9أساسي ثلاثي 3 .pdf



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‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﻤﻌﺎﺩﻻﺕ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪.:‬‬
‫ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫)‪3/ x ( 5x - 4 ) = 4 ( x 2 - 1‬‬
‫‪6/ x 2 - 1 = 0.‬‬
‫‪2‬‬
‫‪4‬‬
‫‪x-1 = .‬‬
‫‪3‬‬
‫‪3‬‬

‫‪2‬‬
‫‪3‬‬

‫‪2/ ( 3 x - 1 ) 2 -16 = 0‬‬
‫‪2-x 2x-1 4-3x‬‬
‫=‬
‫‬‫‪3‬‬
‫‪3‬‬
‫‪2‬‬

‫‪9/‬‬

‫= ‪1/ x 3‬‬

‫‪5/ - 5x -‬‬

‫‪4 / (2x+3) 2 -(1-x) 2 =0‬‬

‫‪8/ 3 ( x+1) 2 = x 2 -1‬‬

‫‪7 / 2(-x-3) + x = 3x-1‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ ‪:‬‬
‫‪ /1‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪. x ( x+24) = x2 + 8 ( x + 10) :‬‬
‫‪ ABC /2‬ﻫﻮ ﻣﺜﻠﺚ ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪ A‬ﺣﻴﺚ ﻁﻮﻝ ﻭﺗﺮﻩ ]‪ [BC‬ﻳﻔﻮﻕ ﻁﻮﻝ ﺿﻠﻌﻪ ]‪ [AB‬ﺑــ ‪ . 8‬ﺍﺑﺤﺚ ﻋﻦ ﻣﺤﻴﻂ ﻫﺬﺍ ﺍﻟﻤﺜﻠﺚ ﻋﻠﻤﺎ ﺃﻥ‬
‫ﻁﻮﻝ ﺍﻟﻀﻠﻊ ]‪ [AC‬ﻫﻮ ‪.12‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ ‪:‬‬
‫‪ ABCD /1‬ﻫﻮ ﺷﺒﻪ ﻣﻨﺤﺮﻑ ﻗﺎﺋﻢ ﻓﻲ ‪ A‬ﻭ ‪ D‬ﺣﻴﺚ ‪ AB=5‬ﻭ ‪ AD=3‬ﻭ ‪. DC = a‬‬
‫ﺍﺑﺤﺚ ﻋﻦ ﺍﻟﻌﺪﺩ ﺍﻟﺤﻘﻴﻘﻲ ‪ a‬ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ ADC‬ﻫﻮ ﺛﻼﺛﺔ ﺃﺭﺑﺎﻉ ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺷﺒﻪ ﺍﻟﻤﻨﺤﺮﻑ ‪. ABCD‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ ‪:‬‬
‫ﻧﻌﺘﺒﺮ ﻣﻜﻌﺒﺎ ﻗﻴﺲ ﺣﺠﻤﻪ ﻳﺴﺎﻭﻱ ﺛﻼﺛﺔ ﺃﺿﻌﺎﻑ ﻗﻴﺲ ﻁﻮﻝ ﺣﺮﻓﻪ ﺍﺑﺤﺚ ﻋﻦ ﻁﻮﻝ ﺣﺮﻑ ﺍﻟﻤﻜﻌﺐ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ ‪:‬‬
‫ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫‪(x-1) 2 = 3‬‬

‫‪5/ ( x -4 ) 2 - ( 3x + 5 ) 2 = 0‬‬

‫‪3/‬‬

‫‪2/ 7x -2 = 3 - x‬‬

‫‪4/ ( 3x+5)(2x-1) - 4x 2 +1= ( 2 x +1 ) ( 2 x -1 ).‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺩﺱ ‪:‬‬
‫ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫‪3/ 5 - 2x = 5 − 2x.‬‬
‫‪6/ 2 x - 5 = 2x - 2‬‬

‫‪Série F.B.A‬‬

‫‪2/ (2x+3) ( x+1) + 4x 2 +12x+9 =0‬‬
‫‪x - 5 = 3.‬‬

‫‪1/ 16 x 2 +56x +49 = 1‬‬

‫‪4 / (2x-3) 2 - 2 (2x-3) (3x+2) + ( 3x+2) 2 =0‬‬

‫‪5/‬‬

‫‪2‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﻤﻌﺎﺩﻻﺕ)ﻣﺴﺎﺋﻞ(‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫ﺃﻡ ﻋﻤﺮﻫﺎ ‪ 46‬ﺳﻨﺔ ﻟﻬﺎ ﻁﻔﻼﻥ ﺃﺣﺪﻫﻤﺎ ‪ 7‬ﺳﻨﻮﺍﺕ ﻭ ﺍﻵﺧﺮ ‪ 13‬ﺳﻨﺔ‪.‬‬
‫ﺑﻌﺪ ﻛﻢ ﺳﻨﺔ ﻳﺼﺒﺢ ﻋﻤﺮ ﺍﻷﻡ ﺿﻌﻒ ﻣﺠﻤﻮﻉ ﻋﻤﺮﻱ ﻁﻔﻠﻴﻬﻤﺎ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫ﺍﺷﺘﺮﻯ ﺷﺨﺺ ‪ 20‬ﻛﺮﺳﻴﺎ ﻭ ‪ 5‬ﻁﺎﻭﻻﺕ ﺑـ ‪ 225‬ﺩﻳﻨﺎﺭﺍ ﻋﻠﻤﺎ ﺃﻥ ﺛﻤﻦ ﺍﻟﻄﺎﻭﻟﺔ ﻭ ﺍﻟﻜﺮﺳﻲ ﻣﻌﺎ ﻫﻮ ‪ 30‬ﺩﻳﻨﺎﺭﺍ ﺍﺑﺤﺚ ﻋﻦ ﺛﻤﻦ ﺍﻟﻄﺎﻭﻟﺔ ﻭ‬
‫ﺛﻤﻦ ﺍﻟﻜﺮﺳﻲ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬
‫ﻟﻨﺎ ﻓﻲ ﻗﻔﺺ ‪) 36‬ﺑﻴﻦ ﺩﺟﺎﺝ ﻭ ﺃﺭﺍﻧﺐ( ﺍﺑﺤﺚ ﻋﻦ ﻋﺪﺩ ﺍﻟﺪﺟﺎﺝ ﻭ ﻋﺪﺩ ﺍﻷﺭﺍﻧﺐ ﻋﻠﻤﺎ ﺃﻥ ﻋﺪﺩ ﺍﻟﺴﻴﻘﺎﻥ ﻫﻮ ‪. 120‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‪:‬‬
‫‪ ABCD‬ﻣﺴﺘﻄﻴﻞ ﻁﻮﻟﻪ ﻳﺴﺎﻭﻱ ﺿﻌﻒ ﻋﺮﺿﻪ‪ .‬ﺇﺫﺍ ﺃﺿﻔﻨﺎ ‪ 2m‬ﻟﻠﻄﻮﻝ ﻭ ‪ 2m‬ﻟﻠﻌﺮﺽ ﺍﺭﺗﻔﻌﺖ ﻣﺴﺎﺣﺔ ﻫﺬﺍ ﺍﻟﻤﺴﺘﻄﻴﻞ ﺑـ ‪34 m2‬‬
‫ﺍﺑﺤﺚ ﻋﻦ ﻁﻮﻝ ﻭ ﻋﺮﺽ ﻫﺬﺍ ﺍﻟﻤﺴﺘﻄﻴﻞ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‪:‬‬

‫‪2‬‬
‫ﺃﻛﻞ ﺳﻨﺠﺎﺏ‬
‫‪5‬‬

‫ﻣﺪﺧﺮﺍﺗﻪ ﻣﻦ ﺍﻟﺒﻨﺪﻕ ﻓﻲ ﺍﻟﺸﻬﺮﻳﻦ ﺍﻷﻭﻟﻴﻦ ﻣﻦ ﻓﺼﻞ ﺍﻟﺸﺘﺎء ﺛﻢ ﺃﻛﻞ ﺭﺑﻊ ﻣﺎ ﺗﺒﻘﻰ ﻓﻲ ﺍﻟﺸﻬﺮ ﺍﻷﺧﻴﺮ ﻣﻦ ﻓﺼﻞ‬

‫ﺍﻟﺸﺘﺎء ﻭ ﺑﻘﻲ ﻟﻪ ‪ 81‬ﺑﻨﺪﻗﺔ ﻛﻢ ﻛﺎﻥ ﺍﻟﻌﺪﺩ ﺍﻟﺠﻤﻠﻲ ﻟﻠﺒﻨﺪﻕ ﻓﻲ ﺑﺪﺍﻳﺔ ﻓﺼﻞ ﺍﻟﺸﺘﺎء‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺩﺱ‪:‬‬
‫ﻓﻲ ﻋﺎﺋﻠﺔ ﻋﻤﺮ ﺍﻷﺏ ﻳﺴﺎﻭﻱ ‪ 12‬ﻣﺮﺓ ﻋﻤﺮ ﺍﺑﻨﻪ ﺍﻟﺼﻐﻴﺮ ﻭ ‪ 3‬ﺃﺿﻌﺎﻑ ﻋﻤﺮ ﺍﺑﻨﺘﻪ ‪.‬‬
‫ﻋﻠﻤﺎ ﺃﻥ ﺍﻟﺒﻨﺖ ﻳﻔﻮﻕ ﺳﻨﻬﺎ ﺑـ ‪ 15‬ﺳﻨﺔ ﺳﻦ ﺃﺧﻴﻬﺎ ﻣﺎ ﻫﻮ ﻋﻤﺮ ﺍﻻﺑﻦ ﻭ ﺍﻟﺒﻨﺖ ﻭ ﺍﻷﺏ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺑﻊ‪:‬‬

‫‪1‬‬
‫‪3‬‬
‫ﻗﻄﻌﺔ ﻗﻤﺎﺵ ﺛﻢ ﺑﺎﻉ‬
‫ﺗﺎﺟﺮ ﻟﻸﻗﻤﺸﺔ ﺑﺎﻉ‬
‫‪3‬‬
‫‪7‬‬

‫ﻣﻤﺎ ﺗﺒﻘﻰ ﺑﻌﺪ ﻫﺎﺗﻴﻦ ﺍﻟﺒﻴﻌﺘﻴﻦ ﺗﺒﻘﻰ ﻟﻪ ‪ 8‬ﻣﺘﺮ ﻣﻦ ﺍﻟﻘﻤﺎﺵ ﻛﻢ ﻛﺎﻥ ﻁﻮﻝ ﻗﻄﻌﺔ‬

‫ﺍﻟﻘﻤﺎﺵ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻣﻦ‪:‬‬
‫ﻋﻨﺪ ﺍﻟﻜﺘﺒﻲ ﻻﺣﻈﺖ ﻣﻨﻴﺔ ﺃﻧﻪ ﻳﻨﻘﺼﻬﺎ ‪ 120‬ﻣﻠﻴﻤﺎ ﻟﺸﺮﺍء ‪ 7‬ﺃﻗﻼﻡ ﻭ ﻻﺣﻈﺖ ﺃﻳﻀﺎ ﺃﻧﻪ ﺇﺫﺍ ﺍﺷﺘﺮﺕ ‪ 5‬ﺃﻗﻼﻡ ﻓﻘﻂ ﻳﺒﻘﻰ ﻟﻬﺎ ‪ 200‬ﻣﻠﻴﻤﺎ‪.‬‬
‫ﻣﺎ ﻫﻮ ﺛﻤﻦ ﺍﻟﻘﻠﻢ ﺍﻟﻮﺍﺣﺪ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺘﺎﺳﻊ‪:‬‬
‫‪ ABC‬ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ ﺍﻟﻀﻠﻌﻴﻦ ﻭ ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪ A‬ﺑﺤﻴﺚ ‪ AB=x‬ﺃﻭﺟﺪ ‪ x‬ﻋﻠﻤﺎ ﺃﻥ ﻣﺤﻴﻂ ﻫﺬﺍ ﺍﻟﻤﺜﻠﺚ ﻳﺴﺎﻭﻱ ﻣﺤﻴﻂ ﻣﺮﺑﻊ ﺿﻠﻌﻪ‬

‫‪2‬‬

‫‪. 1+‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﻌﺎﺷﺮ‪:‬‬
‫‪ ABCD (1‬ﻣﺮﺑﻊ ﺿﻠﻌﻪ ‪ 4‬ﻭ ‪ M‬ﻧﻘﻄﺔ ﻣﻦ ]‪ [AB‬ﺣﻴﺚ ‪ . AM=x‬ﺍﺣﺴﺐ ﺑﺪﻻﻟﺔ ‪ x‬ﻣﺴﺎﺣﺔ ‪ AMCD‬ﻭ ﻣﺴﺎﺣﺔ ‪. MBC‬‬
‫‪ (2‬ﺃﻭﺟﺪ ‪ x‬ﻋﻨﺪﻣﺎ ﺗﻜﻮﻥ ﻣﺴﺎﺣﺔ ﺷﺒﻪ ﺍﻟﻤﻨﺤﺮﻑ ‪ AMCD‬ﺃﺭﺑﻌﺔ ﺃﺿﻌﺎﻑ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪. MBC‬‬

‫‪Série F.B.A‬‬

‫‪3‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﺤﺼﺮ‬
‫‪ (1‬ﺣﺼﺮ ﻟﻤﺠﻤﻮﻉ ﻋﺪﺩﻳﻦ‪:‬‬

‫‪−3≤ x ≤5‬‬

‫‪−3 2 ≤ x ≤ 3‬‬

‫‪4≤y≤7‬‬

‫‪−3 2 ≤ x ≤ 3‬‬
‫‪....... ≤ x + 3 ≤ ........‬‬

‫‪− 2 ≤ y ≤ 27‬‬

‫‪....... ≤ x + y ≤ ........‬‬

‫‪....... ≤ x + y ≤ ........‬‬

‫‪ (2‬ﺣﺼﺮ ﻟﻔﺮﻕ ﻋﺪﺩﻳﻦ‪X-Y= X+(-Y) :‬‬
‫ﺣﺼﺮ ﻟـ‪........................= x-y‬‬

‫‪−3 ≤ x ≤ 5‬‬
‫‪4≤y≤7‬‬
‫‪..... ≤ − y ≤ ......‬‬
‫‪....... ≤ x + ( − y ) ≤ ........‬‬
‫‪....... ≤ x − y ≤ ........‬‬

‫ﺣﺼﺮ ﻟـ‪..........................= 3x-2y‬‬

‫‪4≤y≤7‬‬

‫ﺣﺼﺮ ﻟـ‪......................= -4x-2y‬‬

‫‪4≤y≤7‬‬

‫‪−3 ≤ x ≤ 5‬‬

‫‪−3 ≤ x ≤ 5‬‬

‫‪..... ≤ 3x ≤ ......‬‬
‫‪....... ≤ −2y ≤ ........‬‬

‫‪..... ≤ −4x ≤ ......‬‬
‫‪....... ≤ −2y ≤ ........‬‬

‫‪....... ≤ 3x + (−2y) ≤ ........‬‬
‫‪....... ≤ 3x − 2y ≤ ........‬‬

‫‪....... ≤ −4x + (−2y) ≤ ........‬‬
‫‪....... ≤ −4x − 2y ≤ ........‬‬

‫‪ (3‬ﺣﺼﺮ ﻟﺠﺬﺍء ﻋﺪﺩﻳﻦ ﻣﻮﺟﺒﻴﻦ‬
‫ﺣﺼﺮ ﻟـ‪ ) x.y‬ﺍﻷﻁﺮﺍﻑ ﻣﻮﺟﺒﺔ(‬
‫ﺣﺼﺮ ﻟـ‪ ) x.y‬ﺍﻷﻁﺮﺍﻑ ﻣﻮﺟﺒﺔ(‬

‫‪− 4 ≤ y ≤ −3‬‬

‫‪−3 ≤ x ≤ −2‬‬

‫ﺍﻷﻁﺮﺍﻑ ﻟﻴﺴﺖ ﻣﻮﺟﺒﺔ‪:‬‬

‫‪7 ≤ x ≤ 10‬‬
‫‪2≤y≤7‬‬
‫‪..... ≤ x.y ≤ ......‬‬

‫ﺣﺼﺮ ﻟـ‪ ) x.y‬ﺍﻷﻁﺮﺍﻑ ﻣﻮﺟﺒﺔ(‬

‫‪4 ≤ y ≤ 13‬‬

‫‪−7 ≤ x ≤ −3‬‬

‫ﺍﻷﻁﺮﺍﻑ ﻟﻴﺴﺖ ﻣﻮﺟﺒﺔ )ﻁﺮﻓﻴﻦ ﺳﺎﻟﺒﻴﻦ(‬

‫‪....... ≤ − x ≤ .........‬‬
‫‪....... ≤ − y ≤ .........‬‬

‫‪....... ≤ − x ≤ .........‬‬
‫‪....... ≤ y ≤ .........‬‬

‫‪....... ≤ ( − x ) . ( − y ) ≤ .........‬‬

‫‪....... ≤ ( − x ) .y ≤ .........‬‬

‫‪......... ≤ x.y ≤ ............‬‬

‫‪......... ≤ x.y ≤ ............‬‬

‫‪ (3‬ﺣﺼﺮ ﻗﺴﻤﺔ ﻋﺪﺩﻳﻦ ﻣﻮﺟﺒﻴﻦ‬

‫‪x‬‬
‫‪1‬‬
‫‪x‬‬
‫ﺣﺼﺮ‬
‫) ‪= x.‬‬
‫‪y‬‬
‫‪y‬‬
‫‪y‬‬
‫‪7 ≤ x ≤ 10‬‬
‫‪2≤y≤7‬‬
‫(‬

‫‪x‬‬
‫‪1‬‬
‫ﺣﺼﺮ ‪= x.‬‬
‫‪y‬‬
‫‪y‬‬

‫ﺣﺼﺮ ﻟـ‪ ) x.y‬ﺍﻷﻁﺮﺍﻑ ﻣﻮﺟﺒﺔ(‬
‫) ﺍﻷﻁﺮﺍﻑ ﻣﻮﺟﺒﺔ(‬

‫‪−3 ≤ x ≤ −2‬‬

‫‪− 4 ≤ y ≤ −3‬‬

‫ﺍﻷﻁﺮﺍﻑ ﻣﻮﺟﺒﺔ‪:‬‬

‫ﺍﻷﻁﺮﺍﻑ ﻟﻴﺴﺖ ﻣﻮﺟﺒﺔ‪:‬‬

‫‪7 ≤ x ≤ 10‬‬
‫‪2≤y≤7‬‬
‫‪1‬‬
‫‪..... ≤ ≤ ......‬‬
‫‪y‬‬
‫‪1‬‬
‫‪..... ≤ x. ≤ ......‬‬
‫‪y‬‬
‫‪x‬‬
‫‪..... ≤ ≤ ......‬‬
‫‪y‬‬

‫‪....... ≤ − x ≤ ......... ....... ≤ − y ≤ .........‬‬
‫‪−1‬‬
‫‪≤ .........‬‬
‫≤ ‪.......‬‬
‫‪y‬‬

‫‪Série F.B.A‬‬

‫‪ 1‬‬
‫‪....... ≤ ( − x ) .  −  ≤ .........‬‬
‫‪ y‬‬
‫‪x‬‬
‫‪......... ≤ ≤ ............‬‬
‫‪y‬‬

‫‪4‬‬

‫‪4 ≤ y ≤ 13‬‬

‫‪−7 ≤ x ≤ −3‬‬

‫ﺍﻷﻁﺮﺍﻑ ﻟﻴﺴﺖ ﻣﻮﺟﺒﺔ‬

‫‪....... ≤ − x ≤ .........‬‬
‫‪1‬‬
‫‪....... ≤ ≤ .........‬‬
‫‪y‬‬
‫‪1‬‬
‫‪....... ≤ ( − x ) . ≤ .........‬‬
‫‪y‬‬
‫‪−x‬‬
‫‪≤ ............‬‬
‫≤ ‪.........‬‬
‫‪y‬‬
‫‪x‬‬
‫‪......... ≤ ≤ ............‬‬
‫‪y‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﺤﺼﺮ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬

‫‪1‬‬
‫‪ /1‬ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺗﻴﻦ‬
‫‪2‬‬

‫‪ /2‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ ‪ (x – 4 )2‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺃﻥ‬

‫‪ A = 2x -‬ﻭ ‪. B = 2 – x‬‬

‫‪5 ≤ x 2 -8x+20 ≤ 40‬‬

‫‪-1‬ﺍﺣﺴﺐ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻌﺪﺩﻳﺔ ﻟﻠﻌﺒﺎﺭﺓ ‪ A‬ﻋﻠﻤﺎ ﺃﻥ ‪x = 2 - 3‬‬
‫‪5‬‬
‫‪7‬‬
‫‪ x -2‬ﻫﻮ ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺑﺤﻴﺚ‬
‫≤ ‪≤ x‬‬
‫‪2‬‬
‫‪2‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺑﻊ‪:‬‬

‫‪5 a + 11‬‬
‫ﻧﻌﺘﺒﺮ ﺍﻟﻌﺪﺩ ‪ a‬ﺑﺤﻴﺚ ‪ -3 < a < 5‬ﻭ ﺍﻟﻌﺒﺎﺭﺓ‬
‫‪a+4‬‬

‫ﺃﻭﺟﺪ ﺣﺼﺮﺍ‬

‫ﻟﻠﻌﺒﺎﺭﺗﻴﻦ ‪ A‬ﻭ‪. B‬‬

‫‪9‬‬
‫‪ /1‬ﺑﻴﻦ ﺃﻥ‬
‫‪a+4‬‬

‫‪A‬‬
‫‪ -3‬ﺗﺤﻘﻖ ﺃﻥ ‪ B ≠ 0‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟﻠﻌﺒﺎﺭﺓ‬
‫‪B‬‬
‫‪3‬‬
‫‪ a‬ﻭ ‪ b‬ﻋﺪﺩﺍﻥ ﺑﺤﻴﺚ‬
‫‪4‬‬

‫‪≤a‬‬

‫‪-‬‬

‫‪1‬‬
‫‪-9‬‬
‫;‬
‫‪a+4‬‬
‫‪a +4‬‬

‫; ‪ a + 4‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟﻠﻌﺒﺎﺭﺓ ‪. b‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻣﻦ‪:‬‬

‫‪ a /1‬ﻭ ‪ b‬ﻋﺪﺩﺍﻥ ﺣﻘﻴﻘﻴﺎﻥ ﺣﻴﺚ ‪ 2 ≤ a ≤ 5‬ﻭ ‪-4 ≤ b ≤ -1‬‬

‫‪ /1‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟﻸﻋﺪﺍﺩ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫‪1‬‬
‫‪-2‬‬
‫;‬
‫‪a+1‬‬
‫‪a+1‬‬

‫‪. b=5-‬‬

‫‪ /2‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟﻜﻞ ﻋﺪﺩ ﻣﻦ ﺍﻷﻋﺪﺍﺩ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬

‫‪5‬‬
‫‪1‬‬
‫‪2‬‬
‫ ﻭ‬‫≤ ‪≤ b‬‬
‫≤‬
‫‪2‬‬
‫‪3‬‬
‫‪3‬‬

‫=‪b‬‬

‫; ‪a+b ; a - b ; 3a + 2b ; 2a - 3b‬‬

‫ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟﻠﻌﺒﺎﺭﺓ ‪. -2b+5‬‬

‫ﺃ‪-‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﻛﺘﺎﺑﺔ ﻣﺨﺘﺼﺮﺓ ﻟﻠﻌﺒﺎﺭﺓ ‪-2 b + 5 - b‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬

‫‪ x‬ﻭ ‪ y‬ﻋﺪﺩﺍﻥ ﺣﻴﺚ ‪ 2 ≤ x ≤ 3‬ﻭ ‪6 ≤ y ≤ 13‬‬

‫= ‪.E‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺘﺎﺳﻊ‪:‬‬

‫‪ a /1‬ﻋﺪﺩ ﺑﺤﻴﺚ ]‪a ∈ [ -1 ; 3‬‬

‫ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟﻜﻞ ﻋﺪﺩ ﻣﻦ ﺍﻷﻋﺪﺍﺩ ﺍﻟﺘﺎﻟﻴﺔ ‪:‬‬

‫‪2‬‬

‫‪x2‬‬
‫‪y+3‬‬

‫ﻭ ﺍﻟﻌﺒﺎﺭﺓ ‪E = 3a -6a-9‬‬

‫; ‪x.y ; 3x - 2y‬‬

‫‪.‬‬

‫ﺃ‪-‬‬
‫ﺏ‪-‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‪:‬‬

‫‪ x /1‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺑﺤﻴﺚ ‪2 ≤ x ≤ 5‬‬

‫ﻭ ‪Y = -3x2+6x+7‬‬

‫ﺑﻴﻦ ﺃﻥ ‪ Y=-3(x-1)2+10‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟــ ‪. Y‬‬

‫‪1‬‬
‫‪ /2‬ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ ‪ A‬ﺑﺤﻴﺚ‬
‫‪3‬‬

‫ﻋﻠﻤﺎ ﺃﻥ ‪≤ x ≤ 5‬‬

‫‪ A = 2x -‬ﺃﻭﺟﺪ ﺣﺼﺮ ﻟﻠﻌﺒﺎﺭﺓ ‪A‬‬

‫ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟـ )‪. (a-1‬‬
‫‪2‬‬

‫ﺕ‪-‬‬
‫ﺙ‪-‬‬

‫ﺍﺣﺴﺐ ﺇﺫﻥ )‪E + 3a(a-2‬‬

‫‪.‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﻌﺎﺷﺮ‪:‬‬

‫‪ a /1‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺑﺤﻴﺚ ]‪a ∈ [1 ; 5‬‬

‫‪.2‬‬

‫ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ‪a-3‬‬

‫ﺛﻢ ﺣﺼﺮﺍ ﻟـ‪. (a-3)2‬‬
‫‪ /2‬ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ )‪ . b= (a-2)(a-4‬ﺑﻴﻦ ﺃﻥ ‪ b= (a-3)2-1‬ﺛﻢ‬

‫‪.‬‬

‫ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ‪. b‬‬

‫‪ /3‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪−2 ≤ b-1 ≤ 2‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺩﺱ‪:‬‬

‫‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺑﺤﻴﺚ ‪-2 ≤ x ≤ 3‬‬

‫)‪(a-3)(b-1‬‬

‫‪ /1‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟــ ‪ (2x+5)2‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺃﻥ‬

‫‪-15 ≤ 2x 2 +10x-3 ≤ 45‬‬

‫‪Série F.B.A‬‬

‫‪2‬‬

‫ﺑﻴﻦ ﺃﻥ ‪ E = 3 ( a-1) -12‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟـ‪E‬‬

