أخيرة لتركيز المكتسبات .pdf



Nom original: أخيرة لتركيز المكتسبات.pdf
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Aperçu du document


‫‪2013-2012‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﺘﺤﻀﻴﺮ ﻟﺸﻬﺎﺩﺓ ﺧﺘﻢ ﺍﻟﺘﻌﻠﻴﻢ‬

‫ﺭﻳﺎﺿﻴﺎﺕ ‪ 9‬ﺃﺳﺎﺳﻲ‬
‫***‬

‫ﺣﺼﺔ ﺃﺧﻴﺮﺓ ﻟﺘﺮﻛﻴﺰ ﺍﻟﻤﻜﺘﺴﺒﺎﺕ‬

‫ﺍﻷﺳﺎﺳﻲ‬

‫*ﺩﻭﺭﺓ ‪* 2013‬‬

‫ﺧﺎﺻﻳﺔ ﻫﺎﻣﺔ ﻓﻲ ﺍﻟﻣﺛﻠﺙ ﺍﻟﻘﺎﺋﻡ‬

‫ﻣﺭﻛﺯ ﺛﻘﻝ ﺍﻟﻣﺛﻠﺙ‬

‫ﺍﻟﻣﺭﻛﺯ ﺍﻟﻘﺎﺋﻡ ﻟﻠﻣﺛﻠﺙ‬

‫‪A‬‬

‫‪A‬‬

‫‪C‬‬

‫'‪B‬‬
‫‪G‬‬

‫‪I‬‬

‫‪H‬‬

‫‪H‬‬

‫‪C‬‬

‫‪B‬‬

‫‪C‬‬
‫‪a‬‬

‫‪A‬‬

‫'‪A‬‬

‫‪B‬‬

‫ﻣﺮﻛﺰ ﺛﻘﻞ ﺍﻟﻤﺜﻠﺚ ﻫﻮ ﻧﻘﻄﺔ‬

‫ﺍﻟﻤﺮﻛﺰ ﺍﻟﻘﺎﺋﻢ ﻟﻠﻤﺜﻠﺚ ﻫﻮ‬

‫ﺗﻘﺎﻁﻊ‪......................................‬‬

‫ﺗﻘﺎﻁﻊ‪...............................‬‬

‫ﺃﺗﻤﻢ ﺍﻟﺠﻤﻞ ﺑﻤﺎ ﻳﻨﺎﺳﺐ‪:‬‬

‫ﺑﻤﺎ ﺃﻥ )‪(BC) ⊥ (AH‬‬

‫ﺑﻤﺎ ﺃﻥ ’‪ A‬ﻣﻨﺘﺼﻒ ]‪[BC‬‬

‫…………=………… = ‪IA‬‬

‫ﻓﺈﻥ‪...................................‬‬

‫ﻓﺈﻥ‪..............................................‬‬

‫ﻣﻨﺘﺼﻒ ﺍﻟﻮﺗﺮ ‪........................‬ﻋﻦ ﺭﺅﻭﺳﻪ ﺍﻟﺜﻼﺛﺔ‬

‫ﻭﺑﻤﺎ ﺃﻥ )‪(AB) ⊥ (BH‬‬

‫ﻭﺑﻤﺎ ﺃﻥ ’‪ B‬ﻣﻨﺘﺼﻒ ]‪[AC‬‬

‫ﻣﺮﻛﺰ ﺍﻟﺪﺍﺋﺮﺓ ﺍﻟﻤﺤﻴﻄﺔ ﺑﻤﺜﻠﺚ ﻗﺎﺋﻢ ﻫﻮ‬

‫ﻓﺈﻥ‪...................................‬‬

‫ﻓﺈﻥ‪..............................................‬‬

‫‪....................‬‬

‫)‪ (AH‬ﻭ )‪ (BH‬ﺍﺭﺗﻔﺎﻋﺎﻥ‬

‫]’‪ [AA‬ﻭ ]’‪ [BB‬ﻣﻮﺳﻄﺎﻥ ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ‬

‫ﺣﺴﺐ ﻧﻈﺮﻳﺔ ﺑﻴﺘﺎ ﻏﻮﺭ‪:‬‬

‫ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ‪ H‬ﺇﺫﻥ‬

