Math-4th-primary-2nd-term رياضيات رابعة إبتدائي تيرم ثاني #خواجه

1. òr톧a@pbî™bíŠÛaòr톧a@pbî™bíŠÛaòr톧a@pbî™bíŠÛaòr톧a@pbî™bíŠÛa@@@@@@@@
óöa†niüa@ÉiaŠÛa@Ñ–Ûaóöa†niüa@ÉiaŠÛa@Ñ–Ûaóöa†niüa@ÉiaŠÛa@Ñ–Ûaóöa†niüa@ÉiaŠÛa@Ñ–Ûa@@@@@@@@
@óa‰†Ûa@Ý–ÐÛa@óa‰†Ûa@Ý–ÐÛa@óa‰†Ûa@Ý–ÐÛa@óa‰†Ûa@Ý–ÐÛaóãbrÛaóãbrÛaóãbrÛaóãbrÛa@@@@@@@@
٢٠١١/٢٠١٢
Mr.youssef Shafik

2. ‫ﻣﻦ‬ ‫ﻳﺘﻜﻮﻥ‬‫ﺟﺰﺃﻳﻦ‬:
‫ﺍﻟﺒﺴﻂ‬
‫ﺍﳌﻘﺎﻡ‬
‫ﺍﻣﺜﻠﺔ‬:
١
٢
،
١
٤
،
١
٨
،
٣
٤
،
٥
٨
،
٢
٩
،
٧
١٠
‫ﺫ‬
]١[òîÛbnÛa@‰ìŽØÛa@cŠÓaòîÛbnÛa@‰ìŽØÛa@cŠÓaòîÛbnÛa@‰ìŽØÛa@cŠÓaòîÛbnÛa@‰ìŽØÛa@cŠÓa
٣
٧
،
٢
٥
،
٩
١٠
،
١
٢
،
١
٦
،
٤
٧
،
١
٣
،
٥
٨
]٢[ómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×c
)١(
٢
٥
=
.....
١٠
)٢(
٣
٤
=
.....
٨
)٣(
١
٣
=
٥
.....
)٤(
٣
٤
=
٩
.....
)٥(
٢
٣
=
.....
١٥
)٦(
١
٢
=
.....
٨
]٣[ómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×c
)١(٨=
.....
١
)٢(٤=
.....
٢
)٣(٧=
١٤
.....
)٤(٣=
.....
٣
)٥(١٠=
٥٠
.....
)٦(٢٠=
.....
٢
)٧(٥=
.....
٢
)٨(٦=
١٢
.....
)٩(٧=
.....
١٠
‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ @Þëüa@÷‰†Ûa@Þëüa@÷‰†Ûa@Þëüa@÷‰†Ûa@Þëüa@÷‰†Ûa@Z@Z@Z@Zòí…bÈÛa@‰ìŽØÛaòí…bÈÛa@‰ìŽØÛaòí…bÈÛa@‰ìŽØÛaòí…bÈÛa@‰ìŽØÛa@@@@@@@@
‫دى‬ ‫اﻝ‬ ‫اﻝ‬
‫ر‬
‫اﻝ‬ ‫د‬ ‫ﻝ‬ ‫اﻝ‬ ‫ر‬ ‫اﻝ‬-‫ا‬
٣=
٣
١
،٥=
٥
١
،٨=
٨
١

3. ]٤[ómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×c
)١(
٣
٤
=
.....
٨
=
٩
.....
=
.....
٢٠
=
٣٠
.....
)٢(
١
٢
=
٥
.....
=
٣
.....
=
٦
.....
=
.....
٢٠
)٣(
١
٣
=
٢
.....
=
٥
.....
=
.....
٢٧
=
.....
٣٠
)٤(١=
٣
.....
=
.....
٨
=
١٠
.....
=
٥
.....
]٤[ómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×c
)١(
٥
٧
+
١
٧
....... =)٢(
٦
١١
-
٣
١١
....... =)٣(
٥
٦
-
٤
٦
......... =
)٤(
٣
٩
+
٢
٩
...... =)٥(
٧
١٢
+
٣
١٢
....... =)٦(
٤
١٧
+
٩
١٧
=.......
)٧(١-
٣
٥
........ =)٨(١-
٤
٧
....... =)٩(١-
٧
٩
......... =
]٥[ómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×cómdí@bß@Ýà×c
)١(
٢
٥
... += ...
٣
٥
)٢(
٤
١١
... += ..
٧
١١
)٣(
٤
٧
-= ........
١
٧
)٤(
٥
٩
-..= ...
٤
٩
)٥(
٣
٤
... += ....١)٦(١-= .........
٣
٥
]٦[‫ﻝ‬ ‫اﻝ‬ ‫ر‬ ‫اﻝ‬
٦
١٢
،
٥
٢٠
،
٧
٢١
،
١٥
٢٧

4. ‫آ‬ ‫رة‬ ‫ﺹ‬
١
٣
٢=
٧
٣
‫وآ‬ ‫ﺹ‬ ‫د‬ ‫رة‬ ‫ﺹ‬
٥
٢
=
١
٢
٣
]١[‫آ‬ ‫رة‬ ‫ﺹ‬
)١(
١
٢
١=...........)٢(
١
٣
٥.......... =)٣(
١
٤
٣........ =
)٤(
١
٣
٧.......... =)٥(
١
٢
١٠......... =)٦(
١
٥
٢=........
)٧(
١
١٠
٤......... =)٨(
١
٤
٢.......... =)٩(
٥
١٠
٥........ =
)١٠(
١
٣
١١........ =)١١(
٥
٧
٣.......... =)١٢(
٢
٧
٦......... =
]١[‫ﺹ‬ ‫د‬ ‫رة‬ ‫ﺹ‬‫وآ‬
)١(
٩
٢
......... =)٢(
١٧
٥
........ =)٣(
٥
٤
........... =
)٤(
١١
١٠
......... =)٥(
٧
٤
........ =)٦(
١٨
٥
........... =
)٧(
٤
٣
........ =)٨(
١٣
١٠
........ =)٩(
٢١
١٠
............ =
)١٠(
١٩
٥
....... =)١١(
٦٣
١٠
........ =)١٢(
٧٦
٧
............. =
‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ ÷‰†Ûa÷‰†Ûa÷‰†Ûa÷‰†ÛaóãbrÛaóãbrÛaóãbrÛaóãbrÛa@Z@@Z@@Z@@Z@@ŠŽ×ë@|îz•@…†Ç@Êìà©@ŠŽ×ë@|îz•@…†Ç@Êìà©@ŠŽ×ë@|îz•@…†Ç@Êìà©@ŠŽ×ë@|îz•@…†Ç@Êìà©@@@@@@@@
‫ل‬)١(
‫ل‬)٢(
‫ر‬

