1. No category

‫ﺗﻤﺮﻳﻦ ‪1‬‬
‫‪ f‬و ‪ g‬داﻟﺘﺎن ﺧﻄﻴﺘﺎن ﻣﻌﺮﻓﺘﺎن آﻤﺎ ﻳﻠﻲ ‪:‬‬
‫‪x‬‬
‫و‬
‫‪f : x → −2x‬‬
‫→ ‪g :x‬‬
‫‪2‬‬
‫أﺣﺴﺐ ﻣﺎ ﻳﻠﻲ ‪:‬‬
‫⎞‪⎛1‬‬
‫) ‪f ( −2‬‬
‫و ⎟ ⎜ ‪f‬‬
‫)‪ g ( −5‬و‬
‫و‬
‫‪f − 3‬‬
‫و‬
‫⎠‪⎝2‬‬
‫)‬
‫⎦⎤ ) ‪f ⎡⎣f ( 5‬‬
‫و‬
‫(‬
‫⎦⎤ )‪g ⎡⎣ g ( −1‬‬
‫و‬
‫⎦⎤ ) ‪f ⎡⎣ g ( −8‬‬
‫و‬
‫)‪g ( 0‬‬
‫و‬
‫⎞‪⎛ 2‬‬
‫⎜‪g‬‬
‫⎟‬
‫‪2‬‬
‫⎝‬
‫⎠‬
‫⎤ ⎞ ‪⎡ ⎛ −3‬‬
‫⎥ ⎟ ⎜ ‪g ⎢f‬‬
‫⎦⎠ ‪⎣ ⎝ 4‬‬
‫ﺗﻤﺮﻳﻦ ‪2‬‬
‫‪ f‬داﻟﺔ ﺧﻄﻴﺔ و ‪ g‬داﻟﺔ ﺗﺂﻟﻔﻴﺔ ﺑﺤﻴﺚ ‪f ( x ) = −3x :‬‬
‫‪ – (1‬أآﺘﺐ ) ‪ g ( x‬ﺑﺪﻻﻟﺔ ‪. x‬‬
‫و ‪g (x ) = f (x ) −1‬‬
‫⎞‪⎛3‬‬
‫⎞‪⎛ 1‬‬
‫‪ – (2‬أﺣﺴﺐ ‪f ⎜ − ⎟ :‬‬
‫و ⎟ ⎜‪. g‬‬
‫⎠‪⎝2‬‬
‫⎠‪⎝ 2‬‬
‫‪ – (3‬أﻧﺸﺊ اﻟﺘﻤﺜﻴﻠﻴﻦ اﻟﻤﺒﻴﺎﻧﻴﻴﻦ ﻟﻜﻞ ﻣﻦ ‪ f‬و ‪ g‬ﻋﻠﻰ ﻧﻔﺲ اﻟﻤﻌﻠﻢ اﻟﻤﺘﻌﺎﻣﺪ اﻟﻤﻤﻨﻈﻢ ) ‪. (O ; I ; J‬‬
‫ﺗﻤﺮﻳﻦ ‪3‬‬
‫ﻧﻌﺘﺒﺮ اﻟﻤﺴﺘﻮى ﻣﻨﺴﻮﺑﺎ إﻟﻰ ﻣﻌﻠﻢ ﻣﺘﻌﺎﻣﺪ ﻣﻤﻨﻈﻢ ) ‪. (O ; I ; J‬‬
‫)‪ A ( 2;3‬و ) ‪ B ( −1; 2‬و )‪ C ( −3; −1‬ﻧﻘﻂ ﻣﻦ اﻟﻤﺴﺘﻮى‪.‬‬
