testi Sedgeba ori _ da _ nawilisagan.

TiToeuli nawili 50 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.

drois amowurvis Sesaxeb gacnobebT meTvalyure.

Tu ar gaqvT romelime davalebis pasuxi, dros nu dakargavT da

gadadiT Semdeg davalebaze.

Canawerebis an naxazebisaTvis gamoiyeneT mxolod da mxolod testis

furclebze arsebuli carieli adgilebi.

verbaluri maTematikuri

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.

Tu gaTvaliswinebulze meti droiT SeyovndebiT testis ama Tu im

nawilze, Tqveni naSromi ar Semowmdeba.

instruqcia

gisurvebT warmatebas !

instruqcia

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.

Tu gaTvaliswinebulze meti droiT SeyovndebiT testis ama Tu im

nawilze, Tqveni naSromi ar Semowmdeba.

gisurvebT warmatebas !

zogadi unarebis testizogadi unarebis testi

IV

2

verbaluri nawili

analogiebi

am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva,

romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. daadgineT, ra

saxisaa es mimarTeba.

savaraudo pasuxTa yovel variantSi aseve mocemulia mniSvnelobiT

urTierTdakavSirebuli sityvebis wyvili. airCieT maTgan is wyvili, romelSic

sityvaTa mniSvnelobebs Soris mimarTeba gamuqebul sityvaTa urTierTmimarTebis

msgavsia (analogiuria). pasuxis arCevisas gaiTvaliswineT wyvilebSi sityvaTa

Tanmimdevroba.

magaliTad: kenWi : qva

(a) velosipedi : manqana

(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi

swori pasuxia (b), radgan mimarTeba _ "biliki aris momcro gza" _ msgavsia mimarTebisa _ "kenWi aris momcro qva".

1. cxvari : fara

(a) simRera : misamReri

(b) nabadi : menabde

(g) uremi : urmuli

(d) buCqi : buCqnari

2. magida : skami

(a) dana : Cangali

(b) sufra : qsovili

(g) lambaqi : WurWeli

(d) doqi : sasmeli

3. koconi : fiCxis Segroveba

(a) urika : tvirTis dadeba

(b) Wa : wylis amoxapva

(g) Rvino : yurZnis dawurva

(d) xili : gemos gasinjva

4. burTi : mrgvali

(a) balaxi : norCi

(b) rZe : aWrili

(g) miwa : nayofieri

(d) Tafli : tkbili

3

5. mexsiereba : gulmaviwyi

(a) fantazia : realuri

(b) emocia : naRvliani

(g) yuradReba : dabneuli

(d) azrovneba : sxarti

6. kompasi : mogzauri

(a) maTraxi : mxedari

(b) gakveTili : maswavlebeli

(g) wamali : eqimi

(d) moTxroba : mwerali

7. qaRaldi : wigni

(a) limoni : citrusi

(b) fqvili : namcxvari

(g) yveli : karaqi

(d) vazi : mtevani

8. cxoveli : fafari

(a) fesvi : rto

(b) Tevzi : qviriTi

(g) cxeni : nali

(d) yvavili : ekali

4

winadadebis Sevseba

am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa

gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiTaa 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.

9. saswavlebelSi sabunebismetyvelo saganTa swavleba ori mimarTulebiT

mimdinareobs: Teoriuli kursis _____ praqtikuli mecadineoba _____ tardeba.

(a) gaxangrZlivebis gamo / aRar

(b) nacvlad / sistematurad

(g) dasrulebis gamo / yoveldRiurad

(d) paralelurad / aucileblad

10. bevri sxva _____, romlebic marto nadiroben, mgeli warmatebuli monadire mxolod _____ nadirobis wyalobiT xdeba, rac nadirobis dros _____

gulisxmobs.

(a) mtaceblisgan gansxvavebiT / jgufuri / funqciebis ganawilebas

(b) mtaceblis msgavsad / jgufuri / damoukideblad moqmedebas

(g) mtaceblis msgavsad / marto / erTobliv moqmedebas

(d) mtaceblisgan gansxvavebiT / marto / TanamoZmeebis aqtiurobas

11. mozardi, patarasTan SedarebiT, xSirad Tavs aridebs Tematur naxats, radgan SiSobs, rom _____ , rogorc Caifiqra. miuxedavad amisa, mozardebis naxatebis

Tematika gacilebiT mravalferovania. es _____ isini xatvis teqnikas _____ .

(a) ise ver daxatavs / gasakviria, miT ufro, rom / mkveTrad aumjobeseben

(b) ise daxatavs / arcaa gasakviri, radgan / kargad ver floben

(g) ise daxatavs / gaugebaria imitom, rom / mudmivad xvewen

(d) ise ver daxatavs / bunebrivia, vinaidan / ukeT floben

5

12. TavisTavad ucxo kapitalis SeWra _____ ama Tu im qveynisTvis, Tu mas win ganviTarebuli Segneba da politikuri Zala _____ . magram roca qveyana erovnul

Segnebasa da saxelmwifo Zalas _____ , ucxo kapitalis gavlena _____ .

(a) sruliad ar warmoadgens safrTxes / ar egebeba / moklebulia /

ganmaviTarebel faqtorad iqceva

(b) seriozul safrTxes warmoadgens / ar egebeba / ar aris moklebuli / Zalze

saxifaTo faqtorad iqceva

(g) seriozul safrTxes warmoadgens / egebeba / ar aris moklebuli / pirdapir

gamanadgurebeli xdeba

(d) sruliad ar warmoadgens safrTxes / egebeba / moklebulia / pirdapir

gamanadgurebeli xdeba

13. damwerlobis ZiriTadi daniSnulebaa raime _____ da ara _____ miRweva. _____ damwerloba yovelTvis _____ zemoqmedebis elements.

(a) cnobis Cawera da gadacema / mxatvruli efeqtis / miuxedavad amisa, / Seicavda

esTetikuri

(b) informaciisadmi SemoqmedebiTi midgoma / esTetikuri zemoqmedebis / swored

amitom / gulisxmobda esTetikuri

(g) informaciis esTetikurad gadmocema / mxatvruli efeqtis / Sesabamisad, /

rodi gulisxmobda esTetikuri

(d) informaciis zustad gadacema / fsiqologiuri zemoqmedebis / miuxedavad

amisa, / ar Seicavda esTetikuri

6

logika

am saxis davalebebi gansxvavdeba erTmaneTisgan winaswari 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.

14. dilaadrian mgelma akelam Tvali mohkra msuqan kurdRels nenis da gaekida mas.

• Tu akela nenis daeweva, neni akelas cocxali ver gadaurCeba

• Tu neni akelas cocxali ver gadaurCeba, SuadRisas akela maZRari

daiZinebs

• SuadRisas akelas SimSilisgan ar daeZina

qvemoT CamoTvlilTagan romeli gamomdinareobs am debulebebidan aucileblad?

(a) akela daewia nenis da neni akelas cocxali ver gadaurCa

(b) akela daewia nenis, magram neni akelas cocxali gadaurCa

(g) akela ver daewia nenis da neni akelas cocxali ver gadaurCa

(d) akela ver daewia nenis da neni akelas cocxali gadaurCa

15. zafxulis erT dRes sofom axal saparikmaxeroSi wasvla gadawyvita. SesasvlelSi mas am saparikmaxeros damlagebeli gamoelaparaka, romelsac qudi

exura. sofos SekiTxvaze: "ratom gaxuravT qudi am sicxeSi?", damlagebelma upasuxa: "parikmaxerma zedmetad mokled SemWra Tma". sofo saswrafod gamovida saparikmaxerodan, radgan damlageblis naTqvamis safuZvelze ivarauda, rom:

am saparikmaxeroSi araprofesionalebi muSaoben.

qvemoT CamoTvlilTagan romeli faqti ayenebs eWvqveS am varauds?

(a) saparikmaxeroSi damlagebels, rogorc sakuTar TanamSromels, gansakuTrebuli

mondomebiT SeWres Tma

(b) miuxedavad imisa, rom damlagebeli am saparikmaxeros TanamSromelia, misTvis

momsaxureba aq ufaso araa

(g) saparikmaxero ar sargeblobs didi popularobiT

(d) damlagebelma Tma sxva saparikmaxeroSi SeiWra

7

16. davuSvaT, rom:

• arc erT meTevzes ar hyavs kata

• yvelas, visac ar hyavs kata, axuravs qudi

qvemoT CamoTvlilTagan romeli gamomdinareobs am debulebebidan aucileblad?

