zogadi unarebis testizogadiunarebis testi · 2018. 6. 10. · kometebi didi zomis ciuri sxeulebia,...

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

III

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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. kaqtusi : qoTani

(a) Citi : bude

(b) Zroxa : boseli

(g) mela : soro

(d) Tevzi : akvariumi

2. cixesimagre : galavani

(a) mdinare : xidi

(b) suraTi : CarCo

(g) veli : arxi

(d) wigni : furceli

3. sityvamoswrebuli : enamaxvili

(a) Zunwi : xelmokle

(b) erTguli : orpiri

(g) natifi : daxvewili

(d) Tamami : Tavxedi

4. saaTi : isari

(a) kari : saxeluri

(b) dafa : carci

(g) savarZeli : skami

(d) Taro : wigni

3

5. metyveleba : sityva

(a) cekva : ritmi

(b) zRapari : legenda

(g) Tvla : ricxvi

(d) anbani : ieroglifi

6. klde : gamoqvabuli

(a) wyali : Wa

(b) xe : fuRuro

(g) fskeri : ormo

(d) mdinare : kalapoti

7. ganaTeba : naTura

(a) gamocxoba : qura

(b) gaxureba : uTo

(g) gasrola : samizne

(d) gadnoba : yinuli

8. mZivi : samkauli

(a) cxeni : gaxednili

(b) bati : gareuli

(g) vefxvi : mtacebeli

(d) xoWo : mfrinavi

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. es zamTari, sinoptikosebis informaciiT, _____ unda yofiliyo, Tumca sinamdvileSi is _____ aRmoCnda.

(a) naleqiani \ sakmaod wvimiani

(b) Tbili da mziani \ sakmaod Tbili

(g) civi da susxiani \ sakmaod civi

(d) civi da susxiani \ sakmaod mziani

10. ar SeiZleba iTqvas, rom qarTvelebs _____ gamogveCinos politikur asparezze, _____ , SeiZleba iTqvas, erT dros didi da Zlieri saxelmwifo _____ , da ara

Tu sakuTar qveyanas, _____ ganvagebdiT.

(a) ugunureba / Sesabamisad / dagvisustebia / sakuTar teritoriebsac ki

ugulisyurod

(b) niWiereba / Sesabamisad / aRgvidgenia / dapyrobil teritoriebsac ki

gonivrulad

(g) sruli uniWoba / piriqiT / gvqonia / dapyrobil teritoriebsac ki brZnulad

(d) didi sibrZne / piriqiT / agviyvavebia / sakuTar teritoriebsac ki

gonivrulad

11. TamaSi, rogorc aRzrdis saSualeba, pedagogikis erT-erTi _____ sakiTxia, miuxedavad amisa, dRes mecnierebi da pedagogebi mas _____ .

(a) umniSvnelo / saTanado yuradRebas ar uTmoben

(b) mniSvnelovani / yuradRebiT ikvleven

(g) araaqtualuri / saTanadod ar ikvleven

(d) aqtualuri / saTanado yuradRebas ar uTmoben

5

12. arseboben adamianebi, romlebic _____ . Sesabamisad, isini _____ arian im sferoebSi, sadac SemoqmedebiTi fantaziaa saWiro. _____ , im sferoSi, sadac

gadamwyveti mniSvneloba realistur alRosa da dakvirvebas aqvs, _____ raime

mniSvnelovans.

(a) ar gamoirCevian fantaziis sicxoveliT da siZlieriT / warumatebelni / amis

sapirispirod / ver qmnian

(b) gamoirCevian fantaziis erTferovnebiTa da simwiriT / warmatebulni / swored

amitom / qmnian

(g) ar gamoirCevian fantaziis sicxoveliT da siZlieriT / warmatebulni / Tumca /

qmnian

(d) gamoirCevian fantaziis sicxoveliT da siZlieriT / Seudarebelni / Tumca /

ver qmnian

13. esa Tu is eri, rogori _____ unda iyos is ekonomikurad, _____ , rodesac _____ .

