Math school-books-6th-primary-2nd-term-khawagah-2019-

1. ١
‫اﻟﻔﺮق‬)-(:‫اﻟﺘﻲ‬ ‫اﻟﻌﻨﺎﺻﺮ‬ ‫وﻫﻲ‬‫اﻟﺜﺎﻧﻴﺔ‬ ‫ﻓﻲ‬ ‫ﺗﻮﺟﺪ‬ ‫وﻻ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻓﻲ‬ ‫ﺗﻮﺟﺪ‬

2. ٢
‫ﻣ‬‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﺠﻤﻮﻋﺔ‬
‫اﻻ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﺗﺘﻜﻮن‬ ‫ﻣﻤﺎ‬‫اﻟﺼﺤﻴﺤﺔ‬ ‫ﻋﺪاد‬‫؟‬
‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻻﻋﺪاد‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫رﻣﺰ‬)W(‫ﻣﻦ‬ ‫وﺗﺘﻜﻮن‬:-
}..............،٥،٤،٣،٢،١،٠،-١،-٢،-٣،-٤،-٥،.........{
)W+(‫اﻟﻤﻮﺟﺒﺔ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﻣﺠﻤﻮﻋﺔ‬:}..........٦،٥،٤،٣،٢،١{
)W-(‫اﻟﺴﺎﻟﺒﺔ‬ ‫اﻟﺼﺠﻴﺠﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﻣﺠﻤﻮﻋﺔ‬:}-١،-٢،-٣،-٤،-٥،.......{
‫ﺍﺫﺍ‬:W=W+U}٠{UW–
-‫ﻳﻠﻰ‬ ‫ﻛﻤﺎ‬ ‫اﻷﻋﺪاد‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ‫وﺗﻤﺜﻞ‬:-
‫ﻫﺎﻣﺔ‬ ‫ﻣﻼﺣﻈﺎت‬:-
)١(‫ﻣﻮﺟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫أﺻﻐﺮ‬ ‫ﻫﻮ‬.)-١(‫ﺳﺎﻟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫أﻛﺒﺮﻋﺪد‬ ‫ﻫﻮ‬‫ﺳﺎﻟﺒﺎ‬ ‫وﻻ‬ ‫ﻣﻮﺟﺒﺎ‬ ‫ﻟﻴﺲ‬ ‫اﻟﺼﻔﺮ‬.
‫ﻳﻮﺟﺪ‬ ‫ﻻ‬)‫ﻣﻮﺟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫اﻛﺒﺮ‬(‫اﺻﻐﺮ‬ ‫وﻻ‬)‫ﺳﺎﻟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬(
‫ﻟﻠﻌﺪد‬ ‫اﻟﻤﻄﻠﻘﺔ‬ ‫اﻟﻘﻴﻤﺔ‬‫اﻟﺼﺤﻴﺢ‬
-‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻫﻰ‬)‫أ‬(‫واﻟﺼﻔﺮ‬=‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻮﻗﻊ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬)‫ب‬(‫اﻷﻋﺪاد‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ‫واﻟﺼﻔﺮ‬.....
‫ﻣﻮﺟﺒﺔ‬ ‫داﺋﻤﺎ‬ ‫وﻫﻰ‬
‫ﺗﻤﺮﻳﻦ‬١‫أ‬‫ﻳﺄ‬ ‫ﻣﺎ‬ ‫ﻛﻤﻞ‬‫ﺗﻰ‬:-
|٨|=..............|-١٠٢|................. =
-|-٤٥|=..........|٩١|+|-١١|=......................
|-٣٤|-|٢٣|................................ =
‫اﻟﻤﻌﻜﻮس‬ ‫ﻫﻮ‬ ‫ﻣﺎ‬)‫اﻟﻨﻈﻴﺮ‬(‫اﻟﻤﻮﺟﺐ‬ ‫اﻟﺼﺤﻴﺢ‬ ‫ﻟﻠﻌﺪد‬ ‫اﻟﺠﻤﻌﻲ‬)‫ـ‬٩(‫؟‬
‫اﻟﻤﻌﻜﻮس‬ ‫ﻫﻮ‬ ‫ﻣﺎ‬)‫اﻟﻨﻈﻴﺮ‬(‫اﻟﻤﻮﺟﺐ‬ ‫اﻟﺼﺤﻴﺢ‬ ‫ﻟﻠﻌﺪد‬ ‫اﻟﺠﻤﻌﻲ‬+)٥(‫؟‬
‫ﻫﻮ‬ ‫ﻣﺎ‬‫؟‬ ‫ﻟﻠﺼﻔﺮ‬ ‫اﻟﺠﻤﻌﻲ‬ ‫اﻟﻤﻌﻜﻮس‬
٧٦٥٤٣٢١٠-١-٢-٣-٤-٥-٦-٧
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086
‫ﻞ‬‫ﻣ‬‫ﺎ‬‫ﻛ‬ ‫ﺮ‬‫ﺑ‬‫ﺎ‬‫ﺟ‬ ‫ﻦ‬‫ﳝ‬‫أ‬ / ‫أ‬
‫ﻞ‬‫ﻣ‬‫ﺎ‬‫ﻛ‬ ‫ﺮ‬‫ﺑ‬‫ﺎ‬‫ﺟ‬ ‫ﻦ‬‫ﳝ‬‫أ‬ / ‫أ‬

3. ٣
١.‫اﻟﺼﻔﺮ‬ ‫ﻫﻮ‬ ‫اﻟﺼﻔﺮ‬ ‫ﻣﻌﻜﻮس‬.٢.‫ﺳﺎﻟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫اﻟﻤﻮﺟﺐ‬ ‫اﻟﺼﺤﻴﺢ‬ ‫اﻟﻌﺪد‬ ‫ﻣﻌﻜﻮس‬.
٣.‫ﻣﻮﺟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫اﻟﺴﺎﻟﺐ‬ ‫اﻟﺼﺤﻴﺢ‬ ‫اﻟﻌﺪد‬ ‫ﻣﻌﻜﻮس‬.٤.، ‫اﻟﻤﻄﻠﻖ‬ ‫ﻧﻔﺲ‬ ‫وﻣﻌﻜﻮﺳﻪ‬ ‫اﻟﺼﺤﻴﺢ‬ ‫ﻟﻠﻌﺪد‬
‫ﺗﻤﺜﻞ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﻣﺘﺴﺎوﻳﻴﻦ‬ ‫ﺑﻌﺪﻳﻦ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻜﻮﻧﺎن‬ ‫وﻣﻌﻜﻮﺳﻪ‬ ‫اﻟﺼﺤﻴﺢ‬ ‫اﻟﻌﺪد‬ ‫أن‬ ‫ﺑﻤﻌﻨﻰ‬‫اﻟﺼﻔﺮ‬
‫ﻋﻠﻰ‬‫ﺧﻂ‬‫اﻷﻋﺪاد‬.
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﻛﻤﺎ‬ ‫اﻻﻋﺪاد‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ‫اﻻﺗﻴﺔ‬ ‫اﻻﻋﺪاد‬ ‫ﻣﺜﻞ‬:
٧،-٥،-٧،٢،٠،١،-١،-٣،٥
‫س‬٢(‫اﻻﺗﻴﺔ‬ ‫اﻻﻋﺪاد‬ ‫ﻣﻦ‬ ‫ﻛﻼ‬ ‫ﻣﻌﻜﻮس‬ ‫اﻛﺘﺐ‬:
١٢٤،٧٦،-٤٦،٢٣،-٥٦،١٢
......،.....،.....،...،......،......
‫س‬٣(‫ﻗﻴﻤﺔ‬ ‫أوﺟﺪ‬)‫س‬(‫ﺻﺤﻴﺤﺔ‬ ‫اﻵﺗﻴﺔ‬ ‫اﻟﻌﺒﺎرة‬ ‫ﺗﺠﻌﻞ‬ ‫اﻟﺘﻲ‬:
)‫أ‬(-٣Ј}١،-١،‫س‬،٥{‫س‬........ =
)‫ب‬(}‫س‬،-٩{∩}١،-١،-٣،٥{=‫س‬........ =
‫س‬٤(‫ﻳﺎﺗﻰ‬ ‫ﻣﺎ‬ ‫أﻛﻤﻞ‬:
)‫أ‬(‫اﻟﻌﺪد‬ ‫ﻣﻌﻜﻮس‬-٤‫ﻫﻮ‬) ........‫ب‬(‫اﻟﻌﺪد‬ ‫ﻣﻌﻜﻮس‬٩‫ﻫﻮ‬........
)‫ج‬(‫اﻟﻌﺪد‬ ‫ﻣﻌﻜﻮس‬|-٧|‫ﻫﻮ‬) .........‫د‬(‫اﻟﻌﺪد‬ ‫ﻣﻌﻜﻮس‬-|-٨|‫ﻫﻮ‬.........
‫س‬٥(‫ﻋﻼﻣﺔ‬ ‫ﺿﻊ‬)√(‫وﻋﻼﻣﺔ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻟﻌﺒﺎرة‬ ‫اﻣﺎم‬)×(‫اﻟﺨﺎﻃﺌﺔ‬ ‫اﻟﻌﺒﺎرة‬ ‫اﻣﺎم‬٠
)‫أ‬(-|-٣|ЈW-( ))‫ب‬(W+UW-=W( )
)‫ج‬(W+=‫ع‬( ))‫د‬(|-٧|W( )
)‫ﻫـ‬(T=W-∩W( ))‫و‬(W+U‫ط‬=W( )
)‫ز‬(}-١،-٢،-٣،-٤،-٥،.......{U‫ط‬GW-( )
٧٦٥٤٣٢١٠-١-٢-٣-٤-٥-٦-٧
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

4. ٤
‫اﻷﻋﺪاد‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﺗﻤﺜﻴﻞ‬
‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﻣﻘﺎرﻧﺔ‬-‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﺗﺮﺗﻴﺐ‬
-‫ﻋﻠﻰ‬ ِ‫ف‬‫ﻟﻠﺘﻌﺮ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﻣﻘﺎرﻧﺔ‬ ‫ﻓﻲ‬ ‫اﻷﻋﺪاد‬ ‫ﺧﻂ‬ ‫ﻧﺴﺘﺨﺪم‬‫واﻷﺻﻐﺮ‬ ‫اﻷﻛﺒﺮ‬.
ِ‫ر‬‫اﻟﻴﺴﺎ‬ ‫ﻋﻠﻰ‬ ُ‫ﻊ‬‫ﺗﻘ‬ ‫اﻟﺴﺎﻟﺒﺔ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫ﺟﻤﻴﻊ‬‫ﻟﻸﺳﻔﻞ‬ ‫أو‬ِ‫ﺮ‬‫اﻟﺼﻔ‬ ‫ﻣﻦ‬.
‫اﻟﺼﻔﺮ‬ ‫ﻣﻦ‬ ‫ﻟﻸﻋﻠﻰ‬ ‫أو‬ ‫اﻟﻴﻤﻴﻦ‬ ‫ﻋﻠﻰ‬ ُ‫ﻊ‬‫ﺗﻘ‬ ‫اﻟﻤﻮﺟﺒﺔ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ِ‫د‬‫اﻷﻋﺪا‬ َ‫ﻊ‬‫ﺟﻤﻴ‬.
١(‫ﺳﺎﻟﺐ‬ ‫ﺻﺤﻴﺢ‬ ٍ‫د‬‫ﻋﺪ‬ ‫ﱢ‬‫ي‬‫أ‬ ‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫اﻟﺼﻔﺮ‬
٢(‫ﻣﻮﺟﺐ‬ ‫ﺻﺤﻴﺢ‬ ٍ‫د‬‫ﻋﺪ‬ ٍ‫ﱢ‬‫ي‬‫أ‬ ‫ﻣﻦ‬ ‫أﺻﻐﺮ‬ ‫اﻟﺼﻔﺮ‬
٣(‫ﺳﺎﻟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫أي‬ ‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫ﻣﻮﺟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫أي‬.
٤(‫ﻣﻮﺟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫أي‬ ‫ﻣﻦ‬ ‫أﺻﻐﺮ‬ ‫ﺳﺎﻟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫أي‬.
‫س‬(‫اﻷﻋﺪاد‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ً‫ﻼ‬‫ﻣﻤﺜ‬ ً‫ﺎ‬‫ﺗﺼﺎﻋﺪﻳ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻷﻋﺪاداﻟﺼﺤﻴﺤﺔ‬ ‫رﺗﺐ‬:
-٣،٤،٠،-٥،٦
-‫ﻫﻮ‬ ‫اﻟﺘﺮﺗﻴﺐ‬........،........،........،........،........
‫س‬(‫اﻷﻋﺪاد‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ً‫ﻼ‬‫ﻣﻤﺜ‬ ً‫ﺎ‬‫ﺗﻨﺎزﻟﻴ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻷﻋﺪاداﻟﺼﺤﻴﺤﺔ‬ ‫رﺗﺐ‬:
٢،٤،-١،-٣،٠
-‫ﻫﻮ‬ ‫اﻟﺘﺮﺗﻴﺐ‬........،........،........،........،........
01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

5. ٥
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫ﺗﺼﺎﻋﺪﻳﺎ‬ ‫ﺗﺮﺗﻴﺒﺎ‬ ‫اﻵﺗﻴﺔ‬ ‫اﻷﻋﺪاد‬ ‫رﺗﺐ‬:
)‫أ‬(٧،-٥،٩،٠،-١،-١١،١٠
.....)،.....،.....،.....،.....،.....،( .....
)‫ب‬(٣،٩،١،٧،٥،١٢،١٠
.....)،.....،.....،.....،.....،.....،( .....
)‫ج‬(-٢،-٦،٠،-١،-٩،١
.....)،.....،.....،.....،.....،(.....
‫ـــــــــــــــــــــــــــــــ‬‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫س‬٢(‫ﻋﻼﻣﺔ‬ ‫ﺿﻊ‬)<(‫أو‬)>(‫أو‬(=)‫ﻳﻠﻰ‬ ‫ﻓﻴﻤﺎ‬:
)‫أ‬(٢٥)‫ب‬(-٢-٦)‫ج‬(|-٣|٣
)‫د‬(-١٢-٩)‫ر‬(٣+|-٣|٨)‫و‬(-|-٦|٤
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــ‬
‫س‬٣(‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﺼﺤﻴﺢ‬ ‫اﻟﻌﺪد‬ ‫اﻛﺘﺐ‬&‫ﺻﺤ‬ ‫ﻋﺪد‬ ‫ﻟﻜﻞ‬ ‫واﻟﺘﺎﻟﻲ‬‫ﻳﻠﻰ‬ ‫ﻓﻴﻤﺎ‬ ‫ﻴﺢ‬:
)‫أ‬(-٤)‫ب‬(١٤
)‫ج‬(-١)‫د‬(٠
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــ‬
‫س‬٤(‫ﻛﻞ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫اﻛﺘﺐ‬‫ﻳﻠﻲ‬ ‫ﻣﻤﺎ‬ ‫ﺻﺤﻴﺤﻴﻦ‬ ‫ﻋﺪدﻳﻦ‬:
)‫أ‬(-٣،......،.......،.......،.....،.......،٣
)‫ب‬(-٦،......،.......،.......،.....،.......،.......،١
)‫ج‬(-٥.......،.......،.......،.......،٠
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـ‬
)٥(‫اﻟﺘﺴﻠﺴﻞ‬ ‫ﺑﻨﻔﺲ‬ ‫أﻛﻤﻞ‬:
)‫أ‬(-٩،-٨،-٧،......،........،.......
)‫ب‬(-٣،٠،٣،......،........،.......
)‫ﺟـ‬(-٦٠،-٥٠،-٤٠،......،........،.......
............
........................
............
01022744086
01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

6. ٦
١‫ﻣﻮﺟﺐ‬ ‫اﻟﻨﺎﺗﺞ‬ ‫ﻳﻜﻮن‬ ‫ﻣﻮﺟﺐ‬ ‫ﻛﻼﻫﻤﺎ‬ ‫ﻋﺪﻳﻦ‬ ‫ﺟﻤﻊ‬ ‫ﻋﻨﺪ‬
٢‫ﺳﺎﻟﺐ‬ ‫اﻟﻨﺎﺗﺞ‬ ‫ﻳﻜﻮن‬ ‫ﺳﺎﻟﺐ‬ ‫ﻛﻼﻫﻤﺎ‬ ‫ﻋﺪدﻳﻦ‬ ‫ﺟﻤﻊ‬ ‫ﻋﻨﺪ‬
‫ﺤﺔ‬‫ﻴ‬‫اﻟﺼﺤ‬ ‫اﻷﻋﺪاد‬ ‫ﺮح‬‫ﻃ‬‫و‬ ‫ﻊ‬‫ﺟﻤ‬
ً‫ﻻ‬‫او‬:‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻻﻋﺪاد‬ ‫ﺟﻤﻊ‬:
-‫ﻓﻲ‬ ‫داﺋﻤﺎ‬ ‫ﻣﻤﻜﻨﺔ‬ ‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬W‫ﻧﺴﺘﺨﺪم‬ ‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫إﺟﺮاء‬ ‫ﻓﻌﻨﺪ‬‫واﻟﺨﺴﺎرة‬ ‫اﻟﻤﻜﺴﺐ‬ ‫ﻣﺒﺪأ‬
‫ﻣﺜﺎل‬١(٥+٣=٨
٨٧٦٥٤٣٢١٠-١-٢-٣-٤
‫ﻣﺜﺎل‬٢) (-١) + (-٢= (-٣
٨٧٦٥٤٣٢١٠-١-٢-٣-٤
‫ﻣﺜﺎل‬٣(٥) +-٣= (٢
٨٧٦٥٤٣٢١٠-١-٢-٣-٤
‫؟‬ ‫ﺗﻌﻠﻤﻨﺎ‬ ‫ﻣﺎذا‬!
‫ﻣﺜﺎل‬(‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
)١(٧+٥=١٢)٢(٨) +-٥= (٣)٣(-٣+١=-٢
)٤()-٤(-)-٩= (٥)٥) (-٤) + (-٩= (-١٣
‫ﺗﻤﺮﻳﻦ‬:‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
)١(٦+٨....... =)٢) (-٥+ (٤) ....... =٣(٣) +-٤....... = (
)٤(٨) +-٨) ....... = (٥) (-٤(-)-١....... = ()٦(١٢) +-١٠....... = (
‫ﻓﻲ‬ ‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺧﻮاص‬W
١.‫اﻹﻧﻐﻼق‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻛﺎﻧﺖ‬ ‫إذا‬hЈW&fЈW‫ﻓﺈن‬:h+f=OЈW
٢.‫اﻻﺑﺪال‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻛﺎﻧﺖ‬ ‫إذا‬h&f‫ﻓﺈن‬ ‫ﺻﺤﻴﺤﻴﻦ‬ ‫ﻋﺪدﻳﻦ‬:h+f=f+h
٣.‫اﻟﺪﻣﺞ‬ ‫ﺧﺎﺻﻴﺔ‬:
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