‫‪ – (1‬ﻋﺮ ف اﻟﺪاﻟﺔ اﻟﺘﺂﻟﻔﻴﺔ ‪ f‬اﻟﺘﻲ ﺗﻤﺜﻴﻠﻬﺎ اﻟﻤﺒﻴﺎﻧﻲ ﻳﻤﺮ ﻣﻦ )‪ A ( 2;3‬و ) ‪. B ( −1;2‬‬
‫‪ – (2‬ﻋﺮف اﻟﺪاﻟﺔ اﻟﺘﺂﻟﻔﻴﺔ ‪ g‬اﻟﺘﻲ ﺗﻤﺜﻴﻠﻬﺎ اﻟﻤﺒﻴﺎﻧﻲ ﻳﻤﺮ ﻣﻦ ) ‪ B ( −1; 2‬و )‪.C ( −3; −1‬‬
‫‪ – (3‬ﻋﺮف اﻟﺪاﻟﺔ اﻟﺘﺂﻟﻔﻴﺔ ‪ h‬اﻟﺘﻲ ﺗﻤﺜﻴﻠﻬﺎ اﻟﻤﺒﻴﺎﻧﻲ ﻳﻤﺮ ﻣﻦ )‪ A ( 2;3‬و )‪. C ( −3; −1‬‬
‫‪ – (4‬أﻧﺸﺊ ﻋﻠﻰ ﻧﻔﺲ اﻟﻤﻌﻠﻢ اﻟﺘﻤﺜﻴﻞ اﻟﻤﺒﻴﺎﻧﻲ ﻟﻜﻞ ﻣﻦ اﻟﺪوال ‪ f‬و ‪ g‬و ‪. h‬‬
‫ﺗﻤﺮﻳﻦ ‪4‬‬
‫ﻧﻌﺘﺒﺮ اﻟﻤﺴﺘﻮى ﻣﻨﺴﻮﺑﺎ إﻟﻰ ﻣﻌﻠﻢ ﻣﺘﻌﺎﻣﺪ ﻣﻤﻨﻈﻢ ) ‪. (O ; I ; J‬‬
‫‪1‬‬
‫ﻟﺘﻜﻦ ‪ f‬داﻟﺔ ﺗﺂﻟﻔﻴﺔ ﺑﺤﻴﺚ ‪. f ( x ) = x − 1 :‬‬
‫‪2‬‬
‫⎞ ‪3‬‬
‫أﻧﺸﺊ اﻟﻨﻘﻂ ‪ A ( −2; f (0) ) :‬و ) ‪ B ( f (−2);4‬و ⎟ ) ( ‪(−5); f‬‬
‫⎠ ‪2‬‬
‫⎛‬
‫‪. C ⎜f‬‬
‫⎝‬
‫‪_www.anissmaths.ift.cx‬ﻣﻮﻗﻊ اﻟﺮﻳﺎﺿﻴﺎت ﺑﺎﻟﺜﺎﻧﻮي اﻹﻋﺪادي ﻟﻸﺳﺘﺎذ اﻟﻤﻬﺪي ﻋﻨﻴﺲ ‪ /‬أﺳﺘﺎذ ﺑﺎﻟﺜﺎﻧﻮﻳﺔ اﻹﻋﺪادﻳﺔ اﺑﻦ رﺷﻴﻖ – ﻧﻴﺎﺑﺔ اﻟﻤﺤﻤﺪﻳﺔ_‬
‫اﻟﻌﻨﻮان ‪ 143 :‬ﺣﻲ رﻳﺎض اﻟﺴﻼم ‪ -‬اﻟﻄﺎﺑﻖ ‪ - 2‬اﻟﻤﺤﻤﺪﻳﺔ ‪ /‬اﻟﻬﺎﺗﻒ اﻟﻨﻘﺎل ‪ / 063 15 37 85 :‬اﻟﻌﻨﻮان اﻹﻟﻜﺘﺮوﻧﻲ ‪[email protected] :‬‬
‫ﺗﻤﺮﻳﻦ ‪5‬‬
‫‪ f‬داﻟﺔ ﺗﺂﻟﻔﻴﺔ و ) ‪ ( Δ‬ﺗﻤﺜﻴﻠﻬﺎ اﻟﻤﺒﻴﺎﻧﻲ ‪.‬‬