(a) ganviTarebulic / Waobidan iwyebs amosvlas / maradiul Rirebulebebs iviwyebs

(b) warmatebulic / mainc aRwevs mizans / maradiul Rirebulebebs ar aRiarebs

(g) Zlieric / ufskrulisken iwyebs svlas / maradiul Rirebulebebs iviwyebs

(d) uZluric / mainc sastikad marcxdeba / maradiul Rirebulebebs aRiarebs

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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. gazafxulobiT qalaqis erT-erT sayvavileSi lamazi Taigulebi iyideba. • Taigulebs konaven mxolod iebisgan, enZelebisgan da yoCivardebisgan –

cal-calke an maTi SereviT

• Tu TaigulSi aris enZelebi, aris yoCivardebic

qvemoT CamoTvlilTagan romeli Semadgenlobis Taiguls ver viyidiT am

sayvavileSi?

(a) Taiguls, romelSic samive saxis yvavilia

(b) Taiguls, romelSic mxolod iebi da enZelebia

(g) Taiguls, romelic mxolod iebisgan aris Sekonili

(d) Taiguls, romelSic mxolod enZelebi da yoCivardebia

15. sawarmos xelmZRvanelobam gadawyvita, sakuTari produqciis Sesaxeb informaciis ukeT gavrcelebis mizniT, saqarTvelos regionebSi am produqciis satelevizio reklama sagazeTo reklamiT Seecvala.

qvemoT CamoTvlilTagan romeli faqti metyvelebs am gadawyvetilebis

marTebulobaze?

(a) regionebSi Zalze xSirad uyureben televizors, magram gazeTebs iSviaTad

kiTxuloben

(b) regionebs eleqtroenergia Zalze SezRudulad miewodeba, xolo gazeTebs

regularulad iReben

(g) wlis sxvadasxva periodSi sareklamo momsaxurebis fasi icvleba

(d) regionis mosaxleobis naxevari informacias iRebs gazeTiT, naxevari ki – televiziiT

16. davuSvaT, rom: • TuTiyuSebi mxolod tropikul tyeSi cxovroben

qvemoT CamoTvlilTagan romeli ewinaaRmdegeba am debulebas?

(a) Jako tropikul tyeSi cxovrobs da is TuTiyuSia

(b) Jako tropikul tyeSi cxovrobs da is ar aris TuTiyuSi

(g) Jako ar cxovrobs tropikul tyeSi da is TuTiyuSia

(d) Jako ar cxovrobs tropikul tyeSi da is ar aris TuTiyuSi

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17. sportuli klubis wevrTa Soris arian mxiaruli, Savgvremani da warmosadegi adamianebi. yovelwliurad klubis wevrebi irCeven klubis prezidents amgvari

pirobebis dacviT:

• prezidenti unda iyos mxiaruli • prezidenti unda iyos an Savgvremani, an warmosadegi, magram ara

orive erTad

qvemoT CamoTvlilTagan romeli debulebidan gamomdinareobs aucileblad, rom

prezidentis arCeva klubis wevrTaganaa SesaZlebeli?

(a) klubis yvela mxiaruli wevri Savgvremania, magram arc erTi maTgani araa

warmosadegi

(b) klubis yvela mxiaruli wevri Savgvremanicaa da warmosadegic

(g) klubis yvela warmosadegi wevri Savgvremania, magram arc erTi ar aris

mxiaruli

(d) klubis arc erTi Savgvremani wevri ar aris arc warmosadegi da arc

mxiaruli

18. ninom, katom, mziam da elenem zafxulis ardadegebze zRvis piras saxli iqiraves. yoveli maTgani sxvadasxva oTaxSi cxovrobs. elenes oTaxs saerTo kari

aqvs katos oTaxTan, aseve saerTo kari aqvs mzias oTaxTan. mzias oTaxs ki ninos

oTaxTan aqvs saerTo kari. oTaxebs Soris sxva damakavSirebeli gza ar arsebobs. vis oTaxSi unda gaiaros katom, rom ninos oTaxSi aRmoCndes?