(a) yvela meTevzes axuravs qudi

(b) yvela, visac axuravs qudi, meTevzea

(g) mxolod zogierT meTevzes axuravs qudi

(d) arc erT meTevzes ar axuravs qudi

17. magidaze oTxi yuTi devs Semdegi TanmimdevrobiT: wiTeli, yviTeli, mwvane da lurji.

TiToeul yuTSi sabam TiTo burTi Cado: erTSi _ wiTeli, erTSi _ yviTeli,

erTSi _ mwvane da erTSi _ lurji, magram ise, rom:

• arc erT yuTSi ar devs amave yuTis feris burTi

• arc wiTel da arc yviTel yuTSi ar devs lurji burTi

yuTebSi burTebis ganlagebis mocemuli variantebidan romelia SeuZlebeli?

(a) yviTeli, wiTeli, lurji, mwvane

(b) mwvane, wiTeli, lurji, yviTeli

(g) mwvane, lurji, wiTeli, yviTeli

(d) yviTeli, mwvane, lurji, wiTeli

18. davuSvaT, rom: • brZolaSi imarjveben is meomrebi, romlebsac mtkice xasiaTi aqvT, an

gonieri sardali hyavT, anda mokavSireebi

• meomrebma brZolaSi ver gaimarjves

Semdegi debulebebidan romliT aixsneba maTi damarcxeba?

(a) meomrebs mtkice xasiaTi hqondaT

(b) meomrebs ar hqondaT mtkice xasiaTi, Tumca maT hyavdaT mokavSireebi

(g) meomrebs ar hyavdaT mokavSireebi, magram hyavdaT gonieri sardali

(d) meomrebs ar hqondaT mtkice xasiaTi, maT arc gonieri sardali da arc

mokavSireebi hyavdaT

8

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

dedamiwaze arsebuli mtacebeli frinvelebis 62 procenti sezonur

gadafrenas (migracias) axorcielebs sabudar da sazamTro adgilebs Soris.

sazogadod, am movlenis ZiriTadi mamoZravebeli Zala sakvebis raodenobis

sezonuri cvlilebaa. mtacebelTa umravlesoba, sxva mravali frinvelisgan (mag.

weroebisa da batebisgan) gansxvavebiT, gundurad ki ar migrirebs, aramed cal-

calke, anu farTo "frontiT", romelic moicavs mraval samigracio gzas

(saSemodgomo da sagazafxulo samigracio gzebi yovelTvis ar emTxveva erTmaneTs).

isini gadafrenisas sakmaod moxerxebulad zogaven energias _ iyeneben mziT

gamTbari miwis zedapiridan haeris zeamaval siTbur nakadebs, e.w. Termalebs, da

qaris zeamaval nakadebs. haeris zeamaval nakadze "damjdari" frinveli asrulebs iraos, igi nel-nela adis maRla manam, sanam amwevi nakadi TandaTan ar gacivdeba

da Sesustdeba. amis Semdeg frinveli livlivis meSveobiT "gadaxteba" maxlobel axalwarmoqmnil Tbil nakadze da iraos meSveobiT isev zemoT adis. ase irao-

livlivis monacvleobiT SeuZlia dafaros 600 km dReSi. aseTi samigracio strategiis gamo mtacebeli frinvelebi eridebian zRvisa

da tbebis gadafrenas im adgilebSi, sadac wylis zedapiris sigane 25 km-ze metia, radgan wylis zedapirze Termalebi da sxva zeamavali haeris nakadebi ar

warmoiqmneba. amaze naTlad metyvelebs amerikisa da evropa-afrikis samigracio

sistema. mravali mtacebeli frinveli gadafrenisas Tavs iyris iseT adgilebSi,

sadac wylis zedapiris sigane mcirea, rogoricaa panamis arxi centralur

amerikaSi, gibraltaris, mesinisa da bosforis sruteebi evropaSi. ramdenime

samigracio gzis Tavmoyris adgils samigracio derefans an "Zabrs" uwodeben. mtacebeli frinvelebi maRali qedebis gadalaxvasac eridebian da maT

Semovlas cdiloben. Rrubliani amindis dros, rodesac Termalebi sustdeba,

gadamfreni mtaceblebi frenas wyveten. unda aRiniSnos, rom SavardnisebrT da

Zelqorebs gadafrenisas ufro aqtiuri frena sCveviaT da amitom Termalebze

naklebad arian damokidebulni. Sesabamisad, maTi samigracio gzebi aSkara Zabrs

ar qmnis.

evropa-afrikis samigracio sistemis erT-erTi mniSvnelovani Zabri mdebareobs

saqarTveloSi, baTumis maxloblad. baTumis Zabri saSemodgomo gadafrenisas ase

iqmneba: mtacebeli frinvelebi didi kavkasionis centralur da dasavleT nawils

gadmolaxaven da eSvebian kolxeTis dablobze. energiis dazogvis mizniT isini

eridebian Savi zRvis zedapirs, lixisa (suramis) da mesxeTis qedebs. amitom maTi

umetesi nawili Tavs iyris baTumis midamoebSi, Semdeg saqarTvelo-TurqeTis

sazRvars gadakveTen, TandaTan isev dascildebian erTmaneTs da ganagrZoben

frenas Tbili qveynebisken.

9

19. ra Tavisebureba axasiaTebs mtacebeli frinvelebis migracias?

(a) maTi migraciis saSemodgomo da sagazafxulo gzebi erTmaneTs emTxveva

(b) isini sabudar da sazamTro adgilebs Soris migrireben

(g) sabudari adgilebidan Tbili qveynebisken isini mifrinaven cal-calke

(d) isini sabudar adgilebs toveben sakvebi bazis sezonur cvlilebebTan

dakavSirebiT

20. ra aris Termalebi?

(a) haeris zeamavali nakadebi

(b) qaris zeamavali nakadebi

(g) miwis mziT gamTbari monakveTebi

(d) wylis sxvadasxva Tbili dineba

21. "irao-livlivis monacvleobis" meSveobiT:

(a) frinvelebi irCeven saSemodgomo da sagazafxulo samigracio gzebs

(b) frinvelebi frenisas inarCuneben simaRles da amasTanave, zogaven energias

(g) frinvelebi advilad pouloben axalwarmoqmnil Termalebs

(d) frinvelebi aregulireben Termalebsa da qaris zeamaval nakadebs

22. amerikisa da evropa-afrikis samigracio gzebze dakvirvebis Semdeg SeiZleba davaskvnaT:

(a) wylis zedapirze warmoiqmneba Termalebi da haeris sxva zeamavali nakadebi

(b) mtacebeli frinvelebi wylis zedapirze gadafrenisas iseTive samigracio gzebs

irCeven, rogorsac weroebi da batebi

(g) zRvis zedapirze warmoqmnili Termalebi exmareba frinvelebs iraos

SesrulebaSi

(d) mtacebeli frinvelebi eridebian gadafrenas iq, sadac wylis zedapiri Zalze

farToa

10

23. ratom wyveten frenas Rrubliani amindis dros gadamfreni mtaceblebi?

(a) am dros wylis zedapiri civdeba

(b) am dros qaris zeamavali nakadebi Zlierdeba

(g) Rrubliani amindis dros samigracio gza ar Cans

(d) Rrubliani amindis dros Termalebi sustdeba

24. Zelqorebisa da SavardnisebrTa samigracio gzebi aSkara "Zabrs" ar qmnis, radgan:

(a) maT migrirebisas gundad frena sCveviaT

(b) gadafrenisas isini moxerxebulad zogaven energias

(g) isini naklebad arian damokidebuli haeris siTbur nakadebze

(d) isini eridebian qedebis gadalaxvas

25. ra mimarTeba aqvs bolo abzacs teqstTan?

(a) bolo abzacSi Sejamebulia teqstSi gamoTqmuli mosazrebani

(b) bolo abzacSi ganzogadebulia teqstSi dawyebuli msjeloba

(g) bolo abzacSi warmodgenilia teqstSi ganxiluli sakiTxis erTi konkretuli

nimuSi

(d) bolo abzacSi ganxilulia teqstSi gamoTqmul mosazrebaTa sawinaaRmdego

argumentebi

11

analogiebi

am saxis davalebebSi mocemulia muqi SriftiT gamokveTili ori sityva,

romelTa mniSvnelobebs Soris arsebobs garkveuli mimarTeba. daadgineT, ra

saxisaa es mimarTeba.

savaraudo pasuxTa yovel variantSi aseve mocemulia mniSvnelobiT

urTierTdakavSirebuli sityvebis wyvili. airCieT maTgan is wyvili, romelSic

sityvaTa mniSvnelobebs Soris mimarTeba gamuqebul sityvaTa urTierTmimarTebis

msgavsia (analogiuria). pasuxis arCevisas gaiTvaliswineT wyvilebSi sityvaTa

Tanmimdevroba.

magaliTad: kenWi : qva

(a) velosipedi : manqana

(b) biliki : gza

(g) oTaxi : bina

(d) foToli : buCqi

swori pasuxia (b), radgan mimarTeba _ "biliki aris momcro gza" _ msgavsia mimarTebisa _ "kenWi aris momcro qva".