‫ﻟﺘﻜﻦ )‪ M ( −2;3‬و ) ‪ N ( 5; −4‬ﻧﻘﻄﺘﻴﻦ ﻣﻦ ) ‪. ( Δ‬‬
‫‪ – (1‬أﺛﺒﺖ أن ‪ :‬ﻣﻌﺎﻣﻞ اﻟﺪاﻟﺔ ‪ f‬ﻳﺴﺎوي ‪. −1‬‬
‫‪ – (2‬اﺳﺘﻨﺘﺞ ﺗﻌﺮف اﻟﺪاﻟﺔ ‪. f‬‬
‫‪ – (3‬أﻧﺸﺊ ) ‪. ( Δ‬‬
‫ﺗﻤﺮﻳﻦ ‪6‬‬
‫‪−2‬‬
‫‪.‬‬
‫ﻟﺘﻜﻦ ‪ f‬داﻟﺔ ﺧﻄﻴﺔ ﻣﻌﺎﻣﻠﻬﺎ‬
‫‪3‬‬
‫⎞ ‪⎛ −3‬‬
‫و ⎟ ⎜ ‪f‬‬
‫و )‪f ( 0‬‬
‫‪ – (1‬أﺣﺴﺐ ‪f ( 2 ) :‬‬
‫‪f −1 + 3‬‬
‫‪f‬‬
‫‪2‬‬
‫و‬
‫و‬
‫⎠ ‪⎝ 2‬‬
‫‪ – (2‬أﻧﺸﺊ ) ‪ ( D‬اﻟﺘﻤﺜﻴﻞ اﻟﻤﺒﻴﺎﻧﻲ ﻟﻠﺪاﻟﺔ ‪ f‬ﻓﻲ اﻟﻤﺴﺘﻮى اﻟﻤﻨﺴﻮب إﻟﻰ ﻣﻌﻠﻢ ﻣﺘﻌﺎﻣﺪ ﻣﻤﻨﻈﻢ ) ‪. (O ; I ; J‬‬
‫‪ – (3‬ﻟﺘﻜﻦ ‪ g‬داﻟﺔ ﺧﻄﻴﺔ ﻣﻌﺎﻣﻠﻬﺎ ‪. a‬‬
‫أﺛﺒﺖ أﻧﻪ ﻣﻬﻤﺎ ﻳﻜﻦ ‪ x‬و ‪ y‬ﻋﺪدﻳﻦ ﺣﻘﻴﻘﻴﻴﻦ ‪:‬‬
‫) ‪g (x + y ) = g (x ) + g ( y‬‬
‫) (‬
‫(‬
‫)‬
‫) ‪g ( a.x ) = a.g ( x‬‬
‫ﺗﻤﺮﻳﻦ ‪7‬‬
‫ﻟﺘﻜﻦ‬
‫‪f‬‬
‫ﻋﻼﻗﺔ ﺑﺤﻴﺚ ‪:‬‬
‫‪f ( x ) = x + ax‬‬
‫ﺣﺪد اﻟﻌﺪد اﻟﺤﻘﻴﻘﻲ ‪ a‬ﺑﺤﻴﺚ ‪ f‬ﺗﺤﻘﻖ ‪:‬‬
‫‪2‬‬
‫و ‪ a‬ﻋﺪد ﺣﻘﻴﻘﻲ ‪.‬‬
‫‪f ( x ) − f ( −x ) = x‬‬
‫و ‪.x ≠ 0‬‬
‫ﺗﻤﺮﻳﻦ ‪8‬‬
‫ﻟﺘﻜﻦ‬
‫أﺛﺒﺖ أن ‪:‬‬
‫‪ f‬داﻟﺔ ﺗﺂﻟﻔﻴﺔ ‪.‬‬
‫)' ‪⎛ x + x ' ⎞ f ( x ) + f ( x‬‬
