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

analogiuria. pasuxis arCevisas gaiTvaliswineT sityvaTa Tanmimdevroba wyvilebSi.

1. wuTi : dro (a) sicxe : temperatura

(b) asaki : wlovaneba

(g) manZili : siCqare

(d) grami : wona

2. Caagdo : Cavarda (a) gaaxara : gauxarda

(b) inatra : usurva

(g) gaisarja : iRvawa

(d) daabruna : daubruna

3. zedapiruli : siRrme (a) urCi : damokidebuleba

(b) uzado : mSveniereba

(g) utyuari : sicrue

(d) uSiSari : riski

4. nawili : fragmenti (a) varaudi : hipoTeza

(b) abzaci : winadadeba

(g) aqsioma : Teorema

(d) sqolio : komentari

5. SarJi : karikatura (a) teritoria : distancia

(b) dedani : originali

(g) eskizi : portreti

(d) figura : profili

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6. zambara : spirali (a) yvavili : fifqi

(b) qarborbala : konusi

(g) mili : rgoli

(d) raketa : vertikali

7. akvareli : plastilini (a) Ruza : ialqani

(b) gemi : TviTmfrinavi

(g) sateliti : kosmosi

(d) porti : akvatoria

4

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. 8. _____ gamowveulia imiT, rom TaobaTa Soris urTierTobam _____ miaRwia, roca umcrosi Taoba _____ ufrosTan kulturul urTierTgagebas, _____ ise

_____ .

(a) tradiciisgan mowyveta / im kritikul zRvars / eswrafvis / Tumca / aRiqvams

mas, rogorc monaTesave ideebis mqones

(b) tradiciis erTguleba / im simaRles ver / kargavs / Sesabamisad, / aRiqvams

mas, rogorc monaTesave ideebis mqones

(g) tradiciisgan mowyveta / im kritikul zRvars / kargavs / amitom / eqceva mas,

rogorc ucxo eTnikur jgufs

(d) tradiciis erTguleba / im simaRles / eswrafvis / amitom / eqceva mas,

rogorc ucxo eTnikur jgufs

9. rac ufro _____ yuradReba erTi mimarTulebiT, miT ufro _____ adamiani sxva mimarTulebiT. magaliTad, _____ adamiani quCaSi nacnobs ver amCnevs, Tumca

SeiZleba ____ .

(a) intensiuria / yuradRebiania / Cafiqrebuli / is dainaxos

(b) `gafantulia~ / uyuradReboa / yuradRebiani / mas miesalmos (g) intensiuria / uyuradReboa / Cafiqrebuli / Sexedos mas

(d) `gafantulia~ / yuradRebiania / uyuradRebo / mas ar miesalmos

10. SuamdinareTi samSeneblo masaliT, xe-tyiTa da liTonebiT _____ mxare iyo, _____ iq taZrebsa da sasaxleebs _____ aSenebdnen. amitom isini _____ .

mSeneblobis Sesaxeb aqauri mmarTvelebis warwerebic ufro xSirad mogviTxrobs

_____ Zveli taZar-sasaxleebis aRdgenaze.

(a) mdidari / ris gamoc / Tixisgan arasodes / iSviaTad ingreoda da TiTqmis ar

saWiroebda restavracias / ara axlis aSenebaze, aramed

(b) Raribi / miuxedavad amisa, / Tixisgan arasodes / xSirad ziandeboda da

restavracias saWiroebda / axlis aSenebaze, da ara

(g) mdidari / Sesabamisad, / ZiriTadad Tixisgan / iSviaTad ingreoda da TiTqmis

ar saWiroebda restavracias / axlis aSenebaze, da ara

(d) Raribi / ris gamoc / ZiriTadad Tixisgan / xSirad ziandeboda da

restavracias saWiroebda / ara axlis aSenebaze, aramed

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.

11. viqtorinis finalSi oTxi megobari monawileobda. Sedegebi aseTi iyo:

• iraklim ufro met SekiTxvas gasca pasuxi, vidre bubam. • ninom ufro met SekiTxvas gasca pasuxi, vidre bubam. • Teom ufro nakleb SekiTxvas gasca pasuxi, vidre iraklim.

qvemoT mocemulia saprizo adgilebis sxvadasxvagvari ganawileba. maTgan romeli

Seesabameba am monacemebs?

adgilebi: I II III IV

(a) nino buba irakli Teo

(b) buba irakli Teo nino

(g) Teo nino irakli buba

(d) nino irakli buba Teo

12. A regionis garda, qveyanaSi yvelgan akrZalulia gzatkecilze ormisabmeliani satvirTo manqanebis moZraoba. amasTan, cnobilia, rom A regionis gzatkecilebze ormisabmeliani satvirTo manqanebis sagzao SemTxvevebis maCvenebeli ufro

dabalia, vidre sxva tipis satvirTo avtomanqanebis Sesabamisi maCvenebeli mTeli

qveynis gzatkecilebze. amis safuZvelze eqspertma ivarauda, rom ormisabmeliani

manqanebi sxva tipis satvirTo avtomanqanebze ufro usafrTxoa avtosagzao

SemTxvevebis TvalsazrisiT.

qvemoT CamoTvlilTagan romeli viTareba ayenebs eWvqveS eqspertis varauds?

(a) ormisabmeliani satvirTo manqanebi, Cveulebriv, tvirTis did manZilze

gadasazidad gamoiyeneba

(b) A regioni mWidrod ar aris dasaxlebuli. amitom aq gzatkecilebi naklebad gadatvirTulia da, Sesabamisad, ufro metad usafrTxoa, vidre gzatkecilebi

mTeli qveynis masStabiT

(g) yvelgan, sadac nebadarTulia satvirTo manqanebiT moZraoba, maTi tarebis

uflebisaTvis mZRolebs gansakuTrebuli licenzia sWirdebaT

(d) ormisabmeliani satvirTo manqanebis gamoyenebiT mcirdeba sawvavis xarji da

naklebi ziani adgeba garemos. amitom garemosdacviTi organizaciebi lobirebas

uweven aseTi manqanebis gamoyenebas mTel qveyanaSi

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13. baRis SesasvlelTan erT mwkrivad dgas oTxi xe _ atmis, vaSlis, blis da msxlis.

• atmis xe vaSlis xis gverdiT dgas.

• msxlis xis gverdiT ar dgas arc blis da arc atmis xeebi.

romeli xe dgas blis xis gverdiT?