7. ٧
-‫ﻛﺎﻧﺖ‬ ‫إذا‬h&‫ﺏ‬&O‫ﻓﺈن‬ ‫ﺻﺤﻴﺤﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬:}h+f{+O=h+}f+O{
٤.‫اﻟﺠﻤﻌﻲ‬ ‫اﻟﻤﺤﺎﻳﺪ‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻓﻲ‬ ‫اﻟﺠﻤﻌﻲ‬ ‫اﻟﻤﺤﺎﻳﺪ‬ ‫ﻫﻮ‬ ‫اﻟﺼﻔﺮ‬W:‫ﻛﺎن‬ ‫اذا‬h‫ﻓﺈن‬ ‫ﺻﺤﻴﺤﺎ‬ ً‫ا‬‫ﻋﺪد‬:h+٠=٠+h=h
٥.‫اﻟﺠﻤﻌﻲ‬ ‫اﻟﻤﻌﻜﻮس‬ ‫ﺧﺎﺻﻴﺔ‬:
‫ﻣﻮﺟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫ﻛﻞ‬)h(‫ﺳﺎﻟﺐ‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬ ‫ﻳﻘﺎﺑﻠﻪ‬)–h(‫إن‬ ‫ﺑﺤﻴﺚ‬:h) +-h= (‫ﺻﻔﺮ‬
‫ﻣﺜﺎل‬(‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫إﻳﺠﺎد‬ ‫ﻓﻲ‬ ‫اﻟﺠﻤﻊ‬ ‫ﺧﻮاص‬ ‫اﺳﺘﺨﺪم‬
٣٦+١٩+٦٤+٨١
=٣٦+٦٤+١٩+٨١)‫اﻹﺑﺪال‬ ‫ﺧﺎﺻﻴﺔ‬(
) =٣٦+٦٤) + (١٩+٨١()‫اﻟﺪﻣﺞ‬ ‫ﺧﺎﺻﻴﺔ‬(
=١٠٠+١٠٠=٢٠٠
‫ﺗﻤﺮﻳﻦ‬:‫إﻳﺠﺎد‬ ‫ﻓﻲ‬ ‫اﻟﺠﻤﻊ‬ ‫ﺧﻮاص‬ ‫اﺳﺘﺨﺪم‬:
٤٧+١٤٥+٢٧٣) +-٤٥(..................................................
..................................................
..................................................
١٠٩) +-٣٨+ (٤٩١+٥٣٨...................................................
...................................................
...................................................
ً‫ﺎ‬‫ﺛﺎﻧﻴ‬:‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻻﻋﺪاد‬ ‫ﻃﺮح‬:
-‫ﺳﺒﻖ‬ ‫ﻣﻤﺎ‬ ‫ﻧﻌﻠﻢ‬‫ﻓﻲ‬ ً‫ﺎ‬‫داﺋﻤ‬ ‫ﻣﻤﻜﻦ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻄﺮح‬ ‫دراﺳﺘﻪ‬'‫ﻓﻲ‬ ‫اﻟﻄﺮح‬ ‫إﻧﻤﺎ‬Wً‫ﺎ‬‫داﺋﻤ‬ ‫ﻣﻤﻜﻦ‬
‫ﻣﺜﻞ‬٩–٥≠٥-٩‫وﻟﻜﻦ‬٩) +-٥= (-٥+٩
‫ﻣﺜﺎل‬(‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
)١(٩-٧&٧–٩
‫اﻻﺟﺎﺑﺔ‬(٩–٧=٢&٧–٩=-٢
‫إذن‬٩–٧≠٧–٩‫اﺑﺪاﻟﻴﻪ‬ ‫ﻟﻴﺴﺖ‬ ‫اﻟﻄﺮح‬ ‫ﻋﻤﻠﻴﺔ‬ ‫إذن‬
)٢(-٧-)٥-٣(&)-٧-٥(-٣
-٧-٢=-٩&-١٢-٣=-١٥
‫إذن‬-٧–)٥–٣(≠)-٧–٥(-٣‫إذن‬‫داﻣﺠﻪ‬ ‫ﻟﻴﺴﺖ‬ ‫اﻟﻄﺮح‬ ‫ﻋﻤﻠﻴﺔ‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

8. ٨
‫ﺗﻤﺮﻳﻦ‬:‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
٩-٤......... =٦–٨......... =
-٤-٧......... =-٧+٢......... =
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫اﻟﺘﺎﻟﻴﺔ‬ ‫واﻟﻄﺮح‬ ‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺎت‬ ‫ﻟﺘﻤﺜﻴﻞ‬ ‫اﻷﻋﺪاد‬ ‫ﺧﻂ‬ ‫اﺳﺘﺨﺪم‬:
)‫أ‬(-٥-٢)‫ب‬(-٨+٩)‫ج‬(٦–)-١(
)‫أ‬............................................................................................ (
)‫ب‬............................................................................................ (
)‫ج‬(............................................................................................
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــ‬
‫س‬٢(‫اﻟﻤﻨﺎﺳﺐ‬ ‫اﻟﺮﻣﺰ‬ ‫ﺿﻊ‬Ј،Ј،G،G‫ﻳﻠﻲ‬ ‫ﻓﻴﻤﺎ‬:
)‫أ‬(-٣......‫ط‬)‫ب‬(‫ط‬.......W
)‫ج‬(-|٦|.....W-)‫د‬(-|-٥|......W-
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــ‬
‫س‬٣(‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫إﻳﺠﺎد‬ ‫ﻓﻲ‬ ‫اﻟﺠﻤﻊ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺧﻮاص‬ ‫اﺳﺘﺨﺪم‬
-١٢٠+١٧+١٣١٨٤٥+٩٦٧+١٥٥+٣٣
٢٣٥٤+٧٠٠) +-٥٤(
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــ‬
‫س‬٤(‫ﻓﻜﺎﻧﺖ‬ ‫ﻣﻮﺳﻜﻮ‬ ‫درﺟﺔ‬ ‫اﻟﺤﺮارة‬ ‫ﻣﻴﺰان‬ ‫ﺳﺠﻞ‬-٧‫اﻟﺴﺎﻋﺔ‬ ‫ﻋﻨﺪ‬ ‫م‬٣‫ﻣﻨﺘﺼﻒ‬ ‫ﺑﻌﺪ‬
‫ﻛﺎﻧﺖ‬ ‫اﻟﻴﻮم‬ ‫ﻧﻔﺲ‬ ‫ﻋﺼﺮ‬ ‫ﻓﻲ‬ ‫ﺑﻴﻨﻤﺎ‬ ‫اﻟﻠﻴﻞ‬١٥‫م‬.‫اﻟﺤﺮارة‬ ‫درﺟﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺰﻳﺎدة‬ ‫أﺣﺴﺐ‬.
...........................................................................................
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــ‬
‫س‬٥(‫ﻋﻤﻖ‬ ‫ﻋﻠﻰ‬ ‫ﻏﻮاﺻﺔ‬٩٠‫ﻣﺘﺮا‬"‫ارﺗﻔﻌﺖ‬ ، ‫اﻟﺒﺤﺮ‬ ‫ﺳﻄﺢ‬ ‫ﻣﺴﺘﻮى‬ ‫ﺗﺤﺖ‬٦٠‫ﻣﺘﺮا‬"٠
‫؟‬ ‫ﻟﻠﻐﻮاﺻﺔ‬ ‫اﻟﺠﺪﻳﺪ‬ ‫اﻟﻌﻤﻖ‬ ‫ﻟﺤﺴﺎب‬ ‫اﻟﻤﻨﺎﺳﺒﺔ‬ ‫اﻟﺤﺴﺎﺑﻴﺔ‬ ‫اﻟﻌﻤﻠﻴﺔ‬ ‫اﺳﺘﺨﺪم‬
...........................................................................................
01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

9. ٩
‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻷﻋﺪاد‬ ‫وﻗﺴﻤﺔ‬ ‫ﺿﺮب‬
ً‫ﻻ‬‫او‬:‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻻﻋﺪاد‬ ‫ﺿﺮب‬:
‫ﻓﻲ‬ ‫اﻟﻀﺮب‬ ‫ﻓﻰ‬ ‫اﻹﺷﺎرات‬ ‫ﻗﺎﻋﺪة‬W
‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬×‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬=‫ﻣﺜﺎل‬ ‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬٥×٣=١٥
‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬×‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬=‫ﻣﺜﺎل‬ ‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬٦×-٣=-١٨
‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬×‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬=‫ﻣﺜﺎل‬ ‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬-٤×٨=-٣٢
‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬×‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬=‫ﻣﺜﺎل‬ ‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬-٥×-٩=٤٥
‫ﻣﺜﺎل‬(‫ﻳﺄﺗﻲ‬ ‫ﻣﻤﺎ‬ ً‫ﻼ‬‫ﻛ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬
)‫أ‬(-٧×٣=-٢١)‫ب‬(-٦×-٩=٥٤)‫ج‬(٧×-)-٦= (٧×٦=٤٢
‫ﺗﻤﺮﻳﻦ‬:‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
-١٢×٦............. =،-٣٤×-٥٤........... =
٤٥٦×١٣............. =،٢٣٤×-٥........... =
‫ﻓﻲ‬ ‫اﻟﻀﺮب‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺧﻮاص‬W
١.‫اﻹﻧﻐﻼق‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻛﺎﻧﺖ‬ ‫إذا‬hЈW&fЈW‫ﻓﺈن‬:h×f=OЈW
٢.‫اﻻﺑﺪال‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻛﺎﻧﺖ‬ ‫إذا‬h&f‫ﻓﺈن‬ ‫ﺻﺤﻴﺤﻴﻦ‬ ‫ﻋﺪدﻳﻦ‬:h×f=f×h
٣.‫اﻟﺪﻣﺞ‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻛﺎﻧﺖ‬ ‫إذا‬h&f&O‫ﻓﺈن‬ ‫ﺻﺤﻴﺤﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬:}h×f{×O=h×}f×O{
٤.‫اﻟﻀﺮﺑﻲ‬ ‫اﻟﻤﺤﺎﻳﺪ‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻓﻲ‬ ‫اﻟﻀﺮﺑﻲ‬ ‫اﻟﻤﺤﺎﻳﺪ‬ ‫ﻫﻮ‬ ‫اﻟﻮاﺣﺪ‬W:‫ﻛﺎن‬ ‫اذا‬h‫ﻓﺈن‬ ‫ﺻﺤﻴﺤﺎ‬ ً‫ا‬‫ﻋﺪد‬:h×١=١×h=h
٥.‫اﻟﺠﻤﻊ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻀﺮب‬ ‫ﺗﻮزﻳﻊ‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻛﺎﻧﺖ‬ ‫إذا‬h&f&O‫إن‬ ‫ﻓﺈن‬ ‫ﺻﺤﻴﺤﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬:}h+f{×O=h×O+f×O
‫ﻣﺜﺎل‬(‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫إﻳﺠﺎد‬ ‫ﻓﻲ‬ ‫اﻟﻀﺮب‬ ‫ﺧﻮاص‬ ‫اﺳﺘﺨﺪم‬
٧×]٨) +-٧[ (
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

10. ١٠
‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬÷‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬=‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬
‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬÷‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬=‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬
‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬÷‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬=‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬
‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬÷‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬=‫ﻣﻮﺟﺐ‬ ‫ﻋﺪد‬
=٧×٨+٧×)-٧= (٥٦) +-٤٩= (٧
١١٢×١٧+١١٢×-١٧
=١١٢×]١٧) +-١٧[ (=١١٢×‫ﺻﻔﺮ‬=‫ﺻﻔﺮ‬
١٢٣×١٠٠٢
=١٢٣×)١٠٠٠+٢= (١٢٣×١٠٠٠+١٢٣×٢=١٢٣٠٠٠+٢٣٦=١٢٣٢٣٦
٤٥٤×٩٩
=٤٥٤×)١٠٠–١= (٤٥٤×١٠٠–٤٥٤×١=٤٥٤٠٠–٤٥٤=٤٤٩٤٦
‫ﺗﻤﺮﻳﻦ‬:‫ﻳﺄﺗﻲ‬ ‫ﻣﺎ‬ ‫اﻳﺠﺎد‬ ‫ﻓﻲ‬ ‫اﻟﻀﺮب‬ ‫ﺧﻮاص‬ ‫اﺳﺘﺨﺪم‬:
٢١٣×٢٣+٢١٣×١٧٧
......................................................................................................
......................................................................................................
......................................................................................................
٣٤٦×٩٩
......................................................................................................
......................................................................................................
......................................................................................................
ً‫ﺎ‬‫ﺛﺎﻧﻴ‬:‫اﻷ‬ ‫ﻗﺴﻤﺔ‬‫اﻟﺼﺤﻴﺤﺔ‬ ‫ﻋﺪاد‬:
‫ﻓﻲ‬ ً‫ﺎ‬‫داﺋﻤ‬ ‫ﻣﻤﻜﻨﺔ‬ ‫ﻏﻴﺮ‬ ‫اﻟﻘﺴﻤﺔ‬W
‫ﺗﻤﺮﻳﻦ‬:‫ﻣﺎذا‬‫ﻧﻼﺣﻆ‬:
١٨÷)٣÷٢= (١٨÷١.٥=١٢
)١٨÷٣(÷٢=٦÷٢=٣
‫ﺗﻨﺴﻰ‬ ‫أوﻋﻰ‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

11. ١١
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬‫ﻳﻠﻲ‬:
)‫أ‬(-١٣١×-٣) ......... =‫ب‬(٣٤×-٥) ......... =‫ج‬(-٩)-٨......... = (
)‫د‬(–)-٦(×-٣...... =)‫ﻫـ‬(-٥٦÷-٢) ......... =‫و‬(–)-٦(×|-٦|......... =
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــ‬
‫س‬٢(‫ﻓﻲ‬ ‫اﻟﻤﻤﻜﻨﺔ‬ ‫اﻟﻘﺴﻤﺔ‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﺣﺪد‬W‫ﻳﻠﻲ‬ ‫ﻓﻴﻤﺎ‬:
)‫أ‬) (-٣٢(÷٨) .............‫ب‬(٤٢٠÷)-١٥............. (
)‫ج‬(٥٦÷]٣) +-٣) ............. [ (‫د‬) (٤-٤(÷٩.............
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ـــ‬
‫س‬٣(‫ﻳﺄﺗﻲ‬ ‫ﻣﺎ‬ ‫اﻳﺠﺎد‬ ‫ﻓﻲ‬ ‫اﻟﻀﺮب‬ ‫ﺧﻮاص‬ ‫اﺳﺘﺨﺪم‬:
)‫أ‬(٦٩×١٠١)‫ب‬(٨٦×٤٥٥+٨٦×٥٥٥)‫ج‬(٣٤×١٥+٦٦×١٥
)‫أ‬(
....................................................................................................
.........................................................................................................
)‫ب‬.................................................................................................... (
.........................................................................................................
)‫ج‬(
.....................................................................................................
.........................................................................................................
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــ‬
‫س‬٤(‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻗﻴﻤﺔ‬ ‫اﺣﺴﺐ‬:‫ﻛﺎن‬ ‫اذا‬)‫س‬=٣(،)‫ص‬=-١(،)‫ع‬=-٧(
)‫أ‬(٢‫س‬+‫ص‬–‫ع‬)‫ب‬(٣‫ص‬ ‫س‬–‫ع‬)‫ج‬) (‫س‬÷‫ص‬(×٣‫ع‬
‫س‬٥(‫ﻛﺎن‬ ‫اذا‬ ‫س‬ ‫ﻗﻴﻤﺔ‬ ‫أوﺟﺪ‬:
)‫أ‬(٨×‫س‬=-٤٨)‫ب‬(‫س‬×٩=٦٣)‫ج‬(‫س‬×)٥×-١٣) = (-٩×٥(×-١٣
)‫أ‬(............................................................................................................
)‫ب‬(............................................................................................................
)‫ج‬........... (..............................................................................................
.........................................................................................................
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