5. ‫ى‬ ‫اﻝ‬ ‫د‬ ‫اﻝ‬:‫أ‬ ‫ن‬‫ء‬ ‫و‬ ، ‫ى‬ ‫ء‬
‫اد‬ ‫أ‬:
٥,٧‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﺳﺒﻌﻪ‬ ‫ﲬﺴﻪ‬ ‫ﻳﻘﺮﺃ‬
٠,٩‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺗﺴﻌﻪ‬ ‫ﻳﻘﺮﺃ‬
]١[‫ا‬ ‫اد‬ ‫ا‬ ‫أ‬ ‫ا‬
)١(٠,٦)٢(٤,٣)٣(٧,٥)٤(٣,٨
)٥(٠,٤)٦(٣,٤)٧(٤٥,٣)٨(٢٧٤,٦
)٩(١٥٨,٧)١٠(٦,٥,٩)١١(١٤١٠,١)١٢(٢٠٠٨,٧
]٢[‫اآ‬
)١(‫ﻳﻜﺘﺐ‬ ‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﲦﺎﻧﻴﻪ‬ ‫ﻭﺳﺘﻮﻥ‬ ‫ﲬﺴﻪ‬ ‫ﺍﻟﻌﺪﺩ‬................
)٢(‫ﻳﻜﺘﺐ‬ ‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﲬﺴﻪ‬ ‫ﻭﺳﺒﻌﻮﻥ‬ ‫ﺍﺭﺑﻌﻪ‬ ‫ﺍﻟﻌﺪﺩ‬..................
)٣(‫ﻳﻜﺘﺐ‬ ‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﺛﻼﺛﻪ‬ ‫ﻭﺍﺭﺑﻌﻮﻥ‬ ‫ﲬﺴﻪ‬ ‫ﺍﻟﻌﺪﺩ‬..................
)٤(‫ﻳﻜﺘﺐ‬ ‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﺗﺴﻌﻪ‬ ‫ﻭﲦﺎﻧﻮﻥ‬ ‫ﻭﺍﺭﺑﻌﻪ‬ ‫ﺳﺒﻌﻤﺎﺋﻪ‬ ‫ﺍﻟﻌﺪﺩ‬................
)٥(‫ﻳﻜﺘﺐ‬ ‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﻭﺍﺣﺪ‬ ‫ﻭﺍﺭﺑﻌﻮﻥ‬ ‫ﻭﻳﺒﻌﻪ‬ ‫ﻭﲬﺴﻤﺎﺋﻪ‬ ‫ﺍﻻﻑ‬ ‫ﻋﺸﺮﺓ‬ ‫ﺍﻟﻌﺪﺩ‬............
]٣[‫اس‬ ‫ا‬ ‫اﻝ‬ ‫ا‬ ‫ا‬
)١(‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﺍﺭﺑﻌﻪ‬ ‫ﲦﺎﻧﻴﻪ‬ ‫ﺍﻟﻌﺪﺩ‬......... =)٤٨،٨٤،٨,٤،٤,٨(
)٢(‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍﺀ‬ ‫ﻭﺛﻼﺛﻪ‬ ‫ﺍﺛﻨﺎﻥ‬ ‫ﺍﻟﻌﺪﺩ‬........ =)٣,٢،٠,٢٣،٢,٣،٢٣(
)٣(٥‫ﻭ‬ ‫ﺍﺣﺎﺩ‬٧‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍﺀ‬........ =)٧,٥،٥,٧،٠,٧٥،٧٥(
)٤(٩‫ﻭ‬ ‫ﺍﺣﺎﺩ‬٥‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍﺀ‬........ =)٩,٥،٥,٩،٩٥،٥٩(
)٥(‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﻭﺳﺒﻌﻪ‬ ‫ﻭﲬﺴﻮﻥ‬ ‫ﻭﲦﺎﻧﻴﻪ‬ ‫ﻣﺎﺋﻪ‬..... =)١٥٨,٧،١٥,٨٧،١,٥٨٧(
‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ ÷‰†Ûa÷‰†Ûa÷‰†Ûa÷‰†ÛasÛbrÛasÛbrÛasÛbrÛasÛbrÛa@Z@@Z@@Z@@Z@@ò튒ÈÛa@…a†Çþa@ò튒ÈÛa@…a†Çþa@ò튒ÈÛa@…a†Çþa@ò튒ÈÛa@…a†Çþa@@@@@@@@
‫د‬ ‫اﻝ‬٢ ٤
‫ى‬ ‫اﻝ‬ ‫ء‬ ‫اﻝ‬‫ء‬ ‫اﻝ‬‫اﻝ‬
‫ر‬

