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1 ‫ا‬ ‫ﻤ‬ ‫ﻮ‬ ‫ر‬ ‫ﺔ‬ ‫ا‬ ‫ﺰ‬ ‫ا‬ ‫ﺋ‬ ‫ﺮ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﻤ‬ ‫ﻮ‬ ‫ﻗ‬ ‫ﺮ‬ ‫ا‬ ‫ﻃ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﻌ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺔ‬ ‫و‬ ‫ز‬ ‫ا‬ ‫ر‬ ‫ة‬ ‫ا‬ ‫ﻟ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﻮ‬ ‫ﻃ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﺛ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﻮ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﺪ‬ ‫ﻋ‬ ‫ﺜ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ن‬ - ‫ﻏ‬ ‫ﻠ‬ ‫ا‬ ‫ن‬ ‫ا‬ ‫ﻻ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ر‬ ‫ا‬ ‫ﻷ‬ ‫و‬ ‫ل‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺜ‬ ‫ﻼ‬ ‫ﺛ‬ ‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬ ‫ﻲ‬ ‫ا‬ ‫ﻷ‬ ‫و‬ ‫ل‬ ‫ﻣ‬ ‫ﺎ‬ ‫د‬ ‫ة‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻠ‬ ‫ﻮ‬ ‫م‬ ‫ا‬ ‫ﻟ‬ ‫ﻔ‬ ‫ﻳ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﻌ‬ ‫ﺐ‬ : 3 ‫ﻋ‬ ‫ﻠ‬ ‫ﻮ‬ ‫م‬ ‫ﺗ‬ ‫ﺠ‬ ‫ﺮ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ا‬ ‫ﳌ‬ ‫ﺪ‬ ‫ة‬ : ‫ﺳ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﺘ‬ ‫ﻴ‬ ‫ـ‬‫ـ‬‫ـ‬‫ـ‬ ‫ﻦ‬ ‫ا‬ ‫ﻟ‬ ‫ﺗ‬ ‫ﻣ‬ ‫ر‬ ‫ﯾ‬ ‫ن‬ ‫ا‬ ‫ﻷ‬ ‫و‬ ‫ل‬ : ) 7 0 ‫ﻧ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ط‬ ( ‫ا‬ ‫ﺰ‬ ‫ء‬ ‫ا‬ ‫ﻷ‬ ‫و‬ ‫ل‬ : ‫ﻧ‬ ‫ﺮ‬ ‫ﺪ‬ ‫أ‬ ‫ن‬ ‫ﻧ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﺮ‬ ‫ف‬ ‫ﻋ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﻣ‬ ‫ﺎ‬ ‫د‬ ‫ة‬ ‫ﻣ‬ ‫ﺸ‬ ‫ﻌ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ل‬ ‫ز‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﻧ‬ ‫ﺼ‬ ‫ﻒ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﺮ‬ ‫و‬ ‫ﻣ‬ ‫ﻦ‬ ‫أ‬ ‫ﺟ‬ ‫ﻞ‬ ‫ذ‬ ‫ﻟ‬ ‫ﻚ‬ ‫ﻧ‬ ‫ﻘ‬ ‫ﻮ‬ ‫م‬ ‫ﺑ‬ ‫ﻮ‬ ‫ا‬ ‫ﺳ‬ ‫ﻄ‬ ‫ﺔ‬ ‫ﻋ‬ ‫ﺪ‬ ‫ا‬ ‫د‬ ‫ر‬ ‫ﻗ‬ ) ‫ﻣ‬ ‫ﻴ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻴ‬ ‫ﮫ‬ ( ‫و‬ ‫ﺎ‬ ‫ﺷ‬ ‫ﻒ‬ ‫أ‬ ‫ﺷ‬ ‫ﻌ‬ ‫ﺔ‬ ‫ﺑ‬ ‫ﺈ‬ ‫ﻧ‬ ‫ﺠ‬ ‫ﺎ‬ ‫ز‬ ‫ا‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ت‬ ‫ا‬ ‫ﻟ‬ ‫ﻼ‬ ‫ز‬ ‫ﻣ‬ ‫ﺔ‬ ‫و‬ ‫ر‬ ‫م‬ ‫ا‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ن‬ ‫ا‬ ‫ﳌ‬ ‫ﻤ‬ ‫ﺜ‬ ‫ﻞ‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﻞ‬ 01 . 1 . ‫ﻣ‬ ‫ﺎ‬ ‫ذ‬ ‫ا‬ ‫ﺗ‬ ‫ﻼ‬ ‫ﺣ‬ ‫ﻆ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﻳ‬ ‫ﺨ‬ ‫ﺺ‬ ‫ا‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ن‬ ln = ( ) ، ‫ﻋ‬ ‫ﻋ‬ ‫ﻨ‬ ‫ﮫ‬ ‫ﺑ‬ ‫ﻤ‬ ‫ﻌ‬ ‫ﺎ‬ ‫د‬ ‫ﻟ‬ ‫ﺔ‬ ‫ر‬ ‫ﺎ‬ ‫ﺿ‬ ‫ﻴ‬ ‫ﺔ‬ . 2 . ‫أ‬ ‫ﻋ‬ ‫ﻂ‬ ‫ﻋ‬ ‫ﺒ‬ ‫ﺎ‬ ‫ر‬ ‫ة‬ ln ‫ﺑ‬ ‫ﺪ‬ ‫ﻻ‬ ‫ﻟ‬ ‫ﺔ‬ ‫و‬ ‫و‬ . 3 . ‫ﺟ‬ ‫ﺪ‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺔ‬ ‫ﺛ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺖ‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ط‬ ‫ا‬ ‫ﻻ‬ ‫ﺷ‬ ‫ﻌ‬ ‫ﺎ‬ . 4 . ‫أ‬ ‫و‬ ‫ﺟ‬ ‫ﺪ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻼ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﺗ‬ ‫ﺮ‬ ‫ﻂ‬ ‫ﺑ‬ ‫ن‬ / ‫و‬ ) ‫ﺛ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺖ‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ط‬ ‫ا‬ ‫ﻻ‬ ‫ﺷ‬ ‫ﻌ‬ ‫ﺎ‬ ( . 5 . ‫ا‬ ‫ﺣ‬ ‫ﺴ‬ ‫ﺐ‬ ‫ز‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﻧ‬ ‫ﺼ‬ ‫ﻒ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﺮ‬ / . ‫ا‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺘ‬ ‫ﺞ‬ ‫ر‬ ‫ﻣ‬ ‫ﺰ‬ ‫ﻧ‬ ‫ﻮ‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ . 6 . ‫ﻟ‬ ‫ﺘ‬ ‫ﻜ‬ ‫ﻦ‬ ‫ﻋ‬ ‫ﺪ‬ ‫د‬ ‫ا‬ ‫ﻷ‬ ‫ﻧ‬ ‫ﻮ‬ ‫ﺔ‬ ‫ﻋ‬ ‫ﻨ‬ ‫ﺪ‬ ‫ا‬ ‫ﻟ‬ ‫ﻈ‬ ‫ﺔ‬ = 0 ‫و‬ ‫ﻛ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ﺬ‬ ‫ﻩ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺔ‬ . ‫أ‬ ‫و‬ ‫ﺟ‬ ‫ﺪ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﻞ‬ ‫ﻣ‬ ‫ﻦ‬ ‫و‬ . ‫ا‬ ‫ﺰ‬ ‫ء‬ ‫ا‬ ‫ﻟ‬ ‫ﺜ‬ ‫ﺎ‬ ‫ﻲ‬ : ‫ﻟ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻗ‬ ‫ﺎ‬ ‫م‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ء‬ ‫إ‬ ‫ﺣ‬ ‫ﺪ‬ ‫ى‬ ‫ا‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻠ‬ ‫ﺪ‬ ‫ا‬ ‫ن‬ ‫ﺑ‬ ‫ﺄ‬ ‫ﺧ‬ ‫ﺬ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ت‬ ‫ﻣ‬ ‫ﻦ‬ ‫أ‬ ‫ر‬ ‫ا‬ ‫ﻣ‬ ‫ﺮ‬ ‫د‬ ‫و‬ ‫ﻣ‬ ‫ﺔ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ل‬ ‫ز‬ ‫ﻻ‬ ‫ز‬ ‫ل‬ ‫ﻗ‬ ‫ﺪ‬ ‫ﻳ‬ ‫ﻤ‬ ‫ﺔ‬ ، ‫ﺣ‬ ‫ﻴ‬ ‫ﺚ‬ ‫ا‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻄ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻮ‬ ‫ا‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﺎ‬ ‫س‬ ‫ﻣ‬ ‫ﻦ‬ ‫أ‬ ‫ﺟ‬ ‫ﻞ‬ ‫ﻞ‬ ‫ز‬ ‫ﻟ‬ ‫ﺰ‬ ‫ا‬ ‫ل‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ط‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻈ‬ ‫ا‬ ‫ﻟ‬ ‫ﻜ‬ ‫ﺮ‬ ‫ﻮ‬ ‫ن‬ 14 ‫ا‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﻊ‬ ‫و‬ ‫ا‬ ‫ﻟ‬ ‫ﺬ‬ ‫ي‬ ‫ﻧ‬ ‫ﺼ‬ ‫ﻒ‬ ‫ﻋ‬ ‫ﻤ‬ ‫ﺮ‬ ‫ﻩ‬ ‫ﻮ‬ 5700 ، ‫ﻓ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﺖ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ت‬ ‫ﺬ‬ ‫ﻩ‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ﻃ‬ ‫ﺎ‬ ‫ت‬ ‫ﻣ‬ ‫ﻦ‬ ‫أ‬ ‫ﺟ‬ ‫ﻞ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ت‬ ‫ﻣ‬ ‫ﺨ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﻔ‬ ‫ﺔ‬ 1979 ‫ﺎ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺎ‬ : 0,251 ، 0,223 ، 0,215 ، 0,233 ‫و‬ ‫ﺣ‬ ‫ﺪ‬ ‫ة‬ ‫د‬ ‫و‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺔ‬ . ‫ﺑ‬ ‫ﻨ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ﺸ‬ ‫ﺎ‬ ‫ط‬ ‫أ‬ ‫ر‬ ‫ض‬ ‫ﻏ‬ ‫ﻣ‬ ‫ﺮ‬ ‫د‬ ‫و‬ ‫ﻣ‬ ‫ﺔ‬ ‫و‬ ‫ا‬ ‫ﻟ‬ ‫ﺬ‬ ‫ي‬ ‫ﻳ‬ ‫ﺒ‬ ‫ﻘ‬ ‫ﻰ‬ ‫ﺛ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﺘ‬ ‫ﺎ‬ ‫ﻮ‬ 0,255 . 