12. ١٢
‫ﻷس‬ ‫ﻣﺮﻓﻮع‬ ‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬ ‫أي‬‫زوﺟﻲ‬‫اﻟﻨﺎﺗﺞ‬ ‫ﻳﻜﻮن‬(+)
‫ﻷس‬ ‫ﻣﺮﻓﻮع‬ ‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬ ‫أي‬‫ﻓﺮدي‬‫اﻟﻨﺎﺗﺞ‬ ‫ﻳﻜﻮن‬)-(
‫اﻟﻤﺘﻜﺮر‬ ‫اﻟﻀﺮب‬
‫ﺑﺄﻧﻪ‬ ‫ﻳﻌﺮف‬:‫اﻟﻤﺮات‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﻧﻔﺴﻪ‬ ‫ﻓﻲ‬ ‫اﻟﻌﺪد‬ ‫ﺿﺮب‬ ‫ﺗﻜﺮار‬
‫ﻓﻤﺜﻼ‬:٢×٢×٢×٢=٤
٢: )‫اﻟﺮﻗﻢ‬٢‫ﻳﺴﻤﻰ‬‫أﺳﺎس‬‫اﻟﺮﻗﻢ‬ ،٤‫ﻳﺴﻤﻰ‬‫أس‬(
‫ﻋﺎﻣﻪ‬ ‫ﺑﺼﻔﺔ‬:‫ﺃ‬‫ﻛﺎﻧﺖ‬ ‫اذا‬hЈW‫ﻓﺎن‬h×h×h×٠٠٠٠٠٠٠٠k‫اﻟﻤﺮات‬ ‫ﻣﻦ‬=h‫ﻥ‬
‫ﺿﺮب‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬‫اﻟﻤﺘﺤﺪة‬ ‫اﻷﺳﺎﺳﺎت‬‫اﻷﺳﺲ‬ ‫ﻧﺠﻤﻊ‬٤
٦×٢
٦=٦
٦
‫اﻟﻤﺘﺤﺪة‬ ‫اﻷﺳﺎﺳﺎت‬ ‫ﻗﺴﻤﺔ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬‫اﻷﺳﺲ‬ ‫ﻧﻄﺮح‬٤
٦÷٢
٦=٢
٦
‫ﻣﺜﺎل‬(‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬‫ﻳﺄﺗﻲ‬ ‫ﻣﻤﺎ‬ ً‫ﻼ‬‫ﻛ‬:
)‫أ‬(٣
٥×٢
٥=٥
٥=٣١٢٥)‫ب‬(٤
٦×٥
٦×٦‫ﺻﻔﺮ‬
=٩
٦×١=١٠٠٧٧٦٩٦
‫ﻣﺜﺎل‬(‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
‫أ‬(-٣
٥×-٢
٥=-٥
٥=-٣١٢٥،‫ب‬()-٦(٤
×)-٦(٢
) =-٦(٦
=٤٦٦٥٦
‫ج‬(٤
٦÷٤
٦=٦)٤-٤(
=٦‫ﺻﻔﺮ‬
=١،‫د‬()٢
٢(٣
=٢
٢×٣
=٦
٢=٦٤
)‫د‬) (٣
٢×)-٢(٤
(÷٥
٢= ===٢٧-٥
=٢
٢=٤
‫ﺗﻤﺮﻳﻦ‬:‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
)-٢(٣
×٣
٣........ =)-٢(٢
×)-٢(٤
÷٦
٢................................... =
٣
٥×٧
٥÷٤
٥×٣
٥=...........................................................
‫ﻫﺎﻣﺔ‬ ‫ﻗﺎﻋﺪﺓ‬
٣
٢×)-٢(٤
٥
٢
٣
٢×٤
٢
٥
٢
٧
٢
٥
٢

13. ١٣
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫أوﺟﺪ‬:
‫أ‬()-٧(٢
............ =‫ب‬()-٥(٢
×٢
٢............ =
‫ج‬) (-٢(٢
) +-٣(٤
........................ =
‫د‬) (-١(١٠٠
) +-١(١٠١
........................ =
‫ﻫـ‬) (-٥(٣
×)-١(٥
........................ =
‫و‬) (-٢(٣
÷)-٢(٢
........................ =
‫ز‬)] (-٤(٥
×)-٤(٣
[÷)-٤(٦
........................ =
)‫ح‬(+-.................. =
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــ‬
‫س‬٢(ً‫ﺎ‬‫ﺗﺼﺎﻋﺪﻳ‬ ً‫ﺎ‬‫ﺗﺮﺗﻴﺒ‬ ‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫رﺗﺐ‬:
-٥
٢،-٢
٣،-٠
٤،-١٥
١،٢
٣
.................................................................................................................................
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــ‬
‫س‬٣(ً‫ﺎ‬‫ﺗﻨﺎزﻟﻴ‬ ً‫ﺎ‬‫ﺗﺮﺗﻴﺒ‬ ‫ﻳﻠﻲ‬ ‫ﻣﺎ‬ ‫رﺗﺐ‬:
٢
١٠،-٥
١،٢
١٠٠،-٣
١٠،١٠٠٠٠٠٠
..................................................................................................
‫ــــــــــــــــــــــــ‬‫ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬‫ــــــــــــــــــــــــــــ‬
‫س‬٤(‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫ﻗﻴﻤﺔ‬ ‫اﺣﺴﺐ‬:‫ﻛﺎن‬ ‫اذا‬)‫أ‬=٢(،)‫ب‬=-٣(
)‫أ‬(٣‫أ‬)‫ب‬(٢‫أ‬+٣‫ب‬)‫ج‬(‫أ‬+‫ب‬+‫ب‬ ‫أ‬
)‫أ‬.................................................................................................. (
)‫ب‬(.................................................................................................
)‫ج‬................................................................................................... (
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫س‬٥(‫ﻋﻼﻣﺔ‬ ‫ﺿﻊ‬)<(،‫أ‬)>(،‫أ‬)=(‫ﻳﻠﻲ‬ ‫ﻓﻴﻤﺎ‬:
)‫أ‬(٢
٤٨)‫ب‬(-٢
٦-١٢
)‫ج‬(٢
٩-٤
٣)‫د‬(١×٥
٧٥
٧
٣
٤×-٤
٤
٥
٤
٣
٥×-٤
٥
٥
٥
٣
٣×٤
٢
٥
٢×٤
٢
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

14. ١٤
‫اﻷﻧﻤﺎط‬‫اﻟﻌﺪدﻳﺔ‬
‫ﺑﺄﻧﻪ‬ ‫اﻟﻌﺪدي‬ ‫اﻟﻨﻤﻂ‬ ‫ﻳﻌﺮف‬:‫ﻣﻌﻴﻨﺔ‬ ‫ﻟﻘﺎﻋﺪة‬ ً‫ﺎ‬‫وﻓﻘ‬ ‫اﻷﻋﺪاد‬ ‫ﻣﻦ‬ ‫ﺗﺘﺎﺑﻊ‬
ً‫ﻼ‬‫ﻓﻤﺜ‬‫ﺑﻤﻘﺪار‬ ‫ﺳﺎﺑﻘﻪ‬ ‫ﻋﻦ‬ ‫ﻳﺰﻳﺪ‬ ‫ﻋﺪد‬ ‫ﻛﻞ‬١‫ذﻟﻚ‬ ‫وﻳﺴﻤﻰ‬‫اﻟﻨﻤﻂ‬ ‫وﺻﻒ‬
‫ﺗﻤﺮﻳﻦ‬:‫ﺷﻜﻞ‬ ‫ﻛﻞ‬ ‫أﺳﻔﻞ‬ ‫اﻟﻤﺜﻠﺜﺎت‬ ‫ﻋﺪد‬ ‫أﻛﺘﺐ‬:
‫اﻟﻤﺜﻠﺜﺎت‬ ‫ﻋﺪد‬........ ........ .......
‫اﻟﻌﺪدي‬ ‫اﻟﻨﻤﻂ‬....................................... :‫اﻟﻨﻤﻂ‬ ‫وﺻﻒ‬........................... :
‫اﻟﻮاﺟﺐ‬‫اﻟﻤﻨﺰﻟﻲ‬
‫س‬١(‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼث‬ ‫ﺑﻜﺘﺎﺑﺔ‬ ‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﻌﺪدﻳﺔ‬ ‫اﻷﻧﻤﺎط‬ ‫أﻛﻤﻞ‬:
)‫أ‬(٦،١٤،٢٢،٣٠،٣٨،........،........،........
)‫ب‬(٣،-٦،١٢،-٢٤،........،........،........
)‫ج‬(٢،٣،٥،٨،١٣،........،........،........
)‫د‬(١،٤،٩،١٦،٢٥،........،........،........
‫س‬٢(‫ﺣﺎﻟﺔ‬ ‫ﻛﻞ‬ ‫ﻓﻲ‬ ‫اﻟﻨﺎﻗﺺ‬ ‫اﻟﻌﺪد‬ ‫واﻛﺘﺐ‬ ‫اﻟﻌﺪدى‬ ‫اﻟﻨﻤﻂ‬ ‫اﻛﺘﺸﻒ‬:
)‫أ‬(٤،٧،........،١٣،١٦،........،........
‫ﻫﻮ‬ ‫اﻟﻨﻤﻂ‬..............................................
)‫ب‬(٧،........،١٥،١٩،٢٣،........،........
‫ﻫﻮ‬ ‫اﻟﻨﻤﻂ‬..............................................
)‫ج‬(١٢٨،٨٤،........،١٦،٨،........،........
‫ﻫﻮ‬ ‫اﻟﻨﻤﻂ‬..............................................
)‫د‬........ (،١٥،١٢،٩،........،........
‫اﻟﻨﻤﻂ‬‫ﻫﻮ‬..............................................
‫س‬٣: (‫ﻣﺼﺮ‬ ‫ﺑﺼﺤﺮاء‬ ‫اراﺿﻰ‬ ‫ﺷﺮﻛﺔ‬ ‫ﺗﺴﺘﺼﻠﺢ‬٦‫ﻻﺳﺘﺼﻼح‬ ‫اﻟﺸﺮﻛﺔ‬ ‫ﻳﻠﺰم‬ ‫ﻳﻮﻣﺎ‬ ‫ﻛﻢ‬ ، ‫اﻟﻮاﺣﺪ‬ ‫اﻟﻴﻮم‬ ‫ﻓﻰ‬ ‫اﻓﺪﻧﺔ‬
‫ﻣﻦ‬ ‫ﻳﻘﺮب‬ ‫ﻣﺎ‬٥٠‫؟‬ ‫وﺻﻔﻪ‬ ‫ذﻟﻚ‬ ‫ﻋﻦ‬ ‫اﻟﻤﻌﻴﺮ‬ ‫اﻟﻌﺪدى‬ ‫اﻟﻨﻤﻂ‬ ‫أﻛﺘﺐ‬ ‫؟‬ ‫ﻓﺪان‬
.........................................................................................................
.........................................................................................................
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

15. ١٥
‫ج‬
‫واﻟﻤﺘﺒﺎﻳﻨﺔ‬ ‫اﻟﻤﻌﺎدﻟﺔ‬‫اﻷوﻟﻰ‬ ‫اﻟﺪرﺟﺔ‬ ‫ﻦ‬‫ﻣ‬
‫اﻟﻤﻌﺎدﻟﺔ‬:‫رﻳﺎﺿﻴﺘﻴﻦ‬ ‫ﻋﺒﺎرﺗﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫ﺗﺴﺎوى‬ ‫ﻋﻼﻗﺔ‬ ‫ﺗﺘﻀﻤﻦ‬ ‫رﻳﺎﺿﻴﺔ‬ ‫ﺟﻤﻠﺔ‬ ‫ﻫﻲ‬
‫س‬+٣=٦)‫رﻳﺎﺿﻴﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬(
‫س‬+٣)‫رﻳﺎﺿﻴﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﻟﻴﺴﺖ‬(
٢–٧=-٥)‫رﻳﺎﺿﻴﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬(
-‫اﻷوﻟﻰ‬:‫ﺗﺴﺎوي‬ ‫ﻋﻼﻗﺔ‬ ‫ﺗﺘﻀﻤﻦ‬ ‫رﻳﺎﺿﻴﺘﻴﻦ‬ ‫ﻋﺒﺎرﺗﻴﻦ‬ ‫ﻷﻧﻬﺎ‬
-‫اﻟﺜﺎﻧﻴﺔ‬:‫ﺗﺴﺎوي‬ ‫ﻋﻼﻗﺔ‬ ‫ﻋﻰ‬ ‫ﺗﺤﺘﻮي‬ ‫ﻻ‬ ‫ﻷﻧﻬﺎ‬
-‫اﻟﺜﺎﻟﺜﺔ‬:‫ﺗﺴﺎوي‬ ‫ﻋﻼﻗﺔ‬ ‫ﺗﺘﻀﻤﻦ‬ ‫ﻷﻧﻬﺎ‬
‫اﻟﻤﻌﺎدﻟﺔ‬ ‫درﺟﺔ‬:‫اﻛﺒﺮ‬ ‫ﻫﻰ‬)‫أس‬(‫اﻟﻤﺠﻬﻮل‬ ‫ﻟﻪ‬ ‫ﻣﺮﻓﻮع‬)‫اﻟﺮﻣﺰ‬(‫ﺑﺎﻟﻤﻌﺎدﻟﺔ‬
‫س‬ ‫ﻣﺜﻞ‬+٥=٩)‫اﻷوﻟﻰ‬ ‫اﻟﺪرﺟﺔ‬(‫س‬ ،٢
+٣=٦)‫اﻟﺜﺎﻧﻴﺔ‬ ‫اﻟﺪرﺟﺔ‬(
‫اﻟﻤﺘﺒﺎﻳﻨﺔ‬:‫رﻳﺎﺿﻴﺘﻴﻦ‬ ‫ﻋﺒﺎرﺗﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﺘﺒﺎﻳﻦ‬ ‫ﻋﻼﻣﺔ‬ ‫ﺗﺘﻀﻤﻦ‬ ‫رﻳﺎﺿﻴﺔ‬ ‫ﺟﻤﻠﺔ‬ ‫ﻫﻲ‬
‫س‬+٣>٥
‫اﻟﻤﺘﺒﺎﻳﻨﺔ‬ ‫أو‬ ‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺣﻞ‬:‫اﻟﻤﺘﺒﺎﻳﻨﺔ‬ ‫أو‬ ‫ﺑﺎﻟﻤﻌﺎدﻟﺔ‬ ‫اﻟﻤﻮﺟﻮد‬ ‫اﻟﺮﻣﺰ‬ ‫ﻟﻘﻴﻤﺔ‬ ‫اﻟﺘﻮﺻﻞ‬ ‫ﺑﻪ‬ ‫ﻳﻘﺼﺪ‬
‫ﻣﺜﺎل‬(‫اوﺟﺪ‬‫ﻣﻦ‬ ‫ﻟﻜﻞ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬:‫ن‬ ‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﺑﺎﻋﺘﺒﺎر‬=}٠،٢،٣،٥{
)‫أ‬(‫س‬+٧=١٠،)‫ب‬(‫س‬+٤>٨
‫اﻟﺤﻞ‬) :‫أ‬(‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻧﺴﺘﺨﺪم‬)‫اﻟﻌﻨﺎﺻﺮ‬ ‫ﻟﺘﺤﺪﻳﺪ‬ ‫اﻷﻳﻤﻦ‬ ‫اﻟﻄﺮف‬ ‫ﻓﻲ‬ ‫ﺑﺎﻟﺘﻌﻮﻳﺾ‬
‫اﻟﺘﻰ‬‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺗﺤﻘﻖ‬(
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=٠‫ﻳﻜﻮن‬٠+٧=٧>١٠
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=٢‫ﻳﻜﻮن‬٢+٧=٩>١٠
‫ﻋﻨﺪﻣﺎ‬‫س‬=٣‫ﻳﻜﻮن‬٣+٧=١٠=١٠
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=٥‫ﻳﻜﻮن‬٥+٧=١٢<١٠‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫إذن‬=}٣{
‫اﻟﺤﻞ‬) :‫ب‬(‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻧﺴﺘﺨﺪم‬
‫ﻋﻨﺪﻣﺎ‬‫س‬=٠‫ﻳﻜﻮن‬٠= +٤>٨
‫ﻋﻨﺪﻣﺎ‬‫س‬=٢‫ﻳﻜﻮن‬٢+٤=٦>٨
‫ﻋﻨﺪﻣﺎ‬‫س‬=٣‫ﻳﻜﻮن‬٣+٤=٧>٨
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=٥‫ﻳﻜﻮن‬٥+٤=٩<٨‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫إذا‬=}٠،٢،٣{
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