26. mindori : yvavilebi

(a) winadadeba : sityvebi

(b) mze : sxivebi

(g) ca : varskvlavebi

(d) rveuli : furclebi

27. qamari : balTa

(a) karmidamo : miwa

(b) WiSkari : urduli

(g) fari : xmali

(d) sayelo : perangi

28. ankesi : bade

(a) yvavili : Taiguli

(b) zurgCanTa : karavi

(g) motocikli : avtobusi

(d) isari : mSvildi

29. meTauri : winamZRoli

(a) xelyumbara : xelSubi

(b) xelsawyo : xelsafqvavi

(g) xelwerili : xelnaweri

(d) xelsaxoci : xelsawmendi

12

30. Senoba : sasaxle

(a) cekva : ritmi

(b) simRera : iavnana

(g) piesa : speqtakli

(d) TamaSi : saTamaSo

31. Teatris scena : reJisori

(a) fexburTis moedani : mwvrTneli

(b) cirkis arena : jambazi

(g) darbazi : mayurebeli

(d) ringi : msaji

32. wyali : CanCqeri

(a) comi : puri

(b) cecxli : koconi

(g) Tiva : Cala

(d) maWari : Rvino

33. fafuki : Sexeba

(a) mZafri : grZnoba

(b) Wreli : mxedveloba

(g) daxSuli : smena

(d) ucnauri : warmosaxva

13

winadadebis Sevseba

am saxis davalebebSi mocemulia winadadebebi, romlebSic ramdenime sityvaa

gamotovebuli. gamotovebuli sityvebi winadadebaSi xazebiTaa 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.

34. gamocdaze _____ is sakiTxi Semxvda, romelic _____ , magram mainc _____ friadze.

(a) SemTxveviT \ saerTod ar vicodi \ ver vupasuxe

(b) swored \ wina dRes gavimeore \ ver vupasuxe

(g) samwuxarod \ kargad vicodi \ vupasuxe

(d) sabednierod \ wina dRes gavimeore \ vupasuxe

35. warumatebeli adamianebi _____ cxovroben arsebuli realobiT. _____ , isini Sinaganad mimarTulni arian _____ .

(a) yovelTvis /miuxedavad amisa / realur gancdebsa da awmyo situaciebze

(b) iSviaTad / Sesabamisad / warsulis mogonebebze an momavlis lodinze

(g) arasodes / aqedan gamomdinare / realur gancdebsa da awmyo situaciebze

(d) xSirad / Sesabamisad / warsulis mogonebebze an momavlis lodinze

36. sascenod gadakeTebisas moTxrobis arsi daumaxinjebiaT: moTxrobis mTavari personaJi - _____ dedakaci scenaze gadaiqca _____ qalad. mizezi amisa is aris,

rom moTxrobaSi misi xasiaTi gamoxatulia _____ , scenaze ki - _____ .

(a) sentimentaluri, ybedi / Zlier, Seudrekel / moqmedebiT, saqcieliT / mxolod

sityvebiTa da replikebiT

(b) Zlieri, Seudrekeli / ybed, sentimentalur / mxolod sityvebiTa da

replikebiT / moqmedebiT, saqcieliT

(g) sentimentaluri, ybedi / Zlier, Seudrekel / mozomili sityviTa da

moqmedebiT / mxolod replikebiTa da qceviT

(d) Zlieri, Seudrekeli / ybed, sentimentalur / moqmedebiT, saqcieliT / mxolod

sityvebiTa da replikebiT

14

37. sakuTari damwerlobisadmi erebis erTgulebas yvelaze kargad espaneTis

ebraelebsa da arabebze dakvirveba gvidasturebs. pirvelni espaneTSi arabTa

batonobis dros _____ Seqmnili mniSvnelovani literatura dagvitoves, magram

igi _____ iyo dawerili. aseve, arabebma mSobliur enad _____ da am enaze

Seqmnes brwyinvale literatura, romelic _____ iyo Sesrulebuli.

(a) arabulad laparakobdnen da arabul enaze / maTive sakuTari ebrauli anbaniT /

espanuri SeiTvises / arabuli damwerlobiT

(b) arabulad laparakobdnen da espanur enaze / maTive sakuTari ebrauli anbaniT /

espanuri SeiTvises / espanuri anbanis gamoyenebiT

(g) ebraul enaze laparakobdnen da ebraul enaze / arabuli anbaniT / espanuri

ver SeiTvises / ebrauli damwerlobiT

(d) ebraul enaze laparakobdnen da espanur enaze / arabuli anbaniT / arabuli

SeiTvises / espanuri anbanis gamoyenebiT

logika

am saxis davalebebi gansxvavdeba erTmaneTisgan winaswari 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.

38. kodala, SoSia, guguli da Cxikvi simindis marcvals Semousxdnen (ara

aucileblad am TanmimdevrobiT). am marcvals isini niskartiT ugorebdnen

erTmaneTs im wesis dacviT, rom marcvlis gagoreba mxolod marcxniv mjdomisTvis

SeiZleboda. simindis marcvali Cxikvisgan axla SoSiam miiRo.

romeli frinveli miiRebs simindis marcvals kidev oTxi gagorebis Sedegad?

(a) kodala

(b) guguli

(g) SoSia

(d) Cxikvi

15

39. davuSvaT rom: • yvela meviolines uyvars poezia

• orkestris zogierT musikoss ar uyvars poezia

Tu es debulebebi WeSmaritia, maSin qvemoT CamoTvlilTagan romeli debuleba

ar SeiZleba iyos WeSmariti?

(a) poeziis moyvaruli zogierTi musikosi ar aris mevioline

(b) mxolod meviolineebs uyvarT poezia

(g) meviolineebi orkestris musikosebi arian

(d) mxolod meviolineebi arian orkestris musikosebi

40. naZvis xis irgvliv xuTi bavSvi dgas xelCakidebuli. kaxas iasTvis aqvs xeli Cakidebuli, sosos – makasTvis, makas ki _ TedosTvis.

qvemoT CamoTvlilTagan romeli SemTxvevaa SeuZlebeli?

(a) ias xeli aqvs Cakidebuli TedosTvis

(b) Tedos xeli aqvs Cakidebuli kaxasTvis

(g) sosos xeli aqvs Cakidebuli iasTvis

(d) kaxas xeli aqvs Cakidebuli makasTvis

41. qalaqis A ubani ufro SemaRlebul adgilas mdebareobs, vidre B ubani. binebi A ubanSi ufro Zviria, vidre B ubanSi. ninom amis safuZvelze ivarauda, rom:

A ubanSi binebis siZvires swored am ubnis adgilmdebareoba ganapirobebs.

qvemoT CamoTvlTagan romelma faqtma SeiZleba ganamtkicos es varaudi?

(a) A ubanTan SedarebiT, B ubanSi binebi ukeTesi proeqtis mixedviTaa aSenebuli (b) B ubanSi gacilebiT uaresi eleqtromomaragebaa, vidre A ubanSi (g) A ubanSi binebi ufro prestiJuli samSeneblo firmis mieraa aSenebuli,

vidre B ubanSi (d) B ubanTan SedarebiT, A ubanSi quCebi gacilebiT ufro keTilmowyobilia

16

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

kavkasionis qedis gaswvriv uZvelesi droidan gavrcelda koSkura sacxovreblebi,

romelTa naSTebi dResac SeiniSneba Savi zRvidan kaspiis zRvamde maRalmTian

regionebSi. bunebrivia, saqarTveloSi koSkebis simravlem warmoSva uamravi legenda

da fsevdomecnieruli hipoTeza _ mTebSi koSkebi Sua saukuneebSi gamoCnda da

warmoadgenda an glexebis mier feodalTa cixesimagreebis mibaZviT agebul nagebobebs,

an gaRaribebuli feodalebis sacxovrebels.

arsebuli koSkura ansamblebis didi nawili agebulia XIV-XVI saukuneebSi,

ganviTarebuli feodalizmis periodSi. magram es garemoeba imis safuZvels ar

gvaZlevs, rom maTi warmoSoba Sua saukuneebs mivakuTvnoT. koSkura sacxovreblebi

mTebSi unda warmoSobiliyo bevrad ufro adreul istoriul epoqaSi _ Temur-

gvarovnuli wyobis stadiaze. garda amisa, antikuri xanis avtorebi aRweren msgavs

nagebobebs amierkavkasiis da, kerZod, kolxeTis teritoriaze. magaliTad, romaeli

moRvawe vitruviusi Tavis traqtatSi "arqiteqturis Sesaxeb" aRwers kolxuri

koSkura saxlebis xis konstruqcias da kolxeTis koSkebs sacxovrebelTa uZveles

tips miakuTvnebs. svaneTSi, sofel xaiSSi, napovnia koSkura saxlis oqros modeli _

amuleti, romelic daTariRebulia I saukunis miwuruliT Cv. w. aR.-mde. svaneTis

sofel xaiSSi napovni sacxovrebeli koSkis modeli TariRdeba periodiT, rodesac

vitruviusma kolxeTis sacxovrebeli koSkebi aRwera, da imaze miuTiTebs, rom

saqarTvelo koSkura sacxovreblis gavrcelebis erT-erTi mniSvnelovani kera iyo.

antikuri wyaroebis didi umravlesoba qarTvelTa sacxovrebeli koSkebis arsebobas

ukavSirebs rogorc gareSe mtris Semosevebs, aseve Sida konfliqtebs qveynis dablob

da mTian regionebs Soris.