‫‪ /3‬ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ ‪ B‬ﺑﺤﻴﺚ ‪ B=-2x+5‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟــ‪ x‬ﻋﻠﻤﺎ ﺃﻥ‬

‫‪-7 ≤ B ≤ -4‬‬

‫ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ ‪. a-1‬‬

‫‪5‬‬

‫ﺛﻢ ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ‬

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‫ﺍﻟﻤﺠﺎﻻﺕ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ ‪:‬‬
‫ﺃﺑﺤﺚ ﻋﻦ ﺗﻘﺎﻁﻊ ﻭ ﺍﺗﺤﺎﺩ ﺍﻟﻤﺠﺎﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬
‫‪I ∩ J = .............................‬‬

‫]‪] -4 ; 5‬‬

‫‪A ∪ B = ..........................‬‬

‫‪A ∩ B = .............................‬‬

‫‪-  5 ; 3 ‬‬

‫‪M ∪ N = ..........................‬‬

‫‪M ∩ N = .............................‬‬

‫‪I ∪ J = .............................‬‬

‫]‬

‫=‪J‬‬

‫[‬

‫‪3‬‬

‫و‬
‫=‪B‬‬

‫;‪N= 1‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ ‪:‬‬

‫]‪[3;7‬‬

‫‪1/‬‬

‫=‪I‬‬

‫و ‪A =  2 ; 5 ‬‬
‫‪ -3‬‬
‫‪‬‬
‫‪ ‬و‪3/ M =  ; 10‬‬
‫‪4‬‬
‫‪‬‬
‫‪‬‬
‫‪2/‬‬

‫ﺃﻛﺘﺐ ﻋﻠﻰ ﺷﻜﻞ ﻣﺠﺎﻝ ﺃﻭ ﺍﺗﺤﺎﺩ ﻣﺠﺎﻻﺕ ﺍﻟﻤﺠﻤﻮﻋﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬
‫‪B = ................................‬‬

‫}‪-3 < x ≤ 5‬‬

‫‪D = ................................‬‬

‫‪‬‬
‫‪3‬‬
‫‪≥ x‬‬
‫‪2‬‬
‫‪‬‬

‫‪F = ................................‬‬

‫}‪-x‬‬

‫‪{x‬‬

‫; ‪; x ∈ ‬‬

‫‪3‬‬
‫‪≤ A = ..........‬‬
‫‪2‬‬

‫= ‪............... B‬‬

‫‪‬‬
‫; ‪................ D =  x ; x ∈ ‬‬
‫‪‬‬

‫‪2 ≥ C }= .........‬‬

‫= ‪................‬‬
‫; ‪F= {x ; x ∈ ‬‬
‫‪x‬‬

‫‪‬‬
‫‪∈ x‬و ‪A =  x ; x‬‬
‫‪‬‬

‫∈ ‪; x‬‬
‫‪ x‬و‬

‫‪{x‬‬

‫=‪C‬‬

‫=‬
‫∈ ‪E= {x ; x‬‬
‫‪ ‬و‬
‫‪x‬‬
‫‪x‬‬
‫‪E }= .........‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ ‪:‬‬
‫ﺃﺗﻤﻢ ﺑﺎﺳﺘﻌﻤﺎﻝ ﻣﺠﺎﻝ‪:‬‬
‫* ]‪ a ∈ [ -2 ; 4‬ﻳﻌﻨﻲ ‪-3a ∈ ...........................‬‬

‫]‪ a ∈ [1 ; 3‬ﻳﻌﻨﻲ ‪a-3 ∈ ...........................‬‬

‫‪1‬‬
‫‪ -1 -1 ‬‬
‫‪ a ∈  ; ‬ﻳﻌﻨﻲ ‪∈ ...........................‬‬
‫‪2‬‬
‫‪2 5‬‬

‫‪1‬‬
‫[∞‪ a ∈ ]1 ; +‬ﻳﻌﻨﻲ ‪- a+ 3 ∈ ...........................‬‬
‫‪2‬‬

‫*‬

‫‪-5a+‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ ‪:‬‬
‫ﻧﻌﺘﺒﺮ ﺍﻟﻤﺠﺎﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ ‪:‬‬

‫[∞ ‪[ 1 ; +‬‬

‫;‬

‫=‪K‬‬

‫[ ‪J = ]- ∞ ; -2‬‬

‫‪I =  -5 ; 3 ‬‬

‫;‬

‫‪ /1‬ﻣﺜﻞ ﻋﻠﻰ ﻧﻔﺲ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻌﺪﺩﻱ ﻛﻼ ﻣﻦ ‪ I‬ﻭ ‪ J‬ﻭ ‪. K‬‬
‫‪ /2‬ﺃﻭﺟﺪ ﺍﻟﻤﺠﻤﻮﻋﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫‪I ∩ ‬‬

‫;‬

‫‪I ∪ J‬‬

‫;‬

‫‪I ∩ K‬‬

‫‪J ∩ K‬‬

‫;‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ ‪:‬‬
‫‪3‬‬
‫‪4‬‬
‫;‬
‫‪ /1‬ﺭﺗﺐ ﺗﺼﺎﻋﺪﻳﺎ ﺍﻷﻋﺪﺍﺩ ‪; 6 ; 2,4‬‬
‫‪5‬‬
‫‪7‬‬
‫‪ /2‬ﻣﺜﻞ ﻋﻠﻰ ﻧﻔﺲ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻌﺪﺩﻱ ﺍﻟﻤﺠﺎﻻﺕ ‪ A‬ﻭ ‪ B‬ﻭ ‪ C‬ﺣﻴﺚ‬
‫‪ 3‬‬
‫‪‬‬
‫‪ 4‬‬
‫‪‬‬
‫‪A= ‬‬
‫‪; 2,4  ; C =  ¨- ∞ ; 6  ; B = ‬‬
‫‪; + ∞‬‬
‫‪ 5‬‬
‫‪‬‬
‫‪ 7‬‬
‫‪‬‬
‫‪ /3‬ﺃﻭﺟﺪ ﺍﻟﻤﺠﻤﻮﻋﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬
‫‪∩ C ; B ∩ C ; A ∩ B‬‬

‫ﺗﺮﺗﻴﺒﺎ ﺗﺼﺎﻋﺪﻳﺎ‬

‫‪Série F.B.A‬‬

‫‪6‬‬

‫‪+‬‬

‫‪‬‬

‫;‬

‫‪A ∪ C‬‬

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‫ﺍﻟﻤﺠﺎﻻﺕ ﺍﻟﺨﺎﺻﺔ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ ‪:‬‬
‫ﻓﻲ ﻛﻞ ﺣﺎﻟﺔ ﻣﻦ ﺍﻟﺤﺎﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ ﺍﺫﻛﺮ ﺇﻟﻰ ﺃﺃﻱ ﻣﺠﺎﻝ ﺃﻭ ﺍﺗﺤﺎﺩ ﻣﺠﺎﻻﺕ ﻳﻨﺘﻤﻲ ﺍﻟﻌﺪﺩ ﺍﻟﺤﻘﻴﻘﻲ ‪: x‬‬

‫‪1‬‬
‫‪2‬‬

‫ ≤ ‪4°) 2x-3‬‬‫‪3‬‬
‫‪2‬‬

‫‪3°) 2x-1 ≤ 5‬‬
‫‪1‬‬
‫‪2‬‬

‫‪8°) 2- x ≤ -‬‬

‫‪x ≥3‬‬

‫‪7°) x − 4 ≤ -‬‬

‫)‪2°‬‬

‫‪1°) x < 5‬‬

‫‪6°) 1 ≤ x ≤ 3‬‬

‫‪5°) 1-3x >2‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ ‪:‬‬

‫‪ /1‬ﻟﻴﻜﻦ ﺍﻟﻌﺪﺩ ‪ x‬ﺑﺤﻴﺚ ‪-2x+3 ≤ 3‬‬

‫ﺇﻟﻰ ﺃﻱ ﻣﺠﺎﻝ ﻳﻨﺘﻤﻲ ﺍﻟﻌﺪﺩ ‪. x‬‬

‫‪1‬‬
‫‪5‬‬
‫‪ /2‬ﻟﻴﻜﻦ ﺍﻟﻌﺪﺩ ‪ y‬ﺑﺤﻴﺚ‬
‫< ‪≤ y‬‬
‫‪2‬‬
‫‪3‬‬
‫‪4‬‬

‫‪1‬‬

‫ﺇﻟﻰ ﺃﻱ ﻣﺠﺎﻝ ﻳﻨﺘﻤﻲ ﺍﻟﻌﺪﺩ ‪. y‬‬

‫‪‬‬

‫ ‪ . x ∈ ‬ﻭ ﺍﻟﻌﺒﺎﺭﺓ ‪ A‬ﺑﺤﻴﺚ‬‫‪ x /3‬ﻫﻮ ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺑﺤﻴﺚ ‪; ‬‬
‫‪3‬‬
‫‪ 3‬‬

‫‪8‬‬
‫ﺃ‪ -‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟﻜﻞ ﻣﻦ ﺍﻟﻌﺪﺩﻳﻦ ‪ -3 x+4‬ﻭ‬
‫‪3‬‬

‫ﺏ‪ -‬ﺑﻴﻦ ﺃﻥ ‪2 − 1‬‬

‫‪8‬‬
‫‪3‬‬

‫‪A= -3x+4 - 2x-‬‬

‫‪2x -‬‬

‫‪4‬‬

‫‪1‬‬

‫‪‬‬

‫‪. ‬‬‫ﻳﻨﺘﻤﻲ ﺇﻟﻰ ﺍﻟﻤﺠﺎﻝ ‪; ‬‬
‫‪3‬‬
‫‪ 3‬‬

‫ﺝ‪ -‬ﺃﻋﻂ ﻛﺘﺎﺑﺔ ﻣﺨﺘﺼﺮﺓ )ﺑﺪﻭﻥ ﻋﻼﻣﺔ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﻄﻠﻘﺔ ( ﻟﻠﻌﺒﺎﺭﺓ ‪. A‬‬

‫ﺩ‪ -‬ﺃﻭﺟﺪ ﺇﺫﻥ ﻗﻴﻤﺔ ﺍﻟﻌﺒﺎﺭﺓ ‪ A‬ﺇﺫﺍ ﻛﺎﻥ ‪2 − 1‬‬

‫=‪.x‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ ‪:‬‬

‫‪ /1‬ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺓ ‪ A‬ﺑﺤﻴﺚ ‪x + 2 - x - 1‬‬

‫= ‪.A‬‬

‫ﺃ‪-‬‬

‫ﺍﺣﺴﺐ ‪ A‬ﺇﺫﺍ ﻛﺎﻥ [ ‪] -2 ; 1‬‬

‫ﺏ‪-‬‬

‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪ A‬ﺇﺫﺍ ﻛﺎﻥ [ ‪] -∞ ; -2‬‬

‫∈ ‪x‬‬

‫∈‬

‫‪.x‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ ‪:‬‬

‫‪2x‬‬
‫‪ 2‬‬
‫‪‬‬
‫‪ /1‬ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺓ ‪ A‬ﺑﺤﻴﺚ ‪ E = x +2‬ﺣﻴﺚ ‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﻳﻨﺘﻤﻲ ﺇﻟﻰ ﺍﻟﻤﺠﺎﻝ ﺍﻟﻤﻐﻠﻖ‪ - 3 ; 2  .‬‬
‫ﺃ‪-‬‬

‫‪4‬‬
‫ﺑﻴﻦ ﺃﻥ ‪≤ x + 2 ≤ 4‬‬
‫‪3‬‬
‫‪4‬‬
‫‪ /2‬ﺗﺤﻘﻖ ﺃﻥ‬
‫‪x +2‬‬

‫‪ /3‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪E ≤ 1‬‬

‫‪Série F.B.A‬‬

‫‪1‬‬
‫ﺏ ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟـ‬
‫‪x+2‬‬

‫‪. E=2-‬‬

‫‪.‬‬

‫‪7‬‬

‫‪.‬‬

‫‪-4‬‬
‫ﺝ ‪ -‬ﺑﻴﻦ ﺃﻥ ‪≤ -1‬‬
‫‪x+2‬‬

‫≤ ‪−3‬‬

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‫ﺍﻟﻤﺘﺮﺍﺟﺤﺎﺕ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﺘﺮﺍﺟﺤﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ ‪:‬‬

‫‪x-3‬‬
‫‪2-3x‬‬
‫≥‬
‫‪3‬‬
‫‪2‬‬
‫‪x‬‬
‫‪3+x‬‬
‫≥ ‪6/ +1‬‬
‫‪-x‬‬
‫‪2‬‬
‫‪2‬‬
‫‪9/ - 2 x + 3 ≤ 0‬‬
‫‪3/‬‬

‫‪1 - x - 4 ≤ -3‬‬

‫‪5‬‬
‫‪3‬‬

‫)‪2/ 3 ( 2x-1)-5x ≤ 4x - 2 ( x+1‬‬

‫‪1/ 4 ( x - 3 ) ≤ 2 x - 6‬‬

‫‪5/‬‬

‫) ‪4 / 3 ( x 3 - 2 ) ≤ x 3 ( 3-1‬‬

‫‪8/ x ( x+ 1 ) ≤ ( x+2) 2‬‬

‫‪7/4 2 x - 2 2 ≥ 6 x + 3‬‬

‫‪11/ 9 9-x‬‬

‫‪10 / 2x − 3 ≤ 1‬‬

‫‪5 x - 13 3 x+1‬‬
‫‪5x-3‬‬
‫‬‫≥‬
‫‪3‬‬
‫‪2‬‬
‫‪2‬‬

‫‪≤ 5‬‬

‫‪12 /‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺓ ‪ E‬ﺑﺤﻴﺚ ‪. E = 4x2-5x+1‬‬

‫‪5 2 9‬‬
‫‪ /1‬ﺑﻴﻦ ﺃﻥ‬
‫ )‬‫‪4‬‬
‫‪16‬‬

‫‪. E = (2x -‬‬

‫‪ /2‬ﺍﺳﺘﻨﺘﺞ ﺗﻔﻜﻴﻜﺎ ﺇﻟﻰ ﺟﺬﺍء ﻋﻮﺍﻣﻞ ﻟﻠﻌﺒﺎﺭﺓ ‪. E‬‬
‫‪ /3‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪. E=0‬‬
‫‪2‬‬

‫‪ /4‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪. E – 4 x < -14‬‬

‫‪ /5‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪5 4x − 5‬‬
‫= ‪ . - 4x +‬ﻭ ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪(x − 1) 2 ≤ 5‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ ‪:‬‬

‫= ‪- 4x +‬‬
‫‪ /1‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪5 4x − 5‬‬

‫‪.‬‬

‫‪ /2‬ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺓ ‪. A = (3x-1)2-(5-2x)2‬‬
‫ﺃ‪-‬‬

‫ﺑﻴﻦ ﺃﻥ )‪.A = (5x-6) (x+4‬‬

‫ﺏ‪ -‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪ A=0‬ﻭ ﺍﻟﻤﻌﺎﺩﻟﺔ )‪. A = ( x+4‬‬
‫ﺝ‪ -‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪. 5 x2 – A < 0‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ ‪:‬‬
‫ﻟﺘﻜﻦ ﺍﻟﻤﺘﺮﺍﺟﺤﺘﺎﻥ ﺍﻟﺘﺎﻟﻴﺘﺎﻥ‪:‬‬

‫)‪2 − 1)(x 2 + 1) + (x-1) 2 < 3x ( x-2‬‬

‫‪( II ) : (x‬‬

‫‪2x-1‬‬
‫‪2 2+x‬‬
‫≤ ‪-x + 2‬‬
‫‪3‬‬
‫‪2‬‬

‫‪(I ) :‬‬

‫‪ /1‬ﺣﻞ ﻓﻲ ‪ IR‬ﻛﻞ ﻣﻦ ﺍﻟﻤﺘﺮﺍﺟﺤﺘﻴﻦ )‪ (I‬ﻭ )‪. (II‬‬
‫‪ /2‬ﻣﺜﻞ ﻣﺠﻤﻮﻋﺔ ﺣﻠﻮﻝ ﺍﻟﻤﺘﺮﺍﺟﺤﺘﻴﻦ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻌﺪﺩﻱ ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﻣﺠﻤﻮﻋﺔ ﺍﻟﺤﻠﻮﻝ ﺍﻟﻤﺸﺘﺮﻛﺔ ﻟﻠﻤﺘﺮﺍﺟﺤﺘﻴﻦ‪.‬‬

‫‪ /3‬ﺃﺛﺒﺖ ﺃﻥ ﺍﻟﻌﺪﺩ ‪3 − 2‬‬

‫‪ /4‬ﻫﻞ ﺃﻥ ﺍﻟﻌﺪﺩ ‪1 − 2‬‬

‫‪Série F.B.A‬‬

‫ﻫﻮ ﺣﻞ ﻣﺸﺘﺮﻙ ﻟﻠﻤﺘﺮﺍﺟﺤﺘﻴﻦ‪.‬‬
‫ﺣﻞ ﻣﺸﺘﺮﻙ ﻟﻠﻤﺘﺮﺍﺟﺤﺘﻴﻦ ؟‬

‫‪8‬‬

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‫ﺍﻹﺣﺘﻤﺎﻻﺕ‬
‫ﺣﺴﺎﺏ ﺍﻟﻌﺪﺩ ﺍﻟﺠﻤﻠﻲ ﻟﻺﻣﻜﺎﻧﻴﺎﺕ ﺃﺳﺘﻌﻴﻦ ﺑﺸﺠﺮﺓ ﺍﻻﺧﺘﻴﺎﺭ‪.‬‬
‫‪2‬‬

‫‪3‬‬

‫* ﻋﻨﺪﻣﺎ ﻳﻜﻮﻥ ﺍﻟﺴﺤﺐ ﻣﺘﺘﺎﻟﻲ ﻣﻊ ﺍﻹﺭﺟﺎﻉ ﻓﺈﻥ ﺍﻟﻌﺪﺩ ﺍﻟﺠﻤﻠﻲ ﻹﻣﻜﺎﻧﻴﺎﺕ ﺍﻟﺴﺤﺐ ﻫﻮ ‪ n‬ﺇﺫﺍ ﺳﺤﺒﻨﺎ ﻋﻨﺼﺮﻳﻦ ﻭ ‪ n‬ﺇﺫﺍ ﺳﺤﺒﻨﺎ ‪.3‬‬
‫* ﻋﻨﺪﻣﺎ ﻳﻜﻮﻥ ﺍﻟﺴﺤﺐ ﻣﺘﺘﺎﻟﻲ ﺑﺪﻭﻥ ﺍﻹﺭﺟﺎﻉ ﻓﺈﻥ ﺍﻟﻌﺪﺩ ﺍﻟﺠﻤﻠﻲ ﻹﻣﻜﺎﻧﻴﺎﺕ ﺍﻟﺴﺤﺐ ﻫﻮ)‪n (n-1‬ﺇﺫﺍ ﺳﺤﺒﻨﺎ ﻋﻨﺼﺮﻳﻦ ﻭ)‪n (n-1)(n-2‬ﺇ‬
‫ﺇﺫﺍ ﺳﺤﺒﻨﺎ ‪.3‬‬
‫* ﻳﻜﻮﻥ ﺍﻟﺤﺪﺙ ﺃﻛﻴﺪﺍ ﺇﺫﺍ ﻛﺎﻥ ﺍﺣﺘﻤﺎﻟﻪ ﻣﺴﺎﻭ ﻟــ ‪1‬‬

‫* ﻳﻜﻮﻥ ﺍﻟﺤﺪﺙ ﻣﺴﺘﺤﻴﻼ ﺇﺫﺍ ﻛﺎﻥ ﺍﺣﺘﻤﺎﻟﻪ ﻣﺴﺎﻭ ﻟــ ‪0‬‬

‫* ﻳﻜﻮﻥ ﺍﻟﺤﺪﺙ ﻣﻤﻜﻨﺎ ﺇﺫﺍ ﻛﺎﻥ ﺍﺣﺘﻤﺎﻟﻪ ﺃﻛﺒﺮ ﻣﻦ ‪.0‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫ﺻﻨﺪﻭﻕ ﻳﺤﺘﻮﻱ ﻋﻠﻰ ‪ 20‬ﻗﺮﺻﺎ ﻳﺤﻤﻞ ﻛﻞ ﻗﺮﺹ ﻣﻨﻪ ﻋﺪﺩﺍ ﻣﻦ ‪ 1‬ﺇﻟﻰ ‪20‬‬
‫ﻧﻌﺘﺒﺮ ﺍﻟﺘﺠﺮﺑﺔ ﺍﻟﺘﺎﻟﻴﺔ‪ :‬ﻧﺴﺤﺐ ﻗﺮﺻﺎ ﺑﺼﻔﺔ ﻋﺸﻮﺍﺋﻴﺔ ﺛﻢ ﻧﻌﻴﺪﻩ ﺇﻟﻰ ﺍﻟﺼﻨﺪﻭﻕ ﻗﺒﻞ ﺍﻟﺴﺤﺐ ﺍﻟﺜﺎﻧﻲ‪.‬‬
‫‪ (1‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻗﺮﺹ ﻋﺪﺩﻩ ‪.13‬‬
‫‪ (2‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻗﺮﺹ ﻋﺪﺩﻩ ﺯﻭﺟﻲ‪.‬‬
‫‪ (3‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻗﺮﺹ ﻋﺪﺩﻩ ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﻠﻰ ‪.3‬‬
‫‪ (4‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻗﺮﺹ ﻋﺪﺩﻩ ﺃﻭﻟﻲ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫ﺑﻤﺤﻔﻈﺔ ﻋﻠﻲ ‪ 8‬ﻣﻠﻔﺎﺕ ‪ 3 ،‬ﺯﺭﻗﺎء ﻭ ‪ 5‬ﺧﻀﺮﺍء‪ .‬ﻳﺴﺤﺐ ﻋﻠﻲ ﻣﻠﻔﻴﻦ ﺍﻟﻮﺍﺣﺪ ﺗﻠﻮ ﺍﻵﺧﺮ ﺩﻭﻥ ﺍﻟﻨﻈﺮ ﺇﻟﻴﻬﻤﺎ ﻭ ﻓﻲ ﻛﻞ ﻣﺮﺓ ﻳﺮﺟﻊ ﺍﻟﻤﻠﻒ‬
‫ﺍﻟﻤﺴﺤﻮﺏ‪.‬‬
‫‪ (1‬ﻣﺎ ﻫﻮ ﻋﺪﺩ ﺇﻣﻜﺎﻧﻴﺎﺕ ﺍﻟﺴﺤﺐ؟‬
‫‪ (2‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻣﻠﻔﻴﻦ ﺯﺭﻗﺎﻭﻳﻦ‪.‬‬
‫‪ (3‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻣﻠﻔﻴﻦ ﺧﻀﺮﺍﻭﻳﻦ؟‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬
‫ﺭﻣﻰ ﻋﻤﺮ ﻣﺮﺓ ﻭﺍﺣﺪﺓ ﻧﺮﺩﺍ ﻳﺤﻤﻞ ﺃﻭﺟﻪ ﻣﺮﻗﻤﺔ ﻣﻦ ‪ 1‬ﺇﻟﻰ ‪ 6‬ﻭ ﺳﺠﻞ ﺭﻗﻤﻪ ﺍﻟﻔﻮﻗﻲ‪.‬‬
‫‪ (1‬ﺃ‪ -‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺭﻗﻢ ‪6‬؟‬
‫ﺏ‪ -‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﻋﺪﻡ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺭﻗﻢ ‪6‬؟‬
‫‪ (2‬ﻗﺎﻡ ﻋﻤﺮ ﺑﺮﻣﻲ ﻫﺬﺍ ﺍﻟﻨﺮﺩ ﻣﺮﺗﻴﻦ ﻣﺘﺘﺎﻟﻴﺘﻴﻦ ﻭ ﺳﺠﻞ ﺍﻟﺮﻗﻢ ﺍﻟﻔﻮﻗﻲ ﻓﻲ ﻛﻞ ﻣﺮﺓ‪.‬‬
‫ﺃ‪ -‬ﺣﺪﺩ ﻣﺠﻤﻮﻋﺔ ﺍﻟﻨﺘﺎﺋﺞ ﺍﻟﻤﻤﻜﻨﺔ ﻟﻬﺬﻩ ﺍﻟﺘﺠﺮﺑﺔ ﺍﻟﻌﺸﻮﺍﺋﻴﺔ ) ﺗﻜﻮﻳﻦ ﺟﺪﻭﻝ(‪.‬‬
‫ﺏ‪ -‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺭﻗﻤﻴﻦ ﻣﺠﻤﻮﻋﻬﻤﺎ ﻳﺴﺎﻭﻱ ‪8‬؟‬
‫ﺝ‪ -‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺭﻗﻤﻴﻦ ﻣﺠﻤﻮﻋﻬﻤﺎ ﺃﺻﻐﺮ ﺃﻭ ﻳﺴﺎﻭﻱ ‪12‬؟‬
‫ﺩ‪ -‬ﺣﺪﺩ ﺣﺪﺛﺎ ﺍﺣﺘﻤﺎﻝ ﺣﺼﻮﻟﻪ ﻣﺴﺘﺤﻴﻞ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‪:‬‬
‫‪ (1‬ﺑﻮﺍﺳﻄﺔ ﺍﻷﺭﻗﺎﻡ ‪ 5،6،7‬ﺃﻭﺟﺪ ﻛﻞ ﺍﻟﻄﺮﻕ ﺍﻟﻤﻤﻜﻨﺔ ﻟﻠﺤﺼﻮﻝ ﻋﻠﻰ‪:‬‬
‫ﺃ* ﺍﻟﻤﺠﻤﻮﻋﺔ ‪ A‬ﻟﻜﻞ ﻋﺪﺩ ﺫﻱ ﺭﻗﻤﻴﻦ ﻣﺨﺘﻠﻔﻴﻦ ﺛﻢ ﺍﺣﺴﺐ ﻛﻢ )‪. (A‬‬
‫ﺏ* ﺍﻟﻤﺠﻤﻮﻋﺔ ‪ B‬ﻟﻜﻞ ﻋﺪﺩ ﺫﻱ ﺭﻗﻤﻴﻦ ﻣﺨﺘﻠﻔﻴﻦ ﺃﻭ ﻣﺘﺴﺎﻭﻳﻴﻦ ﺛﻢ ﺍﺣﺴﺐ ﻛﻢ )‪. (B‬‬
‫‪ (2‬ﺃ‪ -‬ﺃﻭﺟﺪ ﺍﻟﻤﺠﻤﻮﻋﺔ ‪ C‬ﻟﻸﻋﺪﺍﺩ ﺍﻟﺘﻲ ﻳﻤﻜﻦ ﺗﻜﻮﻳﻨﻬﺎ ﺑﺎﺳﺘﻌﻤﺎﻝ ﺍﻷﺭﻗﺎﻡ ‪ 5‬ﻭ ‪ 6‬ﻭ ‪ 7‬ﺣﺪﺩ ﻛﻢ )‪. (C‬‬
‫ﺏ‪ -‬ﺣﺪﺩ ﺍﻟﺤﺪﺙ ﺍﻟﺘﺎﻟﻲ‪ " :‬ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﻋﺪﺩ ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﻠﻰ ‪ "12‬ﺃﻭﺟﺪ ﺍﺣﺘﻤﺎﻝ ﻫﺬﺍ ﺍﻟﺤﺪﺙ‬
‫ﺝ‪ -‬ﺣﺪﺩ ﺍﻟﺤﺪﺙ ‪ N‬ﺍﻟﺘﺎﻟﻲ‪ " :‬ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﻋﺪﺩ ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﻠﻰ ‪ " 9‬ﺃﻭﺟﺪ ﺍﺣﺘﻤﺎﻝ ﻫﺬﺍ ﺍﻟﺤﺪﺙ‪ .‬ﻣﺎ ﻧﻮﻉ ﻫﺬﺍ ﺍﻟﺤﺪﺙ؟‬
‫ﺩ‪ -‬ﺣﺪﺩ ﺍﻟﺤﺪﺙ ‪ P‬ﺍﻟﺘﺎﻟﻲ‪ " :‬ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﻋﺪﺩ ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﻠﻰ ‪ "50‬ﺃﻭﺟﺪ ﺍﺣﺘﻤﺎﻝ ﻫﺬﺍ ﺍﻟﺤﺪﺙ‪ .‬ﻣﺎ ﻧﻮﻉ ﻫﺬﺍ ﺍﻟﺤﺪﺙ؟‬

