دليل التقويم لـ رياضيات 1

‫اﻟﻤﻤﻠﻜﺔ اﻟﻌﺮﺑﻴﺔ اﻟﺴﻌﻮدﻳﺔ‬       

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                                                                                                                                                                                 

                      (1)   (1)   (2A)    (2B)   (3)                                      

  4 ............................................................... 27 ..................................................    28 ......................................    30 ............................... (2) (1)   8 ..................................................  31 ............................... (4) (3)   9 ......................................    32 ...................................   11 .............................. (2) (1)   33 ..............................................  12 ............................... (4) (3)   34 ......................... (1)    13 ...................................   36 ...................... (2A)     14 ..............................................  38 ........................(2B)    15 ......................... (1)    40 ......................... (3)    17 ...................... (2A)     42 ................... 19 ........................(2B)    43 ............... (1, 2)   21 ......................... (3)    23 ................... 24 .......................(1)  

   65 ..................................................  46 ..................................................  66 ......................................    47 ......................................    68 ............................... (2) (1)   49 .............................. (2) (1)   69 ............................... (4) (3)   50 ............................... (4) (3)   70 ...................................   51 ...................................   71 ..............................................  52 ..............................................  72 ......................... (1)    53 ......................... (1)    73 ...................... (2A)     55 ...................... (2A)     76 ........................(2B)    57 ........................(2B)    78 ......................... (3)    59 ......................... (3)    80 ................... 61 ...................  81 .......................................   62 .................(1-3)   84 ............................................... 

‫‪‬‬ ‫‪‬‬ ‫‪   ‬‬ ‫‪1‬‬ ‫‪ ‬‬ ‫‪ 1‬ﻗﺒﻞ ﺑﺪﺀ ﺍﻟﻔﺼﻞ ﺍﻷﻭﻝ‬ ‫• ﺍﻗﺮﺃ ﻛﻞ ﺟﻤﻠﺔ‪.‬‬ ‫• ﻗ ﹼﺮﺭ ﻣﺎ ﺇﺫﺍ ﻛﻨﺖ ﻣﻮﺍﻓ ﹰﻘﺎ )ﻡ( ﻋﻠﻰ ﻣﻀﻤﻮﻧﻬﺎ‪ ،‬ﺃﻭ ﻏﻴﺮ ﻣﻮﺍﻓﻖ )ﻍ(‪.‬‬ ‫• ﺍﻛﺘﺐ )ﻡ( ﺃﻭ )ﻍ( ﰲ ﺍﻟﻌﻤﻮﺩ ﺍﻷﻭﻝ‪ ،‬ﻭﺇﺫﺍ ﻛﻨﺖ ﻏﲑ ﻣﺘﺄﻛ ﹴﺪ ﻣﻦ ﻣﻮﺍﻓﻘﺘﻚ ﻓﺎﻛﺘﺐ )ﻍ ﻡ(‪.‬‬ ‫‪2‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪ (1‬ﺍﻟﺘﺒﺮﻳﺮ ﺍﻻﺳﺘﻘﺮﺍﺋﻲ ﻫﻮ ﺍﻟﺘﺒﺮﻳﺮ ﺍﻟﺬﻱ ﻳﺴﺘﻌﻤﻞ ﺍﻟﺤﻘﺎﺋﻖ ﻟﻠﻮﺻﻮﻝ ﺇﻟﻰ ﺍﻟﻨﺘﺎﺋﺞ ﺍﻟﻤﻨﻄﻘﻴﺔ‪.‬‬ ‫‪ (2‬ﺍﻟﺘﺨﻤﻴﻦ ﻫﻮ ﺗﻮﻗﻊ ﻳﺴﺘﻨﺪ ﺇﻟﻰ ﻣﻌﻠﻮﻣﺎﺕ ﻣﻌﺮﻭﻓﺔ‪.‬‬ ‫‪ (3‬ﻋﺒﺎﺭﺓ ﺍﻟﻮﺻﻞ ﻫﻲ ﻋﺒﺎﺭﺓ ﻣﺮﻛﺒﺔ ﺗﻨﺘﺞ ﻋﻦ ﺭﺑﻂ ﻋﺒﺎﺭﺗﻴﻦ ﺑﺄﺩﺍﺓ ﺍﻟﺮﺑﻂ \"ﺃﻭ\"‪.‬‬ ‫‪ (4‬ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺘﻲ ﻳﻤﻜﻦ ﻛﺘﺎﺑﺘﻬﺎ ﺑﺼﻴﻐﺔ )ﺇﺫﺍ ﻛﺎﻥ‪ ...‬ﻓﺈﻥ‪ (...‬ﺗﺴﻤﻰ ﻋﺒﺎﺭﺓ ﺷﺮﻃﻴﺔ‪.‬‬ ‫‪ (5‬ﺗﻜﻮﻥ ﺍﻟﻌﺒﺎﺭﺗﺎﻥ ﻣﺘﻜﺎﻓﺌﺘﻴﻦ ﻣﻨﻄﻘ ﹼﹰﻴﺎ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ ﻟﻬﻤﺎ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﻧﻔﺴﻬﺎ‪.‬‬ ‫‪ (6‬ﹸﺗﺴﺘﻌﻤﻞ ﺍﻷﻣﺜﻠﺔ ﰲ ﺍﻟﺘﱪﻳﺮ ﺍﻻﺳﺘﻨﺘﺎﺟﻲ ﻻﺳﺘﻨﺒﺎﻁ ﺍﻟﻨﺘﻴﺠﺔ‪.‬‬ ‫‪ (7‬ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﻫﻲ ﻋﺒﺎﺭﺓ ﺭﻳﺎﺿﻴﺔ ﻳﺘﻌﻴﻦ ﻋﻠﻴﻚ ﺇﺛﺒﺎﺕ ﺻﺤﺘﻬﺎ‪.‬‬ ‫‪ (8‬ﺍﻟﻔﻘﺮﺓ ﺍﻟﺘﻲ ﹸﺗﻜﺘﺐ ﻟﺘﻮﺿﻴﺢ ﺍﻷﺳﺒﺎﺏ ﺍﻟﺘﻲ ﺗﺠﻌﻞ ﺍﻟﺘﺨﻤﻴﻦ ﺻﺤﻴ ﹰﺤﺎ ﺗﺴﻤﻰ ﺑﺮﻫﺎ ﹰﻧﺎ ﺣ ﹼﹰﺮﺍ‪.‬‬ ‫‪ (9‬ﻳﻤﻜﻦ ﺍﺳﺘﻌﻤﺎﻝ ﺟﻤﻴﻊ ﺧﺼﺎﺋﺺ ﺍﻟﻤﺴﺎﻭﺍﺓ ﻭﺍﻟﻤﺴ ﹼﻠﻤﺎﺕ ﻭﺍﻟﻨﻈﺮﻳﺎﺕ؛ ﻟﺘﺒﺮﻳﺮ ﺧﻄﻮﺍﺕ ﺍﻟﺒﺮﻫﺎﻥ‪.‬‬ ‫‪ (10‬ﻋﻨﺪﻣﺎ ﺗﺜﺒﺖ ﺻﺤﺔ ﻋﺒﺎﺭﺓ‪ ،‬ﻳﻤﻜﻦ ﺍﺳﺘﻌﻤﺎﻟﻬﺎ ﻹﺛﺒﺎﺕ ﻋﺒﺎﺭﺍﺕ ﹸﺃﺧﺮ￯‪.‬‬ ‫‪ (11‬ﻋﻼﻗﺔ ﺗﻄﺎﺑﻖ ﺍﻟﺰﻭﺍﻳﺎ ﻫﻲ ﻋﻼﻗﺔ ﺍﻧﻌﻜﺎ ﹴﺱ ﻭﺗﻤﺎﺛ ﹴﻞ ﻻ ﻋﻼﻗﺔ ﺗﻌ ﱟﺪ‪.‬‬ ‫‪ 2‬ﺑﻌﺪ ﺇﻛﲈﻝ ﺍﻟﻔﺼﻞ ﺍﻷﻭﻝ‬ ‫• ﺃﻋﺪ ﻗﺮﺍﺀﺓ ﻛﻞ ﺟﻤﻠﺔ ﺃﻋﻼﻩ‪ ،‬ﺛﻢ ﺍﻣﻸ ﺍﻟﻌﻤﻮﺩ ﺍﻷﺧﻴﺮ ﺑﻜﺘﺎﺑﺔ )ﻡ( ﺃﻭ )ﻍ(‪.‬‬ ‫• ﻫﻞ ﺗﻐ ﹼﻴﺮ ﺭﺃﻳﻚ ﻓﻲ ﺍﻟﺠﻤﻞ ﺍﻟﺴﺎﺑﻘﺔ ﻋ ﹼﻤﺎ ﻫﻮ ﻓﻲ ﺍﻟﻌﻤﻮﺩ ﺍﻷﻭﻝ؟‬ ‫• ﺍﺳﺘﻌﻤﻞ ﻭﺭﻗ ﹰﺔ ﺇﺿﺎﻓﻴ ﹰﺔ ﺗﺒ ﹼﻴﻦ ﻓﻴﻬﺎ ﺳﺒﺐ ﻋﺪﻡ ﻣﻮﺍﻓﻘﺘﻚ ﻋﻠﻰ ﺑﻌﺾ ﺍﻟﺠﻤﻞ‪ ،‬ﺩﺍﻋ ﹰﻤﺎ ﺫﻟﻚ ﺑﺎﻷﻣﺜﻠﺔ ﺇﻥ ﺃﻣﻜﻦ‪.‬‬ ‫‪1‬‬ ‫‪8‬‬ ‫‪‬‬

‫‪‬‬ ‫‪‬‬ ‫‪   1‬‬ ‫ﻫﺬﻩ ﻗﺎﺋﻤﺔ ﺑﺎﳌﻔﺮﺩﺍﺕ ﺍﳉﺪﻳﺪﺓ ﺍﻟﺘﻲ ﺳﺘﺘﻌﻠﻤﻬﺎ ﰲ ﺃﺛﻨﺎﺀ ﺩﺭﺍﺳﺘﻚ ﺍﻟﻔﺼﻞ ‪ .1‬ﺍﻛﺘﺐ ﺗﻌﺮﻳ ﹰﻔﺎ ﺃﻭ ﻭﺻ ﹰﻔﺎ ﻟﻜﻞ ﻣﻔﺮﺩﺓ ﰲ ﺍﳉﺪﻭﻝ ﺣﲔ ﺗﻈﻬﺮ ﻟﻚ‬ ‫ﰲ ﺃﺛﻨﺎﺀ ﺩﺭﺍﺳﺔ ﺍﻟﻔﺼﻞ‪ ،‬ﺛﻢ ﺃﺿﻒ ﺭﻗﻢ ﺍﻟﺼﻔﺤﺔ ﺍﻟﺘﻲ ﻭﺭﺩﺕ ﻓﻴﻬﺎ ﺍﳌﻔﺮﺩﺓ ﺃﻭﻝ ﻣﺮﺓ ﰲ ﺍﻟﻌﻤﻮﺩ ﺍﳌﺨ ﱠﺼﺺ‪ .‬ﺍﺳﺘﻌﻤﻞ ﻫﺬﻩ ﺍﻟﻘﺎﺋﻤﺔ ﰲ ﺃﺛﻨﺎﺀ‬ ‫ﺍﳌﺮﺍﺟﻌﺔ ﻭﺍﻻﺳﺘﻌﺪﺍﺩ ﻻﺧﺘﺒﺎﺭ ﺍﻟﻔﺼﻞ‪.‬‬ ‫‪  ‬‬ ‫‪‬‬ ‫‪‬‬ ‫ﺍﻟﺘﺨﻤﲔ‬ ‫ﺍﻟﺘﱪﻳﺮ ﺍﻻﺳﺘﻘﺮﺍﺋﻲ‬ ‫ﺍﳌﺜﺎﻝ ﺍﳌﻀﺎﺩ‬ ‫ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ‬ ‫ﺍﻟﻌﺒﺎﺭﺓ ﺍﳌﺮﻛﺒﺔ‬ ‫ﻧﻔﻲ ﺍﻟﻌﺒﺎﺭﺓ‬ ‫ﺍﻟﻌﺒﺎﺭﺓ‬ ‫ﻋﺒﺎﺭﺓ ﺍﻟﻮﺻﻞ‬ ‫ﻋﺒﺎﺭﺓ ﺍﻟ ﹶﻔ ﹾﺼﻞ‬ ‫ﺟﺪﻭﻝ ﺍﻟﺼﻮﺍﺏ‬ ‫ﺍﻟﻨﺘﻴﺠﺔ‬ ‫ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﴩﻃﻴﺔ‬ ‫ﺍﻟ ﹶﻔﺮﺽ‬ ‫‪1‬‬ ‫‪9‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪  ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪ ‬‬ ‫‪‬‬ ‫‪‬‬ ‫ﺍﳌﻌﺎﻛﺲ ﺍﻹﳚﺎﰊ‬ ‫ﺍﻟﻌﻜﺲ‬ ‫ﺍﳌﻌﻜﻮﺱ‬ ‫ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻟﴩﻃﻴﺔ ﺍﳌﺮﺗﺒﻄﺔ‬ ‫ﺍﻟﺘﻜﺎﻓﺆ ﺍﳌﻨﻄﻘﻲ‬ ‫ﺍﻟﺘﱪﻳﺮ ﺍﻻﺳﺘﻨﺘﺎﺟﻲ‬ ‫ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﳌﻨﻄﻘﻲ‬ ‫ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﳌﻨﻄﻘﻲ‬ ‫ﺍﳌﺴ ﹼﻠﻤﺔ‬ ‫ﺍﻟﱪﻫﺎﻥ‬ ‫ﺍﻟﱪﻫﺎﻥ ﺍﳊﺮ‬ ‫ﺍﻟﻨﻈﺮﻳﺔ‬ ‫ﺍﻟﱪﻫﺎﻥ ﺍﳉﱪﻱ‬ ‫ﺍﻟﱪﻫﺎﻥ ﺫﻭ ﺍﻟﻌﻤﻮﺩﻳﻦ‬ ‫‪1‬‬ ‫‪10‬‬ ‫‪‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(1-1,1-2) (1)   1‬‬ ‫‪________________(1‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪ (1‬ﺍﻛﺘﺐ ﺗﺨﻤﻴﻨﹰﺎ‪ ،‬ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ‪ ∆ABC‬ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪.‬‬ ‫‪\" (2‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ∠A‬ﹶﻭ ‪ ∠B‬ﻣﺘﺘﺎﻣﺘﻴﻦ‪ ،‬ﻓﺈﻥ ‪ ،\"m ∠A=45‬ﺃﻋ ﹺﻂ ﻣﺜﺎ ﹰﻻ ﻣﻀﺎ ﹼﹰﺩﺍ ﻳﺒ ﱢﻴﻦ ﻋﺪﻡ ﺻﺤﺔ ﻫﺬﺍ ﺍﻟﺘﺨﻤﻴﻦ‪________________(2 .‬‬ ‫‪________________(3‬‬ ‫‪ (3‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ ﻟﻠﻌﺒﺎﺭﺓ ‪ ،(p ∧ q) ∨ r‬ﺣﻴﺚ‬ ‫‪.(-4)2 > 0 :p‬‬ ‫‪ :q‬ﻟﻠﻤﺜﻠﺚ ﺍﳌﺘﻄﺎﺑﻖ ﺍﻟﻀﻠﻌﲔ ﺿﻠﻌﺎﻥ ﻣﺘﻄﺎﺑﻘﺎﻥ‪.‬‬ ‫‪ :r‬ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﻟﻠﺘﺎﻥ ﳎﻤﻮﻉ ﻗﻴﺎ ﹶﺳﻴﻬﲈ ﻳﺴﺎﻭﻱ ‪ ،90°‬ﺗﻜﻮﻧﺎﻥ ﻣﺘﻜﺎﻣﻠﺘﲔ‪.‬‬ ‫‪________________(4‬‬ ‫‪ (4‬ﺍﻓﺘﺮﺽ ﺃﻥ ‪ p‬ﻭ ‪ q‬ﻛﻼﻫﻤﺎ ﺧﺎﻃﺌﺔ‪ ،‬ﻓﻤﺎ ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ ﻟﻠﻌﺒﺎﺭﺓ‪(p ∧ ∼q) ∨∼p :‬؟‬ ‫‪________________(5‬‬ ‫‪ (5‬ﺃﻭﺟﺪ ﺍﻟﺤﺪ ﺍﻟﺘﺎﻟﻲ ﻓﻲ ﺍﻟﻤﺘﺘﺎﺑﻌﺔ ‪.1, 4, 9, 16, 25, …..‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪(1-3,1-4)(2)   1‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪________________(1‬‬ ‫‪ (1‬ﺣ ﹼﺪﺩ ﺍﻟﻨﺘﻴﺠﺔ ﻓﻲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪:‬‬ ‫ﺇﻣﺎ ﺃﻥ ‪ x = 2‬ﺃﻭ ‪ ، x = -2‬ﺇﺫﺍ ﻛﺎﻥ ‪.x2 = 4‬‬ ‫‪________________(2‬‬ ‫‪ (2‬ﺍﻛﺘﺐ ﻋﻜﺲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪\" :‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﻣﺘﻜﺎﻣﻠﺘﻴﻦ ﻭﻣﺘﻄﺎﺑﻘﺘﻴﻦ‪ ،‬ﻓﺈﻧﻬﻤﺎ ﻗﺎﺋﻤﺘﺎﻥ\"‪.‬‬ ‫‪ (3‬ﻣﺴﺘﻌﻤ ﹰﻼ ﻗﺎﻧﻮﻥ ﺍﻟ ﹶﻔ ﹾﺼﻞ ﺍﳌﻨﻄﻘﻲ‪ ،‬ﺣ ﹼﺪﺩ ﻣﺎ ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻨﺘﻴﺠﺔ ﺻﺤﻴﺤﺔ ﺃﻡ ﻻ‪ ،‬ﺍﻋﺘﲈ ﹰﺩﺍ ﻋﲆ ﺍﳌﻌﻄﻴﺎﺕ‪________________(3 ،‬‬ ‫ﻭﺍﻛﺘﺐ \"ﺻﺤﻴﺤﺔ\" ﺃﻭ \"ﻏﲑ ﺻﺤﻴﺤﺔ\"‬ ‫‪ ‬ﺇﺫﺍ ﹸﻗﺪﺕ ﺍﻟﺴﻴﺎﺭﺓ ﺑﺴﺮﻋ ﹴﺔ ﺗﺰﻳﺪ ﻋﻠﻰ ‪ 65‬ﻣﻴ ﹰﻼ ﻓﻲ ﺍﻟﺴﺎﻋﺔ‪ ،‬ﻓﺴﺘﻘﻊ ﻓﻲ ﻣﺨﺎﻟﻔﺔ ﻣﺮﻭﺭﻳﺔ‪.‬‬ ‫ﻭﻗﻊ ﻋ ﹼﲇ ﰲ ﳐﺎﻟﻔﺔ‪.‬‬ ‫‪ ‬ﻗﺎﺩ ﻋﻠ ﹼﻲ ﺳﻴﺎﺭﺗﻪ ﺑﺴﺮﻋﺔ ﺗﺰﻳﺪ ﻋﻠﻰ ‪ 65‬ﻣﻴ ﹰﻼ ﻓﻲ ﺍﻟﺴﺎﻋﺔ‪.‬‬ ‫‪________________(4‬‬ ‫‪   (4‬ﺣ ﹼﺪﺩ ﺃ ﹼﹰﻳﺎ ﻣﻦ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻵﺗﻴﺔ ﺗﻨﺘﺞ ﻣﻨﻄﻘ ﹰﹼﻴﺎ ﻋﻦ ﺍﻟﻌﺒﺎﺭﺗﻴﻦ )‪ (1‬ﹶﻭ )‪.(2‬‬ ‫)‪ (1‬ﺇﺫﺍ ﻛﺎﻥ ﺍﻟﻤﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪ ،‬ﻓﺈﻥ ﻟﻪ ﺛﻼﺛﺔ ﺃﺿﻼﻉ ﻣﺘﻄﺎﺑﻘﺔ‪.‬‬ ‫)‪ (2‬ﺇﺫﺍ ﻛﺎﻧﺖ ﲨﻴﻊ ﺃﺿﻼﻉ ﺍﳌﺜﻠﺚ ﻣﺘﻄﺎﺑﻘﺔ‪ ،‬ﻓﺈﻥ ﻗﻴﺎﺱ ﻛﻞ ﺯﺍﻭﻳﺔ ﻣﻦ ﺯﻭﺍﻳﺎﻩ ‪.60°‬‬ ‫‪ (A‬ﺇﺫﺍ ﱂ ﻳﻜﻦ ﺍﳌﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪ ،‬ﻓﺈﻧﻪ ﻻ ﻳﻤﻜﻦ ﺃﻥ ﻳﻜﻮﻥ ﻓﻴﻪ ﺯﻭﺍﻳﺎ ﻣﺘﻄﺎﺑﻘﺔ‪.‬‬ ‫‪ (B‬ﺍﻟﺸﻜﻞ ﺍﻟﺬﻱ ﻟﻪ ﺛﻼﺛﺔ ﺃﺿﻼﻉ ﻣﺘﻄﺎﺑﻘﺔ‪ ،‬ﻳﻜﻮﻥ ﻣﺜﻠ ﹰﺜﺎ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ ﺩﺍﺋ ﹰﲈ‪.‬‬ ‫‪ (C‬ﺇﺫﺍ ﱂ ﻳﻜﻦ ﺍﳌﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪ ،‬ﻓﻠﻴﺲ ﻓﻴﻪ ﺯﺍﻭﻳﺔ ﻗﻴﺎﺳﻬﺎ ‪.60°‬‬ ‫‪ (D‬ﺇﺫﺍ ﻛﺎﻥ ﺍﳌﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪ ،‬ﻓﺈﻥ ﻗﻴﺎﺱ ﻛﻞ ﺯﺍﻭﻳ ﹴﺔ ﻣﻦ ﺯﻭﺍﻳﺎﻩ ‪.60°‬‬ ‫‪1‬‬ ‫‪11‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(1-5, 1-6) (3)  ‬‬ ‫‪1‬‬ ‫‪________________(1‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫ﺣ ﱢﺪﺩ ﻣﺎ ﺇﺫﺍ ﻛﺎﻧﺖ ﻛﻞ ﺟﻤﻠ ﹴﺔ ﻣﻤﺎ ﻳﻠﻲ ﺻﺤﻴﺤﺔ ﺩﺍﺋ ﹰﻤﺎ‪ ،‬ﺃﻭ ﺻﺤﻴﺤﺔ ﺃﺣﻴﺎ ﹰﻧﺎ‪ ،‬ﺃﻭ ﻏﻴﺮ ﺻﺤﻴﺤﺔ ﺃﺑ ﹰﺪﺍ‪،‬‬ ‫ﻭﺑ ﹼﺮﺭ ﺇﺟﺎﺑﺘﻚ‪.‬‬ ‫‪ (1‬ﻷﻱ ﻣﺴﺘﻘﻴﻢ ﻭﻧﻘﻄﺔ ﻻ ﺗﻘﻊ ﻋﻠﻴﻪ ﻳﻤﺮ ﺑﻬﻤﺎ ﻣﺴﺘﻮ￯ ﻭﺍﺣﺪ ﻓﻘﻂ‪.‬‬ ‫‪________________(2‬‬ ‫‪ (2‬ﻷﻱ ﺛﻼﺙ ﻧﻘﺎﻁ ﻳﻮﺟﺪ ﻣﺴﺘﻮ￯ ﻭﺍﺣ ﹲﺪ ﻓﻘﻂ ﻳﺤﻮﻳﻬﺎ‪.‬‬ ‫‪________________(3‬‬ ‫‪ (3‬ﺃﻛﻤﻞ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪:‬‬ ‫ﺇﺫﺍ ﻛﺎﻥ ‪ ،AB = BC‬ﻭﻛﺎﻧﺖ ﺍﻟﻨﻘﺎﻁ ‪ A,B,C‬ﻋﻠﻰ ﺍﺳﺘﻘﺎﻣﺔ ﻭﺍﺣﺪﺓ‪ ،‬ﻓﺈﻥ ‪.CA ________ B‬‬ ‫‪________________(4‬‬ ‫ﺍﺫﻛﺮ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﻛﻞ ﻋﺒﺎﺭﺓ ﻓﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪: 4, 5‬‬ ‫‪________________(5‬‬ ‫‪ (4‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ،x = 2‬ﻓﺈﻥ ‪2 = x‬‬ ‫‪________________(6‬‬ ‫‪ (5‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x + 3 = y‬ﻓﺈﻥ ‪.x = y - 3‬‬ ‫‪ (6‬ﺣﺪﺩ ﻣﺎ ﺇﺫﺍ ﻛﺎﻥ ﺍﻟﺘﺨﻤﲔ ﺍﻵﰐ ﺻﺤﻴ ﹰﺤﺎ ﺃﻡ ﺧﺎﻃ ﹰﺌﺎ‪.‬‬ ‫‪ ‬ﻣﺴﺘﻮﻳﺎﻥ ﻣﺘﻘﺎﻃﻌﺎﻥ‪.‬‬ ‫‪ ‬ﻳﻤﻜﻦ ﺃﻥ ﻳﺘﻘﺎﻃﻊ ﺍﳌﺴﺘﻮﻳﺎﻥ ﰲ ﻧﻘﻄ ﹴﺔ ﻭﺍﺣﺪ ﹴﺓ ﻓﻘﻂ‪.‬‬ ‫‪‬‬ ‫‪(1-7, 1-8) (4)  ‬‬ ‫‪‬‬ ‫‪________________(1‬‬ ‫‪1‬‬ ‫‪________________(2‬‬ ‫‪________________(3‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪________________(4‬‬ ‫‪_________________(5‬‬ ‫ﺍﺫﻛﺮ ﺍﻟﺘﻌﺮﻳﻒ ﺃﻭ ﺍﻟﺨﺎﺻﻴﺔ ﺃﻭ ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﺃﻭ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻷﺳﺌﻠﺔ ‪:1 – 4‬‬ ‫‪1‬‬ ‫‪ (1‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ، DE FG‬ﻓﺈﻥ ‪. FG DE‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،XY = WZ‬ﻓﺈﻥ‪.XY + TU = WZ + TU :‬‬ ‫‪ (3‬ﺇﺫﺍ ﻛﺎﻥ‪ m ∠1 + m ∠2 = 180° :‬ﹶﻭ ‪ ،m ∠2 + m ∠3 = 180°‬ﻓﺈﻥ ‪.∠1 ∠3‬‬ ‫‪ (4‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ∠1‬ﻭ ‪ ∠2‬ﻣﺘﻘﺎﺑﻠﺘﻴﻦ ﺑﺎﻟﺮﺃﺱ‪ ،‬ﻓﺈﻥ ‪.∠1 ∠2‬‬ ‫‪ (5‬ﺇﺫﺍ ﻛﺎﻥ‪ ، m ∠A = (5x - 12)° :‬ﹶﻭ ‪ ،m ∠B = (2x + 18)°‬ﻭﻛﺎﻧﺖ ‪ ∠A‬ﻭ‪ ∠C‬ﻣﺘﻜﺎﻣﻠﺘﻴﻦ‪،‬‬ ‫ﻭ ‪ ∠B‬ﻭ ‪ ∠C‬ﻣﺘﻜﺎﻣﻠﺘﻴﻦ ﺃﻳ ﹰﻀﺎ‪ ،‬ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪.x‬‬ ‫‪12  ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(1-5  1-1)    1‬‬ ‫‪ ‬‬ ‫‪__________(1‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪ (1‬ﺣ ﱢﺪﺩ ﺃ ﹼﻱ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻵﺗﻴﺔ ﺗﻤﺜﻞ ﺗﺨﻤﻴﻨﹰﺎ ﻣﻨﺎﺳ ﹰﺒﺎ‪ :‬ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ﺍﻟﻨﻘﺎﻁ ‪ A,B,C‬ﺗﻘﻊ ﻋﻠﻰ ﺍﺳﺘﻘﺎﻣ ﹴﺔ ﻭﺍﺣﺪ ﹴﺓ‪،‬‬ ‫ﻭﺃﻥ‪.AC + CB = AB :‬‬ ‫‪ (C‬ﺗﻘﻊ ‪ B‬ﺑﲔ ‪ A‬ﻭ ‪C‬‬ ‫‪ (A‬ﺗﻘﻊ ‪ C‬ﺑﲔ ‪ A‬ﻭ ‪B‬‬ ‫‪ ∆ABC (D‬ﻣﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‬ ‫‪ (B‬ﺗﻘﻊ ‪ A‬ﺑﲔ ‪ B‬ﻭ ‪C‬‬ ‫‪__________(2‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻧﺖ ﻛ ﱞﻞ ﻣﻦ ‪ p‬ﻭ‪ r‬ﺻﺎﺋﺒﺔ‪ q ،‬ﺧﺎﻃﺌﺔ‪ ،‬ﻓﻤﺎ ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ ﻟﻠﻌﺒﺎﺭﺓ ‪(~ p ∨q) ∧ r‬؟‬ ‫‪__________(3‬‬ ‫‪ (D‬ﺍﳌﻌﻄﻴﺎﺕ ﻏﲑ ﻛﺎﻓﻴﺔ‬ ‫‪ (A‬ﺻﺎﺋﺒﺔ ‪ (B‬ﺧﺎﻃﺌﺔ ‪T (C‬‬ ‫‪__________(4‬‬ ‫‪__________(5‬‬ ‫‪ (3‬ﺇﺫﺍ ﻛﺎﻧﺖ ﻛ ﱞﻞ ﻣﻦ‪ p‬ﻭ‪ r‬ﺻﺎﺋﺒﺔ‪ q ،‬ﺧﺎﻃﺌ ﹰﺔ‪ ،‬ﻓﻤﺎ ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ ﻟﻠﻌﺒﺎﺭﺓ ‪(~ p ∨ q) ∨ r‬؟‬ ‫‪ (D‬ﺍﳌﻌﻄﻴﺎﺕ ﻏﲑ ﻛﺎﻓﻴﺔ‬ ‫‪~ T (C‬‬ ‫‪ (B‬ﺧﺎﻃﺌﺔ‬ ‫‪ (A‬ﺻﺎﺋﺒﺔ‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 4‬ﻭ ‪ 5‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﻌﺒﺎﺭﺓ‪\":‬ﺇﺫﺍ ﹶﻧ ﱠﺼ ﹶﻒ ﻣﺴﺘﻘﻴ ﹲﻢ ﺯﺍﻭﻳ ﹰﺔ‪ ،‬ﻓﺈﻧﻪ ﻳﻘﺴﻤﻬﺎ ﺇﻟﻰ ﺯﺍﻭﻳﺘﻴﻦ ﻣﺘﻄﺎﺑﻘﺘﻴﻦ\"‪،‬‬ ‫ﻭﺍﻟﺒﺪﺍﺋﻞ ﺍﻵﺗﻴﺔ ‪:‬‬ ‫‪ (F‬ﺇﺫﺍ ﻗﺴﻢ ﻧﹺﺼ ﹸﻒ ﻣﺴﺘﻘﻴﻢ )‪ ( AB‬ﺯﺍﻭﻳ ﹰﺔ ﺇﱃ ﺯﺍﻭﻳﺘﲔ ﻣﺘﻄﺎﺑﻘﺘﲔ‪ ،‬ﻓﺈﻧﻪ ﻳﻨ ﹼﺼﻒ ﻫﺬﻩ ﺍﻟﺰﺍﻭﻳﺔ‪.‬‬ ‫‪ (G‬ﻳﻨ ﹼﺼﻒ ﻧﹺﺼ ﹸﻒ ﺍﳌﺴﺘﻘﻴﻢ )‪ ( AB‬ﺍﻟﺰﺍﻭﻳﺔ‪ ،‬ﺇﺫﺍ ﻭﻓﻘﻂ ﺇﺫﺍ ﻗﺴﻤﻬﺎ ﺇﱃ ﺯﺍﻭﻳﺘﲔ ﻣﺘﻄﺎﺑﻘﺘﲔ‪.‬‬ ‫‪ (H‬ﺇﺫﺍ ﱂ ﻳﻨ ﹼﺼﻒ ﻧﹺﺼ ﹸﻒ ﺍﳌﺴﺘﻘﻴﻢ )‪ ( AB‬ﺍﻟﺰﺍﻭﻳﺔ‪ ،‬ﻓﺈﻧﻪ ﻻ ﻳﻘﺴﻤﻬﺎ ﺇﱃ ﺯﺍﻭﻳﺘﲔ ﻣﺘﻄﺎﺑﻘﺘﲔ‪.‬‬ ‫‪ (J‬ﺇﺫﺍ ﱂ ﻳﻘﺴﻢ ﻧﹺﺼ ﹸﻒ ﺍﳌﺴﺘﻘﻴﻢ )‪ ( AB‬ﺍﻟﺰﺍﻭﻳﺔ ﺇﱃ ﺯﺍﻭﻳﺘﲔ ﻣﺘﻄﺎﺑﻘﺘﲔ‪ ،‬ﻓﺈﻧﻪ ﻻ ﻳﻨ ﹼﺼﻔﻬﺎ‪.‬‬ ‫‪ (4‬ﻣﺎ ﺍﻟﺒﺪﻳﻞ ﺍﻟﺬﻱ ﹸﻳﻌ ﹼﺪ ﻣﻌﻜﻮ ﹰﺳﺎ ﻟﻠﻌﺒﺎﺭﺓ ﺍﻟ ﹸﻤﻌﻄﺎﺓ؟‬ ‫‪ (5‬ﻣﺎ ﺍﻟﺒﺪﻳﻞ ﺍﻟﺬﻱ ﹸﻳﻌ ﹼﺪ ﺍﻟﻤﻌﺎﻛﺲ ﺍﻹﻳﺠﺎﺑﻲ ﻟﻠﻌﺒﺎﺭﺓ ﺍﻟ ﹸﻤﻌﻄﺎﺓ؟‬ ‫‪‬‬ ‫‪__________(6‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪.a = 6 .2a2 = 72 (6‬‬ ‫ﺃﻋ ﹺﻂ ﻣﺜﺎ ﹰﻻ ﻣﻀﺎ ﹰﹼﺩﺍ ﻳﺒﻴﻦ ﻋﺪﻡ ﺻﺤﺔ ﻫﺬﺍ ﺍﻟﺘﺨﻤﻴﻦ‪.‬‬ ‫‪__________(7‬‬ ‫‪ (7‬ﺍﻛﺘﺐ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ ﺑﺼﻴﻐﺔ )ﺇﺫﺍ‪ ...‬ﻓﺈﻥ‪:(...‬‬ ‫\"ﲨﻴﻊ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﻘﺎﺋﻤﺔ ﻣﺘﻄﺎﺑﻘﺔ\"‪.‬‬ ‫‪__________(8‬‬ ‫‪ (8‬ﺍﺳﺘﻌﻤﻞ ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﻟﻤﻨﻄﻘﻲ ﻟﻜﺘﺎﺑﺔ ﻧﺘﻴﺠ ﹴﺔ ﺻﺤﻴﺤ ﹴﺔ ﻣﻦ ﺍﻟﻌﺒﺎﺭﺗﻴﻦ )‪ (1‬ﹶﻭ )‪.(2‬‬ ‫)‪ (1‬ﺟﻤﻴﻊ ﺍﻷﺳﻤﺎﻙ ﺗﺴﺒﺢ‪.‬‬ ‫‪__________(9‬‬ ‫‪_________(10‬‬ ‫)‪ (2‬ﺍﻟﺴﻠﻤﻮﻥ ﺃﺣﺪ ﺃﻧﻮﺍﻉ ﺍﻟﺴﻤﻚ‪.‬‬ ‫‪F‬‬ ‫‪K‬‬ ‫ﺍﺳﺘﻌﻤﻞ ﺍﻟﺸﻜﻞ ﺍﳌﺠﺎﻭﺭ ﻟﻺﺟﺎﺑﺔ ﻋﻦ ﺍﻟﺴﺆﺍﻟﲔ ‪:9 , 10‬‬ ‫‪ (9‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ، AB BC‬ﻓ ﹺﺼ ﹺﻒ ﺍﻟﻌﻼﻗﺔ ﺑﻴﻦ ﺍﻟﻨﻘﺎﻁ ‪ A‬ﻭ ‪ B‬ﻭ ‪.C‬‬ ‫‪B‬‬ ‫‪C‬‬ ‫‪ (10‬ﺳ ﹼﻢ ﻧﻘﺎ ﹰﻃﺎ ﺗﺤ ﹼﺪﺩ ﺍﻟﻤﺴﺘﻮ￯ ‪.K‬‬ ‫‪A‬‬ ‫‪1‬‬ ‫‪13‬‬ ‫‪ ‬‬ ‫‪C02-23A-873959‬‬