‫‪ G‬ﺇﺫﻥ ‪ G‬ﻫﻮ‪...........................‬‬

‫‪.................................................................‬‬

‫‪ H‬ﻫﻮ‪...........................‬‬

‫ﺑﻤﺎ ﺃﻥ ‪ G‬ﻫﻮ ﻣﺮﻛﺰ ﺛﻘﻞ ﺍﻟﻤﺜﻠﺚ ‪ABC‬‬

‫ﺍﻟﻌﻼﻗﺔ ﺍﻟﻘﻴﺎﺳﻴﺔ‬

‫*ﺑﻤﺎ ﺃﻥ ‪ H‬ﻫﻮ ﺍﻟﻤﺮﻛﺰ ﺍﻟﻘﺎﺋﻢ‬

‫ﻓﺈﻥ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (CG‬ﺣﺎﻣﻞ ﻟﻠﻤﻮﺳﻂ‬

‫…………………………… = ‪AH x BC‬‬

‫ﻟﻠﻤﺜﻠﺚ ﻓﺈﻥ )‪ (CH‬ﻫﻮ ﺍﻻﺭﺗﻔﺎﻉ‬

‫ﺍﻟﺼﺎﺩﺭ ﻣﻦ ‪ .......‬ﻭ ﺑﺎﻟﺘﺎﻟﻲ )‪ (CG‬ﻳﻘﻄﻊ‬

‫‪AH2=…………………………………..‬‬

‫ﺍﻟﺜﺎﻟﺚ ﺍﻟﺼﺎﺩﺭ ﻣﻦ ‪ C‬ﻭ ﺑﺎﻟﺘﺎﻟﻲ‬

‫‪ ..................‬ﻓﻲ ﻣﻨﺘﺼﻔﻪ‪.‬‬

‫‪................................‬‬

‫…………………=‪AG=…………………… A’G‬‬

‫‪B‬‬

‫ﺑﻣﺎ ﺃﻥ ‪ ABC‬ﻣﺜﻠﺚ ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪A‬‬
‫ﻭ ﺑﻤﺎ ﺃﻥ ‪ I‬ﻣﻨﺘﺼﻒ ﻭﺗﺮﻩ ]‪ [BC‬ﻓﺈﻥ‪:‬‬

‫‪ 4‬ﻧﻘﺎﻁ ﻋﻠﻰ ﻧﻔﺱ ﺍﻟﺩﺍﺋﺭﺓ‬

‫ﻣﺛﻠﺙ ﻗﺎﺋﻡ‬
‫ﻟﺪﻳﻨﺎ ]‪ [AB‬ﻗﻄﺮ ﻟﻠﺪﺍﺋﺮﺓ ‪ζ‬‬

‫‪ ACB‬ﻗﺎﺋﻢ ﻓﻲ ‪ B‬ﺇﺫﻥ ﺍﻟﻨﻘﺎﻁ ‪ A‬ﻭ ‪ B‬ﻭ ‪C‬‬

‫ﻭ ‪ E‬ﻧﻘﻄﺔ ﻣﻦ ﻫﺬﻩ ﺍﻟﺪﺍﺋﺮﺓ‬

‫ﺗﻨﺘﻤﻲ ﻟﻨﻔﺲ ﺍﻟﺪﺍﺋﺮﺓ ‪...........................................‬‬

‫ﺇﺫﻥ ‪............................................................‬‬

‫‪ ACD‬ﻗﺎﺋﻢ ﻓﻲ ‪ D‬ﺇﺫﻥ ﺍﻟﻨﻘﺎﻁ ‪ A‬ﻭ ‪ D‬ﻭ ‪C‬‬

‫‪A‬‬

‫ﺗﻨﺘﻤﻲ ﻟﻨﻔﺲ ﺍﻟﺪﺍﺋﺮﺓ ‪...........................................‬‬
‫ﻭ ﺑﺎﻟﺘﺎﻟﻲ‪........................................................‬‬

‫‪E‬‬
‫‪O‬‬

‫‪A‬‬

‫‪B‬‬
‫‪B‬‬

‫‪C‬‬
‫‪D‬‬

‫‪Série F.B.A‬‬

‫‪1‬‬

‫‪2013-2012‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﻣﺘﻮﺍﺯﻱ ﺍﻟﻤﺴﺘﻄﻴﻼﺕ‬