CrdiloeT SuamdinareTSi aRmoaCines Tixis miniaturuli amuleti xis koSkis

gamosaxulebiT, romelic saocrad hgavs saqarTveloSi napovn oqros amulets.

Tumca am or models oTxi aTaswleuli aSorebs erTmaneTs, isini gamosaxaven

formiTa da tipiT identur koSkura saxlebs. Zvel egviptesa da SuamdinareTSi

koSkura sacxovreblis farTo gavrcelebaze miuTiTebs adreuli periodis

ieroglifuri niSnebic, romlebic garkveviT aRniSnaven TavdacviT koSkura saxls.

Tu rukaze sagangebod movniSnavT yvela regions, sadac aRmoCenilia saxli-

simagreebi, TvalSi mogvxvdeba erTi kanonzomiereba: Zvel samyaroSi isini

Tavmoyrilia iq, sadac mdebareobs didi samTo masivebi _ himalai, kavkasioni,

balkaneTi da apeninebi, amerikaSi _ kordilierebi da andebi. mTel msoflioSi

koSkura sacxovreblebis aseTi ganawileba am saxis nagebobebis erTi wyarodan

gavrcelebis Teoriis umweobaze miuTiTebs. safiqrebelia, rom msgavsma

geografiulma pirobebma sazogadoebrivi struqturis da, Sesabamisad,

sacxovreblebis struqturis msgavsebac ganapiroba.

mTiani saqarTvelos koSkura sacxovreblebs didi mniSvneloba eniWeba, rogorc

erT-erT wyaros msoflio kulturis istoriisaTvis, radgan am masalis safuZvelze

SesaZlebeli xdeba ara mxolod aTaswleulebiT daSorebul am ZeglTa aRdgena,

aramed im sazogadoebrivi struqturis Seswavlac, romelmac maTi warmoSoba

ganapiroba.

17

42. qvemoT CamoTvlilTagan romeli mosazrebaa marTebuli? (upasuxeT I-II abzacis mixedviT)

(a) adreul istoriul epoqaSi mTielni feodalTa cixesimagreebis mibaZviT

agebdnen koSkebs

(b) arsebuli koSkura ansamblebi warmoadgens Sua saukuneebSi gaRaribebul

feodalTa sacxovreblebs

(g) Savi zRvidan kaspiis zRvamde maRalmTian regionebSi koSkura nagebobebi XIV-

XVI saukuneebSi unda warmoSobiliyo

(d) kavkasionis qedis gaswvriv gavrcelebuli koSkura sacxovreblebis warmoSoba

Temur-gvarovnuli wyobis stadias unda mivakuTvnoT

43. teqstidan vigebT, rom: I. antikuri xanis avtorebi aRweren amierkavkasiis da, kerZod, kolxeTis

teritoriaze arsebul koSkura ansamblebs.

II. vitruviusi Tavis traqtatSi "arqiteqturis Sesaxeb" aRwers kolxuri koSkura saxlebis xis konstruqcias.

III. dRes arsebuli koSkura ansamblebis didi nawili agebulia ganviTarebuli

feodalizmis periodSi.

IV. svaneTis erT-erT sofelSi napovnia koSkura saxlis oqros modeli, romelic

TariRdeba I saukunis miwuruliT Cv. w. aR.-mde.

romeli sami argumenti ganamtkicebs im mosazrebas, rom saqarTvelos mTebSi

koSkura saxlebi Sua saukuneebamde gacilebiT adre warmoiSva? (a) I, II da IV

(b) I, II da III

(g) II, III da IV

(d) III, IV da I

44. rodis moRvaweobda vitruviusi?

(a) XVI saukunis I naxevarSi

(b) XIV saukunis II naxevarSi

(g) I saukunis II naxevarSi Cv. w. aR.-mde

(d) Cv. w. aR-is II saukunis I naxevarSi

18

45. saqarTvelos mTian regionebSi koSkura nagebobebis gavrceleba ukavSirdeba:

(a) mTielTa Soris gacxovelebul urTierTobas, romelsac maTi kulturis

msgavseba ganapirobebda

(b) qveynis dablob da mTian regionebs Soris konfliqtebs, aseve gareSe mtris

Semosevebs

(g) kavkasionis, kordilierebisa da andebis koSkura sacxovreblebis gavrcelebis

saerTo wyaros

(d) antikuri xanis werilobiTi wyaroebis gavlenas kolxur arqiteqturaze

46. romeli qveynis damwerlobaSi aisaxa koSkis forma?

(a) antikuri saberZneTis

(b) Zveli romis

(g) kolxeTis

(d) Zveli egviptis

47. teqstis mixedviT, romeli debuleba araa marTebuli?

(a) koSkebi sazogadoebrivi struqturis aRdgenas emsaxureba

(b) koSkebi sacxovreblis funqcias asrulebda

(g) koSkebs Tavdacvis mizniT agebdnen

(d) koSkura nagebobebi ZiriTadad mTian regionebSi gvxvdeba

48. CamoTvlilTagan romeli faqti ayenebs eWvqveS sxvadasxva qveyanaSi arsebuli koSkura nagebobebis erTi wyarodan gavrcelebis Teorias?

(a) ieroglifur niSnebSi TavdacviTi koSkura saxlis gamosaxva

(b) antikuri xanis avtorTa mier koSkura saxlebis konstruqciebis aRwera

(g) koSkura nagebobebis Tixisa da oqros modelebis aRmoCena

(d) koSkura nagebobebis ganlageba sxvadasxva geografiul adgilas

19

49. ratom aris mniSvnelovani saqarTvelos mTian regionebSi gavrcelebuli

koSkura sacxovreblebis Seswavla?

(a) is erT-erTi wyaroa msoflio kulturis istoriis kvlevisaTvis

(b) is gvexmareba Zvelegvipturi da Suamdinaruli ieroglifebis gaSifrvaSi

(g) ufro gasagebi xdeba vitruviusis traqtati ,,arqiteqturis Sesaxeb”

(d) SegviZlia warmovidginoT XIV-XVI saukuneebis qarTvel feodalTa yofa

50. ra aris am teqstis mTavari saTqmeli?

(a) kavkasionis qedis gaswvriv SemorCenili koSkebis naSTebi uamravi legendis

warmoSobis safuZvelia

(b) aTaswleulebiT daSorebul ZeglTa aRdgena SesaZlebelia mxolod koSkura

sacxovreblebis Sesaxeb istoriuli masalis safuZvelze

(g) saqarTvelo koSkura sacxovreblebis gavrcelebis erTaderTi mniSvnelovani

keraa

(d) TavdacviTi koSkebis warmoSoba sxvadasxva samTo masivebSi msgavsma

sazogadoebrivma struqturam ganapiroba

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. Semoklebuli gamravlebis formulebi: (a+b)2 = a2 + 2ab + b2

(a - b)2 = a2 – 2ab + b2

(a + b)(a – b) = a2 – b2 8. naxazze kuTxe SeiZleba kuTxis gverdebs Soris

Casmuli patara rkaliT

iyos moniSnuli, marTi

kuTxe ki _ patara

kvadratiT.

∠A aRniSnavs A kuTxis sidides. 9. paraleluri wrfeebi:

• ori paraleluri

wrfis mesame wrfiT

gadakveTisas Siga jvaredina

kuTxeebi tolia: α = β.

10. 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: .

11. 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.

12. 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: L = πr2.

13. 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

51.

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

52.

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

53. a > 0, b > 0

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

54.

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

55.

ABC marTkuTxa samkuTxedSi ∠C = 90° da ∠A < ∠B.