1 . ‫ﻣ‬ ‫ﺎ‬ ‫ﻮ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﺮ‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺮ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻌ‬ ‫ﻴ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ت‬ ‫ا‬ ‫ﳌ‬ ‫ﺪ‬ ‫ر‬ ‫و‬ ‫ﺳ‬ ‫ﺔ‬ ‫؟‬ 2 . ‫ﻣ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫ﺦ‬ ‫ﺣ‬ ‫ﺪ‬ ‫و‬ ‫ث‬ ‫ا‬ ‫ﻟ‬ ‫ﺰ‬ ‫ﻻ‬ ‫ز‬ ‫ل‬ ‫؟‬ ‫ﻌ‬ ‫ﻄ‬ ‫ﻰ‬ : / ( ) = 138,3 / ( ) = 276 / ( ) = 3 ‫ا‬ ‫ﻟ‬ ‫ﺗ‬ ‫ﻣ‬ ‫ر‬ ‫ﯾ‬ ‫ن‬ ‫ا‬ ‫ﻟ‬ ‫ﺛ‬ ‫ﺎ‬ ‫ﻧ‬ ‫ﻲ‬ : ) 6 0 ‫ﻧ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ط‬ ( ‫ﺴ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﻞ‬ ‫ﺧ‬ ‫ﻠ‬ ‫ﻴ‬ ‫ﻂ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ا‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﻮ‬ ‫ر‬ ‫ا‬ ‫ﻧ‬ ‫ﻴ‬ ‫ﻮ‬ ‫م‬ ‫و‬ ‫ا‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﻮ‬ ‫ر‬ ‫ا‬ ‫ﻧ‬ ‫ﻴ‬ ‫ﻮ‬ ‫م‬ ‫ا‬ ‫ﺼ‬ ‫ﺐ‬ ‫ﻮ‬ ‫ﻗ‬ ‫ﻮ‬ ‫د‬ ‫ﳌ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫ﻏ‬ ‫ﻮ‬ ‫ا‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﻧ‬ ‫ﻮ‬ ‫و‬ ‫ﺔ‬ . ‫ﺗ‬ ‫ﺘ‬ ‫ﺞ‬ ‫ا‬ ‫ﻟ‬ ‫ﻄ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ا‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﻠ‬ ‫ﻜ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﻃ‬ ‫ﺮ‬ ‫ف‬ ‫ا‬ ‫ﻟ‬ ‫ﻐ‬ ‫ﻮ‬ ‫ا‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ا‬ ‫ﺸ‬ ‫ﻄ‬ ‫ﺎ‬ ‫ر‬ ‫ا‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﻮ‬ ‫ر‬ ‫ا‬ ‫ﻧ‬ ‫ﻴ‬ ‫ﻮ‬ ‫م‬ ‫إ‬ ‫ﺛ‬ ‫ﺮ‬ ‫ا‬ ‫ﺻ‬ ‫ﻄ‬ ‫ﺪ‬ ‫ا‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻨ‬ ‫و‬ ‫ﻧ‬ ‫ﺎ‬ ‫ت‬ ‫و‬ ‫ذ‬ ‫ﻟ‬ ‫ﻚ‬ ‫ﺣ‬ ‫ﺴ‬ ‫ﺐ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫د‬ ‫ﻟ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫ا‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻮ‬ ‫و‬ ‫ي‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺎ‬ : + → + + 1 . ‫أ‬ ‫و‬ ‫ﺟ‬ ‫ﺪ‬ ‫و‬ ‫ا‬ ‫ﳌ‬ ‫ﻌ‬ ‫ﺎ‬ ‫د‬ ‫ﻟ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻮ‬ ‫و‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻘ‬ ‫ﺔ‬ . 