6. ]٤[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
٦
١٠
=..........)٢(
٩
١٠
=............)٣(
١
١٠
=.........
)٤(
٧
١٠
٨=.........)٥(
٣
١٠
٢=.........)٦(
٩
١٠
١=.......
)٧(
٥
١٠
١٢=........)٨(
٧
١٠
٤=.........)٩(
١
١٠
٥=.......
)١٠(
٣
١٠
١٥=.......)١١(
٥
١٠
١=.........)١٢(
١
١٠
٩=........
]٥[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
١
٢
....... =)٢(
٤
٥
....... =)٣(
٧
٢
.......... =
)٤(
٩
٥
......... =)٥(
١١
٢
........ =)٦(
١٨
٥
......... =
)٧(
٥
٢
........ =)٨(
٧
٥
....... =)٩(
١٧
٢
......... =
]٦[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
١
٢
٧....... =)٢(
٢
٥
٣........ =)٣(
٤
٥
٢........ =
)٤(
١
٥
٤..... =)٥(
١
٢
١........ =)٦(
٣
٥
٧........ =
)٧(
١
٢
٣...... =)٨(
٣
٥
٤......... =)٩(
١
٥
١٠....... =

7. ]٧[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
١٢
٢٠
. =.........)٢(
٨
٤٠
......... =)٣(
٣٥
٥٠
.......... =
)٤(
١٨
٢٠
.......... =)٥(
١٤
٢٠
......... =)٦(
٣٤
٢٠
.......... =
]٨[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(٠,٣........... =)٢(٠,٧....... =)٣(٠,٩......... =
)٤(٦,٧.......... =)٥(١٥,١......... =)٦(٥,٣......... =
)٧(١,٢......... =)٨(١٨,٦......... =)٩(٣,٤......... =

8. ‫اد‬ ‫أ‬:
٨,٢٧‫ﻭ‬ ‫ﲦﺎﻧﻴﻪ‬‫ﺳ‬‫ﻣﺎﺋﻪ‬ ‫ﻣﻦ‬ ‫ﻭﻋﺸﺮﻭﻥ‬ ‫ﺒﻌﻪ‬
٢٦,١٥٣‫ﺳ‬‫ﻭﲬ‬ ‫ﻭﺛﻼﺛﻪ‬ ‫ﻭﻣﺎﺋﻪ‬ ‫ﻭﻋﺸﺮﻭﻥ‬ ‫ﺘﻪ‬‫ﺴ‬‫ﺍﻟﻒ‬ ‫ﻣﻦ‬ ‫ﻮﻥ‬
‫د‬ ‫اﻝ‬ ‫م‬ ‫ر‬ ‫ﻥ‬ ‫اﻝ‬ ‫اﻝ‬
‫ﺍﻟﻌﺪﺩ‬ ‫ﻣﺜﺎﻝ‬٤٦٥,٣١٢
‫ﺍﻟﻒ‬ ‫ﻣﻦ‬ ‫ﺟﺰ‬‫ﻣﺎﺋﻪ‬ ‫ﻣﻦ‬ ‫ﺟﺰ‬‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰ‬‫ﺍﻟﻌﻼﻣﻪ‬‫ﺍﺣﺎﺩ‬‫ﻋﺸﺮﺍﺕ‬‫ﻣﺌﺎﺕ‬
٢١٣.٥٦٤
]١[‫أ‬ ‫أ‬‫ا‬ ‫اد‬ ‫ا‬
)١(١,٥٧)٢(١٩,٦١)٣(١٢٧,٨٣)٤(١,٠٣
)٥(٢,٠١)٦(٨,٢٢)٧(٤٧,٠٩)٨(١,٠٠٤
)٩(٦٣,٠١٧)١٠(٠,٨٩)١١(٠,٧٥)١٢(٠,٠٥٤
)١٣(٧٠٠,٣٣)١٤(٠,٠٢٩)١٥(٠,٢٧٤)١٦(٨,٠٧
]٢[‫ا‬ ‫اد‬ ‫ا‬ ‫اآ‬
)١(‫ﻣﺎﺋﻪ‬ ‫ﻣﻦ‬ ‫ﻭﲬﺴﻮﻥ‬ ‫ﻭﺛﻼﺛﻪ‬ ‫ﺳﺒﻌﻪ‬ ‫ﺍﻟﻌﺪﺩ‬( ............. )
)٢(‫ﺍﻟﻒ‬ ‫ﻣﻦ‬ ‫ﻭﻋﺸﺮﻭﻥ‬ ‫ﺗﺴﻌﻪ‬ ‫ﺍﻟﻌﺪﺩ‬( ............. )
)٣(‫ﺍﻟﻒ‬ ‫ﻣﻦ‬ ‫ﻭﺳﺒﻌﻮﻥ‬ ‫ﻭﺳﺘﻪ‬ ‫ﻭﺍﺭﺑﻌﻮﻥ‬ ‫ﺛﻼﺛﻪ‬ ‫ﺍﻟﻌﺪﺩ‬( ............. )
)٤(‫ﻭﺍﺭﺑﻌﻪ‬ ‫ﻭﲬﺴﻮﻥ‬ ‫ﲦﺎﻧﻴﻪ‬ ‫ﺍﻟﻌﺪﺩ‬‫ﻣﻦ‬‫ﻣﺎﺋﻪ‬( ............. )
)٥(‫ﺍﻟ‬‫ﺍﻟﻒ‬ ‫ﻣﻦ‬ ‫ﻭﺗﺴﻌﻪ‬ ‫ﻭﺛﻼﺛﻮﻥ‬ ‫ﺳﺘﻪ‬ ‫ﻌﻌﺪ‬( ............. )
‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ ÷‰†Ûa÷‰†Ûa÷‰†Ûa÷‰†ÛaÉiaŠÛaÉiaŠÛaÉiaŠÛaÉiaŠÛa@Z@@Z@@Z@@Z@é튒ÈÛa@…a†Çüa@åß@†íŒ½aé튒ÈÛa@…a†Çüa@åß@†íŒ½aé튒ÈÛa@…a†Çüa@åß@†íŒ½aé튒ÈÛa@…a†Çüa@åß@†íŒ½a@@@@@@@@
‫ر‬