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

56.

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

( )334− ( )213−

75648 · 256 – 1 75643 · 253 + 1

a – b 0

94 5,0

∠A 45°

16-is da 20-is udidesi saerTo

gamyofi

12-is da 28-is udi-desi saerTo

gamyofi

23

57.

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

58.

oTxkuTxa piramidas

sul 5 waxnagi aqvs.

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

amocanebi

59. ramdenjeraa naklebi udidesi orniSna ricxvi udides oTxniSna ricxvze?

(a) 2-jer (b) 99-jer (g) 100-jer (d) 101-jer

(e) 900-jer

60. ricxvTa RerZi masze moniSnuli wertilebiT dayofilia tol

monakveTebad (ix. naxazi). moniSnuli

wertilebidan A da B wertilebis koordinatebi miTiTebulia naxazze. C wertilis koordinatia:

(a) 1,9 (b) 2,9 (g) 3,3 (d) 3,5 (e) 3,7

( ) aa 32 2 +−aa 34 2 +−

SvidkuTxa pira-

midis waxnagebis

raodenoba

marTkuTxa parale-

lepipedis waxnagebis

raodenoba

24

61. mas Semdeg, rac gaCerebaze troleibusidan 11 mgzavri Cavida, xolo 7 mgzavri amovida, troleibusSi 29 mgzavri aRmoCnda. ramdeni mgzavri yofila

troleibusSi am gaCerebamde? (a) 18 (b) 22 (g) 26 (d) 33 (e) 36

62. kinoseansi 18 saaTze daiwyo. romel saaTze dasruldeba seansi, Tu is 95 wuTs grZeldeba?

(a) 18 sT 35 wT (b) 18 sT 55 wT (g) 19 sT 25 wT (d) 19 sT 35 wT (e) 19 sT 55 wT

monacemTa analizi

cxrilSi miTiTebulia, Tu ramdeni lari iyo zogierTi sakvebi produqtis

saSualo fasi sxvadasxva wels (1995 wlidan 1998 wlis CaTvliT)

1995 1996 1997 1998 saqonlis xorci (1 kg) 3.72 3.30 3.80 4.10

Roris xorci (1 kg) 3.88 3.70 4.00 4.20

qaTami (1 kg) 4.62 4.50 4.00 3.62

kvercxi (10 cali) 1.30 1.30 1.50 1.60

karaqi (1 kg) 5.20 5.00 5.00 6.20

yveli (1 kg) 4.90 3.80 3.80 3.80

Saqris fxvnili (1 kg) 0.80 0.91 0.84 0.97

xorblis fqvili (1 kg) 0.85 1.00 0.94 1.00

Rvino (0.7 litri) 1.13 1.37 1.37 1.37

mocemuli cxrilis mixedviT upasuxeT Semdeg 4 SekiTxvas:

63. ramdeni lari iyo 1 kg Roris xorcis saSualo fasi 1996 wels? (a) 3.70 (b) 3.88 (g) 4.00 (d) 4.20 (e) 5.20

25

64. qvemoT CamoTvlilTagan romeli produqtis saSualo fasi ar Semcirebula 1996 wels wina welTan SedarebiT?

(a) saqonlis xorcis

(b) qaTmis

(g) karaqis

(d) Saqris fxvnilis

(e) yvelis

65. romeli produqtis saSualo fasi mcirdeboda yovelwliurad 1995-1998 wlebSi?

(a) Roris xorcis

(b) kvercxis

(g) qaTmis

(d) Saqris fxvnilis

(e) Rvinis

66. ra farglebSi meryeobda (icvleboda) saqonlis xorcis saSualo fasi 1995-1998 wlebSi?

(a) 3.72-sa da 3.80 lars Soris (b) 3.30-sa da 3.80 lars Soris (g) 3.30-sa da 4.10 lars Soris (d) 3.72-sa da 4.10 lars Soris (e) 3.80-sa da 4.10 lars Soris

amocanebi

67. Tu 3x + y = 3 da 2x – y = 2 , maSin 3x = (a) 3 (b) 5 (g) 6 (d) 9 (e) 15

68. sibrtyeze mocemulia marTkuTxa koordinatTa sistema. ABC tolferda samkuTxedis AC fuZe y-RerZis paraleluria. A da B wveroebis koordinatebi miTiTebulia naxazze. C wveros koordinatebi (a; b) =

(a) (4; 6) (b) (4; 8) (g) (5; 2) (d) (5: 6) (e) (6: 7)

26

69. maRaziaSi feradi da Sav-TeTri televizorebi gaiyida. gayiduli televizo-

rebis 65 nawili feradi iyo, xolo 8 televizori _ Sav-TeTri. sul ramdeni

televizori gaiyida maRaziaSi? (a) 18 (b) 24 (g) 36 (d) 42 (e) 48

70. mas Semdeg, rac perangis fasi 20%-iT Semcirda, perangi 72 larad iyideboda. ramdeni lari Rirda perangi fasis Semcirebamde?

(a) 100 (b) 96 (g) 92 (d) 90 (e) 80

71. ABCD paralelogramis B wverodan AD gverdze daSvebulia BE marTobi, romelic AB gverdTan 58°-ian kuTxes qmnis (ix. naxazi). ramdeni gradusia am

paralelogramis C kuTxis sidide?

(a) 32°

(b) 38° (g) 42° (d) 58°

(e) 62° 72. ricxvebi 17, b, 16, 10, a, 6 klebis mixedviTaa dalagebuli da cnobilia, rom a = b – 9. CamoTvlili ricxvebidan romeli SeiZleba iyos a-s toli?

(a) 5,8 (b) 6,4 (g) 6,9 (d) 7,5 (e) 8,2

27

73. Tinam TeTri, lurji da wiTeli feris Zafi iyida, TiToeuli _ 1,5 kg. TeTri Zafi Tinam mTlianad gamoiyena mokle Sarfebis mosaqsovad, TiTo Sarfs

dasWirda 0,1 kg; lurji Zafi _ saSualo sigrZis Sarfebis mosaqsovad, TiTo Sarfs dasWirda 0,15 kg; xolo wiTeli Zafi _ grZeli Sarfebis mosaqsovad, TiTo Sarfs dasWirda 0,3 kg. sul ramdeni Sarfi mouqsovia Tinas am ZafebiT?

(a) 10 (b) 18 (g) 25 (d) 28 (e) 30

74. MNKL marTkuTxedi, romlis farTobia 72 sm2,

dayofilia tol marTkuTxedebad (ix. naxazi). ramdeni

kvadratuli santimetria gamuqebuli mravalkuTxedis

farTobi, Tu misi wveroebi dayofis Sedegad miRebuli marTkuTxedebis wveroebs emTxveva?

(a) 48 (b) 50 (g) 52 (d) 56 (e) 60

75. Tu klienti bankSi Seitans x lars, t Tvis Semdeg mis angariSze bankSi iqneba p lari. p gamoiTvleba formuliT: p = x + 0,02xt. ramdeni lari iqneba klientis angariSze 5000 laris Setanidan 5 Tvis Semdeg?

(a) 5300 (b) 5500 (g) 5600 (d) 5800 (e) 6000

28

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

76.

mevenaxem ojaleSis, colikaurisa da

cicqas jiSis yurZeni dakrifa.

dakrefili cicqas wona 2 t iyo. wriul diagramaze miTiTebulia, dak-

refili yurZnis wonis ramdeni procen-

ti iyo ojaleSisa da colikauris wona.

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

77.

mimdevrobis yoveli wevri mis momdevno wevrze 3-iT naklebia.

am mimdevrobis mesame wevri y-is tolia.

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

78.

gaxmobis Sedegad miRebuli sokos wona nedli sokos

wonis 25%-ze naklebia.

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

ojaleSis wona 5 t

y 12

gamxmari sokos wona,

romelic miiReba 16 kg nedli sokosagan

3,8 kg

29

79.

wris radiusis sigrZea 10 sm. kvadratis yvela wvero am

wrewirze mdebareobs.

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

80.

ofisis gasaremonteblad daixarja organizaciis mier

bolo Tvis ganmavlobaSi miRebuli Semosavlis meoT-

xedze meti da mesamedze naklebi. organizaciis

Semosavali bolo TveSi 7200 lari iyo.

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

81.

nebismieri x ricxvisaTvis ( )∗x -iT aRniSnulia

udidesi mTeli ricxvi, romelic naklebia x ricxvze. a da b mTeli ricxvebia.

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

82.

rombis perimetria 24 sm.