2 . ‫أ‬ ‫ﺣ‬ ‫ﺴ‬ ‫ﺐ‬ ‫ا‬ ‫ﻟ‬ ‫ﻄ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﺔ‬ ‫ا‬ ‫ﺮ‬ ‫ر‬ ‫ة‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ـ‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﺬ‬ ‫ا‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ . 3 . ‫ﻣ‬ ‫ﺜ‬ ‫ﻞ‬ ‫ا‬ ‫ﺼ‬ ‫ﻴ‬ ‫ﻠ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﻄ‬ ‫ﺎ‬ ‫ﻗ‬ ‫ﻮ‬ ‫ﺔ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫ا‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻮ‬ ‫و‬ ‫ي‬ ‫ا‬ ‫ﺎ‬ ‫د‬ ‫ث‬ . 4 . ‫أ‬ ‫و‬ ‫ﺟ‬ ‫ﺪ‬ ‫ا‬ ‫ﳌ‬ ‫ﺪ‬ ‫ة‬ ‫ا‬ ‫ﻟ‬ ‫ﺰ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﻠ‬ ‫ﻚ‬ ‫ﺧ‬ ‫ﻼ‬ ‫ﻟ‬ ‫ﺎ‬ ‫ﻛ‬ ‫ﺘ‬ ‫ﻠ‬ ‫ﺔ‬ = 1 g ‫ﻣ‬ ‫ﻦ‬ ‫ا‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﻮ‬ ‫ر‬ ‫ا‬ ‫ﻧ‬ ‫ﻴ‬ ‫ﻮ‬ ‫م‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﻃ‬ ‫ﺮ‬ ‫ف‬ ‫ا‬ ‫ﳌ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫ا‬ ‫ﻟ‬ ‫ﻨ‬ ‫ﻮ‬ ‫و‬ ‫ي‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻐ‬ ‫ﻮ‬ ‫ا‬ ‫ﺻ‬ ‫ﺔ‬ ‫ﻋ‬ ‫ﻠ‬ ‫ﻤ‬ ‫ﺎ‬ ‫أ‬ ‫ن‬ ‫ا‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻄ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﺘ‬ ‫ﮫ‬ 15 . ‫ﻌ‬ ‫ﻄ‬ ‫ﻰ‬ : ( ) = 234,99345 ( ) = 138,88917 ( ) = 93,89451 ( ) = 1,00866 1 = 931,5 1 = 1,6 × 10 1 = 1,66 × 10 = 3 × 10 / = 6,02 × 10
2 ‫ا‬ ‫ﻟ‬ ‫ﺗ‬ ‫ﻣ‬ ‫ر‬ ‫ﯾ‬ ‫ن‬ ‫ا‬ ‫ﻟ‬ ‫ﺗ‬ ‫ﺟ‬ ‫ر‬ ‫ﯾ‬ ‫ﺑ‬ ‫ﻲ‬ : ) 7 0 ‫ﻧ‬ ‫ﻘ‬ ‫ﺎ‬ ‫ط‬ ( ‫ﻣ‬ ‫ﺎ‬ ‫ء‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﻣ‬ ‫ﺤ‬ ‫ﻠ‬ ‫ﻮ‬ ‫ل‬ ‫ﻣ‬ ‫ﺎ‬ ‫ﻲ‬ ‫ﻳ‬ ‫ﺘ‬ ‫ﻤ‬ ‫ﺑ‬ ‫ﺨ‬ ‫ﺼ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺺ‬ ‫ﻣ‬ ‫ﻄ‬ ‫ﺮ‬ ‫ة‬ ‫ﻓ‬ ‫ﻮ‬ ‫ﻣ‬ ‫ﻨ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ج‬ ‫ﻓ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ل‬ ‫ﺿ‬ ‫ﺪ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﺪ‬ ‫و‬ ‫ى‬ ‫ا‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻜ‬ ‫ﺘ‬ ‫ﻳ‬ ‫ﺔ‬ ‫و‬ ‫ا‬ ‫ﻟ‬ ‫ﻔ‬ ‫و‬ ‫ﺳ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻳ‬ ‫ﺤ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ي‬ ‫ﻋ‬ ‫ﺷ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ ‫ا‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺒ‬ ‫ﻮ‬ ‫ﻠ‬ ‫ﻮ‬ ‫ر‬ ‫ﺖ‬ ، ‫ﺷ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ ‫و‬ ‫ﺷ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ . ‫ﺗ‬ ‫ﻀ‬ ‫ﻔ‬ ‫ﻲ‬ ‫ﺷ‬ ‫ﺎ‬ ‫ر‬ ‫د‬ ‫ة‬ ‫ا‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺒ‬ ‫ﻮ‬ ‫ﻠ‬ ‫ﻮ‬ ‫ر‬ ‫ﺖ‬ ‫ﻋ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ء‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ا‬ ‫ﻟ‬ ‫ﺼ‬ ‫ﻔ‬ ‫ﺔ‬ ‫ا‬ ‫ﳌ‬ ‫ﺆ‬ ‫ﻛ‬ ‫ﺴ‬ ‫ﺪ‬ ‫ة‬ . ‫ﻳ‬ ‫ﺤ‬ ‫ﺪ‬ ‫ث‬ ‫ا‬ ‫ﻟ‬ ‫ﻀ‬ ‫ﻮ‬ ‫ء‬ ‫أ‬ ‫ن‬ ‫ﺷ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ ‫ﺗ‬ ‫ﺆ‬ ‫ﻛ‬ ‫ﺴ‬ ‫ﺪ‬ ‫ﺸ‬ ‫ﻞ‬ ‫ﺑ‬ ‫ﻄ‬ ‫ﻲ‬ ‫ء‬ ‫ﺟ‬ ‫ﺰ‬ ‫ﺌ‬ ‫ﺎ‬ ‫ت‬ ‫ا‬ ‫ﳌ‬ ‫ﺎ‬ ‫ء‬ ‫و‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺎ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ء‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ﺳ‬ ‫ﻴ‬ ‫ﻔ‬ ‫ﻘ‬ ‫ﺪ‬ ‫ﻓ‬ ‫ﻌ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺘ‬ ‫ﮫ‬ ‫ﺗ‬ ‫ﺪ‬ ‫ر‬ ‫ﺠ‬ ‫ﻴ‬ ‫ﺎ‬ . ‫و‬ ‫ﻮ‬ ‫ﺟ‬ ‫ﻮ‬ ‫د‬ ‫ﺷ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ ‫ا‬ ‫ﻟ‬ ‫ﻮ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﺖ‬ ‫ﻓ‬ ‫ﺈ‬ ‫ن‬ ‫ﺬ‬ ‫ا‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫ﻳ‬ ‫ﻮ‬ ‫ن‬ ‫أ‬ ‫ﺳ‬ ‫ﺮ‬ ‫ع‬ . 