‫‪‬‬ ‫‪‬‬ ‫‪  1‬‬ ‫ﻧﻔﻲ ﺍﻟﻌﺒﺎﺭﺓ‬ ‫ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ‬ ‫ﺍﻟﻨﺘﻴﺠﺔ‬ ‫ﺍﻟﺘﺨﻤﲔ‬ ‫ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻟﴩﻃﻴﺔ ﺍﳌﺮﺗﺒﻄﺔ‬ ‫ﻋﺒﺎﺭﺓ ﺍﻟ ﹶﻔ ﹾﺼﻞ‬ ‫ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﴩﻃﻴﺔ‬ ‫ﺍﻟﱪﻫﺎﻥ ﺍﳊﺮ‬ ‫ﺍﻟﺘﱪﻳﺮ ﺍﻻﺳﺘﻘﺮﺍﺋﻲ‬ ‫ﺍﻟﱪﻫﺎﻥ ﺍﳉﱪﻱ‬ ‫ﺟﺪﻭﻝ ﺍﻟﺼﻮﺍﺏ‬ ‫ﺍﻟﺘﻜﺎﻓﺆ ﺍﳌﻨﻄﻘﻲ‬ ‫ﺍﻟﻌﻜﺲ‬ ‫ﺍﳌﻌﻜﻮﺱ‬ ‫ﺍﻟﻔﺮﺽ‬ ‫ﺣ ﹼﺪﺩ ﻣﺎ ﺇﺫﺍ ﻛﺎﻧﺖ ﻛﻞ ﺟﻤﻠﺔ ﻣﻤﺎ ﻳﺄﺗﻲ ﺻﺤﻴﺤﺔ ﺃﻡ ﺧﺎﻃﺌﺔ‪ ،‬ﻭﺇﺫﺍ ﻛﺎﻧﺖ ﺧﺎﻃﺌﺔ‪ ،‬ﻓﻐ ﹼﻴﺮ ﻣﺎ ﺗﺤﺘﻪ ﺧﻂ ﻟﺘﺠﻌﻠﻬﺎ ﺻﺤﻴﺤ ﹰﺔ‪:‬‬ ‫‪________________(1‬‬ ‫‪ (1‬ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﻫﻲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺘﻲ ﹸﺃﺛﺒﺘﺖ‪.‬‬ ‫‪ (2‬ﺍﻟﻨﻈﺮﻳﺔ ﻫﻲ ﻋﺒﺎﺭﺓ ﺗﺼﻒ ﻋﻼﻗﺔ ﺃﺳﺎﺳﻴﺔ ﺑﻴﻦ ﻣﻔﺮﺩﺍﺕ ﺃﺳﺎﺳﻴﺔ ﻓﻲ ﺍﻟﻬﻨﺪﺳﺔ‪ ،‬ﻭ ﹸﺗ ﹾﻘ ﹶﺒﻞ ﻋ ﹶﻠﻰ ﺃﻧﻬﺎ ‪________________(2‬‬ ‫ﺻﺤﻴﺤﺔ ﻣﻦ ﺩﻭﻥ ﺑﺮﻫﺎﻥ‪.‬‬ ‫‪ (3‬ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺘﻲ ﺗﻔﻴﺪ ﻣﻌﻨﻰ ﻣﻀﺎ ﹼﹰﺩﺍ ﻟﻤﻌﻨﻰ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻷﺻﻠﻴﺔ‪ ،‬ﻭﻟﻬﺎ ﻋﻜﺲ ﻗﻴﻤﺔ ﺻﻮﺍﺏ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻷﺻﻠﻴﺔ‪________________(3 ،‬‬ ‫ﹸﺗﺴﻤﻰ ﻧﻔﻲ ﺍﻟﻌﺒﺎﺭﺓ‪.‬‬ ‫‪________________(4‬‬ ‫‪ (4‬ﺍﻟﺒﺮﻫﺎﻥ ﺍﻟﺬﻱ ﺗﻜﺘﺐ ﻓﻴﻪ ﻓﻘﺮﺓ ﺗﻔﺴﺮ ﺃﺳﺒﺎﺏ ﺻﺤﺔ ﺍﻟﺘﺨﻤﻴﻦ ﻳﺴﻤﻰ ﺍﻟﺒﺮﻫﺎﻥ ﺫﺍ ﺍﻟﻌﻤﻮﺩﻳﻦ‪.‬‬ ‫‪________________(5‬‬ ‫‪ (5‬ﻳﻘﻮﻡ ﺍﻟﺘﺒﺮﻳﺮ ﺍﻻﺳﺘﻨﺘﺎﺟﻲ ﻋﻠﻰ ﺍﺳﺘﻌﻤﺎﻝ ﺍﻟﺤﻘﺎﺋﻖ‪ ،‬ﻭﺍﻟﻘﻮﺍﻋﺪ‬ ‫ﻭﺍﻟﺘﻌﺮﻳﻔﺎﺕ ﻭﺍﻟﺨﺼﺎﺋﺺ ﻟﻠﻮﺻﻮﻝ ﺇﻟﻰ ﻧﺘﺎﺋﺞ ﻣﻨﻄﻘﻴﺔ‪.‬‬ ‫‪________________(6‬‬ ‫‪ (6‬ﻋﺒﺎﺭﺓ \" ﹸﻳﻘﻴﻢ ﻃﻼﻝ ﻓﻲ ﺍﻟﺮﻳﺎﺽ ﺃﻭ ﹸﻳﻘﻴﻢ ﻓﻲ ﺟﺪﺓ\" ﻣﺜﺎﻝ ﻋﻠﻰ ﻋﺒﺎﺭﺓ ﺍﻟ ﹶﻮ ﹾﺻﻞ ‪.‬‬ ‫‪________________(7‬‬ ‫ﺃﻛﻤﻞ ﺍﻟﺠﻤﻞ ﺍﻵﺗﻴﺔ ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﻤﻔﺮﺩﺓ ﺍﻟﻤﻨﺎﺳﺒﺔ ﻣﻦ ﺍﻟﻤﺴﺘﻄﻴﻞ ﺃﻋﻼﻩ‪:‬‬ ‫‪________________(8‬‬ ‫‪ (7‬ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺘﻲ ﺗﻠﻲ ﻛﻠﻤﺔ \"ﻓﺈﻥ\" ﻣﺒﺎﺷﺮﺓ ﻓﻲ ﻋﺒﺎﺭﺓ )ﺇﺫﺍ‪ ...‬ﻓﺈﻥ‪ ،(...‬ﹸﺗﺴﻤﻰ _____؟_____‬ ‫‪________________(9‬‬ ‫‪ (8‬ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺘﻲ ﺗﻠﻲ ﻛﻠﻤﺔ \"ﺇﺫﺍ ﻛﺎﻥ\" ﻣﺒﺎﺷﺮ ﹰﺓ ﻓﻲ ﻋﺒﺎﺭﺓ ‪)،‬ﺇﺫﺍ‪...‬ﻓﺈﻥ‪ (..‬ﹸﺗﺴﻤﻰ ___؟______‬ ‫‪_______________(10‬‬ ‫‪1‬‬ ‫‪____ (9‬؟______ ﻫﻮ ﺗﻮﻗﻊ ﻳﺴﺘﻨﺪ ﺇﻟﻰ ﻣﻌﻠﻮﻣﺎﺕ ﻭﺣﻘﺎﺋﻖ ﻣﻌﺮﻭﻓﺔ‪.‬‬ ‫‪ (10‬ﹸﻳﺼﺎﻍ ____؟______ ﺑﻨﻔﻲ ﺍﻟﻔﺮﺽ ﻭﺍﻟﻨﺘﻴﺠﺔ ﻓﻲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺸﺮﻃﻴﺔ‪.‬‬ ‫‪14 ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(1)     1‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪__________(1‬‬ ‫‪ (1‬ﺃﻭﺟﺪ ﺍﻟﺤ ﹼﺪ ﺍﻟﺘﺎﻟﻲ ﻓﻲ ﺍﻟﻤﺘﺘﺎﺑﻌﺔ‪.92, 87, 82, 77, 72,….. :‬‬ ‫‪__________(2‬‬ ‫‪__________(3‬‬ ‫‪77 (D‬‬ ‫‪67 (C‬‬ ‫‪62 (B‬‬ ‫‪-5 (A‬‬ ‫‪ (2‬ﺃ ﱞﻱ ﻣﻤﺎ ﻳﺄﺗﻲ ﹸﻳﻌ ﱡﺪ ﺗﺨﻤﻴﻨﹰﺎ ﻣﻨﺎﺳ ﹰﺒﺎ ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ‪ M‬ﻧﻘﻄﺔ ﻣﻨﺘﺼﻒ ‪. BC‬‬ ‫‪ M (J‬ﺗﻨﺼﻒ ‪∠C‬‬ ‫‪MC = BC (H‬‬ ‫‪BM = MC (G‬‬ ‫‪BM = BC (F‬‬ ‫‪ (3‬ﺇﺫﺍ ﻛﺎﻥ‪ a + b ≤ 8 :‬ﻭ ‪ ،a = 2‬ﻓﺈﻥ ‪ ،b ≤ 5‬ﻓﺄ ﱞﻱ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﹸﻳﻌ ﹼﺪ ﻣﺜﺎ ﹰﻻ ﻣﻀﺎ ﹰﹼﺩﺍ؟‬ ‫‪b = a (D‬‬ ‫‪b = 6 (C‬‬ ‫‪b = 5 (B‬‬ ‫‪b = 3 (A‬‬ ‫‪p q ~p‬‬ ‫‪~p ∨q‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 4‬ﻭ ‪ 5‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺟﺪﻭﻝ ﺍﻟﺼﻮﺍﺏ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪__________(4‬‬ ‫‪TT‬‬ ‫‪ (4‬ﻣﺎ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﺍﻟﺘﻲ ﻳﺠﺐ ﺃﻥ ﹸﺗﻜﺘﺐ ﻓﻲ ﻋﻤﻮﺩ ‪ p‬؟‬ ‫‪TF‬‬ ‫‪FT‬‬ ‫‪T F F T (C‬‬ ‫‪F T F T (A‬‬ ‫‪FT‬‬ ‫‪T T F F (D‬‬ ‫‪F F T T (B‬‬ ‫‪__________(5‬‬ ‫‪ (5‬ﻣﺎ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﺍﻟﺘﻲ ﻳﺠﺐ ﺃﻥ ﹸﺗﻜﺘﺐ ﻓﻲ ﻋﻤﻮﺩ ‪~ p ∨ q‬؟‬ ‫‪T F T T (J‬‬ ‫‪T T T T (H‬‬ ‫‪T T T F (G‬‬ ‫‪F F T F (F‬‬ ‫‪__________(6‬‬ ‫‪ (6‬ﻋ ﹼﻴﻦ ﺍﻟﻔﺮﺽ ﻓﻲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪ :‬ﺇﺫﺍ ﻛﺎﻥ ‪ ، x + 4 = 5‬ﻓﺈﻥ ‪. x = 1‬‬ ‫‪x + 4 = 5 (C‬‬ ‫‪ (A‬ﺇﺫﺍ ﻛﺎﻥ ‪ ، x = 1‬ﻓﺈﻥ ‪.x + 4 = 5‬‬ ‫‪x = 1 (D‬‬ ‫‪ (B‬ﺇﺫﺍ ﻛﺎﻥ ‪ x+4 ≠ 5‬ﻓﺈﻥ ‪. x ≠ 1‬‬ ‫‪__________(7‬‬ ‫‪ (7‬ﺃ ﱡﻱ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻵﺗﻴﺔ ﺗﻤ ﱢﺜﻞ ﻋﻜﺲ ﺍﻟﻌﺒﺎﺭﺓ‪\" :‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻄﻄﺔ ﺗﻄﻴﺮ‪ ،‬ﻓﺈﻥ ﺍﻟﺒﻄﺔ ﺗﺰﺃﺭ\"‪.‬‬ ‫‪ (A‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻄﻄﺔ ﻻ ﺗﻄﲑ‪ ،‬ﻓﺈﻥ ﺍﻟﺒﻄﺔ ﻻ ﺗﺰﺃﺭ‪ (C .‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻘﻄﻄﺔ ﺗﺰﺃﺭ‪ ،‬ﻓﺈﻥ ﺍﻟﺒﻄﺔ ﺗﻄﲑ‪.‬‬ ‫‪ (B‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﺒﻄﺔ ﻻ ﺗﺰﺃﺭ ‪ ،‬ﻓﺈﻥ ﺍﻟﻘﻄﻄﺔ ﻻ ﺗﻄﲑ‪ (D .‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﺒﻄﺔ ﺗﺰﺃﺭ‪ ،‬ﻓﺈﻥ ﺍﻟﻘﻄﻄﺔ ﺗﻄﲑ‪.‬‬ ‫‪__________(8‬‬ ‫‪ (8‬ﻋ ﹼﻴﻦ ﻣﻌﻜﻮﺱ ﺍﻟﻌﺒﺎﺭﺓ ‪\" :‬ﺇﺫﺍ ﻛﺎﻥ ﻟﻠﻤﺜﻠﺚ ﺛﻼﺛﺔ ﺃﺿﻼﻉ ﻣﺘﺴﺎﻭﻳﺔ ﺍﻟﻄﻮﻝ‪ ،‬ﻓﺈﻧﻪ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ\"‪.‬‬ ‫‪ (A‬ﺇﺫﺍ ﱂ ﻳﻜﻦ ﻟﻠﻤﺜﻠﺚ ﺛﻼﺛﺔ ﺃﺿﻼﻉ ﻣﺘﺴﺎﻭﻳﺔ ﺍﻟﻄﻮﻝ‪ ،‬ﻓﺈﻧﻪ ﻟﻴﺲ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪.‬‬ ‫‪ (B‬ﺇﺫﺍ ﻛﺎﻥ ﺍﳌﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪ ،‬ﻓﺈﻥ ﻟﻪ ﺛﻼﺛﺔ ﺃﺿﻼﻉ ﻣﺘﺴﺎﻭﻳﺔ ﺍﻟﻄﻮﻝ‪.‬‬ ‫‪ (C‬ﺇﺫﺍ ﱂ ﻳﻜﻦ ﺍﳌﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪ ،‬ﻓﻠﻴﺲ ﻟﻪ ﺛﻼﺛﺔ ﺃﺿﻼﻉ ﻣﺘﺴﺎﻭﻳﺔ ﺍﻟﻄﻮﻝ‪.‬‬ ‫‪ (D‬ﺇﺫﺍ ﻛﺎﻥ ﻃﻮﻻ ﺿﻠﻌﲔ ﰲ ﻣﺜﻠ ﹴﺚ ﻣﺎ ﻣﺘﺴﺎﻭﻳﲔ‪ ،‬ﻓﺈﻥ ﺍﳌﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻟﻀﻠﻌﲔ‪.‬‬ ‫‪__________(9‬‬ ‫‪ (9‬ﺃ ﱡﻱ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻵﺗﻴﺔ ﺗﻮﺿﺢ ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﻟﻤﻨﻄﻘﻲ؟‬ ‫‪[(p → q) ∧ q)] → p (C‬‬ ‫‪[(p → q) ∨ (q → r)] → (p → r) (A‬‬ ‫‪[(p → q) ∧ p)] → q (D‬‬ ‫‪[(p → q) ∧ (q → r)]→ (p → r) (B‬‬ ‫‪1‬‬ ‫‪15‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪(1)    ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪_________(10‬‬ ‫‪[(p → q) ∧ q)] → p (C‬‬ ‫‪ (10‬ﺃ ﱞﻱ ﻣﻤﺎ ﻳﺄﺗﻲ ﻳﻮﺿﺢ ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﻟﻤﻨﻄﻘﻲ؟‬ ‫‪_________(11‬‬ ‫‪[(p → q) ∧ p)] → q (D‬‬ ‫‪_________(12‬‬ ‫‪[(p → q) ∨ (q → r)]→ (p → r) (A‬‬ ‫‪[(p → q) ∧ (q → r)] → (p → r) (B‬‬ ‫‪ (11‬ﺍﳉﻤﻠﺔ‪\" :‬ﳛﺘﻮﻱ ﺍﳌﺴﺘﻮ￯ ﻋﲆ ﺛﻼﺙ ﻧﻘﺎﻁ ﻋﲆ ﺍﻷﻗﻞ ﻟﻴﺴﺖ ﻭﺍﻗﻌ ﹰﺔ ﻋﲆ ﺍﳌﺴﺘﻘﻴﻢ ﻧﻔﺴﻪ\" ﺗﻜﻮﻥ‪:‬‬ ‫‪ (C‬ﻟﻴﺴﺖ ﺻﺤﻴﺤﺔ ﺃﺑ ﹰﺪﺍ‪.‬‬ ‫‪ (A‬ﺻﺤﻴﺤﺔ ﺩﺍﺋ ﹰﲈ‪.‬‬ ‫‪ (D‬ﺍﳌﻌﻄﻴﺎﺕ ﻏﲑ ﻛﺎﻓﻴﺔ‪.‬‬ ‫‪ (B‬ﺻﺤﻴﺤﺔ ﺃﺣﻴﺎ ﹰﻧﺎ‪.‬‬ ‫‪ (12‬ﺃ ﹼﻱ ﺃﻧﻮﺍﻉ ﺍﻟﺒﺮﺍﻫﻴﻦ ﺗﻜﺘﺐ ﻓﻴﻪ ﻓﻘﺮﺓ ﻟﺘﻔﺴﻴﺮ ﺍﻷﺳﺒﺎﺏ ﺍﻟﺘﻲ ﺗﺠﻌﻞ ﺍﻟﺘﺨﻤﻴﻦ ﺻﺤﻴ ﹰﺤﺎ ﻓﻲ‬ ‫ﻣﻮﻗﻒ ﹸﻣﻌ ﹰﻄﻰ؟‬ ‫‪ (C‬ﺍﻟﱪﻫﺎﻥ ﺍﳊﺮ‬ ‫‪ (A‬ﺍﻟﱪﻫﺎﻥ ﺍﳍﻨﺪﳼ‬ ‫‪ (D‬ﺍﻟﱪﻫﺎﻥ ﺫﻭ ﺍﻟﻌﻤﻮﺩﻳﻦ‬ ‫‪ (B‬ﺍﻟﱪﻫﺎﻥ ﺍﳉﱪﻱ‬ ‫‪_________(13‬‬ ‫ﺍﺧﺘﺮ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻷﺳﺌﻠﺔ ‪:13-15‬‬ ‫‪_________(14‬‬ ‫‪ (13‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،3x = 6‬ﻓﺈﻥ ‪.x = 2‬‬ ‫‪_________(15‬‬ ‫‪_________(16‬‬ ‫‪ (F‬ﺍﳉﻤﻊ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (G‬ﺍﻟﻄﺮﺡ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (H‬ﺍﻟﺘﻌﺪﻱ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (J‬ﺍﻟﻘﺴﻤﺔ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (14‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ، y = 10 ، x = 10 :‬ﻓﺈﻥ‪x = y :‬‬ ‫‪ (C‬ﺍﻟﺘﻌﻮﻳﺾ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (A‬ﺍﻻﻧﻌﻜﺎﺱ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (D‬ﺍﳉﻤﻊ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (B‬ﺍﻟﺘﲈﺛﻞ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (15‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،DS WX‬ﻓﺈﻥ ‪.DS = WX‬‬ ‫‪ (C‬ﺗﻌﺮﻳﻒ ﺍﻟﻘﻄﻊ ﺍﳌﺴﺘﻘﻴﻤﺔ ﺍﳌﺘﻄﺎﺑﻘﺔ‬ ‫‪ (A‬ﺍﻻﻧﻌﻜﺎﺱ‬ ‫‪ (E‬ﺍﻟﺘﻌ ﹼﺪﻱ‬ ‫‪ (B‬ﺍﻟﺘﲈﺛﻞ‬ ‫‪ (D‬ﺍﳌﻌﻄﻴﺎﺕ ﻏﲑ ﻛﺎﻓﻴﺔ‬ ‫‪ (16‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ A,N,B‬ﺛﻼﺙ ﻧﻘﺎﻁ ﻋﻠﻰ ﺍﺳﺘﻘﺎﻣ ﹴﺔ ﻭﺍﺣﺪ ﹴﺓ‪ ،‬ﻭﻛﺎﻥ ‪،AB + BN = AN‬‬ ‫ﻓﺄﻱ ﻧﻘﻄﺔ ﺗﻘﻊ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺘﻴﻦ ﺍﻷﺧﺮﻳﻴﻦ؟‬ ‫‪N (C B (B A (A‬‬ ‫‪_________(17‬‬ ‫‪ (17‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ‪ x‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪55° (x + 30)° .‬‬ ‫‪_________(18‬‬ ‫‪_________(19‬‬ ‫‪125 (J‬‬ ‫‪55 (H‬‬ ‫‪35 (G‬‬ ‫‪25 (F‬‬ ‫‪Geo-AS02-01-860179‬‬ ‫‪A‬‬ ‫‪D‬‬ ‫‪ (18‬ﺇﺫﺍ ﻛﺎﻥ ‪ m ∠ABD = 56°‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪ ،‬ﻓﺄﻭﺟﺪ ‪.m ∠DBC‬‬ ‫‪BC‬‬ ‫‪44° (C‬‬ ‫‪124° (A‬‬ ‫‪Geo-AS02-02-8346°01(D79‬‬ ‫‪56° (B‬‬ ‫‪ (19‬ﺇﺫﺍ ﻗﺴﻤﺖ ﺍﻟﺰﺍﻭﻳﺔ ﺍﻟﻘﺎﺋﻤﺔ ﺇﻟﻰ ﺛﻼﺛﺔ ﺃﺟﺰﺍﺀ ﻣﺘﺴﺎﻭﻳﺔ‪ ،‬ﻓﻤﺎ ﻗﻴﺎﺱ ﻛﻞ ﺯﺍﻭﻳﺔ ﻣﻦ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﺼﻐﻴﺮﺓ؟‬ ‫‪90° (D‬‬ ‫‪60° (C‬‬ ‫‪45° (B‬‬ ‫‪30° (A‬‬ ‫‪1‬‬ ‫‪16‬‬ ‫‪‬‬

‫‪‬‬ ‫‪(2A)    ‬‬ ‫‪‬‬ ‫‪__________(1‬‬ ‫‪1‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪G(eDo-AS02-04-8601(7C9‬‬ ‫‪ (1‬ﺃﻭﺟﺪ ﺍﻟﺸﻜﻞ ﺍﻟﺘﺎﻟﻲ ﻓﻲ ﺍﻟﻤﺘﺘﺎﺑﻌﺔ ﺍﻵﺗﻴﺔ‪:‬‬ ‫‪(B (A‬‬ ‫‪__________(2‬‬ ‫‪ -(027-860179‬ﺃ‪2‬ﻱ‪ 0‬ﺍﻟ‪S‬ﺒ‪A‬ﺪﺍ‪-‬ﺋ‪o9‬ﻞ‪e7‬ﺍ‪1‬ﻵ‪0G‬ﺗﻴ‪6‬ﺔ ﹸﻳ‪-8‬ﻌ ﹼﺪ‪ 6‬ﻣ‪0‬ﺜ‪-‬ﺎ ﹰ‪2‬ﻻ‪0‬ﻣ‪S‬ﻀﺎ‪ A‬ﹰ‪-‬ﺩﺍ‪o‬ﻟ‪9‬ﻠ‪e‬ﻌ‪7‬ﺒﺎ‪1G‬ﺭ‪0‬ﺓ‪5n-826:‬ﻋ‪0‬ﺪ‪-‬ﹰﺩﺍ‪2‬ﻣ‪0‬ﻮ‪S‬ﺟ ﹰﺒ‪A‬ﺎ‪-‬ﺩﺍ‪9o‬ﺋ ﹰ‪7e‬ﻤﺎ‪Geo-AS02-08-860G.1‬‬ ‫‪0 (D -1 (C‬‬ ‫‪4 (B 10 (A‬‬ ‫‪p q ~q p ∧~q‬‬ ‫ﺍﺳﺘﻌﻤﻞ ﺟﺪﻭﻝ ﺍﻟﺼﻮﺍﺏ ﺍﻟﻤﺠﺎﻭﺭ ﻟﻺﺟﺎﺑﺔ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪3, 4‬‬ ‫‪__________(3‬‬ ‫‪TT‬‬ ‫‪ (3‬ﺃ ﱡﻱ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﺍﻵﺗﻴﺔ ﻳﺠﺐ ﺃﻥ ﹸﺗﻜﺘﺐ ﻓﻲ ﻋﻤﻮﺩ ‪~q‬؟‬ ‫‪TF‬‬ ‫‪FT‬‬ ‫‪F T F T (C‬‬ ‫‪F F T T (A‬‬ ‫‪FF‬‬ ‫‪T F T F (D‬‬ ‫‪T T F F (B‬‬ ‫‪__________(4‬‬ ‫‪ (4‬ﺃ ﱡﻱ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﺍﻵﺗﻴﺔ ﻳﺠﺐ ﺃﻥ ﹸﺗﻜﺘﺐ ﻓﻲ ﻋﻤﻮﺩ ‪p ∧ ~ q‬؟‬ ‫‪__________(5‬‬ ‫‪T F T F (D‬‬ ‫‪F T F T (C‬‬ ‫‪T T F F (B‬‬ ‫‪F T F F (A‬‬ ‫‪ (5‬ﻋ ﹼﻴﻦ ﺍﻟﻨﺘﻴﺠﺔ ﻓﻲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪\" :‬ﺳﻴﺬﻫﺐ ﺻﺎﻟﺢ ﺇﻟﻰ ﺍﻟﻤﺪﺭﺳﺔ ﺇﺫﺍ ﻛﺎﻥ ﺍﻟﻴﻮﻡ ﻫﻮ ﺍﻷﺣﺪ\"‪.‬‬ ‫‪ (C‬ﺍﻟﻴﻮﻡ ﻫﻮ ﺍﻷﺣﺪ‪.‬‬ ‫‪ (A‬ﺳﻴﺬﻫﺐ ﺻﺎﻟﺢ ﺇﱃ ﺍﳌﺪﺭﺳﺔ‪.‬‬ ‫‪ (D‬ﺍﻟﻴﻮﻡ ﻟﻴﺲ ﻫﻮ ﺍﻷﺣﺪ‪.‬‬ ‫‪ (B‬ﻟﻦ ﻳﺬﻫﺐ ﺻﺎﻟﺢ ﺇﱃ ﺍﳌﺪﺭﺳﺔ‪.‬‬ ‫‪__________(6‬‬ ‫‪ (6‬ﻋ ﹼﻴﻦ ﻣﻌﻜﻮﺱ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪ :‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x = 2‬ﻓﺈﻥ ‪.x + 3 = 5‬‬ ‫‪__________(7‬‬ ‫‪ (C‬ﺇﺫﺍ ﻛﺎﻥ‪ ، x ≠ 2‬ﻓﺈﻥ ‪.x + 3 ≠ 5‬‬ ‫‪ (A‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x + 3 = 5‬ﻓﺈﻥ ‪x = 2‬‬ ‫‪ x = 2 (D‬ﻭ ‪x + 3 = 5‬‬ ‫‪ (B‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x + 3 ≠ 5‬ﻓﺈﻥ ‪x ≠ 2‬‬ ‫‪ (7‬ﻋ ﹼﻴﻦ ﺍﻟﻤﻌﺎﻛﺲ ﺍﻹﻳﺠﺎﺑﻲ ﻟﻠﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪ :‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x = 2‬ﻓﺈﻥ ‪.x + 3 = 5‬‬ ‫‪ (C‬ﺇﺫﺍ ﻛﺎﻥ ‪ ، x ≠ 2‬ﻓﺈﻥ ‪. x + 3 ≠ 5‬‬ ‫‪ (A‬ﺇﺫﺍ ﻛﺎﻥ ‪ ، x+3= 5‬ﻓﺈﻥ ‪.x = 2‬‬ ‫‪ x = 2 (D‬ﻭ ‪.x + 3 = 5‬‬ ‫‪ (B‬ﺇﺫﺍ ﻛﺎﻥ‪ ، x + 3 ≠ 5‬ﻓﺈﻥ ‪x ≠ 2‬‬ ‫‪__________(8‬‬ ‫‪ (8‬ﻣﺎ ﺍﻟﺬﻱ ﻳﺴﺘﻌﻤﻞ ﻟﺒﻴﺎﻥ ﺻﺤﺔ ﺍﻟﻨﺘﻴﺠﺔ‪ ،‬ﺍﻋﺘﻤﺎ ﹰﺩﺍ ﻋﻠﻰ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻟﻤﻌﻄﺎﺓ؟‬ ‫‪1‬‬ ‫‪ ‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﺰﺍﻭﻳﺔ ﺣﺎﺩ ﹰﺓ‪ ،‬ﻓﻤﻦ ﺍﳌﺴﺘﺤﻴﻞ ﺃﻥ ﺗﻜﻮﻥ ﻣﻨﻔﺮﺟﺔ‪ ∠A ،‬ﺯﺍﻭﻳﺔ ﺣﺎﺩﺓ‪.‬‬ ‫‪ ‬ﻳﺴﺘﺤﻴﻞ ﺃﻥ ﺗﻜﻮﻥ ‪ ∠A‬ﻣﻨﻔﺮﺟ ﹰﺔ‪.‬‬ ‫‪ (C‬ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (A‬ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (D‬ﻗﺎﻧﻮﻧﺎ ﺍﻟﻔﺼﻞ ﻭﺍﻟﻘﻴﺎﺱ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (B‬ﺍﻟﺘﺨﻤﲔ‬ ‫‪17 ‬‬