(a) atmis xe

(b) vaSlis xe

(g) atmisa da vaSlis xeebi

(d) mocemuli informacia ar aris sakmarisi kiTxvaze pasuxis gasacemad

14. mocemulia: • yvela mtacebeli Tevzi, romelic vercxlisferia, swrafad dacuravs.

• yvela mtacebeli Tu aramtacebeli Tevzi, romelic swrafad dacuravs,

wylis siRrmeSi binadrobs.

qvemoT CamoTvlilTagan romeli debuleba gamomdinareobs am wanamZRvrebidan?

(a) aramtacebeli Tevzebi, romlebic nela dacuraven, wylis siRrmeSi ar

binadroben

(b) aramtacebeli Tevzebi, romlebic wylis siRrmeSi binadroben, swrafad

dacuraven

(g) yvela mtacebeli Tevzi, romelic wylis siRrmeSi binadrobs, vercxlisferia

(d) yvela mtacebeli Tevzi, romelic vercxlisferia, wylis siRrmeSi binadrobs

7

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

polisuri* cxovrebis ganviTarebas Zv. w. VIII-VII saukuneebis saberZneTSi Tan

axlda politikur da ekonomikur dapirispirebaTa gaZliereba TviT polisebis

SigniT. am procesma ganapiroba pirovnebis rolis win wamoweva, pirovnuli

iniciativis mniSvnelobis gazrda. legendaruli figurebis _ miTologiisa da

mxatvruli Semoqmedebis personaJebis _ gverdiT gamoCndnen realuri adamianebi,

romelTac saxeli da dideba sakuTari niWiT, gonierebiTa Tu gamWriaxobiT

moipoves.

pirovnebis asparezze gamosvlam yvelaze mkafiod Tavi iCina polisebis

politikur cxovrebaSi. arqauli saberZneTisaTvis damaxasiaTebeli xdeba brZolebi

socialuri samarTlianobis dasamyareblad. magram is, Tu ra aris socialuri

samarTlianoba, sxvadasxva fenis warmomadgenlebs sxvadasxvagvarad esmodaT. es ki

zrdida antagonizms, amwvavebda brZolas ZalauflebisTvis. am periodis

berZnulenovani samyaros polisebSi gvxvdeba politikuri wyobis oTxi

modeli: a) monarqia, anu erTis mmarTveloba; b) aristokratia, anu didgvarovanTa

mmarTveloba; g) oligarqia, anu ekonomikurad Zlieri mcirericxovani jgufis

mmarTveloba; d) demokratia, anu Tavisufal moqalaqeTa mmarTveloba. bunebrivia,

gadasvla erTi wyobidan meoreze ar xdeboda TavisTavad. mas Tan axlda

winaaRmdegobebi. am viTarebaSi gamoikveTa ori tipis moRvaweTa saWiroeba _

kanonmdebelTa, romelnic polisebs funqcionirebis normebs, werilobiT

fiqsirebul kanonebs Seuqmnidnen, da mmarTvelTa, romelnic SeZlebdnen polisebis

marTvas kanonebis Sesabamisad.

rogorc Cans, dawerili kanonis Seqmnis idea pirvelad maSin gaCnda, rodesac

polisis mkvidrTaTvis naTeli gaxda, rom mravalferovan urTierTobebs veRar

aregulirebda Taobidan TaobaSi zepiri gziT gadacemuli qcevis normebi _

yvelaze brZen msajulsac ki, romelic mkacrad xelmZRvanelobda am tradiciuli

normebiT, uWirda maTi misadageba siaxleebTan. socialuri problemebi,

dapirispirebaTa zrda ganapirobebda polisis cxovrebis destabilizacias.

aucilebeli gaxda Cawerili, fiqsirebuli kanonebis arseboba, romlebic bolos

mouRebda ganukiTxaobas da polisis samarTliani funqcionirebis iluzias mainc

Seqmnida. es kargad esmoda aristokratiasac da, Sesabamisad, didgvarovanTa wreSi

daiwyo iseTi adamianisa Tu adamianTa jgufis Zieba, romelsac SeiZleboda

dakisreboda kanonmdeblis funqcia. ase gaCndnen saberZneTSi pirveli kanonmdeblebi,

romelTagan sawyiss iRebs Tanamedrove evropuli kanonmdebloba. antikuri

tradicia saberZneTis pirvel kanonmdebelTa Soris moixseniebs aTenel drakons.

drakonis kanonebi ZiriTadad sam sferos moicavda: Temis wevrTa Soris

samarTlebrivi urTierTobis regulirebas, adaTebisa Tu zneobrivi normebis

mowesrigebas da sasjels mZime danaSaulisTvis. drakonis damsaxurebad unda

miviCnioT is, rom man scada sisxlis aRebis wesis sisastikis ramdenadme Semcireba

da misi Secvla saxelmwifo samediatoro sasamarTloTi. masve unda ekuTvnodes

jarimis odenobis kanoniT gansazRvra. ra Tqma unda, pirveli aTeneli kanonmdebeli

ver gadawyvetda socialuri cxovrebis yvela problemas, magram man safuZveli

daudo im kanonmdeblobas, romelzec Semdgom aRmocenda demokratiuli aTenis

marTlmsajuleba.

*polisi _ qalaq-saxelmwifo Zvel saberZneTSi.

8

15. riT SeiZleba avxsnaT is, rom Zv. w. VIII-VII saukuneebis saberZneTSi

gamoCndnen adamianebi axali iniciativebiT?

(a) berZnuli polisebis cxovrebaSi miTologiuri da literaturuli

personaJebis adgili realurma pirovnebebma daikaves

(b) istoriulma viTarebam ganapiroba berZnul sazogadoebaSi politikuri Tu

ekonomikuri xasiaTis gardaqmnebis aucilebloba

(g) calkeulma pirovnebebma mniSvnelovani gavlena moaxdines ekonomikuri da

kulturuli urTierTobebis formirebaze

(d) miTologiuri gmirebis heroizmi realuri adamianebis individualur

iniciativebze aranakleb mniSvnelovani iyo

16. teqstSi polisis mmarTvelobis modelebi gamoyofilia imis mixedviT, Tu:

(a) ra rols asrulebs polisis marTvaSi pirovnuli iniciativis zrda,

individualizmi

(b) sazogadoebis romeli jgufi marTavs qalaq-saxelmwifos _ demokratiuli Tu

Zalauflebismoyvare

(g) rogor esmis sazogadoebis TiToeul wevrs, ra aris socialuri

samarTlianoba

(d) sazogadoebis romeli nawilis xelSi eqceva Zalaufleba _ erTis, garkveuli

tipis umciresobisa Tu umravlesobis

17. arqaul saberZneTSi (Zv. w. VII-VI s.s.) gaCnda dawerili kanonis Seqmnis idea, radgan:

(a) mmarTvelobis sxvadasxva sistemis pirobebSi erTi modelidan meoreze gadasvla

ar xdeboda TavisTavad, es problema unda moegvarebina werilobiT

fiqsirebul kanonebs

(b) mmarTvelobis sxvadasxva sistemis pirobebSi polisur sazogadoebaSi arsebul

mravalmxriv urTierTobebs veRar awesrigebda samarTlis dauwereli,

tradiciuli normebi

(g) sxvadasxva fenis warmomadgenlebs sxvadasxvagvarad esmodaT socialuri

samarTlianoba, mis dasamyareblad ki sakmarisi ar iyo samarTlis dauwereli _

tradiciuli normebi

(d) sxvadasxva fenis warmomadgenlebs sxvadasxvagvarad warmoedginaT polisis

mmarTvelobis modelebi, es gansxvaveba unda asaxuliyo werilobiT fiqsirebul

kanonebSi

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18. teqstSi vxvdebiT aseT azrs: `fiqsirebuli kanonebis arseboba polisis

samarTliani funqcionirebis iluzias mainc Seqmnida.~

qvemoT CamoTvlilTagan am mosazrebis romeli interpretacia aris mcdari?

(a) zepiri gziT gadacemuli qcevis normebi subieqturi interpretirebis

saSualebas iZleoda, dawerili kanoni ki, erTi SexedviT mainc, samarTlianobis

garantis rols Seasrulebda sazogadoebis yvela fenisTvis

(b) xelisufalTa mier dauwereli samarTlis subieqturad gamoyeneba unda

CaenacvlebinaT fiqsirebuli kanonebiT, raTa polisis moqalaqeTaTvis

samarTlianobis STabeWdileba SeeqmnaT

(g) polisis cxovrebis destabilizaciis `mogvarebiT~, upirveles yovlisa,

dainteresebuli iyo aristokratia, raTa fiqsirebuli kanoni gamoeyenebina

Tavis sasargeblod da SeZleboda dabali fenis marTva

(d) samarTlis tradiciuli normebi aRar Seesabameboda axal politikur Tu

ekonomikur urTierTobebs, daweril kanonebs ki SeiZleboda garkveuli roli

Seesrulebina destabilizaciis Tavidan acilebaSi

19. erT-erTma aTenelma kanonmdebelma _ klisTenem _ SemoiRo e. w. `natexTa sasamarTlo~. yovelwliurad saxalxo krebaze ganixileboda sakiTxi, xom ar iyvnen

maT qalaqSi saxelmwifo wyobilebisTvis saSiSi pirebi. Tuki umravlesobis pasuxi

dadebiTi aRmoCndeboda, maSin saxalxo krebis monawileebs urigebdnen

ostrakonebs (anu natexebs, metwilad Tixisas). kenWisyraSi monawileTa raodenoba

6000 kacze naklebi ar unda yofiliyo. pirs, romlis saxels yvelaze xSirad

miuTiTebdnen ostrakonze, polisidan aZevebdnen 10 wlis vadiT.

romel abzacs SeiZleba davukavSiroT es informacia da ratom?

(a) I abzacs, radgan aq saubaria legendarul figurebze, am informaciidan ki

vigebT, rom klisTene aTenis kanonmdebelTa Soris erT-erTi popularuli,

legendaruli pirovneba yofila

(b) II abzacs, radgan aq saubaria berZnuli samyaros politikur modelebze, am

informaciis Tanaxmad ki, `natexTa sasamarTlo~ erTi modelidan meoreze

gadasvlis safuZvels warmoadgenda

(g) III abzacs, radgan aq saubaria polisur cxovrebaSi arsebul ganukiTxaobasa

da samarTlianobis iluziaze _ `natexTa sasamarTloc~ demokratiis iluzias

qmnida

(d) IV abzacs, radgan aq saubaria drakonis kanonebze, romlebsac ukavSirdeba

demokratiuli sasamarTlos sawyisebi _ `natexTa sasamarTloc~ kenWisyris (anu

gadawyvetilebis demokratiulad miRebis) wina safexuria

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20. ra aris am teqstis ZiriTadi mizani?

(a) dawerili kanonis Seqmnis ganmapirobebeli faqtorebis mimoxilva

(b) demokratiuli aTenis marTlmsajulebis mTavari orientirebis gansazRvra

(g) antikuri tradiciuli kanonebisa da Tanamedrove evropuli marTlmsajulebis

urTierTmimarTebis warmoCena

(d) ori tipis moRvaweTa _ kanonmdeblebisa da mmarTvelebis _ progresul

qmedebaTa Sedareba

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 analogiuri iyos.

21. mowoneba : ovacia tkivili :

(a) gayuCeba

(b) tirili

(g) mwuxareba

(d) moTmena

22. tba : napiri gamosaxuleba :

(a) anarekli

(b) landi

(g) silueti

(d) konturi

23. diskusia : pozicia konfliqti :

(a) Sejaxeba

(b) interesi

(g) principi

(d) gansxvaveba

24. mwerali : krebuli msaxiobi :

(a) repertuari

(b) premiera

(g) speqtakli

(d) benefisi

25. ilustracia : TvalsaCino definicia :

(a) adekvaturi

(b) gansazRvruli

(g) dazustebuli

(d) gaugebari

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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.

26. gamoTqma `qviSaSi Tavis Cargva~ siraqlemas stereotipul xats warmogvidgens. rogorc Cans, stereotipuli xatis CamoyalibebisaTvis _____ realuri faqtis

arseboba, _____ , rom _____ qviSaSi.

(a) sulac ar aris aucilebeli / radgan jer aravis unaxavs / siraqlemas Tavi

marTlac Caergos

(b) aucilebelia / magaliTad, zoologebma kvlevis Sedegad daadgines / siraqlema

seriozuli safrTxis SemTxvevaSic ki ar malavs Tavs

(g) sulac ar aris aucilebeli / magaliTad, zoologebma kvlevis Sedegad

daadgines / seriozuli safrTxis moaxloebisas siraqlema marTlac malavs Tavs

(d) aucilebelia / radgan jer aravis unaxavs / siraqlemas Tavi marTlac Caergos

27. samuSao hipoTezis _____ im faqtebis ricxvis _____ , romelTa axsnas da mowesrigebasac is _____ SeZlebs.