‫‪Série F.B.A‬‬

‫‪9‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‪:‬‬
‫ﻟﺰﻳﻨﺐ ﻋﻠﺒﺔ ﺑﻬﺎ ‪ 5‬ﻛﻮﻳﺮﺍﺕ ﺣﻤﺮﺍء ﻭ ‪ 3‬ﺑﻴﻀﺎء ﻭ ‪ 12‬ﻏﻴﺮ ﻣﻠﻮﻧﺔ ﺳﺤﺒﺖ ﻣﻨﻬﺎ ﺯﻳﻨﺐ ﻛﻮﻳﺮﺓ ﺑﻄﺮﻳﻘﺔ ﻋﺸﻮﺍﺋﻴﺔ‪.‬‬
‫‪ /1‬ﻣﺎﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻜﻮﻳﺮﺓ ﺍﻟﻤﺴﺤﻮﺑﺔ ﺣﻤﺮﺍء؟‪.‬‬
‫‪ /2‬ﻣﺎﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻜﻮﻳﺮﺓ ﺍﻟﻤﺴﺤﻮﺑﺔ ﻣﻠﻮﻧﺔ؟‬
‫‪ /3‬ﻣﺎﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻜﻮﻳﺮﺓ ﺍﻟﻤﺴﺤﻮﺑﺔ ﻏﻴﺮ ﻣﻠﻮﻧﺔ‪.‬‬
‫‪ /4‬ﻋﻠﻤﺎ ﺃﻥ ﻓﻲ ﺍﻟﻌﻠﺒﺔ ‪ 4‬ﺣﻤﺮﺍء ﺗﺤﻤﻞ ﻛﻞ ﻣﻨﻬﺎ ﺭﻗﻢ ‪ 0‬ﻭ ‪ 10‬ﻛﻮﻳﺮﺍﺕ ﻏﻴﺮ ﻣﻠﻮﻧﺔ ﺗﺤﻤﻞ ﺭﻗﻢ ‪ 2‬ﻭ ﺍﻟﺒﻘﻴﺔ ﺗﺤﻤﻞ ﺭﻗﻢ‪.1‬‬
‫ﺃ‪-‬‬

‫ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻜﺮﺓ ﺍﻟﻤﺴﺤﻮﺑﺔ ﺣﻤﺮﺍء ﻭ ﺗﺤﻤﻞ ﺭﻗﻢ ‪0‬؟‬

‫ﺏ‪ -‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻜﺮﺓ ﺍﻟﻤﺴﺤﻮﺑﺔ ﺣﻤﺮﺍء ﻭ ﺗﺤﻤﻞ ﺭﻗﻤﺎ ﻓﺮﺩﻳﺎ؟‬
‫ﺕ‪ -‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻜﺮﺓ ﺍﻟﻤﺴﺤﻮﺑﺔ ﻏﻴﺮ ﻣﻠﻮﻧﺔ ﻭ ﺗﺤﻤﻞ ﺭﻗﻢ ‪1‬؟‬
‫ﺙ‪ -‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻜﺮﺓ ﺍﻟﻤﺴﺤﻮﺑﺔ ﺗﺤﻤﻞ ﺭﻗﻢ ﺯﻭﺟﻴﺎ؟‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺩﺱ‪:‬‬
‫ﻛﻴﺲ ﺑﻪ ‪ 5‬ﻛﻮﻳﺮﺍﺕ ‪ 3‬ﺑﻴﻀﺎء ﻣﺮﻗﻤﺔ ‪. B3 ، B2 ، B1‬ﻭ ‪ 2‬ﺳﻮﺩﺍء ‪ N1‬ﻭ ‪. N2‬‬
‫ﻧﺴﺤﺐ ﻣﻦ ﺍﻟﻜﻴﺲ ﻛﺮﺗﻴﻦ ﺍﻟﻮﺍﺣﺪﺓ ﺗﻠﻮ ﺍﻷﺧﺮﻯ ﺩﻭﻥ ﺇﺭﺟﺎﻉ ﺍﻟﻜﻮﻳﺮﺓ ﺍﻷﻭﻟﻰ‪.‬‬
‫‪ (1‬ﺍﺫﻛﺮ ﺟﻤﻴﻊ ﺍﻟﻨﺘﺎﺋﺞ‪.‬‬
‫‪ (2‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﻛﻞ ﺣﺪﺙ ﻣﻦ ﺍﻷﺣﺪﺍﺙ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬
‫‪ : A‬ﻧﺘﺤﺼﻞ ﻋﻠﻰ ﻛﺮﺗﻴﻦ ﻣﻦ ﻧﻔﺲ ﺍﻟﻠﻮﻥ‪.‬‬
‫‪ :B‬ﻧﺘﺤﺼﻞ ﻋﻠﻰ ﻛﺮﺗﻴﻦ ﻣﻦ ﻧﻔﺲ ﺍﻟﺮﻗﻢ‪.‬‬
‫‪ : C‬ﻧﺘﺤﺼﻞ ﻋﻠﻰ ﻛﺮﺗﻴﻦ ﺑﻠﻮﻧﻴﻦ ﻣﺨﺘﻠﻔﻴﻦ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺑﻊ‪:‬‬
‫ﻧﺮﻣﻲ ﻧﺮﺩﻳﻦ ﻣﺘﺸﺎﺑﻬﻴﻦ ﻳﺤﻤﻼﻥ ﺃﻭﺟﻪ ﻣﺮﻗﻤﺔ ﻣﻦ ‪ 1‬ﺇﻟﻰ ‪ 6‬ﻭ ﻓﻲ ﻛﻞ ﻣﺮﺓ ﻧﺴﺠﻞ ﺍﻟﻔﺎﺭﻕ ﺑﻴﻦ ﺍﻟﺮﻗﻤﻴﻦ ﺍﻟﻤﺘﺤﺼﻞ ﻋﻠﻴﻬﻤﺎ‪.‬‬
‫‪ (1‬ﺍﺫﻛﺮ ﺟﻤﻴﻊ ﺍﻟﻨﺘﺎﺋﺞ ﺍﻟﻤﻤﻜﻨﺔ‪.‬‬
‫‪ (2‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺭﻗﻤﻴﻦ ﻳﻜﻮﻥ ﺍﻟﻔﺎﺭﻕ ﺑﻴﻨﻬﻤﺎ ﻋﺪﺩﺍ ﺯﻭﺟﻴﺎ‪.‬‬
‫‪ (3‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺭﻗﻤﻴﻦ ﻳﻜﻮﻥ ﺍﻟﻔﺎﺭﻕ ﺑﻴﻨﻬﻤﺎ ﺃﻛﺒﺮ ﻣﻦ ‪. 6‬‬
‫‪ (4‬ﻧﻌﺘﺒﺮ ﺍﻟﺤﺪﺙ ‪ . A‬ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﻓﺎﺭﻕ ﻗﺎﺑﻞ ﻟﻠﻘﺴﻤﺔ ﻋﻠﻰ ‪ 3‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﻭﻗﻮﻉ ﺍﻟﺤﺪﺙ ‪. A‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻣﻦ‪:‬‬
‫‪ ( I‬ﺃﺗﻤﻢ ﺑﺼﻮﺍﺏ ﺃﻭ ﺧﻄﺄ‪:‬‬
‫‪2‬‬
‫‪ (1‬ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻛﻮﻳﺮﺓ ﺑﻴﻀﺎء ﻣﻦ ﺍﻟﺼﻨﺪﻭﻕ ﺍﻟﻤﻘﺎﺑﻞ ﻫﻮ‬
‫‪3‬‬

‫‪......................... :‬‬

‫‪ (2‬ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻛﻮﻳﺮﺓ ﺳﻮﺩﺍء ﻣﻦ ﺍﻟﺼﻨﺪﻭﻕ ﺍﻟﻤﻘﺎﺑﻞ ﻫﻮ ‪.........................: 2‬‬

‫‪ (II‬ﺑﺼﻨﺪﻭﻕ ‪ 3‬ﻗﺮﻳﺼﺎﺕ ﻳﺤﻤﻠﻦ ﺍﻷﻋﺪﺍﺩ ‪3‬‬

‫ﻭ ‪ -3‬ﻭ ‪-2‬‬

‫ﻟﻨﻌﺘﺒﺮ ﺍﻟﺘﺠﺮﺑﺔ ﺍﻟﻌﺸﻮﺍﺋﻴﺔ ‪ :‬ﺳﺤﺐ ﻣﺘﺘﺎﻟﻲ ﻟﻘﺮﺻﻴﻦ ﻣﻊ ﺇﺭﺟﺎﻉ‬
‫ﺍﻟﻘﺮﺹ ﺍﻷﻭﻝ ﻭ ﺍﻹﻫﺘﻤﺎﻡ ﺑﺠﺬﺍء ﺍﻟﻌﺪﺩﻳﻦ ﺍﻟﻤﺘﺤﺼﻞ ﻋﻠﻴﻬﻤﺎ‪.‬‬
‫‪ (1‬ﻣﺎ ﻫﻲ ﺇﻣﻜﺎﻧﻴﺎﺕ ﺍﻟﺴﺤﺐ‪ ) .‬ﺍﺭﺳﻢ ﺷﺠﺮﺓ ﺍﻻﺧﺘﻴﺎﺭ(‪.‬‬
‫‪ (2‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺟﺬﺍء ﺻﺤﻴﺢ ﻁﺒﻴﻌﻲ‪.‬‬
‫‪ (3‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ ﺟﺬﺍء ﺳﺎﻟﺐ‪.‬‬
‫‪ (4‬ﺃﻋﻂ ﻣﺜﺎﻻ ﻟﺤﺪﺙ ﻣﺴﺘﺤﻴﻞ ﻭ ﻣﺜﺎﻻ ﻟﺤﺪﺙ ﺃﻛﻴﺪ‪.‬‬

‫‪Série F.B.A‬‬

‫‪10‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺃﻧﺸﻄﺔ ﺣﻮﻝ ﺍﻟﺮﺑﺎﻋﻴﺎﺕ‬
‫ﻫﺎﻡ‪:‬‬

‫ﺭﺑﺎﻋﻲ‬
‫ﻟﻪ ﺿﻠﻌﺎﻥ ﻣﺘﻘﺎﺑﻼﻥ‬
‫ﻣﺘﻘﺎﻳﺴﺎﻥ ﻭ ﺣﺎﻣﻼﻫﻤﺎ‬
‫ﻣﺘﻮﺍﺯﻳﺎﻥ‬

‫ﻟﻪ ﻗﻄﺮﺍﻥ ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ‬
‫ﺍﻟﻤﻨﺘﺼﻒ‬

‫ﺃﺿﻼﻋﻪ ﺍﻟﻤﺘﻘﺎﺑﻠﺔ‬
‫ﻣﺘﻘﺎﻳﺴﺔ‬

‫ﺯﻭﺍﻳﺎﻩ ﺍﻟﻤﺘﻘﺎﺑﻠﺔ‬
‫ﻣﺘﻘﺎﻳﺴﺔ‬

‫ﺃﺿﻼﻋﻪ ﺍﻟﻤﺘﻘﺎﺑﻠﺔ‬
‫ﻣﺘﻮﺍﺯﻳﺔ‬

‫ﻣﺘﻮﺍﺯﻱ ﺍﻷﺿﻼﻉ‬
‫ﻟﻪ ﻗﻄﺮﺍﻥ‬
‫ﻣﺘﻘﺎﻳﺴﺎﻥ‬

‫ﻟﻪ ﺯﺍﻭﻳﺔ ﻗﺎﺋﻤﺔ‬

‫ﺭﺑﺎﻋﻲ ﻟﻪ ‪4‬‬
‫ﺃﺿﻼﻉ ﻣﺘﻘﺎﻳﺴﺔ‬

‫ﺭﺑﺎﻋﻲ ﻟﻪ ‪3‬‬
‫ﺯﻭﺍﻳﺎ ﻗﺎﺋﻤﺔ‬

‫ﻟﻪ ﻗﻄﺮﺍﻥ‬
‫ﻣﺘﻌﺎﻣﺪﺍﻥ‬

‫ﻣﻌﻴﻦ‬

‫ﻣﺴﺘﻄﻴﻞ‬

‫ﻟﻪ ﻗﻄﺮﺍﻥ ﻣﺘﻌﺎﻣﺪﺍﻥ‬

‫ﻟﻪ ﺿﻠﻌﺎﻥ ﻣﺘﺘﺎﻟﻴﺎﻥ‬
‫ﻣﺘﻘﺎﻳﺴﺎﻥ‬

‫ﻟﻪ ﺿﻠﻌﺎﻥ ﻣﺘﺘﺎﻟﻴﺎﻥ‬
‫ﻣﺘﻘﺎﻳﺴﺎﻥ‬

‫ﻗﻄﺮﺍﻩ ﻣﺘﻘﺎﻳﺴﺎﻥ‬

‫ﻟﻪ ﺯﺍﻭﻳﺔ ﻗﺎﺋﻤﺔ‬

‫ﻣﺮﺑﻊ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫‪ (1‬ﻟﻴﻜﻦ )‪ (O,I,J‬ﻣﻌﻴﻨﺎ ﻓﻲ ﺍﻟﻤﺴﺘﻮﻱ ﺣﻴﺚ )‪ (OJ) ⊥ (OI‬ﻭ ‪.OI=OJ=1‬ﻭ ﺍﻟﻨﻘﺎﻁ )‪ A(-3,0‬ﻭ )‪ B(2,0‬ﻭ )‪ C(0,-4‬ﺍﺣﺴﺐ ‪ AB‬ﻭ ‪AC‬‬
‫ﻭ ‪ BC‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﻁﺒﻴﻌﺔ ﺍﻟﻤﺜﻠﺚ ‪. ABC‬‬
‫‪ (2‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ D‬ﺣﻴﺚ ‪ A‬ﻣﻨﺘﺼﻒ ]‪ .[DC‬ﺣﺪﺩ ﺇﺣﺪﺍﺛﻴﺎﺕ ‪ D‬ﺛﻢ ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ BCD‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‪.‬‬
‫‪ (3‬ﺍﺑﻦ ‪ E‬ﻣﻨﺎﻅﺮﺓ ‪ B‬ﺑﺎﻟﻨﺴﺒﺔ ﺇﻟﻰ ‪ A‬ﺛﻢ ﺑﻴﻦ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ BCED‬ﻣﺴﺘﻄﻴﻞ‪.‬‬
‫‪ (4‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ M‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟـ‪ A‬ﻋﻠﻰ )‪ (BD‬ﻭ ﺍﻟﻨﻘﻄﺔ ‪ F‬ﺣﻴﺚ ‪ M‬ﻣﻨﺘﺼﻒ ]‪ .[AF‬ﺑﻴﻦ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ ADFB‬ﻣﻌﻴﻦ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫‪ /1‬ﺍﺭﺳﻢ ﻣﺴﺘﻄﻴﻼ ‪ ABCD‬ﻣﺮﻛﺰﻩ ‪ O‬ﺣﻴﺚ ‪AB = 6‬ﻭ ‪ AD = 3‬ﻭﺍﺣﺴﺐ ‪.BD‬‬
‫‪ /2‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ E‬ﻣﻨﺘﺼﻒ ]‪ .[AB‬ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (EC‬ﻳﻘﻄﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (AD‬ﻓﻲ ‪ F‬ﻭ ﻳﻘﻄﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (BD‬ﻓﻲ ‪. I‬‬
‫ﺃ‪-‬‬

‫ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ )‪ (AF‬ﻭ )‪ (OE‬ﻣﺘﻮﺍﺯﻳﺎﻥ ﻭ ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪ E‬ﻣﻨﺘﺼﻒ ]‪.[CF‬‬

‫ﺏ‪ -‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (IA‬ﻳﻘﻄﻊ ]‪ [BC‬ﻓﻲ ﻣﻨﺘﺼﻔﻪ‪.‬‬

‫ﺕ‪ -‬ﺑﻴﻦ ﺃﻥ ‪5‬‬

‫= ‪. BI‬‬

‫‪ /3‬ﻟﺘﻜﻦ ‪ J‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟﻠﻨﻘﻄﺔ ‪ F‬ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪.(BD‬‬
‫ﺃ‪-‬‬

‫ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (AB‬ﻳﻘﻄﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (FJ‬ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪ .K‬ﺑﻴﻦ ﺃﻥ )‪ (BF‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪.(DK‬‬

‫‪Série F.B.A‬‬

‫‪11‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺏ‪ -‬ﻟﺘﻜﻦ ‪ L‬ﻧﻘﻄﺔ ﺗﻘﺎﻁﻊ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ )‪ (DK‬ﻭ )‪ .(BF‬ﺑﻴﻦ ﺃﻥ ‪.OA = OL‬‬
‫‪ /4‬ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ A‬ﻭ ﺍﻟﻤﻮﺍﺯﻱ ﻟــ )‪ (DL‬ﻳﻘﻄﻊ )‪ (BF‬ﻓﻲ ‪ .M‬ﺍﺣﺴﺐ ‪.AM‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬

‫ﻳﻤﺜﻞ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺼﺎﺣﺐ ﻣﺜﻠﺜﺎ ‪ ABC‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪ A‬ﺣﻴﺚ ‪ AB = 2 :‬ﻭ ‪2‬‬

‫‪. AC = 4‬‬

‫‪ /1‬ﺑﻴﻦ ﺃﻥ ‪. BE = 6‬‬
‫‪ /2‬ﺃ – ﺍﺭﺳﻢ ﺍﻟﻤﺜﻠﺚ ‪ ABC‬ﺛﻢ ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ E‬ﻋﻠﻰ ﻧﺼﻒ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ [BA‬ﺑﺤﻴﺚ ‪. BE = 6‬‬
‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪. EC‬‬

‫‪C‬‬

‫‪ /3‬ﻟﺘﻜﻦ ﺍﻟﻨﻘﻄﺔ ‪ D‬ﺻﻮﺭﺓ ﺍﻟﻨﻘﻄﺔ ‪ E‬ﺑﺎﻟﺘﻨﺎﻅﺮ ﺍﻟﻤﺮﻛﺰﻱ ‪. SB‬‬
‫ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ BCD‬ﻣﺘﻘﺎﻳﺲ ﺍﻟﻀﻠﻌﻴﻦ ﻗﻤﺘﻪ ﺍﻟﺮﺋﻴﺴﻴﺔ ‪. B‬‬

‫ﺃ‪-‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ ECD‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪. C‬‬

‫‪ /4‬ﻟﺘﻜﻦ ﺍﻟﻨﻘﻄﺔ ‪ I‬ﻣﻨﺘﺼﻒ ]‪ . [DC‬ﺑﻴﻦ ﺃﻥ ‪3‬‬

‫‪. BI = 2‬‬

‫‪ /5‬ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ )‪ (BI‬ﻭ )‪ (AC‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ‪. F‬‬

‫‪BF 1‬‬
‫ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ =‬
‫‪EC 2‬‬

‫‪.‬‬

‫‪B‬‬

‫‪A‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪ B‬ﻣﻨﺘﺼﻒ ]‪. [IF‬‬
‫ﺝ‪ -‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ )‪ (EI‬ﻭ )‪ (FD‬ﻣﺘﻮﺍﺯﻳﺎﻥ‪.‬‬
‫‪ /6‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ )‪ (FD‬ﻭ )‪ (BC‬ﻣﺴﺘﻘﻴﻤﺎﻥ ﻣﺘﻌﺎﻣﺪﺍﻥ‪.‬‬
‫ﺏ‪ (EI) -‬ﻳﻘﻄﻊ )‪ (CA‬ﻓﻲ ‪ H‬ﻭ ﻳﻘﻄﻊ )‪ (BC‬ﻓﻲ ‪ G‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻨﻘﺎﻁ ‪ A‬ﻭ ‪ B‬ﻭ ‪ G‬ﻭ ‪ H‬ﺗﻨﺘﻤﻲ ﻟﻨﻔﺲ ﺍﻟﺪﺍﺋﺮﺓ ‪ .‬ﺣﺪﺩ ﻗﻄﺮﻫﺎ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‪:‬‬
‫ﻧﻌﺘﺒﺮ ﻣﺜﻠﺜﺎ ‪ ABC‬ﻣﺘﻘﺎﻳﺲ ﺍﻟﻀﻠﻌﻴﻦ ﻗﻤﺘﻪ ﺍﻟﺮﺋﻴﺴﻴﺔ ‪ B‬ﺣﻴﺚ ‪BA = BC= 5‬‬
‫ﻭ ‪. AC = 6‬ﻭ ]‪ [BD‬ﺍﻹﺭﺗﻔﺎﻉ ﺍﻟﺼﺎﺩﺭ ﻣﻦ ‪ B‬ﻭ ]‪ [AE‬ﺍﻻﺭﺗﻔﺎﻉ ﺍﻟﺼﺎﺩﺭ ﻣﻦ ‪. A‬‬
‫‪ /1‬ﺍﺣﺴﺐ ‪ DC‬ﻭ ‪. DB‬‬
‫‪ /2‬ﻟﺘﻜﻦ ﺍﻟﻨﻘﻄﺔ ‪ F‬ﺻﻮﺭﺓ ﺍﻟﻨﻘﻄﺔ ‪ C‬ﺑﺎﻟﺘﻨﺎﻅﺮ ﺍﻟﻤﺮﻛﺰﻱ ‪. SB‬‬
‫ﺃ‪-‬‬

‫ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ AFC‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪. A‬‬

‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪ AF‬ﻭ ‪. AE‬‬
‫‪ /3‬ﻟﺘﻜﻦ ‪ ζ‬ﺍﻟﺪﺍﺋﺮﺓ ﺍﻟﻤﺤﻴﻄﺔ ﺑﺎﻟﻤﺜﻠﺚ ‪ . AFC‬ﺃ‪ -‬ﺣﺪﺩ ﻣﺮﻛﺰ ﻫﺬﻩ ﺍﻟﺪﺍﺋﺮﺓ‪.‬‬
‫ﺃ‪-‬‬

‫ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ B‬ﻭ ﺍﻟﻤﻮﺍﺯﻱ ﻟـ )‪ (AE‬ﻳﻘﻄﻊ )‪(AF‬ﻓﻲ ﺍﻟﻨﻘﻄﺔ ’‪ B‬ﻭ ﻧﺼﻒ ﺍﻟﻤﺴﺘﻘﻴﻢ )’‪ [BB‬ﻳﻘﻄﻊ ‪ ζ‬ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪K‬‬
‫ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ KFC‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻭ ﻣﺘﻘﺎﻳﺲ ﺍﻟﻀﻠﻌﻴﻦ‪..‬‬

‫‪ /4‬ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ )‪ (BD‬ﻭ )‪ (AE‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪ J‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (AB‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪.(CJ‬‬
‫‪ /5‬ﻟﺘﻜﻦ ‪ H‬ﻧﻘﻄﺔ ﺗﻘﺎﻁﻊ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ )‪ (AB‬ﻭ )‪ .(CJ‬ﺑﻴﻦ ﺃﻥ ‪ H‬ﺗﻨﺘﻤﻲ ﺇﻟﻰ ﺍﻟﺪﺍﺋﺮﺓ ﺍﻟﻤﺤﻴﻄﺔ ﺑﺎﻟﻤﺜﻠﺚ ‪.BCD‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‪:‬‬
‫ﻧﻌﺘﺒﺮ ﺩﺍﺋﺮﺓ ‪ ζ‬ﻣﺮﻛﺰﻫﺎ ‪ O‬ﻭ ]‪ [BC‬ﻗﻄﺮﺍ ﻣﻨﻬﺎ ﺑﺤﻴﺚ ‪ BC= 10‬ﻭ ‪. CH= 2‬‬
‫ﻧﺼﻒ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ [Hx‬ﺍﻟﻌﻤﻮﺩﻱ ﻋﻠﻰ ]‪ [BC‬ﻓﻲ ‪ H‬ﻳﻘﻄﻊ ﺍﻟﺪﺍﺋﺮﺓ ‪ ζ‬ﻓﻲ ‪. A‬‬
‫‪ /1‬ﺍﺣﺴﺐ ‪ OH‬ﺛﻢ ﺑﻴﻦ ﺃﻥ ‪. AH = 4‬‬
‫‪ /2‬ﺍﺣﺴﺐ ‪AB‬ﺛﻢ ﺍﺣﺴﺐ ‪. AC‬‬
‫‪ /3‬ﻟﺘﻜﻦ ‪ M‬ﺑﺤﻴﺚ ‪ O‬ﻣﻨﺘﺼﻒ ]‪. [HM‬‬
‫ﺍﻟﻌﻤﻮﺩﻱ ﻋﻠﻰ ]‪ [AB‬ﻭ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ M‬ﻳﻘﻄﻌﻪ ﻗﻲ ‪ N‬ﻛﻤﺎ ﻳﻘﻄﻊ )‪ (OA‬ﻓﻲ ‪. K‬‬

‫‪Série F.B.A‬‬

‫‪12‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫‪BN MN‬‬
‫ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ‬
‫=‬
‫‪BA AC‬‬
‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ OKN‬ﻣﺘﻘﺎﻳﺲ ﺍﻟﻀﻠﻌﻴﻦ‪.‬‬

