math2

‫ﺍﻟﺠﻤﻬﻭﺭﻴﺔ ﺍﻟﺠﺯﺍﺌﺭﻴﺔ ﺍﻟﺩﻴﻤﻘﺭﺍﻁﻴﺔ ﺍﻟﺸﻌﺒﻴﺔ‬ ‫ﻭﺯﺍﺭﺓ ﺍﻟﺘﺭﺒﻴﺔ ﺍﻟﻭﻁﻨﻴﺔ‬‫ﺍﻟﺩﻴﻭﺍﻥ ﺍﻟﻭﻁﻨﻲ ﻟﻠﺘﻌﻠﻴﻡ ﻭﺍﻟﺘﻜﻭﻴﻥ ﻋﻥ ﺒﻌﺩ‬ ‫ﺍﻟﻤﺴﺘﻭﻯ ﻭﺍﻟﺸﻌﺒﺔ ‪ 3 :‬ﺜﺎ ‪ /‬ﺁ ﻓﻠﺴﻔﺔ‬ ‫ﺍﻤﺘﺤﺎﻥ ﺍﻟﻤﺴﺘﻭﻯ – ﺩﻭﺭﺓ ﻤﺎﻱ ‪2010‬‬ ‫ﺍﻟﻤﺎﺩﺓ‪ :‬ﺭﻴﺎﻀﻴﺎﺕ ﺍﻟﺘﻭﻗﻴﺕ‪ 10:‬ﺴﺎ ‪15‬ﺩ‪ 12-‬ﺴﺎ ‪15‬ﺩ‬ ‫ﺍﻟﺘﻤﺭﻴﻥ ﺍﻷﻭل ‪ 5 ) :‬ﻨﻘﺎﻁ (‬‫ﻨﻌﺘﺒﺭ ﺍﻟﻌﺩﺩﻴﻥ ﺍﻟﻁﺒﻴﻌﻴﻴﻥ ‪. b = 1954 ، a = 2010‬‬ ‫‪ (1‬ﺘﺤﹼﻘﻕ ﺃﻥ ‪. a − b ≡ 0[7] :‬‬ ‫‪ (2‬ﻤﺎ ﻫﻭ ﺒﺎﻗﻲ ﻗﺴﻤﺔ ﺍﻟﻌﺩﺩ ‪ 3a² - 26²‬ﻋﻠﻰ ‪ 7‬؟‬ ‫‪ (3‬ﺒ‪‬ﻴﻥ ﺃﻥ ‪4a + 56 ≡ 2[7] :‬‬ ‫‪ (4‬ﻤﺎ ﻫﻭ ﺒﺎﻗﻲ ﻗﺴﻤﺔ ‪ a1430‬ﻭ ‪ b1962‬ﻋﻠﻰ ‪ 7‬؟‬ ‫ﺍﻟﺘﻤﺭﻴﻥ ﺍﻟﺜﺎﻨﻲ ‪ 5 ) :‬ﻨﻘﺎﻁ (‬ ‫)‪ (Un‬ﻤﺘﺘﺎﻟﻴﺔ ﻤﻌﺭﻓﺔ ﺒﺤﺩﻫﺎ ﺍﻷﻭل ‪ U0 = 4‬ﻭﺒﺎﻟﻌﺒﺎﺭﺓ ‪ Un+1 = 2Un – 3‬ﻤﻥ ﺃﺠل ﻜل ﻋﺩﺩ ﻁﺒﻴﻌﻲ ‪. n‬‬ ‫ﻭ )‪ (Vn‬ﻤﺘﺘﺎﻟﻴﺔ ﻤﻌﺭﻓﺔ ﺒـ ‪Vn = Un – 3 :‬‬ ‫‪ (1‬ﺒﺭﻫﻥ ﺃﻥ )‪ (Vn‬ﻤﺘﺘﺎﻟﻴﺔ ﻫﻨﺩﺴﻴﺔ ﻤﻌﻴﻨﺎ ﺃﺴﺎﺴﻬﺎ ﻭﺤﺩﻫﺎ ﺍﻷﻭل‪.‬‬ ‫‪ (2‬ﺍﻜﺘﺏ ‪ Vn‬ﺒﺩﻻﻟﺔ ‪ n‬ﺜﻡ ﺍﺴﺘﻨﺘﺞ ‪ Un‬ﺒﺩﻻﻟﺔ ‪. n‬‬‫‪ (3‬ﺍﺤﺴﺏ ﻜﻼ ﻤﻥ ﺍﻟﻤﺠﻤﻭﻋﻴﻥ ‪ S = V0 + V1 + … + Vn :‬ﻭ ‪. S’ = V2 + V3 + … + V10‬‬ ‫ﺍﻟﺘﻤﺭﻴﻥ ﺍﻟﺜﺎﻟﺙ ‪ 10 ) :‬ﻨﻘﺎﻁ (‬ ‫ﻟﺘﻜﻥ ‪ f‬ﺩﺍﻟﺔ ﻤﻌﺭﻓﺔ ﺒﺎﻟﻌﺒﺎﺭﺓ ‪. f(x) = -2x3 + 6x – 4 :‬‬ ‫‪GG‬‬ ‫‪‬ﻭ )‪ (Cf‬ﺍﻟﺘﻤﺜﻴل ﺍﻟﺒﻴﺎﻨﻲ ﻟﻠﺩﺍﻟﺔ ‪ f‬ﻓﻲ ﻤﻌﻠﻡ ﻤﺘﻌﺎﻤﺩ ﻤﺘﺠﺎﻨﺱ ) ‪.( O; i , j‬‬ ‫‪ (1‬ﺍﺩﺭﺱ ﺘﻐﻴﺭﺍﺕ ﺍﻟﺩﺍﻟﺔ ‪. f‬‬ ‫‪ (2‬ﺒ‪‬ﻴﻥ ﺃﻥ ﺍﻟﻨﻘﻁﺔ )‪ A ( 0 ; - 4‬ﻤﺭﻜﺯ ﺘﻨﺎﻅﺭ ﻟﻠﻤﻨﺤﻨﻰ )‪.(Cf‬‬ ‫‪ (3‬ﺍﻜﺘﺏ ﻤﻌﺎﺩﻟﺔ ﺍﻟﻤﻤﺎﺱ ﻟﻠﻤﻨﺤﻨﻰ )‪ (Cf‬ﻋﻨﺩ ‪. A‬‬‫‪ (4‬ﺒ‪‬ﻴﻥ ﺃﻨﻪ ﻴﻤﻜﻥ ﻜﺘﺎﺒﺔ )‪ f(x‬ﻋﻠﻰ ﺍﻟﺸﻜل ‪ f(x) = (x – 1)2 ( –2x – 4) :‬ﻤﻥ ﺃﺠل ﻜل ﻋﺩﺩ ﺤﻘﻴﻘﻲ ‪. x‬‬ ‫‪ (5‬ﻋ‪‬ﻴﻥ ﻨﻘﻁﺔ ﺘﻘﺎﻁﻊ )‪ (Cf‬ﻤﻊ ﺤﺎﻤﻠﻲ ﺍﻟﻤﺤﻭﺭﻴﻥ‪.‬‬ ‫‪ (6‬ﺃﻨﺸﺊ )‪.(Cf‬‬ ‫‪1/1‬‬