(a) mxolod elenes oTaxSi

(b) jer mzias, Semdeg ki elenes oTaxSi

(g) jer elenes, Semdeg ki mzias oTaxSi

(d) mxolod mzias oTaxSi

8

wakiTxuli teqstis gaazreba

yuradRebiT waikiTxeT da gaiazreT teqsti. TiToeuli SekiTxvis savaraudo

pasuxebidan airCieT is varianti, romelic marTebulia mocemuli teqstis mixedviT.

kometebi didi zomis ciuri sxeulebia, romlebic iSviaTad gamoCndebian da

moulodneli SemoWriT arRveven cis Cveulebriv, sayovelTaod cnobil suraTs.

isini adamianma uxsovari droidan SeniSna. kometebi periodulad gamoCndebian,

uaxlovdebian mzes da, Sesabamisad, dedamiwasac, da isev uCinardebian Soreul

sivrceSi.

1577 w. tixo brahem (dania) Teoriulad daaskvna, rom kometebi mTvareze ufro Sors arian. haleim (inglisi) ki daamtkica, rom kometebi gawelil elifsur

orbitebze* moZraoben mzis garSemo. amitom erTi da igive kometa ramdenjerme

SeiZleba mogviaxlovdes. kerZod, man daadgina, rom 1531, 1607 da 1682 wlebSi gamoCenili kometebi erTi da igive obieqtia, romlis mzis irgvliv garemoqcevis

periodi daaxloebiT 76 welia. haleim amave kometis xelaxali gamoCenis weli iwinaswarmetyvela, rac dadasturda kidec. amis gamo am kometas haleis saxeli

uwodes. ukanasknelad haleis kometam mzis siaxloves 1986 wels gaiara. mzis siaxloves gavlisas mzis sinaTlis wnevis ZaliT kometebidan

amoityorcneba mtvris nawilakebi da Cndeba e.w. kudi, romelic mzis

sawinaaRmdego mxaresaa mimarTuli. Sesabamisad, kometebs kudian varskvlavebs

uwodeben. zogierTi kometis kudi aseulobiT kilometris sigrZisaa. arsebobs

orkudiani da samkudiani kometebic, aseve, anomaliurkudiani kometebi, romelTa

mokle kudi mziskenaa mimarTuli. es imaze metyvelebs, rom kudebis warmoqmnis

meqanizmi sxvadasxvagvari SeiZleba iyos.

kometebis birTvi Sedgeba gayinuli CH4, NH3, H2O da CO2-sagan. kometebi varskvlavTSorisi sivrcidan SemoiWrebian da periheliumSi** gavlis Semdeg kvlav

uCinardebian. zogjer didi planetebis zemoqmedebiT ama Tu im kometis orbita

sagrZnoblad icvleba. rogorc Cans, ase Seiqmna kometaTa e. w. iupiteris jgufi,

saturnis jgufi da sxva.

zogi kometa mzis zemoqmedebiT TandaTan kargavs masas da iSleba. magaliTad,

bielas kometa or kometad daiSala, Semdeg erT-erTi maTgani daikarga,

samagierod gamoCnda meteoruli nakadi imave orbitaze. axlaxan wamoayenes

hipoTeza, rom 1908 w. tunguskaSi Camovardnili meteoriti erT-erTi kometis _ enkes namsxvrevi iyo.

zogierTi kometa mzes Sordeba plutonis orbitaze aTasjer meti manZiliT.

am kometebis garemoqcevis periodebi milion wels aRwevs. magaliTad, vestis

kometis garemoqcevis periodi daaxloebiT erTi milioni welia, delavanis

kometisa ki _ daaxloebiT ocdaoTxi milioni weli. es sxeulebi mzis sistemis

sazRvrebamde aRweven, zogi ki tovebs kidec mas da varskvlavTSorisSi gadis.

