e) 22

77. ramdeni Wiqa gaawonasworebs or saSaqres

marjvena sasworze ?

(a) 2

(b) 3

(g) 4

(d) 5

(e) 6

35

78. erT sibrtyeze mdebare ori wrewiri erTmaneTs kveTs. erTi wrewiris

radiusis sigrZea 3 sm, meorisa _ 18 sm. qvemoT CamoTvlilTagan romlis toli SeiZleba iyos am wrewirTa centrebs Soris manZili?

(a) 22 sm

(b) 18 sm

(g) 14 sm

(d) 10 sm

(e) 3 sm

79. kunZulze ori sakurorto zonaa: erTi _ dasavleT nawilSi, meore _

aRmosavleT nawilSi. ingliseli

turistebi mxolod kunZulis

dasavleT nawilSi isveneben, xolo

frangebi _ rogorc dasavleT, ise _

aRmosavleT nawilSi.

diagramebze mocemulia, turistebis raodenobis ra nawils Seadgenda frang

da inglisel turistTa raodenoba rogorc kunZulis dasavleT nawilSi, aseve,

mTlianad kunZulze. ramdeni frangi turisti isvenebda kunZulis dasavleT

nawilSi, Tu aRmosavleT nawilSi 72 frangi turisti isvenebda? (a) 36

(b) 48

(g) 60

(d) 72

(e) 108

80. klasis moswavleTagan 12 gogonaa. CamoTvlilTagan romlis toli SeiZleba iyos biWebis raodenobis Sefardeba am klasis moswavleTa saerTo raodenobasTan?

(a) 72

(b) 83

(g) 94

(d) 103

(e) 115

36

Savi samuSaosTvis