‫‪8 5‬‬
‫ﺃ‪ -‬ﺍﺣﺴﺐ ‪ MK‬ﺛﻢ ﺑﻴﻦ ﺃﻥ‬
‫‪5‬‬

‫= ‪NK‬‬

‫‪ /4‬ﺍﺣﺴﺐ ‪ BK‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ OKB‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‪.‬‬
‫‪ /5‬ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ )‪ (BK‬ﻭ )‪ (AH‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ‪ T‬ﺑﻴﻦ ﺃﻥ )‪ (OT‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪ (AB‬ﻓﻲ ﻧﻘﻄﺔ ‪ L‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪. L = A*B‬‬
‫‪ /6‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ P‬ﻣﻦ ]‪ [OA‬ﺑﺤﻴﺚ ‪ . OP = 1‬ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ )‪ (BP‬ﻭ )‪ (KL‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ‪ G‬ﺍﺣﺴﺐ ‪. GK‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺴﺎﺑﻊ‪:‬‬
‫ﺍﺭﺳﻢ ﺷﺒﻪ ﻣﻨﺤﺮﻑ ‪ ABCD‬ﻗﺎﺋﻢ ﻓﻲ ‪ A‬ﻭ ‪ D‬ﺑﺤﻴﺚ ‪ AB=4‬ﻭ ‪ AD=6‬ﻭ ‪.CD=13‬ﻭ ﻋﻴﻦ ‪ I‬ﻣﻨﺘﺼﻒ ]‪ .[AD‬ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ I‬ﻭ‬
‫ﺍﻟﻤﻮﺍﺯﻱ ﻟـ)‪ (CD‬ﻳﻘﻄﻊ )‪ (BC‬ﻓﻲ ‪ J‬ﻭ ﻳﻘﻄﻊ )‪ (BD‬ﻓﻲ ‪.O‬‬
‫‪ (1‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ‪ J‬ﻣﻨﺘﺼﻒ ]‪ [BC‬ﻭ ﺃﻥ ‪ O‬ﻣﻨﺘﺼﻒ ]‪.[BD‬‬

‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪. IJ‬‬

‫‪ (2‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ E‬ﻋﻠﻰ ]‪ [CD‬ﺑﺤﻴﺚ ‪ . DE=4‬ﺑﻴﻦ ﺃﻥ ‪ ABED‬ﻣﺴﺘﻄﻴﻞ ﺛﻢ ﺍﺣﺴﺐ ‪ BD‬ﻭ‪ .BC‬ﻭ ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪ BCD‬ﻗﺎﺋﻢ ﻓﻲ ‪B‬‬
‫‪ (3‬ﺍﺣﺴﺐ ﻛﻞ ﻣﻦ ﻣﺴﺎﺣﺔ ﻭ ﻣﺤﻴﻂ ﺷﺒﻪ ﺍﻟﻤﻨﺤﺮﻑ ‪. IJCD‬‬
‫‪ (4‬ﻋﻴﻦ ‪ K‬ﻣﻨﺘﺼﻒ ]‪ [CD‬ﺛﻢ ﺑﻴﻦ ﺃﻥ ‪ OBJK‬ﻣﺴﺘﻄﻴﻞ‪.‬‬
‫‪ (5‬ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ )‪ (AB‬ﻭ )‪ (OK‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ‪ . F‬ﺑﻴﻦ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ BFDK‬ﻣﻌﻴﻦ ﻭ ﺍﺣﺴﺐ ﻣﺴﺎﺣﺘﻪ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻣﻦ ‪:‬‬
‫‪ M‬ﻧﻘﻄﺔ ﻣﻦ ﺩﺍﺋﺮﺓ ﻗﻄﺮﻫﺎ ]‪ [AB‬ﻭ ‪ E‬ﻭ ‪ F‬ﻣﻨﺎﻅﺮﺗﺎ ‪ A‬ﻭ ‪ B‬ﻋﻠﻰ ﺍﻟﺘﻮﺍﻟﻲ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻨﻘﻄﺔ ‪. M‬‬
‫‪ (1‬ﺣﺪﺩ ﻁﺒﻴﻌﺔ ﺍﻟﻤﺜﻠﺚ ‪. AMB‬‬
‫‪ (2‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪ ABEF‬ﻣﻌﻴﻦ‪.‬‬
‫‪ (3‬ﻋﻠﻤﺎ ﺃﻥ ‪ MB=2cm‬ﻭ ‪ AB=7cm‬ﺍﺣﺴﺐ ‪ AM‬ﺛﻢ ﺍﺣﺴﺐ ﻣﺴﺎﺣﺔ ﺍﻟﻤﻌﻴﻦ ‪.ABEF‬‬
‫‪ (4‬ﻟﻴﻜﻦ )‪ (M,E,F‬ﻣﻌﻴﻦ ﻓﻲ ﺍﻟﻤﺴﺘﻮﻱ ﺣﺪﺩ ﺇﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻨﻘﺎﻁ ‪ A‬ﻭ ‪ B‬ﻭ ‪ F‬ﻭ ‪ E‬ﻭ ‪. M‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺘﺎﺳﻊ‬
‫ﻟﻴﻜﻦ )‪ (O,I,J‬ﻣﻌﻴﻨﺎ ﻓﻲ ﺍﻟﻤﺴﺘﻮﻱ ﺣﻴﺚ )‪ (OJ) ⊥ (OI‬ﻭ ‪.OI=OJ=1‬ﻭ ﺍﻟﻨﻘﺎﻁ )‪ A(4, 0‬ﻭ)‪. B(8, 0‬‬
‫‪ (1‬ﻋﻴﻦ ‪ C‬ﺑﺤﻴﺚ ‪ ABC‬ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ ﺍﻷﺿﻼﻉ ﻭ ﺗﺮﺗﻴﺒﺔ ‪ C‬ﺳﺎﻟﺒﺔ‪ .‬ﺛﻢ ﺍﺣﺴﺐ ‪ AB‬ﻭ ‪. AC‬‬
‫‪ (2‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ H‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟــ‪ C‬ﻋﻠﻰ )‪ (OB‬ﺛﻢ ﺍﺣﺴﺐ ‪. CH‬‬
‫‪ (3‬ﻣﺎ ﻫﻲ ﺇﺣﺪﺍﺛﻴﺎﺕ ‪ C‬ﻓﻲ ﺍﻟﻤﻌﻴﻦ )‪. (O,I,J‬‬
‫‪ (4‬ﺑﻴﻦ ﺃﻥ ‪A‬ﻣﻨﺘﺼﻒ ]‪ . [OB‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ OCB‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‪.‬‬
‫‪ (5‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ D‬ﻣﻨﺎﻅﺮﺓ ‪ C‬ﺑﺎﻟﻨﺴﺒﺔ ﻟــ‪ A‬ﺛﻢ ﺍﺣﺴﺐ ﺇﺣﺪﺍﺛﻴﺎﺕ ‪ . D‬ﺛﻢ ﺑﻴﻦ ﺃﻥ ‪ OCBD‬ﻣﺴﺘﻄﻴﻞ‪.‬‬
‫‪ (6‬ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ )‪ E (6 , 2 3‬ﺛﻢ ﺑﻴﻦ ﺃﻥ ‪ E‬ﻣﻨﺎﻅﺮﺓ ‪ C‬ﺑﺎﻟﻨﺴﺒﺔ ﺇﻟﻰ )‪.(OI‬‬
‫‪ (7‬ﺑﻴﻦ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ AEBC‬ﻣﻌﻴﻦ‪.‬‬

‫‪Série F.B.A‬‬

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‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﺘﻌﺎﻣﺪ ﻓﻲ ﺍﻟﻔﻀﺎء‬
‫ﻣﻠﺨﺺ ﺍﻟﺪﺭﺱ‪:‬‬
‫‪ (1‬ﻛﻴﻒ ﻧﺒﻴﻦ ﺃﻥ ﻣﺴﺘﻘﻴﻤﺎ ﻣﻮﺍﺯ ﻟﻤﺴﺘﻮ‪:‬‬
‫‪……………………………………………………..…………………………………………………………………………………………..‬‬
‫‪ (2‬ﻛﻴﻒ ﻧﺒﻴﻦ ﺃﻥ ﻣﺴﺘﻘﻴﻤﺎ ﻋﻤﻮﺩﻳﺎ ﻋﻠﻰ ﻣﺴﺘﻮﻱ‪:‬‬
‫……………………………………………………………………………………………‪……………………………………….…………….‬‬
‫‪ (3‬ﻛﻴﻒ ﻧﺒﻴﻦ ﺃﻥ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻟﻴﺴﺎ ﻣﻦ ﻧﻔﺲ ﺍﻟﻤﺴﺘﻮﻱ‬
‫‪……………………………………………………….………………………………………………………………………………………….‬‬
‫‪ (4‬ﻋﺮﻑ ﺑﺎﻟﻬﺮﻡ ﺍﻟﻤﻨﺘﻈﻢ‬
‫‪……………………………………………………….………………………………………………………………………………………….‬‬

‫‪ ABCDEFGH‬ﻣﺘﻮﺍﺯﻱ ﻣﺴﺘﻄﻴﻼﺕ ﺣﻴﺚ ‪ AB=AD=4‬ﻭ ‪. AE=6‬‬

‫‪ (1‬ﺃﺗﻤﻢ ﺑــ ∈ ‪ ⊂ ، ∉ ،‬ﺃﻭ ⊄‬
‫)‪C ………..(HGI‬‬
‫)‪I………(ABE‬‬
‫)‪(AB)…….(EFA‬‬
‫)‪(AB)….(AHG‬‬

‫‪B‬‬

‫)‪E……….(HGF‬‬

‫)‪I……….(ACD‬‬
‫)‪(EC)……….(ACG‬‬

‫‪A‬‬

‫)‪B…………..(ACG‬‬

‫‪D‬‬

‫‪x‬‬
‫‪I‬‬

‫‪C‬‬

‫)‪(IE)………(ADH‬‬

‫)‪(IC)…….(EFH‬‬

‫‪E‬‬

‫‪F‬‬

‫‪H‬‬

‫‪G‬‬
‫‪ (1‬ﺑﻴﻦ ﺃﻥ )‪ (AI‬ﻭ )‪ (BC‬ﻣﺘﻘﺎﻁﻌﺎﻥ‪.‬‬

‫‪ (3‬ﻣﺎ ﻫﻲ ﺍﻟﻮﺿﻌﻴﺔ ﺍﻟﻨﺴﺒﻴﺔ ﻟـ )‪ (AB‬ﻭ )‪ (EF‬؟ ﻋﻠﻞ‪.‬‬

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

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

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

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

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

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

‫‪......‬‬

‫‪......‬‬

‫‪ (2‬ﺑﻴﻦ ﺃﻥ )‪.(EHG) // (AB‬‬

‫‪ (5‬ﺑﻴﻦ ﺃﻥ )‪ (AB‬ﻭ )‪ (GE‬ﻟﻴﺴﺎ ﻣﻦ ﻧﻔﺲ ﺍﻟﻤﺴﺘﻮﻱ‪.‬‬

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

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

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

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

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

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

‫‪......‬‬

‫‪......‬‬

‫‪ (3‬ﺑﻴﻦ ﺃﻥ )‪ (CG‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪. (BCD‬‬

‫‪ (8‬ﺍﺭﺳﻢ ﻧﻘﻄﺔ ﺗﻘﺎﻁﻊ )‪ (AI‬ﻭﺍﻟﻤﺴﺘﻮﻱ )‪(BFG‬‬

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

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

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

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

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

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

‫‪Série F.B.A‬‬

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‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﻣﻠﺨﺺ ﺍﻟﺘﻌﺎﻣﺪ ﻓﻲ ﺍﻟﻔﻀﺎء‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬

‫‪A‬‬

‫ﺍﻟﺮﺳﻢ ﺍﻟﻤﺠﺎﻭﺭ ﻳﻤﺜﻞ ﻫﺮﻣﺎ ﺛﻼﺛﻲ ﺍﻟﻘﺎﻋﺪﺓ‬
‫‪ /1‬ﺃﻛﻤﻞ ﻣﺎ ﻳﻠﻲ ‪:‬‬

‫; ‪( AD) ∩ ( ABC ) = ..............‬‬

‫‪( AB) ∩ ( BCD) = .............‬‬

‫= )‪( CD‬‬
‫) ‪∩ ( ABC‬‬
‫; ‪..............‬‬
‫= )‪( AB‬‬
‫) ‪∩ ( ABC‬‬
‫; ‪..............‬‬

‫= )‪( AD‬‬
‫)‪∩ ( BCD‬‬
‫‪..........‬‬
‫= )‪( BD‬‬
‫)‪∩ ( ABC‬‬
‫‪.............‬‬

‫‪B‬‬

‫‪D‬‬

‫‪M‬‬

‫‪N‬‬

‫‪ /2‬ﺃﻛﻤﻞ ﺑﺄﺣﺪ ﺍﻟﺮﻣﺰﻳﻦ ⊂ ﺃﻭ ⊄‬

‫‪.‬‬

‫‪C‬‬

‫) ‪( CD ) .........( ABC‬‬

‫) ‪( AC ) .........( ABD‬‬

‫) ‪( CD ) .........( BCD‬‬

‫) ‪( AC ) .........( ABC‬‬

‫) ‪( AC ) .........( BCD‬‬

‫) ‪( CD ) .........( ABD‬‬

‫‪ /3‬ﺃﺗﻤﻢ ‪:‬‬

‫‪( AMN) ∩ ( ABC ) = ..............‬‬

‫;‬

‫‪( AMN) ∩ ( ACD) = .............‬‬

‫; ‪( AMN) ∩ ( BCD ) = ..............‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫ﺃﺗﻤﻢ ﺍﻟﺠﻤﻞ ﺍﻟﺘﺎﻟﻴﺔ ﺑﻤﺎ ﻳﻨﺎﺳﺐ‪:‬‬
‫‪ (1‬ﺑﻤﺎ ﺃﻥ ‪ BFCG‬ﻣﺴﺘﻄﻴﻞ ﻓﺈﻥ ‪ (BF)//………………..‬ﻭ ﺑﻤﺎ ﺃﻥ )‪ (CG) ⊂ ( DCG‬ﻓﺈﻥ ‪........................................‬‬
‫‪ (2‬ﺑﻤﺎ ﺃﻥ )‪ I ∈ ( DCG‬ﻭ ﺑﻤﺎ ﺃﻥ )‪ J ∈ ( DCG‬ﻓﺈﻥ ‪(IJ) ………………………………..‬‬
‫‪ (3‬ﻟﻴﻜﻦ ﺍﻟﺮﺳﻢ ﺍﻟﺘﺎﻟﻲ‪:‬‬

‫‪H‬‬

‫‪E‬‬

‫‪M‬‬

‫‪I‬‬
‫‪D‬‬

‫‪A‬‬
‫‪G‬‬

‫‪F‬‬
‫‪J‬‬

‫‪C‬‬

‫‪B‬‬

‫ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ )‪ (AB‬ﻭ ﺍﻟﻤﺴﺘﻮﻱ )‪ (DCG‬ﻣﺘﻘﺎﻁﻌﺎﻥ‪:‬‬
‫ﻟﺪﻳﻨﺎ ‪ ABCD‬ﺷﺒﻪ ﻣﻨﺤﺮﻑ ﻗﺎﻋﺪﺗﺎﻩ ]‪ [AD‬ﻭ ]‪ [BC‬ﺇﺫﻥ )‪ (AB‬ﻭ )‪................................................................... (DC‬‬
‫ﻭ ﺑﻤﺎ ﺃﻥ )‪ (DC) ⊂ ( DCG‬ﻭ )‪ B ∉ ( DCG‬ﻓﺈﻥ‬

‫)‪ (AB) (AB) ⊄ ( DCG‬ﻭ )‪ (DCG‬ﻭ ﺑﺎﻟﺘﺎﻟﻲ ‪..........................‬‬

‫ﺏ‪ -‬ﺑﻴﻦ ﺃﻥ )‪ (CIJ‬ﻭ )‪ (ABF‬ﻣﺘﻘﺎﻁﻌﺎﻥ‪:‬‬
‫ﺍﻟﻤﺴﺘﻮﻳﺎﻥ )‪ (CIJ‬ﻭ )‪ (ABF‬ﻏﻴﺮ ﻣﻨﻔﺼﻠﻴﻦ ﻷﻧﻬﻤﺎ ﻳﺸﺘﺮﻛﺎﻥ ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪.............‬‬
‫ﻭ ﺑﻤﺎ ﺃﻥ )‪ C ∈ ( CIJ‬ﻭ‬

‫)‪ C ∉ ( ABF‬ﻓﺈﻥ )‪ (CIJ‬ﻭ )‪ (ABF‬ﻏﻴﺮ ﻣﻨﻔﺼﻠﻴﻦ ﻭ ﻏﻴﺮ ﻣﻨﻄﺒﻘﻴﻦ ﺇﺫﻥ ﻫﻤﺎ ‪.....................‬‬

‫ﺝ‪ -‬ﺑﻴﻦ ﺃﻥ )‪ (CI‬ﻭ )‪ (AB‬ﻟﻴﺴﺎ ﻣﻦ ﻧﻔﺲ ﺍﻟﻤﺴﺘﻮﻱ‬
‫ﻟﻨﺎ ‪ (CI) ⊂ .................‬ﻭ )‪ (AB‬ﻳﻘﻄﻊ )‪ (CIJ‬ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪............‬ﻭ )‪ J ∉ ( CI‬ﺇﺫﻥ )‪ (CI‬ﻭ )‪..................... (AB‬‬
‫ﺩ‪ -‬ﺑﻴﻦ ﺃﻥ )‪ (AD‬ﻭ )‪ (CBG‬ﻣﺘﻮﺍﺯﻳﺎﻥ‬
‫ﻟﻨﺎ )‪ (AD‬ﻣﻮﺍﺯ ﻟـ ‪ .............‬ﻷﻥ ‪................................. ABCD‬ﻭ ﺑﻤﺎ ﺃﻥ )‪ (CB) ⊂ (CBG‬ﻓﺈﻥ ‪...............................‬‬

‫‪Série F.B.A‬‬

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‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫ﻳﻤﺜﻞ ﺍﻟﺸﻜﻞ ﺍﻟﻤﻘﺎﺑﻞ ﻫﺮﻣﺎ ‪SABCD‬ﻗﺎﻋﺪﺗﻪ ﻣﺮﺑﻊ ‪ ABCD‬ﺍﻟﺬﻱ ﻣﺮﻛﺰﻩ ‪ O‬ﺑﺤﻴﺚ ‪ DC= 3 2‬ﻭ ‪. SA=6cm‬ﻭ )‪(SO‬ﻋﻤﻮﺩﻱ‬
‫ﻋﻠﻰ)‪ (ABC‬ﻭ ‪ I‬ﻣﻨﺘﺼﻒ ]‪. [SC‬‬
‫‪ (1‬ﻓﻲ ﺍﻟﻤﺴﺘﻮﻱ )‪ (SAC‬ﺑﻴﻦ ﺃﻥ ‪. IO=3cm‬‬
‫‪.......................................................................................................................................................‬‬
‫‪.......................................................................................................................................................‬‬
‫‪ (2‬ﺃﺛﺒﺖ ﺃﻥ )‪ (SO‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪. (DO‬‬
‫‪S‬‬
‫‪.................................................................................................‬‬
‫‪.................................................................................................‬‬
‫‪ (3‬ﺃﺛﺒﺖ ﺃﻥ )‪ (OS‬ﻣﺤﺘﻮ ﻓﻲ ﺍﻟﻤﺴﺘﻮﻱ )‪. (SAC‬‬
‫‪................................................................................................‬‬
‫‪................................................................................................‬‬
‫‪ (4‬ﺑﻴﻦ ﺃﻥ )‪ (DO‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪. (ACS‬‬

‫‪I‬‬

‫‪A‬‬

‫‪B‬‬

‫‪...............................................................................................‬‬
‫‪................................................................................................‬‬
‫‪ (5‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ DOI‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‪.‬‬

‫‪O‬‬
‫‪D‬‬

‫‪C‬‬

‫‪.......................................................................................................................................................‬‬
‫ﺍﺣﺴﺐ ‪: DI‬‬
‫‪(6‬‬
‫‪.......................................................................................................................................................‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫ﻳﻤﺜﻞ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺼﺎﺣﺐ ﻣﻮﺷﻮﺭﺍ ﻗﺎﺋﻤﺎ ﻗﺎﻋﺪﻩ ﺷﺒﻪ ﺍﻟﻤﻨﺤﺮﻑ‬

‫‪F‬‬

‫‪E‬‬

‫‪ ABCD‬ﺍﻟﻘﺎﺋﻢ ﻓﻲ ‪ A‬ﻭ ‪D‬‬
‫ﺣﻴﺚ ‪ AB= 2 3‬ﻭ ‪ AD=2‬ﻭ ‪ DC= 5‬ﻭ ‪. AE= 6‬‬

‫‪H‬‬

‫‪G‬‬

‫ﻟﺘﻜﻦ ‪ M‬ﻣﻨﺘﺼﻒ ]‪ [AB‬ﻭ ‪ N‬ﻣﻨﺘﺼﻒ ]‪. [BD‬‬
‫‪ (1‬ﺍﺣﺴﺐ ‪.BD‬‬
‫‪ (2‬ﺑﻴﻦ ﺃﻥ )‪ (AE‬ﻭ )‪ (BDH‬ﻣﺘﻮﺍﺯﻳﺎﻥ‪.‬‬
‫‪ (3‬ﺑﻴﻦ ﺃﻥ )‪ (BF‬ﻭ )‪ (BD‬ﻣﺘﻌﺎﻣﺪﺍﻥ‪.‬‬

‫‪B‬‬

‫‪ (4‬ﺑﻴﻦ ﺃﻥ )‪ (MN‬ﻭ )‪ (ABE‬ﻣﺘﻌﺎﻣﺪﺍﻥ‪.‬‬

‫‪ (5‬ﺑﻴﻦ ﺃﻥ ﺣﺠﻢ ﺍﻟﻤﻮﺷﻮﺭ ﻳﺴﺎﻭﻱ ‪. 30+12 3‬‬

‫‪M‬‬

‫‪A‬‬

‫‪N‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬

‫‪C‬‬

‫‪D‬‬

‫‪S‬‬
‫‪ SABC‬ﻫﺮﻡ ﻗﺎﻋﺪﺗﻪ ﺍﻟﻤﺜﻠﺚ ‪ ABC‬ﺍﻟﻘﺎﺋﻢ ﻓﻲ ‪ A‬ﻭ )‪ (SA‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪(AC‬‬

‫‪K‬‬

‫ﻭ )‪ (SA) ⊥ (AB‬ﻭ ﺍﻟﻨﻘﻂ ‪ I‬ﻣﻨﺘﺼﻒ ]‪. [SA‬ﻭ ‪ J‬ﻣﻨﺘﺼﻒ ]‪ [SB‬ﻭ ‪ K‬ﻣﻨﺘﺼﻒ ]‪. [SC‬‬

‫‪I‬‬

‫‪ (1‬ﺑﻴﻦ ﺃﻥ )‪ (BA) ⊥ (SAC‬ﻭ ﺍﺳﺘﻨﺘﺞ ﻧﻮﻉ ﺍﻟﻤﺜﻠﺚ ‪. ABK‬‬
‫‪ (2‬ﺑﻴﻦ ﺃﻥ )‪ (SA) ⊥ (IJ‬ﻭ ﺃﻥ )‪. (SA) ⊥ (IK‬‬

‫‪J‬‬
‫‪C‬‬

‫‪A‬‬

‫‪ (3‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ )‪. (ABC) // (IJK‬‬
‫‪ (4‬ﻋﻠﻤﺎ ﺃﻥ ‪ SA= 6cm‬ﻭ ‪ AC=8cm‬ﻭ ‪ . AB=5cm‬ﺍﺣﺴﺐ ‪ AK‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ‪BK‬‬

‫‪B‬‬

‫‪Série F.B.A‬‬

‫‪.‬‬

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‫ﻧﻤﻮﺫﺝ‪ 1‬ﻟﻔﺮﺽ ﻋﺪﺩ ‪5‬‬

‫ﻣﻘﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﺍﻟﻨﻤﻮﺫﺟﻴﺔ ‪2010‬‬

‫ﺗﻤﺮﻳﻦ ﻋﺪﺩ ‪1‬‬
‫ﺃﺟﻴﺐ ﺑﺼﻮﺍﺏ ﺃﻭ ﺧﻄﺄ‪:‬‬

‫‪ 2‬‬
‫‪........................ 2 - 1 ∈ 0,  (1‬‬
‫‪ 5‬‬

‫‪.......... 1, 2 3  ∩ −2, 3 =1, 3 (2‬‬
‫‪‬‬
‫‪‬‬

‫‪1‬‬
‫‪1‬‬
‫‪3‬‬
‫‪ ≤ x + 1 ≤ (3‬ﻳﻌﻨﻲ ‪≤ −2‬‬
‫‪x‬‬
‫‪2‬‬
‫‪4‬‬

‫≤ ‪−4‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‬
‫ﺃﺟﺮﻳﺖ ﺩﺭﺍﺳﺔ ﺇﺣﺼﺎﺋﻴﺔ ﺣﻮﻝ ﻋﺪﺩ ﺍﻟﻜﺘﺐ ﺍﻟﻤﻘﺮﻭءﺓ ﺧﻼﻝ ﺍﻟﺜﻼﺛﻲ ﺍﻷﻭﻝ ﺑﺄﺣﺪ ﺃﻗﺴﺎﻡ ﺍﻟﺘﺎﺳﻌﺔ ﺃﺳﺎﺳﻲ ﻭ ﺟﺎء ﻛﺎﻵﺗﻲ‪.‬‬
‫‪ (1‬ﻣﺎ ﻫﻮ ﻧﻮﻉ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﺍﻹﺣﺼﺎﺋﻴﺔ؟‬
‫‪ (2‬ﺃﻛﻤﻞ ﺗﻌﻤﻴﺮ ﺍﻟﺠﺪﻭﻝ ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ﺍﻟﺘﻮﺍﺗﺮ ﺍﻟﻤﻮﺍﻓﻖ ﻟﻠﻘﻴﻤﺔ ‪ 3‬ﻫﻮ ‪0.25‬‬
‫‪ (3‬ﺣﺪﺩ ﻣﺪﻯ ﻭ ﻣﻨﻮﺍﻝ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‬

‫ﺍﻟﻜﺘﺐ ﺍﻟﻤﻘﺮﻭءﺓ‬
‫ﻋﺪﺩ ﺍﻟﺘﻼﻣﻴﺬ‬
‫ﺍﻟﺘﻜﺮﺍﺭ ﺍﻟﺘﺮﺍﻛﻤﻲ ﺍﻟﺼﺎﻋﺪ‬

‫‪ (4‬ﺃﻭﺟﺪ ﻣﻮﺳﻂ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﺍﻹﺣﺼﺎﺋﻴﺔ ﻣﻌﻠﻼ ﺟﻮﺍﺑﻚ‪.‬‬
‫‪ (5‬ﺍﺭﺳﻢ ﻣﻀﻠﻊ ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‪.‬‬