(a) mcdarobis albaToba iklebs / SemcirebasTan erTad / warmatebiT

(b) WeSmaritebis albaToba iklebs / Semcirebis Sesabamisad / ver

(g) mcdarobis albaToba izrdeba / SemcirebasTan erTad / ver

(d) WeSmaritebis albaToba izrdeba / zrdasTan erTad / warmatebiT

28. pirvelyofili adamianebisgan gansxvavebiT, romlebic _____ , an kidev

berZnebis sapirispirod, romlebic _____ bunebis yvela aspeqts Tu Zalas,

Tanamedrove adamianis moTxovnilebaa yovelive imis _____ warmodgena, rac mas

yvelaze metad ainteresebs.

(a) apirovnebdnen samyaros mxolod mcire nawils / meqanikuri principebiT

xsnidnen / depersonalizacia, anu gaupirovneblad

(b) meqanikuri ZalebiT xsnidnen yvelafers / gasulierebulad warmoidgendnen /

depersonalizacia, anu gaupirovneblad

(g) apirovnebdnen yvelafers, rac moZraobs / gasulierebulad warmoidgendnen /

depersonalizacia, anu gaupirovneblad

(d) meqanikuri ZalebiT samyaros mxolod mcire nawils xsnidnen / apirovnebdnen /

personalizacia, anu gapirovnebulad

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29. radgan adamianebisTvis calmxrivoba yovelTvis ______ , xolo

mravalmxrivoba _ ______ , gabatonebul SexedulebaTa revoluciuri

cvlilebebis periodSi ______ erTad, Cveulebriv, ______ .

(a) wesi iyo / gamonaklisi / WeSmaritebis garkveuli nawilis aRzevebasTan /

iZireba misi sxva romelime nawili

(b) wesi iyo / gamonaklisi / axal WeSmaritebaTa aRmoCenasTan / gamoswordeba

Zveli Secdomebic

(g) gamonaklisi iyo / iSviaTi movlena / WeSmaritebis garkveuli nawilis

aRzevebasTan / Tavs iCens axali Secdomebic

(d) gamonaklisi iyo / arcTu iSviaTi movlena / axal WeSmaritebaTa aRmoCenasTan /

daviwyebas eZleva Zveli codna

30. cnobilia jon raskinis fraza Tvalis `umankoebis~ Sesaxeb: `sinamdvilis

amsaxveli WeSmariti xedva _____ , sagnis _____ Cveni Semecnebis, gamocdilebis

da swavlis Sedegia.~ amgvari gamonaTqvamebi aqvT XIX saukunis sxva

Teoretikosebsac. maTSi _____ , rom yovelgvari cnebisa da codnis ukugdeba

_____ mxatvars, Caswvdes xiluli samyaros WeSmarit arss.

(a) aris mxolod sibrtyeze ferebis monacvleobis aRqma / namdvili arsis wvdoma

swored / uaryofilia mosazreba / xels uSlis

(b) mxolod sibrtyeze ferebis monacvleobis aRqmas rodi gulisxmobs / namdvili

arsis wvdoma / ikveTeba is azri / SesaZleblobas aZlevs

(g) aris mxolod sibrtyeze ferebis monacvleobis aRqma / Sesaxeb yoveli sxva

warmodgena ki / ikveTeba is azri / SesaZleblobas aZlevs

(d) mxolod sibrtyeze ferebis monacvleobis aRqmas rodi gulisxmobs / Sesaxeb

yoveli warmodgena / uaryofilia mosazreba / xels uSlis

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. bolo wlebSi mTel msoflioSi gaxSirda SemTxvevebi, rodesac futkrebis koloniebi nadgurdeba imis gamo, rom muSa futkrebi masobrivad iRupebian.

zogierTi mecnieris varaudiT, am movlenis mizezi isaa, rom industriuli

mefutkreobis ganviTarebasTan erTad, futkrebis sakvebi sul ufro erTferovani

xdeba.

qvemoT CamoTvlilTagan romeli viTareba ganamtkicebs aRniSnul varauds?

(a) fermerTa mier axali tipis pesticidebis gamoyeneba zemoqmedebs futkrebis

janmrTelobaze, radgan sasoflo-sameurneo kulturebi futkrebisTvis sakvebis

mniSvnelovani wyaroa

(b) futkrebisTvis sakvebis mniSvnelovani wyaroa xexilis baRebi da bostneulis

plantaciebi, xolo mTel msoflioSi fermebSi sul ufro xSirad gamoiyeneba

xilisa da bostneulis genetikurad modificirebuli jiSebi

(g) erT-erTma kvlevam aCvena, rom futkars, romelic sxvadasxva saxeobis

mcenareebs mtveravs, ufro jansaRi imunuri sistema aqvs, vidre futkars,

romelic erTi da imave saxeobis mcenaris neqtriT ikvebeba

(d) erT-erTma kvlevam aCvena, rom futkrebze uaryofiT zemoqmedebas axdens

eleqtromagnituri gamosxiveba, romelic mobiluri satelefono qselebis

ganviTarebis gamo bolo wlebSi mTel msoflioSi mniSvnelovnad gaizarda

32. megobrebma giorgis dabadebis dRisTvis aseTi siurprizi moumzades: saCuqari daumales da giorgim maTi miTiTebebis mixedviT unda ipovos is. megobrebi

karnaxoben giorgis, rom saCuqari:

• an magidis ujraSia, an tansacmlis karadaSi.

• an wignis Tarozea, an saTamaSoebis yuTSi.

• saTamaSoebis yuTSi namdvilad ar aris.

sad aris saTamaSo, Tu cnobilia, rom am miTiTebebidan mxolod erTia swori?

(a) magidis ujraSi

(b) tansacmlis karadaSi

(g) wignis Taroze

(d) saTamaSoebis yuTSi

15

33. mocemulia: • maRalmTiani dasaxlebis zogierTi mkvidri kargi moTxilamurea.

• yvela kargi moTxilamure, romelic maRalmTiani dasaxlebis mkvidria,

zamTar-zafxul garujulia.

• maRalmTiani dasaxlebis yvela mkvidrs exerxeba cxeniT jiriTi.

qvemoT CamoTvlilTagan romeli daskvna gamomdinareobs am wanamZRvrebidan?