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

2500 lari ofisis gasaremon-

teblad daxarjuli

Tanxa

( ) ( )** ba − ba −

am rombis farTobi 38 sm2

wris farTobs

gamoklebuli

kvadratis farTobi

110 sm2

30

amocanebi

83. romelia is ricxvi, romlis 47 nawili udris 35-s?

(a) 18 (b) 20 (g) 21 (d) 25 (e) 27

84. Teatris ganaTebisaTvis erTnairi naTurebi SeiZines. TiToeuli anTebuli naTura yovel saaTSi erTi da imave Rirebulebis eleqtroenergias xarjavs.

10 erTdroulad anTebuli naTura 5 saaTSi 30 TeTri Rirebulebis eleqtro-energias xarjavs. ramdeni TeTri Rirebulebis eleqtroenergias daxarjavs 40 erT-droulad anTebuli naTura 3 saaTSi?

(a) 48 (b) 70 (g) 72 (d) 90 (e) 120

85. ofisSi mxolod erTujriani, orujriani an samujriani magidebi dgas, sul _ 24 cali. am magidebSi 41 ujraa. erTujriani magidebi imdenia, ramdenic

orujriani da samujriani magidebi erTad. ramdeni orujriani magidaa am ofisSi? (a) 6 (b) 7 (g) 8 (d) 9 (e) 11

86. marTkuTxedi dayofilia or kvadratad. TiToeuli kvadratis perimetria 40 sm. ramdeni santimetria am marTkuTxedis perimetri?

(a) 60 (b) 64 (g) 70 (d) 76 (e) 80

31

monacemTa analizi

saTamaSoebis maRaziaSi mxolod manqanebi, Tojinebi, burTebi, konstruqtorebi da

naZvis xis saTamaSoebi iyideboda. svetovan diagramaze warmodgenilia am maRaziaSi

erTi Tvis ganmavlobaSi gayiduli sxvadasxva saxis saTamaSoTa raodenobebi:

mocemuli diagramis mixedviT upasuxeT Semdeg oTx SekiTxvas:

87. ra saxis saTamaSoebi gayidula yvelaze mcire raodenobiT?

(a) Tojinebi

(b) naZvis xis saTamaSoebi

(g) konstruqtorebi

(d) manqanebi

(e) burTebi

88. ramdenjer metia gayiduli Tojinebis raodenoba gayiduli naZvis xis saTamaSoebis raodenobaze?

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

89. gayiduli saTamaSoebis saerTo raodenobis ramdeni procentia gayiduli konstruqtorebis raodenoba?

(a) 10%

(b) 15%

(g) 18%

(d) 20%

(e) 25%

32

90. gayiduli saTamaSoebis saerTo raodenobis meoTxedze metia, magram mesamedze naklebi:

(a) gayiduli manqanebisa da konstruqtorebis raodenobaTa jami

(b) gayiduli manqanebisa da naZvis xis saTamaSoebis raodenobaTa jami

(g) gayiduli naZvis xis saTamaSoebisa da Tojinebis raodenobaTa jami

(d) gayiduli burTebisa da Tojinebis raodenobaTa jami

(e) gayiduli burTebis da konstruqtorebis raodenobaTa jami

amocanebi

91. maRaziaSi qurTukebi ramdenime dRis ganmavlobaSi iyideboda. pirvel dRes gaiyida 60 qurTuki. yovel momdevno dRes iyideboda 10 qurTukiT naklebi, vidre wina dRes. bolo dRes ukanaskneli 10 qurTuki gaiyida. sul ramdeni qurTuki gayidula maRaziaSi am dReebis ganmavlobaSi?

(a) 70 (b) 80 (g) 120 (d) 210 (e) 600

92. tolferda samkuTxedis fuZis sigrZea 12 dm, xolo fuZeze daSvebuli simaRle _ 8 dm. ramdeni decimetria am tolferda samkuTxedis ferdis sigrZe?

(a) 8 (b) 9 (g) 10 (d) 11 (e) 13

93. mimdevrobis pirveli wevric da meore wevric aris a + 3 , mesame wevri 4-iT metia meore wevrze da 7-iT naklebia meoTxe wevrze. qvemoT CamoTvlilTagan romeli gamosaxulebiT Caiwereba am mimdevrobis pirveli oTxi wevris jami?

(a) 4a + 9

(b) 4a + 12 (g) 4a + 15 (d) 4a + 21 (e) 4a + 27

33

94. mTargmnelTa biuroSi sul 10 TanamSromelia, maTgan 6 inglisur enaze Targmnis, danarCeni 4 _ germanul enaze. inglisur enaze mTargmnelTa saSualo xelfasi 400 laria, germanul enaze mTargmnelTa saSualo xelfasi ki _ 500 lari. ramdeni laria biuros TanamSromelTa saSualo xelfasi ?

(a) 440 (b) 445 (g) 455 (d) 460 (e) 465

95. marTkuTxa paralelepipedi, romlis fuZis wiboebis sigrZeebia 10 sm da 2 sm, dayves 5 tol kubad. ramdeni kuburi santimetri iyo am marTkuTxa paralelepipedis

moculoba? (a) 20 (b) 40 (g) 50 (d) 100 (e) 200

96. naturaluri m ricxvis 8-ze gayofisas miRebuli naSTia 7. risi toli iqneba 2m-is 8-ze gayofisas miRebuli naSTi?

(a) 1 (b) 3 (g) 4 (d) 6 (e) 7

97. kalaTSi 9 wiTeli, 8 yviTeli da 6 mwvane feris vaSlia. minimum ramdeni vaSli unda amoiRos liam kalaTidan (masSi Cauxedavad), rom amoRebul vaSlebs

Soris aucileblad iyos samive feris vaSli? (a) 14 (b) 15 (g) 16 (d) 17 (e) 18

34

98. Tu x, y da z iseTi mTeli dadebiTi ricxvebia, rom 8 < x < 11, 4 < y < 9, 1 < z < 4 , maSin ( )zyx −: gamosaxulebis umciresi mniSvnelobaa:

(a) 1 (b)

23

(g) 49

(d) 67

(e) 2

99. sofelSi TiToeul ojaxs hyavs ZaRli an kata. ZaRli hyavs ojaxebis 85%-s, xolo kata _ 40%-s. sofelSi mcxovreb 50 ojaxs hyavs ZaRlic da katac. sul ramdeni ojaxia am sofelSi?

(a) 150 (b) 180 (g) 200 (d) 250 (e) 300

100. maqsimaluri daSoreba ori figuris wertilebs Soris! vuwodoT udidesi monakveTis sigrZes im monakveTebidan, romlebic erTi figuris wertilebs meore

figuris wertilebTan aerTebs.

sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 1 sm. maqsima-luri daSoreba pirveli da meore wreebis wertilebs Soris 40 sm-ia, xolo meo-re da mesame wreebis wertilebs Soris _ 3 sm. qvemoT CamoTvlilTagan romlis toli SeiZleba iyos maqsimaluri daSoreba pirveli da mesame wreebis wertilebs

Soris?

(a) 36 sm (b) 37 sm (g) 38 sm (d) 43 sm (e) 44 sm

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. Semoklebuli gamravlebis formulebi: (a+b)2 = a2 + 2ab + b2

(a - b)2 = a2 – 2ab + b2

(a + b)(a – b) = a2 – b2 8. naxazze kuTxe SeiZleba kuTxis gverdebs Soris

Casmuli patara rkaliT

iyos moniSnuli, marTi

kuTxe ki _ patara

kvadratiT.

∠A aRniSnavs A kuTxis sidides. 9. paraleluri wrfeebi:

• ori paraleluri wrfis mesame wrfiT

gadakveTisas Siga jvaredina

kuTxeebi tolia: α = β.

10. 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: .

11. 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.

12. 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: L = πr2.

13. 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

51.

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

52.

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

53.

x < 0, y > 0

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

54.

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

55.

ABC marTkuTxa samkuTxedSi ∠C = 90° da ∠A > ∠B.

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

( )367− 67 −

(675 – 179) · 87 (673 – 188) · 87

1 xy

74 8,0

∠B 40°

23

56.

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

57.

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

58.

xuTkuTxa piramidas

sul 10 wibo aqvs.

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

amocanebi

59. ramdenjeraa meti udidesi samniSna ricxvi umcires orniSna ricxvze? (a) 10-jer

(b) 9,9-jer (g) 99,9-jer

(d) 10,1-jer

(e) 10,9-jer

60. ricxvTa RerZi masze moniSnuli wertilebiT dayofilia tol

monakveTebad (ix. naxazi). moniSnuli

wertilebidan B da C wertilebis koordinatebi miTiTebulia naxazze.