9. ]٣[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
٢١
١٠٠
)٢(
١٨
١٠٠
)٣(
٧
١٠٠
)٤(
٤
١٠٠
)٥(
٢٧
١٠٠
٨)٦(
٥١
١٠٠
١٩
)٧(
٨٣
١٠٠
١٢٧)٨(
١
١٠٠
٢)٩(
٩
١٠٠
١٥
)١٠(
٤٧
١٠٠
٣)١١(
٢١٤
١٠٠
)١٢(
٦٠٥
١٠٠
)١٣(
٨٣٤
١٠٠
)١٤(
٣٤١٦
١٠٠
)١٥(
١٥٨٩
١٠٠
]٤[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
١٥٣
١٠٠٠
)٢(
٥٠٣
١٠٠٠
)٣(
١٤٥
١٠٠٠
)٤(
٦٣
١٠٠٠
)٥(
١٤
١٠٠٠
)٦(
٩
١٠٠٠
)٧(
٣
١٠٠٠
)٨(
١٢٤٥
١٠٠٠
)٩(
٨٠١٥
١٠٠٠
)١٠(
٥٠٠٣
١٠٠٠
)١١(
١٧٤
١٠٠٠
٨٦)١٢(
٢٧٥
١٠٠٠
٦٤
)١٣(
١٧
١٠٠٠
٥٤)١٤(
١٢
١٠٠٠
٣٤)١٥(
٦
١٠٠٠
٨٥

10. ]٥[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
٣
٢٥
)٢(
٦
٥٠
)٣(
٣
٤
)٤(
١
٢٥
٢٦)٥(
١١
٥٠
٨)٦(
١
٤
٩
)٧(
٩
٥٠
١٤)٨(
٨
٢٥
٢٣)٩(
٣
٤
١٠٦
]٦[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(
٣
٥٠٠
)٢(
٢٧
٥٠٠
)٣(
٧٢
٢٠٠
)٤(
٢٤
٤٠٠
)٥(
١٠٠٢
٣٠٠
)٦(
١٤
٢٠٠٠
]٧[‫اﻝ‬ ‫رة‬ ‫اﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(٤,٢٦)٢(٥,٤٣)٣(٠,٥٧
)٤(٠,٠٦٣)٥(٢,٠١)٦(٣٧,٣٧
]٨[‫وآ‬ ‫ﺹ‬ ‫د‬ ‫رة‬ ‫ﺹ‬ ‫اﻝ‬ ‫ل‬ ‫ﺡ‬
)١(٣,١)٢(١٧,٥٦)٣(٦,٠٩
)٤(٥,٠١٧)٥(٢٨,٠٠١)٦(٥٣,٠٢٦

11. ]٩[‫أآ‬
)١(‫ﺍﻟﺮﻗﻢ‬ ‫ﻗﻴﻤﺔ‬٧‫ﺍﻟﻌﺪﺩ‬ ‫ﰱ‬٢٣,١٧٩‫ﻫﻰ‬...............
)٢(‫ﺍﻟﺮﻗﻢ‬ ‫ﻗﻴﻨﺔ‬٣‫ﺍﻟﻌﺪ‬ ‫ﰱ‬‫ﺩ‬١٤,٣٥‫ﻫﻰ‬.................
)٣(‫ﺍﻟﺮﻗﻢ‬ ‫ﻗﻴﻤﺔ‬٢‫ﺍﻟﻌﺪﺩ‬ ‫ﰱ‬٥٤,١٩٢‫ﻫﻰ‬.................
)٤(‫ﻟﻠﺮﻗﻢ‬ ‫ﺍﳌﻜﺎﻧﻴﺔ‬ ‫ﺍﻟﻘﻴﻤﺔ‬٧‫ﺍﻟﺮﻗﻢ‬ ‫ﰱ‬١٢٣,١٧٩‫ﻫﻰ‬.................
)٥(‫ﻟﻠﺮﻗﻢ‬ ‫ﺍﳌﻜﺎﻧﻴﺔ‬ ‫ﺍﻟﻘﻴﻤﺔ‬٦‫ﺍﻟﻌﺪﺩ‬ ‫ﰱ‬١٦,٢٥‫ﻫﻰ‬..................
]١٠[‫اﻝ‬ ‫ا‬ ‫ا‬‫اس‬ ‫ا‬
)١(٨‫ﻭ‬ ‫ﺍﺣﺎﺩ‬٥‫ﻣﺎﺋﺔ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍ‬....... =)٥,٨،٥,٠٨،٨,٥،٨,٠٥(
)٢(٥‫ﻭ‬ ‫ﺍﺣﺎﺩ‬٧‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍﺀ‬...... =)٥,٧،,٧٥،٠,٧٥،٧٥(
)٣(٥‫ﻭ‬ ‫ﺍﺣﺎﺩ‬٧‫ﻣﺎﺋﺔ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍﺀ‬......... =)٥,٧،٧,٥،٥,٠٧،٧٠٥(
)٤(‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍﺀ‬ ‫ﻭﺛﻼﺛﺔ‬ ‫ﺍﺛﻨﺎﻥ‬....... =)٣,٢،٠,٢٣،٢,٣،٣٢(
)٥(٩‫ﻭ‬ ‫ﺍﺣﺎﺩ‬٥‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺍﺟﺰﺍﺀ‬...... =)٩,٥،٥,٩،٩٥،٥٩(

