I Tavi

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I <strong>Tavi</strong> 50 K y = x 2 A B –3 –2 –1 K 23 1-el naxazze mocemul y = x 2 funqciis grafikze aRebuli A, B, da O wertilebi tolgverda samkuTxedis wveroebia. ipoveT A da B wertilebis koordinatebi, Tu A da B simetriuli wertilebia y RerZis mimarT da O(0;0). 24 wrfes, romelic gadis 1) A(3;0), 2) A(0;4) wertilze, y = x 2 parabolasTan aqvs erTi saerTo wertili. ipoveT: a) am wrfis daxris koeficienti; b) wrfisa da parabolis saerTo wertilis koordinatebi. 25 students gamocdis Casabareblad unda gaemeorebina wignis 360 gverdi. avadmyofobis gamo pirvel sam dRes man ver SeZlo mecadineoba da amitom darCenili dReebis ganmavlobaSi igi yoveldRiurad imeorebda 20 gverdiT mets, vidre dagegmili hqonda. ramden dReSi gaimeora studentma sagani? 26 wiladis mricxveli 11-iT metia mniSvnelze. Tu am wiladis mricxvels davumatebT 5-s, xolo mniSvnels ki – 12-s, miviRebT wilads, romelic samjer naklebi iqneba mocemul wiladze. ipoveT Tavdapirveli wiladi. 27 katerma 12km mdinaris dinebis sawinaaRmdego mimarTulebiT da 5km mdinaris dinebis mimarTulebiT gaiara imave droSi, rac mas tbaze 18km-is gasavlelad dasWirdeboda. ipoveT kateris sakuTari siCqare, Tu mdinaris dinebis siCqare 3km/sT-ia. 28 SeadgineT geometriuli Sinaarsis amocana, romelic amoixsneba Semdegi gantolebis saSualebiT: M 0 1 2 3 nax. 1 a) x(x – 2) = 36; b) (x – 2)(x + 2) = 12. B C A D M B C A D 29. marTkuTxedis formis muyaos furclisgan, romlis sigrZe 1,5-jer metia siganeze, unda daamzadon TavRia yuTi, amisTvis muyaos furcels kuTxeebSi 8sm sigrZis gverdis mqone kvadratebi amoaWres. ipoveT Tavdapirveli muyaos furclis sigrZe da sigane, Tu dasamzadebeli yuTis moculoba 6080 sm 3 unda iyos.
30 A qalaqidan B qalaqisken ori avtomobili gaemgzavra. pirvelis siCqare 10km/sT-iT metia meoris siCqareze da amitomac igi 2 saaTiT adre Cavida B qalaqSi, vidre meore. ipoveT TiToeuli avtomobilis siCqare, Tu qalaqebs Soris manZili 600km-ia. 31 A punqtidan mdinaris dinebis mimarTulebiT tivi gagzavnes. 5sT da 20 wT-is Semdeg imave punqtidan tivs motoriani navi daedevna da gaiara ra 20km, daewia tivs. ipoveT tivis siCqare, Tu motoriani navi saa- TSi 12km-iT met manZils gadis, vidre tivi. 32 matarebeli gzaSi 6 wT-iT SeaCeres. memanqanem es dagvianeba 20km-ian gadasarbenze aanazRaura, romelic 10km/sT-iT meti siCqariT gaiara, vidre ganrigiT iyo dadgenili. gansazRvreT matareblis ganrigiT gaTvaliswinebuli siCqare. 33 600 km sigrZis gadasarbenis 1/4 nawilis gavlis Semdeg matarebeli SeaCeres 1 sT 30 wT-iT. daniSnulebis adgilze droze rom Casuliyo, memanqanem siCqare 15 km/sT-iT gazarda, ra dro moandoma matarebelma mTeli gzis gavlas? 