* orbita _ ciuri sxeulis samoZrao gza

** periheliumi _ ciuri sxeulis orbitis wertili, romelic yvelaze ufro

axlosaa mzesTan

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19. qvemoT CamoTvlilTagan romeli gadmoscems pirveli abzacis ZiriTad azrs?

(a) kometebi moulodnelad SemoiWrebian caze da uaxlovdebian dedamiwas

(b) adamianma uxsovari droidan SeniSna, rom kometebi caze periodulad Cndeba

(g) kometebi ciuri obieqtebia, romlebic periodulad gamoCndebian, uaxlovdebian

mzes da uCinardebian

(d) adamianma uxsovari droidan SeniSna, Tu rogor icvleba cis suraTi

kometebis gamoCeniT

20. ingliseli mecnieris, haleis mosazrebis Tanaxmad:

(a) kometebi mzisgan dedamiwaze ufro Sors arian

(b) zogierTi kometa wrfiv orbitaze moZraobs

(g) kometa SeiZleba orjer an metjer miuaxlovdes mzes

(d) erT-erTi kometa dedamiwis irgvliv moZraobs

21. romel welsaa mosalodneli haleis kometis gamoCena mzis siaxloves?

(a) 2010 wels (b) 2062 wels (g) 2167 wels (d) 2276 wels

22. kometebs kudian varskvlavebsac uwodeben, radgan:

(a) mzis zemoqmedebiT kometebidan erTi mimarTulebiT amoityorcneba mtvris

nawilakebi

(b) mzis sinaTlis wnevis ZaliT kometebis orbita sagrZnoblad icvleba

(g) zogierT kometas ori an sami kudi aqvs, zogs _ arc erTi

(d) zogierTi kometis kudi mziskenaa mimarTuli, zogis ki _ mzis sawinaaRmdego

mxares

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23. rogor Seiqmna kometaTa e.w. iupiterisa da saturnis jgufebi?

(a) kometebis periheliumSi gavliT

(b) didi planetebis zemoqmedebiT

(g) mzis sinaTlis wnevis ZaliT

(d) meteoruli nakadis zemoqmedebiT

24. qvemoT CamoTvlilTagan romeli movlena araa ganxiluli teqstSi, rogorc mzis zemoqmedebis Sedegi?

(a) enkes namsxvrevis Camovardna

(b) kometebis masis Semcireba

(g) bielas kometis daSla

(d) kometebis birTvis warmoqmna

25. ra aris teqstis ZiriTadi mizani?

(a) kometebis arsebiTi niSnebis mimoxilva

(b) kometebis garemoqcevis periodis gansazRvra

(g) kometebis qimiuri Semadgenlobis dadgena

(d) kometebis Sesaxeb ZiriTadi Teoriebis ganxilva

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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. urduli : WiSkari

(a) karmidamo : miwa

(b) balTa : qamari

(g) xmali : fari

(d) perangi : sayelo

27. cecxli : naperwkali

(a) grigali : niavi

(b) wyali : Sxefi

(g) miwa : qviSa

(d) xe : kvirti

28. galia : sakani

(a) ezo : Robe

(b) soro : bude

(g) koSki : sarkmeli

(d) bunagi : saxli

29. ankesi : bade

(a) yvavili : Taiguli

(b) zurgCanTa : karavi

(g) motocikli : avtobusi

(d) isari : mSvildi

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30. rTveli : mevenaxe

(a) doRi : mayurebeli

(b) koncerti : momRerali

(g) qorwili : mzareuli

(d) konkursi : Jiuri

31. talRa : zvirTi

(a) Zewkvi : jaWvi

(b) Rori : taxi

(g) marTve : arwivi

(d) wigni : wignaki

32. sasaxle : Senoba

(a) bgera : musika

(b) speqtakli : piesa

(g) samaia : cekva

(d) saTamaSo : TamaSi

33. gemos SegrZneba : tkbili

(a) ynosva : gamZafrebuli

(b) mxedveloba : vardisferi

(g) smena : daxSuli

(d) Sexeba : faqizi

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 orientirebulni arian _____ .