12. ٥,٣<<<<٥,١٢,٩٥>>>>٢,٩٦٤,٨=٤,٨
]١[<<<<‫او‬>>>>‫او‬=
٣,٤٥٧,١٥,١٥,٣
٤٩,٠١٤٩,٩٨٣٢,٥٢٧
١٦,٣١٦,٣١٤,٧١٤,٤٧
٢٧٢٣,٩١٦,٣٦,٦٣
٥,٨٥,٠٨٥,٠٧٦
٣,١٤٣,٢٢٨,٤٢,٨٤
]٢[<<<<‫او‬>>>>‫او‬=
٤,٦٤,٧٦,٥٦,٩
٣,١٧٣,٠٦١٥,٤١٥,٢٧
٣,٤٠٣,٤٤٠,٤٤٠,١٤
٠,٦٠,٢٦٥٧٥٧,٠٢
١٨,٥١٨,٠٥٠,٧٣٠,٧٣
٣,٥٣,٠٥٠٧٦٠,٩
٤,٨٤,٥٢٠,٢٥٠,٢٥٠
‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ ÷‰†Ûa÷‰†Ûa÷‰†Ûa÷‰†Ûa@ßb¨a@ßb¨a@ßb¨a@ßb¨a@Z@Z@Z@Zò튒ÈÛa@…a†Çüa@kîmŠmë@òã‰bÔßò튒ÈÛa@…a†Çüa@kîmŠmë@òã‰bÔßò튒ÈÛa@…a†Çüa@kîmŠmë@òã‰bÔßò튒ÈÛa@…a†Çüa@kîmŠmë@òã‰bÔß@@@@@@@@
‫ل‬
‫ر‬

13. ]٣[‫ر‬:
)‫ا‬‫ا‬‫ا‬‫ا‬(٤,٢٣,٦٤,٠٨٤,٥
)‫ﺏ‬(٥,٨٥,٠٨٨٥٨,٥
]٤[‫زﻝــ‬ ‫ر‬:
)‫ا‬‫ا‬‫ا‬‫ا‬(٧,١٠,٧٥٠,٩١,٣
)‫ﺏ‬(٠,٩٢٠,٢٩٠,٤٧٠,٠٧٤٠,٩٤
]٥[‫اس‬ ‫ا‬ ‫اﻝ‬ ‫ا‬ ‫ا‬
)١(‫ﺑﲔ‬ ‫ﺍﶈﺼﻮﺭ‬ ‫ﺍﻟﻌﺸﺮﻯ‬ ‫ﺍﻟﻜﺴﺮ‬٠,٦‫ﻭ‬٠,٧‫ﻫﻮ‬...........)٠,٧١،٠,٦٧،٠,٥٩،٠,٧٦(
)٢(‫ﺑﲔ‬ ‫ﺍﶈﺼﻮﺭ‬ ‫ﺍﻟﻌﺸﺮﻯ‬ ‫ﺍﻟﻜﺴﺮ‬٠,٢١‫ﻭ‬٠,٤٧‫ﻫﻮ‬......)٠,٢٠،٠,٣٠،٠,٠٢١،٠,٠٤٧(
)٣(‫ﺑﲔ‬ ‫ﺍﶈﺼﻮﺭ‬ ‫ﺍﻟﻌﺸﺮﻯ‬ ‫ﺍﻟﻜﺴﺮ‬٠,٥‫ﻭ‬٠,٦‫ﻫﻮ‬.........)٠,٦٥،٠,٥٦،٠,٠٦٥،٠,٠٠٦٥(
)٤(‫ﺑﲔ‬ ‫ﺍﶈﺼﻮﺭ‬ ‫ﺍﻟﻌﺸﺮﻯ‬ ‫ﺍﻟﻜﺴﺮ‬٠,٦٢‫ﻭ‬٠,٦٣‫ﻫﻮ‬.......)٠,٦٤٥،٠,٦٣٥،٠,٦٢٥،٠,٦١٥(
)٥(‫ﺑﲔ‬ ‫ﺍﶈﺼﻮﺭ‬ ‫ﺍﻟﻌﺸﺮﻯ‬ ‫ﺍﻟﻜﺴﺮ‬٠,٣‫ﻭ‬٠,٤‫ﻫﻮ‬...........)٠,٤١،٠,٣١،٠,١٣،٠,٤(
]٦[‫ﺑﲔ‬ ‫ﺗﻨﺤﺼﺮ‬ ‫ﻋﺸﺮﻳﺔ‬ ‫ﺍﻋﺪﺍﺩ‬ ‫ﺛﻼﺛﺔ‬ ‫ﺍﻛﺘﺐ‬١٧‫ﻭ‬١٨
]٧[‫ﺑﲔ‬ ‫ﺗﻨﺤﺼﺮ‬ ‫ﻋﺸﺮﻳﺔ‬ ‫ﺍﻋﺪﺍﺩ‬ ‫ﺛﻼﺛﺔ‬ ‫ﺍﻛﺘﺐ‬١٧,١‫ﻭ‬١٧,٢
]٨[‫ﺑﲔ‬ ‫ﺗﻨﺤﺼﺮ‬ ‫ﻋﺸﺮﻳﺔ‬ ‫ﺍﻋﺪﺍﺩ‬ ‫ﺛﻼﺛﺔ‬ ‫ﺍﻛﺘﺐ‬٥٧,٧‫ﻭ‬٥٧,٩

