I Tavi

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I <strong>Tavi</strong> 24 15% 1,5 < n ≤ 2 20% 1 < n ≤ 1,5 11 SeamCnieT kanonzomiereba da dawereT mimdevrobis kidev sami wevri: a) − ; 2 ; −4 ; ... b) 4; 12; 36; ... g) 2 − ; 1; 2 + ; ... d) 1; 1+ ; 1+ 2 ; ... 12 rogorc viciT, saaTze wuTebis 60 danayofia. didi isari 1 saaTSi gadis 60 danayofs, patara ki _ 5 danayofs. amasTan, didi isari erT saaTSi asrulebs 360°-ian bruns. a) gamosaxeT danayofebiT: 1°, 30°, 45°, 90°, 180°; b) gamosaxeT gradusebiT: 1; 5; 10; 30 danayofi; g) gamosaxeT danayof-saaTebiT (dan/sT) saaTis didi da patara isrebis siCqareebi. A 35% 0 < n ≤ 0,5 30% 0,5 < n ≤ 1 B D C E 13 ramdeni gradusia naxatze gamosaxul saa- Tis isrebs Soris? 14 Svidis 10 wuTze ramdeni gradusia saaTis isrebs Soris? 15 Tu axla 2 saaTia, ramdeni saaTis Semdeg iqneba pirvelad saaTis isrebs Soris kuTxe 90 gradusi? 16 skolaSi, romelSic 1200 moswavle swavlobs, Caatares gamokiTxva – saSualod ramden saaTs (n) uTmobs moswavle kompiuterul TamaSebs. kiTxvas ar upasuxa 100-ma moswavlem, danarCen moswavleTa pasuxebi mocemulia wriul diagramaze. a) ramdeni moswavle uTmobs kompiuterul TamaSebs 0,5 sT-ze mets? b) ramdeni moswavle uTmobs kompiuterul TamaSebs 1 sT-ze naklebs? 17 naxazze Sefardebulia wris 1 ; ∠B=25°. 4 ipoveT CDE kuTxis gradusuli zoma.
4 kvadratuli gantolebis grafikuli amoxsna 1. kvadratuli formis yvavilnars 1m siganis zoli miuerTes. miRebuli nakveTis farTobi 6 m 2 -ia. ipoveT Tavdapirveli nakveTis gverdis sigrZe. amoxsna: vTqvaT, Tavdapirveli nakveTis gverdis sigrZe x m iyo, maSin miRebuli marTkuTxa nakveTis farTobi iqneba x(x+1). miviReT gantoleba: x(x + 1) = 6 x 2 + x – 6 = 0 miRebul gantolebas kvadratul gantolebas uwodeben. ax 2 +bx+c=0 saxis gantolebas, sadac a,b,c∈R, a≠0, xolo x ucnobia, kvadratuli gantoleba ewodeba . a-s kvadratuli gantolebis pirvel koeficients uwodeben, b-s _ meore koeficients, xolo c-s _ mesame koeficients (<strong>Tavi</strong>sufal wevrs). amovxsnaT grafikulad ax 2 + bx + c = 0, a ≠ 0 (1) gantoleba. I. (1) gantolebas mivceT x2 = kx + m saxe. (ax2 + bx + c = 0) ⇔ |:a (x2 + b c x + a a = 0) ⇔ (x2 = – b c x – a a ) Tu – b c ≡ k da – ≡ m, a a maSin miviRebT x2 = kx + m. II. erTsa da imave marTkuTxa sakoordinato sistemaSi avagoT y = x 2 da y = kx + m funqciaTa grafikebi. magaliTad, x 2 = _0,5x + 1,5 (x 2 = –0,5x +1,5) ⇔ x = –1,5 x =1 III. grafikebis gadakveTis wertilTa abscisebi iqneba (1) gantolebis amonaxsnebi. ramdeni saerTo wertili SesaZlebelia hqondes wrfesa da parabolas? parabolas wrfesTan SesaZlebelia hqondes: I. ori saerTo wertili II. erTi saerTo wertili III. arc erTi saerTo wertili 25
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 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 52 and 53: I Tavi 50 K y = x 2 A B -3 -2 -1 K
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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