‫‪‬‬ ‫‪(2A)    ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪_________(10‬‬ ‫‪ (9‬ﻣﺎ ﺍﻟﺬﻱ ﻳﺴﺘﻌﻤﻞ ﻟﺒﻴﺎﻥ ﺻﺤﺔ ﺍﻟﻨﺘﻴﺠﺔ‪ ،‬ﺍﻋﺘﻤﺎ ﹰﺩﺍ ﻋﻠﻰ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻟﻤﻌﻄﺎﺓ؟‬ ‫‪ ‬ﺇﺫﺍ ﻛﺎﻥ ﻟﻠﺸﻜﻞ ﺃﺭﺑﻊ ﺯﻭﺍﻳﺎ ﻗﺎﺋﻤﺔ‪ ،‬ﻓﺈﻧﻪ ﻣﺴﺘﻄﻴﻞ‪ .‬ﻟﻠﻤﺴﺘﻄﻴﻞ ﺯﻭﺟﺎﻥ ﻣﻦ ﺍﻷﺿﻼﻉ ﺍﳌﺘﻮﺍﺯﻳﺔ‪.‬‬ ‫‪ ‬ﺇﺫﺍ ﻛﺎﻥ ﻟﻠﺸﻜﻞ ﺃﺭﺑﻊ ﺯﻭﺍﻳﺎ ﻗﺎﺋﻤﺔ‪ ،‬ﻓﺈﻥ ﻟﻪ ﺯﻭﺟﲔ ﻣﻦ ﺍﻷﺿﻼﻉ ﺍﳌﺘﻮﺍﺯﻳﺔ‪.‬‬ ‫‪ (C‬ﺍﻟﺘﺨﻤﲔ‬ ‫‪ (A‬ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (D‬ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﻭﺍﻟﻔﺼﻞ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (B‬ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﳌﻨﻄﻘﻲ‬ ‫‪_________(11‬‬ ‫‪ (10‬ﺍﻟﺠﻤﻠﺔ \"ﺇﺫﺍ ﺗﻘﺎﻃﻊ ﻣﺴﺘﻮﻳﺎﻥ‪ ،‬ﻓﺈﻥ ﺗﻘﺎﻃﻌﻬﻤﺎ ﻳﻜﻮﻥ ﻧﻘﻄﺔ\" ﺗﻜﻮﻥ‪:‬‬ ‫‪ (D‬ﻻ ﻳﻤﻜﻦ ﺍﻟﺘﺤﺪﻳﺪ‬ ‫‪ (A‬ﺻﺤﻴﺤﺔ ﺩﺍﺋ ﹰﲈ ‪ (B‬ﺻﺤﻴﺤﺔ ﺃﺣﻴﺎ ﹰﻧﺎ ‪ (C‬ﻏﲑ ﺻﺤﻴﺤﺔ ﺃﺑ ﹰﺪﺍ‬ ‫‪_________(12‬‬ ‫‪ (11‬ﻣﺎ ﺍﻟﺒﺮﻫﺎﻥ ﺍﻟﺬﻱ ﹸﻳﺴﺘﺨﺪﻡ ﻟﻜﺘﺎﺑﺔ ﻣﻌﺎﺩﻟ ﹴﺔ ﺑﺪﻻﻟﺔ ﻣﻌﺎﺩﻟ ﹴﺔ ﻣﻌﻄﺎ ﹴﺓ؟‬ ‫‪_________(13‬‬ ‫‪_________(14‬‬ ‫‪ (C‬ﺍﻟﱪﻫﺎﻥ ﺍﳍﻨﺪﳼ‬ ‫‪ (A‬ﺍﻟﱪﻫﺎﻥ ﺫﻭ ﺍﻟﻌﻤﻮﺩﻳﻦ‬ ‫‪_________(15‬‬ ‫‪ (D‬ﺍﻟﱪﻫﺎﻥ ﺍﳉﱪﻱ‬ ‫‪ (B‬ﺍﻟﱪﻫﺎﻥ ﺍﳊﺮ‬ ‫‪_________(16‬‬ ‫‪ (12‬ﺍﺧﺘﺮ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪\" :‬ﺇﺫﺍ ﻛﺎﻥ‪ x = 2 :‬ﻭ ‪ ،x + y = 3‬ﻓﺈﻥ ‪.\"2 + y = 3‬‬ ‫‪ (A‬ﺍﻻﻧﻌﻜﺎﺱ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (B‬ﺍﻟﺘﲈﺛﻞ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (C‬ﺍﻟﺘﻌ ﹼﺪﻱ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (D‬ﺍﻟﺘﻌﻮﻳﺾ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (13‬ﺍﺧﺘﺮ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ‪.\"m ∠A = m ∠A\" :‬‬ ‫‪ (A‬ﺍﻻﻧﻌﻜﺎﺱ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (B‬ﺍﻟﺘﲈﺛﻞ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (C‬ﺍﻟﺘﻌ ﹼﺪﻱ ﻟﻠﻤﺴﺎﻭﺍﺓ ‪ (D‬ﺍﻟﺘﻌﻮﻳﺾ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (14‬ﺍﺧﺘﺮ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ‪\" :‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،GH FD‬ﻓﺈﻥ ‪.\"FD GH‬‬ ‫‪ (C‬ﺍﻟﺘﻌﺪﻱ ﻟﻠﺘﻄﺎﺑﻖ‬ ‫‪ (A‬ﺍﻻﻧﻌﻜﺎﺱ ﻟﻠﺘﻄﺎﺑﻖ‬ ‫‪ (D‬ﺗﻌﺮﻳﻒ ﺍﻟﻘﻄﻊ ﺍﳌﺴﺘﻘﻴﻤﺔ ﺍﳌﺘﻄﺎﺑﻘﺔ‬ ‫‪ (B‬ﺍﻟﺘﲈﺛﻞ ﻟﻠﺘﻄﺎﺑﻖ‬ ‫‪ (15‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ X,Y,Z‬ﻋﻠﻰ ﺍﺳﺘﻘﺎﻣ ﹴﺔ ﻭﺍﺣﺪ ﹴﺓ‪ ،‬ﻭﻛﺎﻥ‪ XY = 6 :‬ﹶﻭ ‪ YZ = 4‬ﹶﻭ ‪،XZ = 2‬‬ ‫ﻓﺄ ﱡﻱ ﻧﻘﻄ ﹴﺔ ﺗﻘﻊ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺘﻴﻦ ﺍﻷﺧﺮﻳﻴﻦ؟‬ ‫‪ (D Z (C Y (B X (A‬ﺍﳌﻌﻄﻴﺎﺕ ﻏﲑ ﻛﺎﻓﻴﺔ‬ ‫‪AFB‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 16‬ﹶﻭ ‪ 17‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪ (16‬ﺇﺫﺍ ﻛﺎﻥ ‪ ، m ∠BFC = 70°‬ﻓﺄﻭﺟﺪ ‪. m ∠EFD‬‬ ‫‪_________(17‬‬ ‫‪ED‬‬ ‫‪C‬‬ ‫‪_________(18‬‬ ‫‪70° (DGeo-AS02-09-83650°17(9C‬‬ ‫‪20° (B‬‬ ‫‪10° (A‬‬ ‫‪_________(19‬‬ ‫‪_________(20‬‬ ‫‪ (17‬ﺇﺫﺍ ﻛﺎﻥ ‪ m ∠AFB = (5x - 10)°‬ﹶﻭ ‪ ، m∠BFC = (3x + 20)°‬ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪.x‬‬ ‫‪23.3 (D‬‬ ‫‪21.25 (C‬‬ ‫‪15 (B‬‬ ‫‪10 (A‬‬ ‫‪AJ‬‬ ‫‪E‬‬ ‫‪G‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 18‬ﹶﻭ ‪ 19‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻠﻴﻦ ﺍﻟﻤﺠﺎﻭﺭﻳﻦ‪.‬‬ ‫‪C‬‬ ‫‪ (18‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ∠ABC ∠EFG :‬ﹶﻭ ‪ ،m∠ABC = 72°‬ﻓﺄﻭﺟﺪ ‪B D F H.m∠GFH‬‬ ‫‪108° (D‬‬ ‫‪90° (C‬‬ ‫‪72° (B‬‬ ‫‪18° (A‬‬ ‫‪ (19‬ﺇﺫﺍ ﻛﺎﻥ‪ ،m ∠ABJ = 28°, ∠ABC ∠DBJ :‬ﻓﺄﻭﺟﺪ ‪.m ∠JBC‬‬ ‫‪34° (D‬‬ ‫‪45° (C‬‬ ‫‪56° (B‬‬ ‫‪90° (A‬‬ ‫‪1‬‬ ‫‪18‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪(2B)    ‬‬ ‫‪‬‬ ‫‪______________(1‬‬ ‫‪1‬‬ ‫‪______________(2‬‬ ‫‪______________(3‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪______________(4‬‬ ‫‪ (1‬ﺃﻭﺟﺪ ﺍﻟﺤ ﹼﺪ ﺍﻟﺘﺎﻟﻲ ﻓﻲ ﺍﻟﻤﺘﺘﺎﺑﻌﺔ‪-11,-7, -3, 1, 5,…. :‬‬ ‫‪______________(5‬‬ ‫‪______________(6‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪ ، XY = YZ‬ﻓﺈﻥ ‪ Y‬ﻧﻘﻄﺔ ﻣﻨﺘﺼﻒ ‪.XZ‬‬ ‫‪______________(7‬‬ ‫ﺃﻋ ﹺﻂ ﻣﺜﺎ ﹰﻻ ﻣﻀﺎ ﹰﹼﺩﺍ ﻳﺒ ﱢﲔ ﻋﺪﻡ ﺻﺤﺔ ﻫﺬﺍ ﺍﻟﺘﺨﻤﲔ‪.‬‬ ‫‪______________(8‬‬ ‫‪ (3‬ﻣﺎ ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ ﻟﻠﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ؟‬ ‫‪______________(9‬‬ ‫‪ √16 =-4‬ﹶﻭ ‪2 > 2‬‬ ‫‪______________(10‬‬ ‫‪ (4‬ﺍﻓﺘﺮﺽ ﺃﻥ ‪ p‬ﺻﺎﺋﺒﺔ ﹶﻭ ‪ q‬ﺧﺎﻃﺌﺔ‪،‬‬ ‫‪1‬‬ ‫ﻓﲈ ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ ﻟﻠﻌﺒﺎﺭﺓ ‪ ~p ∨ ~ q‬؟‬ ‫‪ (5‬ﺍﻛﺘﺐ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ ﺑﺼﻴﻐﺔ )ﺇﺫﺍ‪ ...‬ﻓﺈﻥ‪:(...‬‬ ‫\"ﻟﻜﻞ ﺣﺼﺎﻥ ﺃﺭﺑﻊ ﺃﺭﺟﻞ\" ‪.‬‬ ‫‪ (6‬ﻋ ﹼﻴﻦ ﺍﻟﻔﺮﺽ ﻓﻲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪:‬‬ ‫\"ﺇﺫﺍ ﻛﻨﺖ ﺗﻘﻴﻢ ﰲ ﺍﻟﺪ ﹼﻣﺎﻡ‪ ،‬ﻓﺈﻧﻚ ﺗﻘﻴﻢ ﰲ ﺍﻟﺴﻌﻮﺩﻳﺔ\"‪.‬‬ ‫‪ (7‬ﺍﻛﺘﺐ ﻋﻜﺲ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺸﺮﻃﻴﺔ ﺍﻵﺗﻴﺔ‪:‬‬ ‫\"ﺇﺫﺍ ﻋﺎﻣﺪ ﻣﺴﺘﻘﻴﲈﻥ ﺍﳌﺴﺘﻘﻴﻢ ﻧﻔﺴﻪ‪ ،‬ﻓﺈﳖﲈ ﻣﺘﻮﺍﺯﻳﺎﻥ\"‪.‬‬ ‫‪ (8‬ﺍﺳﺘﻌﻤﻞ ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﳌﻨﻄﻘﻲ ﻟﻜﺘﺎﺑﺔ ﻧﺘﻴﺠﺔ ﺻﺤﻴﺤﺔ ﻣﻦ ﺍﻟﻌﺒﺎﺭﺗﲔ )‪:(2) ،(1‬‬ ‫)‪ (1‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﻣﺘﻜﺎﻣﻠﺘﲔ‪ ،‬ﻓﺈﻥ ﳎﻤﻮﻉ ﻗﻴﺎﺳﻴﻬﲈ ‪.180°‬‬ ‫)‪ ∠X (2‬ﻭ ‪ ∠Y‬ﻣﺘﻜﺎﻣﻠﺘﺎﻥ‪.‬‬ ‫‪ (9‬ﺍﺳﺘﻌﻤﻞ ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﻟﻤﻨﻄﻘﻲ ﻟﻜﺘﺎﺑﺔ ﻧﺘﻴﺠ ﹴﺔ ﺻﺤﻴﺤ ﹴﺔ ﻣﻦ ﺍﻟﻌﺒﺎﺭﺗﻴﻦ )‪:(2) ،(1‬‬ ‫)‪ (1‬ﺇﺫﺍ ﻛﺎﻥ ﻫﺬﺍ ﺍﻟﻴﻮﻡ ﻫﻮ ﺍﻷﻭﻝ ﻣﻦ ﺷ ﹼﻮﺍﻝ‪ ،‬ﻓﺈﻧﻪ ﻳﻮﻡ ﻋﻴﺪ ﺍﻟﻔﻄﺮ‪.‬‬ ‫)‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ﻫﺬﺍ ﺍﻟﻴﻮﻡ ﻫﻮ ﻳﻮﻡ ﻋﻴﺪ ﺍﻟﻔﻄﺮ‪ ،‬ﻓﺈﻧﻪ ﻳﻮﻡ ﻋﻄﻠ ﹴﺔ ﺭﺳﻤﻴ ﹴﺔ‪.‬‬ ‫‪ (10‬ﺍﺫﻛﺮ ﺍﻟﻌﻤﻠﻴﺔ ﺍﻟﺘﻲ ﺗﺤ ﹼﻮﻝ ﺍﻟﻤﻌﺎﺩﻟﺔ‪ 3x + 6 = 5x – 8 :‬ﺇﻟﻰ ‪،3x = 5x – 14‬‬ ‫ﺛﻢ ﺃﻭﺟﺪ ﻗﻴﻤﺔ ‪.x‬‬ ‫‪19 ‬‬

‫‪‬‬ ‫‪(2B)    ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪_______________(11‬‬ ‫‪ (11‬ﺍﻛﺘﺐ ﺍﻟﻤﺒﺮﺭ ﻟﻠﺨﻄﻮﺓ ﺍﻟﺮﺍﺑﻌﺔ ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺍﻵﺗﻲ ‪:‬‬ ‫‪_______________(12‬‬ ‫=‪.x‬‬ ‫_‪_11‬‬ ‫‪ ،2x – 7 = 4‬ﻓﺈﻥ‬ ‫ﺇﺫﺍ ﻛﺎﻥ‬ ‫‪2‬‬ ‫‪ ‬‬ ‫‪‬‬ ‫‪(1‬‬ ‫‪ (1‬ﹸﻣﻌﻄﻰ‬ ‫‪2x – 7 = 4‬‬ ‫‪(2‬ﺧﺎﺻﻴﺔ ﺍﻟﺠﻤﻊ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪2x – 7 + 7 = 4 + 7 (2‬‬ ‫‪ (3‬ﺑﺎﻟﺘﺒﺴﻴﻂ‬ ‫‪2x = 11 (3‬‬ ‫‪___________ (4‬‬ ‫_‪_2x‬‬ ‫=‬ ‫_‪_11‬‬ ‫‪(4‬‬ ‫‪(5‬‬ ‫‪ (5‬ﺑﺎﻟﺘﺒﺴﻴﻂ‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪x‬‬ ‫=‬ ‫_‪_11‬‬ ‫‪2‬‬ ‫‪ (12‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ‪،m ∠1 = x +50 ، m ∠2 = 3x -20 :‬‬ ‫ﻓﺄﻭﺟﺪ ‪1 2 .m ∠1‬‬ ‫‪C‬‬ ‫ﺍﻛﺘﺐ ﻓﻲ ﻓﺮﺍﻏﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 13‬ﹶﻭ ‪ 14‬ﻣﺒﺮﺭﺍﺕ ﺍﻟﺨﻄﻮﺗﻴﻦ ‪ 94‬ﹶﻭ‪0617‬ﻋ‪6‬ﻠ‪8‬ﻰ ﺍﻟ‪-‬ﺘ‪3‬ﺮﺗ‪1‬ﻴ‪-‬ﺐ‪2‬ﻓ‪0‬ﻲ ﺍ‪S‬ﻟﺒ‪A‬ﺮﻫ‪-‬ﺎ‪o‬ﻥ ﺍ‪e‬ﻟﺘﺎ‪G‬ﻟﻲ‪:‬‬ ‫‪24‬‬ ‫‪ AC ‬ﺗﻨ ﹼﺼﻒ ‪ AC ، ∠BAD‬ﺗﻨ ﹼﺼﻒ ‪∠BCD ، ∠1 ∠2‬‬ ‫‪BD‬‬ ‫‪∠3 ∠4 ‬‬ ‫‪13‬‬ ‫‪A‬‬ ‫‪‬‬ ‫‪Geo-AS02-14-860179‬‬ ‫‪ ‬‬ ‫‪‬‬ ‫‪ (1‬ﻣﻌﻄﻰ‬ ‫‪ AC (1‬ﺗﻨ ﹼﺼﻒ ‪∠BAD‬‬ ‫‪(2‬ﻣﻌﻄﻰ‬ ‫‪ AC (2‬ﺗﻨ ﹼﺼﻒ ‪∠BCD‬‬ ‫‪ (3‬ﻣﻌﻄﻰ‬ ‫‪∠1 ∠2 (3‬‬ ‫‪_______________(13‬‬ ‫‪ ∠1 ∠3 (4‬ﻭ ‪(4 ∠2 ∠4‬‬ ‫‪_______________(14‬‬ ‫‪ (5‬ﺧﺎﺻﻴﺔ ﺍﻟﺘﻌﺪﻱ‬ ‫‪∠1 ∠4 (5‬‬ ‫‪(6 ∠3 ∠4 (6‬‬ ‫‪_______________(15‬‬ ‫ﺍﺫﻛﺮ ﺍﻟﺘﻌﺮﻳﻒ ﺃﻭ ﺍﻟﺨﺎﺻﻴﺔ ﺃﻭ ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﺃﻭ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻷﺳﺌﻠﺔ ‪:15-19‬‬ ‫‪_______________(16‬‬ ‫‪ (15‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ M‬ﻧﻘﻄﺔ ﻣﻨﺘﺼﻒ ‪ ،AB‬ﻓﺈﻥ ‪. MA MB‬‬ ‫‪_______________(17‬‬ ‫‪ (16‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ∠A ∠B :‬ﹶﻭ ‪ ،∠B ∠C‬ﻓﺈﻥ ‪.∠A ∠C‬‬ ‫‪_______________(18‬‬ ‫‪ (17‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ∠X‬ﻭ ‪ ∠Y‬ﻣﺘﺘﺎﻣﺘﻴﻦ‪ ،‬ﹶﻭ ‪ ∠Q‬ﻭ ‪ ∠Z‬ﻣﺘﺘﺎﻣﺘﻴﻦ ﺃﻳ ﹰﻀﺎ‪،‬‬ ‫‪_______________(19‬‬ ‫‪_______________(20‬‬ ‫ﻭﻛﺎﻧﺖ ‪ ،∠Z ∠X‬ﻓﺈﻥ ‪.∠Y ∠Q‬‬ ‫‪ (18‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ، PR QT‬ﻓﺈﻥ ‪.PR = QT‬‬ ‫‪1‬‬ ‫‪ (19‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪. AB + BC = AC ،‬‬ ‫‪ (20‬ﺍﻛﺘﺐ ﺍﻟﻤﻌﺎﻛﺲ ﺍﻹﻳﺠﺎﺑﻲ ﻟﻠﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ‪\" :‬ﺍﻟﻤﻌﻴﻦ ﻣﺘﻮﺍﺯﻱ ﺃﺿﻼﻉ‪\".‬‬ ‫‪20 ‬‬

‫‪‬‬ ‫‪(3)    ‬‬ ‫‪‬‬ ‫‪_______________(1‬‬ ‫‪1‬‬ ‫‪_______________(2‬‬ ‫‪_______________(3‬‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪_______________(4‬‬ ‫‪ (1‬ﺍﻛﺘﺐ ﺗﺨﻤﻴﻨﹰﺎ ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ‪ m ∠A = m ∠B :‬ﻭ ‪.m ∠B = m ∠C‬‬ ‫‪_______________(5‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ‪ AB CD :‬ﻭ ‪ ،BD AC‬ﻓﺈﻥ ‪ ABCD‬ﻣﺴﺘﻄﻴﻞ‪ .‬ﺃﻋ ﹺﻂ ﻣﺜﺎ ﹰﻻ ﻣﻀﺎ ﹼﹰﺩﺍ ﻳﺒ ﱢﲔ ﻋﺪﻡ ﺻﺤﺔ‬ ‫‪_______________(6‬‬ ‫ﻫﺬﺍ ﺍﻟﺘﺨﻤﲔ‪.‬‬ ‫‪_______________(7‬‬ ‫‪_______________(8‬‬ ‫‪ (3‬ﻣﺎ ﻗﻴﻤﺔ ﺻﻮﺍﺏ ﺍﻟﻌﺒﺎﺭﺓ‪ \" :‬ﻟﻠﻤﺮﺑﻊ ‪ 4‬ﺃﺿﻼﻉ ﻣﺘﻄﺎﺑﻘﺔ‪ ،‬ﻭﻟﻠﻤﺴﺘﻄﻴﻞ ‪ 4‬ﺃﺿﻼﻉ ﻣﺘﻮﺍﺯﻳﺔ\"؟‬ ‫‪_______________(9‬‬ ‫‪ (4‬ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻟﺜﻼﺙ ‪ r, q, p‬ﲨﻴﻌﻬﺎ ﺧﺎﻃﺌﺔ‪،‬‬ ‫‪______________(10‬‬ ‫ﻓﲈ ﻗﻴﻤﺔ ﺻﻮﺍﺏ ﺍﻟﻌﺒﺎﺭﺓ‪(p ∨ ~q) ∧ ~ r :‬؟‬ ‫‪1‬‬ ‫‪ (5‬ﻓﻲ ﺍﺳﺘﻄﻼﻉ ﻵﺭﺍﺀ ‪ 30‬ﻃﺎﻟ ﹰﺒﺎ ﻣﻦ ﺍﻟﺼﻒ ﺍﻷﻭﻝ ﺍﻟﺜﺎﻧﻮﻱ‪ ،‬ﺣﻮﻝ ﺍﻟﺮﻳﺎﺿﺔ ﺍﻟﺘﻲ ﳛ ﹼﺒﻮﻥ‬ ‫ﻣﺸﺎﻫﺪﲥﺎ‪ ،‬ﹸﻭﺟﺪ ﺃﻥ ‪ 22‬ﻃﺎﻟ ﹰﺒﺎ ﳛ ﹼﺒﻮﻥ ﻣﺸﺎﻫﺪﺓ ﻛﺮﺓ ﺍﻟﻘﺪﻡ‪ ،‬ﻭﺃﻥ‪ 17‬ﻃﺎﻟ ﹰﺒﺎ ﳛ ﹼﺒﻮﻥ ﻣﺸﺎﻫﺪﺓ ﻛﺮﺓ‬ ‫ﺍﻟﺴﻠﺔ‪ ،‬ﻭﺃﻥ ‪ 12‬ﻃﺎﻟ ﹰﺒﺎ ﳛ ﹼﺒﻮﻥ ﻣﺸﺎﻫﺪﺓ ﻛﻠﺘﺎ ﺍﻟﻠﻌﺒﺘﲔ‪ .‬ﻣ ﹼﺜﻞ ﻫﺬﻩ ﺍﻟﺒﻴﺎﻧﺎﺕ ﺑﺄﺷﻜﺎﻝ ﭬﻦ‪ ،‬ﻭﻣﺎ‬ ‫ﻋﺪﺩ ﺍﻟﻄﻼﺏ ﺍﻟﺬﻳﻦ ﻻ ﳛ ﹼﺒﻮﻥ ﻣﺸﺎﻫﺪﺓ ﺃ ﹼﻱ ﻣﻦ ﺍﻟﻠﻌﺒﺘﲔ؟‬ ‫‪ (6‬ﺍﻛﺘﺐ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ ﺑﺼﻴﻐﺔ )ﺇﺫﺍ‪ ...‬ﻓﺈﻥ‪\" :(...‬ﺍﻟﻔﻴﻞ ﻣﻦ ﺍﻟﺜﺪﻳﻴﺎﺕ‪\".‬‬ ‫‪ (7‬ﺍﻛﺘﺐ ﺍﻟﻤﻌﺎﻛﺲ ﺍﻹﻳﺠﺎﺑﻲ ﻟﻠﻌﺒﺎﺭﺓ‪\" :‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺯﺍﻭﻳﺘﺎﻥ ﻣﻜ ﹼﻤﻠﺘﻴﻦ ﻟﻠﺰﺍﻭﻳﺔ ﻧﻔﺴﻬﺎ‪،‬‬ ‫ﻓﺈﻥ ﻫﺎﺗﻴﻦ ﺍﻟﺰﺍﻭﻳﺘﻴﻦ ﻣﺘﻄﺎﺑﻘﺘﺎﻥ\"‪.‬‬ ‫‪ (8‬ﺍﺳﺘﻌﻤﻞ ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﻟﻤﻨﻄﻘﻲ؛ ﻟﻜﺘﺎﺑﺔ ﻧﺘﻴﺠ ﹴﺔ ﺻﺤﻴﺤ ﹴﺔ ﻣﻦ ﺍﻟﻌﺒﺎﺭﺗﻴﻦ )‪ (1‬ﻭ )‪.(2‬‬ ‫)‪ (1‬ﻳﺘﺪﺭﺏ ﻓﺮﻳﻖ ﺍﻟﺴﺒﺎﺣﺔ ﻳﻮﻡ ﺍﻟﺴﺒﺖ‪.‬‬ ‫)‪ (2‬ﻣﺎﺟﺪ ﺃﺣﺪ ﺃﻋﻀﺎﺀ ﻓﺮﻳﻖ ﺍﻟﺴﺒﺎﺣﺔ‪.‬‬ ‫‪ (9‬ﺍﺳﺘﻌﻤﻞ ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﻟﻤﻨﻄﻘﻲ؛ ﻟﻜﺘﺎﺑﺔ ﻧﺘﻴﺠ ﹴﺔ ﺻﺤﻴﺤ ﹴﺔ ﻣﻦ ﺍﻟﻌﺒﺎﺭﺗﻴﻦ )‪ (1‬ﻭ )‪.(2‬‬ ‫)‪ (1‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x + 6 = 10‬ﻓﺈﻥ ‪.x = 4‬‬ ‫)‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x = 4‬ﻓﺈﻥ ‪.x2 = 16‬‬ ‫‪ (10‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺃﺩﻧﺎﻩ‪ ،‬ﺍﺫﻛﺮ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﻳﻤﻜﻦ ﺍﺳﺘﻌﻤﺎﻟﻬﺎ ﻻﺳﺘﻨﺘﺎﺝ ﺃﻥ‪،AB BC ، AD DB :‬‬ ‫ﻭ‪ ،BE EC‬ﺇﺫﺍ ﻋﻠﻤﺖ ﺃﻥ ‪ B‬ﻧﻘﻄﺔ ﻣﻨﺘﺼﻒ ‪ ،AC‬ﻭﺃﻥ ‪ D‬ﻧﻘﻄﺔ ﻣﻨﺘﺼﻒ ‪ ،AB‬ﻭﺃﻥ ‪ E‬ﻧﻘﻄﺔ‬ ‫ﻣﻨﺘﺼﻒ ‪.BC‬‬ ‫‪ADB E C‬‬ ‫‪21  ‬‬ ‫‪Geo-AS02-19-860179‬‬