‫‪1‬‬

‫‪2‬‬
‫‪12‬‬
‫‪16‬‬

‫‪3‬‬

‫‪4‬‬
‫‪24‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬

‫ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ )‪ A=(x-3)(2x+3‬ﺣﻴﺚ ‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﻭ ‪. −1 ≤ x ≤ 3‬‬
‫‪ (1‬ﺃ‪ -‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟــ ‪ x-3‬ﻭ ‪. 2x+3‬‬

‫ﺏ‪ -‬ﺑﻴﻦ ﺃﻥ ‪A ∈ −36, 0 .‬‬

‫‪ (2‬ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺓ ‪. B=4x2+12x+7‬‬
‫ﺃ‪ -‬ﻓﻜﻚ ‪ B+2‬ﺇﻟﻰ ﺟﺬﺍء ﻋﻮﺍﻣﻞ ‪.‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟــ ‪. B‬‬

‫‪ (3‬ﻗﺎﺭﻥ ﺑﻴﻦ ‪ A‬ﻭ ‪. B + 2‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‪:‬‬
‫ﻟﻴﻜﻦ )‪ (O,I,J‬ﻣﻌﻴﻨﺎ ﻓﻲ ﺍﻟﻤﺴﺘﻮﻱ ﺣﻴﺚ )‪ (OI‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪ (OJ‬ﻭ ‪. OI=OJ=1‬ﻭ ﻟﺘﻜﻦ ﺍﻟﻨﻘﺎﻁ )‪ A(-5,0‬ﻭ )‪ B(0,-2‬ﻭ )‪ C(2,0‬ﻭ‬
‫)‪ M(0,3‬ﻭ )‪. D(-3,5‬‬
‫‪ (1‬ﺑﻴﻦ ﺃﻥ ‪ ONCM‬ﻣﺴﺘﻄﻴﻞ‪.‬‬
‫‪ (2‬ﺍﺣﺴﺐ ‪ AB‬ﻭ ‪ AC‬ﻭ ‪. BC‬‬
‫‪ (3‬ﺍﺳﺘﻨﺘﺞ ﻁﺒﻴﻌﺔ ﺍﻟﻤﺜﻠﺚ ‪. ABC‬‬
‫‪ (4‬ﻟﺘﻜﻦ ‪ E‬ﻣﻨﺘﺼﻒ ]‪ .[AC‬ﺃ‪ -‬ﺣﺪﺩ ﺯﻭﺝ ﺇﺣﺪﺍﺛﻴﺎﺕ ‪ E‬ﺛﻢ ﺑﻴﻦ ﺃﻥ ‪ ABCD‬ﻣﺮﺑﻊ‪.‬‬

‫‪Série F.B.A‬‬

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‫ﻧﻤﻮﺫﺝ ‪2‬ﻟﻔﺮﺽ ﻋﺪﺩ ‪5‬‬

‫ﻣﻘﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﺍﻟﺒﺴﺘﺎﻥ ‪ 2012‬ﻟﻸﺳﺘﺎﺫﺓ ﻧﻮﺭﺓ ﺍﻟﺼﺎﻓﻲ‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫ﺍﻧﻘﻞ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﻋﻠﻰ ﻭﺭﻗﺘﻚ‪.‬‬

‫‪ −16 −1 ‬‬
‫‪x2 ∈ ‬‬
‫ﺏ‪,  -‬‬
‫‪ 25 4 ‬‬

‫‪ 16 ‬‬
‫ﺝ‪x 2 ∈ 0,  -‬‬
‫‪ 25 ‬‬

‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪x ≤ 0‬‬

‫ﻓﺈﻥ ﺃ‪x ∈ −∞; 0 -‬‬

‫ﺏ‪x ∈  -‬‬

‫ﺝ‪x = 0 -‬‬

‫‪ (3‬ﺇﺫﺍ ﻛﺎﻥ ‪x ≤ 3‬‬

‫‪1  −1 1 ‬‬
‫∈‬
‫ﻓﺈﻥ ﺃ‪; -‬‬
‫‪x  3 3 ‬‬

‫‪1  1‬‬
‫‪‬‬
‫‪‬‬
‫ﺏ‪x ∈  −∞, −  ∪  , +∞  -‬‬
‫‪3 3‬‬
‫‪‬‬
‫‪‬‬

‫‪1  1‬‬
‫ﺝ‪∈ 0; -‬‬
‫‪x  3 ‬‬

‫‪4‬‬
‫‪1‬‬
‫‪ 1 16 ‬‬
‫‪ (1‬ﺇﺫﺍ ﻛﺎﻥ ‪ − ≤ x ≤ −‬ﻓﺈﻥ ﺃ‪x 2 ∈  ,  -‬‬
‫‪5‬‬
‫‪2‬‬
‫‪ 4 25 ‬‬

‫‪B‬‬

‫‪ ABCEFG (4‬ﻣﻮﺷﻮﺭ ﻗﺎﺋﻢ ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ )‪ (EF‬ﻭ )‪: (CG‬‬
‫ﺃ‪ -‬ﻣﺘﻮﺍﺯﻳﺎﻥ‬

‫ﺏ‪ -‬ﻣﺘﻘﺎﻁﻌﺎﻥ‬

‫‪A‬‬

‫ﺝ ﻏﻴﺮ ﻣﺘﻮﺍﺯﻳﺎﻥ ﻭ ﻏﻴﺮ ﻣﺘﻘﺎﻁﻌﺎﻥ‬

‫‪C‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫‪ (1‬ﺃﻛﺘﺐ ﺍﻟﻤﺠﻤﻮﻋﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ ﻓﻲ ﺷﻜﻞ ﻣﺠﺎﻻﺕ‪.‬‬

‫}‪{x ∈  , −3 < x < 1‬‬

‫=‪; I‬‬

‫‪F‬‬

‫}‪{y ∈  , −2 < y < 2‬‬

‫=‪K‬‬
‫= ‪{z ∈  , z ≥ 1} ; J‬‬

‫‪E‬‬

‫‪G‬‬

‫ﻋﺪﺩ ﺍﻟﺤﺮﻓﺎء‬

‫‪ (2‬ﻣﺜﻞ ‪ I‬ﻭ ‪ J‬ﻭ ‪ K‬ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻌﺪﺩﻱ ﺛﻢ ﺣﺪﺩ ‪. I ∩ J ; I ∩ K ; I ∪ K‬‬
‫‪ (3‬ﻟﻴﻜﻦ ‪ x ∈ I‬ﻭ ‪ y ∈ J‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟــ ‪ y+x‬ﺛﻢ ﻟــ ‪. y-x‬‬

‫‪ (4‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ‪x+1 < 2‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟــ ‪. xy+y‬‬

‫‪20‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ ‪:‬‬

‫‪2x − 1‬‬
‫‪ -3 ‬‬
‫ﻟﻴﻜﻦ ‪ x‬ﻋﺪﺩﺍ ﺣﻘﻴﻘﻴﺎ ﺣﻴﺚ ‪ x ∈  ,2 ‬ﻭ‬
‫‪x+3‬‬
‫‪2 ‬‬
‫‪1‬‬
‫‪ (1‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟــ ‪ 2x-1‬ﻭ ‪ x+3‬ﺛﻢ‬
‫‪x+3‬‬
‫‪7‬‬
‫‪ . A= 2 −‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟﻠﻌﺒﺎﺭﺓ ‪. A‬‬
‫‪ (2‬ﺑﻴﻦ ﺃﻥ‬
‫‪x+3‬‬

‫= ‪.A‬‬

‫‪14‬‬
‫‪10‬‬
‫‪8‬‬
‫‪4‬‬
‫‪2‬‬

‫ﺍﻟﺰﻣﻦ‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ ‪:‬‬

‫‪100‬‬

‫‪80‬‬

‫‪60‬‬

‫‪40‬‬

‫‪20‬‬

‫ﻳﻤﺜﻞ ﺍﻟﻤﺨﻄﻂ ﺃﻋﻼﻩ ﺗﻮﺯﻳﻌﺎ ﻟﺤﺮﻓﺎء ﻣﺮﻛﺰ ﻋﻤﻮﻣﻲ ﻟﻸﻧﺘﺮﻧﺎﺕ ﺣﺴﺐ ﻣﺪﺓ ﺍﻹﺑﺤﺎﺭ‪.‬‬
‫‪ (1‬ﻣﺎ ﻫﻮ ﻧﻮﻉ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﺍﻹﺣﺼﺎﺋﻴﺔ؟‬

‫ﺍﻟﺰﻣﻦ‬

‫‪ (2‬ﺃﻛﻤﻞ ﺗﻌﻤﻴﺮ ﺍﻟﺠﺪﻭﻝ‬
‫ﻋﺪﺩ ﺍﻟﺤﺮﻓﺎء‬
‫‪ (3‬ﺣﺪﺩ ﻣﺪﻯ ﻭ ﻣﻨﻮﺍﻝ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ‪.‬‬
‫ﺍﻟﺘﻜﺮﺍﺭ ﺍﻟﺘﺮﺍﻛﻤﻲ‬
‫‪ (4‬ﺍﺣﺴﺐ ﻣﻌﺪﻝ ﺍﻟﺰﻣﻦ ﺍﻟﺬﻱ ﻳﻘﻀﻴﻪ ﻛﻞ ﺣﺮﻳﻒ‬
‫ﺍﻟﺼﺎﻋﺪ‬
‫‪ (5‬ﺍﺭﺳﻢ ﻣﻀﻠﻊ ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ ﻭ ﺍﺳﺘﻨﺘﺞ ﺍﻟﻤﻮﺳﻂ‪.‬‬

‫[‪[ 80;100 [ 60;80[ [ 40;60[ [ 20;40[ [ 0;20‬‬

‫‪ (6‬ﻣﺎﻫﻲ ﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺎﺋﻮﻳﺔ ﻟﻠﺤﺮﻓﺎء ﺍﻟﺬﻳﻦ ﻳﻘﻀﻮﻥ ﻣﺪﺓ ﺗﺴﺎﻭﻱ ﺳﺎﻋﺔ ﺃﻭ ﺃﻛﺜﺮ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‪:‬‬
‫ﺻﻨﺪﻭﻕ ﺑﻪ ‪ 5‬ﺃﻭﺭﺍﻕ ﺑﻴﻀﺎء ﻭ ‪ 4‬ﺃﻭﺭﺍﻕ ﺣﻤﺮﺍء‪.‬ﺃﺭﺍﺩ ﺃﺣﻤﺪ ﺳﺤﺐ ﻭﺭﻗﺘﻴﻦ ﺍﻟﻮﺍﺣﺪﺓ ﺗﻠﻮ ﺍﻷﺧﺮﻯ ﻣﻊ ﺇﺭﺟﺎﻉ ﺍﻷﻭﻟﻰ‪.‬‬
‫‪ (1‬ﻣﺎ ﻫﻮ ﻋﺪﺩ ﺍﻹﻣﻜﺎﻧﻴﺎﺕ‪.‬‬
‫‪ (2‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻭﺭﻗﺘﻴﻦ ﻟﻬﻤﺎ ﻧﻔﺲ ﺍﻟﻠﻮﻥ‪ .‬ﺛﻢ ﺍﺣﺘﻤﺎﻝ ﻭﺭﻗﺘﻴﻦ ﻣﺨﺘﻠﻔﺘﻲ ﺍﻟﻠﻮﻥ‪.‬‬
‫‪ (3‬ﻣﺎﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻭﺭﻗﺘﻴﻦ ﻟﻬﻤﺎ ﻧﻔﺲ ﺍﻟﻠﻮﻥ ﺛﻢ ﻭﺭﻗﺘﻴﻦ ﻣﺨﺘﻠﻔﺘﻲ ﺍﻟﻠﻮﻥ ‪.‬‬
‫‪ (4‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻭﺭﻗﺘﻴﻦ ﺇﺣﺪﺍﻫﻤﺎ ﺣﻤﺮﺍء ﻭ ﺍﻟﺜﺎﻧﻴﺔ ﺻﻔﺮﺍء‪.‬‬

‫‪Série F.B.A‬‬

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‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺜﺎﻟﺚ ﻟﻔﺮﺽ ﻋﺪﺩ ‪5‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬

‫ﺍﻟﻤﻌﻄﻴﺎﺕ‬

‫‪a‬‬

‫‪b‬‬

‫‪c‬‬

‫‪ -5 5 ‬‬
‫‪x∈ ; ‬‬
‫‪ 2 2‬‬

‫‪−5‬‬
‫‪5‬‬
‫<‪<x‬‬
‫‪2‬‬
‫‪2‬‬

‫ﺇﺫﻥ)‪(x-2)(2x+5‬‬

‫}‪S  = {2‬‬

‫‪ -5 ‬‬
‫‪S  = -2; ‬‬
‫‪2‬‬
‫‪‬‬

‫‪ -5 5 ‬‬
‫‪x∈ ; ‬‬
‫‪ 2 2‬‬
‫‪ -5 ‬‬
‫‪S  =  ;2 ‬‬
‫‪2 ‬‬

‫‪E=9-x2‬‬

‫‪E=(1-x)2‬‬

‫)‪E=(x-3)(x+3‬‬

‫)‪E=(x+3)(3-x‬‬

‫‪5‬‬
‫ﺇﺫﺍ‬
‫‪2‬‬

‫ﺍﻟﻌﺪﺩ)ﻣﻦ‬
‫‪(20‬‬
‫ﻋﺪﺩ‬
‫ﺍﻟﺘﻼﻣﻴﺬ‬
‫)ﺍﻟﺘﻜﺮﺍﺭ(‬

‫ﺍﻟﺠﻮﺍﺏ‬
‫ﺍﻟﺼﺤﻴﺢ‬

‫≤‪x‬‬

‫‪2.5‬‬

‫‪9‬‬

‫‪10‬‬

‫‪13‬‬

‫‪15‬‬

‫‪1‬‬

‫‪2‬‬

‫‪2‬‬

‫‪3‬‬

‫‪1‬‬

‫‪08‬‬

‫‪10.5‬‬

‫‪10‬‬

‫ﻣﻌﺪﻝ ﻫﺬﻩ ﺍﻷﻋﺪﺍﺩ ﻫﻮ‬
‫ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ‪ABC‬‬
‫ﺍﻷﺿﻼﻉ ﻭ ]‪[AH‬‬
‫ﺍﺭﺗﻔﺎﻋﻪ‬

‫‪3‬‬
‫ﺣﻴﺚ‬
‫‪2‬‬

‫=‪AH‬‬

‫‪3‬‬
‫‪2‬‬

‫=‪AB‬‬

‫‪2 3‬‬
‫‪3‬‬

‫‪AB= 3‬‬

‫=‪AB‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‬

‫=‬
‫‪ (1‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ‪3) 3x+1 − 4 7 :‬‬
‫‪1‬‬
‫‪ (2‬ﺑﻴﻦ ﺃﻥ‬
‫‪4‬‬

‫= )‪1‬‬
‫‪( x+2 ) (4x − 7) 0‬‬

‫=‪2) ( x-1‬‬
‫‪) − 9(2x + 1)2 0‬‬
‫‪2‬‬

‫‪3‬‬
‫‪2‬‬

‫‪ x 2 − 3x + 2 = (x − )2 −‬ﺛﻢ ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪. x 2 + 2 =−3x :‬‬
‫‪B‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‬

‫‪H‬‬

‫‪A‬‬

‫‪ ABCD‬ﻣﺴﺘﻄﻴﻞ ﻭ ‪ E‬ﻧﻘﻄﺔ ﻣﻦ ]‪ [DC‬ﺣﻴﺚ ‪ DE = x‬ﻭ ‪ AB=14cm‬ﻭ ‪. BC=8cm‬‬
‫‪ (1‬ﻛﻴﻒ ﻧﺨﺘﺎﺭ ‪ x‬ﻟﻴﻜﻮﻥ ﻟﻠﻤﺜﻠﺜﻴﻦ ‪ BCE‬ﻭ ‪ ADE‬ﻧﻔﺲ ﺍﻟﻤﺴﺎﺣﺔ؟‬

‫‪C‬‬

‫‪ (2‬ﺍﺑﺤﺚ ﻋﻦ ‪ x‬ﻋﻠﻤﺎ ﺃﻥ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ BCE‬ﺗﺴﺎﻭﻱ ﺛﻠﺚ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺴﺘﻄﻴﻞ ‪. ADEH‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‬
‫‪ ABCD‬ﻣﺴﺘﻄﻴﻞ ﺑﺤﻴﺚ ‪ AB=9‬ﻭ ‪. BC= 3‬‬
‫‪ (1‬ﺍﺣﺴﺐ ‪MB‬‬

‫‪ (2‬ﺑﻴﻦ ﺃﻥ ‪. AC = 3 10‬‬

‫‪ (3‬ﺍ ﺭﺳﻢ ﺍﻟﻨﻘﻄﺔ ‪ M‬ﻣﻦ ]‪ [AB‬ﻭ ‪ N‬ﻣﻦ ]‪ [CD‬ﺑﺤﻴﺚ ‪ AM=CN=6‬ﺑﻴﻦ ﺃﻥ ‪ AMCN‬ﻣﺘﻮﺍﺯﻱ ﺍﻷﺿﻼﻉ‪.‬‬
‫‪ (4‬ﻟﺘﻜﻦ ‪ H‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟـ‪ M‬ﻋﻠﻰ )‪ (CD‬ﺑﻴﻦ ﺃﻥ ‪ MBCH‬ﻣﺮﺑﻊ ﺛﻢ ﺍﺳﺘﻨﺘﺞ ‪. MC‬‬
‫‪ (5‬ﺑﻴﻦ ﺃﻥ ‪ H‬ﻣﻨﺘﺼﻒ ]‪ [CN‬ﻭ ﺃﻥ ‪ N‬ﻣﻨﺘﺼﻒ ]‪. [DH‬‬
‫‪ (6‬ﺑﻴﻦ ﺃﻥ ‪MCN‬ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ ﺍﻟﻀﻠﻌﻴﻦ ﻭ ﻗﺎﺋﻢ ﻓﻲ ‪M‬‬
‫‪ (AN) (7‬ﻳﻘﻄﻊ )‪ (MH‬ﻓﻲ ‪ I‬ﻣﺎﻫﻲ ﻁﺒﻴﻌﺔ ﻛﻞ ﻣﻦ ﺍﻟﺮﺑﺎﻋﻴﻴﻦ ‪ HADI‬ﻭ ‪. MCIN‬‬

‫‪Série F.B.A‬‬

‫‪19‬‬

‫‪E‬‬

‫‪D‬‬

‫‪2014-2013‬‬
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‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺮﺍﺑﻊ ﻟﻔﺮﺽ ﻋﺪﺩ ‪5‬‬
‫ﻣﻘﺘﺮﺡ ﻣﻦ ﺍﻷﺳﺘﺎﺫ ﻋﺮﻭﺱ‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫‪ 7‬‬
‫‪‬‬
‫‪A = ‬‬‫‪; 2‬‬
‫‪ 4‬‬
‫‪‬‬

‫‪ 1‬‬
‫‪‬‬
‫‪; B = ‬‬‫ﻧﻌﺘﺒﺮ ﺍﻟﻤﺠﺎﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ‪; +∞  ; C = -3 ; 0  :‬‬
‫‪ 2‬‬
‫‪‬‬

‫‪ (1‬ﻣﺜﻞ ﻋﻠﻰ ﻣﺴﺘﻘﻴﻢ ﻋﺪﺩﻱ ﺍﻟﻤﺠﺎﻻﺕ ‪ A‬ﻭ ‪ B‬ﻭ ‪. C‬‬

‫‪ (2‬ﺃﻭﺟﺪ ‪A ∪ C ; A ∪ B ; B ∩  - ; B ∩ C ; A ∩ B ; B ∩  -‬‬
‫‪ (3‬ﺃﺛﺒﺖ ﺃﻥ ‪2 ∈ A‬‬

‫‪−‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬

‫‪3‬‬
‫‪1‬‬
‫‪ x‬ﻭ ‪ y‬ﻋﺪﺩﺍﻥ ﺣﻘﻴﻘﻴﺎﻥ ﺑﺤﻴﺚ ‪≤ x ≤ 3‬‬
‫ﻭ‬
‫‪2‬‬
‫‪3‬‬

‫≤‬
‫‪y‬‬

‫‪1‬‬
‫≤‬
‫‪4‬‬

‫‪.‬‬

‫‪ (1‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـــ ‪ x+y‬ﻭ ﺣﺼﺮﺍ ﻟــ‪ x-y‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟـ ‪. x2-y2‬‬

‫‪1 1‬‬
‫‪−‬‬
‫‪ (2‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ ‪ x.y‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟــ‬
‫‪y x‬‬
‫‪ (3‬ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ ‪. E=4x2-4x+1‬‬
‫ﺃ‪ -‬ﻓﻜﻚ ﺍﻟﻌﺒﺎﺭﺓ ‪ E‬ﺇﻟﻰ ﺟﺬﺍء ﻋﻮﺍﻣﻞ ‪.‬‬
‫ﺏ‪ -‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟـ ‪ 2x-1‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟـ ‪. E‬‬
‫ﺍﻟﻬﻨﺪﺳﺔ‬
‫‪ (1‬ﺍﺭﺳﻢ ﻣﺜﻠﺜﺎ ‪ ABC‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪ A‬ﺣﻴﺚ ‪ AB=4‬ﻭ ‪ AC= 8‬ﺍﺣﺴﺐ ‪. BC‬‬
‫‪ (2‬ﺍﻟﺪﺍﺋﺮﺓ ‪ C‬ﺍﻟﺘﻲ ﻣﺮﻛﺰﻫﺎ ‪ O‬ﻭ ﻗﻄﺮﻫﺎ ]‪ [AC‬ﺗﻘﻄﻊ ]‪ [BC‬ﻓﻲ ‪. H‬‬
‫ﺃ‪ -‬ﻣﺎ ﻫﻲ ﻁﺒﻴﻌﺔ ﺍﻟﻤﺜﻠﺚ ‪ ACH‬؟ ﻋﻠﻞ ﺟﻮﺍﺑﻚ‪.‬‬
‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪. AH‬‬
‫‪ (3‬ﺍﺑﻦ ﺍﻟﻨﻘﻄﺔ ‪ K‬ﺑﺤﻴﺚ ‪. SA(O)=K‬‬
‫ﺃ‪ -‬ﺃﺛﺒﺖ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ OBK‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‪.‬‬
‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪. BK‬‬

‫‪Série F.B.A‬‬

‫‪20‬‬

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‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻷﻭﻝ ﻟﻔﺮﺽ ﻋﺪﺩ ‪6‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬

‫ﻧﻌﺘﺒﺮ ‪ a‬ﻋﺪﺩﺍ ﺣﻘﻴﻘﻴﺎ ﺑﺤﻴﺚ ‪ a ∈ −1; 3‬ﻭ ‪. E = 3a2 − 6a − 9‬‬
‫‪ (1‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟــ‪. a-1‬‬
‫‪ (2‬ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟــ‪. (a-1)2‬‬
‫‪ (3‬ﺑﻴﻦ ﺃﻥ ‪ E=3(a-1)2-12‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﺣﺼﺮﺍ ﻟــ ‪. E‬‬

‫‪ (4‬ﺍﺣﺴﺐ ﺇﺫﻥ )‪. E + 3a(a − 2‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻻﺕ ﻭ ﺍﻟﻤﺘﺮﺍﺟﺤﺎﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫‪3) -2x - 3 ≤ 3x + 7.‬‬

‫‪2) (2x-3)2 =4x 2 -5x-5‬‬

‫‪1) x - 2 x + 1 = 4‬‬

‫‪5) x -‬‬

‫‪4) x 2 +2x+1= 3-2 2‬‬

‫‪1 9‬‬
‫≥‬
‫‪2 4‬‬

‫‪6) 5 - 2-3x ≥ 1‬‬

‫ﻓﻴﻤﺎ ﻳﻠﻲ ﻣﺨﻄﻂ ﻳﻤﺜﻞ ﺗﺼﻨﻴﻒ ﺗﻼﻣﻴﺬ ﻗﺴﻢ ﺣﺴﺐ ﻣﻌﺪﻻﺗﻬﻢ ﻓﻲ ﻧﻬﺎﻳﺔ ﺍﻟﺜﻼﺛﻴﺔ ﺍﻟﺜﺎﻧﻴﺔ‪.‬‬
‫ﻋﺪﺩ ﺍﻟﺘﻼﻣﻴﺬ‬

‫‪12‬‬
‫‪10‬‬
‫‪8‬‬
‫‪6‬‬
‫‪4‬‬
‫‪2‬‬

‫ﻣﻌﺪﻝ ﺍﻟﺜﻼﺛﻲ‬
‫ﺍﻟﺜﺎﻧﻲ‬

‫‪10 12 14 16 18 20‬‬

‫‪8‬‬

‫‪4 6‬‬

‫‪ (1‬ﺣﺪﺩ ﻣﻨﻮﺍﻝ ﻭ ﻣﺪﻯ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﺍﻻﺣﺼﺎﺋﻴﺔ‪.‬‬
‫‪ (2‬ﺃﻛﻤﻞ ﺍﻟﺠﺪﻭﻝ ﺍﻟﺘﺎﻟﻲ‪.‬‬
‫ﻣﻌﺪﻝ ﺍﻟﺜﻼﺛﻲ ﺍﻟﺜﺎﻧﻲ‬

‫[‪[ 6;8‬‬

‫[‪[18;20[ [16;18[ [14;16[ [12;14[ [10;12[ [ 8;10‬‬

‫ﺍﻟﺘﻜﺮﺍﺭ‬
‫ﻣﺮﻛﺰ ﺍﻟﻔﺌﺔ‬
‫ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‬
‫ﺍﻟﺘﻮﺍﺗﺮ ﺑﺎﻷﻋﺪﺍﺩ ﺍﻟﻜﺴﺮﻳﺔ‬