16. ١٦
‫ﺗﻤﺮﻳﻦ‬:‫ﻣﻦ‬ ‫ﻟﻜﻞ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أوﺟﺪ‬:
‫ل‬ ‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﺑﺎﻋﺘﺒﺎر‬=}-٣،٥،١{
)‫أ‬(‫س‬-٢=٦،)‫ب‬(‫س‬+٢>٦
‫اﻟﺤﻞ‬) :‫أ‬(‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻧﺴﺘﺨﺪم‬‫ل‬=}-٣،٥،١{
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=.....‫ﻳﻜﻮن‬............................................
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=.....‫ﻳﻜﻮن‬............................................
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=.....‫ﻳﻜﻮن‬............................................
‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫إذا‬=}.............{
‫اﻟﺤﻞ‬) :‫ب‬(‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻧﺴﺘﺨﺪم‬‫ل‬=}-٣،٥،١{
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=.....‫ﻳﻜﻮن‬............................................
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=.....‫ﻳﻜﻮن‬............................................
‫س‬ ‫ﻋﻨﺪﻣﺎ‬=.....‫ﻳﻜﻮن‬............................................
‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫إذا‬=}.............{
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫اﻟﻤﻌﺎدﻻت‬ ‫ﻣﻦ‬ ‫ﻟﻜﻞ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أوﺟﺪ‬‫اﻟﺘﺎﻟﻴﺔ‬ ‫واﻟﻤﺘﺒﺎﻳﻨﺎت‬:
)١(‫س‬–٢=٥‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬}-٣،٧،١{
)٢(٣‫س‬+١=١٦‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬}٥،-٥{
)٣(٢)‫س‬-٣= (‫س‬+١‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬}-٣،٧،١{
)٤(‫س‬-١<١‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬}-٣،٣{
)٥(٣‫س‬-١<-٢‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬}-٣،٠،١{
)٦(-‫س‬+١>٤‫اﻟﺘﻌﻮﻳﺾ‬ ‫ﻣﺠﻤﻮﻋﺔ‬}-٣،-٥{
‫ﻻت‬‫اﻟﻤﻌﺎد‬ ‫ﺣﻞ‬‫وﻟﻰ‬‫ﻷ‬‫ا‬ ‫اﻟﺪرﺟﺔ‬ ‫ﻣﻦ‬‫واﺣﺪ‬ ‫ﻣﺠﻬﻮل‬ ‫ﻓﻲ‬
-‫ﻓﻰ‬ ‫اﻟﺘﺴﺎوي‬ ‫ﺧﻮاص‬ ‫ﻋﻠﻰ‬ ‫ﺗﻌﺘﻤﺪ‬ ‫ﻃﺮق‬ ‫اﻳﺠﺎد‬ ‫ﺗﻢ‬'،W‫وﻫﻲ‬:-
١.‫واﻟﺤﺬف‬ ‫اﻹﺿﺎﻓﺔ‬ ‫ﺧﺎﺻﻴﺔ‬:
-‫ﻛﺎﻧﺖ‬ ‫إذا‬hЈW&fЈW‫ﻓﺈن‬) :٤+٦) = (١٠(،‫ﺑﺎﻻﺿﺎﻓﺔ‬)٤+٦+ (٣) =١٠+ (٣
)٤+٦) = (١٠(‫ﺑﺎﻟﺤﺬف‬)٤+٦(-٣) =١٠(-٣
‫ﻣﺜﺎل‬(‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺣﻞ‬ ‫أوﺟﺪ‬‫س‬-١=٣‫ﻓﻲ‬W
‫اﻟﺤﻞ‬:‫ﺑﺎﺿﺎﻓﺔ‬+١)‫اﻟﺠﻤﻌﻲ‬ ‫اﻟﻤﻌﻜﻮس‬(‫ﻟﻠﻄﺮﻓﻴﻦ‬E‫س‬–١+١=٣+١
E‫س‬=٤‫م‬٠‫ح‬=}٤{
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

17. ١٧
‫ﺗﻤﺮﻳﻦ‬:‫اﻻﺗﻴﺔ‬ ‫ﻟﻠﻤﻌﺎدﻻت‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أوﺟﺪ‬:
)١(‫س‬+٢=٥)٢(‫س‬+٤=-٢
)٣(‫س‬–٥=-٣)٤(‫س‬-٢=١
٢.‫واﻟﻘﺴﻤﺔ‬ ‫اﻟﻀﺮب‬ ‫ﺧﺎﺻﻴﺔ‬:
‫اﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬ ‫ﺟـ‬ ، ‫ب‬ ، ‫ا‬ ‫ﻛﺎن‬ ‫اذا‬J'‫أ‬،W
‫ا‬ ‫وﻛﺎﻧﺖ‬=‫ﻓﺈن‬ ‫ب‬‫ا‬×‫ج‬=‫ب‬×‫ج‬،‫ا‬÷‫ج‬=‫ب‬÷‫ج‬
‫ﻣﺜﺎل‬١(‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺣﻞ‬ ‫أوﺟﺪ‬٢‫س‬=١٠‫ﻓﻰ‬W
‫اﻟﺤﻞ‬:‫ﺑﺎﻟﻘﺴﻤﺔ‬÷٢E٢‫س‬÷٢=١٠÷٢
E‫س‬=٥‫م‬٠‫ح‬=}٥{
‫ﻣﺜﺎل‬٢(‫اﻟﻤﻌﺎدﻟﺔ‬ ‫ﺣﻞ‬ ‫أوﺟﺪ‬
‫ﺱ‬
٤
=٣‫ﻓﻰ‬'
‫اﻟﺤﻞ‬:‫ﺑﺎﻟﻀﺮب‬×٤E×٤=٣×٤E‫ﺱ‬=١٢‫م‬٠‫ح‬=}١٢{
‫ﺗﻤﺮﻳﻦ‬‫ﻓﻰ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أوﺟﺪ‬W
)١(‫س‬+٢=٥)٢(‫س‬+٤=٢)٣(‫س‬+١=-١
)٤(‫س‬–٣=٢)٥(‫س‬–٥=-٣)٦(‫س‬–٢=-٥
‫ج‬١(‫س‬+٢=٥
‫س‬=٥–٢
‫س‬=٣
‫م‬٠‫ح‬=}٣{
‫ج‬٢(‫س‬+٤=٢
‫س‬=٢–.......
‫س‬............ =
‫م‬٠‫ح‬=}......{
‫ج‬٣(‫س‬+١=-١
.......................
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‫ﻣﺜﺎل‬(‫اﻵﺗﻴﺔ‬ ‫ﻟﻠﻤﻌﺎدﻟﺔ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫اوﺟﺪ‬W:
٣‫س‬–٢=٥‫س‬+٨
‫اﻟﺤﻞ‬:E٣‫س‬–٥‫س‬=٨+٢E-٢‫س‬=١٠)‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻘﺴﻤﺔ‬-٢(
E-٢‫س‬÷)-٢= (١٠÷)-٢(E‫س‬=-٥‫م‬٠‫ح‬=}-٥{
‫س‬
٤
‫س‬
٤
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

18. ١٨
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬(‫ﻓﻲ‬ ‫ﻳﺄﺗﻲ‬ ‫ﻣﻤﺎ‬ ‫ﻟﻜﻞ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أوﺟﺪ‬W:
)١(‫س‬+٣=٧)٢(‫س‬-١=٣)٣(‫س‬+٦=١
)٤(‫س‬–٦=-٢)٥(‫س‬–٥=٤)٦(‫س‬+٤=-٢
)٧(‫س‬+٢=-٥)٨(-٣‫س‬=٦)٩(٤‫س‬=٢٤
)١٠(٦‫س‬=-١٨)١١(٢‫س‬+٨=٠)١٢(٣‫س‬-٢١=٠
)١٣(٣‫س‬-٧=٢)١٤(٢‫س‬+١=٩)١٥(٢‫س‬+١١+٣‫س‬=١
)١٦(٤‫س‬–٩=‫س‬+٣)١٧(٣‫س‬+٢=‫س‬+٨)١٨(‫س‬–٥=٦‫س‬–٥
‫ﻓﻲ‬ ‫اﻷوﻟﻰ‬ ‫اﻟﺪرﺟﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﻌﺎدﻻت‬ ‫ﺣﻞ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻄﺒﻴﻘﺎت‬W
‫ﻣﺜﺎل‬١
)١(‫ﺿﻌﻔﻪ‬ ‫اﻟﻰ‬ ‫اﺿﻴﻒ‬ ‫اذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬٥‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬١٧‫اﻟﻌﺪد؟‬ ‫أوﺟﺪ‬
)٢(‫أﻣﺜﺎﻟﻪ‬ ‫ارﺑﻊ‬ ‫ﻣﻦ‬ ‫ﻃﺮح‬ ‫اذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬٢‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬١٤‫اﻟﻌﺪد؟‬ ‫أوﺟﺪ‬
‫اﻟﺤﻞ‬
‫اﻟﻌﺪد‬ ‫ﻧﻔﺮض‬‫س‬
‫اﻟﻌﺪد‬ ‫ﺿﻌﻒ‬٢‫س‬
E‫اﻟﻤﻌﺎدﻟﺔ‬:٢‫س‬+٥=١٧
٢‫س‬+٥–٥=١٧-٥
٢‫س‬=١٢)‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻘﺴﻤﺔ‬٢(
E‫س‬=٦E‫ﻫﻮ‬ ‫اﻟﻌﺪد‬٦
‫اﻟﻌﺪد‬ ‫ﻧﻔﺮض‬‫ص‬
‫اﻣﺜﺎﻟﻪ‬ ‫ارﺑﻊ‬٤‫ص‬
E‫اﻟﻤﻌﺎدﻟﺔ‬:٤‫ص‬-٢=١٤
٢‫ص‬-٢+٢=١٤+٢
٤‫ص‬=١٦)‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻘﺴﻤﺔ‬٤(
E‫س‬=٤E‫ﻫﻮ‬ ‫اﻟﻌﺪد‬٦
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

19. ١٩
‫ﺗﻤﺮﻳﻦ‬
)١(‫أﻣﺜﺎﻟﻪ‬ ‫ﺛﻼﺛﺔ‬ ‫إﻟﻰ‬ ‫أﺿﻴﻒ‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬١٤‫؟‬ ‫اﻟﻌﺪد‬ ‫أوﺟﺪ‬ ، ‫اﻟﻌﺪد‬ ‫ﻧﻔﺲ‬ ‫ﻫﻮ‬ ‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬
)٢(‫إﻟﻴﻪ‬ ‫أﺿﻴﻒ‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬٥‫اﻟﻤﻌﻜﻮس‬ ‫ﻫﻮ‬ ‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬‫اﻟﻴﻪ‬ ‫ﻣﻀﺎﻓﺎ‬ ‫اﻟﻌﺪد‬ ‫ﻟﻨﻔﺲ‬ ‫اﻟﺠﻤﻌﻲ‬٢١‫؟‬ ‫أوﺟﺪه‬ ،
‫اﻟﺤـــــــــﻞ‬:
‫س‬ ‫اﻟﻌﺪد‬ ‫ﻧﻔﺮض‬
‫أﻣﺜﺎﻟﻪ‬ ‫ﺛﻼﺛﺔ‬.......
E‫اﻟﻤﻌﺎدﻟﺔ‬................ :
......................................
......................................
E‫س‬=....E‫ﻫﻮ‬ ‫اﻟﻌﺪد‬.....
‫اﻟﻌﺪد‬ ‫ﻧﻔﺮض‬‫ص‬
E‫اﻟﻤﻌﺎدﻟﺔ‬................ :
......................................
......................................
......................................
E‫س‬.... =E‫ﻫﻮ‬ ‫اﻟﻌﺪد‬.....
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
)١(‫ﻣﺠﻤﻮﻋﻬﻤﺎ‬ ‫ﻣﺘﺘﺎﻟﻴﺎن‬ ‫ﺻﺤﻴﺤﺎن‬ ‫ﻋﺪدان‬١٧‫؟‬ ‫اﻟﻌﺪدان‬ ‫أوﺟﺪ‬ ،
......................................................................................................................................
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)٢(‫ﺑﻤﻘﺪار‬ ‫اﻵﺧﺮ‬ ‫ﻋﻦ‬ ‫ﻳﺰﻳﺪ‬ ‫أﺣﺪﻫﻤﺎ‬ ‫ﻋﺪدان‬٣‫وﻣﺠﻤﻮﻋﻬﻤﺎ‬١٩‫؟‬ ‫اﻟﻌﺪدان‬ ‫أوﺟﺪ‬ ،
......................................................................................................................................
......................................................................................................................................
)٣(‫وﻣﺠﻤﻮﻋﻬﻢ‬ ‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫ﺻﺤﻴﺤﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬١٨‫؟‬ ‫اﻷﻋﺪاد‬ ‫ﻫﺬه‬ ‫أوﺟﺪ‬ ،
......................................................................................................................................
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)٤(‫وﻣﺠﻤﻮﻋﻬﻢ‬ ‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫زوﺟﻴﺔ‬ ‫ﺻﺤﻴﺤﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬١٨‫؟‬ ‫اﻷﻋﺪاد‬ ‫ﻫﺬه‬ ‫أوﺟﺪ‬ ،
......................................................................................................................................
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‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

20. ٢٠
)٥(‫ﺿﻌﻔﻪ‬ ‫إﻟﻰ‬ ‫أﺿﻴﻒ‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬٤‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬١٤‫؟‬ ‫اﻟﻌﺪد‬ ‫اوﺟﺪ‬ ،
......................................................................................................................................
......................................................................................................................................
)٦(‫ﺿﻌﻔﻪ‬ ‫إﻟﻰ‬ ‫أﺿﻴﻒ‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬٣‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬١٧‫اﻟﻌﺪد؟‬ ‫اوﺟﺪ‬ ،
......................................................................................................................................
......................................................................................................................................
)٧(‫ﻋﺪ‬‫ﺿﻌﻔﻪ‬ ‫إﻟﻲ‬ ‫أﺿﻴﻒ‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫د‬١٤‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬٤٨‫اﻟﻌﺪد؟‬ ‫اوﺟﺪ‬ ،
......................................................................................................................................
......................................................................................................................................
)٨(‫ﺿﻌﻔﻪ‬ ‫ﻣﻦ‬ ‫ﻃﺮح‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬٣‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬٩‫اﻟﻌﺪد؟‬ ‫اوﺟﺪ‬ ،
......................................................................................................................................
......................................................................................................................................
)٩(‫ﺿﻌﻔﻪ‬ ‫ﻣﻦ‬ ‫ﻃﺮح‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬٤‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬١٠‫اﻟﻌﺪد؟‬ ‫اوﺟﺪ‬ ،
......................................................................................................................................
......................................................................................................................................
)١٠(‫إﻟﻴﺔ‬ ‫أﺿﻴﻒ‬ ‫إذا‬ ‫ﺻﺤﻴﺢ‬ ‫ﻋﺪد‬١٠‫؟‬ ‫اﻟﻌﺪد‬ ‫أوﺟﺪ‬ ، ‫اﻟﻌﺪد‬ ‫ﻟﻨﻔﺲ‬ ‫اﻟﺠﻤﻌﻲ‬ ‫اﻟﻤﻌﻜﻮس‬ ‫اﻟﻨﺎﺗﺞ‬ ‫ﻛﺎن‬
......................................................................................................................................
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)١١(‫ﻣﺠﻤﻮﻋﻬﻤﺎ‬ ‫ﻣﺘﺘﺎﻟﻴﺎن‬ ‫ﻋﺪدان‬١٥‫؟‬ ‫اﻟﻌﺪدﻳﻦ‬ ‫اوﺟﺪ‬
......................................................................................................................................
......................................................................................................................................
)١٢(‫ﻣﺠﻤﻮﻋﻬﻢ‬ ‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬٢٧‫؟‬ ‫اﻷﻋﺪاد‬ ‫ﻫﺬه‬ ‫أوﺟﺪ‬
......................................................................................................................................
......................................................................................................................................
)١٣(‫ﻣﺠﻤﻮﻋﻬﻢ‬ ‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫ﻓﺮدﻳﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬٣٣‫؟‬ ‫اﻷﻋﺪاد‬ ‫ﻫﺬه‬ ‫أوﺟﺪ‬
......................................................................................................................................
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‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

21. ٢١
)١٤(‫ﻣﺠﻤﻮﻋﻬﻢ‬ ‫ﻣﺘﺘﺎﻟﻴﺔ‬ ‫زوﺟﻴﺔ‬ ‫أﻋﺪاد‬ ‫ﺛﻼﺛﺔ‬٦٦‫؟‬ ‫اﻷﻋﺪاد‬ ‫ﻫﺬه‬ ‫أوﺟﺪ‬
......................................................................................................................................
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)١٥(‫ﻛﺎن‬ ‫اذا‬hЈW-،h<f،O‫ﻓﺈن‬h O........fO‫؟‬
‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺘﺒﺎﻳﻦ‬ ‫ﻋﻼﻣﺎت‬ ‫أﺣﺪ‬ ‫اﺧﺘﺮ‬:)>،=،<(
......................................................................................................................................
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‫واﺣﺪ‬ ‫ﻣﺠﻬﻮل‬ ‫اﻷوﻟﻰ‬ ‫اﻟﺪرﺟﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺒﺎﻳﻨﺔ‬ ‫ﺣﻞ‬
-‫ﻃﺮﻳﻘﺘﻴﻦ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺒﺎﻳﻨﺎت‬ ‫ﺣﻞ‬ ‫ﻳﻌﺘﻤﺪ‬:-
١.‫واﻟﺤﺬف‬ ‫اﻻﺿﺎﻓﺔ‬ ‫ﺧﺎﺻﻴﺔ‬٢.‫واﻟﻘﺴﻤﺔ‬ ‫اﻟﻀﺮب‬ ‫ﺧﺎﺻﻴﺔ‬
‫ﻣﺜﺎل‬(‫اﻵﺗﻴﺔ‬ ‫ﻟﻠﻤﺘﺒﺎﻳﻨﺔ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫اوﺟﺪ‬:
‫س‬+١>٣‫ﻓﻲ‬'‫ﺑﺈﺿﺎﻓﺔ‬)-١(‫ﻟﻠﻄﺮﻓﻴﻦ‬E‫س‬+١-١>٣–١
E‫س‬>٢E‫م‬.‫ح‬=}١،٠{
‫س‬-٢M١‫ﻓﻲ‬W‫ﺑﺈﺿﺎﻓﺔ‬+)٢(‫ﻟﻠﻄﺮﻓﻴﻦ‬E‫س‬–٢+٢M١+٢
E‫س‬M٢E‫م‬.‫ح‬=}٢،٣،٤،............{
‫ﻣﻠﺤﻮﻇﺔ‬ً‫ا‬‫ﺟﺪ‬ ‫ﻣﻬﻤﺔ‬
‫ﻋ‬‫اﻛﺒﺮ‬ ‫ﻣﻦ‬ ‫اﻟﺘﺒﺎﻳﻦ‬ ‫ﻋﻼﻣﺔ‬ ‫ﻧﻐﻴﺮ‬ ‫ﺳﺎﻟﺐ‬ ‫ﻋﺪد‬ ‫ﻓﻲ‬ ‫اﻟﻤﺘﺒﺎﻳﻨﺔ‬ ‫ﻗﺴﻤﺔ‬ ‫أو‬ ‫ﺿﺮب‬ ‫ﻨﺪ‬
‫إﻟﻰ‬‫اﺻﻐﺮ‬‫واﻟﻌﻜﺲ‬
-٢‫س‬>٤‫ﻓﻲ‬W)‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻘﺴﻤﺔ‬-٢(E-٢‫س‬÷-٢>٤÷-٢E‫س‬<-٢E
‫ح‬ ‫م‬=}-١،٠،١،٢،............{
-٢‫س‬+١>٧‫ﻓﻲ‬W)‫ﺑﺈﺿﺎﻓﺔ‬-١‫ﻟﻠﻄﺮﻓﻴﻦ‬(-٢‫س‬+١-١>٧-١
E-٢‫س‬>٦‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻘﺴﻤﺔ‬-٢E-٢‫س‬÷-٢<٦÷-٢
E‫س‬<-٣E‫م‬٠‫ح‬=}-٢،-١،٠،١،٢،......{
-٥‫س‬N١٠‫ﻋﻠﻰ‬ ‫ﺑﺎﻟﻘﺴﻤﺔ‬-٥E-٥‫س‬÷-٥M١٠÷-٥
E‫س‬M-٢E‫م‬٠‫ح‬=}-٢،-١،٠،١،٢،......{
‫ﺗﻤﺮﻳﻦ‬)١(‫اﻵﺗﻴﺔ‬ ‫ﻟﻠﻤﺘﺒﺎﻳﻨﺔ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أوﺟﺪ‬
-١>‫س‬–٣N٤)‫ﻓﻲ‬W(
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