1 . ‫أ‬ ‫ﻛ‬ ‫ﺘ‬ ‫ﺐ‬ ‫ﻣ‬ ‫ﻌ‬ ‫ﺎ‬ ‫د‬ ‫ﻟ‬ ‫ﺔ‬ ‫ﺗ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫ا‬ ‫ﻷ‬ ‫ﻛ‬ ‫ﺴ‬ ‫ﺪ‬ ‫ة‬ ‫ا‬ ‫ﻹ‬ ‫ر‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻴ‬ ‫ﺔ‬ . ‫ﻌ‬ ‫ﻄ‬ ‫ﻰ‬ ‫ا‬ ‫ﻟ‬ ‫ﺜ‬ ‫ﻨ‬ ‫ﺎ‬ ‫ﺋ‬ ‫ﺘ‬ ‫ﺎ‬ ‫ن‬ / ‫و‬ / . 2 . ‫ﻟ‬ ‫ﺪ‬ ‫ر‬ ‫ا‬ ‫ﺳ‬ ‫ﺔ‬ ‫ﺳ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﺔ‬ ‫ﺗ‬ ‫ﻔ‬ ‫ﻜ‬ ‫ﻚ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ء‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﻞ‬ ) ‫ﺑ‬ ‫ﻮ‬ ‫ﺟ‬ ‫ﻮ‬ ‫د‬ ‫ﺷ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ ( ‫ﻧ‬ ‫ﻘ‬ ‫ﺲ‬ ‫د‬ ‫ر‬ ‫ﺟ‬ ‫ﺔ‬ ‫ا‬ ‫ﺮ‬ ‫ا‬ ‫ر‬ ‫ة‬ 20° ‫و‬ ‫ﺗ‬ ‫ﺤ‬ ‫ﺖ‬ ‫ﺿ‬ ‫ﻐ‬ ‫ﻂ‬ 1,013 × 10 ‫ﻢ‬ ‫ﻏ‬ ‫ﺎ‬ ‫ز‬ ‫ا‬ ‫ﻷ‬ ‫ﻛ‬ ‫ن‬ ‫ا‬ ‫ﳌ‬ ‫ﺸ‬ ‫ﻞ‬ ‫ﻞ‬ ‫ﻈ‬ ‫ﺔ‬ ‫ﻓ‬ ‫ﻨ‬ ‫ﺘ‬ ‫ﺤ‬ ‫ﺼ‬ ‫ﻞ‬ ‫ﻋ‬ ‫ﺟ‬ ‫ﺪ‬ ‫و‬ ‫ل‬ ‫ا‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ت‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺎ‬ : 480 450 420 360 300 240 180 120 60 0 ( ) 316 316 312 298 273 248 203 148 79 0 ( ) ( ) ‫أ‬ - ‫ا‬ ‫ﻧ‬ ‫ﺠ‬ ‫ﺰ‬ ‫ﺟ‬ ‫ﺪ‬ ‫و‬ ‫ل‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﺪ‬ ‫م‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫؟‬ ‫ب‬ - ‫أ‬ ‫ﻛ‬ ‫ﻤ‬ ‫ﻞ‬ ‫ﺟ‬ ‫ﺪ‬ ‫و‬ ‫ل‬ ‫ا‬ ‫ﻟ‬ ‫ﻘ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ت‬ ‫ﺑ‬ ‫ﺤ‬ ‫ﺴ‬ ‫ﺎ‬ ‫ب‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﻢ‬ ‫ﺗ‬ ‫ﻘ‬ ‫ﺪ‬ ‫م‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫و‬ ‫أ‬ ‫ر‬ ‫ﺳ‬ ‫ﻢ‬ ‫ا‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ن‬ = ( ) . ‫ﺑ‬ ‫ﺎ‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﺎ‬ ‫ل‬ ‫ا‬ ‫ﻟ‬ ‫ﺮ‬ ‫ﺳ‬ ‫ﻢ‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﺎ‬ : ‫ﻣ‬ ‫ﻊ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻠ‬ ‫ﻢ‬ ‫أ‬ ‫ن‬ ‫ا‬ ‫ﻢ‬ ‫ا‬ ‫ﳌ‬ ‫ﻮ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﻐ‬ ‫ﺎ‬ ‫ز‬ ‫ا‬ ‫ت‬ = 24 / ‫ﺟ‬ ‫ـ‬ - ‫ﻋ‬ ‫ن‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻘ‬ ‫ﺪ‬ ‫م‬ ‫ا‬ ‫ﻷ‬ ‫ﻋ‬ ‫ﻈ‬ ‫ﻟ‬ ‫ﻠ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ ‫ﺛ‬ ‫ﻢ‬ ‫ا‬ ‫ﺳ‬ ‫ﺘ‬ ‫ﺘ‬ ‫ﺞ‬ ‫ا‬ ‫ﻟ‬ ‫ﻛ‬ ‫ا‬ ‫ﳌ‬ ‫ﻮ‬ ‫ا‬ ‫ﻻ‬ ‫ﺑ‬ ‫ﺘ‬ ‫ﺪ‬ ‫ا‬ ‫ﻲ‬ [ ] ‫ﻟ‬ ‫ﺸ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ ‫ا‬ ‫ﻟ‬ ‫ﻴ‬ ‫ﺒ‬ ‫ﻮ‬ ‫ﻠ‬ ‫ﻮ‬ ‫ر‬ ‫ﺖ‬ ‫؟‬ ‫ﻢ‬ ‫ﻣ‬ ‫ﺎ‬ ‫ء‬ ‫ﺟ‬ ‫ﺎ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ﻞ‬ ‫ا‬ ‫ﳌ‬ ‫ﺴ‬ ‫ﺘ‬ ‫ﻌ‬ ‫ﻤ‬ ‫ﻞ‬ = 0,11 . 3 . ‫ﻋ‬ ‫ﺮ‬ ‫ف‬ ‫ز‬ ‫ﻣ‬ ‫ﻦ‬ ‫ﻧ‬ ‫ﺼ‬ ‫ﻒ‬ ‫ا‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ﻋ‬ ‫ﻞ‬ / ‫و‬ ‫ا‬ ‫ﺣ‬ ‫ﺴ‬ ‫ﺐ‬ ‫ﻗ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺘ‬ ‫ﮫ‬ . 4 . ‫أ‬ ‫ﺛ‬ ‫ﺖ‬ ‫ﺔ‬ ‫ا‬ ‫ﻟ‬ ‫ﻌ‬ ‫ﻼ‬ ‫ﻗ‬ ‫ﺔ‬ : = −2 5 . ‫ا‬ ‫ﺣ‬ ‫ﺴ‬ ‫ﺐ‬ ‫ا‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﺮ‬ ‫ﻋ‬ ‫ﺔ‬ ‫ا‬ ‫ﻤ‬ ‫ﻴ‬ ‫ﺔ‬ ‫ﻻ‬ ‫ﺧ‬ ‫ﺘ‬ ‫ﻔ‬ ‫ﺎ‬ ‫ء‬ ‫ﺷ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ ‫ا‬ ‫ﻟ‬ ‫ﻈ‬ ‫ﺎ‬ ‫ت‬ = 120 ، = 360 . ‫ﻗ‬ ‫ﺎ‬ ‫ر‬ ‫ن‬ ‫ﺑ‬ ‫ﻴ‬ ‫ﻤ‬ ‫ﺎ‬ ‫؟‬ 6 . ‫ﺣ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﺔ‬ ‫ﻋ‬ ‫ﺪ‬ ‫م‬ ‫و‬ ‫ﺟ‬ ‫ﻮ‬ ‫د‬ ‫ا‬ ‫ﻟ‬ ‫ﺸ‬ ‫ﻮ‬ ‫ا‬ ‫ر‬ ‫د‬ . ‫أ‬ ‫ر‬ ‫ﺳ‬ ‫ﻢ‬ ‫ﻛ‬ ‫ﻴ‬ ‫ﻔ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ﺷ‬ ‫ﻞ‬ ‫ا‬ ‫ﳌ‬ ‫ﻨ‬ ‫ﺤ‬ = ( ) ‫ﻋ‬ ‫ا‬ ‫ﻟ‬ ‫ﺒ‬ ‫ﻴ‬ ‫ﺎ‬ ‫ن‬ ‫ا‬ ‫ﻟ‬ ‫ﺴ‬ ‫ﺎ‬ ‫ﺑ‬ ‫ﻖ‬ . ‫أ‬ ‫ﺳ‬ ‫ﺎ‬ ‫ﺗ‬ ‫ﺬ‬ ‫ة‬ ‫ا‬ ‫ﳌ‬ ‫ﺎ‬ ‫د‬ ‫ة‬ ‫ﺑ‬ ‫ﺎ‬ ‫ﻟ‬ ‫ﺘ‬ ‫ﻮ‬ ‫ﻓ‬ ‫ﻴ‬ ‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬ ‫ﻖ‬ 1 → 60 1 → 1,3
C l i c k t o B U Y N O W ! P D F-XChange Edit o r w w w . tracker-software . c o m C l i c k t o B U Y N O W ! P D F-XChange Edit o r w w w . tracker-software . c o m
C l i c k t o B U Y N O W ! P D F-XChange Edit o r w w w . tracker-software . c o m C l i c k t o B U Y N O W ! P D F-XChange Edit o r w w w . tracker-software . c o m

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