‫‪1‬‬
‫‪32‬‬

‫‪ (3‬ﻭﻗﻊ ﺗﻜﺮﻳﻢ ﻛﻞ ﺗﻠﻤﻴﺬ ﻛﺎﻥ ﻣﻌﺪﻟﻪ ﻣﺴﺎﻭﻳﺎ ﺃﻭ ﺃﻛﺒﺮ ﻣﻦ ‪ 12‬ﺃﻭﺟﺪ ﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺎﺋﻮﻳﺔ ﻟﻌﺪﺩ ﺍﻟﺘﻼﻣﻴﺬ ﺍﻟﺬﻳﻦ ﺗﻢ ﺗﻜﺮﻳﻤﻬﻢ‪.‬‬
‫‪ (4‬ﺣﻀﺮ ﻛﻞ ﺗﻼﻣﻴﺬ ﺍﻟﻘﺴﻢ ﺃﺛﻨﺎء ﺍﻟﺘﻜﺮﻳﻢ ﺑﺎﺳﺘﺜﻨﺎء ﺗﻠﻤﻴﺬ ﻭﺍﺣﺪ‪ .‬ﻣﺎ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﻳﻜﻮﻥ ﺍﻟﺘﻠﻤﻴﺬ ﺍﻟﻤﺘﻐﻴﺐ ﻣﻦ ﺑﻴﻦ ﺍﻟﻤﻜﺮﻣﻴﻦ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‬
‫‪ ABCD‬ﻣﺴﺘﻄﻴﻞ ﺣﻴﺚ ‪ AB=8.2cm‬ﻭ ‪ AD=4.8cm‬ﻭ ‪ E‬ﻧﻘﻄﺔ ﻣﻦ ]‪ [AB‬ﺑﺤﻴﺚ ‪.AE=6,4cm‬‬
‫‪ (1‬ﺍﺣﺴﺐ ‪. DE‬‬
‫‪ (2‬ﻟﺘﻜﻦ ‪ F‬ﺍﻟﻨﻘﻄﺔ ﻣﻦ )‪ [DC‬ﺣﻴﺚ ‪ .DF=10cm‬ﺑﻴﻦ ﺃﻥ ‪ BECF‬ﻣﺘﻮﺍﺯﻱ ﺍﻷﺿﻼﻉ‪.‬‬
‫‪ (BC) (3‬ﻭ )‪ (EF‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ‪. I‬‬
‫ﺃ‪-‬‬

‫ﺑﻴﻦ ﺃﻥ ‪. BI=2, 4cm‬‬

‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪. EI‬‬

‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪ EF‬ﻭ ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ DEF‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‪.‬‬

‫‪Série F.B.A‬‬

‫‪21‬‬

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‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
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‫ﻧﻤﻮﺫﺝ ‪ 2‬ﻟﻔﺮﺽ ﻋﺎﺩﻱ ﻋﺪﺩ ‪6‬‬
‫)ﺍﻗﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﺍﻟﻨﻤﻮﺫﺟﻴﺔ(‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫‪C‬‬

‫‪B‬‬

‫ﻋﺪﺩ ﺍﻟﺘﻼﻣﻴﺬ‬

‫ﺃﺟﻴﺐ ﺑﺼﻮﺍﺏ ﺃﻭ ﺧﻄﺄ‪:‬‬
‫‪ (1‬ﻓﻲ ﻣﺘﻮﺍﺯﻱ ﺍﻟﻤﺴﺘﻄﻴﻼﺕ ‪ABCDEFGH‬‬

‫‪A‬‬

‫‪D‬‬

‫‪F‬‬

‫‪G‬‬

‫ﺃ‪ -‬ﺍﻟﻨﻘﺎﻁ ‪ A‬ﻭ ‪ B‬ﻭ ‪ D‬ﻭ ‪ E‬ﻓﻲ ﻧﻔﺲ ﺍﻟﻤﺴﺘﻮﻱ‪....................................... :‬‬
‫‪..........................................................‬‬
‫ﺏ‪ -‬ﺍﻟﻤﺜﻠﺚ ‪ AFG‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ‪:‬‬
‫‪H‬‬

‫‪E‬‬

‫‪ (2‬ﻳﻤﺜﻞ ﺍﻟﺮﺳﻢ ﺍﻟﺘﺎﻟﻲ ﻣﺨﻄﻂ ﺍﻟﻤﺴﺘﻄﻴﻼﺕ ﻟﺴﻠﺴﻠﺔ ﺇﺣﺼﺎﺋﻴﺔ ﻣﺴﺘﺮﺳﻠﺔ ﺇﺫﻥ‪:‬‬
‫ﺃ‪ -‬ﻣﺪﻯ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﻫﻮ ‪..................................................... : 5‬‬

‫ﺏ‪-‬ﻣﻮﺳﻂ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﻳﻨﺘﻤﻲ ﻟﻠﻔﺌﺔ ‪. 15,16‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫ﻳﻤﺜﻞ ﺍﻟﺮﺳﻢ ﺍﻟﻤﺼﺎﺣﺐ ‪ ABCD‬ﺷﺒﻪ ﻣﻨﺤﺮﻑ ﻗﺎﺋﻢ ﻓﻲ ‪ A‬ﻭ ‪D‬‬
‫ﺑﺤﻴﺚ ‪ AD = 2 2‬ﻭ ‪ CD=3cm‬ﻭ ‪ AB= 5cm‬ﻭ ‪ M‬ﻧﻘﻄﺔ ﻣﻦ ]‪ [AB‬ﻣﺨﻠﻔﺔ ﻟـ‪ A‬ﻭ ‪ . B‬ﺃﻋﺪﺍﺩ ﺍﻟﺘﻼﻣﻴﺬ‬

‫‪C‬‬

‫‪D‬‬

‫‪ (1‬ﻧﻀﻊ ‪ . AM=x‬ﺇﻟﻰ ﺃﻱ ﻣﺠﺎﻝ ﻳﻨﺘﻤﻲ ‪. x‬‬
‫‪ (2‬ﺃﻭﺟﺪ ‪ S‬ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ DAM‬ﻭ ’‪ S‬ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ MBC‬ﺑﺪﻻﻟﺔ ‪x‬‬

‫‪ (3‬ﺑﻴﻦ ﺃﻥ '‪ S ≥ S‬ﻳﻌﻨﻲ ﺃﻥ ‪x ∈ 2.5;5‬‬
‫‪B‬‬

‫‪ (4‬ﺍﺳﺘﻨﺘﺞ ﻣﻘﺎﺭﻧﺔ ﻟــ ‪ S‬ﻭ ’‪ S‬ﻓﻲ ﺣﺎﻟﺔ )‪ [DM‬ﻣﻨﺼﻒ ﺍﻟﺰﺍﻭﻳﺔ ˆ‬
‫‪. ADC‬‬

‫‪A‬‬

‫‪M‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬
‫ﻳﻘﺪﻡ ﺍﻟﺠﺪﻭﻝ ﺍﻟﺘﺎﻟﻲ ﻧﺘﺎﺋﺞ ﺩﺭﺍﺳﺔ ﺇﺣﺼﺎﺋﻴﺔ ﺣﻮﻝ ﻣﻌﺪﻻﺕ ﺍﻟﺜﻼﺛﻲ ﺍﻟﺜﺎﻧﻲ ﻟﺘﻼﻣﻴﺬ ﺍﻟﺴﻨﻮﺍﺕ ﺍﻟﺘﺎﺳﻌﺔ ﺃﺳﺎﺳﻲ ﻓﻲ ﻣﺪﺭﺳﺔ ﺇﻋﺪﺍﺩﻳﺔ‬
‫ﻧﻤﻮﺫﺟﻴﺔ‪.‬‬
‫ﺍﻟﻤﻌﺪﻝ‬
‫ﻋﺪﺩ ﺍﻟﺘﻼﻣﻴﺬ‬
‫ﻣﺮﻛﺰ ﺍﻟﻔﺌﺔ‬

‫[‪[19;20[ [18;19[ [17;18[ [16;17[ [15;16[ [14;15‬‬
‫‪18‬‬

‫‪124‬‬

‫‪10‬‬

‫‪30‬‬

‫‪2‬‬

‫‪16‬‬

‫ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‬
‫ﺑﺎﻟﻨﺴﺐ ﺍﻟﻤﺎﺋﻮﻳﺔ‬
‫‪ (1‬ﻣﺎﻫﻮ ﻣﻨﻮﺍﻝ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ؟ ﻓﺴﺮ ﻣﺪﻟﻮﻟﻪ‪.‬‬
‫‪ (2‬ﺃﺗﻤﻢ ﺗﻌﻤﻴﺮ ﺍﻟﺠﺪﻭﻝ ﺛﻢ ﺍﺭﺳﻢ ﻣﻀﻠﻊ ﺍﻟﺘﻮﺍﺗﺮﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ ﺑﺎﻟﻨﺴﺐ ﺍﻟﻤﺌﻮﻳﺔ‪.‬‬
‫‪ (3‬ﺃﻋﻂ ﻗﻴﻤﺔ ﺗﻘﺮﻳﺒﻴﺔ ﻟﻤﻮﺳﻂ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‪ .‬ﻓﺴﺮ ﻣﺪﻟﻮﻟﻪ‪.‬‬

‫‪M‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‪:‬‬
‫ﻳﻤﺜﻞ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﻟﻲ ﻣﻜﻌﺒﺎ ‪ ABCDEFGH‬ﻗﻴﺲ ﺣﺮﻓﻪ ‪ ∆ . 4cm‬ﻣﺴﺘﻘﻴﻤﺎ ﻣﻦ ﺍﻟﻤﺴﺘﻮﻱ )‪(BDF‬‬

‫‪A‬‬
‫‪B‬‬

‫ﻭ ﻋﻤﻮﺩﻱ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻮﻱ )‪ (ABC‬ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪ O‬ﻣﺮﻛﺰ ﺍﻟﻤﺮﺑﻊ ‪. ABCD‬‬

‫‪O‬‬
‫‪C‬‬

‫‪ (1‬ﺑﻴﻦ ﺃﻥ )‪ (DB‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ ∆‪.‬‬

‫‪xJ‬‬

‫‪D‬‬

‫‪ (2‬ﺑﻴﻦ ﺃﻥ )‪ (DH‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪. (ABC‬‬
‫‪ (3‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ )‪ (DB‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪. (DH‬‬

‫‪E‬‬

‫‪F‬‬

‫‪ (4‬ﺑﻴﻦ ﺃﻥ ∆‪. (DH)//‬‬
‫‪ (5‬ﻟﺘﻜﻦ ‪ J‬ﻣﻨﺘﺼﻒ]‪ . [OD‬ﺑﻴﻦ ﺃﻥ )‪ (JH‬ﻭ ∆ ﻣﺘﻘﺎﻁﻌﺎﻥ‪ .‬ﻭ ﻟﺘﻜﻦ ‪ M‬ﻧﻘﻄﺔ ﺗﻘﺎﻁﻌﻬﻤﺎ‪.‬‬
‫‪ (6‬ﺍﺣﺴﺐ ﺣﺠﻢ ﺍﻟﻬﺮﻡ ‪ MABCD‬ﺍﻟﺬﻱ ﻗﻤﺘﻪ ‪ M‬ﻭ ﻗﺎﻋﺪﺗﻪ ﺍﻟﻤﺮﺑﻊ ‪. ABCD‬‬

‫‪Série F.B.A‬‬

‫‪22‬‬

‫‪G‬‬

‫‪H‬‬

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‫ﻧﻤﻮﺫﺝ‪ 3‬ﻟﻔﺮﺽ ﻋﺎﺩﻱ ﻋﺪﺩ ‪6‬‬
‫)ﺍﻗﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﻣﺼﻄﻔﻰ ﺍﻟﺴﻼﻣﻲ(‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫‪ OABC‬ﻫﺮﻡ ﻗﺎﻋﺪﺗﻪ ﺍﻟﻤﺮﺑﻊ ‪ ABCD‬ﺣﻴﺚ‪:‬‬

‫‪O‬‬

‫‪ AB=4cm‬ﻭ ‪ OA= 8 cm‬ﻭ ) ‪ (OA ) ⊥ ( BC‬ﻭ ) ‪. (OB ) ⊥ ( AB‬‬
‫ﻟﺘﻜﻦ ﺍﻟﻨﻘﺎﻁ ‪ I‬ﻭ ‪ J‬ﻭ ‪ K‬ﻭ ‪ L‬ﻣﻨﺘﺼﻔﺎﺕ ﻛﻞ ﻣﻦ ‪:‬‬

‫] ‪[OA‬‬

‫‪K‬‬

‫ﻭ ] ‪ [OB‬ﻭ ] ‪ [OC‬ﻭ ] ‪ [OD‬ﻋﻠﻰ ﺍﻟﺘﻮﺍﻟﻲ‪.‬‬

‫‪I‬‬

‫‪L‬‬

‫‪ (1‬ﺑﻴﻦ ﺃﻥ ) ‪. ( BC ) ⊥ (OAB‬‬
‫‪(2‬‬

‫‪J‬‬

‫‪B‬‬

‫ﺃ‪ -‬ﺍﺳﺘﻨﺘﺞ ﻧﻮﻉ ﺍﻟﻤﺜﻠﺚ ‪.IBC‬‬
‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪. IB‬‬

‫‪O‬‬

‫ﺝ‪ -‬ﺑﻴﻦ ﺃﻥ ‪. IC = 4 2‬‬

‫‪A‬‬

‫‪D‬‬

‫‪ (3‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ‪(OB ) ⊥ (IJ ) :‬‬

‫ﺏ‪ -‬ﺑﻴﻦ ﺃﻥ ) ‪(OB ) ⊥ (JK‬‬

‫‪ (4‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ) ‪. (ABC ) ⊥ (IJK‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫‪ ( I‬ﺃﺟﻴﺐ ﺑﺼﻮﺍﺏ ﺃﻭ ﺧﻄﺄ‪:‬‬

‫‪ (1‬ﺇﺫﺍ ﻛﺎﻥ ‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺣﻴﺚ ‪ -2x > 6‬ﻓﺈﻥ [‪............................ : x ∈ ]-∞ ; -3‬‬
‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺣﻴﺚ ‪ -3 ≤ x+1 ≤ 5‬ﻓﺈﻥ ‪............................ : x ≤ 4‬‬
‫‪(3‬‬

‫‪2‬‬
‫‪‬‬

‫‪3‬‬
‫‪13 ‬‬
‫‪‬‬
‫‪‬‬
‫; ‪................................................... : 1 ;  ∩  2‬‬
‫; ‪= 1‬‬
‫‪‬‬
‫‪2‬‬
‫‪8 ‬‬
‫‪‬‬
‫‪‬‬

‫‪ (II‬ﺃﻛﻤﻞ ﺍﻟﻨﻘﺎﻁ ﺑﺤﺼﺮ ﺃﻭ ﺑﻤﺠﺎﻝ ﺃﻭ ﺍﺗﺤﺎﺩ ﻣﺠﺎﻟﻴﻦ ﻣﻦ ‪: ‬‬

‫}‬

‫{‬

‫‪∈  / ......................} = -2 ; 3‬‬

‫‪{x‬‬

‫‪A = x ∈  / x ≤ - 2 = .....................................‬‬
‫=‬
‫‪B‬‬

‫∈= ‪C‬‬
‫‪{x  / x > 2} = ........................................‬‬
‫‪D = {x ∈  / x ≤ 5} = ..................................‬‬
‫‪D = {x ∈  / 3x-2 ≤ 5} = ..................................‬‬

‫‪Série F.B.A‬‬

‫‪23‬‬

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‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬
‫ﻳﻤﺜﻞ ﺍﻟﺠﺪﻭﻝ ﺃﺳﻔﻠﻪ ﻣﺠﻤﻮﻋﺔ ﻣﻦ ﺍﻟﺘﻼﻣﻴﺬ ﻓﻲ ﻓﺮﺽ ﻣﺮﺍﻗﺒﺔ‪.‬‬
‫ﺍﻟﻌﺪﺩ‬

‫[‪[ 4;8‬‬

‫ﺍﻟﺘﻜﺮﺍﺭ‬
‫ﻣﺮﻛﺰ ﺍﻟﻔﺌﺔ‬

‫‪4‬‬

‫[‪[16;20[ [12;16[ [ 8;12‬‬
‫‪8‬‬

‫ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‬

‫‪ (1‬ﻣﺎ ﻫﻮ ﻧﻮﻉ ﺍﻟﻤﻴﺰﺓ ؟‬
‫‪ (2‬ﺣﺪﺩ ﺍﻟﺘﻜﺮﺍﺭ ﺍﻟﺠﻤﻠﻲ ﻟﻬﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﺍﻹﺣﺼﺎﺋﻴﺔ؟ ﺛﻢ ﺃﺗﻤﻢ ﺍﻟﺠﺪﻭﻝ‪.‬‬
‫‪ (3‬ﻣﺎ ﻫﻮ ﻣﻌﺪﻝ ﺍﻟﻘﺴﻢ ﻓﻲ ﻫﺬﺍ ﺍﻟﻔﺮﺽ؟‬
‫‪ (4‬ﻣﺎ ﻫﻲ ﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺎﺋﻮﻳﺔ ﻟﻠﺘﻼﻣﻴﺬ ﺍﻟﺬﻳﻦ ﺗﺤﺼﻠﻮﺍ ﻋﻠﻰ ﻋﺪﺩ ﺩﻭﻥ ‪ 12‬؟‬
‫‪ (5‬ﺍﺭﺳﻢ ﺍﻟﻤﻀﻠﻊ ﺍﻟﻤﻮﺍﻓﻖ ﻟﻠﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‪.‬‬
‫‪ (6‬ﺍﺳﺘﻨﺘﺞ ﻣﻮﺳﻄﺎ ﻟﻬﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬
‫‪ X‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ﺣﻴﺚ ‪. -1 <2 x 2 - 3 < 7‬‬
‫‪ (1‬ﺃﻭﺟﺪ ﺣﺼﺮﺍ ﻟﻠﻌﺪﺩ ‪. x2‬‬
‫‪ (2‬ﺑﻴﻦ ﺃﻥ ‪. 1 < x < 5‬‬
‫‪ (3‬ﺍﺳﺘﻨﺘﺞ ﺍﻟﻤﺠﺎﻝ ﺍﻟﺬﻱ ﻳﻨﺘﻤﻲ ﺇﻟﻴﻪ ‪. x‬‬

‫‪Série F.B.A‬‬

‫‪24‬‬

‫‪5‬‬

‫‪3‬‬

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‫ﻧﻤﻮﺫﺝ‪ 4‬ﻟﻔﺮﺽ ﻋﺎﺩﻱ ﻋﺪﺩ ‪6‬‬
‫)ﺍﻗﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﺍﻟﺒﺴﺘﺎﻥ(‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫ﺍﻧﻘﻞ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ‪:‬‬

‫‪ -1‬ﻣﺠﻤﻮﻋﺔ ﺣﻠﻮﻝ ﺍﻟﻤﻌﺎﺩﻟﺔ ‪0‬‬
‫= ‪: x - 2 x +1‬‬

‫ﺃ‪{−1;1} -‬‬

‫ﺏ‪S  = {1} -‬‬

‫= ‪S‬‬

‫ﺝ‪S  = ∅ -‬‬

‫‪ -2‬ﺇﺫﺍ ﻛﺎﻥ ﻣﺤﻴﻂ ﺍﻟﻤﺴﺘﻄﻴﻞ ﻳﺴﺎﻭﻱ ﻣﺤﻴﻂ ﺍﻟﻤﺜﻠﺚ ﻓﺈﻥ ‪:‬‬

‫‪2‬‬
‫‪2‬‬

‫ﺃ‪-‬‬
‫‪-3‬‬

‫ﺏ‪2 -‬‬

‫‪x=1-‬‬

‫=‪x‬‬

‫‪x‬‬

‫ﺝ‪2 -‬‬

‫‪x=1-‬‬

‫‪ ABC‬ﻣﺜﻠﺚ ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪ A‬ﻭ ﻣﺤﺘﻮﺍ ﻓﻲ ﺍﻟﻤﺴﺘﻮﻱ ‪P‬‬

‫‪ I ∈ BC ‬ﻭ‬

‫) ‪( AB‬‬

‫) ‪( AI‬‬

‫⊥ ‪Δ‬‬

‫ﺃ‪-‬‬

‫⊥ ‪ Δ‬ﻭ‬
‫ﺏ‪-‬‬

‫) ‪( AC‬‬

‫) ‪( AC‬‬

‫⊥ ‪ Δ‬ﺇﺫﻥ ‪:‬‬

‫‪A‬‬
‫‪C‬‬

‫) ‪( AI‬‬

‫⊥‬

‫ﺝ‪⊥ P -‬‬

‫) ‪( AI‬‬

‫‪I‬‬
‫‪B‬‬

‫‪P‬‬

‫‪ SABC -4‬ﻫﺮﻡ ﻗﺎﻋﺪﺗﻪ ﻣﺜﻠﺚ ‪ ABC‬ﻗﺎﺋﻢ ﻓﻲ ‪A‬‬
‫ﻭ ﺍﺭﺗﻔﺎﻋﻪ )‪ (SA‬ﻭ ‪ I ∈ SC ‬ﺇﺫﻥ ‪:‬‬
‫ﺃ‪-‬‬

‫) ‪( SBC‬‬

‫‪S‬‬

‫⊥ ) ‪. ( AB‬‬

‫ﺏ‪-‬‬

‫) ‪( ABI‬‬

‫⊥‬

‫) ‪( AB‬‬

‫ﺕ‪-‬‬

‫) ‪( SAC‬‬

‫⊥‬

‫) ‪( AB‬‬

‫‪I‬‬

‫‪A‬‬

‫‪C‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬

‫‪B‬‬

‫‪ (1‬ﺣﻞ ﻓﻲ ‪ ‬ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﺘﺎﻟﻴﺔ‪:‬‬

‫‪x‬‬
‫‪4x-1 x‬‬
‫‬‫=‬
‫* ‪−1‬‬
‫‪2‬‬
‫‪3‬‬
‫‪6‬‬

‫= ‪9x 2 − 30x + 25‬‬
‫* ‪0‬‬

‫= ‪9x 2 − 30x + 25‬‬
‫* ‪16‬‬

‫‪ (2‬ﻟﺘﻜﻦ ﺍﻟﻌﺒﺎﺭﺓ ‪ A = 4x 2 − 12x + 5‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ‪. A = ( 2x − 3 ) − 4‬‬
‫‪2‬‬

‫ﺏ‪ -‬ﺣﻞ ﻓﻲ ‪ ‬ﺃ‪A=0 -‬‬

‫ﺏ‪-‬‬

‫‪2‬‬

‫)‪( 2x − 1‬‬

‫=‬
‫‪A‬‬

‫ﺝ‪A = 4x 2 -‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬

‫‪ SABCD‬ﻫﺮﻡ ﻣﻨﺘﻈﻢ ﻗﺎﻋﺪﺗﻪ ﻣﺮﺑﻊ ‪ ABCD‬ﺣﻴﺚ ﻣﺮﻛﺰﻩ ‪ O‬ﻭ ‪ SA=8cm‬ﻭ ‪. AB = 4 2‬‬
‫‪ I‬ﻣﻨﺘﺼﻒ ]‪. M ∈ SB  [SA‬‬
‫‪ (1‬ﺑﻴﻦ ﺃﻥ )‪. (OI) // (SCD‬‬

‫‪Série F.B.A‬‬

‫‪25‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫‪ (2‬ﺍﺣﺴﺐ ‪. OI‬‬
‫‪ (3‬ﺑﻴﻦ ﺃﻥ‬
‫‪(4‬‬

‫) ‪( OD‬‬

‫⊥‬

‫‪S‬‬

‫) ‪( SO‬‬
‫‪M‬‬

‫ﺍﺣﺴﺐ ‪. SO‬‬

‫‪ (5‬ﺑﻴﻦ ﺃﻥ‬

‫) ‪( SAC‬‬

‫⊥ ) ‪. ( OD‬‬
‫‪I‬‬

‫‪ (6‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ OID‬ﻗﺎﺋﻢ ‪.‬‬
‫‪ (7‬ﺍﺣﺴﺐ ‪. DI‬‬

‫‪C‬‬

‫‪B‬‬

‫‪ (8‬ﻟﺘﻜﻦ ‪ N‬ﻧﻘﻄﺔ ﻣﻦ ]‪ [SA‬ﺣﻴﺚ )‪. (MN) // (AB‬‬

‫‪O‬‬

‫ﺍﺣﺴﺐ ‪ MN‬ﻋﻠﻤﺎ ﺃﻥ ‪.SM=2‬‬

‫‪A‬‬

‫‪Série F.B.A‬‬

‫‪26‬‬

‫‪D‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻷﻭﻝ ﻟﻔﺮﺽ ﺗﺄﻟﻴﻔﻲ ﻋﺪﺩ‪3‬‬

‫ﻓﺮﺽ ﺍﻗﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﺍﻟﻨﻤﻮﺫﺟﻴﺔ‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‪:‬‬
‫ﻳﻠﻲ ﻛﻞ ﺳﺆﺍﻝ ‪ 3‬ﻣﻘﺘﺮﺣﺎﺕ‪ ،‬ﺃﺣﺪﻫﺎ ﻓﻘﻂ ﺻﺤﻴﺢ ﺿﻊ )‪ (x‬ﺃﻣﺎﻡ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ‪.‬‬

‫‪ ABCD (1‬ﻭ ‪ EBHK‬ﻭ ‪ AEFG‬ﻣﺮﺑﻌﺎﺕ ﺣﻴﺚ ﻗﻴﺲ ﻣﺴﺎﺣﺔ ‪ ABCD‬ﻫﻲ ‪12 2 + 18‬‬
‫ﻭ ‪ AE = 2 3‬ﻭ ﻗﻴﺲ ﺍﻟﻤﺴﺎﺣﺔ ﺍﻟﺪﺍﻛﻨﺔ ﻫﻲ ‪ 2 2‬ﺇﺫﻥ ‪ EB‬ﻳﺴﺎﻭﻱ‪:‬‬

‫‪30‬‬

‫‪2 3‬‬

‫‪ (2‬ﻣﺟﻣﻭﻋﺔ ﺣﻠﻭﻝ ﺍﻟﻣﺗﺭﺍﺟﺣﺔ ‪2 < 2 x − 1 :‬‬
‫‪1; +∞‬‬

‫‪6‬‬

‫ ‪ x‬ﻫﻲ‬‫‪−∞; −1‬‬

‫‪−1; +∞‬‬

‫‪ (3‬ﻓﻲ ﻧﺎﺩﻱ ﺃﻁﻔﺎﻝ ﻗﻤﻨﺎ ﺑﺪﺭﺍﺳﺔ ﺇﺣﺼﺎﺋﻴﺔ ﻣﺴﺘﺮﺳﻠﺔ ﻷﻭﺯﺍﻥ ﻣﺠﻤﻮﻋﺔ ﻣﻦ ﻣﻨﺨﺮﻁﻴﻪ ﻓﺘﺤﺼﻠﻨﺎ ﻋﻠﻰ ﻣﺨﻄﻂ ﺍﻟﺘﻜﺮﺍﺭﺍﺕ‬

‫ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ ﺍﻟﺗﺎﻟﻲ‪:‬‬
‫ﺍﻟﺘﻜﺮﺍﺭ ﺍﻟﺘﺮﺍﻛﻤﻲ ﺍﻟﺼﺎﻋﺪ‬