‫‪‬‬ ‫‪(3)    ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪______________(11‬‬ ‫ﺍﻛﺘﺐ ﻓﻲ ﻓﺮﺍﻏﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 11, 12‬ﻣﺒﺮﺭﺍﺕ ﺍﻟﺨﻄﻮﺗﻴﻦ ‪ 2, 4‬ﻋﻠﻰ ﺍﻟﺘﺮﺗﻴﺐ ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺍﻟﺘﺎﻟﻲ‪:‬‬ ‫‪______________(12‬‬ ‫‪3 - 2(4 - x) = 11 + 6x :‬‬ ‫‪______________(13‬‬ ‫‪x = - 4 ‬‬ ‫‪______________(14‬‬ ‫‪‬‬ ‫‪______________(15‬‬ ‫‪______________(16‬‬ ‫‪ ‬‬ ‫‪‬‬ ‫‪______________(17‬‬ ‫‪______________(18‬‬ ‫‪ (1‬ﻣﻌﻄﻴﺎﺕ‬ ‫‪3 - 2 (4 - x) = 11 + 6x (1‬‬ ‫‪______________(19‬‬ ‫‪______________(20‬‬ ‫‪(2 3 -8 + 2x = 11 + 6x (2‬‬ ‫‪1‬‬ ‫‪ (3‬ﺑﺎﻟﺘﺒﺴﻴﻂ‬ ‫‪-5 + 2x = 11 + 6x (3‬‬ ‫‪(4 2x = 16 + 6x (4‬‬ ‫‪ (5‬ﺧﺎﺻﻴﺔ ﺍﻟﻄﺮﺡ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪-4x = 16‬‬ ‫‪(5‬‬ ‫‪ (6‬ﺧﺎﺻﻴﺔ ﺍﻟﻘﺴﻤﺔ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪x = -4 (6‬‬ ‫ﺍﻛﺘﺐ ﻓﻲ ﻓﺮﺍﻏﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 13, 14‬ﻣﺒﺮﺭﺍﺕ ﺍﻟﺨﻄﻮﺗﻴﻦ ‪ 5, 8‬ﻋﻠﻰ ﺍﻟﺘﺮﺗﻴﺐ ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺍﻟﺘﺎﻟﻲ‪:‬‬ ‫‪ ∠EFG ،AB⊥BD ‬ﻭ ‪ ∠CBD‬ﻣﺘﺘﺎ ﹼﻣﺘﺎﻥ ‪A C E‬‬ ‫‪∠EFG ∠ABC‬‬ ‫‪B DF G‬‬ ‫‪‬‬ ‫‪G eo- AS02-21-860179‬‬ ‫‪‬‬ ‫‪ (1‬ﻣﻌﻄﻴﺎﺕ‬ ‫‪AB ⊥ BD (1‬‬ ‫‪ ∠CBD , ∠EFG (2‬ﺯﺍﻭﻳﺘﺎﻥ ﻣﺘﺘﺎﻣﺘﺎﻥ ‪ (2‬ﻣﻌﻄﻴﺎﺕ‬ ‫‪ (3‬ﺍﳌﺴﺘﻘﻴﲈﺕ ﺍﳌﺘﻌﺎﻣﺪﺓ ﺗﻜ ﹼﻮﻥ ﺯﺍﻭﻳ ﹰﺔ ﻗﺎﺋﻤ ﹰﺔ‪.‬‬ ‫‪ ∠ABD (3‬ﺯﺍﻭﻳﺔ ﻗﺎﺋﻤﺔ‬ ‫‪ (4‬ﺗﻌﺮﻳﻒ ﺍﻟﺰﺍﻭﻳﺔ ﺍﻟﻘﺎﺋﻤﺔ‬ ‫‪m ∠ABD =90 (4‬‬ ‫‪(5 m ∠ABC+ m ∠CBD= m ∠ABD (5‬‬ ‫‪ (6‬ﺑﺎﻟﺘﻌﻮﻳﺾ‬ ‫‪m ∠ABC+ m ∠CBD= 90 (6‬‬ ‫‪ (7‬ﺗﻌﺮﻳﻒ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺘﺎ ﹼﻣﺘﲔ‬ ‫‪ ∠ABC (7‬ﻭ ‪ ∠CBD‬ﺯﺍﻭﻳﺘﺎﻥ ﻣﺘﺘﺎﻣﺘﺎﻥ‬ ‫‪(8‬‬ ‫‪∠EFG ∠ABC (8‬‬ ‫ﺍﺫﻛﺮ ﺍﻟﺘﻌﺮﻳﻒ ﺃﻭ ﺍﻟﺨﺎﺻﻴﺔ ﺃﻭ ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﺃﻭ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﻛﻞ ﻋﺒﺎﺭ ﹴﺓ )ﻓﻲ ﺍﻷﺳﺌﻠﺔ ‪:(15-20‬‬ ‫‪ (15‬ﺍﻟﻨﻘﺎﻁ ‪ A‬ﻭ‪ C‬ﻭ ‪ E‬ﺗﻘﻊ ﻓﻲ ﻣﺴﺘﻮ￯ ﻭﺍﺣ ﹴﺪ‪.‬‬ ‫‪ (16‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ،AB CD‬ﻓﺈﻥ‪.AB + EF= CD + EF :‬‬ ‫‪ (17‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،AB XY‬ﻓﺈﻥ ‪.XY AB‬‬ ‫‪ (18‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،x(y + z) = a‬ﻓﺈﻥ ‪.xy + xz = a‬‬ ‫‪ (19‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﻣﺘﻘﺎﺑﻠﺘﻴﻦ ﺑﺎﻟﺮﺃﺱ‪ ،‬ﻓﺈﻧﻬﻤﺎ ﻣﺘﻄﺎﺑﻘﺘﺎﻥ‪.‬‬ ‫‪ (20‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ∠1‬ﻭ ‪ ∠2‬ﻗﺎﺋﻤﺘﻴﻦ‪ ،‬ﻓﺈﻥ ‪.∠1 ∠2‬‬ ‫‪22  ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪       1‬‬ ‫ﹸﺣ ﹼﻞ ﻛﻞ ﻣﺴﺄﻟﺔ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﺑﺼﻮﺭ ﹴﺓ ﻭﺍﺿﺤ ﹴﺔ ﻭﺩﻗﻴﻘ ﹴﺔ ﻣﺴﺘﻔﻴ ﹰﺪﺍ ﻣﻦ ﻣﻌﺮﻓﺘﻚ ﺍﻟﺴﺎﺑﻘﺔ‪ ،‬ﺛﻢ ﺗﺤ ﹼﻘﻖ ﻣﻦ ﺗﻀﻤﻴﻨﻚ ﺍﻟﺤﻞ ﺍﻟﺮﺳﻮﻡ ﻭﺍﻟﺘﺒﺮﻳﺮﺍﺕ‬ ‫ﺍﻟﻼﺯﻣﺔ‪ ،‬ﻛﻤﺎ ﻳﻤﻜﻨﻚ ﻋﺮﺽ ﺍﻟﺤ ﹼﻞ ﺑﺄﻛﺜﺮ ﻣﻦ ﻃﺮﻳﻘﺔ‪ ،‬ﺃﻭ ﺃﻥ ﺗﺴﺘﻘﺼﻲ ﺃﻛﺜﺮ ﻣﻤﺎ ﻫﻮ ﻣﻄﻠﻮﺏ ﻓﻲ ﺍﻟﻤﺴﺄﻟﺔ‪) .‬ﺍﺳﺘﻌﻤﻞ ﻭﺭﻗﺔ ﻣﻨﻔﺼﻠﺔ ﺇﺫﺍ‬ ‫ﻛﺎﻥ ﺫﻟﻚ ﺿﺮﻭﺭ ﹼﹰﻳﺎ(‪.‬‬ ‫‪ (1‬ﺍﺳﺘﻌﻤﻞ ﺟﺪﺍﻭﻝ ﺍﻟﺼﻮﺍﺏ ﻹﺛﺒﺎﺕ ﺃﻥ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺸﺮﻃﻴﺔ ﻭﺍﻟﻤﻌﺎﻛﺲ ﺍﻹﻳﺠﺎﺑﻲ ﻟﻬﺎ ﻣﺘﻜﺎﻓﺌﺎﻥ‪ ،‬ﻭﺃﻥ ﻋﻜﺴﻬﺎ‬ ‫ﻭﻣﻌﻜﻮﺳﻬﺎ ﻣﺘﻜﺎﻓﺌﺎﻥ ﺃﻳ ﹰﻀﺎ‪.‬‬ ‫‪ (2‬ﺍﻛﺘﺐ ﻋﺒﺎﺭﺍ ﹴﺕ ﺗﻮﺿﺢ ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﻟﻤﻨﻄﻘﻲ‪.‬‬ ‫‪ (3‬ﺍﻛﺘﺐ ﻋﺒﺎﺭﺍ ﹴﺕ ﺗﻮﺿﺢ ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﻟﻤﻨﻄﻘﻲ ‪.‬‬ ‫‪ (4‬ﺍﻛﺘﺐ ﻣﺜﺎ ﹰﻻ ﻋﻠﻰ ﺧﺎﺻﻴﺔ ﺍﻟﺘﻌ ﹼﺪﻱ‪ ،‬ﻭﻣﺜﺎ ﹰﻻ ﺁﺧﺮ ﻋﻠﻰ ﺧﺎﺻﻴﺔ ﺍﻟﺘﻌﻮﻳﺾ‪ ،‬ﺗﻮﺿﺢ ﻣﻦ ﺧﻼﻟﻬﻤﺎ ﺍﻟﻔﺮﻕ ﺑﻴﻦ ﺍﻟﺨﺎﺻﻴﺘﻴﻦ‪.‬‬ ‫‪ (5‬ﺍﺭﺳﻢ ﺯﺍﻭﻳﺘﻴﻦ ﻣﺘﻘﺎﺑﻠﺘﻴﻦ ﺑﺎﻟﺮﺃﺱ ﻗﻴﺎﺱ ﻛ ﱟﻞ ﻣﻨﻬﻤﺎ ‪ ،40°‬ﻭﻋ ﹼﱪ ﻋﻦ ﻗﻴﺎ ﹶﳼ ﻫﺎﺗﲔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺑﻤﻘﺎﺩﻳﺮ ﺟﱪﻳﺔ ﲢﻮﻱ ‪ ،x‬ﺛﻢ ﹸﺣ ﹼﻞ ﺍﳌﻌﺎﺩﻟﺔ‬ ‫ﺍﻟﻨﺎﲡﺔ‪ ،‬ﻭﺃﺛﺒﺖ ﺃﻥ ﻗﻴﺎﺱ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺰﺍﻭﻳﺘﲔ ﻳﺴﺎﻭﻱ ‪.40°‬‬ ‫‪ (a (6‬ﺍﻛﺘﺐ ﻋﺒﺎﺭ ﹰﺓ ﺻﺤﻴﺤ ﹰﺔ ﺑﺼﻴﻐﺔ )ﺇﺫﺍ‪ ...‬ﻓﺈﻥ‪ (...‬ﰲ ﺣﲔ ﻳﻜﻮﻥ ﻋﻜﺴﻬﺎ ﺧﺎﻃ ﹰﺌﺎ‪.‬‬ ‫‪ (b‬ﺍﻛﺘﺐ ﺍﻟﻌﻜﺲ ﻭﺍﳌﻌﻜﻮﺱ ﻭﺍﳌﻌﺎﻛﺲ ﺍﻹﳚﺎﰊ ﻟﻠﻌﺒﺎﺭﺓ ﺍﻟﺘﻲ ﻛﺘﺒﺘﻬﺎ‪.‬‬ ‫‪ (c‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﺍﻟﺼﻮﺍﺏ ﻟﻜﻞ ﻋﺒﺎﺭﺓ ﻛﺘﺒﺘﻬﺎ ﰲ ﺍﻟﻔﺮﻉ ‪.b‬‬ ‫‪ (7‬ﺍﺭﺳﻢ ﺷﻜ ﹰﻼ ﻳﻮﺿﺢ ﻛ ﹼﹰﻼ ﻣﻦ ﺍﻟﻨﻈﺮﻳﺎﺕ ﺍﻵﺗﻴﺔ‪ ،‬ﻭﺳ ﱢﻢ ﺍﻟﺰﻭﺍﻳﺎ‪ ،‬ﺛﻢ ﹺﺻ ﹾﻒ ﻛﻞ ﻧﻈﺮﻳﺔ ﺑﻜﺘﺎﺑﺔ ﺍﻟﻌﻼﻗﺔ ﺑﻴﻦ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﺘﻲ ﺳ ﱠﻤﻴ ﹶﺘﻬﺎ‪.‬‬ ‫‪ (a‬ﻧﻈﺮﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﻜﺎﻣﻠﺘﲔ ‪.‬‬ ‫‪ (b‬ﻧﻈﺮﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺘﺎﻣﺘﲔ ‪.‬‬ ‫‪ (c‬ﻧﻈﺮﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﻘﺎﺑﻠﺘﲔ ﺑﺎﻟﺮﺃﺱ‪.‬‬ ‫‪1‬‬ ‫‪23‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(1)     1‬‬ ‫ﺍﻟﺠﺰﺀ‪ :1‬ﺍﺳﺌﻠﺔ ﺍﻻﺧﺘﻴﺎﺭ ﻣﻦ ﻣﺘﻌﺪﺩ‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﰲ ﺍﳌﻜﺎﻥ ﺍﳌﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪\" (1‬ﺇﺫﺍ ﻛﺎﻥ ‪ 3b + 4 < 16‬ﻓﺈﻥ ‪ ،\"b > 0‬ﺃﻱ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﹸﻳﻌ ﹼﺪ ﻣﺜﺎ ﹰﻻ ﻣﻀﺎ ﹰﹼﺩﺍ ﻟﻠﻌﺒﺎﺭﺓ ﺍﻟﺴﺎﺑﻘﺔ؟ ‪1-1‬‬ ‫‪________(1‬‬ ‫‪b = 4 (D‬‬ ‫‪b = 3.5 (C‬‬ ‫‪b = 16 (B‬‬ ‫‪b = -1 (A‬‬ ‫‪________(2‬‬ ‫‪________(3‬‬ ‫‪ (2‬ﻣﺎ ﺍﻟﺬﻱ ﻳﺴﺘﻌﻤﻞ ﻟﺒﻴﺎﻥ ﺻﺤﺔ ﺍﻟﻨﺘﻴﺠﺔ‪ ،‬ﺍﻋﺘﻤﺎ ﹰﺩﺍ ﻋﻠﻰ ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﻤﻌﻄﺎﺓ؟‬ ‫‪________(4‬‬ ‫‪ ‬ﺇﺫﺍ ﻛﺎﻥ ﺍﻟﻌﺪﺩ ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﲆ ‪ ، 9‬ﻓﺈﻧﻪ ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﲆ ‪ . 3‬ﺍﻟﻌﺪﺩ ‪ 144‬ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﲆ ‪.9‬‬ ‫‪________(5‬‬ ‫‪ ‬ﺍﻟﻌﺪﺩ ‪ 144‬ﻳﻘﺒﻞ ﺍﻟﻘﺴﻤﺔ ﻋﲆ ‪1-4 .3‬‬ ‫‪ (C‬ﺍﻟﺘﺨﻤﲔ‬ ‫‪ (A‬ﻗﺎﻧﻮﻥ ﺍﻟﻔﺼﻞ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (D‬ﻗﺎﻧﻮﻧﺎ ﺍﻟﻘﻴﺎﺱ ﻭﺍﻟﻔﺼﻞ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (B‬ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﳌﻨﻄﻘﻲ‬ ‫‪ (3‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ p q‬ﻋﺒﺎﺭﺓ ﺷﺮﻃﻴﺔ‪ ،‬ﻓﺈﻥ ﻋﻜﺴﻬﺎ ﻫﻮ ______؟ ‪1-3‬‬ ‫‪q → ~p (D‬‬ ‫‪q → p (C‬‬ ‫‪~q → p (B‬‬ ‫‪~q → ~p (A‬‬ ‫‪ (4‬ﺃ ﹼﻱ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻵﺗﻴﺔ ﺻﺤﻴﺤﺔ ﺩﺍﺋ ﹰﻤﺎ؟ ‪1-2‬‬ ‫‪x ≠ 0 (D‬‬ ‫‪3(x + 1) = 4x (C 3(x+1)+5 = 3x + 8 (B‬‬ ‫‪x = 2 (A‬‬ ‫‪ (5‬ﻋﻠﻢ ﺣﻤ ﹲﺪ ﺃﻥ‪ ∠1 ∠2 :‬ﹶﻭ ‪ ،∠2 ∠3‬ﻓﺎﺳﺘﻨﺘﺞ ﺛﻼﺙ ﻧﺘﺎﺋﺞ ﻫﻲ‪1-6 :‬‬ ‫‪m ∠1 = m ∠2 (I‬‬ ‫‪∠1 ∠3 (II‬‬ ‫‪m∠1 + m ∠2 = m ∠3 (III‬‬ ‫ﻓﺄﻱ ﻧﺘﺎﺋﺞ ﲪﺪ ﻫﻲ ﺍﻟﺼﺤﻴﺤﺔ؟‬ ‫‪III, I (D‬‬ ‫‪II, I (C‬‬ ‫‪ II (B‬ﻓﻘﻂ‬ ‫‪III, II, I (A‬‬ ‫ﺍﺫﻛﺮ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 6‬ﻭ‪: 7‬‬ ‫‪ (6‬ﺇﺫﺍ ﻛﺎﻥ‪ AB = CD :‬ﻭ ‪ ،CD = 11‬ﻓﺈﻥ ‪ 1-7  .AB = 11‬‬ ‫‪________(6‬‬ ‫‪ (D‬ﺍﻻﻧﻌﻜﺎﺱ‬ ‫‪ (C‬ﺍﻟﺘﻄﺎﺑﻖ‬ ‫‪ (B‬ﺍﻟﺘﲈﺛﻞ‬ ‫‪ (A‬ﺍﻟﺘﻌ ﹼﺪﻱ‬ ‫‪ (7‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ،∠YXZ ∠PQR‬ﻓﺈﻥ‪1-8 . ∠PQR ∠XYZ‬‬ ‫‪ (D‬ﺍﻻﻧﻌﻜﺎﺱ ﻟﻠﺘﻄﺎﺑﻖ ‪________(7‬‬ ‫‪ (C‬ﺍﻟﺘﻌﻮﻳﺾ‬ ‫‪ (A‬ﺍﻟﺘﻌ ﹼﺪﻱ ﻟﻠﺘﻄﺎﺑﻖ ‪ (B‬ﺍﻟﺘﲈﺛﻞ ﻟﻠﺘﻄﺎﺑﻖ‬ ‫‪ (8‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻨﺴﺒﺔ ﺑﻴﻦ ﻗﻴﺎ ﹶﺳﻲ ﺯﺍﻭﻳﺘﻴﻦ ﻣﺘﻜﺎﻣﻠﺘﻴﻦ ﻫﻲ ‪ ،4:1‬ﻓﻤﺎ ﻗﻴﺎﺱ ﺍﻟﺰﺍﻭﻳﺔ ﺍﻟﻜﺒﺮ￯؟ ‪.1-8‬‬ ‫‪________(8‬‬ ‫‪144° (D‬‬ ‫‪160° (C‬‬ ‫‪118° (B‬‬ ‫‪72° (A‬‬ ‫‪1‬‬ ‫‪24‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(1‬‬ ‫‪(1)    ‬‬ ‫‪1‬‬ ‫‪ (9‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ∠1‬ﻭ ‪ ∠2‬ﻣﺘﻘﺎﺑﻠﺘﻴﻦ ﺑﺎﻟﺮﺃﺱ‪ ،‬ﻭﻛﺎﻥ ‪،m∠1 = (17 - x)°‬‬ ‫‪________(9‬‬ ‫‪ ، m ∠2 = (2x - 7 )°‬ﻓﺄﻭﺟﺪ ‪1-8 .m ∠1‬‬ ‫‪_______(10‬‬ ‫‪18° (D‬‬ ‫‪16° (C‬‬ ‫‪9° (B‬‬ ‫‪8° (A‬‬ ‫‪_______(11‬‬ ‫‪_______(12‬‬ ‫ﺍﺳﺘﻌﻤﻞ ﺍﻟﺒﺮﻫﺎﻥ ﺍﻵﺗﻲ ﻟﻺﺟﺎﺑﺔ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪1-6 :10-12‬‬ ‫‪_______(13‬‬ ‫‪1‬‬ ‫‪x + 3 = 15x - 53‬‬ ‫‪.x = 4 ‬‬ ‫‪‬‬ ‫‪ ‬‬ ‫‪‬‬ ‫‪ (1‬ﻣﻌﻄﻴﺎﺕ‬ ‫‪x + 3 = 15x - 53 (1‬‬ ‫‪ (2‬ﺧﺎﺻﻴﺔ ﺍﻟﻄﺮﺡ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪x - x + 3 = 15x - x– 53 (2‬‬ ‫‪ (3‬ﺑﺎﻟﺘﺒﺴﻴﻂ‬ ‫‪(3‬‬ ‫‪(4 3 + 53 = 14x - 53 + 53 (4‬‬ ‫‪ (5‬ﺑﺎﻟﺘﺒﺴﻴﻂ‬ ‫‪56 = 14x (5‬‬ ‫‪ (6‬ﺧﺎﺻﻴﺔ ﺍﻟﻘﺴﻤﺔ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪(6‬‬ ‫‪ (7‬ﺑﺎﻟﺘﺒﺴﻴﻂ‬ ‫‪4 = x (7‬‬ ‫‪ (8‬ﺧﺎﺻﻴﺔ ﺍﻟﺘﲈﺛﻞ‬ ‫‪x = 4 (8‬‬ ‫‪3 = 14x - 53 (H‬‬ ‫‪ (10‬ﻣﺎ ﺍﻟﻌﺒﺎﺭﺓ )‪ (3‬ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺃﻋﻼﻩ؟‬ ‫‪3x = 14 (J‬‬ ‫‪3x = 15x - 53 (F‬‬ ‫‪ (C‬ﺧﺎﺻﻴﺔ ﺍﻟﺘﻌﻮﻳﺾ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪x = 16x + 56 (G‬‬ ‫‪ (D‬ﺧﺎﺻﻴﺔ ﺍﳉﻤﻊ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (11‬ﻣﺎ ﻣﺒ ﱢﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ )‪ (4‬ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺃﻋﻼﻩ؟‬ ‫‪ (A‬ﺧﺎﺻﻴﺔ ﺍﻟﺘﲈﺛﻞ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (B‬ﺧﺎﺻﻴﺔ ﺍﻟﻘﺴﻤﺔ ﻟﻠﻤﺴﺎﻭﺍﺓ‬ ‫‪ (12‬ﻣﺎ ﺍﻟﻌﺒﺎﺭﺓ )‪ (6‬ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺃﻋﻼﻩ؟‬ ‫_‪_5_6‬‬ ‫=‬ ‫_‪_1_4x‬‬ ‫‪(H‬‬ ‫=‪x‬‬ ‫‪_1_4‬‬ ‫‪(F‬‬ ‫‪14‬‬ ‫‪14‬‬ ‫‪56‬‬ ‫=_‪_55_66‬‬ ‫‪_1_4_x‬‬ ‫‪(J‬‬ ‫‪56 -14 = x (G‬‬ ‫‪56‬‬ ‫‪C‬‬ ‫‪ (13‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ‪،m ∠1 = 23° ، m∠ABC = 131° :‬‬ ‫‪1‬‬ ‫ﻓﺄﻭﺟﺪ ‪1-8. m∠3‬‬ ‫‪2‬‬ ‫‪35° (C‬‬ ‫‪23° (A‬‬ ‫‪3B‬‬ ‫‪18° (D‬‬ ‫‪67° (B‬‬ ‫‪A‬‬ ‫‪25  ‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(2‬‬ ‫‪(1)    ‬‬ ‫‪1‬‬ ‫ﺍﻟﺠﺰﺀ ‪  :2‬ﺃﺳﺌﻠﺔ ﺫﺍﺕ ﺇﺟﺎﺑﺎﺕ ﻗﺼﻴﺮﺓ‬ ‫ﺍﻗﺮﺃ ﻛﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﰲ ﺍﳌﻜﺎﻥ ﺍﳌﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪______________(14‬‬ ‫‪ (14‬ﺃﻭﺟﺪ ﺍﻟﺤﺪ ﺍﻟﺘﺎﻟﻲ ﻓﻲ ﺍﻟﻤﺘﺘﺎﺑﻌﺔ ﺍﻵﺗﻴﺔ‪1-1 :‬‬ ‫…‪3,3,6,9,15,‬‬ ‫‪‬‬ ‫ﺍﻟﺴﺒﺎﺣﺔ ﺍﻟﺘﻨﺲ‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 15‬ﻭ ‪ ،16‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺷﻜﻞ ﻓﻦ ﺍﻟﻤﺠﺎﻭﺭ‪ ،‬ﻭﺍﻟﺬﻱ‬ ‫‪36‬‬ ‫ﻧﻳﺒﺎ ﹼﻴ ﹴﺩﻦﺭﻳﻧﺎﺘﺎﺋﺿﺞﻲ‪.‬ﺩﺭﺍﺳ ﹴﺔ ﻣﺴﺤﻴ ﹴﺔ ﺷﻤﻠﺖ ‪ 229‬ﻋﻀ ﹰﻮﺍ ﻓﻲ‬ ‫‪12‬‬ ‫‪5‬‬ ‫‪62‬‬ ‫‪19‬‬ ‫ﺍﳉﺮﻱ‬ ‫‪45‬‬ ‫‪______________(15‬‬ ‫‪ (15‬ﻣﺎ ﻋﺪﺩ ﺍﻷﻋﻀﺎﺀ ﺍﻟﺬﻳﻦ ﻳﻤﺎﺭﺳﻮﻥ ﺭﻳﺎﺿ ﹶﺘﻲ ﺍﻟﺴﺒﺎﺣﺔ ﺃﻭ ﺍﻟﺘﻨﺲ؟ ‪1-2‬‬ ‫‪______________(16‬‬ ‫‪ (16‬ﻣﺎ ﻋﺪﺩ ﺍﻷﻋﻀﺎﺀ ﺍﻟﺬﻳﻦ ﻻ ﻳﲈﺭﺳﻮﻥ ﺃ ﹰﹼﻳﺎ ﻣﻦ ﺍﻷﻧﺸﻄﺔ ﺍﻟﺜﻼﺛﺔ؟ ‪1-2‬‬ ‫‪______________(17‬‬ ‫‪ (17‬ﺇﺫﺍ ﻭﻗﻌﺖ ‪ B‬ﰲ ﺩﺍﺧﻞ ‪ ،∠DEF‬ﻭﻛﺎﻥ‪m ∠DEB = 27.2° :‬‬ ‫ﻭ ‪ ،m ∠DEF = 92.5°‬ﻓﺄﻭﺟﺪ ‪1-8 . m ∠BEF‬‬ ‫ﺍﺳﺘﻌﻤﻞ ﺟﺪﻭﻝ ﺍﻟﺼﻮﺍﺏ ﺍﻟﻤﺠﺎﻭﺭ ﻟﻺﺟﺎﺑﺔ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪p q ~p ~p ∨ q q→(~p ∨ q) :18-20‬‬ ‫‪TT‬‬ ‫‪TF‬‬ ‫‪FT‬‬ ‫‪FF‬‬ ‫‪______________(18‬‬ ‫‪ (18‬ﻣﺎ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﺍﻟﺘﻲ ﻳﺠﺐ ﺃﻥ ﹸﺗﻜﺘﺐ ﻓﻲ ﻋﻤﻮﺩ ‪~p‬؟ ‪1-2‬‬ ‫‪______________(19‬‬ ‫‪ (19‬ﻣﺎ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﺍﻟﺘﻲ ﻳﺠﺐ ﺃﻥ ﹸﺗﻜﺘﺐ ﻓﻲ ﻋﻤﻮﺩ ‪~p∨q‬؟ ‪1-2‬‬ ‫‪______________(20‬‬ ‫‪ (20‬ﻣﺎ ﻗﻴﻢ ﺍﻟﺼﻮﺍﺏ ﺍﻟﺘﻲ ﻳﺠﺐ ﺃﻥ ﹸﺗﻜﺘﺐ ﻓﻲ ﻋﻤﻮﺩ ])‪[q→(~p∨q‬؟ ‪1-3‬‬ ‫ﺍﻋﺘﻤﺪ ﻋﻠﻰ ﺍﻟﺸﻜﻞ ﺍﻵﺗﻲ ﻟﻺﺟﺎﺑﺔ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪1-8 21 - 23‬‬ ‫‪______________(21‬‬ ‫‪T‬‬ ‫‪______________(22‬‬ ‫‪S‬‬ ‫‪______________(23‬‬ ‫˚‪48‬‬ ‫‪1‬‬ ‫‪W UR‬‬ ‫‪V‬‬ ‫‪ (21‬ﺳ ﹼﻢ ﺯﻭ ﹰﺟﺎ ﻣﻦ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﻤﺘﻜﺎﻣﻠﺔ‪.‬‬ ‫‪ (22‬ﺳ ﹼﻢ ﺯﻭ ﹰﺟﺎ ﻣﻦ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﻤﺘﺘﺎﻣﺔ‪.‬‬ ‫‪ (23‬ﺃﻭﺟﺪ ‪.m ∠RUV‬‬ ‫‪26 ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪  ‬‬ ‫‪2‬‬ ‫‪ ‬‬ ‫‪ 1‬ﻗﺒﻞ ﺑﺪﺀ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﲏ‬ ‫• ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺟﻤﻠﺔ‪.‬‬ ‫• ﻗ ﹼﺮﺭ ﻣﺎ ﺇﺫﺍ ﻛﻨﺖ ﻣﻮﺍﻓ ﹰﻘﺎ )ﻡ( ﻋﻠﻰ ﻣﻀﻤﻮﻧﻬﺎ‪ ،‬ﺃﻭ ﻏﻴﺮ ﻣﻮﺍﻓﻖ )ﻍ(‪.‬‬ ‫• ﺍﻛﺘﺐ )ﻡ( ﺃﻭ )ﻍ( ﰲ ﺍﻟﻌﻤﻮﺩ ﺍﻷﻭﻝ‪ ،‬ﻭﺇﺫﺍ ﻛﻨﺖ ﻏﲑ ﻣﺘﺄﻛﺪ ﻣﻦ ﻣﻮﺍﻓﻘﺘﻚ ﻓﺎﻛﺘﺐ )ﻍ ﻡ(‪.‬‬ ‫‪2‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪ (1‬ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ ﻏﻴﺮ ﺍﻟﻤﺘﻘﺎﻃﻌﻴﻦ ﺍﻟﻮﺍﻗﻌﺎﻥ ﻓﻲ ﻣﺴﺘﻮﻳﻴﻦ ﻣﺨﺘﻠﻔﻴﻦ ﻳﻜﻮﻧﺎﻥ ﻣﺘﻮﺍﺯﻳﻴﻦ‪.‬‬ ‫‪ (2‬ﻳﻤﻜﻦ ﺃﻥ ﺗﻜﻮﻥ ﺍﻟﻤﺴﺘﻮﻳﺎﺕ ﻣﺘﻮﺍﺯﻳ ﹰﺔ ﻣﺜﻞ ﺍﻟﻤﺴﺘﻘﻴﻤﺎﺕ‪.‬‬ ‫‪ (3‬ﺍﻟﻘﺎﻃﻊ ﻫﻮ ﻣﺴﺘﻘﻴ ﹲﻢ ﻳﻘﻄﻊ ﻣﺴﺘﻘﻴﻤﺎ ﹴﺕ ﻣﺘﻮﺍﺯﻳ ﹰﺔ ﻓﻲ ﻧﻘﺎ ﹴﻁ ﻣﺨﺘﻠﻔ ﹴﺔ‪.‬‬ ‫‪ (4‬ﺇﺫﺍ ﻗﻄﻊ ﻗﺎﻃﻊ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻣﺘﻮﺍﺯﻳﻴﻦ‪ ،‬ﻓﺈﻥ ﺍﻟﺰﺍﻭﻳﺘﻴﻦ ﺍﻟﻤﺘﻨﺎﻇﺮﺗﻴﻦ ﺗﻜﻮﻧﺎﻥ ﻣﺘﻜﺎﻣﻠﺘﻴﻦ‪.‬‬ ‫‪ (5‬ﻓﻲ ﺍﻟﻤﺴﺘﻮ￯‪ ،‬ﺇﺫﺍ ﻛﺎﻥ ﻣﺴﺘﻘﻴ ﹲﻢ ﻣﺎ ﻋﻤﻮﺩ ﹰﹼﻳﺎ ﻋﻠﻰ ﺃﺣﺪ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻣﺘﻮﺍﺯﻳﻴﻦ‪ ،‬ﻓﺈﻧﻪ ﻳﻜﻮﻥ ﻋﻤﻮﺩ ﹼﹰﻳﺎ‬ ‫ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻵﺧﺮ ﺃﻳ ﹰﻀﺎ‪.‬‬ ‫‪ (6‬ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﻳﺴﺎﻭﻱ ﻧﺴﺒﺔ ﺍﻟﺘﻐﻴﺮ ﺍﻟﺮﺃﺳﻲ ﺇﻟﻰ ﺍﻟﺘﻐﻴﺮ ﺍﻷﻓﻘﻲ‪.‬‬ ‫‪ (7‬ﺣﺎﺻﻞ ﺿﺮﺏ ﻣﻴ ﹶﻠﻲ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻣﺘﻌﺎﻣﺪﻳﻦ ﻳﺴﺎﻭﻱ ‪.1‬‬ ‫‪ (8‬ﺇﺫﺍ ﻛﺎﻧﺖ ﻣﻌﺎﺩﻟﺔ ﻣﺴﺘﻘﻴ ﹴﻢ‪ ، y – 4 = 2(x – 7) :‬ﻓﺈﻧﻪ ﻳﻤﺮ ﺑﺎﻟﻨﻘﻄﺔ )‪.(-4 ,-7‬‬ ‫‪ (9‬ﺇﺫﺍ ﻗﻄﻊ ﻗﺎﻃ ﹲﻊ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻓﻲ ﻣﺴﺘﻮ￯‪ ،‬ﻭﻛﺎﻧﺖ ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﻟﻤﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹼﹰﻴﺎ ﻣﺘﻄﺎﺑﻘﺘﻴﻦ‪ ،‬ﻓﺈﻥ‬ ‫ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ﻣﺘﻮﺍﺯﻳﺎﻥ‪.‬‬ ‫‪ (10‬ﺃﻗﺼﺮ ﻣﺴﺎﻓﺔ ﻣﻦ ﻧﻘﻄ ﹴﺔ ﺇﻟﻰ ﻣﺴﺘﻘﻴ ﹴﻢ ﻫﻲ ﺍﻟﻤﺴﺎﻓﺔ ﺍﻟﻌﻤﻮﺩﻳﺔ‪.‬‬ ‫‪ 2‬ﺑﻌﺪ ﺇﻛﲈﻝ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﲏ‬ ‫• ﺃﻋﺪ ﻗﺮﺍﺀﺓ ﻛ ﹼﻞ ﺟﻤﻠﺔ ﺃﻋﻼﻩ‪ ،‬ﻭﺍﻣﻸ ﺍﻟﻌﻤﻮﺩ ﺍﻷﺧﻴﺮ ﺑﻜﺘﺎﺑﺔ )ﻡ( ﺃﻭ )ﻍ(‪.‬‬ ‫• ﻫﻞ ﺗﻐ ﹼﻴﺮ ﺭﺃﻳﻚ ﻓﻲ ﺍﻟﺠﻤﻞ ﺍﻟﺴﺎﺑﻘﺔ ﻋ ﹼﻤﺎ ﻫﻮ ﻓﻲ ﺍﻟﻌﻤﻮﺩ ﺍﻷﻭﻝ؟‬ ‫• ﺍﺳﺘﻌﻤﻞ ﻭﺭﻗﺔ ﺇﺿﺎﻓﻴﺔ ﺗﺒ ﹼﻴﻦ ﻓﻴﻬﺎ ﺳﺒﺐ ﻋﺪﻡ ﻣﻮﺍﻓﻘﺘﻚ ﻋﻠﻰ ﺑﻌﺾ ﺍﻟﺠﻤﻞ‪ ،‬ﺩﺍﻋ ﹰﻤﺎ ﺫﻟﻚ ﺑﺎﻷﻣﺜﻠﺔ ﺇﻥ ﺃﻣﻜﻦ‪.‬‬ ‫‪2‬‬ ‫‪27‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪   2‬‬ ‫ﻫﺬﻩ ﻗﺎﺋﻤﺔ ﺑﺎﳌﻔﺮﺩﺍﺕ ﺍﳉﺪﻳﺪﺓ ﺍﻟﺘﻲ ﺳﺘﺘﻌﻠﻤﻬﺎ ﰲ ﺃﺛﻨﺎﺀ ﺩﺭﺍﺳﺘﻚ ﺍﻟﻔﺼﻞ ‪ .2‬ﺍﻛﺘﺐ ﺗﻌﺮﻳ ﹰﻔﺎ ﺃﻭ ﻭﺻ ﹰﻔﺎ ﻟﻜﻞ ﻣﻔﺮﺩ ﹴﺓ ﰲ ﺍﳉﺪﻭﻝ ﺣﲔ ﺗﻈﻬﺮ ﻟﻚ‬ ‫ﰲ ﺃﺛﻨﺎﺀ ﺩﺭﺍﺳﺔ ﺍﻟﻔﺼﻞ‪ ،‬ﺛﻢ ﺃﺿﻒ ﺭﻗﻢ ﺍﻟﺼﻔﺤﺔ ﺍﻟﺘﻲ ﻭﺭﺩﺕ ﻓﻴﻬﺎ ﺍﳌﻔﺮﺩﺓ ﺃﻭﻝ ﻣﺮﺓ ﰲ ﺍﻟﻌﻤﻮﺩ ﺍﳌﺨ ﱠﺼﺺ‪ .‬ﺍﺳﺘﻌﻤﻞ ﻫﺬﻩ ﺍﻟﻘﺎﺋﻤﺔ ﰲ ﺃﺛﻨﺎﺀ‬ ‫ﺍﳌﺮﺍﺟﻌﺔ ﻭﺍﻻﺳﺘﻌﺪﺍﺩ ﻻﺧﺘﺒﺎﺭ ﺍﻟﻔﺼﻞ‪.‬‬ ‫‪ ‬‬ ‫‪‬‬ ‫‪‬‬ ‫ﺍﳌﺴﺘﻘﻴﲈﻥ ﺍﳌﺘﺨﺎﻟﻔﺎﻥ‬ ‫ﺍﳌﺴﺘﻮﻳﺎﻥ ﺍﳌﺘﻮﺍﺯﻳﺎﻥ‬ ‫ﺍﳌﺴﺘﻘﻴﲈﻥ ﺍﳌﺘﻮﺍﺯﻳﺎﻥ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹼﹰﻴﺎ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹰﹼﻴﺎ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﺤﺎﻟﻔﺘﺎﻥ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﻨﺎﻇﺮﺗﺎﻥ‬ ‫‪2‬‬ ‫ﺍﻟﻘﺎﻃﻊ‬ ‫‪28 ‬‬