34 A-dan B-mde 240 km manZili avtomanqanam gansazRvrul droSi gaiara. ukan dabrunebisas man Sua gzamde iara imave siCqariT, xolo Semdeg 10 km/sT-iT gazarda siCqare, amitom ukan dabrunebas 2/5 sT-iT naklebi dro moandoma. ipoveT avtomobilis Tavdapirveli siCqare. 35 A-dan B-mde 400 km manZili matarebelma gansazRvruli siCqariT gaiara. ukan dabrunebisas, gzis 2/5-ze midioda imave siCqariT, xolo Semdeg 20 km/sT-iT Seamcira siCqare. ipoveT matareblis siCqare gzis bolo monakveTze, Tu mTeli gzis gavlas man 11 sT moandoma. 36 matarebels 840km unda gaevlo. Sua gzaze igi 30 wT-iT SeaCeres da daniSnul adgilze droze rom misuliyo, siCqare 2km/sT-iT gazarda. ra droSi gaiara matarebelma mTeli gza? 37 motorianma navma mdinaris dinebis sawinaaRmdego mimarTulebiT gaiara 35 km, Semdeg gaagrZela gza mdinaris SenakadSi da gaiara kidev 18 km, amasTan mTeli gzis gavlas 8 saaTi moandoma. mdinaris dinebis siCqare 1 km/sT-iT naklebia Senakadis dinebis siCqareze. ipoveT mdinaris dinebis siCqare, Tu navis siCqare mdgar wyalSi 10 km/sT-ia. 38 N punqtidan mebaduri naviT mdinaris dinebis sawinaaRmdego mimarTulebiTgaemgzavra.6km-isgacurvisSemdegxeligauSvaniCbebs da mdinaris dinebam 4 sT 30 wuTis Semdeg igi kvlav N punqtSi miiyvana. ipoveT mdinaris dinebis siCqare, Tu navis siCqare mdgar wyalSi 90 m/wT-ia. 51
Page 3: nana jafariZe maia wilosani nani
Page 6 and 7: IV Tavi . . . . . . . . . . . . . .
Page 8 and 9: 6 rogor visargebloT wigniT wignze m
Page 10 and 11: I Tavi 8 f funqciaa h ar aris funqc
Page 12 and 13: I Tavi gasaxseneblad! p(A) = m n ,
Page 14 and 15: I Tavi -4 12 4 a) savarjiSoebi: 1 r
Page 16 and 17: I Tavi 14 4) rodis moawyves turiste
Page 18 and 19: I Tavi 16 2 amovicnoT wrfivi funqci
Page 20 and 21: I Tavi 18 SeavseT gamotovebuli adgi
Page 22 and 23: I Tavi 20 proeqti: gazomvebidan fun
Page 24 and 25: I Tavi 22 y 10 -3 -2 -1 0 1 2 3 9 8
Page 26 and 27: I Tavi 24 15% 1,5 < n ≤ 2 20% 1 <
Page 28 and 29: I Tavi 26 nax. 1 kvadratul gantoleb
Page 30 and 31: I Tavi 28 3 dawereT kvadratuli gant
Page 32 and 33: I Tavi davazustoT! roca D = 0, kvad
Page 34 and 35: I Tavi 32 amovxsnaT formuliT (3x 2
Page 36 and 37: I Tavi 34 z) 10x 2 −120 + 6x = 98
Page 38 and 39: I Tavi navis sakuTari siCqarea navi
Page 40 and 41: I Tavi 38 6 amovxsnaT jgufuri mecad
Page 42 and 43: I Tavi x 1 da x 2 ricxvebi arian x
Page 44 and 45: I Tavi 42 17 amoxseniT gantoleba: a
Page 46 and 47: I Tavi 44 yuradReba: Tu D=0, maSin,
Page 48 and 49: I Tavi gavixsenoT! x = a, maSin a 2
Page 50 and 51: I Tavi 48 I Tavis damatebiTi savarj
Page 54 and 55: I Tavi 52 39 A punqtidan B punqtisa
Page 56 and 57: I Tavi narevSi gaxsnili nivTierebis
Page 58: 56 I TavSi Seswavlili masalis mokle

I Tavi

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