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

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

(g) arasodes / swored amitom / 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

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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. giorgi, levani da sandro erTi saxlis pirvel, meore da mesame sarTulebze cxovroben (ara aucileblad am TanmimdevrobiT). maTgan erT-erTma icis mxolod

fexburTis TamaSi, meorem _ mxolod Wadrakis, mesamem ki _ mxolod kalaTburTis.

• is, vinc pirvel sarTulze cxovrobs, TamaSobs kalaTburTs • is, vinc giorgis binis zemoT cxovrobs, TamaSobs fexburTs • is, vinc levanis binis qvemoT cxovrobs, TamaSobs Wadraks

qvemoT CamoTvlilTagan romeli debuleba ar SeiZleba iyos WeSmariti am

mocemulobis pirobebSi?

(a) levani TamaSobs kalaTburTs

(b) giorgi TamaSobs Wadraks

(g) sandro TamaSobs kalaTburTs

(d) levani TamaSobs fexburTs

15

39. viciT, rom arsebobs mdinareebi, romlebic tbaSi Caedineba. mocemulia:

• yvela mdinare, romelic tbaSi Caedineba, civia • wyalmcenare mxolod im mdinareSia, romelic tbaSi Caedineba

qvemoT CamoTvlilTagan romeli gamomdinareobs am debulebebidan aucileblad?

(a) yvela civi mdinare tbaSi Caedineba

(b) mdinare, romelSic aris wyalmcenare, civia

(g) mdinare, romelSic ar aris wyalmcenare, ar aris civi

(d) yvela civ mdinareSi aris wyalmcenare

40. davuSvaT, rom arseboben wiTeli lomebi da amasTanave mocemulia:

• yvela wiTel loms aqvs Savi fafari

Tu es debuleba WeSmaritia, maSin qvemoT CamoTvlilTagan romeli SeiZleba iyos

mcdari?

(a) ar arsebobs wiTeli lomi, romelsac ar aqvs Savi fafari

(b) yvela Savfafriani arseba aris wiTeli lomi

(g) arc erTi arseba, romelsac Savi fafari ara aqvs, ar aris wiTeli lomi

(d) arseboben Savfafriani wiTeli lomebi

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 CamoTvlilTagan 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.

tim severins _ inglisel mkvlevar-mogzaurs _ miznad dausaxavs Zvelad

ganxorcielebul mogzaurobaTa rekonstruqcia werilobiT wyaroebSi Semonaxuli

cnobebis safuZvelze, imave wesiTa da xerxebiT, romlebic aRweril epoqas

Seesatyviseboda.

1984 wels man eqsperimenti ganaxorciela: gaimeora argonavtebis laSqroba. mecnierTa erTi nawili amtkicebda, rom Zalian Zlieri da swrafi dinebis gamo

SeuZlebeli iqneboda dardanelisa da bosforis sruteebis gacurva da Sav

zRvaSi Sesvla Zv. w. VII saukunemde, e. i. manam, sanam berZnebi gamoigonebdnen e.

w. pentakonters, anu ormocdaaTniCbian xomalds. radgan mikenur epoqaSi (Zv. w. II

aTaswleulis II naxevarSi) berZnuli xomaldebi gacilebiT patara zomis iyo, tim

severinma gadawyvita eqsperimentis Catareba _ ocniCbiani naviT Sav zRvaSi

Semosvla da rionze (Zvel fazisze) aRmasvla.