14. ‫ﻳﺄﺗﻰ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫ﺃﻭﺟﺪ‬
)١(٥,٧+١,٤)٢(٣,٢+٧,١٨)٣(٢٣,٤+٧,٨
)٤(١٨,٧٥+٤,٢)٥(١٧,٣+٤,٦)٦(٢,٦٥+٩,٣
)٧(١٣,٨+٥,٧٥)٨(٠,٨٧٥+٠,٤٣)٩(٩,٨+٤,٣
)٠١(٦,٥+٨,١١)١١(١,٠٠٧+٩)١٢(١٣+٢,٦٥
)١٣(٨٠,٣+١٩,٨٥)١٤(,٥١٥٩+٣٧٥,٣)١٥(٤,٥+٨,٢
‫ﻳﺄﺗﻰ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫ﺃﻭﺟﺪ‬
)١(٥,٧–١,٤)٢(١٢,٧٨–٣,٥)٣(٢,٣٢٥–٠,٢١٤
)٤(٨٩,٧٥–٥,٣٤)٥(٦٧,٠٠٥–٢٤,٢٥)٦(١٣–٢,٦٥
)٧(٠,٦–٠,٢٧٥)٨(٣١٢,٥–١٥٧,١٢٥)٩(٢٠٠–٧٦,٥٤٤
)١(٥٨÷١٠)٢(٧٨÷١٠)٣(٤٥÷١٠
)٤(٣٤٨÷١٠)٥(٢٥٠÷١٠)٦(٢٨٩÷١٠٠
)٧(٦٣٥÷١٠٠)٨(٨٤٦÷١٠٠)٩(٢٣٥٠÷١٠٠
)١٠(٤٢٥٧÷١٠٠٠)١١(٨٣٧٦÷١٠٠٠)١٢(٩٨٠٠÷١٠٠٠
‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ ÷‰†Ûa÷‰†Ûa÷‰†Ûa÷‰†Ûa@÷…bŽÛa@÷…bŽÛa@÷…bŽÛa@÷…bŽÛa@Z@Z@Z@Za@pbîÜàÈÛaa@pbîÜàÈÛaa@pbîÜàÈÛaa@pbîÜàÈÛa@òîibŽ§@òîibŽ§@òîibŽ§@òîibŽ§@@@@@@@@
‫او‬:‫ــ‬ ‫اﻝ‬
‫ﻥ‬ ‫ﺙ‬:‫ح‬ ‫ــ‬ ‫اﻝ‬
‫ﻝ‬ ‫ﺙ‬:‫اﻝ‬١٠،١٠٠،١٠٠٠
]١[‫ﻳﺄﺗﻰ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫ﺍﻭﺟﺪ‬

15. )١(٧٨٥÷١٠)٢(٦٧÷١٠)٣(٤٣٨÷١٠
)٤(١٧٥÷١٠٠)٥(٤١٢÷١٠٠)٦(٤٨٥٩٧÷١٠٠
)٧(٣٥٩٨÷١٠٠٠)٨(٣٥٩٨÷١٠٠٠)٩(٢٤٢٦٩÷١٠٠٠
)١(٣٨٩÷١٠)٢(٢٧٥÷١٠)٣(٦٧٨١٣÷١٠
)٤(٢٨٥٧÷١٠٠)٥(٧٢٨٠÷١٠٠)٦(٤١٢÷١٠٠
)٧(٤١٢÷١٠٠٠)٨(٤٢٥٠÷١٠٠٠)٩(٤٧٢٩÷١٠٠٠
]١[‫ﻋﺎﺩﻝ‬ ‫ﻣﻊ‬٤٨,٥‫ﲟﺒﻠﻎ‬ ‫ﻗﻤﻴﺼﺎ‬ ‫ﺍﺷﺘﺮﻯ‬ ‫ﺟﻨﻴﻪ‬٣٦,٧٥‫ﺟﻨﻴﻪ‬.‫ﻣﻌﻪ‬ ‫ﺗﺒﻘﻰ‬ ‫ﻣﺎ‬ ‫ﺍﺣﺴﺐ‬
]٢[‫ﺍﲪﺪ‬ ‫ﻣﻊ‬٣٥‫ﲟﺒﻠﻎ‬ ‫ﻛﺮﻩ‬ ‫ﺍﺷﺘﺮﻯ‬ ‫ﺟﻨﻴﻬﺎ‬١٩,٧٥‫ﺟﻨﻴﻪ‬.‫ﻣﻌﻪ‬ ‫ﻳﺘﺒﻘﻰ‬ ‫ﻓﻜﻢ‬
]٣[‫ﺍﲪﺪ‬ ‫ﻣﻊ‬٣٠٠‫ﲟﺒﻠﻎ‬ ‫ﺣﺬﺍﺀ‬ ‫ﺍﺷﺘﺮﻯ‬ ‫ﺟﻨﻴﻪ‬٨٨,٩‫ﺟﻨﻴﻪ‬‫ﲟﺒﻠﻎ‬ ‫ﻭﺣﻘﻴﺒﻪ‬٥٦,٧٥.‫؟‬ ‫ﻣﻌﻪ‬ ‫ﻳﺘﺒﻘﻰ‬ ‫ﻓﻜﻢ‬
]٤[‫ﻣ‬ ‫ﻣﻊ‬‫ﺎﺯﻥ‬٣٥‫ﲟﺒﻠﻎ‬ ‫ﻛﺮﻩ‬ ‫ﺍﺷﺘﺮﻯ‬ ‫ﻓﺎﺫﺍ‬ ‫ﺟﻨﻴﻬﺎ‬٩,٧٥‫ﲦﻨﻪ‬ ‫ﻭﻛﺘﺎﺏ‬ ‫ﺟﻨﻴﻪ‬٨٤٠‫ﻗﺮﺷﺎ‬.‫ﻣﻌﻪ‬ ‫ﻳﺘﺒﻘﻰ‬ ‫ﻓﻜﻢ‬
]٥[‫ﺣﺴﺎﻡ‬ ‫ﻣﻊ‬ ‫ﻛﺎﻥ‬ ‫ﺍﺫﺍ‬٤٢٥‫ﻫﺒﻪ‬ ‫ﺍﺧﺘﻪ‬ ‫ﻭﻣﻊ‬ ‫ﻗﺮﺷﺎ‬٩٨٠‫؟‬ ‫ﺑﺎﳉﻨﻴﻪ‬ ‫ﻣﻌﻬﻤﺎ‬ ‫ﻣﺎ‬ ‫ﺑﲔ‬ ‫ﺍﻟﻔﺮﻕ‬ ‫ﺍﻭﺟﺪ‬ ، ‫ﻗﺮﺷﺎ‬
]٢[‫ﻳﺄﺗﻰ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫ﺍﻭﺟﺪ‬
]٣[‫ﻳﺄﺗﻰ‬ ‫ﻣﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫ﺍﻭﺟﺪ‬
‫اﻝ‬ ‫ﻝ‬ ‫ا‬