‫)‪ (ED) ⊥ (EH‬ﻷﻥ ‪....................................................‬‬

‫‪C‬‬

‫)‪ (ED) ⊥ (EF‬ﻷﻥ ‪....................................................‬‬

‫‪D‬‬

‫‪(EH) ⊂ .................‬‬
‫‪(EF) ⊂ .................‬‬

‫‪A‬‬

‫‪B‬‬

‫‪K‬‬

‫}‪(EH) ∩ ( EF) = {E‬‬
‫ﺇﺫﻥ )‪(ED) ⊥ ( …………..‬‬

‫‪E‬‬

‫‪F‬‬

‫‪H‬‬

‫‪G‬‬

‫ﻭ ﺑﻤﺎ ﺃﻥ )‪ (EG) ⊂ (EGF‬ﻓﺈﻥ ﺍﻟﻤﺜﻠﺚ ‪..................DEG‬‬
‫‪ K‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟـ ‪ E‬ﻋﻠﻰ )‪ (DG‬ﺣﺴﺐ ﺍﻟﻌﻼﻗﺔ ﺍﻟﻘﻴﺎﺳﻴﺔ‬
‫ﻓﻲ ﺍﻟﻤﺜﻠﺚ ‪EK x DG = ……………………………………: DEG‬‬
‫‪EK2 = ………………………………………………………………..‬‬

‫ﻣﺨﺘﺎﺭﺍﺕ‪:‬‬
‫ﺃﺗﻤﻢ ﺑﻤﺎ ﻳﻨﺎﺳﺐ‪:‬‬
‫‪(1‬‬

‫‪-2‬‬
‫‪ X<3‬ﺇﺫﻥ ‪x .....................‬‬
‫‪3‬‬

‫‪(2‬‬

‫‪ -2x+3 ≤ 5‬ﻳﻌﻨﻲ ‪.......................................................................................................................‬‬

‫‪(3‬‬

‫‪1 4‬‬
‫ﺣﻞ ﻓﻲ ﺍﻟﻤﺠﺎﻝ ‪  ; ‬ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪+ 4‬‬
‫‪2 3‬‬

‫ﻭ ﺑﺎﻟﺘﺎﻟﻲ ﺣﻞ ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ﻫﻮ ‪...............................................................‬‬

‫‪2‬‬

‫‪. (4x -1)(1 − 3x) ≤ −12 x‬‬

‫‪.........................................................................................................................................................‬‬
‫‪.........................................................................................................................................................‬‬

‫‪18‬‬
‫‪ (4‬ﻛﻴﻒ ﻧﺨﺘﺎﺭ ‪ x‬ﻟﻴﻜﻮﻥ ﺍﻟﻌﺪﺩ‬
‫‪x-5‬‬

‫ﺻﺤﻴﺤﺎ ﻁﺒﻴﻌﻴﺎ‪.‬‬

‫‪..........................................................................................................................................................‬‬
‫‪ (5‬ﺃﻛﺘﺐ ﺍﻟﻤﺠﺎﻣﻴﻊ ﺍﻟﺘﺎﻟﻴﺔ ﻓﻲ ﺻﻴﻐﺔ ﻣﺮﺑﻊ‪.‬‬
‫…………………………………………………………………………………………………………………………………………………… = ‪- 5+2 6‬‬

‫‪- 14+6 5 =…………………………………………………………………………………………………………………………………………………..‬‬
‫‪- 37-20 3 =…………………………………………………………………………………………………………………………………………………..‬‬
‫‪. 2, 359 (6‬ﺍﻟﺮﻗﻢ ﺍﻟﺬﻱ ﺭﺗﺒﺘﻪ ‪ 425‬ﻋﻠﻲ ﻳﻤﻴﻦ ﺍﻟﻔﺎﺻﻞ ﻫﻮ ‪......................................................................................‬‬