22. ٢٢
W
S
‫أ‬ ‫ب‬
‫ج‬
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬(‫ﻓﻲ‬ ‫اﻟﺤﻞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫أوﺟﺪ‬W‫ﻟﻠﻤﺘﺒ‬‫ﺎ‬‫ﻳ‬‫ﻨ‬‫اﻵﺗﻴﺔ‬ ‫ﺎت‬:
)١(‫س‬+٣>٤)٢(‫س‬–٢<١
)٣(‫س‬–٢‫س‬N٣)٤(-١>‫س‬+٢>٣
)٥(٧‫س‬M-١٤)٦(٢‫س‬+٧N١١
‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ﻧﻘﻄﺘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬
‫ﻣﺴﺘﻘﻴﻢ‬ ‫أو‬ ‫ﺷﻌﺎع‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬:
-‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻻﺣﻆ‬‫ج‬‫ب‬‫أ‬
١١١٠٩٨٧٦٥٤٣٢١٠
‫ﻫﻰ‬ ‫ب‬ ، ‫أ‬ ‫اﻟﻨﻘﻄﺘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬٦‫ﻧﻘﻮل‬ ‫أن‬ ‫وﻳﻤﻜﻦ‬ ‫ﺧﻄﻮات‬...
]‫أب‬ ‫ﻃﻮل‬=‫إ‬‫اﻟﻨﻬﺎﻳﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺣﺪاﺛﻲ‬)‫ب‬(–‫اﻟﺒﺪاﻳﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫إﺣﺪاﺛﻲ‬)‫أ‬([=٧–١=٦‫ﺳﻢ‬
‫ﺗﻤﺮﻳﻦ‬‫أﻛﻤﻞ‬:‫ج‬ ‫ب‬...... =–٧...... =‫ﺳﻢ‬
‫ج‬ ‫ا‬=٦...... = ...... +‫ﺳﻢ‬
‫ط‬ ‫ﻓﻰ‬ ‫اﻹﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ﻧﻘﻄﺘﻴﻦ‬ ‫ﺑﻴﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬:
‫اﻟﻨﻘﻂ‬ ‫اﻟﻤﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ﺣﺪد‬
‫ا‬)٣،٣(‫ب‬ ،)٣،٧(‫ج‬ ،)٧،٣(
‫اﻟﺜﻼﺛﺔ‬ ‫اﻟﻨﻘﺎط‬ ‫ﺻﻞ‬.
‫اﻟﺸﻜﻞ‬ ‫اﺳﻢ‬............... :
‫ب‬ ‫أ‬ ‫ﻫﻞ‬n‫ﺟ‬ ‫أ‬‫ـ‬)‫ﻧﻌﻢ‬) (‫ﻻ‬(
٩
٨
٧
٦
٥
٤
٣
٢
١
١٥١٤١٣١٢١١١٠٩٨٧٦٥٤٣٢١
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

23. ٢٣
‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ﺣﺪد‬W
‫ا‬)٠،٣(‫ب‬ ،)-٣،٠(‫ﺟـ‬ ،)٠،١(
‫ﻃﻮل‬ ‫أوﺟﺪ‬ ‫ﺛﻢ‬ ‫اﻟﺜﻼﺛﺔ‬ ‫اﻟﻨﻘﺎط‬ ‫ﺻﻞ‬
‫ب‬ ‫ا‬‫اﻟﻤﺜﻠﺚ‬ ‫ﻧﻮع‬ ‫أذﻛﺮ‬ ‫ﺛﻢ‬ ‫ﺟـ‬ ‫ب‬ ، ‫أﺟـ‬ ،
‫ﻷﺿﻼﻋﻪ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬‫؟‬ ‫وزواﻳﺎه‬
‫أب‬ ‫ﻃﻮل‬.............. =‫ﺳﻢ‬
‫أﺟـ‬ ‫ﻃﻮل‬.............. =‫ﺳﻢ‬
‫ﺟـ‬ ‫ب‬ ‫ﻃﻮل‬.............. =‫ﺳﻢ‬
‫ﻧﻮع‬"‫ﺟـ‬ ‫ب‬ ‫أ‬.............
‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ارﺳﻢ‬:
‫ا‬)٣،٥(‫ب‬ ،)٥،-٣(‫ﺟـ‬ ،)-٣،-٥(
‫د‬ ،)-٥،٣(
-‫أﻛﻤﻞ‬:
‫أب‬ ‫ﻃﻮل‬.............. =‫ﺳﻢ‬
‫د‬ ‫أ‬ ‫ﻃﻮل‬.............. =‫ﺳﻢ‬
‫اﻟﻤﺴﺎﻓﺔ‬‫اﻹﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻧﻘﻄﺘﻴﻦ‬ ‫ﺑﻴﻦ‬W:
‫ﺏ‬
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

24. ٢٤
‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ﺣﺪد‬:
‫س‬)٢،١(‫ص‬ ،)-٢،٠(،
‫ع‬)-٢،١(‫ل‬ ،)٠،٤(‫أﻛﻤﻞ‬ ‫ﺛﻢ‬:
‫ل‬ ‫ع‬ ‫ص‬ ‫س‬ ‫اﻟﺸﻜﻞ‬ ‫ﻣﺤﻴﻂ‬
...............................................
....... =
‫ل‬ ‫ع‬ ‫ص‬ ‫س‬ ‫اﻟﺸﻜﻞ‬ ‫ﻣﺴﺎﺣﺔ‬
...............................................
‫ﺔ‬‫ﺳﻴ‬‫اﻟﻬﻨﺪ‬ ‫اﻟﺘﺤﻮﻳﻼت‬–‫ﺎﻻﻧﺘﻘﺎل‬‫ﺑ‬ ‫اﻟﺘﺤﻮﻳﻞ‬
‫اﻟﻬﻨﺪﺳﻴﺔ‬ ‫اﻟﺘﺤﻮﻳﻠﺔ‬:
‫ﻧﻘﻄﺔ‬ ‫ﻛﻞ‬ ‫ﺗﺤﻮل‬h‫ﻧﻘﻄﺔ‬ ‫اﻟﻰ‬ ‫اﻟﻤﺴﺘﻮى‬ ‫ﻓﻲ‬hَ‫اﻟﻤﺴﺘﻮى‬ ‫ﻧﻔﺲ‬ ‫ﻓﻲ‬-‫ﺷﻴﺌﻴﻦ‬ ‫ﻣﻌﺮﻓﺔ‬ ‫ﻳﺠﺐ‬ ‫اﻻﻧﺘﻘﺎل‬ ‫ﻳﺘﻢ‬ ‫ﻟﻜﻰ‬
‫اﻻﻧﺘﻘﺎل‬ ‫ﻣﻘﺪار‬،‫اﻻﻧﺘﻘﺎل‬ ‫اﺗﺠﺎه‬
-‫ﻫﻲ‬ ‫اﻻﻧﺘﻘﺎل‬ ‫ﺣﺎﻻت‬ ‫أﻣﺎ‬:
١(‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ﻧﻘﻄﺔ‬ ‫اﻧﺘﻘﺎل‬:‫ﻟﻨﻮﻋﻴﻦ‬ ‫وﺗﻨﻘﺴﻢ‬:-
‫أ‬.‫اﻟﺼﻔﺤﺔ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫ﻧﻘﻄﺔ‬ ‫اﻧﺘﻘﺎل‬:
‫ﻣﺜﺎل‬(‫اﻟﻨﻘﻄﺔ‬ ‫إزاﺣﺔ‬ ‫اﻟﻤﻄﻠﻮب‬‫أ‬‫ﻣﺴﺎﻓﺔ‬٥‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫ﺳﻢ‬‫ن‬ ‫م‬Ehhَ=٥‫ﺳﻢ‬
)hَ(‫اﻟﻨﻘﻄﺔ‬ ‫ﺻﻮرة‬ ‫ﻫﻲ‬)h(‫ﺑﺎﻧﺘﻘﺎل‬‫ﻗﺪره‬٥‫ن‬ ‫م‬ ‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫ﺳﻢ‬
‫ب‬.‫اﻧﺘﻘﺎل‬)‫ﻧﻘﻄﺔ‬-‫ﻣﺴﺘﻘﻴﻤﺔ‬ ‫ﻗﻄﻌﺔ‬-‫ﻫﻨﺪﺳﻲ‬ ‫ﺷﻜﻞ‬(‫اﻟﺼﺤﻴﺤﺔ‬ ‫ﻟﻸﻋﺪاد‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬:
‫ﻧﻘﻄﺔ‬ ‫ﻛﻞ‬ ‫ﻳﺤﻮل‬ ‫اﻻﺣﺪاﺛﻴﺎت‬ ‫ﻣﺴﺘﻮى‬ ‫ﻓﻲ‬ ‫اﻻﻧﺘﻘﺎل‬)h(‫ﻧﻘﻄﺔ‬ ‫إﻟﻰ‬ ‫اﻟﻤﺴﺘﻮى‬ ‫ﻓﻲ‬)hَ(‫ﻋﻦ‬ ‫ﻧﻔﺴﻪ‬ ‫اﻟﻤﺴﺘﻮى‬ ‫ﻓﻲ‬
‫ازاﺣﺔ‬ ‫ﻃﺮﻳﻖ‬)‫ﺟـ‬(‫اﺗﺠﺎه‬ ‫ﻓﻲ‬)S(‫ازاﺣﺔ‬ ‫ﻳﺘﺒﻌﻬﺎ‬)‫ﺩ‬(‫اﺗﺠﺎه‬ ‫ﻓﻲ‬)W(‫ﺑﺤﻴﺚ‬:
h)‫ﺹ‬ ، ‫ﺱ‬= (hَ)‫ﺱ‬+‫ﺹ‬ ، ‫ﺟـ‬+‫ﺩ‬(
‫م‬
‫ن‬
hَ
h
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

25. ٢
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫اﻷﻗﻮاس‬ ‫ﺑﻴﻦ‬ ‫ﻣﻤﺎ‬ ‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻻﺟﺎﺑﺔ‬ ‫اﺧﺘﺮ‬:
١(‫ﻛﺎﻧﺖ‬ ‫إذا‬h)١،٢(‫ﻗﺪره‬ ‫ﺑﺎﻧﺘﻘﺎل‬ ‫ﺻﻮرﺗﻬﺎ‬ ‫ﻓﺈن‬)‫س‬+١‫ص‬ ،-١(‫ﻫﻲ‬..........
])٢،١(،)٠،٣(،)١،١(،)٣،٠[ (
٢(‫اﻟﻨﻘﻄﺔ‬ ‫ﺻﻮرة‬h)-٤،-٢(‫ﻗﺪره‬ ‫ﺑﺎﻧﺘﻘﺎل‬)-١،-٤(‫ﻫﻲ‬..........
])-٥،-٦(،)-٦،-٥(،)-٧،٢(،)٢،-٧[ (
‫ﻣﺜﺎل‬(
)١(‫اﻟﻨﻘﻄﺘﻴﻦ‬ ‫ﺻﻮرة‬ ‫أوﺟﺪ‬h)-٣،١(،‫ب‬)١،١(‫ﻗﺪره‬ ‫ﺑﺎﻧﺘﻘﺎل‬)‫س‬+٢،‫ص‬-١(‫؟‬ ‫اﻟﺠﺪﻳﺪة‬ ‫اﻟﻨﻘﺎط‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ذﻛﺮ‬ ‫ﻣﻊ‬
‫اﻹﺟﺎﺑــــــﺔ‬
hَ)١،٢(،‫ب‬َ)٣،٠(‫ﹰ‬‫ﺎ‬‫ﻭﺃﻴﻀ‬hf‫اﻻﻧﺘﻘﺎل‬ ‫ﺑﻌﺪ‬hَfَ
)٢(‫ﺑﻤﻘﺪار‬ ‫ﻳﻨﺘﻘﻞ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ع‬ ‫ص‬ ‫س‬ ‫اﻟﺸﻜﻞ‬ ‫رؤس‬ ‫ﺻﻮر‬ ‫اﺣﺪاﺛﻲ‬ ‫أوﺟﺪ‬)‫س‬+٢‫ص‬ ،-٤(
‫اﻹﺟﺎﺑــــــﺔ‬
‫اﻟﺸﻜﻞ‬:‫ﻣﺜﻠﺚ‬،‫س‬َ)-٢،٠(َ‫ص‬)-١،-٢(‫ع‬َ)-٣،-٢(
hَ
‫ب‬َ
‫ب‬
h
‫ص‬‫ع‬
‫س‬َ
‫ص‬َ‫ع‬َ
‫س‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086 ٥
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

26. ٢٦
‫س‬٢(‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﺠﺪول‬ ‫أﻛﻤﻞ‬:
‫اﻟﺼﻮرة‬‫اﻻﻧﺘﻘﺎل‬‫اﻟﻨﻘﻄﺔ‬
...)،(...)‫س‬+٣‫ص‬ ،+١()٢،٣(
)-٣،٣()‫س‬+٢‫ص‬ ،-١(...)،(...
)٠،٠()‫س‬....+‫ص‬ ،(..... +)٠،-٣(
...)،(...)‫س‬+٣‫ص‬ ،+١()-٤،-١(
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
‫س‬٤(‫اﻻﺣﺪاﺛﻲ‬ ‫اﻟﻤﺴﺘﻮى‬ ‫ﻋﻠﻰ‬‫اﻟﺘﺎﻟﻴﺔ‬ ‫اﻟﺼﻔﺤﺔ‬ ‫ﻓﻲ‬‫اﻟﻨﻘﺎط‬ ‫ﺣﺪد‬:
h)٢،-٢(،‫ب‬)٠،٠(،‫ﺟـ‬)٠،-٢(‫أوﺟﺪ‬hَ‫ﺻﻮرة‬h‫ﺑﺈﻧﺘﻘﺎل‬‫ﻗﺪره‬)٢،-١(
َ‫ب‬ ‫اوﺟﺪ‬َ‫ـ‬‫ﺟ‬‫ﻗﺪره‬ ‫ﺑﺈﻧﺘﻘﺎل‬ ‫ﺟـ‬ ‫ب‬ ‫ﺻﻮرة‬)٣،١(
َ‫ب‬ ‫ب‬ ‫ﻃﻮل‬................... =‫ﺟـ‬ ‫ب‬ ‫ﻃﻮل‬................. =
َ‫ـ‬‫ﺟ‬ َ‫ب‬ ‫ب‬ ‫اﻟﺸﻜﻞ‬ ‫ﻣﺤﻴﻂ‬‫ﺟـ‬........ =
َ‫ـ‬‫ﺟ‬ َ‫ب‬ ‫ب‬ ‫اﻟﺸﻜﻞ‬ ‫ﻣﺴﺎﺣﺔ‬‫ﺟـ‬....... =
َ‫ـ‬‫ﺟ‬ َ‫ب‬ ‫ب‬ ‫اﻟﺸﻜﻞ‬ ‫ﺗﻤﺎﺛﻞ‬ ‫ادرس‬‫ﺟـ‬..................................... =
‫س‬٣(
‫أﻣﺎﻣﻚ‬ ‫اﻟﺬي‬ ‫اﻟﺸﻜﻞ‬ ‫ﺻﻮرة‬ ‫اوﺟﺪ‬
‫ﻗﺪره‬ ‫ﺑﺎﻧﺘﻘﺎل‬)‫س‬+٥‫،ص‬-٤(
‫؟‬ ‫اﻟﺠﺪﻳﺪة‬ ‫اﻟﻨﻘﺎط‬ ‫اﺣﺪاﺛﻴﺎت‬ ‫ذﻛﺮ‬ ‫ﻣﻊ‬
...............................
...............................
...............................
...............................
..................................
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