A wertilis koordinatia: (a) 800 (b) 810 (g) 820 (d) 830 (e) 840

15-isa da 25-is umciresi saerTo

jeradi

18-isa da 24-is umciresi saerTo

jeradi

( ) xx 63 2 +− 102 +x

eqvskuTxa piramidis

wiboebis raodenoba

kubis wiboebis

raodenoba

24

61. mas Semdeg, rac gaCerebaze avtobusidan 4 mgzavri Cavida, xolo 9 mgzavri amovida, avtobusSi 32 mgzavri aRmoCnda. ramdeni mgzavri yofila avtobusSi am gaCerebamde?

(a) 22 (b) 27 (g) 28 (d) 36 (e) 41

62. koncerti dagvianebiT daiwyo. is 85 wuTs gagrZelda da 22 saaTze

damTavrda. romel saaTze dawyebula koncerti? (a) 19 sT 35 wT (b) 20 sT 25 wT (g) 20 sT 35 wT (d) 21 sT 25 wT (e) 21 sT 35 wT

monacemTa analizi

cxrilSi miTiTebulia, Tu ramdeni lari iyo zogierTi sakvebi produqtis

saSualo fasi sxvadasxva wels (1995 wlidan 1998 wlis CaTvliT)

1995 1996 1997 1998 saqonlis xorci (1 kg) 3.72 3.30 3.80 4.10

Roris xorci (1 kg) 3.88 3.70 4.00 4.20

qaTami (1 kg) 4.62 4.50 4.00 3.62

kvercxi (10 cali) 1.30 1.40 1.50 1.60

karaqi (1 kg) 5.20 5.00 5.00 6.20

yveli (1 kg) 4.90 3.80 3.80 3.80

Saqris fxvnili (1 kg) 0.80 0.91 0.84 0.97

xorblis fqvili (1 kg) 0.85 1.00 0.94 1.00

Rvino (0.7 litri) 1.13 1.37 1.37 1.37

mocemuli cxrilis mixedviT upasuxeT Semdeg oTx SekiTxvas:

63. ramdeni lari iyo 1 kg yvelis saSualo fasi 1995 wels? (a) 3.60 (b) 3.80 (g) 4.50 (d) 4.62 (e) 4.90

25

64. qvemoT CamoTvlilTagan romeli produqtis saSualo fasi Semcirda 1997 wels wina welTan SedarebiT?

(a) saqonlis xorcis

(b) Roris xorcis

(g) yvelis

(d) xorblis fqvilis

(e) Rvinis

65. romeli produqtis saSualo fasi imatebda yovelwliurad 1995-1998 wlebSi?

(a) Roris xorcis

(b) qaTmis

(g) Saqris fxvnilis

(d) xorblis fqvilis

(e) kvercxis

66. ra farglebSi meryeobda (icvleboda) Roris xorcis saSualo fasi 1995-1998 wlebSi?

(a) 3.70-sa da 4.00 lars Soris (b) 3.88-sa da 4.00 lars Soris (g) 3.70-sa da 4.20 lars Soris (d) 4.00-sa da 4.20 lars Soris (e) 3.88-sa da 4.20 lars Soris

amocanebi

67. Tu x – 2y = 1 da – x + 6y = 7 , maSin 5y = (a) 5 (b) 10 (g) 15 (d) 20 (e) 25

68. sibrtyeze mocemulia marTkuTxa koor-dinatTa sistema. ABC tolferda samkuTxedis AC fuZe x-RerZis paraleluria. samkuTxedis A da B wveroebis koordinatebi miTiTebulia naxazze. C wveros koordinatebi (a; b) =

(a) (5; 7) (b) (7; 8) (g) (2; 7) (d) (8; 2) (e) (9; 2)

26

69. kolofSi mxolod Savi da wiTeli feris fanqrebia. Savi fanqrebis raode-noba fanqrebis saerTo raodenobis

87 nawilia, xolo wiTelia 4 cali fanqari.

sul ramdeni cali fanqaria am kolofSi? (a) 24 (b) 28 (g) 30 (d) 32 (e) 36

70. mariamis xelfasi 10%-iT momatebis Semdeg 132 lari gaxda. ramdeni lari iyo mariamis xelfasi momatebamde?

(a) 108 (b) 110 (g) 120 (d) 122 (e) 130

71. erT sibrtyeze mdebare a, b, c da d wrfeebidan a wrfe paraleluria b wrfis, xolo c wrfe _ d-si. a da c wrfeebiT Seqmnili blagvi kuTxis sididea 115° (ix. naxazi). risi tolia b da d wrfeebiT Seqmnili maxvili kuTxis sidide?

(a) 35° (b) 45° (g) 55° (d) 65° (e) 75°

72. ricxvebi m, 7, 9, 13, n, 17 zrdis mixedviTaa dalagebuli da cnobilia, rom m = n – 11. CamoTvlili ricxvebidan romeli ar SeiZleba iyos m-is toli?

(a) 3,2 (b) 4,6 (g) 5 (d) 5,8 (e) 6,3

27

73. dedam zamTrisTvis sami saxis xilis wveni moimaraga: vaSlis, qliavis da

alublis, TiToeuli _ 4 litri. vaSlis wveni mTlianad Seinaxa 0,5 l tevadobis qilebSi, qliavis _ 0,8 l tevadobis qilebSi, xolo alublis _ 1 l tevadobis qilebSi (dedam yvela qila bolomde Seavso). sul ramdeni qila gamouyenebia

dedas xilis wvenis Sesanaxad? (a) 12 (b) 14 (g) 15 (d) 16 (e) 17

74. ABCD marTkuTxedi dayofilia tol marTkuT-xedebad. M da N wertilebi dayofis Sedegad miRe-buli marTkuTxedebis wveroebs emTxveva (ix. naxazi).

MNCD oTxkuTxedis farTobia 18 dm2. ramdeni

kvadratuli decimetria ABCD marTkuTxedis farTobi?

(a) 20 (b) 24 (g) 26 (d) 28 (e) 30

75. Tu klienti bankSi Seitans x lars, k wlis Semdeg mis angariSze bankSi iqneba p lari. p gamoiTvleba formuliT: p = x(1 + 0,2k). Tanxis Setanidan 5 wlis Semdeg klientis angariSze iyo 7000 lari. ramdeni lari Seutania klients bankSi?

(a) 1400 (b) 2200 (g) 3000 (d) 3500 (e) 3800

28

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

76.

glexma vaSli, msxali da qliavi ga-

yida. gayiduli vaSlis wona 80 kg-ia. wriul diagramaze miTiTebulia,

gayiduli xilis wonis ra nawilia

msxlisa da vaSlis wona.

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

77.

mimdevrobis yoveli wevri mis momdevno wevrze 2-iT naklebia. am mimdevrobis meaTe wevria 17, xolo meeqvse wevria b.

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

78.

soia Seicavs cxims, romlis wona soias wonis 20%-ia.

rZe Seicavs cxims, romlis wona rZis wonis 4%-ia.

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

gayiduli qliavis

wona 35 kg

b 10

cximis wona, romel-

sac Seicavs 12 kg soia

cximis wona,

romelsac Seicavs

60 kg rZe

29

79.

kvadratis gverdis sigrZea 8 sm, wris diametris sigrZec 8 sm-ia.

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

80.

biznesmeni, romlis wliuri Semosavali 75 aTas larze metia da 85 aTas larze naklebi, yovelwli-urad Semosavlis mexuTeds qvelmoqmedebaze xarjavs.

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

81.

nebismieri a ricxvisaTvis ( )∗a -iT aRniSnulia

udidesi mTeli ricxvi, romelic naklebia a ricxvze.

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

82. rombis farTobia 36 sm2

.

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

biznesmenis mier qvelmo-

qmedebaze yovelwliurad

daxarjuli Tanxa

16 aTasi lari

( ) ( )** 3,8−a ( )*3,8−a

am rombis perimetri 22 sm

kvadratis farTobs gamok-

lebuli wris farTobi 16 sm2

30

amocanebi

83. 36-is meramdenedi nawilia 27?

(a) 31

(b) 32

(g) 42

(d) 43

(e) 276

84. auzSi wyali ori miliT Caedineba. erTi milis gaxsnisas yovel saaTSi auzSi erTi da imave raodenobis wyali Caedineba. meore milis gaxsnis SemTxvevaSic

auzSi yovel saaTSi erTi da imave raodenobis wyali Caedineba. marto pirveli

miliT carieli auzi 4 saaTSi ivseba, marto meoreTi _ 6 saaTSi. ramden saaTSi aivseba carieli auzi, Tu orive mils erTdroulad gaxsnian?