(a) yvela karg moTxilamures exerxeba cxeniT jiriTi

(b) maTgan, visac cxeniT jiriTi exerxeba, zogierTi zamTar-zafxul garujulia

(g) maRalmTiani dasaxlebis zogierTi mkvidri ar aris zamTar-zafxul garujuli

(d) yvela moTxilamure, romelic zamTar-zafxul garujulia, maRalmTiani

dasaxlebis mkvidria

34. mocemulia ori debuleba: • saqarTvelos teritoriaze arsebuli zogierTi tbis wyali mlaSea.

• zogierTi mlaSewyliani tbis irgvliv marilis sabadoebia.

maSasadame, saqarTvelos teritoriaze arsebuli zogierTi tbis irgvliv marilis

sabadoebia.

es daskvna:

(a) gamomdinareobs mxolod pirveli debulebidan

(b) gamomdinareobs mxolod meore debulebidan

(g) gamomdinareobs orive debulebidan erTad

(d) ar gamomdinareobs mocemuli debulebebidan

16

nax. 1

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

mecnierebi eqsperimentulad Seiswavlian, Tu rogor aRiqvams adamiani gare

samyaros, ra faqtorebi moqmedebs mis aRqmaze. am sakiTxebis asaxsnelad Seiqmna

mravali Teoria, romelTa marTebulobis Sesamowmeblad xSirad iyenebdnen iluziebs.

iluzia aRsaqmeli obieqtis TvisebaTa damaxinjebuli, araadekvaturi asaxvaa. yvelaze xSirad kvlevis obieqti iyo e. w. miuler-laierisa (nax. 1) da

horizontalur-vertikaluri (nax. 2) iluziebi. naxatebze monakveTebi sigrZiT

erTmaneTis tolia, Tumca zeda xazi pirvel naxatze da vertikaluri xazi meore

naxatze ufro grZeli gveCveneba, vidre meore

monakveTi. am iluziebis erT-erTi axsna ukavSirdeba

Tvalis baduraze mocemuli organzomilebiani

gamosaxulebis safuZvelze samganzomilebiani xatis Seqmnis meqanizms. safiqrebelia,

rom mxedvelobis sistema iyenebs siRrmisa da daSorebulobis, anu perspeqtivis

niSnebs _ manZilis zrdasTan erTad obieqtis gamosaxulebis zomebi Tvalis

baduraze mcirdeba. vinaidan monakveTebi erTmaneTis tolia, magram sxvadasxva

manZiliT daSorebulad gveCveneba, mxedvelobis sistemas dagrovili gamocdilebis

safuZvelze `Sesworebebi~ Seaqvs obieqtis aRqmul xatSi, rac iluzias ganapirobebs.

XIX saukunis bolos evropaSi jer kidev popularuli iyo mosazreba evropeli

da araevropeli xalxebis ganviTarebis sxvadasxva donis Sesaxeb. u. riversma inglisSi,

samxreT indoeTsa da axal gvineaSi Caatara kvleva im hipoTezis Sesamowmeblad, rom

naklebad ganviTarebuli qveynebis mkvidrT ufro maxvili mxedveloba aqvT da,

Sesabamisad, ufro metad unda eqvemdebarebodnen iluziebs. aRmoCnda, rom

ingliselebi, danarCeni ori kulturis warmomadgenlebTan SedarebiT, ufro metad

eqvemdebarebian miuler-laieris iluzias, axali gvineisa da indoeTis mkvidrni ki _

horizontalur-vertikalur iluzias. riversma daaskvna, rom adamianis mier samyaros

aRqmaze gavlenas axdens ara ganviTarebis an ganaTlebis done, aramed garemo,

romelSic is cxovrobs.

gansxvavebul Tvalsazriss iziarebda r. polaki, romelmac kvlevis Sedegad

gamoavlina kavSiri adamianis Tvalis baduris pigmentaciasa da konturebis danaxvis

unars Soris _ rac ufro muqia pigmentacia, miT ufro naklebadaa ganviTarebuli es unari. muqi pigmentacia muqi kanis mqone adamianebs ufro Zlierad aqvT

gamoxatuli da amitom naklebad eqvemdebarebian miuler-laieris iluzias.

v. stiuartma cal-calke Seiswavla garemosa da rasis roli miuler-laieris

iluziis warmoqmnaSi. man jer gamoikvlia amerikis erT qalaqSi mcxovrebi

TeTrkaniani da Savkaniani bavSvebi da iluziebis mxriv ver gamoavlina maT Soris

gansxvaveba. Semdeg igive kvleva Caatara zambiaSi qalaqisa da soflis mkvidr

bavSvebTan. aRmoCnda, rom iluzias ufro metad eqvemdebarebian qalaqeli bavSvebi.

garemos gadamwyveti roli iluziebis warmoqmnaSi eWvqveS daayena

cxovelebTan da frinvelebTan Catarebulma eqsperimentebma. mtredebs jer aswavles

ori monakveTidan ufro grZelis amorCeva, ris Semdegac miuler-laieris

monakveTebiani naxati aCvenes. mtredebma maSinve airCies zeda xazi (nax. 1), romelic

adamianebsac ufro grZeli eCvenebaT. erT-erT kvlevaSi axladgamoCekil kiborCxalasa

da kus ekranze sinaTlis laqas uCvenebdnen, romelic farTovdeboda da masTan

Sejaxebis iluzias qmnida. cxovelebi sxvadasxvagvarad reagirebdnen: kiborCxala

miwas ekvroda, ku baknis qveS malavda Tavs _ isini safrTxis Tavidan acilebas

cdilobdnen.

17

35. qvemoT CamoTvlilTagan romeli mosazrebaa gamoTqmuli varaudis saxiT? (upasuxeT II abzacis mixedviT)

(a) mxedvelobis sistema iyenebs perspeqtivis niSnebs

(b) perspeqtivis principebi gulisxmobs daSorebulobisa da siRrmis niSnebs

(g) obieqtis zomebi mcirdeba damkvirveblisgan misi daSorebis zrdasTan erTad

(d) baduraze organzomilebiani gamosaxulebis safuZvelze iqmneba samyaros

samganzomilebiani xati

36. inglisSi, samxreT indoeTsa da axal gvineaSi Catarebuli kvlevis Sedegebma:

(a) axali faqtebiT gaamdidra da ganamtkica sakvlevi hipoTeza

(b) uaryo sakvlevi hipoTeza, Tumca ver Seqmna safuZveli axali mosazrebis

Camosayalibeblad

(g) eWvqveS daayena sakvlevi hipoTezis marTebuloba da ganapiroba gansxvavebuli

Sexedulebis Camoyalibeba

(d) stimuli misca axal kvlevebs, romelTac unda daedasturebinaT sakvlevi

hipoTeza

37. CamoTvlilTagan romeli aRwers yvelaze srulad v. stiuartis kvlevis mizans?

stiuartis mizani iyo:

(a) daedgina rasobrivi gansxvavebebis gavlena iluziebis warmoqmnaze sxvadasxva

kulturaSi

(b) daedgina iluziebis warmoqmnaze garemos gavlenis xarisxi sxvadasxva rasis

warmomadgenlebTan

(g) erTmaneTisgan gaemijna garemosa da rasobrivi gansxvavebebis gavlena iluziebis

warmoqmnaze

(d) erTmaneTisTvis Seedarebina gansxvavebuli kulturis mqone qveynebis

warmomadgenlebi iluziebis warmoqmnis TvalsazrisiT

18

38. qvemoT CamoTvlilTagan romeli debuleba asaxavs sworad riversis, polakisa da stiuartis mier Catarebul kvlevaTa urTierTmimarTebas?

(a) riversisa da stiuartis mier Seswavlil or faqtors Soris gamoikveTa

iluziis gamomwvevi erTi gadamwyveti faqtori, romelic gansxvavdeboda

polakis kvlevis Sedegad dadgenilisgan

(b) samive kvlevaSi Seiswavles or-ori faqtori, maTgan riversisa da polakis

kvlevebSi gamoikveTa iluziis erTi da igive mizezi, xolo stiuartis

kvlevaSi _ gansxvavebuli

(g) samive kvlevaSi Semowmda gansxvavebuli faqtorebi, Tumca polakisa da

stiuartis kvlevebiT gamovlinda iluziis erTi ZiriTadi mizezi, romelic

gansxvavdeboda riversis mier gamovlenilisgan

(d) riversma da stiuartma gamoavlines iluziis gamomwvevi gansxvavebuli

mizezebi, romelTagan erT-erTi daemTxva polakis kvlevaSi gamovlenil

faqtors

39. cxovelebTan da frinvelebTan gamovlenili iluziebis magaliTebi safuZvels gvaZlevs, vivaraudoT, rom:

(a) cxovelebTan da frinvelebTan iluziebi ganpirobebulia mxolod garemoSi

SeZenili gamocdilebiT

(b) cxovelebisa da frinvelebis iluziebi ukavSirdeba evoluciuri ganviTarebis

Sedegad maT mier SeZenil gamocdilebas

(g) cxovelebisa da frinvelebis iluziebi SesaZlebelia damokidebuli iyos maT

saxeobaze

(d) cxovelebsa da frinvelebSi gamovlenili iluziebi SesaZlebelia

ganpirobebuli iyos Tandayolili fiziologiuri meqanizmebiT

40. teqstSi ganxilul kvlevaTa Sedegebis safuZvelze SeiZleba davaskvnaT:

(a) iluziebis warmoqmnis asaxsnelad gasaTvaliswinebelia rogorc garemosa da

gamocdilebis Taviseburebebi, ise Tandayolili fiziologiuri meqanizmebi

(b) miuxedavad imisa, rom gamovlenili iyo iluziebis gamomwvevi sami mizezi –

ganviTarebis done, gamocdileba da fiziologiuri faqtorebi, savsebiT

SesaZlebelia maTi dayvana erT ZiriTad faqtorze _ garemos Taviseburebebze

(g) garemo, romelSic cxovrobs adamiani, gavlenas axdens mis aRqmaze, Tumca

iluziebis warmoqmnaSi gadamwyveti mniSvneloba rasas eniWeba

(d) miuxedavad imisa, rom iluziis aRmoceneba damokidebulia sxvadasxva

faqtorze, ganviTarebuli qveynebis warmomadgenlebi eqvemdebarebian nebismier

iluzias, xolo naklebad ganviTarebuli qveynebisa _ mxolod erT-erTs

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)

mnmn aaa +=⋅

mnmn aaa −=:

mnmn aa ⋅=)(

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:

( ) 222 2 bababa ++=+

( ) 222 2 bababa +−=−

( )( ) 22 bababa −=−+ 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: βα = .

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.

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

43.

marTkuTxedis mcire gverdis

sigrZea a, didi gverdisa _ b. MN am marTkuTxedis mcire gverdebis SemaerTebeli

monakveTia (ix. naxazi).

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

121481046 −+−+−111315171618 −+−+−

5 m/wm18 km/sT

MN monakveTis sigrZe a + b

23

44.

vaSli da broweuli erTad 190 g-s iwonis, vaSli da komSi ki _ 180 g-s.

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

45.

ramdenime Sesakrebis jami 42,85-is tolia. TiToeuliSesakrebi aRemateba 7-s.

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

46.

α-Ti aRniSnulia marTkuTxa samkuTxedis udidesi

maxvili kuTxis sidide, xolo β-Ti _ maxvilkuTxa

samkuTxedis udidesi kuTxis sidide.

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

broweulis wona komSis wona

5SesakrebTa raodenoba

100° α + β

24

amocanebi

47. bukinistma pirvel kviraSi 9 leqsikoni gayida, 7 ki _ SeiZina. meore kviraSi gayida 3 leqsikoni, SeiZina _ 8. mesame kviraSi gayida _ 4, SeiZina _ 1. amis Semdeg bukinists sul 15 leqsikoni aRmoaCnda. ramdeni leqsikoni hqonia

bukinists Tavdapirvelad?

(a) 12 (b) 13 (g) 14 (d) 15 (e) 16

48. pirvel sastumroSi samjer meti damsvenebelia, vidre _ meoreSi, xolo

mesameSi _ orjer meti, vidre pirvel da meore sastumroebSi erTad. ramdenjer

meti damsvenebelia mesame sastumroSi meoresTan SedarebiT?

(a) 4-jer (b) 5-jer (g) 6-jer (d) 7-jer (e) 8-jer

49. oTxkuTxa piramidas 5 wvero da 8 wibo aqvs. ramdeni wibo aqvs piramidas, romelsac 10 wvero aqvs?

(a) 10 (b) 12 (g) 16 (d) 18 (e) 20

25

50. vanos mxolod 1-TeTriani, 2-TeTriani, 5-TeTriani, 10-TeTriani da 20-TeTriani monetebi aqvs. man Tavis 7 megobars TiTo moneta aCuqa. aRmoCnda, rom sam

maTgans erTnairi monetebi Sexvda, xolo danarCenebs _ sxvadasxvanairi. maqsimum

ramdeni TeTri SeiZleba iyos vanos mier gaCuqebuli Tanxis raodenoba?