‫ﺃﻭﺯﺍﻥ ﺍﻟﺘﻼﻣﻴﺬ‬

‫[‬

‫[‬

‫* ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ﺍﻷﻁﻔﺎﻝ ﺍﻟﺬﻳﻦ ﺃﻭﺯﺍﻧﻬﻢ ﺗﻨﺘﻤﻲ ﻟﻠﻔﺌﺔ ‪ 22;23‬ﺗﻤﺜﻞ ‪ 16%‬ﻣﻦ ﻋﺪﺩ ﻣﻨﺨﺮﻁﻲ ﺍﻟﻨﺎﺩﻱ ﻓﺈﻥ ﻋﺪﺩ ﻣﻨﺨﺮﻁﻲ ﺍﻟﻨﺎﺩﻱ‬
‫ﻫﻮ‪:‬‬

‫‪25‬‬

‫‪75‬‬

‫‪50‬‬

‫* ﺍﻟﻘﻴﻤﺔ ﺍﻟﺘﻘﺮﻳﺒﻴﺔ ﻟﻤﻮﺳﻂ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﻫﻮ ‪:‬‬

‫‪23‬‬

‫‪25‬‬

‫‪24‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‪:‬‬
‫= ‪ M‬ﺣﻴﺚ ‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ‪.‬‬
‫ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ ‪−2x 2 − 5x + 25‬‬
‫‪2‬‬

‫‪1 ‬‬
‫‪9‬‬
‫‪ (1‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ‪x  − x 2‬‬
‫‪2 ‬‬
‫‪4‬‬

‫‪‬‬

‫= ‪.M‬‬
‫‪5 −‬‬

‫‪H‬‬

‫‪B‬‬

‫‪‬‬

‫ﺏ‪ -‬ﻓﻜﻚ ﺍﻟﻌﺒﺎﺭﺓ ‪ M‬ﺇﻟﻰ ﺟﺬﺍء ﻋﻮﺍﻣﻞ‪.‬‬

‫‪A‬‬

‫‪E‬‬

‫ﺝ‪ -‬ﺣﻞ ﻓﻲ ‪ ‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪. M=0‬‬

‫‪O‬‬

‫‪ (2‬ﺣﻞ ﻓﻲ ‪ ‬ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪. 2x 2 < ( x + 5 ) 2‬‬
‫‪ (3‬ﻓﻲ ﺍﻟﺮﺳﻢ ﺍﻟﻤﻘﺎﺑﻞ ‪ ABCD‬ﻣﺮﺑﻊ ﻣﺮﻛﺰﻩ ‪ O‬ﻭ ‪ H‬ﺍﻟﻨﻘﻄﺔ ﻣﻦ ]‪[AB‬‬

‫‪Série F.B.A‬‬

‫‪27‬‬

‫‪C‬‬

‫‪D‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺣﻴﺚ ‪ HB = x‬ﻭ ‪ AH=5‬ﻭ ‪ H‬ﻣﺨﺎﻟﻔﺔ ﻟــ‪. B‬‬

‫ﻭ ‪ E‬ﻧﻘﻄﺔ ﺗﻘﺎﻁﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ H‬ﻭ ﺍﻟﻌﻤﻮﺩﻱ ﻋﻠﻰ ]‪ [AB‬ﻭ ﺍﻟﻘﻄﺮ ]‪ . [BD‬ﺑﻴﻦ ﺃﻥ ‪2‬‬
‫‪ (4‬ﻓﻲ ﺣﺎﻟﺔ ‪ BE<OB‬ﺑﻴﻦ ﺃﻥ ‪. x ∈ 0;5‬‬

‫)‪( x + 5‬‬
‫‪2‬‬

‫= ‪. OB‬‬
‫ﻋﺪﺩ ﺍﻟﻼﻋﺒﻴﻦ‬

‫‪ (5‬ﻓﻲ ﺣﺎﻟﺔ ‪ SABCD= 6 SAEB‬ﺑﻴﻦ ﺃﻥ ‪ x‬ﻳﺤﻘﻖ ﺍﻟﻤﻌﺎﺩﻟﺔ ‪. M=0‬ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﻗﻴﻤﺔ ‪. x‬‬
‫‪ (6‬ﺍﺑﻦ ﺍﻟﺮﺳﻢ ﺍﻟﺴﺎﺑﻖ ﻓﻲ ﺣﺎﻟﺔ ‪. x=2,5‬‬
‫‪ (7‬ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (AE‬ﻳﻘﻄﻊ )‪ (BC‬ﻓﻲ ‪ F‬ﺑﻴﻦ ﺃﻥ ‪ F‬ﻣﻨﺘﺼﻒ ]‪. [BC‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‪:‬‬
‫)‪ I‬ﺍﺳﺘﻌﺪﺍﺩﺍ ﻟﻤﻘﺎﺑﻠﺔ ﻣﺼﻴﺮﻳﺔ ﻗﺎﻡ ﻣﺪﺭﺏ ﻛﺮﺓ ﺍﻟﺴﻠﺔ ﻓﻲ ﺑﺪﺍﻳﺔ ﺍﻷﺳﺒﻮﻉ‬
‫ﺑﺎﺧﺘﺒﺎﺭ ﻟﻼﻋﺒﻲ ﺍﻟﻔﺮﻳﻖ ﻋﻠﻰ ﺗﺴﺠﻴﻞ ﺭﻣﻴﺎﺕ ﻣﺒﺎﺷﺮﺓ ﻓﻲ ﺍﻟﺴﻠﺔ‬
‫ﻟﺘﺤﺪﻳﺪ ﺍﻟﺘﺸﻜﻴﻠﺔ ﺍﻟﻤﻨﺎﺳﺒﺔ ﻓﻜﺎﻧﺖ ﺍﻟﻨﺘﺎﺋﺞ ﻭﻓﻖ ﺍﻟﻤﺨﻄﻂ ﺍﻟﺘﺎﻟﻲ‪:‬‬
‫ﻋﺪﺩ ﺍﻟﺮﻣﻴﺎﺕ‬
‫ﺍﻟﻤﺴﺠﻠﺔ‬

‫‪ (1‬ﻣﺎ ﻫﻮ ﻣﺪﻯ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ؟‬
‫‪ (2‬ﺃﻭﺟﺪ ﻣﻮﺳﻄﺎ ﻟﻬﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﻣﻔﺴﺮﺍ ﻣﺪﻟﻮﻟﻪ‪.‬‬

‫‪ ( II‬ﻓﻲ ﻭﺳﻂ ﺍﻷﺳﺒﻮﻉ ﻭ ﺑﻌﺪ ﺗﻤﺮﻳﻦ ﻣﺨﺼﺺ ﻟﻠﺮﻣﻴﺎﺕ ﺍﻟﻤﺒﺎﺷﺮﺓ ﻗﺎﻡ ﺍﻟﺪﺭﺏ ﺑﺎﺧﺘﺒﺎﺭ ﺛﺎﻥ ﺗﻐﻴﺐ ﻋﻨﻪ ﺃﺣﺪ ﺍﻟﻼﻋﺒﻴﻦ ﺍﻟﺴﺎﺑﻘﻴﻦ ﻓﻜﺎﻧﺖ‬
‫ﺍﻟﻨﺘﺎﺋﺞ ﻛﻤﺎ ﻳﻠﻲ‪:‬‬
‫ﻋﺪﺩ ﺍﻟﺮﻣﻴﺎﺕ‬

‫‪15‬‬

‫‪16‬‬

‫‪17‬‬

‫‪18‬‬

‫‪19‬‬

‫‪20‬‬

‫ﻋﺪﺩ ﺍﻟﻼﻋﺒﻴﻦ‬

‫‪5‬‬

‫‪5‬‬

‫‪2‬‬

‫‪4‬‬

‫‪4‬‬

‫‪3‬‬

‫‪ (1‬ﺃ‪ -‬ﻣﻘﺎﺭﻧﺔ ﻣﺪﻯ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﺑﺴﺎﺑﻘﺘﻬﺎ ﻫﻞ ﻳﻤﻜﻦ ﺍﻟﻘﻮﻝ ﺃﻥ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ ﺃﺻﺒﺤﺖ ﺃﻛﺜﺮ ﺗﺠﺎﻧﺴﺎ ؟ ﻋﻠﻞ ﺟﻮﺍﺑﻚ‪.‬‬
‫ﺏ‪ -‬ﻣﺎ ﻫﻮ ﻋﺪﺩ ﺍﻟﻼﻋﺒﻴﻦ ﺍﻟﺬﻳﻦ ﺍﻟﺬﻳﻦ ﺳﺠﻠﻮﺍ ﻋﺪﺩ ﺭﻣﻴﺎﺕ ﻻ ﺗﻘﻞ ﻋﻦ ‪ 16‬ﻭ ﻻ ﺗﺘﺠﺎﻭﺯ ‪.19‬‬
‫‪ (2‬ﺍﻟﻼﻋﺐ ﺍﻟﻤﺘﻐﻴﺐ ﺃﺟﺮﻯ ﻫﺬﺍ ﺍﻹﺧﺘﺒﺎﺭ ﻻﺣﻘﺎ ﻋﻠﻰ ﺍﻧﻔﺮﺍﺩ ﻓﻜﺎﻧﺖ ﻋﺪﺩ ﺍﻟﺮﻣﻴﺎﺕ ﺃﺣﺪ ﻗﻴﻢ ﺍﻟﺴﻠﺴﻠﺔ ‪ II‬ﻭ ﻧﺘﺞ ﻋﻦ ﺫﻟﻚ ﺑﻌﺪ‬
‫ﺿﻢ ﻫﺬﺍ ﺍﻟﻌﺪﺩ ﻟﻠﺴﻠﺴﻠﺔ ‪: II‬‬
‫•‬

‫ﺍﻟﻤﻮﺳﻂ ﻳﺴﺎﻭﻱ ‪. 17,5‬‬

‫•‬

‫ﺍﻟﻨﺴﺒﺔ ﺍﻟﻤﺎﺋﻮﻳﺔ ﻟﻠﻼﻋﺒﻴﻦ ﺍﻟﺬﻳﻦ ﺳﺠﻠﻮﺍ ﻋﺪﺩ ﺭﻣﻴﺎﺕ ﻻ ﺗﻘﻞ ﻋﻦ ‪ 16‬ﻭ ﻻ ﺗﺘﺠﺎﻭﺯ ‪ 19‬ﻫﻲ ‪ 62,5%‬ﺑﺎﻟﻨﺴﺒﺔ ﺇﻟﻰ ﻛﺎﻣﻞ‬
‫ﺍﻟﻔﺮﻳﻖ‬

‫•‬

‫ﻣﺎ ﻫﻮ ﻋﺪﺩ ﺍﻟﺮﻣﻴﺎﺕ ﺍﻟﻤﺴﺠﻠﺔ ﻣﻦ ﻁﺮﻑ ﻫﺬﺍ ﺍﻟﻼﻋﺐ؟ ﻋﻠﻞ ﺟﻮﺍﺑﻚ‪.‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‪:‬‬
‫ﻳﻤﺜﻞ ﺍﻟﺮﺳﻢ ﻣﺜﻠﺜﺎ ‪ ABC‬ﺑﺤﻴﺚ ‪ AC = 18‬ﻭ ‪ I‬ﺍﻟﻨﻘﻄﺔ ﻣﻦ]‪ [AC‬ﺑﺤﻴﺚ ‪ CI= 6‬ﻭ ‪ IB = 2 6‬ﻭ ﺍﻟﻨﻘﻄﺔ ‪ N‬ﻣﻦ ]‪ [AB‬ﺣﻴﺚ ‪IN= 4‬‬

‫‪NB 1‬‬
‫ﻭ =‬
‫‪NA 2‬‬

‫‪M‬‬

‫‪B‬‬

‫‪ (1‬ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﻮﺍﺯﻱ ﻟــ )‪ (AC‬ﻭ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ B‬ﻳﻘﻄﻊ )‪ (IN‬ﻓﻲ ‪. M‬‬
‫ﺃ‪-‬‬

‫‪NM 1‬‬
‫ﺑﻴﻦ ﺃﻥ‬
‫=‬
‫‪NI 2‬‬

‫‪MB‬‬
‫‪AI‬‬

‫‪O‬‬

‫= ‪.‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ MBCI‬ﻣﻌﻴﻦ‪.‬‬

‫‪C‬‬

‫‪ (2‬ﻟﺘﻜﻦ ‪ O‬ﻣﺮﻛﺰ ﺍﻟﻤﻌﻴﻦ ‪.MBCI‬‬
‫ﺃ‪-‬‬

‫ﺍﺣﺴﺐ ‪. OC‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺍﻟﺮﺑﺎﻋﻲ ‪ MBCI‬ﺗﺴﺎﻭﻱ ‪12 5‬‬

‫‪Série F.B.A‬‬

‫‪N‬‬

‫‪28‬‬

‫‪I‬‬

‫‪H‬‬

‫‪A‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺕ‪ -‬ﻟﺘﻜﻦ ‪ H‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟــ‪ M‬ﻋﻠﻰ )‪ (AC‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ HIN‬ﻣﺘﻘﺎﻳﺲ ﺍﻟﻀﻠﻌﻴﻦ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‪:‬‬
‫ﻳﻤﺜﻞ ﺍﻟﺮﺳﻢ ﺍﻟﺘﺎﻟﻲ ﻫﺮﻣﺎ ‪ SABCD‬ﻗﺎﻋﺪﺗﻪ ﺍﻟﻤﺮﺑﻊ ‪ ABCD‬ﺍﻟﺬﻱ ﻣﺮﻛﺰﻩ ‪ O‬ﻭ ‪ SDC‬ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ ﺍﻷﺿﻼﻉ ﻭ ‪ I‬ﻣﻨﺘﺼﻒ‬
‫‪. SA‬‬
‫‪= SB‬‬
‫]‪ [SC‬ﻭ ‪ SBC‬ﻣﺜﻠﺚ ﻗﺎﺋﻢ ﻓﻲ ‪ C‬ﺑﺤﻴﺚ ‪ DC= 4‬ﻭ ‪= 4 2‬‬

‫‪ (1‬ﺑﻴﻦ ﺃﻥ ‪DI = 2 3‬‬
‫‪(2‬‬

‫ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ‪. OI = 2 2‬‬
‫ﺕ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ DIB‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪. I‬‬

‫‪ (3‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ‬

‫) ‪(DI ) ⊥ ( SBC‬‬

‫ﺏ‪ -‬ﻟﺘﻜﻦ ‪ J‬ﻣﻨﺘﺼﻒ ]‪ [BC‬ﺍﺣﺴﺐ ‪.SJ‬‬
‫ﺙ‪ -‬ﻟﺘﻜﻦ ‪ K‬ﻣﻨﺘﺼﻒ ]‪ [DJ‬ﻭ ‪ P‬ﻣﻨﺎﻅﺮﺓ ‪ I‬ﺑﺎﻟﻨﺴﺒﺔ ﺇﻟﻰ ‪ .K‬ﺍﺣﺴﺐ ‪. SP‬‬

‫‪S‬‬

‫‪I‬‬

‫‪C‬‬

‫‪B‬‬
‫‪O‬‬

‫‪D‬‬

‫‪A‬‬

‫‪Série F.B.A‬‬

‫‪29‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺜﺎﻧﻲ ﻟﻔﺮﺽ ﺗﺄﻟﻴﻔﻲ ﻋﺪﺩ‪3‬‬
‫ﻓﺮﺽ ﺍﻗﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﻣﺼﻄﻔﻰ‬
‫ﺍﻟﺴﻼﻣﻲ‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‬
‫ﻳﻠﻲ ﻛﻞ ﺳﺆﺍﻝ ‪ 3‬ﻣﻘﺘﺮﺣﺎﺕ‪ ،‬ﺃﺣﺪﻫﺎ ﻓﻘﻂ ﺻﺤﻴﺢ ﺿﻊ )‪ (x‬ﺃﻣﺎﻡ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ‪.‬‬

‫‪ X (1‬ﻫﻮ ﻋﺪﺩ ﺣﻘﻴﻘﻲ ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ ‪x < 3‬‬

‫‪( x + 3)( x − 3) < 0‬‬
‫‪ (2‬ﻣﺠﻤﻮﻋﺔ ﺣﻠﻮﻝ ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪:‬‬

‫ﻓﺈﻥ‪:‬‬

‫‪( x + 3)( x − 3) > 0‬‬
‫‪≤Π‬‬

‫‪0‬‬
‫= )‪( x + 3)( x − 3‬‬

‫‪ - 3x +Π‬ﻫﻲ‬

‫‪−∞;0 ‬‬

‫‪0; +∞‬‬

‫‪0; +∞ ‬‬

‫‪ (3‬ﺇﺫﺍ ﻛﺎﻥ ‪ ABCDEFGH‬ﻣﻜﻌﺒﺎ ﻗﻴﺲ ﺣﺮﻓﻪ ‪ 2 3‬ﻓﺈﻥ‬

‫‪A‬‬
‫‪B‬‬
‫‪D‬‬

‫‪C‬‬

‫‪E‬‬

‫‪F‬‬

‫‪G‬‬

‫‪AG = 6‬‬

‫‪H‬‬

‫‪AG = 2 6‬‬

‫‪AG = 3 6‬‬

‫‪ (4‬ﻧﻘﻮﻡ ﺑﺴﺤﺐ ﻛﻮﻳﺮﺓ ﺑﺼﻔﺔ ﻋﺸﻮﺍﺋﻴﺔ ﻣﻦ ﻛﻴﺲ ﻳﺤﻮﻱ ﻛﻮﻳﺮﺍﺕ ﻣﺘﺸﺎﺑﻬﺔ ﻭ ﻟﻬﺎ ﻧﻔﺲ ﺍﻟﻠﻮﻥ ﻭ ﻣﺮﻗﻤﺔ ﻣﻦ ‪ 1‬ﺇﻟﻰ ‪ 10‬ﺇﺫﻥ‬
‫ﺍﺣﺘﻤﺎﻝ ﺳﺤﺐ ﻛﻮﻳﺮﺓ ﺭﻗﻤﻬﺎ ﻓﺮﺩﻱ ﻭ ﻻ ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﻠﻰ ‪ 5‬ﻫﻮ‬

‫‪1‬‬
‫‪2‬‬

‫‪2‬‬
‫‪5‬‬

‫‪3‬‬
‫‪10‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‬
‫ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ ‪ A = x 2 + 2x − 35‬ﺣﻴﺚ ‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ ‪1‬‬
‫‪ (1‬ﺍﺣﺴﺐ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻌﺪﺩﻳﺔ ﻟـﻠﻌﺒﺎﺭﺓ ‪ A‬ﺇﺫﺍ ﻛﺎﻥ ‪. x=5‬‬

‫‪ (2‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ‪A =( x + 1) − 36‬‬
‫‪2‬‬

‫ﺝ‪ -‬ﺣﻞ ﻓﻲ ‪A=0 : ‬‬

‫ﺏ‪ -‬ﻓﻜﻚ ‪ A‬ﺇﻟﻰ ﺟﺬﺍء ﻋﻮﺍﻣﻞ‬

‫‪ (3‬ﺗﺄﻣﻞ ﺍﻟﺸﻜﻞ ﺍﻟﻤﻘﺎﺑﻞ ﺣﻴﺚ ﺍﻟﻤﺴﺘﻘﻴﻢ )‪ (AB‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ )‪ (AD‬ﻭ ﻋﻠﻰ )‪.(BC‬‬

‫‪C‬‬

‫ﻭ ‪ BC=7‬ﻭ ‪ AD=3‬ﻭ ‪ AB=10‬ﻭ ‪ M ∈ AB ‬ﻭ ‪ M ≠ A‬ﻭ ‪ M ≠ B‬ﻭ ‪. AM = x‬‬
‫ﺃ‪-‬‬

‫ﺇﻟﻰ ﺃﻱ ﻣﺠﺎﻝ ﻳﻨﺘﻤﻲ ﺍﻟﻌﺪﺩ ‪.x‬‬

‫‪D‬‬

‫ﺏ‪ -‬ﻋﺒﺮ ﺑﺪﻻﻟﺔ ‪ x‬ﻋﻦ ﻣﺴﺎﺣﺔ ﻛﻞ ﻣﻦ ﺍﻟﻤﺜﻠﺜﻴﻦ ‪ ADM‬ﻭ ‪. BMC‬‬
‫ﺕ‪ -‬ﺃﻭﺟﺪ ﺍﻟﻘﻴﻤﺔ ﺍﻟﻤﻤﻜﻨﺔ ﻟﻠﻌﺪﺩ ‪ x‬ﺑﺤﻴﺚ ﻳﻜﻮﻥ ﻣﺠﻤﻮﻉ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ADM‬‬
‫‪M‬‬

‫ﻭﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ BCM‬ﻣﺴﺎﻭﻳﺎ ﻟــ‪. x2‬‬

‫‪A‬‬

‫ﺙ‪ -‬ﺃﻭﺟﺪ ﺍﻟﻘﻴﻢ ﺍﻟﻤﻤﻜﻨﺔ ﻟﻠﻌﺪﺩ ‪ x‬ﺑﺤﻴﺚ ﺗﻜﻮﻥ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ADM‬‬
‫ﺃﻛﺒﺮ ﻗﻄﻌﺎ ﻣﻦ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪. BCM‬‬

‫‪Série F.B.A‬‬

‫‪30‬‬

‫‪B‬‬
‫‪x‬‬

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‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‬
‫ﻳﻘﺪﻡ ﺍﻟﺠﺪﻭﻝ ﺍﻟﺘﺎﻟﻲ ﺇﺣﺼﺎء ﻟﻌﺪﺩ ﻛﺘﺐ ﺍﻟﻤﻄﺎﻟﻌﺔ ﺍﻟﺘﻲ ﻁﺎﻟﻌﻬﺎ ﺗﻼﻣﻴﺬ ﻗﺴﻢ ﺳﻨﺔ ﺗﺎﺳﻌﺔ ﺃﺳﺎﺳﻲ ﺧﻼﻝ ﺳﻨﺔ‬
‫ﺩﺭﺍﺳﻴﺔ‪.‬‬

‫ﻋﺪﺩ ﺍﻟﻜﺘﺐ‬

‫[‪[ 4;8‬‬

‫[‪[ 8;12‬‬

‫ﻋﺪﺩ ﺍﻟﺘﻼﻣﻴﺬ‬
‫ﻣﺮﻛﺰ ﺍﻟﻔﺌﺔ‬

‫‪12‬‬

‫‪6‬‬

‫[‪[ 20;24[ [16;20[ [12;16‬‬
‫‪8‬‬

‫‪2‬‬

‫‪4‬‬

‫ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‬

‫‪ (1‬ﺃﺗﻤﻢ ﺍﻟﺠﺪﻭﻝ‬
‫‪ (2‬ﺍﺣﺴﺐ ﺍﻟﻤﻌﺪﻝ ﺍﻟﺤﺴﺎﺑﻲ ﻟﻬﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‪.‬‬
‫‪ (3‬ﺍﺭﺳﻢ ﻣﺨﻄﻂ ﺍﻟﻤﺴﺘﻄﻴﻼﺕ ﻭ ﻣﻀﻠﻊ ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ ﺛﻢ ﺍﺳﺘﻨﺘﺞ ﻣﻮﺳﻄﺎ ﻟﻬﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‪.‬‬
‫‪ (4‬ﻟﺘﺸﺠﻴﻊ ﺍﻟﺘﻼﻣﻴﺬ ﻋﻠﻰ ﺍﻟﻤﻄﺎﻟﻌﺔ ﻭﻗﻊ ﺗﻜﺮﻳﻢ ﻛﻞ ﺗﻠﻤﻴﺬ ﻁﺎﻟﻊ ﻋﺪﺩﺍ ﻣﻦ ﺍﻟﻜﺘﺐ ﻻ ﻳﻘﻞ ﻋﻦ ‪ 16‬ﻭ ﺇﺳﻨﺎﺩ ﺟﺎﺋﺰﺓ‬
‫ﺍﻟﺴﻠﻮﻙ ﺍﻟﺤﻀﺎﺭﻱ ﻟﺘﻠﻤﻴﺬ ﻣﻦ ﺍﻟﻘﺴﻢ ﻳﻜﻮﻥ ﻗﺪ ﺗﺤﻠﻰ ﺑﺤﺴﻦ ﺳﻠﻮﻛﻪ ﻁﻴﻠﺔ ﺍﻟﺴﻨﺔ ﺍﻟﺪﺭﺍﺳﻴﺔ‪ .‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ‬
‫ﻳﻜﻮﻥ ﺍﻟﺘﻠﻤﻴﺬ ﺍﻟﻤﺤﺮﺯ ﻋﻠﻰ ﺟﺎﺋﺰﺓ ﺍﻟﺴﻠﻮﻙ ﺍﻟﺤﻀﺎﺭﻱ ﻣﻦ ﺑﻴﻦ ﺍﻟﻤﻜﺮﻣﻴﻦ ﻓﻲ ﺍﻟﻤﻄﺎﻟﻌﺔ ؟‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‬
‫‪ (1‬ﺍﺭﺳﻢ ﻣﺜﻠﺜﺎ ‪ EFG‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪ E‬ﺣﻴﺚ ‪ EF=3‬ﻭ ‪ FG = 9‬ﺛﻢ ﻋﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ M‬ﻣﻨﺘﺼﻒ ]‪. [FG‬‬
‫‪ (2‬ﺍﺣﺴﺐ ‪ EG‬ﻭ ‪. EM‬‬
‫‪ (3‬ﻟﺘﻜﻦ ﺍﻟﻨﻘﻄﺔ ‪ H‬ﻣﻨﺎﻅﺮﺓ ﺍﻟﻨﻘﻄﺔ ‪ E‬ﺑﺎﻟﻨﺴﺒﺔ ﺇﻟﻰ ﺍﻟﻨﻘﻄﺔ ‪ M‬ﺑﻴﻦ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ EFHG‬ﻣﺴﺘﻄﻴﻞ‪.‬‬
‫‪ (4‬ﺃ‪ -‬ﺍﺑﻦ ﺍﻟﻨﻘﻄﺔ ‪ N‬ﺑﺤﻴﺚ ﻳﻜﻮﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ MENG‬ﻣﺘﻮﺍﺯﻱ ﺍﻷﺿﻼﻉ ‪.‬‬
‫ﺏ‪ -‬ﺃﺛﺒﺖ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ MENG‬ﻣﻌﻴﻦ ﻭ ﺍﺣﺴﺐ ﻣﺴﺎﺣﺘﻪ ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‬
‫ﻳﻤﺜﻞ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﻟﻲ ﻫﺮﻣﺎ ﻣﻨﺘﻈﻤﺎ ‪ SABCD‬ﻗﻤﺘﻪ ‪ S‬ﻭ ﻗﺎﻋﺪﺗﻪ ﺍﻟﻤﺮﺑﻊ ‪ ABCD‬ﺍﻟﺬﻱ ﻣﺮﻛﺰﻩ ‪ H‬ﺣﻴﺚ ‪ AB=4‬ﻭ ‪ SH = 4 2‬ﻭ ﺍﻟﻨﻘﻄﺔ ‪I‬‬
‫ﻣﻨﺘﺼﻒ ]‪. [SA‬‬