‫‪Série F.B.A‬‬

‫‪2‬‬

‫‪2013-2012‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺍﺧﺘﺼﺮ ﺍﻟﻌﺒﺎﺭﺓ‬

‫‪A= (x+2)2-1‬‬

‫(‬

‫)‬

‫ﺍﺣﺴﺐ ‪ A‬ﻋﻠﻤﺎ ﺃﻥ ‪X= 1-2 3‬‬

‫‪B = 5 98 - 5 8 + 7 32‬‬

‫‪B = .....................................‬‬

‫‪A= …………………………………..‬‬
‫‪A= …………………………………..‬‬

‫‪B = .....................................‬‬

‫‪1‬‬
‫)‪+ 3‬‬
‫‪2‬‬

‫= ‪A‬‬
‫‪3 + 2 - 2- 3 -( - 2 -‬‬

‫‪A= ………………………………………..‬‬
‫‪A= ………………………………………..‬‬
‫‪A= ………………….……………………..‬‬

‫‪A= …………………………………..‬‬
‫‪1/ …………………………………………..‬‬

‫‪2‬‬
‫ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ‬
‫‪3‬‬

‫ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺓ ‪ A‬ﺍﻟﺘﺎﻟﻴﺔ‪A= x2 + 5x + 6 :‬‬

‫‪……………………………………………….‬‬

‫‪1‬ﺍﺣﺴﺒﻬﺎ ﻋﻠﻤﺎ ﺃﻥ ‪x = 2 - 1‬‬

‫……………………………………………‪2/‬‬

‫‪x < -‬‬

‫ﺑﻴﻦ ﺃﻥ ‪. 3 x + 2 < 0‬‬

‫‪………………………………………..‬‬
‫………………………………………‬

‫………………………………………………‬

‫‪2‬‬

‫‪ /2‬ﺑﻴﻦ ﺃﻥ ‪A =  x + 5  - 1‬‬
‫‪2 4‬‬
‫‪‬‬

‫‪3/…………………………………………..‬‬

‫‪ /3‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪A = 0‬‬

‫‪……………………………………………..‬‬

‫‪ /4‬ﺣﻞ ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪. A > x2‬‬

‫‪……………………………………………..‬‬

‫‪……………………………………….‬‬

‫‪4/………………………………………….‬‬
‫‪……………………………………………..‬‬

‫ﻧﻌﺘﺒﺮ ﺍﻟﻌﺪﺩ ‪ a‬ﺑﺤﻴﺚ ‪-3 < a < 5‬‬

‫‪5 a + 11‬‬
‫ﻭ ﺍﻟﻌﺒﺎﺭﺓ‬
‫‪a+4‬‬

‫=‪. b‬‬

‫‪9‬‬
‫‪ /1‬ﺑﻴﻦ ﺃﻥ‬
‫‪a+4‬‬

‫‪b=5-‬‬

‫‪ /2‬ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟﻠﻌﺒﺎﺭﺓ ‪.b‬‬

‫ﻗﺎﺭﻥ ‪7‬‬

‫ﻭ ‪4 3‬‬

‫‪1‬‬
‫ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﻣﻘﺎﺭﻧﺔ ﻟـ‬
‫‪6‬‬

‫ﻭ‬

‫‪1‬‬
‫‪4 3 -1‬‬

‫‪................................................‬‬
‫‪................................................‬‬
‫‪.................................................‬‬

‫‪ /3‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ‪(a-1)2‬‬

‫……………………………………………‪2/‬‬
‫‪……………………………………………..‬‬

‫‪ /3‬ﻗﺎﺭﻥ ‪ - 3 2‬ﻭ ‪. − 2 5‬‬

‫‪3‬‬
‫‪3‬‬
‫‪.‬‬
‫ﻭ‪b-2 5‬‬
‫‪ /4‬ﻗﺎﺭﻥ ‪a - 3 2‬‬
‫‪2‬‬
‫‪2‬‬

‫‪………………………………………………..‬‬
‫‪................................................‬‬
‫‪...............................................‬‬
‫‪...............................................‬‬

‫‪3/……………………………………………..‬‬

‫………………………………………………‬
‫‪……………………………………………….‬‬
‫‪……………………………………………….‬‬
‫………………………………………………‬