(a) 42 (b) 48 (g) 63 (d) 78 (e) 140

51. =++ 100007

10003

105

(a) 537,0

(b) 5037,0

(g) 50307,0

(d) 5307,0

(e) 05037,0

26

monacemTa analizi

diagramaze mocemulia, qalTa da mamakacTa ramdeni procenti iyo dasaqmebuli

saqarTveloSi 2007 wels asakobrivi jgufebis mixedviT.

cxrilSi ki mocemulia, Tu ramdeni aTasi qali da mamakaci iyo dasaqmebuli

saqarTveloSi 2005-2007 wlebSi asakobrivi jgufebis mixedviT.

2005 2006 2007 qali mamakaci qali mamakaci qali mamakaci

15-24 wlis 50,7 89,5 51,3 89,5 45,1 84,0 25-34 wlis 122,6 164,2 117,6 177,2 118,0 162,5 35-44 wlis 188,7 203,7 186,3 181,8 170,7 185,2 45-54 wlis 184,6 197,1 189,3 202,7 144,0 168,0

55 an meti wlis 281,9 260,5 281,9 269,4 287,7 263,6

diagramisa da cxrilis mixedviT upasuxeT Semdeg 4 SekiTxvas:

52. romel wels da romel asakobriv jgufSi iyo dasaqmebul mamakacTa raodenoba 170 aTasze meti, magram 180 aTasze naklebi?

(a) 2005 wels, 35-44 wlis asakobriv jgufSi (b) 2005 wels, 45-54 wlis asakobriv jgufSi (g) 2006 wels, 25-34 wlis asakobriv jgufSi (d) 2006 wels, 35-44 wlis asakobriv jgufSi (e) 2007 wels, 55 an meti wlis asakobriv jgufSi

53. ramdenjer metia 2007 wels 55 wlis an ufro meti asakis dasaqmebul

mamakacTa raodenoba dausaqmebel mamakacTa raodenobaze?

(a) 1,2-jer (b) 1,5-jer (g) 1,8-jer (d) 2,2-jer (e) 2,5-jer

27

54. 2007 wels romel asakobriv jgufSia dasaqmebuli qalTa aranakleb 1/2, xolo mamakacebis ara umetes 4/5 nawilisa?

(a) 15-24 wlis (b) 25-34 wlis (g) 35-44 wlis (d) 45-54 wlis (e) 55 an meti wlis

55. 45-54 wlis adamianTa ramdeni procenti iyo dasaqmebuli 2007 wels?

(a) 72%

(b) 74%

(g) 76%

(d) 78%

(e) 80%

amocanebi

56. ∇ da ◊ niSnebiT cifrebia aRniSnuli. risi tolia ∇ + ◊, Tuki 338372 4 =−∇ ◊ ?

(a) 11 (b) 10 (g) 9 (d) 8 (e) 7

57. p da q iseTi naturaluri ricxvebia, rom 223 qp =+ . CamoTvlilTagan

romlis toli SeiZleba iyos p ?

(a) 7 (b) 13 (g) 19 (d) 23 (e) 29

28

58. ABCD kvadrati dayofilia tol kvadratebad, romelTagan zogierTi gamuqebulia (ix. naxazi).

minimum ramdeni kvadrati unda gavamuqoT kidev,

rom miRebuli gamuqebuli figura iyos

simetriuli BD RerZis mimarT?

(a) 1 (b) 2 (g) 3 (d) 4 (e) 5

59. ramdenjer Semcirdeba dadebiTi ricxvi, Tu mas Tavis mexuTeds gamovaklebT?

(a) 1,25-jer (b) 1,5-jer (g) 2-jer (d) 2,25-jer (e) 2,5-jer

60. erTmaneTis momdevno 8 naturaluri ricxvisgan Sedgenili mimdevrobis bolo 4 wevris jami 62-is tolia. risi tolia am mimdevrobis pirveli 4 wevris jami? (a) 46

(b) 50 (g) 54 (d) 58 (e) 62

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.

maRaziaSi feradi furclebi iyideba. 60-furcliani Sekvra 5 lari Rirs, 40-furcliani _ 4 lari, xolo calobiT TiTo feradi furceli _ 20 TeTri. giam am maRaziaSi feradi furclebi SeiZina, raSic sul

13 lari gadaixada.

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

62.

nebismieri n naturaluri ricxvisaTvis n* aRniSnavs 1-dan n-is CaTvliT yvela naturaluri ricxvis jams. magaliTad, 104321*4 =+++= .

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

63.

mocemulia ori toli marTkuTxedi.

pirveli marTkuTxedidan amoWrilia wre,

romlis radiusis sigrZea 4 sm, xolo meore marTkuTxedidan _ ori wre,

romelTagan erTis radiusis sigrZea

3 sm, meorisa _ 1 sm.

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

SeZenili feradi

furclebis raodenoba 142

*n n2

meore marTkuTxedis

darCenili nawilis

farTobi

pirveli marTkuTxedis

darCenili nawilis

farTobi

30

64.

samecniero konferenciaSi mxolod fizikosebi da

qimikosebi monawileoben. fizikosebis saSualo asakia

30 weli, xolo qimikosebisa _ 40 weli.

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

65.

moWadrakem wlis II naxevarSi 2-jer meti partia

iTamaSa, vidre _ I naxevarSi. misi mogebiT dasrulda

mis mier wlis I naxevarSi gamarTuli partiebis 70% da wlis II naxevarSi gamarTuli partiebis 50%.

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

amocanebi

66. Tu n naturaluri ricxvia, maSin ( )4+nn :

(a) aucileblad luwia

(b) aucileblad kentia

(g) kentia mxolod maSin, roca n kentia (d) luwia mxolod maSin, roca n kentia (e) kentia, roca n luwia

67. ABCD oTxkuTxedis A da C wertilebi x RerZze mdebareobs, xolo B da D wertilebis koordinatebia, Sesabamisad, ( )6,3;4− da

( )2,1;2 − (ix. naxazi).

risi tolia ABC samkuTxedis farTobis Sefardeba ACD samkuTxedis farTobTan?