  ()    2     ‫ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﺪﺍﺧﻠﻴﺔ‬ ‫ﺍﻟﺰﻭﺍﻳﺎ ﺍﳋﺎﺭﺟﻴﺔ‬ ‫ﺍﳌﻴﻞ‬ ‫ﻣﻌ ﹼﺪﻝ ﺍﻟﺘﻐﲑ‬ ‫ﺻﻴﻐﺔ ﺍﳌﻴﻞ ﻭﻧﻘﻄﺔ‬ ‫ﺻﻴﻐﺔ ﺍﳌﻴﻞ ﻭﺍﳌﻘﻄﻊ‬ ‫ﻣﺘﺴﺎﻭﻱ ﺍﻟﺒﻌﺪ‬ ‫ﺍﳌﺤﻞ ﺍﳍﻨﺪﳼ‬ 2 29  

‫‪‬‬ ‫‪‬‬ ‫‪(2-2 2-1) (1)   2‬‬ ‫‪GH‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫ﺣ ﱢﺪﺩ ﻛ ﹰﹼﻼ ﻣﻤﺎ ﻳﺄﺗﻲ ﻓﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 1‬ﻭ ‪ 2‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪________________(1‬‬ ‫‪E‬‬ ‫‪C‬‬ ‫‪L‬‬ ‫‪J‬‬ ‫‪F‬‬ ‫‪DM‬‬ ‫‪K‬‬ ‫‪ (1‬ﻣﺴﺘﻮ￯ ﻳﻮﺍﺯﻱ ﺍﻟﻤﺴﺘﻮ￯ ‪EGH‬‬ ‫‪________________(2‬‬ ‫‪BA‬‬ ‫‪ (2‬ﺗﻘﺎﻃﻊ ﺍﻟﻤﺴﺘﻮﻳﻴﻦ ‪ ABC‬ﻭ ‪.EFB‬‬ ‫‪Geo-AS03-33-860180‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ 3-8‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪________________ (3 a‬‬ ‫‪12‬‬ ‫‪63‬‬ ‫‪4‬‬ ‫ﺻ ﹼﻨﻒ ﻛ ﹼﻞ ﺯﻭﺝ ﻣﻦ ﺍﻟﺰﻭﺍﻳﺎ ﻓﻲ ﺍﻷﺳﺌﻠﺔ ‪ 3-6‬ﺇﻟﻰ ﺯﺍﻭﻳﺘﻴﻦ ﻣﺘﺒﺎﺩﻟﺘﻴﻦ ﺩﺍﺧﻠ ﹰﹼﻴﺎ‪،‬‬ ‫‪87‬‬ ‫‪5‬‬ ‫‪________________ (4‬‬ ‫‪b‬‬ ‫‪9 10‬‬ ‫‪11 12‬‬ ‫ﺃﻭ ﻣﺘﺒﺎﺩﻟﺘﻴﻦ ﺧﺎﺭﺟ ﹼﹰﻴﺎ‪ ،‬ﺃﻭ ﻣﺘﻨﺎﻇﺮﺗﻴﻦ‪ ،‬ﺃﻭ ﻣﺘﺤﺎﻟﻔﺘﻴﻦ ‪:‬‬ ‫‪16 15‬‬ ‫‪14 13‬‬ ‫‪cd‬‬ ‫‪________________ (5‬‬ ‫‪ ∠6 (4‬ﻭ ‪∠12‬‬ ‫‪ ∠2 (3‬ﻭ ‪∠10‬‬ ‫‪________________ (6‬‬ ‫‪ ∠14 (6‬ﻭ ‪∠15‬‬ ‫‪ ∠1 (5‬ﻭ‪∠5‬‬ ‫ﺇﺫﺍ ﻛﺎﻥ‪ a b :‬ﹶﻭ ‪ ، m∠7 = 94°‬ﻓﺄﻭﺟﺪ ﻗﻴﺎﺱ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺰﺍﻭﻳﺘﻴﻦ ﺍ‪0‬ﻵﺗ‪8‬ﻴﺘ‪1‬ﻴ‪0‬ﻦ‪________________ (7 Geo-AS03-34-8:6‬‬ ‫‪________________ (8‬‬ ‫‪a‬‬ ‫‪∠9 (8‬‬ ‫‪∠10 (7‬‬ ‫‪________________ (9‬‬ ‫‪(5x - 7)° (4y + 3)°‬‬ ‫‪b‬‬ ‫‪ (9‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﻛ ﱟﻞ ﻣﻦ ‪ x, y‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪(3x + 17)°‬‬ ‫‪_______ (10‬‬ ‫‪U‬‬ ‫‪ (10‬ﺍﺧﺘﻴﺎﺭ ﻣﻦ ﻣﺘﻌﺪﺩ‪ :‬ﺃﻭﺟﺪ ‪ m∠UVW‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪138°‬‬ ‫‪81° (C‬‬ ‫‪39° (A‬‬ ‫‪V‬‬ ‫‪Geo-AS031-3385° -(D860180‬‬ ‫‪42° (B‬‬ ‫‪39°‬‬ ‫‪W‬‬ ‫‪ Geo-AS03-36-860180‬‬ ‫‪‬‬ ‫‪(2-3)(2)  ‬‬ ‫‪2‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪g‬‬ ‫ﻫﻞ ﻳﻤﻜﻦ ﺇﺛﺒﺎﺕ ﺃﻥ ﺃ ﹰﹼﻳﺎ ﻣﻦ ﻣﺴﺘﻘﻴﻤﺎﺕ ﺍﻟﺸﻜﻞ ﻣﺘﻮﺍﺯﻳﺔ‪ ،‬ﺍﻋﺘﻤﺎ ﹰﺩﺍ‬ ‫‪h‬‬ ‫‪1‬‬ ‫‪34‬‬ ‫ﻋﻠﻰ ﺍﻟﻤﻌﻄﻴﺎﺕ ﻓﻲ ﺍﻷﺳﺌﻠﺔ ‪ ،1-4‬ﻭﺇﺫﺍ ﻛﺎﻥ ﺃ ﱡﻳﻬﺎ ﻣﺘﻮﺍﺯ ﹼﹰﻳﺎ‪،‬‬ ‫‪2‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫ﻓﺎﺫﻛﺮ ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﺃﻭ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺇﺟﺎﺑﺘﻚ‪.‬‬ ‫‪78‬‬ ‫‪9‬‬ ‫‪________________(1‬‬ ‫‪p qj‬‬ ‫‪________________(2‬‬ ‫‪∠2 ∠3 (2‬‬ ‫‪∠1 ∠ 6 (1‬‬ ‫‪________________(3‬‬ ‫‪________________(4‬‬ ‫‪m∠ 7 + m∠ 6 = 180 (4‬‬ ‫‪∠4 ∠9 (3‬‬ ‫‪Geo-AS03-37-860180‬‬ ‫‪________________(5‬‬ ‫‪ (5‬ﺇﺫﺍ ﻛﺎﻥ‪ m∠3 = (5x - 17)° :‬ﹶﻭ ‪، m∠7 = (3x + 35)°‬‬ ‫‪2‬‬ ‫ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪ x‬ﺣﺘﻰ ﻳﻜﻮﻥ ‪. g h‬‬ ‫‪30 ‬‬

‫‪‬‬ ‫‪(2-4 ,2-5) (3)  ‬‬ ‫‪‬‬ ‫‪________________(1‬‬ ‫‪2‬‬ ‫‪________________(2‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫ﻋ ﹼﻴﻦ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻳﻤ ﹼﺮ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ ﺍﻟﻤﺤ ﹼﺪﺩﺗﻴﻦ ﻓﻲ ﻛ ﱟﻞ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ‪:‬‬ ‫‪Y(-1, -12), P(3, 8) (2‬‬ ‫‪E(-5,6), Z(4, -3)) (1‬‬ ‫‪________________(3‬‬ ‫‪R(-5,-7), Q(5, -5) (4‬‬ ‫‪B(-2, 7), N(8, -8) (3‬‬ ‫‪________________(4‬‬ ‫‪________________(5‬‬ ‫‪ (5‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ‪ y‬ﺍﻟﺘﻲ ﺗﺠﻌﻞ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ )‪B(-7, -2), A(-9, y‬‬ ‫‪________________(6‬‬ ‫ﻳﺴﺎﻭﻱ ‪.-3‬‬ ‫‪________________(7‬‬ ‫‪________________(8‬‬ ‫‪.(3,‬‬ ‫)‪8‬‬ ‫ﺑﺎﻟﻨﻘﻄﺔ‬ ‫ﻭﻳﻤ ﹼﺮ‬ ‫‪،‬‬ ‫‪-‬‬ ‫_‪_1‬‬ ‫ﻣﻴﻠﻪ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻟﻤﺴﺘﻘﻴﻢ‬ ‫ﻣﻌﺎﺩﻟﺔ‬ ‫ﻭﺍﻟﻨﻘﻄﺔ‬ ‫ﺍﻟﻤﻴﻞ‬ ‫ﺑﺼﻴﻐﺔ‬ ‫ﺍﻛﺘﺐ‬ ‫‪(6‬‬ ‫‪3‬‬ ‫‪ (7‬ﺍﻛﺘﺐ ﺑﺼﻴﻐﺔ ﺍﻟﻤﻴﻞ ﻭﺍﻟﻤﻘﻄﻊ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻣﻴﻠﻪ_‪ ،_35‬ﻭﻣﻘﻄﻌﻪ ﺍﻟﻤﺤﻮﺭ ‪ y‬ﻳﺴﺎﻭﻱ ‪.-2‬‬ ‫‪ (8‬ﺍﻛﺘﺐ ﺑﺼﻴﻐﺔ ﺍﻟﻤﻴﻞ ﻭﺍﻟﻤﻘﻄﻊ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎ ﹼﺭ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ )‪ (-1, 7‬ﻭ)‪.(3, -9‬‬ ‫‪ (9‬ﺗﺘﻘﺎ ﹶﺿﻰ ﺷﺮﻛﺔ ﺍﺗﺼﺎﻻﺕ ﺭﺳﻮ ﹰﻣﺎ ﺷﻬﺮﻳﺔ ﻣﻘﺪﺍﺭﻫﺎ ‪ 30‬ﺭﻳﺎ ﹰﻻ ﺇﺿﺎﻓﺔ ﺇﻟﻰ ‪ 0.30‬ﺭﻳﺎ ﹰﻻﻋﻦ ﻛﻞ ﺩﻗﻴﻘﺔ ‪________________(9‬‬ ‫ﺍﺗﺼﺎﻝ‪ .‬ﺍﻛﺘﺐ ﻣﻌﺎﺩﻟ ﹰﺔ ﺗﻤ ﹼﺜﻞ ﺍﻟﺘﻜﻠﻔﺔ ﺍﻟﺸﻬﺮﻳﺔ ‪ C‬ﺇﺫﺍ ﻛﺎﻥ ﻋﺪﺩ ﺩﻗﺎﺋﻖ ﺍﻻﺗﺼﺎﻝ ‪.b‬‬ ‫‪‬‬ ‫‪(2-6) (4)  ‬‬ ‫‪‬‬ ‫‪________________(1‬‬ ‫‪2‬‬ ‫‪________________(2‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪________________(3‬‬ ‫‪ (1‬ﺃﻧﺸﺊ ﺍﻟﻘﻄﻌﺔ ﺍﻟﻤﺴﺘﻘﻴﻤﺔ ﺍﻟﺘﻲ ﺗﻤ ﹼﺜﻞ ﺍﻟ ﹸﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ B‬ﹶﻭ ‪. DC‬‬ ‫‪________________(4‬‬ ‫‪________________(5‬‬ ‫‪ (2‬ﻳﻤ ﱡﺮ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ )‪ ،(0, 4), (1, -3‬ﺇﺫﺍ ﻛﺎﻥ ﺇﺣﺪﺍﺛ ﹼﻴﺎ ﺍﻟﻨﻘﻄﺔ‬ ‫‪2‬‬ ‫‪ H‬ﻫﻤﺎ )‪ ،(-1, 3‬ﻓﺄﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ H‬ﻭﺍﻟﻤﺴﺘﻘﻴﻢ ‪.‬‬ ‫ﺃﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﻛ ﹼﻞ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻣﺘﻮﺍﺯﻳﻴﻦ ﻓﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ﺍﻵﺗﻴﻴﻦ‪:‬‬ ‫‪y = -x - 9 (4‬‬ ‫‪y = -8 (3‬‬ ‫‪y=-x–7‬‬ ‫‪y=4‬‬ ‫‪ (5‬ﻣﺎ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ )‪ A(-1, 5‬ﻭﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻣﻌﺎﺩﻟﺘﻪ ‪4x - 5y = 12‬؟‬ ‫‪31  ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(2-3  2-1)    2‬‬ ‫‪ ‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪__________(1‬‬ ‫‪G‬‬ ‫‪J‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 1‬ﻭ‪ 2‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪__________(2‬‬ ‫‪H‬‬ ‫‪ (1‬ﺃ ﹼﻱ ﻗﻄﻌ ﹴﺔ ﻣﺴﺘﻘﻴﻤ ﹴﺔ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﺗﺨﺎﻟﻒ ‪ IJ‬؟‬ ‫‪__________(3‬‬ ‫‪F EI‬‬ ‫‪__________(4‬‬ ‫‪__________(5‬‬ ‫‪B A HI (C‬‬ ‫‪GH (A‬‬ ‫‪CD‬‬ ‫‪AJ (B‬‬ ‫‪AB (D‬‬ ‫‪ (2‬ﺃ ﹼﻱ ﻣﺴﺘﻮ￯ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﻳﻮﺍﺯﻱ ﺍﻟﻤﺴﺘﻮ￯ ‪CDF‬؟ ‪Geo-AS03-41-860180‬‬ ‫‪ (H‬ﺍﳌﺴﺘﻮ￯ ‪ABE‬‬ ‫‪ (F‬ﺍﳌﺴﺘﻮ￯ ‪BEF‬‬ ‫‪ (J‬ﺍﳌﺴﺘﻮ￯ ‪ABC‬‬ ‫‪ (G‬ﺍﳌﺴﺘﻮ￯ ‪HIJ‬‬ ‫‪17‬‬ ‫‪p‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ 5-3‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪28‬‬ ‫‪q‬‬ ‫‪54131190‬‬ ‫‪r‬‬ ‫ﺍﺫﻛﺮ ﺍﻻﺳﻢ ﺍﻟﺨﺎﺹ ﻟﺰﻭﺝ ﺍﻟﺰﻭﺍﻳﺎ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ‪: 4, 3‬‬ ‫‪6 12‬‬ ‫‪∠2 (3‬ﻭ‪∠4‬‬ ‫‪s‬‬ ‫‪ (C‬ﻣﺘﻨﺎﻇﺮﺗﺎﻥ‪.‬‬ ‫‪ (A‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹼﹰﻴﺎ‪.‬‬ ‫‪ (D‬ﻣﺘﺤﺎﻟﻔﺘﺎﻥ‪.‬‬ ‫‪ (B‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹰﹼﻴﺎ‪.‬‬ ‫‪ (H‬ﻣﺘﻨﺎﻇﺮﺗﺎﻥ‪Geo-AS03-40-86018.0‬‬ ‫‪∠3 (4‬ﻭ ‪∠12‬‬ ‫‪ (J‬ﻣﺘﺤﺎﻟﻔﺘﺎﻥ‪.‬‬ ‫‪ (F‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹰﹼﻴﺎ‪.‬‬ ‫‪ (G‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹰﹼﻴﺎ‪.‬‬ ‫‪ (5‬ﺇﺫﺍ ﻛﺎﻥ‪ p r :‬ﻭ ‪ ،m∠8 = 119°‬ﻓﺄﻭﺟﺪ ‪.m∠11‬‬ ‫‪151° (D‬‬ ‫‪119° (C‬‬ ‫‪61° (B‬‬ ‫‪29° (A‬‬ ‫‪________________(6‬‬ ‫‪(4x - 6)°‬‬ ‫‪‬‬ ‫‪(5y + 11)°‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪(3x + 22)°‬‬ ‫‪ (6‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﻛ ﱟﻞ ﻣﻦ ‪ x, y‬ﰲ ﺍﻟﺸﻜﻞ ﺍﳌﺠﺎﻭﺭ‪.‬‬ ‫‪qt‬‬ ‫ﻫﻞ ﻳﻤﻜﻦ ﺇﺛﺒﺎﺕ ﺃﻥ ﺃ ﹼﹰﻳﺎ ﻣﻦ ﻣﺴﺘﻘﻴﲈﺕ ﺍﻟﺸﻜﻞ ﺍﻵﰐ ﻣﺘﻮﺍﺯﻳ ﹰﺔ‪،‬‬ ‫ﺍﻋﺘﲈ ﹰﺩﺍ ﻋﲆ ﺍﳌﻌﻄﻴﺎﺕ ﰲ ﻛ ﱟﻞ ﳑﺎ ﻳﺄﰐ؟ ﻭﺇﺫﺍ ﻛﺎﻧﺖ ﻣﺘﻮﺍﺯﻳ ﹰﺔ‪،‬‬ ‫‪Geo-1AS2303-642-860r 180‬‬ ‫ﻓﺎﺫﻛﺮ ﺍﻟﻤﺴﻠﻤﺔ ﺃﻭ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﺗﺒ ﱢﺮﺭ ﺇﺟﺎﺑﺘﻚ‪.‬‬ ‫‪________________(7‬‬ ‫‪4 56 s‬‬ ‫‪∠3 ∠4 (7‬‬ ‫‪∠3 ∠6 (8‬‬ ‫‪________________(8‬‬ ‫‪m ∠ 2 + m ∠ 6 = 180° (9‬‬ ‫‪________________(9 Geo-AS03-46-860180‬‬ ‫‪ ‬‬ ‫‪2‬‬ ‫‪32‬‬