‫‪……………………………………………….‬‬

‫‪Série F.B.A‬‬

‫‪1 1‬‬
‫ﻭ‬
‫‪ /2‬ﺍﺳﺘﻨﺘﺞ ﻣﻘﺎﺭﻧﺔ ﻟـ‬
‫‪b a‬‬

‫‪.‬‬

‫‪………………………………………………..‬‬

‫‪1/ …………………………………………..‬‬
‫‪……………………………………………….‬‬

‫‪ a /4‬ﻭ ‪ b‬ﻋﺪﺩﺍﻥ ﺣﻘﻴﻘﻴﺎﻥ ﺑﺤﻴﺚ‬
‫‪ a = 2-4 3‬ﻭ‪. b = 1-4 3‬‬
‫‪ /1‬ﻗﺎﺭﻥ ‪ a‬ﻭ ‪ b‬ﺛﻢ ‪ a2‬ﻭ ‪b2‬‬

‫‪3‬‬

‫‪2013-2012‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺗﻄﺒﻴﻖ ﻟﻄﺎﻟﺲ‬
‫‪ ABCD‬ﺷﺒﻪ ﻣﻨﺤﺮﻑ ﻗﺎﺋﻢ ﻓﻲ ‪ A‬ﻭ ‪ D‬ﺍﻟﻘﻄﺮﺍﻥ ]‪ [AC‬ﻭ ]‪ [BD‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪ I‬ﻭ ﻟﺘﻜﻦ ﺍﻟﻨﻘﻄﺔ ‪ H‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟـ ‪I‬‬
‫ﻋﻠﻰ ]‪. [AD‬‬
‫‪IH IH‬‬
‫‪+‬‬
‫=‬
‫‪ /1‬ﺑﻴﻦ ﺃﻥ ‪1‬‬
‫‪AB CD‬‬

‫‪.‬‬

‫‪ /2‬ﻋﻠﻤﺎ ﺃﻥ ‪ AB=5‬ﻭ ‪ DC=6‬ﺍﺣﺴﺐ ‪.IH‬‬
‫‪ /3‬ﺍﺣﺴﺐ ‪ AH‬ﻋﻠﻤﺎ ﺃﻥ ‪. AD= 4‬‬

‫……………………………………………………………………………………………………………‬
‫‪…………………………………………………………………………………………………………..‬‬
‫……………………………………………………………………………………………………………‬

‫‪B‬‬

‫‪…………………………………………………………………………………………………………..‬‬

‫‪A‬‬

‫……………………………………………………………………………………………………………‬
‫‪…………………………………………………………………………………………………………..‬‬
‫……………………………………………………………………………………………………………‬

‫‪D‬‬

‫‪C‬‬

‫‪…………………………………………………………………………………………………………..‬‬

‫ﻣﺨﺘﺎﺭﺍﺕ‪:‬‬
‫‪ ABC /I‬ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ ﺍﻷﺿﻼﻉ ﺣﻴﺚ ‪ AB = 5‬ﻭ ‪ O‬ﻣﺮﻛﺰ ﺩﺍﺋﺮﺗﻪ ﺍﻟﻤﺤﻴﻄﺔﺑﻪ ﻭ ‪ I‬ﻣﻨﺘﺼﻒ ]‪ [BC‬ﻭ ∆ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻌﻤﻮﺩﻱ ﻋﻠﻰ‬

‫‪5 6‬‬
‫ﺍﻟﻤﺴﺘﻮﻱ ‪ ABC‬ﻭ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ O‬ﻭ ‪ S‬ﻧﻘﻄﺔ ﻣﻦ ﺍﻟﻤﺴﺘﻘﻴﻢ ∆ ﺑﺤﻴﺚ‬
‫‪3‬‬

‫= ‪. OS‬‬
‫‪S‬‬

‫‪ /1‬ﺍﺣﺴﺐ ‪. OA‬‬
‫‪.....................................................................................................‬‬

‫‪A‬‬

‫‪....................................................................................................‬‬
‫‪ /2‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ SOA‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻭ ﺍﺣﺴﺐ ‪. AS‬‬

‫‪O‬‬

‫‪...........................................................................................................‬‬

‫‪B‬‬

‫‪I‬‬

‫‪C‬‬

‫‪...........................................................................................................‬‬
‫‪ /3‬ﻟﺘﻜﻦ ‪ F=A*S‬ﻭ ‪ E= O*S‬ﺍﺣﺴﺐ ‪. EF‬‬
‫‪......................................................................................................................................................................‬‬
‫‪.....................................................................................................................................................................‬‬

‫‪Série F.B.A‬‬

‫‪4‬‬


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