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

2
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

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.
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

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.

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

5
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

6
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.
7
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

8
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

9
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

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 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

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.

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

12
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

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. 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

14
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

15
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
nax. 1
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.
16
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

17
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

18
 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; 10. paraleluri wrfeebi:
1 ar aris martivi ricxvi. ori paraleluri wrfis mesame
wrfiT gadakveTisas Siga jvaredina
2. procenti: a ricxvis k% aris .
kuTxeebi tolia: = .
n
3. xarisxi: a = a a a ... a (n-jer) 11. samkuTxedi:
n+ m
a a
n m
=a samkuTxedis kuTxeebis sidideTa jami
n m nm 180-is tolia;
a :a =a
piTagoras Teorema:
(a
n m
) = a nm marTkuTxa samkuTxedis
4. proporcia: Tu , maSin ad = bc. hipotenuzis sigrZis
kvadrati kaTetebis sigrZeTa
manZili
5. siCqare: siCqare = kvadratebis jamis tolia:
dro
AB2 = AC2 + BC2
6. saSualo ariTmetikuli:
samkuTxedis farTobi samkuTxedis
monacemTa jami
monacemTa saSualo = gverdis sigrZisa da Sesabamisi simaRlis
monacemTa raodenoba namravlis naxevris tolia: .
7. albaToba: Tu yvela elementaruli 12. oTxkuTxedi:
xdomiloba Tanabrad mosalodnelia, maSin oTxkuTxedis kuTxeebis sidideTa jami
xdomilobis albaToba tolia am xdomilobis 360-is tolia;
xelSemwyob elementarul xdomilobaTa marTkuTxedis farTobi misi sigrZisa da
raodenobis Sefardebisa elementarul siganis namravlis tolia: S = ab;
xdomilobaTa saerTo raodenobasTan. paralelogramis farTobi misi gverdis
Tu amocanis pirobaSi sawinaaRmdego araa sigrZisa da am gverdis Sesabamisi simaRlis
naTqvami, yovelTvis igulisxmeba, rom elementa- namravlis tolia: S = ah.
ruli xdomilobebi Tanabrad mosalodnelia. 13. wre, wrewiri:
8. Semoklebuli gamravlebis formulebi: wrewiris sigrZe L misi
(a + b )2 = a 2 + 2ab + b 2 radiusis mixedviT gamoiTvleba
formuliT: L = 2r;
(a b )2 = a 2 2ab + b 2 ricxvi, measedis sizustiT, 3,14-is tolia;
(a + b )(a b ) = a 2 b2 r radiusiani wris farTobi
gamoiTvleba formuliT: S = r2.
9. naxazze kuTxe SeiZleba
moniSnuli iyos kuTxis 14. marTkuTxa paralelepipedi:
gverdebs Soris Casmuli marTkuTxa paralelepipedis
patara rkaliT, marTi kuTxe moculoba misi sigrZis, siganisa da
ki _ patara kvadratiT. simaRlis namravlis tolia: V = abc;
A aRniSnavs A kuTxis sidides. kubis SemTxvevaSi: a = b = c.

21
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. 18 16 + 17 15 + 13 11 6 4 + 10 8 + 14 12 (a) (b) (g) (d)

42. 18 km/sT 5 m/wm (a) (b) (g) (d)

marTkuTxedis mcire gverdis

sigrZea a, didi gverdisa _ b.
43. MN am marTkuTxedis mcire
gverdebis SemaerTebeli (a) (b) (g) (d)
monakveTia (ix. naxazi).
MN monakveTis sigrZe a+b

22
 vaSli da broweuli erTad 190 g-s iwonis, vaSli
44. da komSi ki _ 180 g-s. (a) (b) (g) (d)
broweulis wona komSis wona

ramdenime Sesakrebis jami 42,85-is tolia. TiToeuli

Sesakrebi aRemateba 7-s. (a) (b) (g) (d)
45.
SesakrebTa raodenoba 5

-Ti aRniSnulia marTkuTxa samkuTxedis udidesi

maxvili kuTxis sidide, xolo -Ti _ maxvilkuTxa
46. samkuTxedis udidesi kuTxis sidide. (a) (b) (g) (d)

+ 100

23
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
24
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. 5 + 3 + 7 =
10 1000 10000
(a) 0,537
(b) 0,5037
(g) 0,50307
(d) 0,5307
(e) 0,05037

25
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

26
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

72 3 4 = 338 ?
(a) 11
(b) 10
(g) 9
(d) 8
(e) 7

57. p da q iseTi naturaluri ricxvebia, rom p + 3 = 2q 2 . CamoTvlilTagan

romlis toli SeiZleba iyos p ?
(a) 7
(b) 13
(g) 19
(d) 23
(e) 29

27
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

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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

maRaziaSi feradi furclebi iyideba. 60-furcliani

Sekvra 5 lari Rirs, 40-furcliani _ 4 lari, xolo
calobiT TiTo feradi furceli _ 20 TeTri. giam
61. am maRaziaSi feradi furclebi SeiZina, raSic sul (a) (b) (g) (d)
13 lari gadaixada.

SeZenili feradi
142
furclebis raodenoba

nebismieri n naturaluri ricxvisaTvis n* aRniSnavs

1-dan n-is CaTvliT yvela naturaluri ricxvis jams.
(a) (b) (g) (d)
62. magaliTad, 4* = 1 + 2 + 3 + 4 = 10 .

n* 2n

mocemulia ori toli marTkuTxedi.

pirveli marTkuTxedidan amoWrilia wre,
romlis radiusis sigrZea 4 sm, xolo
meore marTkuTxedidan _ ori wre,
63. romelTagan erTis radiusis sigrZea (a) (b) (g) (d)
3 sm, meorisa _ 1 sm.

pirveli marTkuTxedis meore marTkuTxedis

darCenili nawilis darCenili nawilis
farTobi farTobi

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 samecniero konferenciaSi mxolod fizikosebi da
qimikosebi monawileoben. fizikosebis saSualo asakia
64. 30 weli, xolo qimikosebisa _ 40 weli. (a) (b) (g) (d)

konferenciaSi monawile 35 weli

mecnierTa saSualo asaki

moWadrakem wlis II naxevarSi 2-jer meti partia

iTamaSa, vidre _ I naxevarSi. misi mogebiT dasrulda
mis mier wlis I naxevarSi gamarTuli partiebis 70%
65. da wlis II naxevarSi gamarTuli partiebis 50%. (a) (b) (g) (d)

moWadrakis mier mogebuli

partiebis procentuli wili 60%
mTeli wlis ganmavlobaSi

amocanebi

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

(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, ( 4; 3,6 ) 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

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68. Tu (x + 2)(4 x 10) = 0 da x 2 , maSin 2 x =
(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) 5
6
(b) 7
12
(g) 5
9
(d) 2
3
(e) 7
9

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

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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

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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. ab < 0
II. a + b > 0

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

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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 x y ?

(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) m 3
m + n 5
(b) m 3
m + n 3
(g) m
n
(d) m
m+n
(e) m 3
n2

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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

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