‫‪S‬‬

‫‪ (1‬ﺍﺣﺴﺐ ‪. AH‬‬

‫‪ (2‬ﺑﻴﻦ ﺃﻥ )‪. ( SH) ⊥ ( AH‬‬
‫‪ (3‬ﺍﺣﺴﺐ ‪ SA‬ﻭ ‪. IH‬‬
‫‪ (4‬ﺃ‪ -‬ﺃﺛﺒﺖ ﺃﻥ‬

‫‪I‬‬

‫) ‪(BH) ⊥ ( SAC‬‬

‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﻁﺒﻴﻌﺔ ﺍﻟﻤﺜﻠﺚ ‪. BHI‬‬
‫ﺝ‪ -‬ﺍﺣﺴﺐ ﺍﻟﺒﻌﺪ ‪. IB‬‬

‫‪D‬‬

‫‪A‬‬

‫‪H‬‬
‫‪B‬‬

‫‪Série F.B.A‬‬

‫‪31‬‬

‫‪C‬‬

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‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
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‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺜﺎﻟﺚ ﻟﻔﺮﺽ ﺗﺄﻟﻴﻔﻲ ﻋﺪﺩ‪3‬‬

‫ﻓﺮﺽ ﺍﻗﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﻋﻠﻲ ﺑﻠﻬﻮﺍﻥ‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‬
‫ﻳﻠﻲ ﻛﻞ ﺳﺆﺍﻝ ‪ 3‬ﻣﻘﺘﺮﺣﺎﺕ‪ ،‬ﺃﺣﺪﻫﺎ ﻓﻘﻂ ﺻﺤﻴﺢ ﺿﻊ )‪ (x‬ﺃﻣﺎﻡ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ‪.‬‬
‫‪ (1‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪(2x+1)-(x-3)=0‬‬

‫‪1‬‬
‫ﻟﻬﺎ ﺣﻼﻥ‬
‫‪2‬‬

‫‪1‬‬
‫ﻟﻬﺎ ﺣﻼﻥ‬
‫‪2‬‬

‫‪ −‬ﻭ‪3‬‬

‫ﻭ‪-3‬‬

‫ﻟﻬﺎ ﺣﻞ ﻭﺍﺣﺪ ‪-4‬‬

‫‪ (2‬ﻣﺠﻤﻮﻋﺔ ﺣﻠﻮﻝ ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪ - 3x - 4 ≤ −7 :‬ﻫﻲ‬

‫‪ 3; +∞ ‬‬
‫‪‬‬
‫‪‬‬

‫‪ −∞; 3 ‬‬
‫‪‬‬
‫‪‬‬

‫‪ 3; +∞ ‬‬
‫‪‬‬
‫‪‬‬

‫‪ (3‬ﺇﺫﺍ ﻛﺎﻥ ‪ ABCD‬ﻣﺮﺑﻊ ﻣﺮﻛﺰﻩ ‪ O‬ﺣﻴﺚ ‪ OA=2‬ﺇﺫﻥ‬

‫‪AB = 2‬‬

‫‪AB = 2 2‬‬

‫‪AB = 2‬‬

‫‪ (4‬ﻧﺮﻣﻲ ﺑﻨﺮﺩ ﻣﻜﻌﺐ ﺍﻟﺸﻜﻞ ﻣﺮﻗﻢ ﻣﻦ ‪ 1‬ﺇﻟﻰ ‪ 6‬ﺇﺫﻥ ﺍﺣﺘﻤﺎﻝ ﺍﻟﺤﺼﻮﻝ ﻋﻠﻰ‬
‫ﻋﻠﻰ ﻋﺪﺩ ﺯﻭﺟﻲ‬
‫ﻫﻮ ‪0.5‬‬

‫ﻋﻠﻰ ﺍﻟﻌﺪﺩ ‪7‬‬
‫ﻫﻮ ‪1‬‬

‫ﻋﻠﻰ ﻋﺪﺩ ﻣﻀﺎﻋﻒ‬
‫ﻟـ‪ 3‬ﻫﻮ ‪0.3‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‬
‫ﺗﺒﺮﻉ ﻋﻤﺎﻝ ﻣﺆﺳﺴﺔ ﺑﻤﺒﻠﻎ ﻣﺎﻟﻲ ﻣﻦ ﺍﻟﻤﺎﻝ ﻟﺘﻜﺮﻳﻢ ﺃﺣﺪ ﺯﻣﻼﺋﻬﻢ ﺑﻤﻨﺎﺳﺒﺔ ﺇﺣﺎﻟﺘﻪ ﻋﻠﻰ ﺍﻟﺘﻘﺎﻋﺪ ﻭ ﺍﻟﺠﺪﻭﻝ ﺍﻟﺘﺎﻟﻲ ﻳﻤﺜﻞ ﺍﻟﻤﺒﻠﻎ‬
‫ﺑﺎﻟﺪﻳﻨﺎﺭ ﺣﺴﺐ ﻋﺪﺩ ﺍﻟﻤﺘﺒﺮﻋﻴﻦ‪.‬‬
‫ﺍﻟﻤﺒﻠﻎ ﺑﺎﻟﺪﻳﻨﺎﺭ‬

‫[‪[ 2;6‬‬

‫[‪[ 6;10‬‬

‫ﻋﺪﺩ ﺍﻟﻤﺘﺒﺮﻋﻴﻦ‬
‫ﻣﺮﻛﺰ ﺍﻟﻔﺌﺔ‬

‫‪6‬‬

‫‪10‬‬

‫[‪[18;22[ [14;18[ [10;14‬‬
‫‪15‬‬

‫‪12‬‬

‫‪7‬‬

‫ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‬
‫‪ (1‬ﺃﻭﺟﺪ ﻣﺪﻯ ﻭ ﻣﻨﻮﺍﻝ ﻫﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‪.‬‬
‫‪ (2‬ﺃﺗﻤﻢ ﺗﻌﻤﻴﺮ ﺍﻟﺠﺪﻭﻝ‬
‫‪ (3‬ﺍﺭﺳﻢ ﻣﻀﻠﻊ ﺍﻟﺘﻜﺮﺍﺭﺍﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ‬
‫‪ (4‬ﺍﺳﺘﻨﺘﺞ ﻣﻮﺳﻄﺎ ﻟﻬﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‬
‫‪ (5‬ﺍﺧﺘﺎﺭ ﺍﻟﻌﻤﺎﻝ ﻣﻦ ﻳﻨﻮﺑﻬﻢ ﻟﺘﻘﺪﻳﻢ ﻫﺬﻩ ﺍﻟﻬﺪﻳﺔ‪ .‬ﻣﺎ ﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﻳﻜﻮﻥ ﺍﻟﻨﺎﺋﺐ ﻣﻦ ﺑﻴﻦ ﺍﻟﺬﻳﻦ ﺳﺎﻫﻤﻮﺍ ﺑﻤﺒﻠﻎ ﺃﻛﺒﺮ ﺃﻭ ﻣﺴﺎﻭ‬
‫ﻟـ ‪10‬ﺩﻧﺎﻧﻴﺮ ‪.‬‬

‫‪A‬‬

‫‪ (6‬ﺍﺣﺴﺐ ﻣﻌﺪﻝ ﺍﻟﺘﺒﺮﻋﺎﺕ ﻟﻠﻌﺎﻣﻞ ﺍﻟﻮﺍﺣﺪ‪.‬‬
‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‬
‫ﻧﻌﺘﺒﺮ ﺍﻟﻤﺜﻠﺚ ‪ ABC‬ﺍﻟﻘﺎﺋﻢ ﻓﻲ ‪ B‬ﺑﺤﻴﺚ ‪ AB=8cm‬ﻭ ‪ BC=4‬ﻭ ‪. AM=x‬‬
‫ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ M‬ﻭ ﺍﻟﻤﻮﺍﺯﻱ ﻟــ)‪ (BC‬ﻳﻘﻄﻊ )‪ (AC‬ﻓﻲ ‪. N‬‬

‫‪N‬‬

‫‪M‬‬

‫‪ (1‬ﺃﻭﺟﺪ ‪ MN‬ﺑﺪﻻﻟﺔ ‪. x‬‬
‫‪ (2‬ﺃﻭﺟﺪ ‪ S1‬ﻭ ‪ S2‬ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ AMN‬ﻭ ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺍﻟﺮﺑﺎﻋﻲ ‪ MNCB‬ﺑﺪﻻﻟﺔ ‪. x‬‬
‫‪ (3‬ﺃﻭﺟﺪ ﺍﻟﻌﺪﺩ ‪ x‬ﺑﺤﻴﺚ ﺗﻜﻮﻥ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪ AMN‬ﺗﺴﺎﻭﻱ ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﺍﻟﺮﺑﺎﻋﻲ ‪.MNCB‬‬

‫‪Série F.B.A‬‬

‫‪32‬‬

‫‪C‬‬

‫‪B‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫‪A‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‬
‫‪I‬‬

‫ﻳﻤﺜﻞ ﺍﻟﺸﻜﻞ ﺍﻟﻤﻘﺎﺑﻞ ﻣﻮﺷﻮﺭﺍ ﻗﺎﺋﻤﺎ ﺣﻴﺚ ‪ ABC‬ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ ﺍﻷﺿﻼﻉ‬
‫ﻭ ‪ AB=4cm‬ﻭ ‪ BF=6cm‬ﻭ ‪ I‬ﻣﻨﺘﺼﻒ ]‪. [AC‬‬

‫‪B‬‬

‫‪C‬‬

‫‪ (1‬ﺑﻴﻦ ﺃﻥ )‪ (BF‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻮﻱ )‪. (ABC‬‬

‫‪N‬‬

‫‪ (2‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ BIF‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪. B‬‬

‫‪M‬‬

‫‪ (3‬ﺍﺣﺴﺐ ‪. IF‬‬
‫‪ (4‬ﻟﺘﻜﻦ ‪ M‬ﻧﻘﻄﺔ ﻣﻦ ]‪ .[BF‬ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ M‬ﻭ ﺍﻟﻤﻮﺍﺯﻱ ﻟــ)‪(BI‬‬

‫‪E‬‬

‫ﻳﻘﻄﻊ )‪ (FI‬ﻓﻲ ‪ . N‬ﺑﻴﻦ ﺃﻥ )‪ (MN‬ﻣﻮﺍﺯ ﻟﻠﻤﺴﺘﻮﻱ )‪.(ABC‬‬

‫‪F‬‬

‫‪G‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‬
‫‪ ABCD‬ﻣﺘﻮﺍﺯﻱ ﺃﺿﻼﻉ ﺑﺤﻴﺚ ‪ AD=4‬ﻭ ‪ CD = 8‬ﻭ ‪ H‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟــ‪ A‬ﻋﻠﻰ )‪. (CD‬‬

‫‪ (1‬ﺃﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ﻗﻴﺲ ﻣﺴﺎﺣﺔ ﻣﺘﻮﺍﺯﻱ ﺍﻷﺿﻼﻉ ‪ ABCD‬ﺗﺴﺎﻭﻱ ‪16 3‬‬
‫ﺑﻴﻦ ﺃﻥ ‪. AH = 2 3‬‬
‫‪ (2‬ﺃ‪ -‬ﺍﺣﺴﺐ ‪ DH‬ﻭ ‪ HC‬ﻭ ‪. AC‬‬
‫ﺏ‪ -‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ ADC‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪. A‬‬
‫‪ (3‬ﻟﺘﻜﻦ ‪ E‬ﻣﻨﺎﻅﺮﺓ ‪ B‬ﺑﺎﻟﻨﺴﺒﺔ ﻟــ‪ C‬ﺑﻴﻦ ﺃﻥ ‪ ADEC‬ﻣﺴﺘﻄﻴﻞ‪.‬‬
‫‪ (4‬ﺃ‪ (AE) -‬ﻭ )‪ (DC‬ﻳﺘﻘﺎﻁﻌﺎﻥ ﻓﻲ ‪ . O‬ﺑﻴﻦ ﺃﻥ ‪ ADO‬ﻣﺘﻘﺎﻳﺲ ﺍﻷﺿﻼﻉ‪.‬‬
‫ﺏ‪ -‬ﺍﺳﺘﻨﺘﺞ ﺃﻥ ‪ H‬ﻣﻨﺘﺼﻒ ]‪. [DO‬‬
‫‪ (5‬ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻌﻤﻮﺩﻱ ﻋﻠﻰ )‪ (DE‬ﻭ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ O‬ﻳﻘﻄﻊ )‪ (HA‬ﻓﻲ ‪. F‬‬
‫ﺑﻴﻦ ﺃﻥ ‪ AFDO‬ﻣﻌﻴﻦ‪.‬‬

‫‪A‬‬

‫‪B‬‬

‫‪H‬‬
‫‪D‬‬

‫‪C‬‬

‫‪E‬‬
‫‪Série F.B.A‬‬

‫‪33‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪---------------------------------------------------------------------------------------------------------------------------‬‬

‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺮﺍﺑﻊ ﻟﻔﺮﺽ ﺗﺄﻟﻴﻔﻲ ﻋﺪﺩ‪3‬‬

‫ﻓﺮﺽ ﺍﻗﺘﺮﺡ ﺑﺎﻟﻤﺪﺭﺳﺔ ﺍﻹﻋﺪﺍﺩﻳﺔ ﺍﻟﺒﺴﺘﺎﻥ‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻷﻭﻝ‬
‫ﻳﻠﻲ ﻛﻞ ﺳﺆﺍﻝ ‪ 3‬ﻣﻘﺘﺮﺣﺎﺕ‪ ،‬ﺃﺣﺪﻫﺎ ﻓﻘﻂ ﺻﺤﻴﺢ ﺿﻊ )‪ (x‬ﺃﻣﺎﻡ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ‪.‬‬
‫‪ (1‬ﺍﺗﺮﺷﺢ ‪ 5‬ﺗﻼﻣﻴﺬ ) ﻭﻟﺪﺍﻥ ﻭ ‪ 3‬ﺑﻨﺎﺕ( ﻟﺨﺘﻴﺎﺭ ﻣﺴﺆﻭﻝ ﻋﻦ ﻗﺴﻢ ﻭ ﻧﺎﺋﺒﻪ ﻓﻮﻗﻊ ﺳﺤﺐ ﺍﺳﻤﻴﻦ ﺍﻟﻮﺍﺣﺪ ﺗﻠﻮ ﺍﻵﺧﺮ‪.‬‬
‫ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﻳﻜﻮﻥ ﺍﻟﻤﺴﺆﻭﻝ ﻭ ﻧﺎﺋﺒﻪ ﺑﻨﺘﺎﻥ ﻫﻮ‬

‫‪3‬‬
‫‪5‬‬

‫‪3‬‬
‫‪20‬‬

‫‪6‬‬
‫‪20‬‬

‫‪ (2‬ﻣﺠﻤﻮﻋﺔ ﺣﻠﻮﻝ ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪ 3-2x < 0 :‬ﻫﻲ‬

‫‪3‬‬
‫‪‬‬
‫‪ 2 ; +∞ ‬‬
‫‪‬‬
‫‪‬‬

‫‪3‬‬
‫‪2‬‬

‫‪3‬‬
‫‪‬‬
‫‪ −∞; 2 ‬‬
‫‪‬‬
‫‪‬‬

‫‪ (3‬ﺇﺫﺍ ﻛﺎﻥ ‪ ABCD‬ﻣﺮﺑﻊ ﻣﺮﻛﺰﻩ ‪ O‬ﻣﺤﺎﻁ ﺑﺪﺍﺋﺮﺓ ﺷﻌﺎﻋﻬﺎ ﺣﻴﺚ ‪3‬‬

‫= ‪ OA‬ﺇﺫﻥ ﻣﺤﻴﻂ ﺍﻟﻤﺮﺑﻊ ﻫﻮ‬

‫‪P=6‬‬

‫‪P=4 6‬‬

‫‪P=4 2‬‬

‫=‪x‬‬

‫‪ SABC (4‬ﻫﻮ ﻫﺮﻡ ﻣﻨﺘﻈﻢ ﻭ ]‪ [AH‬ﺍﺭﺗﻔﺎﻉ ﻟﻠﻤﺜﻠﺚ ‪ ABC‬ﺇﺫﻥ‪:‬‬
‫‪A‬‬

‫‪B‬‬

‫‪D‬‬

‫‪H‬‬
‫‪C‬‬

‫)‪( SH) ⊥ (ABC‬‬

‫)‪( AH) ⊥ (SBH‬‬

‫)‪(BH) ⊥ (SAC‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ‬

‫ﺍﻟﺘﻜﺮﺍﺭﺍﺕ‬

‫ﻳﻤﺜﻞ ﻣﺨﻄﻂ ﺍﻟﻤﺴﺘﻄﻴﻼﺕ ﺍﻟﺘﺎﻟﻲ ﺳﻠﺴﻠﺔ ﺇﺣﺼﺎﺋﻴﺔ ﺗﻮﺯﻉ ‪ 250‬ﺳﻴﺎﺭﺓ‬
‫ﺣﺴﺐ ﺗﻮﻗﻴﺖ ﻭﺻﻮﻟﻬﺎ ﺇﻟﻰ ﻣﺤﻄﺔ ﺍﻻﺳﺘﺨﻼﺹ ﺧﻼﻝ ﺍﻟﻤﺪﺓ ﺍﻟﻔﺎﺻﻠﺔ‬
‫ﺑﻴﻦ ﻣﻨﺘﺼﻒ ﺍﻟﻠﻴﻞ ﻭ ﺍﻟﺴﺎﺩﺳﺔ ﺻﺒﺎﺣﺎ ‪.‬‬
‫‪ (1‬ﻛﻮﻥ ﺟﺪﻭﻻ ﺇﺣﺼﺎﺋﻴﺎ ﻣﺒﺮﺯﺍ ﻓﻴﻪ ﺍﻟﺘﻜﺮﺍﺭﺍﻟﺘﺮﺍﻛﻤﻲ ﺍﻟﺼﺎﻋﺪ‪.‬‬
‫‪ (2‬ﺣﺪﺩ ﺍﻟﻤﺪﻯ ﻭ ﺍﻟﻔﺌﺔ ﺍﻟﻤﻨﻮﺍﻟﻴﺔ‪.‬‬
‫‪ (3‬ﺍﺣﺴﺐ ﺍﻟﻤﻌﺪﻝ ﺍﻟﺤﺴﺎﺑﻲ‬
‫‪ (4‬ﺗﻌﻄﺒﺖ ﺇﺣﺪﻯ ﺍﻟﺴﻴﺎﺭﺍﺕ ﺍﻟﺘﻲ ﻣﺮﺕ ﻣﻦ ﺍﻟﻤﺤﻄﺔ‬
‫ﻣﺎﻫﻮ ﺍﺣﺘﻤﺎﻝ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﺴﻴﺎﺭﺓ ﻣﻦ ﺑﻴﻦ ﺍﻟﺴﻴﺎﺭﺍﺕ ﺍﻟﺘﻲ ﻭﺻﻠﺖ‬
‫ﺇﻟﻰ ﺍﻟﻤﺤﻄﺔ ﻗﺒﻞ ﺍﻟﺜﺎﻧﻴﺔ ﺻﺒﺎﺣﺎ‪.‬‬
‫ﺍﻟﻔﺌﺎﺕ‬
‫‪ (5‬ﺍﺭﺳﻢ ﻣﺨﻄﻂ ﺍﻟﺘﻜﺮﺍﺭﺕ ﺍﻟﺘﺮﺍﻛﻤﻴﺔ ﺍﻟﺼﺎﻋﺪﺓ ﻭ ﺍﺳﺘﻨﺘﺞ ﻣﻮﺳﻄﺎ ﻟﻬﺬﻩ ﺍﻟﺴﻠﺴﻠﺔ‪.‬‬

‫‪Série F.B.A‬‬

‫‪34‬‬

‫‪2014-2013‬‬
‫ﺭﻳﺎﺿﻳﺎﺕ ‪9‬ﺃﺳﺎﺳﻲ‬
‫‪--------------------------------------------------------------------------------------------------------------------------‬‬‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺜﺎﻟﺚ‬

‫‪B‬‬

‫‪M‬‬

‫‪x+2‬‬

‫‪A‬‬

‫‪ (1‬ﻧﻌﺘﺒﺮ ﺍﻟﻌﺒﺎﺭﺓ ‪ A=x2-8x+12‬ﺣﻴﺚ ‪ x‬ﻋﺪﺩ ﺣﻘﻴﻘﻲ‪.‬‬
‫ﺃ‪-‬‬

‫ﺑﻴﻦ ﺃﻥ )‪. A=(6-x)(2-x‬‬

‫ﺏ‪ -‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﻌﺎﺩﻟﺔ ‪. A=4-x2‬‬

‫‪N‬‬

‫‪E‬‬

‫‪Q‬‬

‫ﺕ‪ -‬ﺣﻞ ﻓﻲ ‪ IR‬ﺍﻟﻤﺘﺮﺍﺟﺤﺔ ‪A − x 2 ≤ 4‬‬
‫‪ (2‬ﻳﻤﺜﻞ ﺍﻟﺮﺳﻢ ﺍﻟﻤﻘﺎﺑﻞ ﻣﺮﺑﻌﺎ ﻁﻮﻝ ﺿﻠﻌﻪ ‪. 4cm‬‬
‫‪ M‬ﻫﻲ ﻧﻘﻄﺔ ﻣﻦ ]‪ [AB‬ﺣﻴﺚ ‪AM=x+2‬‬
‫ﺃ‪-‬‬

‫)‪( x + 2 ∈ 0; 4‬‬

‫ﺑﻴﻦ ﺃﻥ ‪. x < 2‬‬

‫‪D‬‬

‫‪C‬‬

‫‪ (3‬ﺃ‪ -‬ﺃﺛﺒﺖ ﺃﻥ ‪. NE=2-x‬‬
‫ﺏ‪ -‬ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ AMNQ‬ﻣﺮﺑﻊ ﺍﺣﺴﺐ ﻣﺴﺎﺣﺘﻪ ﺑﺪﻻﻟﺔ ‪x‬‬
‫ﺕ‪ -‬ﺑﻴﻦ ﺃﻥ ﻣﺴﺎﺣﺔ ﺷﺒﻪ ﺍﻟﻤﻨﺤﺮﻑ ‪ ENDC‬ﺗﺴﺎﻭﻱ ﻧﺼﻒ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺮﺑﻊ ‪. AMNQ‬‬
‫‪A‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺮﺍﺑﻊ‬
‫‪ ABC (1‬ﻣﺜﻠﺚ ﻣﺘﻘﺎﻳﺲ ﺍﻷﺿﻼﻉ ﻁﻮﻝ ﺿﻠﻌﻪ ‪ 2 3‬ﺍﺣﺴﺐ ﺍﺭﺗﻔﺎﻋﻪ ‪. AH‬‬
‫‪ (2‬ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﻣﻦ ‪ a‬ﻭ ﺍﻟﻤﻮﺍﺯﻱ ﻟــ)‪ (BC‬ﻳﻘﻄﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ‬
‫ﺍﻟﻤﺎﺭ ﻣﻦ ‪ C‬ﻭ ﺍﻟﻤﻮﺍﺯﻱ ﻟــ)‪ (AB‬ﻓﻲ ﺍﻟﻨﻘﻄﺔ ‪. D‬‬
‫ﺃ‪-‬‬

‫ﺃﺛﺒﺖ ﺃﻥ ﺍﻟﺮﺑﺎﻋﻲ ‪ ABCD‬ﻣﻌﻴﻦ‪.‬‬

‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪. DH‬‬
‫ﺕ‪ -‬ﺍﺣﺴﺐ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ‪. BDH‬‬

‫‪H‬‬

‫‪C‬‬

‫‪3 7‬‬
‫‪ (3‬ﻟﺘﻜﻦ ‪ K‬ﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟﻠﻨﻘﻄﺔ ‪ B‬ﻋﻠﻰ )‪ (DH‬ﺑﻴﻦ ﺃﻥ‬
‫‪7‬‬

‫‪B‬‬

‫= ‪BK‬‬

‫ﺍﻟﺘﻤﺮﻳﻦ ﺍﻟﺨﺎﻣﺲ‬
‫ﻳﻤﺜﻞ ﺍﻟﺮﺳﻢ ﺍﻟﻤﻘﺎﺑﻞ ﻣﻮﺷﻮﺭﺍ ﻗﺎﺋﻤﺎ ‪ ABCDEFGH‬ﻗﺎﻋﺪﺗﻪ ﺷﺒﻪ ﻣﻨﺤﺮﻑ ‪ ABCD‬ﻗﺎﺋﻢ ﻓﻲ ‪ A‬ﻭ ‪ B‬ﺑﺤﻴﺚ‪:‬‬
‫‪ AB=AD=4cm‬ﻭ ‪ BC=2cm‬ﻭ ‪. BF = 2 3‬‬

‫‪D‬‬
‫‪J‬‬

‫ﺍﻟﻨﻘﻄﺔ ‪ I‬ﻫﻲ ﻣﻨﺘﺼﻒ ]‪. [AB‬‬
‫‪ (1‬ﺃﺛﺒﺖ ﺃﻥ‬

‫‪C‬‬

‫) ‪( IE ) ⊂ ( ABE‬‬

‫‪ (2‬ﺍﻟﻨﻘﻄﺔ ‪ J‬ﻫﻲ ﻣﻨﺘﺼﻒ ]‪[DC‬‬
‫ﺃ‪-‬‬

‫ﺍﺣﺴﺐ ‪. IJ‬‬

‫‪A‬‬

‫ﺏ‪ -‬ﺑﻴﻦ ﺃﻥ )‪. (IJ)//(ADH‬‬

‫‪B‬‬
‫‪I‬‬

‫‪H‬‬

‫‪ (3‬ﺑﻴﻦ ﺃﻥ ) ‪ ( AD ) ⊥ ( ABE‬ﻭ ﺍﺳﺘﻨﺘﺞ ﺃﻥ ) ‪. ( IJ ) ⊥ ( ABE‬‬

‫‪G‬‬

‫‪ (4‬ﺃ‪ -‬ﺑﻴﻦ ﺃﻥ ﺍﻟﻤﺜﻠﺚ ‪ EIJ‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ ‪. I‬‬
‫ﺏ‪ -‬ﺍﺣﺴﺐ ‪ IE‬ﺛﻢ ‪. JE‬‬
‫‪E‬‬

‫‪Série F.B.A‬‬

‫‪35‬‬

‫‪F‬‬




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