16. ‫ﻣﺘﻨﻮﻋﻪ‬ ‫ﺍﻣﺜﻠﺔ‬)١(٤٥٧~٤٦٠‫ﻋﺸﺮﻩ‬ ‫ﻷﻗﺮﺏ‬
)٢(٨٣٤~٨٣٠‫ﻋﺸﺮﻩ‬ ‫ﻷﻗﺮﺏ‬
)٣(٩٧٥~٩٨٠‫ﻋﺸﺮﻩ‬ ‫ﻷﻗﺮﺏ‬
@}Q@{@@ê‹“Ç@l‹Óþ@éîmüa@†a‡Çüa@l‹Ó@@
)١(٢٣٦)٢(٤٨٨)٣(٧٦٥١
)٤(٨٦٠٢٩)٥(٩٠٠٤)٦(٢١٣٩٥
)٧(٩٤٩)٨(٨٠٣٥)٩(٦١٩٨
)١٠(٩٩٩٩)١١(٨٥٠٤)١٢(٨٩٣٧٨
)١٣(٩٦٤,٧)١٤(١٩٩,٨)١٥(٨٤,٥٦
@}R@@{@ómdí@bß@wmbã@‡uëa@@
)١(٢٣٦٥+١٤٥٨............................. =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)٢(٢٥٣٠٤+٩٤٦٧............................ =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)٣(٣٦٥٢٣+٣٦٥٨٢.......................... =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)٤(٦٤,٣+٧٥,٢.................. =.............)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)٥(٤٦٢٥٧–١٥٣٩١.......................... =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)٦(٧٠٠٠٠٠–٦٥٠٩٣........................ =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)٧(٨٣,٦٧–١٤,٥١٢......................... =)‫ﻋﺸﺮ‬ ‫ﻷﻓﺮﺏ‬‫ﻩ‬(
)٨(١٣٤٥٢÷١٠............................... =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)٩(٢٣٤٥٦÷١٠٠.............................. =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
)١٠(٧٣٦٤١÷١٠٠٠............................ =)‫ﻋﺸﺮﻩ‬ ‫ﻷﻓﺮﺏ‬(
‫ة‬ ‫ا‬‫ا‬ @Þëüa@÷‰†Ûa@Þëüa@÷‰†Ûa@Þëüa@÷‰†Ûa@Þëüa@÷‰†Ûa@Z@Z@Z@ZꊒÇ@lŠÓþ@kíŠÔnÛaꊒÇ@lŠÓþ@kíŠÔnÛaꊒÇ@lŠÓþ@kíŠÔnÛaꊒÇ@lŠÓþ@kíŠÔnÛa@@@@@@@@
‫ر‬

17. ‫ﻣﺘﻨﻮﻋﻪ‬ ‫ﺍﻣﺜﻠﺔ‬)١(٩٣٨٢~٩٤٠٠‫ﻣﺎﺋ‬ ‫ﻷﻗﺮﺏ‬‫ﻪ‬
)٢(٦٨٣٥~٦٨٠٠‫ﻣﺎﺋﻪ‬ ‫ﻷﻗﺮﺏ‬
)٣(١٥٨٤٧~١٦٠٠٠‫ﺍﻟﻒ‬ ‫ﻷﻗﺮﺏ‬
)٤(٩٧١٣٨~٩٧٠٠٠‫ﺍﻟﻒ‬ ‫ﻷﻗﺮﺏ‬
@}Q@{@@l‹Óþ@éîmüa@†a‡Çüa@l‹Óéöbß@@@
)١(٥٨١٩)٢(١٧٨٤٧)٣(٧٦٨٩١
)٤(٨٣٦٥)٥(٥٣٨٢٤)٦(٥٠٩٤٥
)٧(٤٣٥٧)٨(٦٠٣٤٩٩)٩(٨٩٩٥٠
)١٠(٩٩٠٩٠٩)١١(٨٠٤٥١,٨)١٢(٢٣٩٥,٩٨
@}R@{@@l‹Óþ@éîmüa@†a‡Çüa@l‹Ó@ÑÛa@@@
)١(٤٢٧٥)٢(٧٣٦٢)٣(٦٤٩٣
)٤(٧٤٢٥)٥(٨٣١٥٦)٦(٧٨٦٢٩٦
)٧(٦٥٤٣٢١٧)٨(١٩٨٥٠٠)٩(٧١٩٥١٠
)١٠(٦٤٣٥,٥)١١(٤٣٢١,٩٩)١٢(٩٩٩٥٠٠
@}R@@{@ómdí@bß@wmbã@‡uëa@@
)١(٢٤٧٨+٩٨٣٥.................. =............)‫ﻣﺎﺋﻪ‬ ‫ﻷﻓﺮﺏ‬(
)٢(٣٢١٤٥-٩٣٧٨............................ =)‫ﺍﻟﻒ‬ ‫ﻷﻓﺮﺏ‬(
)٣(٤٢٢٥÷١٠............... =...................)‫ﻷﻓﺮﺏ‬‫ﻣﺎﺋﻪ‬(
)٤(٣٤٩٨٧+٩٧٥٤٢.......................... =)‫ﺍﻟﻒ‬ ‫ﻷﻓﺮﺏ‬(
‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaóãbrÛaóãbrÛaóãbrÛaóãbrÛa@Z@@Z@@Z@@Z@ÑÛaë@éöbß@lŠÓþ@kíŠÔnÛaÑÛaë@éöbß@lŠÓþ@kíŠÔnÛaÑÛaë@éöbß@lŠÓþ@kíŠÔnÛaÑÛaë@éöbß@lŠÓþ@kíŠÔnÛa@@@@@@@@
‫ر‬