‫‪‬‬ ‫‪‬‬ ‫‪  2‬‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﺤﺎﻟﻔﺘﺎﻥ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹰﹼﻴﺎ‬ ‫ﺍﳌﺴﺘﻮﻳﺎﻥ ﺍﳌﺘﻮﺍﺯﻳﺎﻥ‬ ‫ﺍﳌﺴﺘﻘﻴﲈﻥ ﺍﳌﺘﻮﺍﺯﻳﺎﻥ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﳌﺘﻨﺎﻇﺮﺗﺎﻥ‬ ‫ﺍﳌﺴﺘﻘﻴﲈﻥ ﺍﳌﺘﺨﺎﻟﻔﺎﻥ‬ ‫ﻣﻌﺪﻝ ﺍﻟﺘﻐﲑ‬ ‫ﺻﻴﻐﺔ ﺍﳌﻴﻞ ﻭﻧﻘﻄﺔ‬ ‫ﺻﻴﻐﺔ ﺍﳌﻴﻞ ﻭﺍﳌﻘﻄﻊ‬ ‫ﺍﳌﻴﻞ‬ ‫ﺍﻟﻘﺎﻃﻊ‬ ‫‪r‬‬ ‫‪12‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ ،1-4‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪ ،‬ﻭﺣ ﹼﺪﺩ ﻣﺎ ﺇﺫﺍ‬ ‫‪43‬‬ ‫ﻛﺎﻧﺖ ﻛ ﹼﻞ ﺟﻤﻠﺔ ﻣﻤﺎ ﻳﺄﺗﻲ ﺻﺤﻴﺤﺔ ﺃﻡ ﺧﺎﻃﺌ ﹰﺔ‪ ،‬ﻭﺇﺫﺍ ﻛﺎﻧﺖ ﺧﺎﻃﺌ ﹰﺔ‪،‬‬ ‫‪65‬‬ ‫‪t‬‬ ‫‪78‬‬ ‫ﻓﻐ ﹼﻴﺮ ﻣﺎ ﺗﺤﺘﻪ ﺧﻂ ﻟﺘﺠﻌﻠﻬﺎ ﺻﺤﻴﺤ ﹰﺔ‪:‬‬ ‫‪________________(1‬‬ ‫‪p‬‬ ‫‪ ∠4 (1‬ﻭ ‪ ∠5‬ﺯﺍﻭﻳﺘﺎﻥ ﻣﺘﻨﺎﻇﺮﺗﺎﻥ‪.‬‬ ‫‪________________(2‬‬ ‫ﻓﺈﻥ‪0‬ﺍﻟ‪8‬ﻤ‪1‬ﺴﺘ‪0‬ﻘﻴ‪6‬ﻢ‪ r8‬ﻳ‪-‬ﻮﺍ‪2‬ﺯ‪3‬ﻱ ﺍ‪-‬ﻟﻤ‪3‬ﺴ‪0‬ﺘﻘ‪S‬ﻴﻢ‪Geo-t A‬‬ ‫ﺍﻟﻤﺘﻮﺍﺯﻳﺎﻥ\"‪،‬‬ ‫\"ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ‬ ‫ﻣﺴ ﹼﻠﻤﺔ‬ ‫ﺑﻨﺎ ﹰﺀ ﻋﻠﻰ‬ ‫‪(2‬‬ ‫‪.∠ 3‬‬ ‫ﺇﺫﺍ ﻛﺎﻧﺖ‬ ‫‪∠8‬‬ ‫‪________________(3‬‬ ‫‪ (3‬ﺇﺫﺍ ﻛﺎﻥ ‪، r t‬ﻓﺈﻥ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺤﺎﻟﻔﺘﲔ ‪∠4‬ﻭ ‪∠6‬ﻣﺘﻜﺎﻣﻠﺘﺎﻥ‪.‬‬ ‫‪________________(4‬‬ ‫‪ (4‬ﺍﻟﻤﺴﺘﻘﻴﻢ ‪ p‬ﻗﺎﻃﻊ ﻷ ﹼﻧﻪ ﻳﻘﻄﻊ ﻣﺴﺘﻘﻴﻤﻴﻦ ﺃﻭ ﺃﻛﺜﺮ ﻓﻲ ﺍﻟﻤﺴﺘﻮ￯ ﻓﻲ ﻧﻘﺎ ﹴﻁ ﻣﺨﺘﻠﻔ ﹴﺔ‪.‬‬ ‫‪________________(5‬‬ ‫ﺍﺧﺘﺮ ﺍﻟﻤﻔﺮﺩﺓ ﺍﻟﻤﻨﺎﺳﺒﺔ ﺍﻟﺘﻲ ﺗﺠﻌﻞ ﺍﻟﺠﻤﻠﺔ ﻓﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 5‬ﹶﻭ ‪ 6‬ﺻﺤﻴﺤ ﹰﺔ‪:‬‬ ‫‪________________(6‬‬ ‫‪ (5‬ﻋﻨﺪ ﻛﺘﺎﺑﺔ ﻣﻌﺎﺩﻟﺔ ﻣﺴﺘﻘﻴ ﹴﻢ ﺑﺼﻴﻐﺔ ‪ ،y = mx + b‬ﺗﻤﺜﻞ ‪m‬‬ ‫)ﻗﺎﻃﻊ‪ ،‬ﻣﻴﻞ( ﺍﻟﻤﺴﺘﻘﻴﻢ ﻭ ‪ b‬ﻣﻘﻄﻊ ﺍﻟﻤﺤﻮﺭ ‪.y‬‬ ‫‪ (6‬ﺗﻘﻊ )ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﻟﻤﺘﻨﺎﻇﺮﺗﺎﻥ‪ ،‬ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﻟﻤﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹼﹰﻴﺎ( ﺑﻴﻦ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻳﻘﻄﻌﻬﻤﺎ ﻗﺎﻃﻊ‪.‬‬ ‫‪________________(7‬‬ ‫ﺃﻛﻤﻞ ﻛ ﹰﹼﻼ ﻣﻦ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻵﺗﻴﺔ ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﻤﻔﺮﺩﺓ ﺍﻟﻤﻨﺎﺳﺒﺔ ﻣﻦ ﺍﻟﻤﺴﺘﻄﻴﻞ ﺃﻋﻼﻩ ‪.‬‬ ‫‪________________(8‬‬ ‫‪ (7‬ﺍﳌﻌﺎﺩﻟﺔ‪ y + 6 = - _85_(x - 5) :‬ﹸﻛﺘﺒﺖ ﺑ ﹺـ _____؟_____‬ ‫‪________________(9‬‬ ‫‪ (8‬ﺇﺫﺍ ﹸﻗﻄﻊ ___؟______ ﺑﻘﺎﻃ ﹴﻊ‪ ،‬ﻓﺈﻥ ﻛ ﹼﻞ ﺯﺍﻭﻳﺘﲔ ﻣﺘﺒﺎﺩﻟﺘﲔ ﺩﺍﺧﻠ ﹰﹼﻴﺎ ﺗﻜﻮﻧﺎﻥ ﻣﺘﻄﺎﺑﻘﺘﲔ‪.‬‬ ‫‪________________(10‬‬ ‫‪____ (9‬؟_____ ﻳﺼﻒ ﻛﻴﻒ ﺗﺘﻐﲑ ﻛﻤﻴ ﹲﺔ ﻣﺎ ﻣﻊ ﺍﻟﺰﻣﻦ‪.‬‬ ‫‪2‬‬ ‫‪ (10‬ﺍﳌﺴﺘﻘﻴﲈﻥ ﻏﲑ ﺍﳌﺘﻘﺎﻃﻌﲔ ﺍﻟﻠﺬﺍﻥ ﻻ ﻳﻘﻌﺎﻥ ﰲ ﻣﺴﺘ ﹰﻮ￯ ﻭﺍﺣ ﹴﺪ ﹸﻳﺴ ﱠﻤﻴﺎﻥ _____؟____‪.‬‬ ‫‪33 ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(1)     2‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ ،3-1‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪C .‬‬ ‫‪__________(1‬‬ ‫‪B FD‬‬ ‫‪ (1‬ﻋ ﹼﻴﻦ ﺍﻟﻤﺴﺘﻮ￯ ﺍﻟﺬﻱ ﻳﻮﺍﺯﻱ ﺍﻟﻤﺴﺘﻮ￯ ‪.BCD‬‬ ‫‪__________(2‬‬ ‫‪__________(3‬‬ ‫‪ (C‬ﺍﳌﺴﺘﻮ￯ ‪AEF‬‬ ‫‪ (A‬ﺍﳌﺴﺘﻮ￯ ‪ABE‬‬ ‫‪ (D‬ﺍﳌﺴﺘﻮ￯ ‪A E DEF‬‬ ‫‪ (B‬ﺍﳌﺴﺘﻮ￯ ‪ABF‬‬ ‫‪__________(4‬‬ ‫‪__________(5‬‬ ‫‪Geo-AS03-01-860180‬‬ ‫‪ (2‬ﺃ ﱡﻱ ﻗﻄﻌ ﹴﺔ ﻣﺴﺘﻘﻴﻤ ﹴﺔ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﺗﻮﺍﺯﻱ ‪CD‬؟‬ ‫‪__________(6‬‬ ‫‪__________(7‬‬ ‫‪EF (J‬‬ ‫‪BC (H‬‬ ‫‪AE (G‬‬ ‫‪AB (F‬‬ ‫‪__________(8‬‬ ‫‪__________(9‬‬ ‫‪ (3‬ﺃﻱ ﻗﻄﻌ ﹴﺔ ﻣﺴﺘﻘﻴﻤ ﹴﺔ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﺗﺨﺎﻟﻒ ‪DE‬؟‬ ‫‪_________(10‬‬ ‫‪CD (D‬‬ ‫‪BD (C‬‬ ‫‪BC (B‬‬ ‫‪AB (A‬‬ ‫‪a‬‬ ‫‪12‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ ،4-7‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪34‬‬ ‫ﺣ ﹼﺪﺩ ﺍﻻﺳﻢ ﺍﻟﺨﺎﺹ ﻟﺰﻭﺝ ﺍﻟﺰﻭﺍﻳﺎ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 4‬ﻭ‪: 5‬‬ ‫‪b‬‬ ‫‪56‬‬ ‫‪∠1 (4‬ﻭ ‪∠8‬‬ ‫‪78‬‬ ‫ﻣﻣﺘﺘﻨﺤﺎﺎ‪0‬ﻟﻇ‪8‬ﻔﺮﺘﺗ‪1‬ﺎﺎ‪0‬ﻥﻥ‪Geo-AS03-02-86..‬‬ ‫‪(H‬‬ ‫‪ (F‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹰﹼﻴﺎ‪.‬‬ ‫‪(J‬‬ ‫‪ (G‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪.‬‬ ‫‪ ∠3 (5‬ﻭ‪∠7‬‬ ‫‪ (C‬ﻣﺘﺤﺎﻟﻔﺘﺎﻥ‪.‬‬ ‫‪ (A‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹼﹰﻴﺎ‪.‬‬ ‫‪ (D‬ﻣﺘﻨﺎﻇﺮﺗﺎﻥ‬ ‫‪ (B‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹰﹼﻴﺎ‪.‬‬ ‫‪ (6‬ﺇﺫﺍ ﻛﺎﻥ‪ a b :‬ﹶﻭ ‪ ،m∠2 = 65°‬ﻓﺄﻭﺟﺪ ‪.m∠6‬‬ ‫‪140° (J‬‬ ‫‪115° (H‬‬ ‫‪65° (G‬‬ ‫‪25° (F‬‬ ‫‪ (7‬ﺇﺫﺍ ﻛﺎﻥ‪ a b :‬ﹶﻭ ‪ m∠3 = (5 x + 10)°‬ﹶﻭ ‪ ،m∠5 = (3x + 10)°‬ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪.x‬‬ ‫‪2.5 (D‬‬ ‫‪20 (C‬‬ ‫‪70 (B‬‬ ‫‪110 (A‬‬ ‫‪3645 p‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ 8-10‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪m‬‬ ‫‪1827‬‬ ‫‪ (8‬ﺃﻱ ﻋﻼﻗﺎﺕ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻵﺗﻴﺔ ﺗﺒ ﹼﺮﺭ ﺃﻥ ‪ m‬؟‬ ‫‪∠4 ∠5 (H‬‬ ‫‪∠1 ∠7 (F‬‬ ‫‪∠6 ∠8 (J‬‬ ‫‪∠3 ∠4 (G‬‬ ‫‪ (9‬ﺇﺫﺍ ﻛﺎﻥ‪ m∠2 = (6 x + 8)° :‬ﻭ ‪ ،m∠6 = (8x - 6)°‬ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪ x‬ﺑﺤﻴﺚ ﻳﻜﻮﻥ ‪. m‬‬ ‫‪Geo-AS03-0314-(8D60180‬‬ ‫‪7 (C‬‬ ‫‪1 (B -7 (A‬‬ ‫‪ (10‬ﺇﺫﺍ ﻛﺎﻥ‪ ،m∠6 + m∠7 = 180° :‬ﻓﺄ ﹼﻱ ﻣﺴ ﹼﻠﻤﺔ ﺃﻭ ﻧﻈﺮ ﹼﻳﺔ ﺗﺜﺒﺖ ﺃﻥ ‪ m‬؟‬ ‫‪ (H‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺒﺎﺩﻟﺘﲔ ﺧﺎﺭﺟ ﹰﹼﻴﺎ‪.‬‬ ‫‪ (F‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺤﺎﻟﻔﺘﲔ‪.‬‬ ‫‪ (J‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺒﺎﺩﻟﺘﲔ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪.‬‬ ‫‪ (G‬ﻣﺴ ﹼﻠﻤﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﻨﺎﻇﺮﺗﲔ‪.‬‬ ‫‪2‬‬ ‫‪34‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(‬‬ ‫‪(1)    ‬‬ ‫‪2‬‬ ‫‪_________(11‬‬ ‫ﻋ ﹼﻴﻦ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ ﺍﻟﻤﺤ ﹼﺪﺩﺗﻴﻦ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 11‬ﻭ‪. 12‬‬ ‫‪_________(12‬‬ ‫‪_________(13‬‬ ‫‪A(0,5), B(5,0) (11‬‬ ‫‪_________(14‬‬ ‫‪_________(15‬‬ ‫‪5 (D 1 (C 0 (B -1 (A‬‬ ‫‪_________(16‬‬ ‫‪_________(17‬‬ ‫‪F(-2 ,-4) ,G(1 ,2) (12‬‬ ‫‪_________(18‬‬ ‫‪2 (D‬‬ ‫_‪_1‬‬ ‫‪(C‬‬ ‫‪-‬‬ ‫‪_1‬‬ ‫‪(B‬‬ ‫‪-2 (A‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪ (13‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ،A(1, 7), B(8, 4), C(3, 10) :‬ﻓﻤﺎ ﺇﺣﺪﺍﺛ ﹼﻴﺎﺕ ‪ D‬ﺍﻟﺘﻲ ﺗﺠﻌﻞ ‪ AB‬ﺗﻮﺍﺯﻱ ‪ CD‬؟‬ ‫‪D(10, 13) (D‬‬ ‫‪D(10, 7) (C‬‬ ‫‪D(6, 17) (B‬‬ ‫‪D(0, 17) (A‬‬ ‫‪ (14‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ،A(-1, 4), B(2, -5), C(3, 4) :‬ﻓﻤﺎ ﺇﺣﺪﺍﺛ ﹼﻴﺎﺕ ‪ D‬ﺍﻟﺘﻲ ﺗﺠﻌﻞ ‪ AB‬ﺗﻌﺎﻣﺪ ‪ CD‬؟‬ ‫‪D(6, 3) (D‬‬ ‫‪D(5, -2) (C‬‬ ‫‪D(0, 3) (B‬‬ ‫‪D(0, 5) (A‬‬ ‫‪ (15‬ﻣﺎ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻣﻴﻠﻪ ‪ ، 4‬ﻭﻣﻘﻄﻊ ﺍﻟﻤﺤﻮﺭ ‪ y‬ﻳﺴﺎﻭﻱ ‪-3‬؟‬ ‫‪y‬‬ ‫=‬ ‫‪4x‬‬ ‫‪-‬‬ ‫‪_3‬‬ ‫‪(D‬‬ ‫‪y =4x – 3 (C‬‬ ‫‪y‬‬ ‫=‬ ‫‪-3x‬‬ ‫‪+‬‬ ‫‪_3‬‬ ‫‪(B‬‬ ‫‪y = -3x + 4 (A‬‬ ‫‪4‬‬ ‫‪4‬‬ ‫‪ (16‬ﻣﺎ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻣﻴﻠﻪ ‪ ، 2‬ﻭﻳﻤ ﹼﺮ ﺑﺎﻟﻨﻘﻄﺔ )‪(3, 1‬؟‬ ‫‪y – 3 = 2(x – 1) (C‬‬ ‫‪y – 1 = 2(x – 3) (A‬‬ ‫‪y – 3 = (x – 2) (D‬‬ ‫‪y + 1 = 2(x + 3) (B‬‬ ‫‪ (17‬ﺍﺷﱰﻙ ﻳﺎ ﹲﴎ ﰲ ﻣﺮﻛ ﹴﺰ ﺭﻳﺎ ﱟﴈ‪ ،‬ﻓﺪﻓﻊ ‪ 480‬ﺭﻳﺎ ﹰﻻ ﺭﺳﻢ ﺍﺷﱰﺍ ﹴﻙ ﺳﻨﻮ ﱟﻱ‪.‬‬ ‫ﻭﺑﺎﻹﺿﺎﻓﺔﺇﱃ ﺫﻟﻚ ﻳﻜ ﱢﻠﻔﺔ ﺗﻌ ﹼﻠﻢ ﺍﻟﺴﺒﺎﺣﺔ ‪ 20‬ﺭﻳﺎ ﹰﻻ ﻟﻠﺪﺭﺱ ﺍﻟﻮﺍﺣﺪ‪،‬‬ ‫ﻓﲈ ﺍﳌﻌﺎﺩﻟﺔ ﺍﻟﺘﻲ ﲤ ﹼﺜﻞ ﺍﻟﺘﻜﻠﻔﺔ ﺍﻟﻜﻠ ﹼﻴﺔ ﺍﻟﺴﻨﻮﻳﺔ ‪ C‬ﳊﻀﻮﺭ ﻣﻦ ﺩﺭﻭﺱ ﺍﻟﺴﺒﺎﺣﺔ؟‬ ‫‪C = 20 - 480 (C‬‬ ‫‪C = 20 (A‬‬ ‫‪C = 20( + 120) (D‬‬ ‫‪C = 20ℓ + 480 (B‬‬ ‫‪yn‬‬ ‫‪ (18‬ﻣﺎ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ P‬ﻭﺍﻟﻤﺴﺘﻘﻴﻢ ‪ n‬ﻓﻲ ﺍﻟﺘﻤﺜﻴﻞ ﺍﻟﺒﻴﺎﻧﻲ ﺍﻟﻤﺠﺎﻭﺭ؟‬ ‫‪P‬‬ ‫‪2 (C‬‬ ‫‪-2 (A‬‬ ‫‪√2 (D‬‬ ‫‪1 (B‬‬ ‫‪Ox‬‬ ‫‪_________(19‬‬ ‫ﺃﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ﺍﻟﻤﺘﻮﺍﺯﻳﻴﻦ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ‪20, 19‬‬ ‫‪_________(20‬‬ ‫‪2‬‬ ‫‪y = 4 (19‬‬ ‫‪y=6‬‬ ‫‪10 (D‬‬ ‫‪6 (C 4 (B 2 (A‬‬ ‫‪2 (D‬‬ ‫‪y = x (20‬‬ ‫‪y=x+2‬‬ ‫‪√2 (C‬‬ ‫‪1.5 (B‬‬ ‫‪1 (A‬‬ ‫‪35 ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(2A)     2‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪RS‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ ، 2، 1‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪__________(1‬‬ ‫‪Q‬‬ ‫‪P‬‬ ‫‪ (1‬ﻋ ﹼﻴﻦ ﺍﻟﻤﺴﺘﻮ￯ ﺍﻟﻤﻮﺍﺯﻱ ﻟﻠﻤﺴﺘﻮ￯ ‪.PQT‬‬ ‫‪__________(2‬‬ ‫‪V‬‬ ‫‪ (A‬ﺍﳌﺴﺘﻮ￯ ‪PQS‬‬ ‫‪ (C‬ﺍﳌﺴﺘﻮ￯ ‪W RSV‬‬ ‫‪ (B‬ﺍﳌﺴﺘﻮ￯ ‪PTS‬‬ ‫‪__________(3‬‬ ‫‪__________(4‬‬ ‫‪ (D‬ﺍﳌﺴﺘﻮ￯ ‪TUW‬‬ ‫‪__________(5‬‬ ‫‪__________(6‬‬ ‫‪UT‬‬ ‫‪ (2‬ﺃ ﹼﻱ ﺍﻟﻘﻄﻊ ﺍﻟﻤﺴﺘﻘﻴﻤﺔ ﺍﻵﺗﻴﺔ ﺗﺨﺎﻟﻒ ‪ RV‬؟‬ ‫‪__________(7‬‬ ‫‪__________(8‬‬ ‫‪GeoS-P (AJS03-05-860S1W80(H‬‬ ‫‪RQ (G‬‬ ‫‪RS (F‬‬ ‫‪__________(9‬‬ ‫‪_________(10‬‬ ‫‪r‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ ، 3- 10‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪4‬‬ ‫‪3‬‬ ‫ﺣ ﹼﺪﺩ ﺍﻻﺳﻢ ﺍﻟﺨﺎﺹ ﻟﺰﻭﺝ ﺍﻟﺰﻭﺍﻳﺎ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 3‬ﻭ‪:4‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪ ∠3 (3‬ﻭ‪∠10‬‬ ‫‪8‬‬ ‫‪7‬‬ ‫‪s 9 10‬‬ ‫‪13 14‬‬ ‫‪ (C‬ﻣﺘﺤﺎﻟﻔﺘﺎﻥ‪.‬‬ ‫‪ (A‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹰﹼﻴﺎ‪.‬‬ ‫‪12 1p1‬‬ ‫‪16 15‬‬ ‫‪ (D‬ﻣﺘﻨﺎﻇﺮﺗﺎﻥ‪.‬‬ ‫‪ (B‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹰﹼﻴﺎ‪.‬‬ ‫‪q‬‬ ‫‪Geo-AS03-06-860180‬‬ ‫‪ ∠9 (4‬ﻭ‪∠13‬‬ ‫‪ (H‬ﻣﺘﺤﺎﻟﻔﺘﺎﻥ‪.‬‬ ‫‪ (F‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹼﹰﻴﺎ‪.‬‬ ‫‪ (J‬ﻣﺘﻨﺎﻇﺮﺗﺎﻥ‪.‬‬ ‫‪ (G‬ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪.‬‬ ‫‪ (5‬ﺇﺫﺍ ﻛﺎﻥ‪ p q :‬ﹶﻭ ‪ ،m∠3 = 75°‬ﻓﺈﻥ ‪ m∠5‬ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪120° (D‬‬ ‫‪105° (C‬‬ ‫‪75° (B‬‬ ‫‪15° (A‬‬ ‫‪ (6‬ﺇﺫﺍ ﻛﺎﻥ‪ p q :‬ﹶﻭ ‪ m∠10 = (3x - 7)°‬ﻭ ‪ ،m∠13 = (4x - 9)°‬ﻓﺈﻥ ﻗﻴﻤﺔ ‪ x‬ﺗﺴﺎﻭﻱ‪:‬‬ ‫‪28 (J 16 (H 2 (G -2 (F‬‬ ‫‪ (7‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ،∠1 ∠5‬ﻓﺄﻱ ﻣﺴ ﹼﻠﻤ ﹴﺔ ﺃﻭ ﻧﻈﺮ ﹼﻳ ﹴﺔ ﺗﺒ ﹼﺮﺭ ﺃﻥ ‪ p q‬؟‬ ‫‪ (C‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺒﺎﺩﻟﺘﲔ ﺧﺎﺭﺟ ﹰﹼﻴﺎ‪.‬‬ ‫‪ (A‬ﻣﺴ ﹼﻠﻤﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﻨﺎﻇﺮﺗﲔ‪.‬‬ ‫‪ (D‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺒﺎﺩﻟﺘﲔ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪.‬‬ ‫‪ (B‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺤﺎﻟﻔﺘﲔ‪.‬‬ ‫‪ (8‬ﺇﺫﺍ ﻛﺎﻧﺖ ‪ ،∠12 ∠14‬ﻓﺄﻱ ﻣﺴ ﹼﻠﻤ ﹴﺔ ﺃﻭ ﻧﻈﺮ ﹼﻳ ﹴﺔ ﺗﺒ ﹼﺮﺭ ﺃﻥ ‪ p q‬؟‬ ‫‪ (H‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺒﺎﺩﻟﺘﲔ ﺧﺎﺭﺟ ﹰﹼﻴﺎ‪.‬‬ ‫‪ (F‬ﻣﺴ ﹼﻠﻤﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﻨﺎﻇﺮﺗﲔ‪.‬‬ ‫‪ (J‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺒﺎﺩﻟﺘﲔ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪.‬‬ ‫‪ (G‬ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﲔ ﺍﳌﺘﺤﺎﻟﻔﺘﲔ‪.‬‬ ‫‪ (9‬ﺇﺫﺍ ﻛﺎﻥ ‪ p q‬ﻭﻓﻖ ﻧﻈﺮ ﹼﻳﺔ ﺍﻟﺰﺍﻭﻳﺘﻴﻦ ﺍﻟﻤﺘﺤﺎﻟﻔﺘﻴﻦ‪ ،‬ﻓﺄﻱ ﺯﺍﻭﻳﺘﻴﻦ ﻳﺘﻌ ﹼﻴﻦ ﺃﻥ ﺗﻜﻮﻧﺎ ﻣﺘﻜﺎﻣﻠﺘﻴﻦ؟‬ ‫‪ ∠15 (D‬ﹶﻭ ‪∠16‬‬ ‫‪ ∠8 (C‬ﹶﻭ ‪∠ 13‬‬ ‫‪ ∠3 (B‬ﹶﻭ ‪∠8‬‬ ‫‪ ∠10 (A‬ﹶﻭ ‪∠3‬‬ ‫‪ (10‬ﺇﺫﺍ ﻛﺎﻥ‪ ، m∠8 = (5x + 18)°, m∠4 = (7x – 20)° :‬ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪ x‬ﺣﺘﻰ ﻳﻜﻮﻥ ‪.p q‬‬ ‫‪19 (J‬‬ ‫‪1 (H‬‬ ‫‪-1 (G‬‬ ‫‪219 (F‬‬ ‫‪2‬‬ ‫‪36‬‬ ‫‪‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(‬‬ ‫‪(2A)    ‬‬ ‫‪2‬‬ ‫‪_________(11‬‬ ‫ﺃﻭﺟﺪ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎ ﹼﺭ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ ﺍﻟﻤﺤ ﹼﺪﺩﺗﻴﻦ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ﺍﻵﺗﻴﻴﻦ‪:‬‬ ‫‪_________(12‬‬ ‫‪Q(12, 9), P(-6, 3) (11‬‬ ‫‪_________(13‬‬ ‫‪_________(14‬‬ ‫‪3 (D‬‬ ‫_‪_1‬‬ ‫‪(C‬‬ ‫‪-‬‬ ‫_‪_1‬‬ ‫‪(B‬‬ ‫‪-3 (A‬‬ ‫‪_________(15‬‬ ‫‪3‬‬ ‫‪3‬‬ ‫‪_________(16‬‬ ‫‪_________(17‬‬ ‫‪N(2, -11), M(-8, 14) (12‬‬ ‫‪_________(18‬‬ ‫_‪_5‬‬ ‫‪(J‬‬ ‫_‪_2‬‬ ‫‪(H‬‬ ‫‪-‬‬ ‫_‪_2‬‬ ‫‪(G‬‬ ‫‪-‬‬ ‫_‪_5‬‬ ‫‪(F‬‬ ‫‪_________(19‬‬ ‫‪2‬‬ ‫‪5‬‬ ‫‪5‬‬ ‫‪2‬‬ ‫‪_________(20‬‬ ‫‪ (13‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ،A(-1, 4), B(1, 5), C(-5, 3) :‬ﻓﻤﺎ ﺇﺣﺪﺍﺛ ﹼﻴﺎﺕ ‪ D‬ﺍﻟﺘﻲ ﺗﺠﻌﻞ ‪ AB‬ﺗﻮﺍﺯﻱ ‪CD‬؟‬ ‫‪D(-3, 4) (D‬‬ ‫‪D(-4, 5) (C‬‬ ‫‪D(-6, 1 ) (B‬‬ ‫‪D(-7, 4) (A‬‬ ‫‪ (14‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ،A(2, 3), B(8, 7), C(6, 1) :‬ﻓﻤﺎ ﺇﺣﺪﺍﺛ ﹼﻴﺎﺕ ‪ D‬ﺍﻟﺘﻲ ﺗﺠﻌﻞ ‪ AB‬ﺗﻌﺎﻣﺪ ‪CD‬؟‬ ‫‪D(9, 3) (J‬‬ ‫‪D(8, 4) (H‬‬ ‫‪D(4, 4 ) (G‬‬ ‫‪D(3, 3) (F‬‬ ‫‪(-4,‬؟‬ ‫)‪7‬‬ ‫ﺑﺎﻟﻨﻘﻄﺔ‬ ‫ﻭﻳﻤ ﹼﺮ‬ ‫_‪_1‬‬ ‫ﻣﻴﻠﻪ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻟﻤﺴﺘﻘﻴﻢ‬ ‫ﻣﻌﺎﺩﻟﺔ‬ ‫ﻣﺎ‬ ‫‪(15‬‬ ‫‪2‬‬ ‫‪y‬‬ ‫–‬ ‫‪7‬‬ ‫=‬ ‫‪-4x‬‬ ‫‪+‬‬ ‫_‪_1‬‬ ‫‪(C‬‬ ‫‪y‬‬ ‫–‬ ‫‪7‬‬ ‫=‬ ‫_‪_1‬‬ ‫‪(x‬‬ ‫‪+‬‬ ‫)‪4‬‬ ‫‪(A‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪y + 7 = _21(x + 4) (D‬‬ ‫‪y‬‬ ‫–‬ ‫‪7‬‬ ‫=‬ ‫_‪_1‬‬ ‫‪(x‬‬ ‫–‬ ‫)‪4‬‬ ‫‪(B‬‬ ‫‪2‬‬ ‫‪ (16‬ﻣﺎ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻣﻘﻄﻊ ﺍﻟﻤﺤﻮﺭ ‪ x‬ﻟﻪ ﻳﺴﺎﻭﻱ ‪ ،2‬ﻭﻣﻘﻄﻊ ﺍﻟﻤﺤﻮﺭ ‪ y‬ﻟﻪ ﻳﺴﺎﻭﻱ ‪12‬؟‬ ‫‪y = 12x + 2 (J‬‬ ‫‪y = 6x + 12 (H‬‬ ‫‪y = 2x + 12 (G y = -6x + 12 (F‬‬ ‫‪ (17‬ﻣﺎ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻳﻤﺮ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ )‪ (1, -3‬ﻭ)‪(7, 15‬؟‬ ‫‪y = 3x - 10 (D‬‬ ‫‪y = 3x – 6 (C‬‬ ‫‪y = 3x (B‬‬ ‫‪y = -3x + 8 (A‬‬ ‫‪ (18‬ﻳﻨﺎﻝ ﺧﺎﻟﺪ ‪ 4‬ﺩﺭﺟﺎ ﹴﺕ ﻋﻦ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﻣﻦ ‪ q‬ﻣﻦ ﺍﻷﺳﺌﻠﺔ ﻓﻲ ﺍﺧﺘﺒﺎﺭ ﺍﻟﺮﻳﺎﺿﻴﺎﺕ‪،‬‬ ‫ﻭ ‪ 5‬ﺩﺭﺟﺎﺕ ﻋﻦ ﺳﺆﺍﻝ ﺇﺿﺎﻓ ﱟﻲ ﻭﺍﺣ ﹴﺪ‪ ،‬ﺃ ﹼﻱ ﻣﻌﺎﺩﻟﺔ ﳑﹼﺎ ﻳﺄﰐ ﲤ ﹼﺜﻞ ﺍﳌﺠﻤﻮﻉ ﺍﻟﻜﲇ ‪T‬‬ ‫ﻟﻠﺪﺭﺟﺎﺕ ﺍﻟﺘﻲ ﻳﻤﻜﻨﻪ ﺃﻥ ﻳﻨﺎﳍﺎ ﰲ ﺍﻻﺧﺘﺒﺎﺭ؟‬ ‫‪4 T = q + 5 (I‬‬ ‫‪T = 4(q + 5) (H‬‬ ‫‪T = 4q + 5 (G‬‬ ‫‪T + 5 = 4q (F‬‬ ‫‪ (19‬ﻣﺎ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ D‬ﻭﺍﻟﻤﺴﺘﻘﻴﻢ ‪ t‬ﻓﻲ ﺍﻟﺘﻤﺜﻴﻞ ﺍﻟﺒﻴﺎﻧﻲ ﺍﻟﻤﺠﺎﻭﺭ؟ ‪y‬‬ ‫‪D‬‬ ‫‪O‬‬ ‫‪x‬‬ ‫‪5 (C‬‬ ‫‪2 √5 (A‬‬ ‫‪√5 (D‬‬ ‫‪3 (B‬‬ ‫‪t‬‬ ‫‪ (20‬ﻣﺎ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ﺍﻟﻤﺘﻮﺍﺯﻳﻴﻦ ﺍﻟﻠﺬﻳﻦ ﻣﻌﺎﺩﻟﺘﺎﻫﻤﺎ‪0y1=802x + 7 :‬ﹶﻭ‪Geo-AS0.3y-=027x-–836‬‬ ‫‪4 √2 (J‬‬ ‫‪2 √5 (H‬‬ ‫‪√5 (G‬‬ ‫‪√2 (F‬‬ ‫‪2‬‬ ‫‪37‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪(2B)    ‬‬ ‫‪‬‬ ‫‪______________(1‬‬ ‫‪2‬‬ ‫‪______________(2‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪______________(3‬‬ ‫‪______________(4‬‬ ‫‪ST‬‬ ‫ﻓﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 1‬ﻭ ‪ 2‬ﺣ ﱢﺪﺩ ﻛ ﹰﹼﻼ ﻣﻤﺎ ﻳﺄﺗﻲ ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪______________(5‬‬ ‫‪VU‬‬ ‫‪______________(6‬‬ ‫‪ (1‬ﺗﻘﺎﻃﻊ ﺍﻟﻤﺴﺘﻮ￯ ‪ SVX‬ﻭﺍﻟﻤﺴﺘﻮ￯ ‪. STU‬‬ ‫‪______________(7‬‬ ‫‪XW‬‬ ‫‪ (2‬ﻗﻄﻌﺔ ﻣﺴﺘﻘﻴﻤﺔ ﲣﺎﻟﻒ ‪. WY‬‬ ‫‪______________(8‬‬ ‫‪______________(9‬‬ ‫‪ZY‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ ، 3-7‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪______________(10‬‬ ‫ﻣ‪5‬ﺘ–ﺤﺎﻟ‪3‬ﻔﺇﺘﻟﻴﻰﻦ‪:‬ﺯﺍ‪0‬ﻭﻳ‪8‬ﺘﻴ‪1‬ﻦ‪0‬ﻣ‪6‬ﺘﺒ‪8‬ﺎﺩﻟ‪-‬ﺘﻴ‪1‬ﻦ‪1‬ﺩﺍ‪-‬ﺧ‪3‬ﻠ ﹼﹰﻴ‪0‬ﺎ‪Geo-AS،‬‬ ‫ﺍﻟﺰﻭﺍﻳﺎ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻷﺳﺌﻠﺔ‬ ‫ﺻ ﹼﻨﻒ ﺯﻭﺝ‬ ‫‪______________(11‬‬ ‫ﺧﺎﺭﺟ ﹰﹼﻴﺎ‪،‬ﺃﻭ ﻣﺘﻨﺎﻇﺮﺗﻴﻦ‪ ،‬ﺃﻭ‬ ‫ﺃﻭ ﻣﺘﺒﺎﺩﻟﺘﻴﻦ‬ ‫‪______________(12‬‬ ‫‪______________(13‬‬ ‫‪1423‬‬ ‫‪5‬‬ ‫‪6‬‬ ‫‪m‬‬ ‫‪ ∠ 2 (3‬ﻭ‪∠12‬‬ ‫‪______________(14‬‬ ‫‪8‬‬ ‫‪7‬‬ ‫‪n‬‬ ‫‪ ∠3 (4‬ﻭ‪∠5‬‬ ‫‪9121011s‬‬ ‫‪2‬‬ ‫‪13‬‬ ‫‪14‬‬ ‫‪16‬‬ ‫‪15‬‬ ‫‪t‬‬ ‫‪Geo-AS03-12-860180‬‬ ‫‪∠7 (5‬ﻭ‪∠15‬‬ ‫‪ (6‬ﺇﺫﺍ ﻛﺎﻥ‪ m n :‬ﹶﻭ ‪ ،m∠8 = 86°‬ﻓﺄﻭﺟﺪ ‪.m∠13‬‬ ‫‪ (7‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﻛ ﱟﻞ ﻣﻦ ‪ x‬ﻭ ‪ y‬ﺇﺫﺍ ﻛﺎﻥ‪، m∠4 = (6x – 5)° ,m n :‬‬ ‫‪.m∠9 = (3y – 10)° , m∠10 = (5x + 8)°‬‬ ‫ﺃﻭﺟﺪ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻳﻤﺮ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ ﺍﻟﻤﺤ ﹼﺪﺩﺗﻴﻦ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻷﺳﺌﻠﺔ ‪:8-10‬‬ ‫‪W(5, 5), V(-10, -4) (8‬‬ ‫‪C(2, -15), A(-2, 9) (9‬‬ ‫‪L(-3, 9), G(-6, 14) (10‬‬ ‫ﻓﻲ ﺍﻷﺳﺌﻠﺔ ‪ ،11 – 13‬ﺣ ﹼﺪﺩ ﻣﺎ ﺇﺫﺍ ﻛﺎﻥ ‪ CS‬ﹶﻭ ‪ KP‬ﻣﺘﻮﺍﺯﻳﻴﻦ ﺃﻭ ﻣﺘﻌﺎﻣﺪﻳﻦ‪ ،‬ﺃﻭ ﻏﻴﺮ ﺫﻟﻚ‪.‬‬ ‫‪P(6, -6), K(1, 9), S(5, 4),C(1,-12) (11‬‬ ‫‪P(1, 4), K(-2, 10), S(-3, 2), C(-5, 6) (12‬‬ ‫‪P(9, 7), K(3, 3), S(-3, -5), C(-6, -7) (13‬‬ ‫‪ (14‬ﻳﺘﻘﺎ ﹶﺿﻰ ﻣﻜﺘﺐ ﺧﺪﻣﺎﺕ ﻃﻼﺑﻴﺔ ﻣﺒﻠﻎ ‪ 5.5‬ﺭﻳﺎ ﹰﻻ ﻋﻦ ﻛ ﹼﻞ ﺻﻔﺤ ﹴﺔ‪،‬‬ ‫ﻋﻨﺪ ﻃﺒﻊ ﺗﻘﺮﻳ ﹴﺮ ﻋﺪﺩ ﺻﻔﺤﺎﺗﻪ ‪ ، p‬ﻣﻀﺎ ﹰﻓﺎ ﺇﻟﻰ ﺫﻟﻚ ‪ 12‬ﺭﻳﺎ ﹰﻻ ﻟﺘﺠﻠﻴﺪﻩ‪.‬‬ ‫ﺍﻛﺘﺐ ﻣﻌﺎﺩﻟ ﹰﺔ ﺗﻤ ﱢﺜﻞ ﺍﻟﺘﻜﻠﻔﺔ ﺍﻟﻜﻠﻴﺔ ‪ C‬ﻟﻄﺒﻊ ﻭﺗﺠﻠﻴﺪ ﺍﻟﺘﻘﺮﻳﺮ‪.‬‬ ‫ﻣﺎ ﺗﻜﻠﻔﺔ ﻃﺒﻊ ﻭﺗﺠﻠﻴﺪ ﺗﻘﺮﻳ ﹴﺮ ﻣﻜ ﹼﻮ ﹴﻥ ﻣﻦ ‪ 50‬ﺻﻔﺤ ﹰﺔ؟‬ ‫‪38  ‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(‬‬ ‫‪(2B)    ‬‬ ‫‪2‬‬ ‫ﺍﻛﺘﺐ ﺑﺼﻴﻐﺔ ﺍﻟﻤﻴﻞ ﻭﺍﻟﻤﻘﻄﻊ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻳﺤﻘﻖ ﺍﻟﺸﺮﻭﻁ ﺍﻟﻤﻌﻄﺎﺓ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻷﺳﺌﻠﺔ ‪.15-17‬‬ ‫‪_______________(15‬‬ ‫‪ ،m = -9 (15‬ﻭﻣﻘﻄﻊ ﺍﻟﻤﺤﻮﺭ ‪ y‬ﻳﺴﺎﻭﻱ ‪.3‬‬ ‫‪_______________(16‬‬ ‫‪ ،m = 3 (16‬ﻭﻳﻤ ﹼﺮ ﺑﺎﻟﻨﻘﻄﺔ )‪.(-1, 5‬‬ ‫‪_______________(17‬‬ ‫‪ (17‬ﻣﻘﻄﻊ ﺍﻟﻤﺤﻮﺭ ‪ x‬ﻳﺴﺎﻭﻱ ‪ ، 3‬ﻭﻣﻘﻄﻊ ﺍﻟﻤﺤﻮﺭ ‪ y‬ﻳﺴﺎﻭﻱ ‪-1‬‬ ‫‪_______________(18‬‬ ‫‪ (18‬ﺑﺪﺃﺕ ﻣﺠﻤﻮﻋﺔ ﻣﻦ ﺍﻟﻄﻼﺏ ﺗﻜﻮﻳﻦ ﻣﺠﻤﻮﻋ ﹴﺔ ﻟﻠﻤﺴﺎﻫﻤﺔ ﻓﻲ ﺍﻷﻧﺸﻄﺔ ﺍﻟﺘﻄﻮﻋﻴﺔ‪ ،‬ﻭﰲ ﺃﻭﻝ‬ ‫ﺍﺟﺘﲈ ﹴﻉ‪ ،‬ﺳ ﹼﺠﻞ ‪ 5‬ﻃﻼ ﹴﺏ‪ ،‬ﻭﺑﻌﺪ ‪ 12‬ﻳﻮ ﹰﻣﺎ ﻭﺻﻞ ﻋﺪﺩ ﺍﻟﻄﻼﺏ ﺇﱃ ‪ 23‬ﻃﺎﻟ ﹰﺒﺎ‪ .‬ﺇﺫﺍ ﻛﺎﻥ ﻋﺪﺩ ﺍﻟﻄﻼﺏ‬ ‫ﻳﺰﺩﺍﺩ ﺑﺎﳌﻌﺪﻝ ﻧﻔﺴﻪ‪ ،‬ﻓﻜﻢ ﺳﻴﻜﻮﻥ ﻋﺪﺩ ﺍﻟﻄﻼﺏ ﺑﻌﺪ ﺛﻼﺛﲔ ﻳﻮ ﹰﻣﺎ ﻣﻦ ﺍﻻﺟﺘﲈﻉ ﺍﻷﻭﻝ؟‬ ‫‪_______________(19‬‬ ‫‪AD‬‬ ‫ﺑﻨﺎ ﹰﺀ ﻋﻠﻰ ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﻤﻌﻄﺎﺓ ﻓﻲ ﺍﻷﺳﺌﻠﺔ ‪، 19–21‬‬ ‫‪_______________(20‬‬ ‫‪1‬‬ ‫ﻫﻞ ﻳﻤﻜﻦ ﺇﺛﺒﺎﺕ ﺃﻥ ﺃ ﹼﹰﻳﺎ ﻣﻦ ﻣﺴﺘﻘﻴﻤﺎﺕ ﺍﻟﺸﻜﻞ ﻣﺘﻮﺍﺯﻳﺔ‪ ،‬ﺍﻋﺘﻤﺎ ﹰﺩﺍ‬ ‫‪_______________(21‬‬ ‫‪B 2E‬‬ ‫‪_______________(22‬‬ ‫ﻋﻠﻰ ﺍﻟﻤﻌﻄﻴﺎﺕ ﻓﻲ ﺍﻷﺳﺌﻠﺔ ‪ ،19 - 21‬ﻭﺇﺫﺍ ﻛﺎﻥ ﺃ ﱡﻳﻬﺎ ﻣﺘﻮﺍﺯ ﹼﹰﻳﺎ‪،‬‬ ‫‪CF‬‬ ‫ﻓﺎﺫﻛﺮ ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﺃﻭ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺇﺟﺎﺑﺘﻚ‪.‬‬ ‫‪_______________(23‬‬ ‫‪_______________(24‬‬ ‫‪∠1 ∠2 (19‬‬ ‫‪_______________(25‬‬ ‫‪Geo-AS03-13-860180‬‬ ‫‪∠DAB ∠EBC (20‬‬ ‫‪m∠ ADE + m∠ BED = 180° (21‬‬ ‫‪(9x - 44)°‬‬ ‫‪ (22‬ﺃﻭﺟﺪ ﻣﻦ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ ﻗﻴﻤﺔ ‪ x‬ﺍﻟﺘﻲ ﺗﺠﻌﻞ ‪.a b‬‬ ‫‪a (6x + 10)°‬‬ ‫‪b‬‬ ‫ﺃﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ﺍﻟﻤﺘﻮﺍﺯﻳﻴﻦ ﻓﻲ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ‪. 23, 24‬‬ ‫‪Geo-AS03-14-860180‬‬ ‫‪y = x – 6 (23‬‬ ‫‪y=x+8‬‬ ‫‪y = -2x + 10 (24‬‬ ‫‪y = -2x – 5‬‬ ‫‪ (25‬ﺃﻧﺸﺊ ﻣﻦ ﺍﻟﻨﻘﻄﺔ )‪ B(-2,5‬ﻣﺴﺘﻘﻴ ﹰﻤﺎ ﻋﻤﻮﺩ ﹰﹼﻳﺎ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪،‬‬ ‫ﺛﻢ ﺃﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ B‬ﻭﺍﻟﻤﺴﺘﻘﻴﻢ ‪.‬‬ ‫‪2‬‬ ‫‪39‬‬ ‫‪ ‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(3)     2‬‬ ‫‪_______________(1‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪_______________(2‬‬ ‫‪ (1‬ﺍﺭﺳﻢ ﻣﻨﺸﻮ ﹰﺭﺍ ﺛﻼﺛ ﹰﹼﻴﺎ‪ ،‬ﻭﺳ ﹼﻢ ﺍﻟﻤﺴﺘﻮﻳﻴﻦ ﺍﻟﻤﺘﻮﺍﺯﻳﻴﻦ ‪.ABC, DEF‬‬ ‫‪_______________(3‬‬ ‫‪ (2‬ﻋ ﹼﻴﻦ ﻣﺴﺘﻮﻳﻴﻦ ﻣﺘﻘﺎﻃﻌﻴﻦ ﻓﻲ ﺍﻟﻤﻨﺸﻮﺭ ﺍﻟﺜﻼﺛﻲ ﺍﻟﺬﻱ ﺭﺳﻤﺘﻪ ﻓﻲ ﺍﻟﺴﺆﺍﻝ ‪ ،1‬ﻭﺳ ﹼﻢ ﺗﻘﺎﻃﻌﻬﻤﺎ‪.‬‬ ‫‪_______________(4‬‬ ‫‪_______________(5‬‬ ‫‪ (3‬ﺳ ﹼﻢ ﻣﺴﺘﻘﻴﻤﻴﻦ ﻣﺘﺨﺎﻟﻔﻴﻦ ﻓﻲ ﺍﻟﻤﻨﺸﻮﺭ ﺍﻟﺜﻼﺛﻲ ﺍﻟﺬﻱ ﺭﺳﻤﺘﻪ ﻓﻲ ﺍﻟﺴﺆﺍﻝ ‪.1‬‬ ‫‪_______________(6‬‬ ‫‪_______________(7‬‬ ‫‪f 2198‬‬ ‫ﺻ ﱢﻨﻒ‪ ،‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪ ،‬ﻛ ﹼﻞ ﺯﻭﺝ ﻣﻦ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻵﺗﻴﺔ ﺇﻟﻰ ﺯﺍﻭﻳﺘﻴﻦ‬ ‫ﻣﺘﺒﺎﺩﻟﺘﻴﻦ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪ ،‬ﺃﻭ ﻣﺘﺒﺎﺩﻟﺘﻴﻦ ﺧﺎﺭﺟ ﹼﹰﻴﺎ‪ ،‬ﺃﻭ ﻣﺘﻨﺎﻇﺮﺗﻴﻦ ‪ ،‬ﺃﻭ ﻣﺘﺤﺎﻟﻔﺘﻴﻦ‪.‬‬ ‫‪g 43105 611217‬‬ ‫‪∠9 (4‬ﻭ‪∠12‬‬ ‫‪∠2 (5‬ﻭ‪h ∠3‬‬ ‫‪Geo-AS03-24-860180‬‬ ‫‪∠4 (6‬ﻭ‪∠11‬‬ ‫‪12‬‬ ‫‪p‬‬ ‫‪ (7‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ‪،m∠8 = 30° , m∠9 = 110° :‬‬ ‫‪43‬‬ ‫ﻓﺄﻭﺟﺪ ‪m∠6‬‬ ‫‪12‬‬ ‫‪9 10‬‬ ‫‪q‬‬ ‫‪11‬‬ ‫‪8‬‬ ‫‪56‬‬ ‫‪7‬‬ ‫‪13‬‬ ‫‪r‬‬ ‫‪t‬‬ ‫‪s14‬‬ ‫‪_______________(8‬‬ ‫‪Geo-AS03-25-860180‬‬ ‫‪ (8‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﻛ ﱟﻞ ﻣﻦ ‪ z, y, x‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪(8x - 7)°‬‬ ‫‪(3x - 11)°‬‬ ‫‪(2y + 23)° (3z 2 - 5)°‬‬ ‫‪(4y + 8)°‬‬ ‫‪_______________(9‬‬ ‫ﺃﻭﺟﺪ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻳﻤ ﹼﺮ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ ﺍﻟﻤﺤ ﹼﺪﺩﺗﻴﻦ ﻓ‪0‬ﻲ‪8‬ﻛ‪1‬ﱟﻞ‪0‬ﻣ‪6‬ﻦ‪ 8‬ﺍﻟ‪-‬ﺴ‪6‬ﺆﺍ‪2‬ﻟﻴ‪-‬ﻦ‪ 093‬ﹶﻭ‪Geo-:1A0S‬‬ ‫‪______________(10‬‬ ‫‪F(12, 23), D(-6, -7) (9‬‬ ‫‪U(4, -2.5), V(-2, -0.25) (10‬‬ ‫‪______________(11‬‬ ‫ﺣ ﹼﺪﺩ ﻣﺎ ﺇﺫﺍ ﻛﺎﻥ ‪ RM , QV‬ﻣﺘﻮﺍﺯﻳﻴﻦ ﺃﻭ ﻣﺘﻌﺎﻣﺪﻳﻦ ﺃﻭ ﻏﻴﺮ ﺫﻟﻚ‪.‬‬ ‫‪Q(-3, -8), V(5, 12), R(-2.5, 1), M(-5, 2) (11‬‬ ‫‪______________(12‬‬ ‫‪2‬‬ ‫‪Q(-2, 4.5), V(4, 9), R(-4, -12), M(10, -1.5) (12‬‬ ‫‪40  ‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(‬‬ ‫‪(3)    ‬‬ ‫‪2‬‬ ‫‪______________(13‬‬ ‫‪ (13‬ﺗﺘﺤﺮﻙ ﺳﻴﺎﺭﺗﺎﻥ ﻓﻲ ﻃﺮﻳﻘﻴﻦ ﻣﺘﻌﺎﻣﺪﻳﻦ‪.‬‬ ‫ﻓﺈﺫﺍ ﺑﺪﺃﺕ ﺍﻟﺴﻴﺎﺭﺓ ﺍﻷﻭﱃ ﺍﳊﺮﻛﺔ ﻋﲆ ﺧﺮﻳﻄﺔ ﺇﺣﺪﺍﺛﻴﺔ ﻣﻦ ﺍﻟﻨﻘﻄﺔ )‪،(-5, -8‬‬ ‫ﺛﻢ ﺗﻮﻗﻔﺖ ﻋﻨﺪ ﺍﻟﻨﻘﻄﺔ )‪ ،(2, 7‬ﻭﺑﺪﺃﺕ ﺍﻟﺴﻴﺎﺭﺓ ﺍﻟﺜﺎﻧﻴﺔ ﻣﻦ ﺍﻟﻨﻘﻄﺔ )‪(-5, 1‬‬ ‫ﺛﻢ ﺗﻮﻗﻔﺖ ﻋﻨﺪ )‪ ،(10,y‬ﻓﲈ ﺍﻹﺣﺪﺍﺛﻲ ‪ y‬ﻟﻠﻤﻮﻗﻒ ﺍﻟﻨﻬﺎﺋﻲ ﻟﻠﺴﻴﺎﺭﺓ ﺍﻟﺜﺎﻧﻴﺔ؟‬ ‫‪______________(14‬‬ ‫‪ (14‬ﺍﻛﺘﺐ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎﺭ ﺑﺎﻟﻨﻘﻄﺔ )‪،(-4, -5‬‬ ‫‪______________(15‬‬ ‫ﻭﺍﻟﻌﻤﻮﺩﻱ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻣﻌﺎﺩﻟﺘﻪ ‪.3x – 4y = 9‬‬ ‫‪ (15‬ﺗﺘﻘﺎ ﹶﺿﻰ ﺷﺮﻛﺔ ﺗﺄﺟﻴﺮ ﺳﻴﺎﺭﺍﺕ ﻣﺒﻠﻎ ‪ 120‬ﺭﻳﺎ ﹰﻻ ﻓﻲ ﺍﻟﻴﻮﻡ ﻣﻀﺎ ﹰﻓﺎ ﺇﻟﻴﻬﺎ ‪ 1.2‬ﺭﻳـﺎﻝ‬ ‫ﻋﻦ ﻛ ﹼﻞ ﻛﻴﻠﻮﻣﺘﺮ ﺑﻌﺪ ﺍﻟﻤﺎﺋﺔ ﻣﻦ ‪ m‬ﻛﻴﻠﻮﻣﺘ ﹰﺮﺍ ﺗﻘﻄﻌﻬﺎ ﺍﻟﺴﻴﺎﺭﺓ‪ ،‬ﺍﻛﺘﺐ ﻣﻌﺎﺩﻟﺔ ﺗﻤﺜﻞ‬ ‫ﺍﻟﺘﻜﻠﻔﺔ ﺍﻟﻜﻠﻴﺔ ‪ C‬ﻻﺳﺘﺌﺠﺎﺭ ﺳﻴﺎﺭ ﹴﺓ ﻣﺪﺓ ‪ 5‬ﺃﻳﺎ ﹴﻡ‪ ،‬ﻭﻣﺎ ﺍﻟﻤﺒﻠﻎ ﺍﻟﻜﻠﻲ ﺍﻟﺬﻱ ﺳﻴﺪﻓﻌﻪ ﺳﻌﺪ‬ ‫ﺇﺫﺍ ﺍﺳﺘﺄﺟﺮ ﺳﻴﺎﺭﺓ ﻣﺪﺓ ‪ 5‬ﺃﻳﺎ ﹴﻡ ﻭﻗﺎﺩﻫﺎ ﻣﺴﺎﻓﺔ ‪255 km‬؟‬ ‫‪MNP‬‬ ‫ﻫﻞ ﻳﻤﻜﻦ ﺇﺛﺒﺎﺕ ﺃﻥ ﺃ ﹰﹼﻳﺎ ﻣﻦ ﻣﺴﺘﻘﻴﻤﺎﺕ ﺍﻟﺸﻜﻞ ﻣﺘﻮﺍﺯﻳﺔ‪ ،‬ﺍﻋﺘﻤﺎ ﹰﺩﺍ‬ ‫ﻋﻠﻰ ﺍﻟﻤﻌﻄﻴﺎﺕ ﻓﻲ ﺍﻷﺳﺌﻠﺔ ‪ ،16, 17‬ﻭﺇﺫﺍ ﻛﺎﻥ ﺃ ﱡﻳﻬﺎ ﻣﺘﻮﺍﺯ ﹰﹼﻳﺎ‪،‬‬ ‫‪______________(16‬‬ ‫‪R‬‬ ‫‪ST‬‬ ‫‪______________(17‬‬ ‫‪U‬‬ ‫‪V‬‬ ‫ﻓﺎﺫﻛﺮ ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﺃﻭ ﺍﻟﻨﻈﺮﻳﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺇﺟﺎﺑﺘﻚ‪.‬‬ ‫‪______________(18‬‬ ‫‪∠RNS ∠PSN (16‬‬ ‫‪______________(19‬‬ ‫‪Geo-AS03-27-860180‬‬ ‫‪.m∠MRS + m∠RSN = 180° (17‬‬ ‫‪(229 - 4x)°‬‬ ‫‪ (18‬ﺃﻭﺟﺪ ﻣﻦ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ ﻗﻴﻤﺔ ‪ x‬ﺍﻟﺘﻲ ﺗﺠﻌﻞ ‪.a b‬‬ ‫‪ab (6x - 13)°‬‬ ‫‪ (19‬ﺃﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ﺍﻟﻤﺘﻮﺍﺯﻳﻴﻦ ﺍﻟﻠﺬﻳﻦ ﻣﻌﺎﺩﻟﺘﻴﻬﻤﺎ‪:‬‬ ‫‪Geo-AS03-28-860180‬‬ ‫‪y‬‬ ‫=‬ ‫‪-‬‬ ‫‪_41_x‬‬ ‫‪+‬‬ ‫‪2‬‬ ‫‪,‬‬ ‫‪y‬‬ ‫=‬ ‫‪-‬‬ ‫‪_41_x‬‬ ‫‪-‬‬ ‫_‪_9‬‬ ‫‪4‬‬ ‫‪______________(20‬‬ ‫‪ (20‬ﻣ ﹼﺜﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪ m‬ﺍﻟﺬﻱ ﻣﻌﺎﺩﻟﺘﻪ ‪ -6x – 3y = 9‬ﺑﻴﺎﻧ ﹰﹼﻴﺎ‪،‬‬ ‫‪______________(21‬‬ ‫ﻭﺃﻧﺰﻝ ﻣﻦ ﺍﻟﻨﻘﻄﺔ )‪ P (3,1‬ﻋﻤﻮ ﹰﺩﺍ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪،m‬‬ ‫ﺛﻢ ﺃﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ ‪ P‬ﻭﺍﻟﻤﺴﺘﻘﻴﻢ ‪.m‬‬ ‫‪ (21‬ﺍﻓﺘﺮﺽ ﺃﻥ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪ p‬ﻋﻤﻮﺩﻱ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪ ،s‬ﻭﺃﻥ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪q‬‬ ‫ﻋﻤﻮﺩﻱ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪ ،s‬ﻓﻬﻞ ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ ‪ p‬ﹶﻭ ‪ q‬ﻣﺘﻮﺍﺯﻳﺎﻥ ﺩﺍﺋ ﹰﻤﺎ؟‬ ‫ﺍﺭﺳﻢ ﺷﻜ ﹰﻼ ﻳﻮ ﹼﺿﺢ ﺇﺟﺎﺑﺘﻚ‪.‬‬ ‫‪2‬‬ ‫‪41‬‬ ‫‪‬‬