27. ٢٧
‫أن‬ ‫ﺗﺬﻛﺮ‬:-
-‫اﻟﺼﻮرة‬ ‫اﺣﺪاﺛﻲ‬=‫اﻟﻨﻘﻄﺔ‬ ‫اﺣﺪاﺛﻲ‬+‫اﻻﻧﺘﻘﺎل‬ ‫اﺣﺪاﺛﻲ‬
-‫اﻟﻨﻘﻄﺔ‬ ‫اﺣﺪاﺛﻲ‬=‫اﻟﺼﻮرة‬ ‫اﺣﺪاﺛﻲ‬–‫اﻻﻧﺘﻘﺎل‬ ‫اﺣﺪاﺛﻲ‬
-‫اﻻﻧﺘﻘﺎل‬ ‫اﺣﺪاﺛﻲ‬=‫اﻟﺼﻮرة‬ ‫اﺣﺪاﺛﻲ‬–‫اﻟﻨﻘﻄﺔ‬ ‫اﺣﺪاﺛﻲ‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

28. ٢٨
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬
‫أن‬ ‫ﺗﺬﻛﺮ‬:
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺤﻴﻂ‬=٢‫ﻧﻖ‬ ‫ط‬=‫ط‬×‫اﻟﻘﻄﺮ‬ ‫ﻃﻮل‬
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬=‫ﻧﻖ‬ ‫ط‬٢
‫ﺣﻴﺚ‬)‫ط‬(‫وﺗﺴﺎوي‬ ‫داﺋﻤﺎ‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﻗﻴﻤﺔ‬٢٢/٧‫أن‬٣.١٤
‫ﻣﺜﺎل‬١(‫ﻗﻄﺮﻫﺎ‬ ‫ﻧﺼﻒ‬ ‫ﻃﻮل‬ ‫اﻟﺘﻲ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬٤‫ﺳﻢ‬)‫ط‬=٢٢/٧(
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬=‫ط‬×‫ﻧﻖ‬×‫ﻧﻖ‬
=٢٢/٧×٤×٤=١٦‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٢(‫ﻗﻄﺮﻫﺎ‬ ‫ﻃﻮل‬ ‫اﻟﺘﻲ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬١٤‫ﺳﻢ‬)‫ط‬=
٢٢
٧(
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬=‫ط‬×‫ﻧﻖ‬×‫ﻧﻖ‬
=
٢٢
٧
×
١٤
٢
×
١٤
٢
....... =‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٣(‫ﺑﺎﻟﺮﺳﻢ‬ ‫ﻛﻤﺎ‬ ‫ﻗﻄﺎﻋﺎت‬ ‫ﻟﺨﻤﺲ‬ ‫اﻟﻤﻘﺴﻤﺔ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻟﻬﺬه‬ ‫اﻟﻮاﺣﺪة‬ ‫اﻟﻘﻄﺎع‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬)‫ط‬=٣.١٤(
‫ﻛﻠﻬﺎ‬ ‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬=‫ط‬×‫ﻧﻖ‬٢
=٣.١٤×٢٣.٥....... =‫ﺳﻢ‬٢
‫اﻟﻮاﺣﺪ‬ ‫اﻟﻘﻄﺎع‬ ‫ﻣﺴﺎﺣﺔ‬.......... =÷= ................‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٤(‫ﻣﺤﻴﻄﻬﺎ‬ ‫داﺋﺮة‬٥٧‫ﺳﻄﺤﻬﺎ‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬ ‫ﺳﻢ‬)‫ط‬=٣.١٤(
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺤﻴﻂ‬=٢‫ﻧﻖ‬ ‫ط‬
٨٨=٢×٣.١٤×‫ﻧﻖ‬E‫ﻧﻖ‬=
٨٨
٢×٣.١٤
=١٤‫ﺳﻢ‬
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬=‫ط‬×‫ﻧﻖ‬٢
=٣.١٤×٢
١٤....... =‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٥(‫ﻣﺴﺎﺣﺘﻬﺎ‬ ‫داﺋﺮة‬١٥٤‫ﺳﻢ‬٢‫ﻣﺤﻴﻄﻬﺎ‬ ‫اﺣﺴﺐ‬)‫ط‬=
٢٢
٧(
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬=‫ط‬×‫ﻧﻖ‬٢
١٥٤=
٢٢
٧×‫ﻧﻖ‬٢،
E‫ﻧﻖ‬٢
=١٥٤÷
٢٢
٧=٤٩‫ﺴﻡ‬،E‫ﻧﻖ‬=٧‫ﺳﻢ‬
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺤﻴﻂ‬=٢‫ﻧﻖ‬ ‫ط‬
=٢×
٢٢
٧×٧=٤٤‫ﺳﻢ‬
٣.٥‫ﺳﻢ‬
٤٩٧
٧٧
١
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

29. ٢٩
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫ﻗﻄﺮﻫﺎ‬ ‫ﻧﺼﻒ‬ ‫ﻃﻮل‬ ‫اﻟﺸﻜﻞ‬ ‫داﺋﺮﻳﺔ‬ ‫ﺳﻔﺮة‬٠.٧٥‫ﺳﻄﺤﻬﺎ‬ ‫ﺗﻐﻄﻴﺔ‬ ‫ﻳﺮاد‬ ‫م‬
‫اﻟﻤﺘﺮ‬ ‫اﻟﻤﻔﺮوﺷﺎت‬ ‫ﻣﻦ‬ ‫ﺑﻨﻮع‬٢
‫ﻳﺘﻜﻠﻒ‬ ‫ﻣﻨﻪ‬١٠‫اﻟﻤﻔﺮش‬ ‫ﺗﻜﻠﻔﺔ‬ ‫ﻓﻜﻢ‬ ‫ﺟﻨﻴﻬﺎت‬
‫س‬٢(‫ﻣﺮﺳﻮم‬ ‫ﻣﺮﺑﻊ‬‫ﻗﻄﺮﻫﺎ‬ ‫ﻃﻮل‬ ‫داﺋﺮة‬ ‫ﺑﺪاﺧﻠﻪ‬١٠‫ﺳﻢ‬.
‫اﻟﻤﻈﻠﻞ‬ ‫اﻟﺠﺰء‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬
‫س‬٣(‫اﻟﻘﻄﺎع‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻣﺘﺴﺎوﻳﺔ‬ ‫ﻗﻄﺎﻋﺎت‬ ‫ﻟﺜﻼث‬ ‫ﻣﻘﺴﻤﺔ‬ ‫داﺋﺮة‬ ‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﻛﻤﺎ‬
٣٧.٧‫ﺳﻢ‬.‫ﻗﻄﺮﻫﺎ‬ ‫ﻧﺼﻒ‬ ‫ﻃﻮل‬ ‫أوﺟﺪ‬.
‫س‬٤(‫ﻣﺴﺎﺣﺘﻬﺎ‬ ‫داﺋﺮة‬٣١٤‫ﺳﻢ‬٢
–‫ﻣﺤﻴﻄﻬﺎ‬ ‫ﻃﻮل‬ ‫أﺣﺴﺐ‬
‫س‬٥(
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

30. ٣٠
‫ﻟﻠﻤﻜﻌﺐ‬ ‫واﻟﻜﻠﻴﺔ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬
-‫أن‬ ‫ﺗﺬﻛﺮ‬:
‫ﻟﻪ‬ ‫اﻟﻤﻜﻌﺐ‬٦‫ﻣﺘﻄﺎﺑﻘﺔ‬ ‫أوﺟﻪ‬
‫اﻟﻤﺮﺑﻊ‬ ‫ﻣﺤﻴﻂ‬=‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬×٤
‫اﻟﻤﺮﺑﻊ‬ ‫ﻣﺴﺎﺣﺔ‬=‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬×‫ﻧﻔﺴﻪ‬
‫ﻟﻠﻤﻜﻌﺐ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬×‫اﻻرﺗﻔﺎع‬
‫ﻟﻠﻤﻜﻌﺐ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬×٤
‫ﻟﻠﻤﻜﻌﺐ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬×٦
‫ﻣﺜﺎل‬١(‫أوﺟﻬﻪ‬ ‫اﺣﺪ‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﻟﺬي‬ ‫ﻟﻠﻤﻜﻌﺐ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬٦‫ﺳﻢ‬٢
‫اﻟﺤﻞ‬:‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=٦×٦=٣٦‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٢(‫اﻟﻜﻠﻴﺔ‬ ‫ﻣﺴﺎﺣﺘﻪ‬ ‫ﻣﻜﻌﺐ‬٤٢‫ﺳﻢ‬٢
.‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫ﻣﺴﺎﺣﺘﻪ‬ ‫اﺣﺴﺐ‬
‫اﻟﺤﻞ‬:‫اﻟﻮاﺣﺪ‬ ‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬=٤٢÷٦=٧‫ﺳﻢ‬٢
‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫ﻣﺴﺎﺣﺘﻪ‬=٧×٤=٢٨‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٣(‫اﻟﺬي‬ ‫ﻟﻤﻜﻌﺐ‬ ‫واﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬
‫ﺣﺮﻓﻪ‬ ‫ﻃﻮل‬٥‫ﺳﻢ‬
‫اﻟﺤﻞ‬:‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬=٥×٥=٢٥‫ﺳﻢ‬٢
‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=٢٥×٤=١٠٠‫ﺳﻢ‬٢
‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=٢٥×٦=١٥٠‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٤(‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫ﻣﺴﺎﺣﺘﻪ‬ ‫ﻣﻜﻌﺐ‬٣٢٤‫ﺳﻢ‬٢
.‫ﻟﻪ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫واﻟﻤﺴﺎﺣﺔ‬ ‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬ ‫اﺣﺴﺐ‬.
‫اﻟﺤﻞ‬:‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬×٤
٣٢٤=‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬×٤
‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬=٣٢٤÷٤=٨١‫ﺳﻢ‬٢
‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=٨١×٦=٤٨٦‫ﺳﻢ‬٢
٥‫ﺳﻢ‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

31. ٣١
‫اﻟﻤﺴﺘﻄﻴﻼت‬ ‫ﻟﻤﺘﻮازي‬ ‫واﻟﻜﻠﻴﺔ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬
-‫أن‬ ‫ﺗﺬﻛﺮ‬:
‫ﻟﻪ‬ ‫اﻟﻤﺴﺘﻄﻴﻼت‬ ‫ﻣﺘﻮازي‬٦‫ﻣﺘﻄﺎﺑﻘﺎن‬ ‫ﻣﺘﻘﺎﺑﻼن‬ ‫وﺟﻬﺎن‬ ‫وﻛﻞ‬ ‫أوﺟﻪ‬
‫اﻟﻤﺴﺘﻄﻴﻞ‬ ‫ﻣﺤﻴﻂ‬) =‫اﻟﻄﻮل‬+‫اﻟﻌﺮض‬(×٢
‫اﻟﻤﺮﺑﻊ‬ ‫ﻣﺴﺎﺣﺔ‬=‫اﻟﻄﻮل‬×‫اﻟﻌﺮض‬
‫اﻟﻤﺴﺘﻄﻴﻼت‬ ‫ﻟﻤﺘﻮازي‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬×‫اﻻرﺗﻔﺎع‬
‫اﻟﻤﺴﺘﻄﻴﻼت‬ ‫ﻟﻤﺘﻮازي‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬) =‫اﻟﻄﻮل‬+‫اﻟﻌﺮض‬(×٢×‫اﻻرﺗﻔﺎع‬
‫اﻟﻤﺴﺘﻄﻴﻼت‬ ‫ﻟﻤﺘﻮازي‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬+‫اﻟﻘﺎﻋﺪﺗﻴﻦ‬ ‫ﻣﺴﺎﺣﺘﻲ‬ ‫ﻣﺠﻤﻮع‬
=‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬) +‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺴﺎﺣﺔ‬×٢(
‫ﻣﺜﺎل‬١(‫اﻟﺸﻜﻞ‬ ‫ﻣﺮﺑﻌﺔ‬ ‫ﻗﺎﻋﺪﺗﻪ‬ ‫ﻣﺴﺘﻄﻴﻼت‬ ‫ﻣﺘﻮازي‬ ‫ﺷﻜﻞ‬ ‫ﻋﻠﻰ‬ ‫دواء‬ ‫ﻋﻠﺒﺔ‬
‫ﺿﻠﻌﻬﺎ‬ ‫ﻃﻮل‬٤‫وارﺗﻔﺎﻋﻬﺎ‬ ‫ﺳﻢ‬٩‫ﺳﻢ‬.‫اﻟﻜﻠﻴﺔ‬ ‫ﻣﺴﺎﺣﺘﻪ‬ ‫اﺣﺴﺐ‬
‫اﻟﺤﻞ‬:‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬=٤×٤=١٦‫ﺳﻢ‬
‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺴﺎﺣﺔ‬=٤×٤=١٦‫ﺳﻢ‬٢
‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=١٦×٩=١٤٤‫ﺳﻢ‬٢
‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=١٤٤) +١٦×٢(
١٤٤+٣٢=١٧٦‫ﺳﻢ‬٢
‫ﻣﺜﺎل‬٢(‫ﻃﻮﻟﻬﺎ‬ ‫ﻣﺴﺘﻄﻴﻼت‬ ‫ﻣﺘﻮازي‬ ‫ﺷﻜﻞ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻠﺒﺔ‬١٦‫وﻋﺮﺿﻬﺎ‬ ‫ﺳﻢ‬
١٠‫وارﺗﻔﺎﻋﻬﺎ‬ ‫ﺳﻢ‬٢٠‫ﺳﻢ‬.‫واﻟﻜﻠﻴﺔ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫ﻣﺴﺎﺣﺘﻪ‬ ‫اﺣﺴﺐ‬
‫اﻟﺤﻞ‬:‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬) =‫اﻟﻄﻮل‬+‫اﻟﻌﺮض‬(×٢
) =١٦+١٠(×٢=٥٢‫ﺳﻢ‬
‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬×‫اﻻرﺗﻔﺎع‬=٥٢×٢٠=١٠٤٠‫ﺳﻢ‬٢
‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺴﺎﺣﺔ‬=‫اﻟﻄﻮل‬×‫اﻟﻌﺮض‬=١٦×١٠=١٦٠‫ﺳﻢ‬٢
‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=١٠٤٠) +١٦٠×٢= (١٣٦٠‫ﺳﻢ‬٢
‫ﺗﻄﺒﻴﻘﻲ‬ ‫ﻧﺸﺎط‬(‫أرﺿﻴﺘﻬﺎ‬ ‫ﺣﺠﺮة‬‫ﺿﻠﻌﻬﺎ‬ ‫ﻃﻮل‬ ‫اﻟﺸﻜﻞ‬ ‫ﻣﺮﺑﻌﺔ‬٤‫وارﺗﻔﺎﻋﻬﺎ‬ ‫م‬٣‫ﻋﺮﺿﻪ‬ ‫ﺑﺎب‬ ‫وﻟﻬﺎ‬ ‫م‬٩٥‫ﻢ‬‫ﺳ‬
‫وارﺗﻔﺎﻋﻪ‬٢.١‫ﻃﻮﻟﻪ‬ ‫ﻣﻨﻬﻤﺎ‬ ‫ﻛﻞ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﻣﺘﺴﺎوﻳﺎ‬ ‫ﺷﺒﻠﻜﺎن‬ ‫وﻟﻬﺎ‬ ‫م‬٩٠‫وﻋﺮﺿﻪ‬ ‫ﺳﻢ‬٦٥‫ﺳﻢ‬.
-‫ﺑـ‬ ‫ﻣﻨﻪ‬ ‫اﻟﻤﺮﺑﻊ‬ ‫اﻟﻤﺘﺮ‬ ‫ﺑﺪﻫﺎن‬ ‫واﻟﺴﻘﻒ‬ ‫اﻟﻐﺮﻓﺔ‬ ‫ﺟﺪران‬ ‫ﻃﻼء‬ ‫ﺗﻜﻠﻔﺔ‬ ‫اﺣﺴﺐ‬٩‫ﺟﻨﻴﻬﺎت‬.
‫اﻟﺤﻞ‬:‫اﻟﺘﻜﻠﻔﺔ‬=‫ﻃﻼﺋﻬﺎ‬ ‫اﻟﻤﺮاد‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬ ‫ﺻﺎﻓﻲ‬×٩
‫ﻟﻠﻐﺮﻓﺔ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬×‫اﻻرﺗﻔﺎع‬
٤‫ﺳﻢ‬
٩‫ﺳﻢ‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

32. ٣٢
) =٤×٤(×٣=٤٨‫م‬٢
=٤٨٠٠٠٠‫ﺳﻢ‬٢
‫اﻟﺒﺎب‬ ‫ﻣﺴﺎﺣﺔ‬=٠.٩٥×٢.١=١.٩٩٥‫م‬٢
=١٩٩٥٠‫ﺳﻢ‬٢
‫اﻟﺸﺒﺎﻛﺎن‬ ‫ﻣﺴﺎﺣﺔ‬=٢×)٩٠×٦٥= (١١٧٠٠‫ﺳﻢ‬٢
=١.١١٧‫م‬٢
Ε‫اﻟﻤﺮاد‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬‫ﻃﻼﺋﻬﺎ‬=‫ﻟﻠﻐﺮﻓﺔ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬–‫واﻟﺸﺒﺎﻛﺎن‬ ‫اﻟﺒﺎب‬ ‫ﻣﺴﺎﺣﺘﻲ‬ ‫ﻣﺠﻤﻮع‬
=٤٨–)١.٩٩٥+١.١١٧(
=٤٤.٨٨٨‫م‬٢
‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬+‫اﻟﻘﺎﻋﺪﺗﻴﻦ‬ ‫ﻣﺴﺎﺣﺘﻲ‬ ‫ﻣﺠﻤﻮع‬
Ε‫ﻃﻼﺋﻬﺎ‬ ‫اﻟﻤﺮاد‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬=‫ﻃﻼﺋﻬﺎ‬ ‫اﻟﻤﺮاد‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺟﺔ‬+‫اﻟﺴﻘﻒ‬ ‫ﻣﺴﺎﺣﺔ‬
=٤٤.٨٨٨) +٤×٤= (٦٠.٨٨٨‫م‬٢
Ε‫اﻟﺘﻜﻠﻔﺔ‬=٦٠.٨٨٨×٩=٥٤٧.٩٩٢‫ﺟﻨﻴﻪ‬
‫ــــــــــــــــــــــــــــــــــــــــــ‬‫ـ‬‫ـــــــــــــــــــــــــــــــــــــــــ‬
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
١(‫ﺍﺣﺴﺐ‬‫ﻣﻦ‬ ‫ﻟﻜﻼ‬ ‫ﻭﺍﳉﺎﻧﺒﻴﺔ‬ ‫ﺍﻟﻜﻠﻴﺔ‬ ‫ﺍﳌﺴﺎﺣﺔ‬:
)١()٢()٣(
‫ﻟﻠﻤﺠﺴﻢ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)‫أ‬......................................................................... = (
‫ﻟﻠﻤﺠﺴﻢ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)‫أ‬......................................................................... = (
‫ﻟﻠﻤﺠﺴﻢ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)‫ب‬............ = (.............................................................
‫ﻟﻠﻤﺠﺴﻢ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)‫ب‬......................................................................... = (
‫ﻟﻠﻤﺠﺴﻢ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)‫ج‬.......................................................... = (...............
‫ﻟﻠﻤﺠﺴﻢ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬)‫ج‬= (.........................................................................
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬
01022744086

