proeqti moipoveT masala (gamoiyeneT cnobarebi, enciklopediebi,gasuli wle bis saxelmZRvaneloebi) da warmoadgineTricxvTa simravleebis gafarToebis istoriuli mimoxilva,naturaluri ricxvebidan racionalur ricxvebamde ricxvTa simravlisgafarToebis praqtikuli da maTematikuri aspeqtebi (ix. mag.,r. kuranti, h. robinsi _ `ra aris maTematika~, Tbilisi, ganaTleba1965; a. benduqiZe _ maTematika. seriozuli da saxaliso, Tbilisi,2005). gamoiyeneT sxva popularuli literatura, interneti(mag. http://www.mccme.ru). SeadareT ricxvTa sistemis gafarToebisistoriuli Tanamimdevroba skolaSi maTi Seswavlis Tanamimdevrobas.sZvel egvipteSi gamoiyeneboda mxolod 32 da is wiladebi, romelTamricxveli erTis tolia. magaliTad, , , , ...2 1 3 1 4 1 5 1 sxvawiladebs isini aRniSnuli ricxvebis jamis saxiT warmoadgendnen,magaliTad,5,6=2 1 +3 1 2019 =2 1 +4 1 +5 1 .ricxvebis aseTi warmodgenisas dauSvebeli iyo raimeSesakrebis gameoreba. magaliTad, 1+1+1 . 3 5 5SeecadeT egvipturi wiladebiT warmodginoTricxvebi:5,7,7,9,17.8 8 12 10 30aSearCieT swori pasuxi31 Tu ricxviT wrfeze raime wertilidan saTavemde manZili 4,7-ia,maSin es wertili aucileblad gamosaxavs1) 4,7-s 2) –4,7-s 3) 3,7-s 4) 4,7-s an –4,7-s.32 Tu ricxvis moduli 3,2-ia, maSin ricxviT wrfeze misi gamomsaxveliP wer tili SeiZleba iyos1) mxolod P(3,2) 2) mxolod P(–3,2)3) P(3,2) an P(–3,2) 4) P(3,2) an P(6,4).33 vTqvaT, a da b racionaluri ricxvebia.suraTis mixedviT1) a>b 2) |a||b| 4) |a|=|b|.a 0 b16
34 vTqvaT, x racionaluri ricxvia, x>2. maSin ricxviT wrfeze x-isa da2-is Sesabamis wertilebs Soris manZilia1) 2x 2) 2+x 3) 2-x 4) x-2.35 Tu ricxviT wrfeze x-isa da 2-is Sesabamis wertilebs Soris man-Zili 7-ia, maSin aucileblad1) x-2=7 2) 2-x=7 3) |x-2|=7 4) x-2=14.36 Tu a da b racionaluri ricxvebis Sesabamis wertilebs Soris man-Zili 10 erTeulia, maSin SeuZlebelia1) |a-b|=10 2) a-b=10 3) b-a=10 4) a-b=b-a.37 Tu ricxviT wrfeze x racionaluri ricxvi daSorebulia saTavidan7,5-ze naklebi manZiliT, maSin aucileblad1) x
- Page 5 and 6: sarCevirogor visargebloT wigniTI Ta
- Page 7 and 8: VII Tavi albaToba§6.1. elementarul
- Page 9 and 10: 1gameoreba. iracionaluri ricxvebi.e
- Page 11 and 12: 5 CamoTvlili winadadebebidan romeli
- Page 13: magaliTi 1CavweroT wiladis saxiT: 0
- Page 17: 3) axla racionaluri ricxvebis geome
- Page 21 and 22: 49 gamoiyeneT geometriuli warmodgen
- Page 23 and 24: Tu naturalur ricxvTa mwkrividan _1,
- Page 25: sagzao SemTxvevisas moasfaltebulgza
- Page 48: nebismieri namdvili ricxvi SeiZleba
- Page 54 and 55: 1.5 n-uri xarisxis Nfesvi. fesvis T
- Page 56 and 57: CvenileqsikonimaTematikur niSans ,
- Page 58 and 59: 22 romel or momdevno mTel ricxvs So
- Page 60 and 61: 1.6 proporcia da ukuproporcia1) saR
- Page 62 and 63: aSearCieT swori pasuxi1 romeli tolo
- Page 64 and 65: 19 erTnairi sigrZis ori oTaxidan er
- Page 66 and 67: 34 vTqvaT, S manZilia (km-Si), t _
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4 Tu samkuTxedis gverdebi 6, 8, 10-
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1.8 ricxviTi utoloba. utolobaTa dam
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sutolobis > da < niSnebi ingliselma
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23 x>-15, y≤-2,5. CamoTvlilTagan
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40 daasabuTeT: Tu a>0, b>0, c>0, ma
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amoxsna. vTqvaT, moZraobis siCqarea
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7 a-s mniSvnelobebi, romlebisTvisac
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18 erT-erTi raionis pensionerebisTv
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arauaryofiTi mTeli amonaxsnebis mis
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28 |x|>5 utolobis amonaxsnTa simrav
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II xerxi|3x-6|>6, 3|x-2|>6, |x-2|>2
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2) Tu dajarimdi, maSin avtomobilis
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30 nikam 8000 lari or sxvadasxva ba