‫‪‬‬ ‫‪‬‬ ‫‪      2‬‬ ‫ﹸﺣ ﹼﻞ ﻛ ﹼﻞ ﻣﺴﺄﻟ ﹴﺔ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﺑﺼﻮﺭ ﹴﺓ ﻭﺍﺿﺤ ﹴﺔ ﻭﺩﻗﻴﻘ ﹴﺔ ﻣﺴﺘﻌﻴ ﹰﻨﺎ ﺑﻤﻌﺮﻓﺘﻚ ﺍﻟﺴﺎﺑﻘﺔ‪ ،‬ﺛﻢ ﺗﺤ ﹼﻘﻖ ﻣﻦ ﺗﻀﻤﻴﻨﻚ ﺍﻟﺤﻞ ﺍﻟﺮﺳﻮﻡ ﻭﺍﻟﺘﺒﺮﻳﺮﺍﺕ ﺍﻟﻼﺯﻣﺔ‪،‬‬ ‫ﻛﻤﺎ ﻳﻤﻜﻨﻚ ﻋﺮﺽ ﺍﻟﺤ ﹼﻞ ﺑﺄﻛﺜﺮ ﻣﻦ ﻃﺮﻳﻘ ﹴﺔ‪ ،‬ﺃﻭ ﺃﻥ ﺗﺴﺘﻘﺼﻲ ﺃﻛﺜﺮ ﻣﻤﺎ ﻫﻮ ﻣﻄﻠﻮﺏ ﻓﻲ ﺍﻟﻤﺴﺄﻟﺔ‪) .‬ﺍﺳﺘﻌﻤﻞ ﻭﺭﻗ ﹰﺔ ﻣﻨﻔﺼﻠ ﹰﺔ‪ ،‬ﺇﺫﺍ ﻛﺎﻥ ﺫﻟﻚ‬ ‫ﺿﺮﻭﺭ ﹰﹼﻳﺎ(‪.‬‬ ‫‪ (1‬ﺍﻟﻤﺴﺘﻘﻴﻤﺎﺕ ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻵﺗﻲ ﺗﻤ ﹼﺜﻞ ﺗﻘﺎﻃﻌﺎﺕ ﺍﻟﺸﻮﺍﺭﻉ ﻗﺮﺏ ﺑﻴﺖ ﻣﺤﻤﺪ‪.‬‬ ‫ﻓﺘﻤ ﹼﺜﻞ ﻣﻮﻗﻊ ﺑﻴﺖ ﻣﺤﻤﺪ‪ ،‬ﻭﺗﻤ ﹼﺜﻞ ﻣﻮﻗﻊ ﺍﻟﻤﻜﺘﺒﺔ‪ ،‬ﻭﺗﻤ ﹼﺜﻞ ﺍﻷﺭﻗﺎﻡ ‪1, 2, 3, 4, 5‬‬ ‫ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﻨﺎﺗﺠﺔ ﻋﻦ ﻣﻦ ﺗﻘﺎﻃﻌﺎﺕ ﺍﻟﺸﻮﺍﺭﻉ‪.‬‬ ‫‪a 1B‬‬ ‫‪b‬‬ ‫‪23‬‬ ‫‪5A‬‬ ‫‪c‬‬ ‫‪4‬‬ ‫‪de‬‬ ‫‪f‬‬ ‫‪ (a‬ﺇﺫﺍ ﺃﺭﺩﺕ ﺃﻥ ﺗﺘﺄﻛﺪ ﻣﻦ ﺗﻮﺍﺯﻱ ﺍﻟﺸ‪0‬ﻮﺍ‪8‬ﺭ‪1‬ﻉ‪0‬ﺍﳌ‪6‬ﻤ‪ 8‬ﱠﺜﻠﺔ‪ -‬ﺑ‪1‬ﺎﳌ‪3‬ﺴﺘ‪-‬ﻘ‪3‬ﻴﲈ‪S0‬ﺕ‪G،ae،ob-، cA‬‬ ‫ﻓﲈ ﺍﳌﻌﻠﻮﻣﺎﺕ ﺍﻟﺘﻲ ﲢﺘﺎﺝ ﺇﻟﻴﻬﺎ؟ ﻭ ﹼﺿﺢ ﺗﱪﻳﺮﻙ‪.‬‬ ‫‪ (b‬ﺍﻓﱰﺽ ﺃﻥ ﺍﻟﺸﺎﺭﻋﲔ ﺍﳌﻤ ﹼﺜ ﹶﻠﲔ ﺑﺎﳌﺴﺘﻘﻴﻤﲔ ‪ e, d‬ﻣﺘﻮﺍﺯﻳﺎﻥ‪ ،‬ﻭﺇﺫﺍ ﻛﺎﻥ ‪،m∠5 = 112°‬‬ ‫ﻓﺄﻭﺟﺪ ‪ ،m∠4‬ﻭﻭ ﹼﺿﺢ ﻛﻴﻒ ﻭﺟﺪﺕ ﺍﻟﻘﻴﺎﺱ‪.‬‬ ‫‪ (c‬ﺇﺫﺍ ﻛﺎﻥ ‪ m∠1 = (3x – 7)°‬ﻭ ‪ ،m∠4 = (2x + 20)°‬ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪ x‬ﺇﺫﺍ ﻛﺎﻥ ﺍﳌﺴﺘﻘﻴﲈﻥ ‪ c, a‬ﻣﺘﻮﺍﺯﻳﲔ‪.‬‬ ‫ﻭ ﹼﺿﺢ ﻛﻴﻒ ﺗﻮ ﹼﺻﻠﺖ ﺇﱃ ﺇﺟﺎﺑﺘﻚ‪ ،‬ﺛﻢ ﹺﺻ ﹾﻒ ﳌﺎﺫﺍ ﺗﺘﻴﺢ ﻫﺬﻩ ﺍﻟﻘﻴﺎﺳﺎﺕ ﺇﻣﻜﺎﻧﻴﺔ ﲢﺪﻳﺪ ﺗﻮﺍﺯﻱ ﺍﳌﺴﺘﻘﻴﻤﲔ ‪.c, a‬‬ ‫‪ (d‬ﻳﺮﻏﺐ ﳏﻤﺪ ﰲ ﺍﻟﺬﻫﺎﺏ ﻣﻦ ﺍﳌﻜﺘﺒﺔ ﺇﱃ ﺑﻴﺘﻪ‪ .‬ﺇﺫﺍ ﻛﺎﻥ ﺍﻟﺸﺎﺭﻋﺎﻥ ﺍﳌﻤ ﹼﺜﻼﻥ ﺑﺎﳌﺴﺘﻘﻴﻤﲔ ‪ b, a‬ﻣﺘﻮﺍﺯﻳﲔ‪،‬‬ ‫ﻓﻜﻴﻒ ﻳﺴﺘﻄﻴﻊ ﳏﻤﺪ ﺃﻥ ﳛ ﹼﺪﺩ ﺃﻗﴫ ﻣﺴﺎﻓﺔ ﺑﲔ ﺍﳌﻮﻗﻊ ﻭﺍﻟﺸﺎﺭﻉ ‪ b‬ﺍﻟﺬﻱ ﻳﺴﻜﻦ ﻓﻴﻪ؟‬ ‫ﺃﻋ ﹺﻂ ﺗﻔﺴ ﹰﲑﺍ‪ ،‬ﻭﻭﺿﺢ ﺇﺟﺎﺑﺘﻚ ﺑﺎﻟﺮﺳﻢ‪.‬‬ ‫‪ (2‬ﺍﺭﺳﻢ ﻋﻠﻰ ﺷﺒﻜﺔ ﺇﺣﺪﺍﺛ ﹼﻴﺔ ﺍﻟﻤﺴﺘﻘﻴ ﹶﻢ ﺍﻟﺬﻱ ﻳﻤ ﹼﺮ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ )‪.(2, 4), (-3, -1‬‬ ‫‪ (a‬ﺍﻛﺘﺐ ﻣﻌﺎﺩﻟﺔ ﺍﳌﺴﺘﻘﻴﻢ ﺑﺼﻴﻐﺔ ﺍﳌﻴﻞ ﻭﺍﳌﻘﻄﻊ‪ .‬ﻭﺃﻋ ﹺﻂ ﺗﻔﺴ ﹰﲑﺍ ﻟﻜﻞ ﺧﻄﻮﺓ‪.‬‬ ‫‪ (b‬ﺇﺫﺍ ﺭﺳﻤﺖ ﻣﺴﺘﻘﻴ ﹰﲈ ﻣﻮﺍﺯ ﹰﻳﺎ ﻟﻠﻤﺴﺘﻘﻴﻢ ‪ ،‬ﻓﲈ ﻣﻴﻞ ﻫﺬﺍ ﺍﳌﺴﺘﻘﻴﻢ؟ ﻛﻴﻒ ﻋﺮﻓﺖ ﺫﻟﻚ؟‬ ‫ﺍﺭﺳﻢ ﻣﻦ ﺍﻟﻨﻘﻄﺔ )‪ (1,5‬ﻣﺴﺘﻘﻴ ﹰﲈ ﻣﻮﺍﺯ ﹰﻳﺎ ﻟﻠﻤﺴﺘﻘﻴﻢ ‪.‬‬ ‫‪ (c‬ﺃﻭﺟﺪ ﺍﻟﺒﻌﺪ ﺑﲔ ﺍﳌﺴﺘﻘﻴﻤﲔ‪ .‬ﻭﻭ ﹼﺿﺢ ﻛﻴﻒ ﻭﺟﺪﺗﻪ‪.‬‬ ‫‪2‬‬ ‫‪42‬‬ ‫‪‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(1,2)   2‬‬ ‫ﺍﻟﺠﺰﺀ‪ :1‬ﺍﻻﺧﺘﻴﺎﺭ ﻣﻦ ﻣﺘﻌﺪﺩ‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺭﻣﺰ ﺍﻹﺟﺎﺑﺔ ﺍﻟﺼﺤﻴﺤﺔ ﰲ ﺍﳌﻜﺎﻥ ﺍﳌﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪3x‬‬ ‫‪ (1‬ﺑﺎﺳﺘﻌﻤﺎﻝ ﺍﻟﺮﺳﻢ ﺍﻟﻤﻘﺎﺑﻞ‪ ،‬ﺣ ﱢﺪﺩ ﺃ ﹼﻱ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻵﺗﻴﺔ ﻟﻬﺎ‬ ‫‪ABC‬‬ ‫ﻗﻴﻤﺔ ﺻﻮﺍﺏ ﺍﻟﻌﺒﺎﺭﺓ ‪1-2 3 = 5‬‬ ‫‪________(1‬‬ ‫‪BC = 3 + x (D‬‬ ‫‪AB = BC (C‬‬ ‫‪AB = 3 (B‬‬ ‫‪3 = x (A‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﻟﻌﺒﺎﺭﺓ‪ [(p q) ∧ (q r)] :‬ﺻﺤﻴﺤﺔ‪ ،‬ﻓﺄ ﹼﻱ ﺍﻟﻌﺒ‪0‬ﺎ‪8‬ﺭﺍ‪01‬ﺕ‪6‬ﺍ‪8‬ﻵ‪-‬ﺗﻴ‪2‬ﺔ‪Geo-ST03-0‬‬ ‫ﺗﻜﻮﻥ ﺻﺤﻴﺤ ﹰﺔ ﻭﻓﻖ ﻗﺎﻧﻮﻥ ﺍﻟﻘﻴﺎﺱ ﺍﻟﻤﻨﻄﻘﻲ؟ ‪1-4‬‬ ‫‪________(2‬‬ ‫‪q p (H‬‬ ‫‪r p (F‬‬ ‫‪p r (J‬‬ ‫‪r q (G‬‬ ‫‪ (3‬ﺇﺫﺍ ﻣ ﹼﺜﻞ ﺍﻟﺮﻣﺰ ‪ p‬ﺍﻟﻌﺒﺎﺭﺓ‪\":‬ﻗﻄﺮﺍ ﺍﻟﻤﺮﺑﻊ ﻣﺘﻌﺎﻣﺪﺍﻥ\"‪ ،‬ﻭﻣ ﹼﺜﻞ ﺍﻟﺮﻣﺰ ‪ q‬ﺍﻟﻌﺒﺎﺭﺓ‪:‬‬ ‫\"ﻗﻴﺎﺱ ﺍﻟﺰﺍﻭﻳﺔ ﺍﻟﻤﻨﻔﺮﺟﺔ ﺃﻗﻞ ﻣﻦ ‪،\"90º‬ﻓﺄ ﹼﻱ ﺍﻟﻌﺒﺎﺭﺍﺕ ﺍﻟﻤﺮﻛﺒﺔ ﺍﻵﺗﻴﺔ ﺻﺤﻴﺤﺔ؟ ‪1-2‬‬ ‫‪________(3‬‬ ‫‪p ∧ q (D‬‬ ‫‪~p ∧ ~q (C‬‬ ‫‪p ∧ ~q (B‬‬ ‫‪~ p ∧ q (A‬‬ ‫‪________(4‬‬ ‫‪ (4‬ﻣﺎ ﻣﻌﻜﻮﺱ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻟﺸﺮﻃ ﹼﻴﺔ ﺍﻵﺗﻴﺔ؟ ‪1-3‬‬ ‫\"ﺇﺫﺍ ﻛﺎﻧﺖ‪ ، ∠1 ∠2 :‬ﻓﺈﻥ‪\". m∠1 = m∠2 :‬‬ ‫‪________(5‬‬ ‫‪ (F‬ﺇﺫﺍ ﻛﺎﻥ‪ ، m∠1 = m∠2 :‬ﻓﺈﻥ‪.∠1 ∠2 :‬‬ ‫‪m‬‬ ‫‪ (G‬ﺇﺫﺍ ﻛﺎﻥ‪ ، m∠1 ≠ m∠2 :‬ﻓﺈﻥ‪.∠1 ∠2 :‬‬ ‫‪ (H‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ، ∠1 ∠2 :‬ﻓﺈﻥ‪.m∠1 ≠ m∠2 :‬‬ ‫‪________(6‬‬ ‫‪ (J‬ﺇﺫﺍ ﻛﺎﻧﺖ‪ ، ∠1 ∠2 :‬ﻓﺈﻥ‪.m∠1 = m∠2 :‬‬ ‫‪________(7‬‬ ‫‪ (5‬ﺍﺫﻛﺮ ﺍﻟﺨﺎﺻﻴﺔ ﺍﻟﺘﻲ ﺗﺒ ﹼﺮﺭ ﺍﻟﻌﺒﺎﺭﺓ \"ﺇﺫﺍ ﻛﺎﻥ‪ ،b = c, a + b = 25 :‬ﻓﺈﻥ‪1-6 \"a + c = 25 :‬‬ ‫‪ (C‬ﺧﺎﺻﻴﺔ ﺍﻟﺘﻌﺪﻱ ﻟﻠﻤﺴﺎﻭﺍﺓ‪.‬‬ ‫‪ (A‬ﺧﺎﺻﻴﺔ ﺍﻻﻧﻌﻜﺎﺱ ﻟﻠﻤﺴﺎﻭﺍﺓ‪.‬‬ ‫‪ (D‬ﺧﺎﺻﻴﺔ ﺍﻟﺘﻌﻮﻳﺾ ﻟﻠﻤﺴﺎﻭﺍﺓ‪.‬‬ ‫‪ (B‬ﺧﺎﺻﻴﺔ ﺍﻟﺘﲈﺛﻞ ﻟﻠﻤﺴﺎﻭﺍﺓ‪.‬‬ ‫‪12‬‬ ‫‪9 10‬‬ ‫‪q‬‬ ‫‪ (H‬ﺯﺍﻭﻳﺘﺎﻥ ﻣﺘﻨﺎﻇﺮﺗﺎﻥ‪.‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻷﺳﺌﻠﺔ ‪ ، 6-8‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪.‬‬ ‫‪34‬‬ ‫‪11 12‬‬ ‫‪ (6‬ﻣﺎ ﻧﻮﻉ ﺍﻟﺰﺍﻭﻳﺘﻴﻦ‪∠3‬ﻭ‪∠10‬؟ ‪ 2-1 ‬‬ ‫‪56‬‬ ‫‪ (F‬ﺯﺍﻭﻳﺘﺎﻥ ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪.‬‬ ‫‪p11531164‬‬ ‫‪n7 8‬‬ ‫‪ (J‬ﺯﺍﻭﻳﺘﺎﻥ ﻣﺘﺤﺎﻟﻔﺘﺎﻥ‪.‬‬ ‫‪ (G‬ﺯﺍﻭﻳﺘﺎﻥ ﻣﺘﺒﺎﺩﻟﺘﺎﻥ ﺧﺎﺭﺟ ﹼﹰﻴﺎ‪.‬‬ ‫‪Geo-ST03-03-860180‬‬ ‫‪ (7‬ﺣﺪﺩ ﺍﻟﻘﺎﻃﻊ ﺍﻟﺬﻱ ﻳﻜ ﹼﻮﻥ‪2-1 .∠13 ,∠11‬‬ ‫‪q (D p (C m (B‬‬ ‫‪(A‬‬ ‫‪ (8‬ﺇﺫﺍ ﻛﺎﻥ ‪ ،m∠1 = 120°‬ﻓﺄﻭﺟﺪ ‪.2-2 .m∠8‬‬ ‫‪________(8‬‬ ‫‪140° (J‬‬ ‫‪120° (H‬‬ ‫‪110° (G‬‬ ‫‪60° (F‬‬ ‫‪2‬‬ ‫‪43 ‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(1‬‬ ‫‪(1,2)  ‬‬ ‫‪2‬‬ ‫‪ (9‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺍﳌﺴﺘﻘﻴﲈﺕ ‪ j, k,‬ﺗﻘﻊ ﰲ ﺍﳌﺴﺘﻮ￯ ﻧﻔﺴﻪ‪ ،‬ﻭﺍﳌﺴﺘﻘﻴﲈﻥ ‪ k,‬ﻣﺘﻮﺍﺯﻳﲔ‪،‬‬ ‫ﻭﺍﳌﺴﺘﻘﻴﲈﻥ ‪ j,‬ﻣﺘﻌﺎﻣﺪﻳﻦ‪ ،‬ﻓﺄ ﱞﻱ ﳑﹼﺎ ﻳﺄﰐ ﺗﺼﻒ ﺍﻟﻌﻼﻗﺔ ﺑﲔ ﺍﳌﺴﺘﻘﻴﻤﲔ ‪k, j‬‬ ‫ﺑﺼﻮﺭ ﹴﺓ ﺻﺤﻴﺤ ﹴﺔ؟ ‪ 2-2‬‬ ‫‪______________(9‬‬ ‫‪ (C‬ﺍﳌﺴﺘﻘﻴﲈﻥ ‪ j, k‬ﻣﺘﻌﺎﻣﺪﺍﻥ‬ ‫‪ (A‬ﺍﳌﺴﺘﻘﻴﲈﻥ ‪ j, k‬ﻣﺘﺨﺎﻟﻔﺎﻥ‬ ‫‪ (D‬ﺍﳌﺴﺘﻘﻴﲈﻥ ‪ j, k‬ﻻ ﻳﻘﻌﺎﻥ ﰲ ﻧﻔﺲ ﺍﳌﺴﺘﻮ￯‬ ‫‪ (B‬ﺍﳌﺴﺘﻘﻴﲈﻥ ‪ j, k‬ﻣﺘﻮﺍﺯﻳﺎﻥ‬ ‫‪ (10‬ﺩﺭﺟﺔ ﺍﻧﺤﺪﺍﺭ ﺟﺰ ﹴﺀ ﻣﻦ ﻃﺮﻳﻖ ‪ ،9%‬ﺇﺫﺍ ﺗﺤﺮﻛﺖ ﺳﻴﺎﺭﺓ ﻣﻦ ﺑﺪﺍﻳﺔ ﺍﻟﺠﺰﺀ ﺍﻟﻤﻨﺤﺪﺭ ﻣﻦ ﺃﺳﻔﻞ‬ ‫ﺇﻟﻰ ﺃﻥ ﻭﺻﻠﺖ ﺇﻟﻰ ﺍﺭﺗﻔﺎﻉ ‪ 18 ft‬ﻓﻮﻕ ﻣﺴﺘﻮ￯ ﺍﻟﻄﺮﻳﻖ ﺍﻷﻓﻘﻲ‪،‬‬ ‫ﻓﻤﺎ ﺍﻟﻤﺴﺎﻓﺔ ﺍﻷﻓﻘﻴﺔ ﺍﻟﺘﻲ ﻗﻄﻌﺘﻬﺎ ﺍﻟﺴﻴﺎﺭﺓ؟ ‪2-4‬‬ ‫‪______________(10‬‬ ‫‪200 ft (D‬‬ ‫‪100 ft (C‬‬ ‫‪50 ft (G‬‬ ‫‪36 ft (A‬‬ ‫‪ (11‬ﻣﺎ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ‪2y + x = -3‬؟ ‪2-5‬‬ ‫‪______________(11‬‬ ‫‪2 (D‬‬ ‫‪-‬‬ ‫‪_1‬‬ ‫‪(C‬‬ ‫‪-2 (B‬‬ ‫‪-3 (A‬‬ ‫‪2‬‬ ‫‪ (12‬ﻳﻘﻄﻊ ﻗﺎﻃ ﹲﻊ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ‪ k,‬ﻣﻜ ﹼﻮ ﹰﻧﺎ ﺯﻭﺟﻴﻦ ﻣﻦ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﻤﺘﺒﺎﺩﻟﺔ ﺩﺍﺧﻠ ﹼﹰﻴﺎ‪:‬‬ ‫‪ ∠ 4‬ﻭ‪ ∠3 ;∠5‬ﻭ‪ ،∠6‬ﺃ ﱞﻱ ﻣ ﹼﻤﺎ ﻳﺄﺗﻲ ﹸﻳ ﹶﻌ ﱡﺪ ﺿﺮﻭﺭ ﹰﹼﻳﺎ ﻟﻜﻲ ﻳﻜﻮﻥ‬ ‫ﺍﻟﻤﺴﺘﻘﻴﻤﺎﻥ ‪ k, l‬ﻣﺘﻮﺍﺯﻳﻴﻦ؟ ‪2-3‬‬ ‫‪______________(12‬‬ ‫‪ ∠4 ∠ 5 (C‬ﻭ ‪∠3 ∠6‬‬ ‫‪∠4 ∠3 (A‬‬ ‫‪______________(13‬‬ ‫‪m∠3 + m∠6 = 90 (D‬‬ ‫‪m∠3 + m∠6 = 180 (B‬‬ ‫‪ (13‬ﺃﻭﺟﺪ ﺍﻟﻤﺴﺎﻓﺔ ﺑﻴﻦ ﺍﻟﻨﻘﻄﺔ )‪ (2, 3‬ﻭﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻣﻌﺎﺩﻟﺘﻪ ‪2-6 . y = x‬‬ ‫‪______________(14‬‬ ‫‪ (14‬ﻣﺎ ﺍﻟﻤﺴ ﹼﻠﻤﺔ ﺍﻟﺘﻲ ﻳﻤﻜﻨﻚ ﺍﺳﺘﻌﻤﺎﻟﻬﺎ ﻹﺛﺒﺎﺕ ﺻﺤﺔ ﺍﻟﻌﺒﺎﺭﺓ ﺍﻵﺗﻴﺔ؟ ‪1-5‬‬ ‫‪______________(15‬‬ ‫ﻳﻤ ﹼﺮ ﺍﳌﺴﺘﻘﻴﻢ ‪ m‬ﺑﺎﻟﻨﻘﻄﺘﲔ ‪.A,F‬‬ ‫‪2‬‬ ‫‪ (15‬ﺇﺫﺍ ﻛﺎﻥ ﻣﻴﻞ ﺍﻟﻤﺴﺘﻘﻴﻢ ﺍﻟﻤﺎ ﹼﺭ ﺑﺎﻟﻨﻘﻄﺘﻴﻦ )‪C(a, -2), D(-3, 6‬‬ ‫ﻳﺴﺎﻭﻱ _‪ ،_23‬ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪2-4 .a‬‬ ‫‪44  ‬‬