33. ٣٣
‫س‬٣(‫ﻓﺈن‬ ‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻃﺊ‬ ‫ﻋﻨﺪ‬:
‫اﻟﻤﺠﺴﻢ‬ ‫اﺳﻢ‬....................
‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﺠﺎﻧﺒﻴﺔ‬............................................‫ﺳﻢ‬٢
‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﻜﻠﻴﺔ‬.............................................‫ﺳﻢ‬٢
‫س‬٤(‫ارﺗﻔﺎﻋﻪ‬ ‫ﻣﺴﺘﻄﻴﻼت‬ ‫ﻣﺘﻮازي‬١٥‫ﻣﺤﻴﻄﻬﺎ‬ ‫ﻣﺴﺘﻄﻴﻠﺔ‬ ‫وﻗﺎﻋﺪﺗﻪ‬ ‫ﺳﻢ‬٩٠‫وﻃﻮﻟﻬﺎ‬ ‫ﺳﻢ‬٣٠‫ﺳﻢ‬.
-‫اﻟﻤﺴﺘﻄﻴﻼت‬ ‫ﻟﻤﺘﻮازي‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬
-‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﻤﺴﺘﻄﻴﻼت‬ ‫ﻟﻤﺘﻮازي‬ ‫اﻟﻜﻠﻴﺔ‬
...........................................................................................................................
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‫س‬٥(‫اﻟﻜﻤﻌﺐ‬ ‫وﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬.......... =‫اﻟﻜﻠﻴﺔ‬ ‫ﻣﺴﺎﺣﺘﻪ‬.)
١
٢
،
١
٨
،
١
٦
،
١
٤
(
‫س‬٦(‫ﻗﺎﻋﺪﺗﻪ‬ ‫ﺑﻌﺪا‬ ‫ﺳﺒﺎﺣﺔ‬ ‫ﺣﻤﺎم‬٤٠، ‫ﺳﻢ‬١٠‫وارﺗﻔﺎﻋﻪ‬ ‫ﺳﻢ‬٢.٥‫م‬.‫اﻟﺸﻜﻞ‬ ‫ﻣﺮﺑﻊ‬ ‫ﺳﻴﺮاﻣﻴﻚ‬ ‫ﺑﺒﻼط‬ ‫ﺗﻐﻄﻴﺘﻪ‬ ‫ﻳﺮاد‬
‫ﺿﻠﻌﻪ‬ ‫ﻃﻮل‬٢٥‫ﺳﻢ‬.
-‫اﻟﺒﻼط‬ ‫ﻋﺪد‬ ‫اﺣﺴﺐ‬‫ذﻟﻚ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺴﺘﺨﺪم‬.
-‫اﻟﻮاﺣﺪة‬ ‫ﺳﻌﺔ‬ ‫ﻛﺮاﺗﻴﻦ‬ ‫ﻓﻲ‬ ‫اﻟﺒﻼط‬ ‫ﺗﻌﺒﺌﺔ‬ ‫ﺗﻢ‬ ‫واذا‬١٦‫ﺑﻼﻃﺔ‬.‫اﻟﻤﺴﺘﺨﺪﻣﺔ‬ ‫اﻟﻜﺮاﺗﻴﻦ‬ ‫ﻋﺪد‬ ‫ﻓﺎﺣﺴﺐ‬
-‫اﻟﻤﺮﺑﻊ‬ ‫اﻟﻤﺘﺮ‬ ‫ﺗﻜﻠﺔ‬ ‫ﺛﻤﻦ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫اﻟﺤﻤﺎم‬ ‫ﺗﺒﻠﻴﻂ‬ ‫ﺗﻜﻠﻔﺔ‬ ‫اﺣﺴﺐ‬٥٠‫ﺟﻨﻴﻬﺎ‬.
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٦‫ﺳﻢ‬٦‫ﺳﻢ‬٦‫ﺳﻢ‬٦‫ﺳﻢ‬
٦‫ﺳﻢ‬
٦‫ﺳﻢ‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

34. ٣٤
‫دراﺳﺘﻪ‬ ‫ﺳﻖ‬ ‫ﻟﻤﺎ‬ ‫ﻫﺎﻣﺔ‬ ‫ﻗﻮاﻧﻴﻦ‬
‫اﻟﻤﺮﺑﻊ‬ ‫ﻣﺤﻴﻂ‬‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬×٤
‫اﻟﻤﺮﺑﻊ‬ ‫ﻣﺴﺎﺣﺔ‬‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬×‫ﻧﻔﺴﻪ‬=‫اﻟﻘﻄﺮ‬ ‫ﻃﻮل‬ ‫ﻧﺼﻒ‬×‫اﻟﻘﻄﺮ‬ ‫ﻃﻮل‬
‫اﻟﻤﺴﺘﻄﻴﻞ‬ ‫ﻣﺤﻴﻂ‬)‫اﻟﻄﻮل‬+‫اﻟﻌﺮض‬(×٢
‫اﻟﻤﺴﺘﻄﻴﻞ‬ ‫ﻣﺴﺎﺣﺔ‬‫اﻟﻄﻮل‬×‫اﻟﻌﺮض‬
‫اﻟﻤﻌﻴﻦ‬ ‫ﻣﺤﻴﻂ‬‫اﻟﻀﻠﻊ‬ ‫ﻃﻮل‬×٤
‫اﻟﻤﻌﻴﻦ‬ ‫ﻣﺴﺎﺣﺔ‬‫ﻗﻄﺮﻳﻪ‬ ‫ﻃﻮﻻ‬ ‫ﺿﺮب‬ ‫ﺣﺎﺻﻞ‬ ‫ﻧﺼﻒ‬=‫اﻟﻘﺎﻋﺪة‬ ‫ﻃﻮل‬×‫اﻻرﺗﻔﺎع‬
‫اﻟﻤﺜﻠﺚ‬ ‫ﻣﺤﻴﻂ‬‫اﺿﻼﻋﻪ‬ ‫أﻃﻮال‬ ‫ﻣﺠﻤﻮع‬
‫اﻟﻤﺜﻠﺚ‬ ‫ﻣﺴﺎﺣﺔ‬‫اﻟﻘﺎﻋﺪة‬ ‫ﻧﺼﻒ‬×‫اﻻرﺗﻔﺎع‬
‫اﻷﺻﻼع‬ ‫ﻣﺘﻮازي‬ ‫ﻣﺤﻴﻂ‬)‫اﻟﻄﻮل‬+‫اﻟﻌﺮض‬(×٢
‫ﻣﺴﺎﺣﺔ‬‫اﻷﺿﻼع‬ ‫ﻣﺘﻮازي‬‫اﻟﻘﺎﻋﺪة‬ ‫ﻃﻮل‬×‫اﻻرﺗﻔﺎع‬
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺤﻴﻂ‬‫ط‬×‫اﻟﻘﻄﺮ‬ ‫ﻃﻮل‬=٢‫ﻧﻖ‬ ‫ط‬:‫ط‬=٣.١٤=٢٢/٧
‫اﻟﺪاﺋﺮة‬ ‫ﻣﺴﺎﺣﺔ‬‫ﻧﻖ‬ ‫ط‬٢
‫ﻟﻠﻤﻜﻌﺐ‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬×٤
‫ﻟﻠﻤﻜﻌﺐ‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﻮﺟﻪ‬ ‫ﻣﺴﺎﺣﺔ‬×٦=‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬×‫اﻻرﺗﻔﺎع‬
‫اﻷﺿﻼع‬ ‫ﻟﻤﺘﻮازي‬ ‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﻘﺎﻋﺪة‬ ‫ﻣﺤﻴﻂ‬×‫اﻻرﺗﻔﺎع‬
‫اﻷﺿﻼع‬ ‫ﻟﻤﺘﻮازي‬ ‫اﻟﻜﻠﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬‫اﻟﺠﺎﻧﺒﻴﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ‬+‫اﻟﻘﺎﻋﺪﺗﻴﻦ‬ ‫ﻣﺴﺎﺣﺘﻰ‬ ‫ﻣﺠﻤﻮع‬
‫اﻟﻬﻨﺪﺳﻴﺔ‬ ‫اﻷﺷﻜﺎل‬ ‫ﻟﺒﻌﺾ‬ ‫اﻟﺘﻤﺎﺛﻞ‬ ‫ﻣﺤﺎور‬ ‫ﻋﺪد‬
‫اﻟﻤﺮﺑﻊ‬٤
‫اﻟﻤﺴﺘﻄﻴﻞ‬٢
‫اﻷﺿﻼع‬ ‫ﻣﺘﻮازي‬‫ﺻﻔﺮ‬
‫اﻟﻤﻌﻴﻦ‬٢
‫اﻟﻤﻨﺘﻈﻢ‬ ‫اﻟﻤﻨﺤﺮف‬ ‫ﺷﺒﻪ‬)‫اﻟﺴﺎﻗﻴﻦ‬ ‫ﻣﺘﺴﺎوي‬(١
‫اﻟﻤﻨﺤﺮف‬ ‫ﺷﺒﻪ‬‫ﺻﻔﺮ‬
‫اﻟﻤﺜﻠﺚ‬‫اﻷﺿﻼع‬ ‫ﻣﺘﺴﺎوي‬٣
‫اﻟﺴﺎﻗﻴﻦ‬ ‫اﻟﻤﺘﺴﺎوي‬ ‫اﻟﻤﺜﻠﺚ‬١
‫اﻷﺿﻼع‬ ‫اﻟﻤﺨﺘﻠﻒ‬ ‫اﻟﻤﺜﻠﺚ‬‫ﺻﻔﺮ‬
‫اﻟﺪاﺋﺮة‬ً‫ا‬‫ﺟﺪ‬ ‫ﻛﺒﻴﺮ‬ ‫ﻋﺪد‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

35. ٣٥
‫اﻟﺪاﺋﺮﻳﺔ‬ ‫ﺑﺎﻟﻘﻄﺎﻋﺎت‬ ‫اﻟﺒﻴﺎﻧﺎت‬ ‫ﺗﻤﺜﻴﻞ‬
‫اﻟﺪاﺋﺮي‬ ‫اﻟﻘﻄﺎع‬ ‫زاوﻳﺔ‬
‫زاوﻳﺔ‬ ‫وﻫﻲ‬ ‫داﺋﺮي‬ ‫ﻗﻄﺎع‬ ‫ﺑﺄي‬ ‫اﻟﺨﺎﺻﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫ﻫﻲ‬‫اﻟﺪاﺋﺮة‬ ‫ﻣﺮﻛﺰ‬ ‫رأﺳﻬﺎ‬ ‫ﻣﺮﻛﺰﻳﺔ‬
‫اﻟﺪاﺋﺮﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫ﻗﻴﺎس‬=٣٦٠
‫ﻧﻘﻄﺔ‬ ‫ﺣﻮل‬ ‫اﻟﻤﺘﺠﻤﻌﺔ‬ ‫اﻟﺰواﻳﺎ‬ ‫ﻗﻴﺎﺳﺎت‬ ‫ﻣﺠﻤﻮع‬=٣٦٠
‫ﻣﺜﺎل‬١(‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﺸﻜﻞ‬ ‫ادرس‬:
)١(‫اﻟﻘﻄﺎع‬ ‫ﺳﻄﺢ‬ ‫ﻣﺴﺎﺣﺔ‬)١= (
١
٤
‫اﻟﺪاﺋﺮة‬ ‫ﺳﻄﺢ‬ ‫ﻣﺴﺎﺣﺔ‬
)٢(‫اﻟﻘﻄﺎع‬ ‫ﺳﻄﺢ‬ ‫ﻣﺴﺎﺣﺔ‬)٣= (
١
٦
×٣٦٠°
=٦٠°
‫ﻣﺜﺎل‬:‫ﻣﻨﺼﻮر‬ ‫ﺻﺮف‬٢٠%‫وادﺧﺮ‬ ‫واﻟﻔﺎﻛﻬﺔ‬ ‫اﻟﺨﻀﺎر‬ ‫ﺷﺮاء‬ ‫ﻋﻠﻰ‬ ‫ﻣﺮﺗﺒﻪ‬ ‫ﻣﻦ‬‫اﻟﺒﺎﻗﻲ‬.
‫اﻟﺪاﺋﺮﻳﺔ‬ ‫اﻟﻘﻄﺎﻋﺎت‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ً‫ﺎ‬‫ﺑﻴﺎﻧﻴ‬ ‫ذﻟﻚ‬ ‫ﻣﺜﻞ‬.
٢٠%‫ﻣﻦ‬‫ﻣﺮﺗﺒﻪ‬=
٢٠
١٠٠
=
١
٥
‫اﻟﺪاﺋﺮة‬
‫وﻫﻲ‬=
٢٠
١٠٠
×٣٦٠°
=٧٢°
‫ﺗﻤﺮﻳﻦ‬–‫اﻟﺴﺎدس‬ ‫اﻟﺼﻒ‬ ‫ﻟﻄﻼب‬ ‫اﻟﻤﻔﻀﻠﺔ‬ ‫اﻟﺪراﺳﻴﺔ‬ ‫ﻟﻠﻤﻮاد‬ ‫اﻟﻤﺌﻮﻳﺔ‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ﻳﻮﺿﺢ‬ ‫اﻟﺘﺎﻟﻲ‬ ‫اﻟﺠﺪول‬
‫اﻟﻤﺪارس‬ ‫ﺑﺈﺣﺪى‬:‫اﻟﺪاﺋﺮﻳﺔ‬ ‫ﺑﺎﻟﻘﻄﺎﻋﺎت‬ ‫ﻣﺜﻞ‬.
‫اﻟﺪراﺳﻴﺔ‬ ‫اﻟﻤﺎدة‬‫اﻟﻌﺮﺑﻴﺔ‬ ‫اﻟﻠﻐﺔ‬‫اﻟﺮﻳﺎﺿﻴﺎت‬‫اﻟﻌﻠﻮم‬‫اﻻﺟﺘﻤﺎﻋﻴﺔ‬ ‫اﻟﺪراﺳﺎت‬
‫ﻧﺴﺒﺔ‬‫ﻋﺪد‬‫اﻟﺘﻼﻣﻴﺬ‬٣٥%٢٥%٢٢%‫س‬
‫ﻗﻴﻤﺔ‬‫س‬=١٠٠%-)٣٥+٢٥+٢٢= %(١٨%
‫اﻟﻌﺮﺑﻴﺔ‬ ‫اﻟﻠﻐﺔ‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬=٣٥%×٣٦٠=١٢٦°
‫اﻟﺮﻳﺎﺿﻴﺎت‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬=٢٥%×٣٦٠=٩٠°
‫اﻟﻌﻠﻮم‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬=٢٢%×٣٦٠=٧٩.٢°
‫اﻻﺟﺘﻤﺎﻋﻴﺔ‬ ‫اﻟﺪراﺳﺎت‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬
=١٨%×٣٦٠=٦٤.٨°
‫ﻗﻄﺎع‬
١
‫ﻗﻄﺎع‬
٥
‫ﻗﻄﺎع‬
٤
‫ﻗﻄﺎع‬
٣ ‫ﻗﻄﺎع‬
٢
٧٢°
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