Seiqmna axali "argo", ocniCbiani galeri _ berZnuli sabrZolo xomaldis zusti asli. xomaldis mSenebloba naxevar welze met xans grZeldeboda. maisis

pirvel ricxvebSi saberZneTis qalaq volosidan (Zveli iolkosidan) axalma "argom" gezi Savi zRvis sanapiroebisken aiRo. tim severinma megzurad apolonios

rodoselis poema "argonavtika" airCia. "argo" zustad imeorebda Zveli argonavtebis ara mxolod marSruts, aramed

curvis wessac. xomaldi micuravda napir-napir, iseve, rogorc es Zvel mwerlebs

aqvT aRwerili. mxolod 16 ivniss SeZlo "argom" Sav zRvaSi Semosvla. tim severinis ekipaJs mravali faTeraki gadaxda Tavs. miuxedavad didi gansacdelisa,

mas arc kompasi gamouyenebia, arc raciisTvis miumarTavs. tim severinma Zveli

mogzaurebis msgavsad, talRebis moyvanilobisa da qaris mimarTulebis mixedviT

zustad gansazRvra xmeleTis adgilmdebareoba da xomaldi sanapiros miayena.

eqsperimenti warmatebiT dasrulda. axalma "argom" zustad gaimeora apolonios rodoselis mier aRwerili gza argonavtebisa, daZlia yvela siZnele,

bosforis srutiT Semovida Sav zRvaSi, moadga Zveli kolxeTis sanapiroze qalaq

foTs da ganaxorciela TiTqmis rvasaaTiani aRmasvla mdinare rionze. tim

severinis eqspediciam saboloo banaki Tanamedrove WyviSTan, vanis naqalaqarTan

axlos daido. eqspediciis mecnieruli Sedegebi aqve Seajames. tim severinma

eqsperimentulad daamtkica, rom berZenTa pirveli mogzauroba Zvel kolxeTSi

namdvilad SesaZlebeli iyo jer kidev Zv. w. XIII saukuneSi, e. i. gvianbrinjaos

epoqaSi.

antikuri xanis kolxuri civilizacia md. rionis gayolebaze jerjerobiT

yvelaze ufro TvalsaCinod vanSia gamovlenili, Tumca gvianbrinjaos xanis

mikenuri arqeologiuri Zeglebi jer ar aRmoCenila. Zveli argonavtebis laSqroba

arsebiTad pirveli eqspedicia iyo mamaci zRvaosnebisa, Soreuli qveynebisken rom

miiltvodnen saxelisa da simdidris mosaxveWad. safiqrebelia, rom aseTi

mogzauroba kolxeTSi ver datovebda nivTier kvals.

17

42. ra daisaxa miznad ingliselma mecnierma-mogzaurma tim severinma?

(a) Zvelad ganxorcielebul mogzaurobaTa gameoreba Tanamedrove teqnikuri

saSualebebis gamoyenebiT

(b) dausaxlebeli miwebis aRmoCena werilobiT wyaroebSi Semonaxuli cnobebis

safuZvelze

(g) Zvelad ganxorcielebul mogzaurobaTa gameoreba Sesabamis epoqaSi (warsulSi)

arsebuli saSualebebis gamoyenebiT

(d) werilobiT wyaroebSi Semonaxuli cnobebis safuZvelze Zveli kolxeTis

migneba

43. tim severinma mogzaurobisaTvis ocniCbiani xomaldi airCia, radgan:

(a) ingliseli mecnierebi ZiriTadad ocniCbiani xomaldebiT mogzauroben

(b) Zv. w. VII saukunemde Zveli berZnebi mxolod pentakonteriT mogzaurobdnen

(g) mikenur epoqaSi berZnebi ocniCbiani xomaldebiT mogzaurobdnen

(d) mikenur epoqaSi bosforis da dardanelis sruteebis gacurva mxolod

pentakonteriT iyo SesaZlebeli

44. axalma "argom" daicva Zveli berZeni mwerlebis mier aRwerili curvis wesic, anu:

(a) gezi Savi zRvis sanapiroebisken aiRo

(b) megzurad apolonios rodoselis "argonavtika" airCia (g) napir-napir micuravda

(d) rionze rvasaaTiani aRmasvla ganaxorciela

45. tim severinma xmeleTis adgilmdebareoba zustad gansazRvra:

(a) Zveli berZnuli kompasis saSualebiT

(b) berZnuli istoriuli rukebis daxmarebiT

(g) Zveli kolxuri wyaroebis daxmarebiT

(d) talRebis moyvanilobisa da qaris mimarTulebis mixedviT

18

46. qvemoT CamoTvlilTagan romelia tim severinis marSruti?

(a) volosi _ dardaneli _ bosfori _ Savi zRva _ WyviSi _ fazisi _ foTi

(b) volosi _ dardaneli _ bosfori _ Savi zRva _ foTi _ fazisi _ WyviSi

(g) iolkosi _ Savi zRva _ foTi _ fazisi _ dardaneli _ bosfori _ WyviSi

(d) iolkosi _ Savi zRva _ dardaneli _ bosfori _ WyviSi _ foTi _ fazisi

47. tim severinma eqsperimentulad daamtkica, rom:

(a) antikuri xanis kolxuri civilizacia Zveli argonavtebis mogzaurobis

gavlenas ganicdida

(b) berZenTa pirveli mogzauroba kolxeTSi jer kidev mikenur epoqaSi iyo

SesaZlebeli

(g) mdinare rionze aRmasvla pentakonteriT SeuZlebeli iyo

(d) axali " argo" berZnuli sabrZolo xomaldis zusti aslia

48. CamoTvlilTagan romeli informacia ar dasturdeba teqstSi?

(a) vanSi SemorCenilia antikuri xanis kolxuri civilizaciis kvali

(b) tim severinis eqspediciam Tavisi Sedegebi vanis naqalaqarTan, WyviSSi Seajama

(g) vanSi jerjerobiT ar aRmoCenila gvianbrinjaos xanis mikenuri kulturis

Zeglebi

(d) tim severinis eqspedicias Sedegad mohyva argonavtebis mogzaurobis

damadasturebeli arqeologiuri masalis aRmoCena

19

49. SeavseT Semdegi winadadeba ise, rom igi marTebuli iyos teqstis mixedviT:

argonavtebis mier _____ ganxorcielebuli mogzauroba simdidrisa da saxelis

moxveWas isaxavda miznad da, savaraudod, _____ . albaT amiT aixsneba is, rom

rionis napirebze _____ .

(a) mikenur epoqaSi \ mniSvnelovan kvals daaCnevda kolxur kulturas \ gvxvdeba

antikuri xanis kolxuri civilizaciis Zeglebi

(b) Zv. w. VII saukuneSi \ mniSvnelovan kvals daaCnevda kolxur kulturas \ am

periodis mravali arqeologiuri Zeglia aRmoCenili

(g) mikenur epoqaSi \ ver datovebda nivTier kvals \ mikenuri arqeologiuri

Zeglebi araa aRmoCenili

(d) Zv. w. II aTaswleulSi \ ver datovebda nivTier kvals \ xSirad gvxvdeba

mikenuri arqeologiuri Zeglebi

50. ra aris mocemuli teqstis ZiriTadi mizani?

(a) sazRvaosno eqspediciaTa mecnieruli Sedegebis Sejameba

(b) ingliseli mkvlevris mier ganxorcielebuli eqsperimentis aRwera

(g) Zvel argonavtTa mier ganxorcielebuli eqspediciis aRwera

(d) mikenur epoqaSi ganxorcielebuli mogzaurobis Sedegebis Sejameba

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


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







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

33

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

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







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


jeradi


jeradi

( ) xx 63 2 +− 102 +x

eqvskuTxa piramidis

wiboebis raodenoba

kubis wiboebis

raodenoba