‫‪‬‬ ‫‪‬‬ ‫)‪(2‬‬ ‫‪(1,2)  ‬‬ ‫‪2‬‬ ‫‪______________(16‬‬ ‫ﺍﻟﺠﺰﺀ‪ : 2‬ﺍﻹﺟﺎﺑﺔ ﺍﻟﻘﺼﻴﺮﺓ‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﰲ ﺍﳌﻜﺎﻥ ﺍﳌﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪ (16‬ﻣﻌﺎﺩﻟﺔ ﺍﳌﺴﺘﻘﻴﻢ ﺍﻟﻌﻤﻮﺩﻱ ﻋﲆ ‪ ، y = -x‬ﻭﻳﻤﺮ ﺑﺎﻟﻨﻘﻄﺔ )‪ (2, 4‬ﻫﻲ‪:‬‬ ‫___؟___ ‪2-5 y = x +‬‬ ‫‪______________(17‬‬ ‫‪ (17‬ﺃﻭﺟﺪ ﻣﻴﻞ ﺍﳌﺴﺘﻘﻴﻢ ﺍﻟﺬﻱ ﻳﻮﺍﺯﻱ ﺍﳌﺴﺘﻘﻴﻢ ‪2-5 .3y – 6x = 9‬‬ ‫‪______________(18‬‬ ‫‪2-3‬‬ ‫‪ (18‬ﺃﻭﺟﺪ ﻗﻴﻤﺔ ‪ x‬ﺣﺘﻰ ﻳﻜﻮﻥ ‪ l m‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺃﺩﻧﺎﻩ‪.‬‬ ‫‪______________(19‬‬ ‫‪(7x + 15)°‬‬ ‫‪m‬‬ ‫‪25°‬‬ ‫‪n‬‬ ‫‪_____________(20a‬‬ ‫‪_____________(20b‬‬ ‫‪Geo-ST03-06-860180‬‬ ‫‪_____________(20c‬‬ ‫‪ (19‬ﺍﻟﻤﺤﻮﺭ ‪ (y = 0) x‬ﻭﺍﻟﻤﺤﻮﺭ ‪ (x = 0) y‬ﻓﻲ ﺍﻟﻤﺴﺘﻮ￯ ﺍﻹﺣﺪﺍﺛ ﹼﻲ ﻣﺘﻌﺎﻣﺪﺍﻥ‪،‬‬ ‫‪_____________(20d‬‬ ‫ﻭﺣﺎﺻﻞ ﺿﺮﺏ ﻣﻴ ﹶﻠﻲ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ﺍﻟﻤﺘﻌﺎﻣﺪﻳﻦ ﻳﺴﺎﻭﻱ ‪. -1‬‬ ‫ﻭﺿ ﹼﺢ ﻟﻤﺎﺫﺍ ﻻ ﻳﻨﻄﺒﻖ ﻫﺬﺍ ﺍﻟﺘﻌﺮﻳﻒ ﻋﻠﻰ ﺍﻟﻤﺴﺘﻘﻴﻤﻴﻦ ‪ y = 0‬ﻭ ‪2-4 .x = 0‬‬ ‫‪ (20‬ﻳﻜ ﹼﻠﻒ ﺍﺷﺘﺮﺍﻙ ﻓﻴﺼﻞ ﻓﻲ ﺍﻟﺘﺄﻣﻴﻦ ﺍﻟﻄﺒﻲ ﻓﻲ ﻧﻈﺎﻡ ﺍﻟﺸﺮﻛﺔ ‪ 3500 ،A‬ﺭﻳﺎ ﹴﻝ ﺳﻨﻮ ﹰﹼﻳﺎ ﹶﻭ ‪ 100‬ﺭﻳﺎﻝ‬ ‫ﻋﻦ ﻛﻞ ﺯﻳﺎﺭﺓ ﻋﻼﺝ‪ ،‬ﻭﻓﻲ ﻧﻈﺎﻡ ﺍﻟﺸﺮﻛﺔ ‪ B‬ﻳﻜ ﹼﻠﻒ ‪ 4000‬ﺭﻳﺎ ﹴﻝ ﺳﻨﻮ ﹰﹼﻳﺎ ﹶﻭ ‪ 50‬ﺭﻳﺎ ﹰﻻ ﻋﻦ ﻛﻞ‬ ‫ﺯﻳﺎﺭﺓ ﻋﻼﺝ‪2-5 .‬‬ ‫‪ (a‬ﺍﻛﺘﺐ ﻣﻌﺎﺩﻟ ﹰﺔ ﻟﻜ ﹼﻞ ﺷﺮﻛﺔ ﺑﺼﻴﻐﺔ ﺍﻟﻤﻴﻞ ﻭﺍﻟﻤﻘﻄﻊ‪.‬‬ ‫‪ (b‬ﻛﻢ ﻳﺪﻓﻊ ﻓﻴﺼ ﹲﻞ ﻭﻓﻖ ﺧﻄﺔ ﺍﻟﺸﺮﻛﺔ ‪ ، A‬ﺇﺫﺍ ﺭﺍﺟﻊ ﺍﻟﻤﺮﺍﻛﺰ ﺍﻟﺼﺤﻴﺔ ‪ 20‬ﻣﺮ ﹰﺓ‪.‬‬ ‫‪ (c‬ﻫﻞ ﻳﻮﻓﺮ ﻓﻴﺼﻞ ﺑﻌﺾ ﺍﻟﻤﺎﻝ ﺇﺫﺍ ﺣ ﹼﻮﻝ ﺍﺷﺘﺮﺍﻛﻪ ﺇﻟﻰ ﺍﻟﺸﺮﻛﺔ ‪ B‬ﻓﻲ ﺣﺎﻝ ﺯﻳﺎﺭﺗﻪ‬ ‫‪ 20‬ﻣﺮ ﹰﺓ ﻟﻠﻤﺮﺍﻛﺰ ﺍﻟﺼﺤﻴﺔ‪.‬‬ ‫‪ (d‬ﺃ ﱡﻱ ﺍﻟﴩﻛﺘﲔ ﺃﻗ ﹼﻞ ﺗﻜﻠﻔ ﹰﺔ ﺇﺫﺍ ﺭﺍﺟﻊ ﻓﻴﺼﻞ ﺍﳌﺮﺍﻛﺰ ﺍﻟﺼﺤﻴﺔ ‪ 10‬ﻣﺮﺍ ﹴﺕ؟‬ ‫‪2‬‬ ‫‪45‬‬ ‫‪‬‬

‫‪‬‬ ‫‪‬‬ ‫‪   ‬‬ ‫‪3‬‬ ‫‪ ‬‬ ‫‪ 1‬ﻗﺒﻞ ﺑﺪﺀ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬ ‫• ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺟﻤﻠﺔ‪.‬‬ ‫• ﻗ ﹼﺮﺭ ﻣﺎ ﺇﺫﺍ ﻛﻨﺖ ﻣﻮﺍﻓ ﹰﻘﺎ )ﻡ( ﻋﻠﻰ ﻣﻀﻤﻮﻧﻬﺎ‪ ،‬ﺃﻭ ﻏﻴﺮ ﻣﻮﺍﻓﻖ )ﻍ(‪.‬‬ ‫• ﺍﻛﺘﺐ )ﻡ( ﺃﻭ )ﻍ( ﰲ ﺍﻟﻌﻤﻮﺩ ﺍﻷﻭﻝ‪ ،‬ﻭﺇﺫﺍ ﻛﻨﺖ ﻏﲑ ﻣﺘﺄﻛﺪ ﻣﻦ ﻣﻮﺍﻓﻘﺘﻚ ﻓﺎﻛﺘﺐ )ﻍ ﻡ(‪.‬‬ ‫‪2‬‬ ‫‪‬‬ ‫‪1‬‬ ‫‪ (1‬ﺣﺘﻰ ﻳﻜﻮﻥ ﺍﻟﻤﺜﻠﺚ ﺣﺎ ﱠﺩ ﺍﻟﺰﻭﺍﻳﺎ‪ ،‬ﻳﺘﻌ ﹼﻴﻦ ﺃﻥ ﺗﻜﻮﻥ ﺯﻭﺍﻳﺎﻩ ﺍﻟﺜﻼﺙ ﺣﺎﺩ ﹰﺓ‪.‬‬ ‫‪ (2‬ﺃﺿﻼﻉ ﺍﻟﻤﺜﻠﺚ ﺍﻟﻤﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ ﺟﻤﻴﻌﻬﺎ ﻣﺘﻄﺎﺑﻘﺔ‪.‬‬ ‫‪ (3‬ﺍﻟﺰﺍﻭﻳﺔ ﺍﻟﺨﺎﺭﺟﻴﺔ ﻫﻲ ﺃﻳﺔ ﺯﺍﻭﻳﺔ ﺧﺎﺭﺝ ﺍﻟﻤﺜﻠﺚ ﺍﻟﻤﻌﻠﻮﻡ‪.‬‬ ‫‪ (4‬ﻣﺠﻤﻮﻉ ﻗﻴﺎﺳﺎﺕ ﺯﻭﺍﻳﺎ ﺍﻟﻤﺜﻠﺚ ﻳﺴﺎﻭﻱ ‪.360º‬‬ ‫‪ (5‬ﺍﻟﻤﺜﻠﺚ ﺍﻟﻤﻨﻔﺮﺝ ﺍﻟﺰﺍﻭﻳﺔ ﻫﻮ ﻣﺜﻠ ﹲﺚ ﻓﻴﻪ ﺛﻼﺙ ﺯﻭﺍﻳﺎ ﻣﻨﻔﺮﺟﺔ‪.‬‬ ‫‪ (6‬ﺍﻟﻤﺜﻠﺜﺎﻥ ﺍﻟ ﱠﻠﺬﺍﻥ ﻟﻬﻤﺎ ﻧﻔﺲ ﻗﻴﺎﺳﺎﺕ ﺍﻟﺰﻭﺍﻳﺎ ﻭﻧﻔﺲ ﻗﻴﺎﺳﺎﺕ ﺍﻷﺿﻼﻉ ﻣﺜﻠﺜﺎﻥ ﻣﺘﻄﺎﺑﻘﺎﻥ‪.‬‬ ‫‪ (7‬ﺇﺫﺍ ﻃﺎﺑﻘﺖ ﺯﻭﺍﻳﺎ ﻣﺜﻠ ﹴﺚ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻟﻤﻨﺎﻇﺮﺓ ﻟﻬﺎ ﻓﻲ ﻣﺜﻠ ﹴﺚ ﺁﺧﺮ ‪ ،‬ﻓﺈﻥ ﺍﻟﻤﺜﻠﺜﻴﻦ ﻣﺘﻄﺎﺑﻘﺎﻥ‪.‬‬ ‫‪ (8‬ﺍﻟﻤﺜﻠﺚ ﺍﻟﻤﺘﻄﺎﺑﻖ ﺍﻟﻀﻠﻌﻴﻦ ﻣﺜﻠ ﹲﺚ ﻓﻴﻪ ﺿﻠﻌﺎﻥ ﻣﺘﻄﺎﺑﻘﺎﻥ‪.‬‬ ‫‪ (9‬ﻳﻤﻜﻦ ﺃﻥ ﻳﻜﻮﻥ ﺍﻟﻤﺜﻠﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻟﺰﻭﺍﻳﺎ ﻭﻏﻴﺮ ﻣﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‪.‬‬ ‫‪ (10‬ﻳﻤﻜﻦ ﺃﻥ ﺗﺠﻌﻞ ﺍﻟﺤﺴﺎﺑﺎﺕ ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺍﻹﺣﺪﺍﺛﻲ ﺃﺳﻬﻞ ﺑﻮﺿﻊ ﻣﺮﻛﺰ ﺍﻟﻤﺜﻠﺚ ﺃﻭ ﺃﺣﺪ ﺭﺅﻭﺳﻪ‬ ‫ﻋﻨﺪ ﻧﻘﻄﺔ ﺍﻷﺻﻞ‪.‬‬ ‫‪ 2‬ﺑﻌﺪ ﺇﻛﲈﻝ ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬ ‫• ﺃﻋﺪ ﻗﺮﺍﺀﺓ ﻛ ﹼﻞ ﺟﻤﻠﺔ ﺃﻋﻼﻩ‪ ،‬ﺛﻢ ﺍﻣﻸ ﺍﻟﻌﻤﻮﺩ ﺍﻷﺧﻴﺮ ﺑﻜﺘﺎﺑﺔ )ﻡ( ﺃﻭ )ﻍ(‪.‬‬ ‫• ﻫﻞ ﺗﻐ ﹼﻴﺮ ﺭﺃﻳﻚ ﻓﻲ ﺍﻟﺠﻤﻞ ﺍﻟﺴﺎﺑﻘﺔ ﻋ ﹼﻤﺎ ﻫﻮ ﻓﻲ ﺍﻟﻌﻤﻮﺩ ﺍﻷﻭﻝ؟‬ ‫• ﺍﺳﺘﻌﻤﻞ ﻭﺭﻗ ﹰﺔ ﺇﺿﺎﻓﻴ ﹰﺔ ﺗﺒ ﹼﻴﻦ ﻓﻴﻬﺎ ﺳﺒﺐ ﻋﺪﻡ ﻣﻮﺍﻓﻘﺘﻚ ﻋﻠﻰ ﺑﻌﺾ ﺍﻟﺠﻤﻞ‪ ،‬ﺩﺍﻋ ﹰﻤﺎ ﺫﻟﻚ ﺑﺎﻷﻣﺜﻠﺔ ﺇﻥ ﺃﻣﻜﻦ‪.‬‬ ‫‪3‬‬ ‫‪46‬‬ ‫‪‬‬

‫‪‬‬ ‫‪‬‬ ‫‪   3‬‬ ‫ﻫﺬﻩ ﻗﺎﺋﻤﺔ ﺑﺎﳌﻔﺮﺩﺍﺕ ﺍﳉﺪﻳﺪﺓ ﺍﻟﺘﻲ ﺳﺘﺘﻌﻠﻤﻬﺎ ﰲ ﺃﺛﻨﺎﺀ ﺩﺭﺍﺳﺘﻚ ﺍﻟﻔﺼﻞ ‪ .3‬ﺍﻛﺘﺐ ﺗﻌﺮﻳ ﹰﻔﺎ ﺃﻭ ﻭﺻ ﹰﻔﺎ ﻟﻜﻞ ﻣﻔﺮﺩﺓ ﰲ ﺍﳉﺪﻭﻝ ﺣﲔ ﺗﻈﻬﺮ ﻟﻚ‬ ‫ﰲ ﺃﺛﻨﺎﺀ ﺩﺭﺍﺳﺔ ﺍﻟﻔﺼﻞ‪ ،‬ﺛﻢ ﺃﺿﻒ ﺭﻗﻢ ﺍﻟﺼﻔﺤﺔ ﺍﻟﺘﻲ ﻭﺭﺩﺕ ﻓﻴﻬﺎ ﺍﳌﻔﺮﺩﺓ ﺃﻭﻝ ﻣﺮﺓ ﰲ ﺍﻟﻌﻤﻮﺩ ﺍﳌﺨ ﱠﺼﺺ‪ .‬ﺍﺳﺘﻌﻤﻞ ﻫﺬﻩ ﺍﻟﻘﺎﺋﻤﺔ ﰲ ﺃﺛﻨﺎﺀ‬ ‫ﺍﳌﺮﺍﺟﻌﺔ ﻭﺍﻻﺳﺘﻌﺪﺍﺩ ﻻﺧﺘﺒﺎﺭ ﺍﻟﻔﺼﻞ‪.‬‬ ‫‪  ‬‬ ‫‪‬‬ ‫‪‬‬ ‫ﺍﳌﺜﻠﺚ ﺍﳊﺎﺩ ﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺍﳌﺜﻠﺚ ﺍﳌﻨﻔﺮﺝ ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﺍﳌﺜﻠﺚ ﺍﻟﻘﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﺍﳌﺜﻠﺚ ﺍﳌﺘﻄﺎﺑﻖ ﺍﻷﺿﻼﻉ‬ ‫ﺍﳌﺜﻠﺚ ﺍﳌﺘﻄﺎﺑﻖ ﺍﻟﻀﻠﻌﲔ‬ ‫ﺍﳌﺜﻠﺚ ﺍﳌﺨﺘﻠﻒ ﺍﻷﺿﻼﻉ‬ ‫ﺍﳌﺴﺘﻘﻴﻢ ﺍﳌﺴﺎ ﹺﻋﺪ‬ ‫ﺍﻟﺰﺍﻭﻳﺔ ﺍﳋﺎﺭﺟﻴﺔ‬ ‫ﺍﻟﺰﺍﻭﻳﺘﺎﻥ ﺍﻟﺪﺍﺧﻠﻴﺘﺎﻥ ﺍﻟﺒﻌﻴﺪﺗﺎﻥ‬ ‫‪3‬‬ ‫ﺍﻟﱪﻫﺎﻥ ﺍﻟﺘﺴﻠﺴ ﹼﲇ‬ ‫‪47  ‬‬

  ()    3    ‫ﺍﻟﻨﺘﻴﺠﺔ‬ ‫ﺍﻟﺘﻄﺎﺑﻖ‬ ‫ﺍﳌﻀﻠﻌﺎﺕ ﺍﳌﺘﻄﺎﺑﻘﺔ‬ ‫ﺍﻟﻌﻨﺎﴏ ﺍﳌﺘﻨﺎﻇﺮﺓ‬ ‫ﺍﻟﺰﺍﻭﻳﺔ ﺍﳌﺤﺼﻮﺭﺓ‬ ‫ﺍﻟﻀﻠﻊ ﺍﳌﺤﺼﻮﺭ‬ ‫ﺳﺎﻗﺎ ﺍﳌﺜﻠﺚ ﺍﳌﺘﻄﺎﺑﻖ ﺍﻟﻀﻠﻌﲔ‬ ‫ﺯﺍﻭﻳﺔ ﺍﻟﺮﺃﺱ‬ ‫ﺯﺍﻭﻳﺘﺎ ﺍﻟﻘﺎﻋﺪﺓ‬ ‫ﺍﻟﱪﻫﺎﻥ ﺍﻹﺣﺪﺍﺛﻲ‬ 3 48 

‫‪‬‬ ‫‪‬‬ ‫‪15°‬‬ ‫‪150°‬‬ ‫)‪3-2)15°(1‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪3‬‬ ‫‪(3-1 ,‬‬ ‫‪________________(1‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫‪________________(2‬‬ ‫‪120°‬‬ ‫‪________________(3‬‬ ‫‪ (1‬ﺻ ﹼﻨﻒ ﺍﻟﻤﺜﻠﺚ ﺍﻟﻤﺠﺎﻭﺭ ﻭﻓ ﹰﻘﺎ ﻟﺰﻭﺍﻳﺎﻩ‪ ،‬ﻭﻭﻓ ﹰﻘﺎ ﻷﺿﻼﻋﻪ‪30° 30° .‬‬ ‫‪________________(4‬‬ ‫‪________________(5‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪ ∆ABC‬ﻣﺘﻄﺎﺑﻖ ﺍﻟﻀﻠﻌﻴﻦ ﻓﻴﻪ ‪،AB = BC‬‬ ‫‪________________(6‬‬ ‫ﻭﻛﺎﻥ‪، AB = 6x + 3, BC = 8x - 1, AC = 10x - 10 :‬‬ ‫‪________________(7‬‬ ‫‪________________(8‬‬ ‫ﻓﺄﻭﺟﺪ ﻗﻴﻤﺔ ‪ ، x‬ﻭﻃﻮﻝ ﻛ ﹼﻞ ﺿﻠ ﹴﻊ ﻣﻦ ﺃﺿﻼﻉ ﺍﻟﻤﺜﻠﺚ‪.‬‬ ‫‪________________(9‬‬ ‫‪ (3‬ﺃﻭﺟﺪ ﺃﻃﻮﺍﻝ ﺃﺿﻼﻉ ‪ ∆ABC‬ﺍﻟﺬﻱ ﺭﺅﻭﺳﻪ‬ ‫‪‬‬ ‫)‪ A(1, 5), B(3, -2), C(-3, 0‬ﻭﺻ ﹼﻨﻔﻪ ﻭﻓﻖ ﺃﺿﻼﻋﻪ‪.‬‬ ‫ﺃﻭﺟﺪ ﻣﻦ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ ﻗﻴﺎﺱ ﻛ ﱟﻞ ﻣﻦ ﺍﻟﺰﻭﺍﻳﺎ ﺍﻵﺗﻴﺔ‪1 :‬‬ ‫‪∠5 (5‬‬ ‫‪∠4 (4‬‬ ‫‪70° 5 65°2‬‬ ‫‪3‬‬ ‫‪∠2 (7‬‬ ‫‪∠1 (6‬‬ ‫‪6 107° 4‬‬ ‫‪43°‬‬ ‫‪∠6 (9‬‬ ‫‪∠3 (8‬‬ ‫‪Geo-AS04-063-860181‬‬ ‫‪‬‬ ‫‪(3-3,3-4) (2)  ‬‬ ‫‪3‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍﻝ ﺑﻌﻨﺎﻳﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪________________(1‬‬ ‫‪ (1‬ﺍﺫﻛﺮ ﺍﻟﻤﺴﻠﻤﺔ ﺍﻟﺘﻲ ﺗﺜﺒﺖ ﺗﻄﺎﺑﻖ ﺍﻟﻤﺜﻠﺜﻴﻦ ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ ‪K .‬‬ ‫‪________________(2‬‬ ‫‪NL‬‬ ‫‪________________(3‬‬ ‫‪M‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪ ، JGO RWI‬ﻓﻤﺎ ﺍﻟﺰﺍﻭﻳﺔ‬ ‫‪________________(4‬‬ ‫‪QS‬‬ ‫ﺍﻟﺘﻲ ﺗﻨﺎﻇﺮ ‪∠I‬؟‬ ‫‪ (3‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪ QR SR :‬ﻭ ‪، PQ TS‬‬ ‫ﻭﺍﻟﻨﻘﻄﺔ ‪ R‬ﻧﻘﻄﺔ ﻣﻨﺘﺼﻒ ‪ ، PT‬ﺣ ﹼﺪﺩ ﺍﻟﻨﻈﺮﻳﺔ ﺃﻭ ﺍﻟ‪1‬ﻤ‪8‬ﺴ‪1‬ﹼﻠ‪0‬ﻤﺔ‪Geo-ASR 04-064-86‬‬ ‫ﺍﻟﺘﻲ ﻳﻤﻜﻨﻚ ﺍﺳﺘﻌﻤﺎﻟﻬﺎ ﻹﺛﺒﺎﺕ ﺃﻥ ‪P T . QRP SRT‬‬ ‫‪ (4‬ﻣﺎ ﺍﻟﻌﻼﻗﺔ ﺑﻴﻦ ‪ ∠Q‬ﻭ ‪ ∠S‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺮﺍﻓﻖ ﻟﻠﺴﺆﺍﻝ ‪ 2‬؟‬ ‫‪________________(5‬‬ ‫‪C04-28A-8(76y3-946)1°‬‬ ‫‪F ، ABC‬‬ ‫‪ (5‬ﻓﻲ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪DEF :‬‬ ‫‪3‬‬ ‫ﺃﻭﺟﺪ ﻗﻴﻤﺔ ﻛ ﱟﻞ ﻣﻦ ‪. x , y‬‬ ‫‪B‬‬ ‫‪E‬‬ ‫‪10 80° 18.8‬‬ ‫‪3x - y‬‬ ‫‪ ‬‬ ‫‪A 70° 30°‬‬ ‫‪CD‬‬ ‫‪19.7‬‬ ‫‪49‬‬

‫‪‬‬ ‫‪‬‬ ‫‪(3-5, 3-6) (3)   3‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪:‬‬ ‫ﺍﻛﺘﺐ ﻓﻲ ﻓﺮﺍ ﹶﻏﻲ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 1, 2‬ﻣﺒ ﱢﺮﺭﺍﺕ ﺍﻟﺨﻄﻮﺗﻴﻦ ‪ 2, 4‬ﻋﻠﻰ ﺍﻟﺘﺮﺗﻴﺐ ﻓﻲ ﺍﻟﺒﺮﻫﺎﻥ ﺫﻱ ﺍﻟﻌﻤﻮﺩﻳﻦ ﺍﻵﺗﻲ‪:‬‬ ‫‪ZAC‬‬ ‫‪∠Z ∠C‬‬ ‫‪ AK‬ﺗﻨﺼﻒ ‪K .∠ZKC‬‬ ‫‪‬ﺇﺛﺒﺎﺕ ﺃﻥ ‪. AKZ AKC‬‬ ‫‪Geo-AS04-067-860181‬‬ ‫‪‬‬ ‫‪________________(1‬‬ ‫‪ ‬‬ ‫‪‬‬ ‫‪________________(2‬‬ ‫‪ AK ، ∠Z ∠C (1‬ﺗﻨ ﹼﺼﻒ ‪ (1 .∠ZKC‬ﻣﻌﻄﻴﺎﺕ‬ ‫‪ (2‬؟‬ ‫‪∠ZKA ∠CKA (2‬‬ ‫‪________________(3‬‬ ‫‪ (3‬ﺧﺎﺻﻴﺔ ﺍﻻﻧﻌﻜﺎﺱ ﻟﻠﺘﻄﺎﺑﻖ‬ ‫‪AK AK (3‬‬ ‫‪ (4‬؟‬ ‫‪AKZ AKC (4‬‬ ‫‪12‬‬ ‫ﺃﺟﺐ ﻋﻦ ﺍﻟﺴﺆﺍﻟﻴﻦ ‪ 3‬ﹶﻭ ‪ ، 4‬ﻣﺴﺘﻌﻤ ﹰﻼ ﺍﻟﺸﻜﻞ ﺍﻟﻤﺠﺎﻭﺭ‪:‬‬ ‫‪________________(4‬‬ ‫‪ (4‬ﺃﻭﺟﺪ ‪m∠2‬‬ ‫‪ (3‬ﺃﻭﺟﺪ ‪m∠1‬‬ ‫‪ (5‬ﺇﺫﺍ ﻛﺎﻥ ﻗﻴﺎﺱ ﺇﺣﺪ￯ ﺯﺍﻭﻳ ﹶﺘﻲ ﺍﻟﻘﺎﻋﺪﺓ ﻓﻲ ﻣﺜﻠ ﹴﺚ ﻣﺘﻄﺎﺑﻖ ﺍﻟﻀﻠﻌﻴﻦ ‪ ، 30°‬ﻓﻤﺎ ﻗﻴﺎﺱ ﺯﺍﻭﻳﺔ ﺭﺃﺳﻪ؟ ‪________________(5‬‬ ‫‪‬‬ ‫‪Geo-AS04-068-860181‬‬ ‫‪‬‬ ‫‪(3-7) (4)  ‬‬ ‫‪3‬‬ ‫‪________________(1‬‬ ‫ﺍﻗﺮﺃ ﻛ ﹼﻞ ﺳﺆﺍ ﹴﻝ ﺑﻌﻨﺎﻳ ﹴﺔ‪ ،‬ﺛﻢ ﺍﻛﺘﺐ ﺇﺟﺎﺑﺘﻚ ﻓﻲ ﺍﻟﻤﻜﺎﻥ ﺍﻟﻤﺨﺼﺺ ﻟﺬﻟﻚ‪.‬‬ ‫‪y‬‬ ‫‪ (1‬ﺃﻭﺟﺪ ﺍﻹﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻤﺠﻬﻮﻟﺔ ﻓﻲ ﺍﻟﻤﺜﻠﺚ ﺍﻟﻤﺠﺎﻭﺭ‪I(?, ?) .‬‬ ‫‪________________(2‬‬ ‫‪M(-b, 0) C(?, ?) x‬‬ ‫‪ (2‬ﺇﺫﺍ ﻛﺎﻥ ‪ DJL‬ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ‪ ،‬ﻭﻭﺗﺮﻩ ‪ ،DJ‬ﻭﻛﺎﻥ ‪، LJ = _21_DL‬‬ ‫ﻭﻃﻮﻝ ‪ DL‬ﻳﺴﺎﻭﻱ ‪ a‬ﻭﺣﺪ ﹰﺓ‪ ،‬ﻓﻤ ﱢﺜﻞ ‪ DJL‬ﻓﻲ ﺍﻟﻤﺴﺘﻮ￯ ﺍﻹﺣﺪﺍﺛﻲ‪،‬‬ ‫‪Geo-AS04-069-860181‬‬ ‫ﻭﺣ ﱢﺪﺩ ﺇﺣﺪﺍﺛﻴﺎﺕ ﺭﺅﻭﺳﻪ‪.‬‬ ‫‪________________(3‬‬ ‫‪ (3‬ﺇﺫﺍ ﻛﺎﻧﺖ ﺇﺣﺪﺍﺛﻴﺎﺕ ﺭﺅﻭﺱ ‪، A(-1, 1), B(5, 1), C(2, 6) ، ABC‬‬ ‫ﻓﻤﺎ ﻧﻮﻋﻪ؟ ﻭﻟﻤﺎﺫﺍ؟‬ ‫‪3‬‬ ‫‪50‬‬ ‫‪ ‬‬