‫⎜ ‪. f‬‬
‫=⎟‬
‫‪2‬‬
‫⎠ ‪⎝ 2‬‬
‫ﺗﻤﺮﻳﻦ ‪9‬‬
‫ﻟﺘﻜﻦ ‪ g‬ﻋﻼﻗﺔ ﺑﺤﻴﺚ ﻟﻜﻞ ﻋﺪد ﺣﻘﻴﻘﻲ ‪7 + 2 ( x − 1) − 3g ( x ) = 5 (1 − 2 g ( x ) ) : x‬‬
‫‪ – (1‬ﺑﻴﻦ أن ‪ g‬داﻟﺔ ﺧﻄﻴﺔ ‪.‬‬
‫)‬
‫‪ – (2‬أﺛﺒﺖ أن ‪2.x = 2.g ( x ) :‬‬
‫(‬
‫‪ ، g‬ﻣﻬﻤﺎ ﻳﻜﻦ اﻟﻌﺪد اﻟﺤﻘﻴﻘﻲ ‪. x‬‬
‫‪ – (3‬ﺣﺪد اﻟﻌﺪدﻳﻦ ‪ a‬و ‪ b‬إذا ﻋﻠﻤﺖ أن اﻟﺘﻤﺜﻴﻞ اﻟﻤﺒﻴﺎﻧﻲ ﻟﻠﺪاﻟﺔ ‪ g‬ﻳﻤﺮ ﻣﻦ اﻟﻨﻘﻄﺘﻴﻦ ‪:‬‬
‫⎞ ‪⎛ −1‬‬
‫⎟ ;‪ A ⎜ a‬و ) ‪. B ( 2;b‬‬
‫⎠ ‪⎝ 2‬‬
‫ﺗﻤﺮﻳﻦ ‪10‬‬
‫ﻟﺘﻜﻦ‬
‫‪ f‬داﻟﺔ ﺗﺂﻟﻔﻴﺔ ﻣﻌﺮﻓﺔ آﻤﺎ ﻳﻠﻲ ‪. f ( x ) = 3x − 3 :‬‬
‫⎞ ‪⎛x‬‬
‫ﻋﺒﺮ ﻋﻦ ) ‪ f ( x + y‬و ) ‪ f ( x − y‬و ) ‪ f ( x . y‬و ⎟ ⎜ ‪≠ 0 ) f‬‬
‫⎠ ‪⎝y‬‬
‫‪(y‬‬
‫ﺑﺪﻻﻟﺔ ‪ x‬و ‪. y‬‬
‫‪_www.anissmaths.ift.cx‬ﻣﻮﻗﻊ اﻟﺮﻳﺎﺿﻴﺎت ﺑﺎﻟﺜﺎﻧﻮي اﻹﻋﺪادي ﻟﻸﺳﺘﺎذ اﻟﻤﻬﺪي ﻋﻨﻴﺲ ‪ /‬أﺳﺘﺎذ ﺑﺎﻟﺜﺎﻧﻮﻳﺔ اﻹﻋﺪادﻳﺔ اﺑﻦ رﺷﻴﻖ – ﻧﻴﺎﺑﺔ اﻟﻤﺤﻤﺪﻳﺔ_‬
‫اﻟﻌﻨﻮان ‪ 143 :‬ﺣﻲ رﻳﺎض اﻟﺴﻼم ‪ -‬اﻟﻄﺎﺑﻖ ‪ - 2‬اﻟﻤﺤﻤﺪﻳﺔ ‪ /‬اﻟﻬﺎﺗﻒ اﻟﻨﻘﺎل ‪ / 063 15 37 85 :‬اﻟﻌﻨﻮان اﻹﻟﻜﺘﺮوﻧﻲ ‪[email protected] :‬‬