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

konferenciaSi monawile

mecnierTa saSualo asaki 35 weli

60%moWadrakis mier mogebuli

partiebis procentuli wili

mTeli wlis ganmavlobaSi

31

68. Tu ( )( ) 01042 =−+ xx da 2−≠x , maSin =x2

(a) 12− (b) 5−

(g) 5 (d) 6 (e) 12

69. wriul diagramaze warmodgenilia monacemebi saeqsportod gatanili citrusebis (mandarinis,

forToxlis, limonis da greipfrutis)

raodenobaTa Sesaxeb.

ramdenjer meti forToxali gautaniaT

saeqsportod limonTan SedarebiT?

(a) 1,5-jer (b) 2-jer (g) 2,5-jer (d) 3-jer (e) 3,5-jer

70. kedlis mopirkeTeba erT xelosans SeuZlia 2 saaTSi, meores _ 3 saaTSi, xolo mesames _ 4 saaTSi. kedlis ra minimaluri nawilis mopirkeTebaa

SesaZlebeli 1 saaTSi am xelosnebidan romelime oris erTad muSaobis Sedegad?

(a) 65

(b) 127

(g) 95

(d) 32

(e) 97

71. 18 m sigrZis Toki wiTeli xazebiT dayves 9 tol nawilad, xolo lurji xazebiT _ 6 tol nawilad. Semdeg dayofis yvela xazze Toki gadaWres. Tokis ramdeni naWeri miiReba sul?

(a) 10 (b) 12 (g) 14 (d) 15 (e) 16

32

monacemTa sakmarisoba

72. ABCD kvadrati dayofilia AMNKCD eqvskuTxedad da MBKN kvadratad.

mocemulia Semdegi ori piroba:

I. ABCD kvadratis perimetria 40 sm. II. MBKN kvadratis perimetria 10 sm.

imis gasarkvevad, Tu risi tolia AMNKCD eqvskuTxedis perimetri:

(a) I piroba sakmarisia, II ki _ ara

(b) II piroba sakmarisia, I ki _ ara

(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi

(d) sakmarisia cal-calke rogorc I, aseve II piroba

(e) mocemuli pirobebi araa sakmarisi

73. avtomanqana 90 km/sT siCqariT moZraobda. mosaxvevSi mZRolma avtomanqanis siCqare Seamcira, mosaxvevis gavlis Semdeg ki siCqare isev gazarda da moZraoba

Tavdapirveli siCqariT ganagrZo.

mocemulia Semdegi ori piroba:

I. mosaxvevSi mZRolma avtomanqanis siCqare 18 km/sT-iT Seamcira. II. mosaxvevSi mZRolma avtomanqanis siCqare 20%-iT Seamcira.

imis gasarkvevad, Tu ramdeni procentiT gazarda mZRolma avtomanqanis siCqare:

(a) I piroba sakmarisia, II ki _ ara

(b) II piroba sakmarisia, I ki _ ara

(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi

(d) sakmarisia cal-calke rogorc I, aseve II piroba

(e) mocemuli pirobebi araa sakmarisi

33

74. turistTa jgufi bakurianSi Cavida. jgufSi mxolod erTia iseTi, romelsac arc TxilamurebiT sriali uyvars da arc _ cigurebiT. danarCenebidan

TiToeuls an mxolod TxilamurebiT sriali uyvars, an mxolod _ cigurebiT.

mocemulia Semdegi ori piroba:

I. im turistTa raodenoba, romlebsac TxilamurebiT sriali uyvarT, 6-is tolia.

II. im turistTa raodenoba, romlebsac cigurebiT sriali uyvarT, 2-jer naklebia im turistTa raodenobaze, romlebsac TxilamurebiT sriali uyvarT.

imis gasarkvevad, Tu risi tolia jgufSi turistTa saerTo raodenoba:

(a) I piroba sakmarisia, II ki _ ara

(b) II piroba sakmarisia, I ki _ ara

(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi

(d) sakmarisia cal-calke rogorc I, aseve II piroba

(e) mocemuli pirobebi araa sakmarisi

75. a da b erTmaneTisgan gansxvavebuli ricxvebia.

mocemulia Semdegi ori piroba:

I. 0<ab

II. 0>+ ba

imis gasarkvevad, dadebiTia Tu ara ricxvi a:

(a) I piroba sakmarisia, II ki _ ara

(b) II piroba sakmarisia, I ki _ ara

(g) I da II piroba erTad sakmarisia, cal-calke ki _ arc erTi araa sakmarisi

(d) sakmarisia cal-calke rogorc I, aseve II piroba

(e) mocemuli pirobebi araa sakmarisi

34

amocanebi

76. marTkuTxa paralelepipedi, romlis sigrZea 8 sm, dayofilia 6 tol marTkuTxa paralelepipedad (ix. naxazi). risi tolia dayofis Sedegad miRebuli TiToeuli

marTkuTxa paralelepipedis moculoba? (a) 72 sm3 (b) 64 sm3

(g) 60 sm3

(d) 56 sm3

(e) 48 sm3 77. x da y martivi ricxvebia. CamoTvlilTagan romlis toli SeiZleba iyos yx − ?

(a) 7 (b) 13 (g) 19 (d) 23 (e) 27

78. saklaso oTaxSi myofi gogonebis raodenoba n-is tolia, xolo vaJebisa _ m-is. gakveTilis Semdeg klasidan gamovida 2 gogona da 3 vaJi. risi tolia imis

albaToba, rom amis Semdeg klasidan gamosuli kidev erTi moswavle vaJi iqneba?

(a) 53−+

−nm

m

(b) 33−+

−nm

m

(g) nm

(d) nmm+

(e) 23

−−

nm

35

79. yoveli marTkuTxedi misi gadamkveTi wrfeebiT SeiZleba daiyos tol marTkuTxedebad. magaliTad,

ABCD marTkuTxedi misi gadamkveTi 3 wrfiT

dayofilia 6 tol marTkuTxedad (ix. naxazi).

maqsimum ramden tol marTkuTxedad SeiZleba

daiyos marTkuTxedi misi gadamkveTi 13 wrfiT?

(a) 50 (b) 52 (g) 54 (d) 56 (e) 60

80. qoreografiuli saswavleblis or darbazSi repeticia mimdinareobda. pirvel darbazSi myof mocekvaveTa raodenoba meore darbazSi myof mocekvaveTa raodenobis

meoTxedi iyo. mas Semdeg, rac meore darbazidan pirvelSi 6 mocekvave gadavida, pirvel darbazSi myof mocekvaveTa raodenoba meore darbazSi myof mocekvaveTa

raodenobis naxevari gaxda. sul ramdeni mocekvave imyofeboda orive darbazSi?

(a) 30 (b) 36 (g) 40 (d) 42 (e) 45