36. ٣٦
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫ﻗﺪره‬ ‫ﻣﺎل‬ ‫ﺑﺮأس‬ ‫ﺗﺠﺎري‬ ‫ﻣﺸﺮوع‬ ‫ﺗﺄﺳﻴﺲ‬ ‫ﻓﻲ‬ ‫اﺻﺪﻗﺎء‬ ‫ﺧﻤﺴﺔ‬ ‫اﺷﺘﺮك‬٦٠٠٠٠‫اﻷول‬ ‫ﻓﺪﻓﻊ‬ ‫ﺟﻨﻴﻪ‬
١٢٠٠٠‫واﻟﺜﺎﻧﻲ‬ ‫ﺟﻨﻴﻪ‬٦٠٠٠‫واﻟﺜﺎﻟﺚ‬ ‫ﺟﻨﻴﻪ‬١٥٠٠٠‫واﻟﺮاﺑﻊ‬ ‫ﺟﻨﻴﻪ‬٩٠٠٠‫اﻟﺒﺎﻗﻲ‬ ‫اﻟﺨﺎﻣﺲ‬ ‫ودﻓﻊ‬ ‫ﺟﻨﻴﻪ‬.
-‫اﻟﺪاﺋﺮﻳﺔ‬ ‫ﺑﺎﻟﻘﻄﺎﻋﺎت‬ ‫ذﻟﻚ‬ ‫وﺿﺢ‬.
‫اﻟﺨﺎﻣﺲ‬ ‫دﻓﻌﺔ‬ ‫ﻣﺎ‬............................ =.........................................
‫اﻷول‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬=×٣٦٠........ =°
‫اﻟﺜﺎﻧﻲ‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬=×٣٦٠........ =°
‫اﻟﺜﺎﻟﺚ‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬=×٣٦٠........ =°
‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬‫اﻟﺮاﺑﻊ‬................................. =
‫اﻟﺨﺎﻣﺲ‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬............................... =
‫س‬٢(‫اﻟﺸﻜﻞ‬ ‫ﻳﻮﺿﺢ‬‫اﻟﻤﺴﺄﻟﺔ‬ ‫اﺳﻔﻞ‬‫اﻟﺴﺎدس‬ ‫ﺑﺎﻟﺼﻒ‬ ‫اﻟﻔﺼﻮل‬ ‫أﺣﺪ‬ ‫ﻟﺘﻼﻣﻴﺬ‬ ‫اﻟﻤﻔﻀﻠﺔ‬ ‫اﻟﻬﻮاﻳﺎت‬
-‫أﺟﺐ‬ ‫ﺛﻢ‬ ‫اﻟﺸﻜﻞ‬ ‫ادرس‬:
-‫اﻟﻬﻮاﻳﺎت‬ ‫ﻟﺒﺎﻗﻲ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﻤﺴﺮح‬ ‫ﻧﺴﺒﺔ‬ ‫ﻣﺎ‬...............................................................
-‫اﻟﻬﻮاﻳﺎت‬ ‫ﻟﺒﺎﻗﻲ‬ ‫اﻟﻤﺪرﺳﻴﺔ‬ ‫اﻻذاﻋﺔ‬ ‫ﻧﺴﺒﺔ‬ ‫ﻣﺎ‬.............................................................
-‫اﻟﻬﻮاﻳﺎت‬ ‫ﻟﺒﺎﻗﻲ‬ ‫اﻟﺠﻮاﻟﺔ‬ ‫ﻧﺴﺒﺔ‬ ‫ﻣﺎ‬..........................................................................
-‫اﻟﻤﻮﺳﻴﻘﻰ‬ ‫ﻟﻘﻄﺎع‬ ‫اﻟﻤﺮﻛﺰﻳﺔ‬ ‫اﻟﺰاوﻳﺔ‬ ‫ﻗﻴﺎس‬ ‫ﻣﺎ‬..........................................................
-‫اﻟﺘﻼﻣﻴﺬ‬ ‫ﺟﺎﻧﺐ‬ ‫ﻣﻦ‬ ً‫ﻼ‬‫ﺗﻔﻀﻴ‬ ‫اﻟﻬﻮاﻳﺎت‬ ‫أﻗﻞ‬ ‫ﻣﺎ‬...........................................................
-‫اﻟﺘﻼﻣﻴﺬ‬ ‫ﺟﺎﻧﺐ‬ ‫ﻣﻦ‬ ً‫ﻼ‬‫ﺗﻔﻀﻴ‬ ‫اﻟﻬﻮاﻳﺎت‬ ‫أﻛﺒﺮ‬ ‫ﻣﺎ‬..........................................................
‫اﻟﻤﻮﺳﻴﻘﻰ‬
٢٢%
‫اﻻذاﻋﺔ‬
٢٢%
‫اﻟﻤﺴﺮح‬
٢٥%
‫اﻟﺼﺤﺎﻓﺔ‬
١٨%
‫اﻟﺠﻮاﻟﺔ‬
% .......
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086

37. ٣٧
‫واﻻﺣﺘﻤﺎل‬ ‫اﻟﻌﺸﻮاﺋﻴﺔ‬ ‫اﻟﺘﺠﺮﺑﺔ‬
‫ﻳﻤﻜﻦ‬ ‫ﻻ‬ ‫وﻟﻜﻦ‬ ‫اﺟﺮاﺋﻬﺎ‬ ‫ﻗﺒﻞ‬ ‫اﻟﻤﻤﻜﻨﺔ‬ ‫ﻧﺘﺎﺋﺠﻬﺎ‬ ‫ﻣﻌﺮﻓﺔ‬ ‫ﻳﻤﻜﻦ‬ ‫ﺗﺠﺮﺑﺔ‬
‫إﺟﺮاﺋﻬﺎ‬ ‫ﺑﻌﺪ‬ ‫إﻹ‬ ً‫ﻼ‬‫ﻓﻌ‬ ‫ﺳﻴﺤﺪث‬ ‫اﻟﺬي‬ ‫اﻟﻨﺎﺗﺞ‬ ‫ﺗﺤﺪﻳﺪ‬
‫ﻋﺸﻮاﺋﻴﺔ‬ ‫ﺗﺠﺮﺑﺔ‬ ‫داﺧﻞ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﻧﺤﺼﻞ‬ ‫ﻧﺘﺎﺋﺞ‬
‫اﻟﻨﻮاﺗﺞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬‫اﻟﻌﺸﻮاﺋﻴﺔ‬ ‫ﻟﻠﺘﺠﺮﺑﺔ‬ ‫اﻟﻤﻤﻜﻨﺔ‬
‫اﻟﻌﻴﻨﺔ‬ ‫ﻓﻀﺎء‬ ‫ﻋﻨﺎﺻﺮ‬ ‫وﻋﺪد‬ ‫اﻟﺤﺪث‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪد‬ ‫ﺑﻴﻦ‬ ‫اﻟﻨﺴﺒﺔ‬
‫ﻣﺜﺎل‬١(‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬ً‫ﺎ‬‫ﻓﺮدﻳ‬ ً‫ا‬‫ﻋﺪد‬ ‫اﻟﻌﻠﻮي‬ ‫ﺑﺎﻟﻮﺟﻪ‬ ‫اﻟﻨﻘﺎط‬ ‫ﻋﺪد‬ ‫ﻳﻜﻮن‬ ‫أن‬ ‫ﻋﻠﻰ‬ ‫ﻧﺮد‬ ‫ﺣﺠﺮ‬ ‫إﻟﻘﺎء‬.
‫اﻟﻌﻴﻨﺔ‬ ‫ﻓﻀﺎء‬}١،٣،٥{‫اﻟﻌﻴﻨﺔ‬ ‫ﻓﻀﺎء‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪد‬=٣
‫ﻣﺜﺎل‬٢(‫اﻟﻈﺎﻫﺮ‬ ‫اﻟﻮﺟﻪ‬ ‫ﻟﻤﻌﺮﻓﺔ‬ ‫ﻣﺘﺘﺎﻟﻴﺘﻴﻦ‬ ‫ﻣﺮﺗﻴﻦ‬ ‫ﻧﻘﻮد‬ ‫ﻗﻄﻌﺔ‬ ‫إﻟﻘﺎء‬ ‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬
‫اﻟﻌﻴﻨﺔ‬ ‫ﻓﻀﺎء‬)‫ف‬(})‫ص‬ ، ‫ص‬(،)‫ك‬ ، ‫ص‬(،)‫ك‬ ، ‫ك‬(،)، ‫ك‬‫ص‬({
‫ﻣﺜﺎل‬٣(‫اﻟﻌﻠﻮﻳﻴﻦ‬ ‫ﺑﺎﻟﻮﺟﻬﻴﻴﻦ‬ ‫اﻟﻨﻘﺎط‬ ‫ﻣﺠﻤﻮع‬ ‫ﻳﻜﻮن‬ ‫أن‬ ‫ﻋﻠﻰ‬ ‫ﻧﺮد‬ ‫ﺣﺠﺮي‬ ‫إﻟﻘﺎء‬ ‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬٧
‫ف‬=})١،٦(،)٢،٥(،)٣،٤(،)٦،١(،)٥،٢(،)٤،٣({،‫ن‬)‫ف‬(=٦
‫ﻣﺜﺎل‬٤(‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫ﺗﻜﻮﻳﻦ‬ ‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬‫اﻟﺮﻗﻤﻴﻦ‬٦،٩‫اﻟﻤﻄﻠﻮﺑﺔ‬ ‫اﻻﺣﺘﻤﺎﻻت‬ ‫أوﺟﺪ‬ ، ‫اﻟﻌﻴﻨﺔ‬ ‫ﻓﻀﺎء‬ ‫اﻛﺘﺐ‬.
-‫اﻵﺣﺎد‬ ‫رﻗﻢ‬ ‫ﺣﻴﺚ‬ ‫أ‬ ‫اﻟﺤﺪث‬=‫اﻟﻌﺸﺮات‬ ‫رﻗﻢ‬
‫أ‬=}٦٦،٩٩{‫ن‬)‫أ‬(=٢‫ل‬)‫أ‬(=
٢
٤
=٠.٥
-‫ﻓﺮدي‬ ‫اﻟﻌﺸﺮات‬ ‫رﻗﻢ‬ ‫ب‬ ‫ﺣﻴﺚ‬ ‫ب‬ ‫اﻟﺤﺪث‬
‫ب‬=}٩٦،٩٩{‫ن‬)‫ب‬(=٢‫ل‬)‫ب‬(=
٢
٤
=٠.٥
‫اﻟﺘﺠﺮﺑﺔ‬
‫اﻟﻌﺸﻮاﺋﻴﺔ‬
‫اﻟﻌﻴﻨﺔ‬ ‫ﻓﻀﺎء‬
)‫ف‬(
‫اﻟﺮﻣﻴﺔ‬‫ك‬
‫ص‬
‫ك‬
‫ص‬
‫ص‬
‫ك‬
‫اﻟﺤﺪث‬)‫أ‬(
‫اﺣﺘﻤﺎل‬
‫اﻟﺤﺪث‬)‫ل‬(
‫ﺧﺪ‬
‫ﺑﺎﻟﻚ‬
‫اﻟﻤﺴﺘﺤﻴﻞ‬ ‫اﻟﺤﺪث‬)‫وﻗﻮﻋﻪ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻻ‬(‫ﻋﻨﻪ‬ ‫وﻧﻌﺒﺮ‬h=T،‫ل‬)T(=‫ﺻﻔﺮ‬
‫اﻟﻤﺆﻛﺪ‬ ‫اﻟﺤﺪث‬)‫اﻟﻤﻤﻜﻨﺔ‬ ‫اﻟﻨﻮاﺗﺞ‬ ‫ﺟﻤﻴﻊ‬(‫ﻋﻨﻪ‬ ‫وﻧﻌﺒﺮ‬h=‫ف‬،‫ل‬)‫ف‬(=١
‫اﻟﻤﻤﻜﻦ‬ ‫اﻟﺤﺪث‬)‫ﻟﻠﺘﺠﺮﺑﺔ‬ ‫اﻟﻤﻤﻜﻨﺔ‬ ‫اﻟﻨﻮاﺗﺞ‬ ‫ﺑﻌﺾ‬(‫ﻋﻨﻪ‬ ‫وﻧﻌﺒﺮ‬
hG‫ف‬:٠N‫ل‬)h(N١
‫ل‬)‫أ‬= (
‫ن‬)‫أ‬(
‫ن‬)‫ف‬(‫أي‬=
‫أ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪد‬
‫ف‬ ‫ﻋﻨﺎﺻﺮ‬ ‫ﻋﺪد‬
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086

38. ٣٨
-‫زوﺟﻲ‬ ‫اﻵﺣﺎد‬ ‫رﻗﻢ‬ ‫ج‬ ‫ﺣﻴﺚ‬ ‫ج‬ ‫اﻟﺤﺪث‬
‫ج‬=}٩٦،٦٦{‫ن‬)‫ج‬= (٢‫ل‬)‫ج‬= (
٢
٤
=٠.٥
‫ﺗﻤﺮﻳﻦ‬‫ﻓﻲ‬‫ﻓﻀﺎء‬ ‫اﻛﺘﺐ‬ ‫اﻟﻌﻠﻮي‬ ‫اﻟﻮﺟﻪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻈﺎﻫﺮ‬ ‫اﻟﻌﺪد‬ ‫وﻣﻼﺣﻈﺔ‬ ‫واﺣﺪة‬ ‫ﻣﺮة‬ ‫ﻧﺮد‬ ‫ﺣﺠﺮ‬ ‫اﻟﻠﻘﺎء‬ ‫ﺗﺠﺮﺑﺔ‬
‫أ‬ ‫ﺣﻴﺚ‬ ‫أ‬ ‫اﻟﺤﺪث‬ ‫اﺣﺘﻤﺎل‬ ‫أوﺟﺪ‬ ‫ﺛﻢ‬ ‫اﻟﻌﻴﻨﺔ‬N٣‫اﻟﺤﺪث‬ ‫ﻧﻮع‬ ‫ﺣﺪد‬ ‫ﺛﻢ‬
‫اﻟﻤﻨﺰﻟﻲ‬ ‫اﻟﻮاﺟﺐ‬
‫س‬١(‫اﻟﺼﺤﻴﺤﺔ‬ ‫اﻻﺟﺎﺑﺔ‬ ‫اﺧﺘﺮ‬:
)١(‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫ﻋﺪد‬ ‫وﻇﻬﻮر‬ ‫واﺣﺪة‬ ‫ﻣﺮة‬ ‫ﻧﺮد‬ ‫ﺣﺠﺮ‬ ‫اﻟﻘﺎء‬ ‫ﺗﺠﺮﺑﺔ‬ ‫ﻓﻲ‬٤‫ل‬ ‫ﻫﻲ‬)‫أ‬...... = (
)
٢
٣
،
١
٦
،
٥
٦
،
١
٢
(
)٢(‫ﺻﻮرة‬ ‫ﻟﻈﻬﻮر‬ ‫ﻣﺘﻮﻗﻊ‬ ‫ﻋﺪد‬ ‫اﻗﺮب‬ ‫ﻓﺎن‬ ‫واﺣﺪة‬ ‫ﻣﺮة‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻧﻘﻮد‬ ‫ﻗﻄﻌﺔ‬ ‫أﻟﻘﻴﺖ‬........ =
)‫ﺻﻔﺮ‬،T،
١
٣
،
١
٦
(
)٣(‫ﺗﻠﻤﻴﺬ‬ ‫ﻧﺠﺎح‬ ‫اﺣﺘﻤﺎل‬‫ﻫﻮ‬
١
٣
‫ﻫﻮ‬ ‫رﺳﻮﺑﻪ‬ ‫اﺣﺘﻤﺎل‬ ‫ﻓﺈن‬.........
)‫ﺻﻔﺮ‬،T،
٢
٣
،
١
٦
(
)٤(‫ﻫﻲ‬ ‫ﺟﺮاح‬ ‫ﺑﻬﺎ‬ ‫ﻳﻘﻮم‬ ‫ﻋﻤﻠﻴﺔ‬ ‫ﻧﺠﺎح‬ ‫اﺣﺘﻤﺎل‬٨٠%‫ﻧﺠﺎﺣﻬﺎ‬ ‫ﻋﺪم‬ ‫اﺣﺘﻤﺎل‬ ‫ﻓﺈن‬............
)٠.٠٣،T،٣٠%،
١
٥
(
‫س‬٢(‫ﻳﺄﺗﻲ‬ ‫ﻋﻤﺎ‬ ‫اﺟﺐ‬:
)١(‫ﻓﻲ‬‫ﺗﻘﺪم‬ ‫اﻟﻤﺪارس‬ ‫ﻷﺣﺪ‬ ‫اﻟﻤﺜﺎﻟﻲ‬ ‫اﻟﻄﺎﻟﺐ‬ ‫ﻣﺴﺎﺑﻘﺔ‬٤٥‫اﻟﻤﺜﺎﻟﻴﺔ‬ ‫اﻟﺘﻠﻤﻴﺬة‬ ‫اﺣﺘﻤﺎل‬ ‫ﻛﺎن‬ ‫ﻓﺈذا‬ ، ‫وﺗﻠﻤﻴﺬة‬ ‫ﺗﻠﻤﻴﺬ‬
٤
٩
‫اﻟﻤﺴﺎﺑﻘﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺸﺘﺮﻛﺎت‬ ‫اﻟﺘﻠﻤﻴﺬات‬ ‫ﻋﺪد‬ ‫ﻓﺈن‬...................... =
)٢(‫اﻟﺘﺨﺴﻴﺲ‬ ‫ﻣﺮاﻛﺰ‬ ‫أﺣﺪ‬ ‫ﻓﻲ‬١٠‫ﺑﻴﻦ‬ ‫ﻣﺎ‬ ‫ارﺑﻌﺔ‬ ‫وزن‬ ‫ﺳﻴﺪات‬١٠٠،١١٠‫واﻟﺒﺎ‬ ‫ﻛﺠﻢ‬‫ﺑﻴﻦ‬ ‫ﻣﺎ‬ ‫ﻗﻴﺎت‬١١٠،
١٢٠‫ﻛﺠﻢ‬.‫اﻵﺗﻴﺔ‬ ‫ﺑﺎﻻﺣﺘﻤﺎﻻت‬ ‫اﺣﺴﺐ‬:
‫أ‬-‫وزﻧﻬﺎ‬ ‫ﺳﻴﺪة‬>١١٠‫ﻛﺠﻢ‬..............‫ب‬-‫وزﻧﻬﺎ‬ ‫ﺳﻴﺪة‬<١١٠‫ﻛﺠﻢ‬.............
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﳝﻦ‬ / ‫أ‬01022744086
‫ﻛﺎﻣﻞ‬ ‫ﺟﺎﺑﺮ‬ ‫أﯾﻤﻦ‬ / ‫أ‬01022744086