(a) 2 (b) 2,4 (g) 5 (d) 6,5 (e) 10

85. sastumroSi mxolod 1-adgiliani, 2-adgiliani da 4-adgiliani nomrebia, sul _ 44 nomeri. 2-adgiliani nomrebi imdenia, ramdenic 1-adgiliani da 4-adgiliani nomrebi erTad. sastumroSi sul 84 adgilia. ramdeni 1-adgiliani nomeria sastumroSi?

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

86. marTkuTxedi dayofilia 3 tol kvadratad. risi tolia am marTkuTxedis perimetris Sefardeba dayofis Sedegad miRebuli kvadratis perimetrTan?

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

31

monacemTa analizi

saTamaSoebis maRaziaSi mxolod manqanebi, Tojinebi, burTebi, konstruqtorebi da

naZvis xis saTamaSoebi iyideboda. svetovan diagramaze warmodgenilia am maRaziaSi

erTi Tvis ganmavlobaSi gayiduli sxvadasxva saxis saTamaSoTa raodenobebi:

mocemuli diagramis mixedviT upasuxeT Semdeg oTx SekiTxvas:

87. ra saxis saTamaSoebi gayidula yvelaze didi raodenobiT? (a) manqanebi

(b) konstruqtorebi

(g) burTebi

(d) naZvis xis saTamaSoebi

(e) Tojinebi

88. ramdenjer naklebia gayiduli konstruqtorebis raodenoba gayiduli manqanebis raodenobaze?

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

89. gayiduli saTamaSoebis saerTo raodenobis ramdeni procentia gayiduli naZvis xis saTamaSoebis raodenoba?

(a) 12%

(b) 15%

(g) 18%

(d) 20%

(e) 25%

32

90. gayidul saTamaSoTa saerTo raodenobis meoTxedze metia, magram mesamedze naklebi:

(a) manqanebisa da konstruqtorebis raodenobaTa jami

(b) Tojinebisa da naZvis xis saTamaSoebis raodenobaTa jami

(g) burTebisa da konstruqtorebis raodenobaTa jami

(d) burTebisa da Tojinebis raodenobaTa jami

(e) naZvis xis saTamaSoebisa da burTebis raodenobaTa jami

amocanebi

91. mewarmis Semosavali ianvarSi 1000 lari iyo. TebervalSi misi Tviuri Semosavali 100 lariT gaizarda, martSi _ kidev 100 lariT. aprilidan moyolebuli sami Tvis ganmavlobaSi mewarmis Semosavali yovelTviurad 200 lariT mcirdeboda. sul ramdeni lari iyo mewarmis Semosavali am 6 Tvis ganmavlobaSi?

(a) 5700 (b) 5900 (g) 6000 (d) 6100 (e) 6300

92. ABCD paralelogramis AB gverdi BD diagonalis tolia. B wverodan AD gverdze daSvebuli marTobis sigrZea 5 sm. ramdeni santimetria AB gverdis sigrZe, Tu AD gverdis sigrZe 24 sm-ia?

(a) 13 (b) 14 (g) 15 (d) 16 (e) 18

93. ninom, vaJam da sandrom wignebi SeiZines. ninom 3-iT meti wigni SeiZina, vidre vaJam, xolo sandrom orjer meti, vidre vaJam. ninos mier SeZenili

wignebis raodenobaa n. qvemoT CamoTvlilTagan romeli gamosaxulebiT Caiwereba ninos, vaJas da sandros mier SeZenili wignebis saerTo raodenoba?

(a) 2n + 12 (b) 3n – 9 (g) 4n – 9 (d) 4n – 6 (e) 4n – 3

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94. sareklamo saagentoSi 7 vaJi da 3 gogona muSaobs. Tu saagentos TanamSromelTa saSualo asaki 27 welia, xolo TanamSromel gogonaTa saSualo asaki _ 20 weli, maSin am saagentos TanamSromel vaJTa saSualo asakia:

(a) 23 weli (b) 24 weli (g) 30 weli (d) 32 weli (e) 34 weli

95. kubi dayves 3 tol marTkuTxa paralelepipedad, romelTagan TiToeulis fuZis wiboebis sigrZeebia 2 sm da 6 sm. ramdeni kuburi santimetria am dayofis Sedegad miRebuli TiToeuli

marTkuTxa paralelepipedis moculoba? (a) 8 (b) 12 (g) 24 (d) 36 (e) 72

96. naturaluri n ricxvis 9-ze gayofisas miRebuli naSTia 7. risi toli iqneba (n + 14)-is 9-ze gayofisas miRebuli naSTi?

(a) 2 (b) 3 (g) 5 (d) 6 (e) 7

97. kolofSi mxolod 8 Savi da 6 wiTeli fanqari awyvia. ilia kolofidan (masSi Cauxedavad) iRebs TiTo fanqars da magidaze debs. minimum ramdeni fanqari

unda amoiRos iliam, rom amoRebul fanqrebs Soris aucileblad iyos orive

feris fanqari? (a) 3 (b) 5 (g) 7 (d) 9 (e) 11

34

98. Tu a, b da c iseTi naturaluri ricxvebia, rom a < 5, b < 3 , c > 20 , maSin

bac − gamosaxulebis umciresi mniSvnelobaa: (a) 3 (b) 4 (g) 5 (d) 6 (e) 7

99. turistTa jgufis yvela wevrma icis germanuli an inglisuri ena. im turistTa raodenoba, romlebmac ician germanuli ena, turistTa saerTo

raodenobis 83 nawilia, xolo im turistTa raodenoba, romlebmac ician

inglisuri ena _ 87 nawili. jgufidan 24-ma turistma icis germanuli enac da

inglisuri enac. sul ramdeni turistia am jgufSi? (a) 64 (b) 72 (g) 80 (d) 88 (e) 96

100. maqsimaluri daSoreba ori figuris wertilebs Soris! vuwodoT udidesi monakveTis sigrZes im monakveTebidan, romlebic erTi figuris wertilebs meore

figuris wertilebTan aerTebs.

sibrtyeze mocemulia sami toli wre, romelTa diametris sigrZea 1 dm. maqsi-maluri daSoreba pirveli da meore wreebis wertilebs Soris 50 dm-ia, xolo meore da mesame wreebis wertilebs Soris _ 4 dm. qvemoT CamoTvlilTagan romlis toli ar SeiZleba iyos maqsimaluri daSoreba pirveli da mesame wreebis

wertilebs Soris? (a) 47 dm (b) 49 dm (g) 50 dm (d) 53 dm (e) 54 dm

kiTxvebi

N varianti 1 varianti 1

(rusuli varianti)

varianti 2 varianti 3 varianti 4

1 d d b d d

2 d g g b a

3 g g d g g

4 b b b a d

5 b b g g g

6 g g g b a

7 a a g a b

8 d d a g d

9 d d d d d

10 b b d g a

11 g g b d d

12 a a d d d

13 g b g g a

14 g g b b d

15 g g g b d

16 b b b g a

17 b b a a g

18 g g a g d

19 b b b g g

20 b b a g a

21 d d g b b

22 g g d a d

23 g g g b d

24 d d d d g

25 a a g a g

26 g g d b g

27 b b a b b

28 d d b d g

29 b b d g d

30 a a d b b

31 g g g a a

32 b b d g b

33 d d g b b

34 d d d b b

35 g g g b b

36 g g g d d

37 a a b a a

38 b b a a g

39 g g b b d

40 a a b b d

41 d d b a a

42 d d a g d

43 a a g g a

44 d d g g g

45 d d d d b

46 b b g b d

47 a a b b a

48 g g b d d

49 a a d g a

50 g g b b d

ver

bal

ur

i n

awil

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kiTxvebi

N varianti 1 varianti 1

(rusuli

varianti)

varianti 2 varianti 3 varianti 4

51 a a b g b

52 b b b a a

53 a a b b d

54 b b a b b

55 g g a d b

56 b b b a g

57 d d g b d

58 b b d g a

59 a a g g d

60 d d d b g

61 g g a b d

62 b d g g d

63 d d g e a

64 d d b d d

65 b b a e g

66 a a d g g

67 b b e b a

68 a a e e b

69 g g b d e

70 d d d g d

71 g g d d a

72 a a g e d

73 g g d e e

74 d d g b a

75 e e b d b

76 d d a a g

77 g g a b d

78 a a b g d

79 b b d b a

80 a a a d a

81 d d a d g

82 d d d a b

83 g g e d b

84 a a d b g

85 g g d e b

86 b b g g a

87 e e e e d

88 b b d g a

89 g g b b a

90 g g d e e

91 e e b a d

92 d b a g

93 a a e g e

94 d d d g a

95 d d a e b

96 e e g b d

97 b b b d e

98 e e b g b

99 d d d e g

100 a a e e g

maT

emat

ikur

i

naw

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