maTematika VII

Matematika Vii-Free PDF

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Transcription:

guram gogiSvili Teimuraz vefxvaZe
ia mebonia lamara qurCiSvili
maTematika
VII klasi
maswavleblis wigni
gamomcemloba inteleqti
Tbilisi 2012
Guram Gogishvili Teimuraz Vepkhvadze
Ia Mebonia Lamara Kurchishvili
M at h s V I I
Teacher s Book
Intelekti Publishers
Tbilisi 2012
ISBN 978 9941 439 08 7
gamomcemloba inteleqti 2012
gamomcemloba inteleqti
Tbilisi ilia WavWavaZDis gamz 5 tel 2 25 05 22 2 91 22 83
www intelekti ge info intelekti ge inteleqti caucasus net
intelekti Publishers
5 Ilia Chavchavadze Ave Tbilisi Georgia Tel 995 32 2 25 05 22 2 91 22 83
s a r G e v i
Sesavali 7
VII klasis maTematikis erovnuli saswavlo gegma 13
Sinaarsisa da miznebis ruka 21
saswavlo masalis wardgenis fazebi da gakveTilis dagegmvis
zogadi principebi 25
Sefasebis zogadi principebi 29
Sefaseba maTematikaSi 30
sanimuSo gakveTilebi 33
I Tavi gameoreba naturaluri ricxvebi geometriuli figurebi
1 1 naturaluri ricxvebi naturaluri ricxvis Caweris sxvadasxva forma 44
jgufuri muSaobis proeqti 48
1 2 naturaluri ricxvebis gayofa gayofadobis niSnebi 49
1 3 martivi da Sedgenili ricxvebi udidesi saerTo gamyofi da
umciresi saerTo jeradi 53
jgufuri muSaobis proeqti 56
sakontrolo wera 57
1 4 simravle qvesimravle 59
amocanebi gameorebisTvis 61
1 5 simravleTa gaerTianeba da TanakveTa venis diagramebi 62
jgufuri muSaobis proeqti 64
amocanebi gameorebisTvis 64
damoukidebeli samuSao 66
1 6 geometriuli figurebi 68
1 7 kuTxe kuTxeTa urTierTganlageba 71
1 8 monakveTis da kuTxis gazomva 73
1 9 kuTxeTa klasifikacia or wrfes Soris kuTxe 76
jgufuri muSaobis proeqti 77
amocanebi gameorebisTvis 78
sakontrolo wera 80
II Tavi racionaluri ricxvebi monacemTa analizi da statistika
zogierTi geometriuli figura
2 1 mTeli ricxvebi 83
2 2 mTeli ricxvis moduli absoluturi mniSvneloba
mTeli ricxvebis Sedareba 85
damoukidebeli samuSao 87
3
2 3 mTeli ricxvebis Sekreba da gamokleba 88
2 4 mTeli ricxvebis gamravleba da gayofa 90
amocanebi gameorebisTvis 91
damoukidebeli wera 92
2 5 dadebiTi racionaluri ricxvebi 93
jgufuri muSaobis proeqti 95
2 6 racionaluri ricxvebi 96
2 7 racionaluri ricxvis naturalurmaCvenebliani xarisxi 97
sakontrolo wera 98
2 8 monacemTa analizi da statistika 101
2 9 texili mravalkuTxedi 104
jgufuri muSaobis proeqti 107
2 10 oTxkuTxedebi 108
damoukidebeli wera 109
amocanebi gameorebisTvis 110
III Tavi cvladiani gamosaxuleba wrfivi erTucnobiani gantoleba
3 1 cvladiani gamosaxuleba
cvladiani gamosaxulebis mniSvnelobis povna 112
jgufuri muSaobis proeqti 114
3 2 naturalurmaCvenebliani xarisxis Tvisebebi 116
jgufuri muSaobis proeqti 118
damoukidebeli wera 119
3 3 erTwevri mravalwevri moqmedebebi mravalwevrebze 120
3 4 Semoklebuli gamravlebis formulebi 121
3 5 mravalwevris mamravlebad daSla 124
sakontrolo wera 127
3 6 gantoleba gantolebis fesvi 129
3 7 wrfivi erTucnobiani gantoleba 132
sakontrolo wera 133
amocanebi maTematikuri SejibrebebisTvis 135
IV Tavi koordinatebi geometriuli gardaqmnebi
4 1 koordinatebi wrfeze ricxviTi Sualedebi 139
4 2 wertilis koordinatebi sibrtyeze 145
4 3 sakoordinato meoTxedebi 148
sakontrolo wera 149
4 4 amocanebis amoxsna gantolebis saSualebiT 152
4 5 amocanebis amoxsnis sxvadasxva xerxi 155
damoukidebeli wera 160
jgufuri muSaobis proeqti 161
sakontrolo wera 162
4 6 RerZuli simetria 165
4
4 7 paraleluri gadatana 168
damoukidebeli wera 170
proeqti 171
amocanebi gameorebisTvis 171
V Tavi sidideebs Soris damokidebulebebi
samkuTxedebis tolobis niSnebi
5 1 Sefardeba 177
5 2 ricxvis dayofa proporciul nawilebad 179
5 3 proporcia 182
5 4 pirdapirproporciuli damokidebuleba 184
sakontrolo wera 187
5 5 samkuTxedi samkuTxedis saxeebi kuTxeebis mixedviT 190
jgufuri muSaobis proeqti 192
5 6 samkuTxedis elementebi 193
5 7 mimdevrobebi 197
5 8 samkuTxedebis tolobis niSnebi 199
amocanebi jgufuri muSaobisTvis 202
5 9 procenti 202
5 10 vaMgrZelebT procMentze amocanebis ganxilvas 204
jgufuri muSaobis proeqti 207
amocanebi gameorebisTvis 208
amocanebi maTematikuri SejibrebisTvis 210
sakontrolo wera 211
VI Tavi statistikis elementebi amocanebi agebaze
6 1 monacemTa Semajamebeli ricxviTi maxasiaTeblebi 214
amocanebi gameorebisTvis 215
6 2 samkuTxedis saxeebi gverdebis mixedviT tolferda samkuTxedi 216
6 3 paraleluri wrfeebi 217
amocanebi gameorebisTvis 218
6 4 samkuTxedis kuTxeebis jami 219
6 5 marTkuTxa samkuTxedi 222
6 6 monakveTis SuamarTobis Tviseba wrewiris qorda da mxebi 224
individualuri muSaobis proeqti 226
sakontrolo wera 226
6 7 amocanebi agebaze 229
amocanebi gameorebisTvis 232
amocanebi maTematikuri SejibrebisTvis 236
maTematikuri terminebis leqsikoni da maTematikuri niSnebi 237
literatura 241
boloTqma 243
5

. moswavleebSi maTematikis rogorc zogadsakacobrio kul turis nawilis Sesaxeb warmodgenis Camoyalibebas xels uwyobs SinaarsSi CarTuli epizodebi mecnierebis istoriidan isini moswavleebs im adamianTa saxelebs acnobs vinc qmnida maTe matikas maT Sorisaa saxelovani qarTveli maTe mati kose bic 10 kacobriobis inteleqtualuri istoriis SesaniSnavi faqtebis gacnoba swav lebaSi kulturul istoriul

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