18. ‫ﻣﺘﻨﻮﻋﻪ‬ ‫ﺍﻣﺜﻠﺔ‬)١(٨٢٧٥١٣~٨٣٠٠٠٠‫ﺍﻻﻑ‬ ‫ﻋﺸﺮﺓ‬ ‫ﻷﻗﺮﺏ‬
)٢(٦١٤٨٢٧~٦١٠٠٠٠‫ﺍﻻﻑ‬ ‫ﻋﺸﺮﺓ‬ ‫ﻷﻗﺮﺏ‬
)٣(٧٣٦١٥٠٢~٧٤٠٠٠٠٠‫ﺍﻟﻒ‬ ‫ﻣﺎﺋﺔ‬ ‫ﻷﻗﺮﺏ‬
)٤(١٦٣٥٠٧٢~١٦٠٠٠٠٠‫ﺍﻟﻒ‬ ‫ﻣﺎﺋﺔ‬ ‫ﻷﻗﺮﺏ‬
@}Q@{@@l‹Óþ@éîmüa@†a‡Çüa@l‹ÓÒüa@ñ‹“Ç@@@
)١(٦٠٧٣٤٥)٢(١٥٣٨٧)٣(١٠٥٠٠
)٤(٦١٧٥٣٢٩١)٥(٦٥٤٣٢,١)٦(١٣٩٥٠,٥
)٧(٧١٥٣٨٤٠)٨(٨٩٤٣٠,٥٢)٩(٢٥١٧١٤
)١٠(٨٧٤٥٠٠,١٣)١١(٩٩١٤٣٢)١٢(٢٣٦٨٤٩,٩٩
@}R@{@@l‹Óþ@éîmüa@†a‡Çüa@l‹Ó@ÑÛa@òöbß@@@
)١(٨٧٦٥٤٣٢١)٢(٦١٧٥٣٢٩١)٣(٤٠٦٠٠٨٩,٩
)٤(٧١٥٣٨٤٠)٥(٦١٩٥٠٠٠٠)٦(٣٨١٤٩٢٠,١٦
)٧(٤٩٩٥٠٠٧)٨(٥٦١٤٧٦٥,٣)٩(١٧٥٤٦٩
)١٠(١٢٣٤٥٦٧٨,٩)١١(٦٩٣٠١٥)١٢(١٠٧٨٥٦
@}S@@{mbã@‡uëa@ómdí@bß@w@@
)١(٣١٥٧٨٤٠+٧٤٢٩٦. =.............................)‫ﻷﻓﺮﺏ‬‫ﺍﻻﻑ‬ ‫ﻋﺸﺮﺓ‬(
)٢(٢٥٨٦٤٣+٨٤١٥٨=............................)‫ﻷﻓﺮﺏ‬‫ﺍﻟﻒ‬ ‫ﻣﺎﺋﺔ‬(
)٣(٦١٠٥٠٣,١–٨٠٧,٠٨...... =............................)‫ﻷﻓﺮﺏ‬‫ﺍﻻﻑ‬ ‫ﻋﺸﺮﺓ‬(
)٤(١٩,٢٨٥٠٠٧+٣٢٨,٧.......................... =)‫ﺍﻟﻒ‬ ‫ﻷﻓﺮﺏ‬(
‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛasÛbrÛasÛbrÛasÛbrÛasÛbrÛa@Z@@Z@@Z@@Z@@@ÑÛa@òöbßë@Òüa@ñŠ’Ç@lŠÓþ@kíŠÔnÛa@@ÑÛa@òöbßë@Òüa@ñŠ’Ç@lŠÓþ@kíŠÔnÛa@@ÑÛa@òöbßë@Òüa@ñŠ’Ç@lŠÓþ@kíŠÔnÛa@@ÑÛa@òöbßë@Òüa@ñŠ’Ç@lŠÓþ@kíŠÔnÛa
‫ر‬

19. ‫ﻣﺘﻨﻮﻋﻪ‬ ‫ﺍﻣﺜﻠﺔ‬)١(٥٣,٨~٥٤‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻭ‬ ‫ﻭﺣﺪﻩ‬ ‫ﻷﻗﺮﺏ‬
)٢(٨٧,٢~٨٧‫ﻷﻗﺮﺏ‬‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻭ‬ ‫ﻭﺣﺪﻩ‬
)٣(
٥
٨
٦٤~٦٥‫ﻷﻗﺮﺏ‬‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻭ‬ ‫ﻭﺣﺪﻩ‬
)٤(
١
٤
١٢~١٢‫ﻷﻗﺮﺏ‬‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻭ‬ ‫ﻭﺣﺪﻩ‬
@@
@}Q@{@@l‹Óþ@éîmüa@†a‡Çüa@l‹Óñ‡yë@@
)١(١٧٣,٢)٢(١٠,١)٣(٤٠٢,٥٠١
)٤(١٤٠,٥)٥(٨,٥)٦(٢٨,٣
)٧(٣٢٩,٥)٨(٩,١)٩(٦٢٤,٠٩
)١٠(٦٠٠,٦٠١)١١(٦٣٧,٦)١٢(٥٣,٥
)١٣(٧٢,٦)١٤(٢٥٣,٣٩٨)١٥(٧,٤٩٩
@}R@{@@l‹Óþ@éîmüa@†a‡Çüa@l‹Óñ‡yë@@
)١(
٧
١٠
١٣٥)٢(
٤
٥
٦٥٧)٣(
٣
٥
٢٠٤
)٤(
١
٤
٩٦٧)٥(
٢
٥
٤٢)٦(
٣
٥
)٧(
٥
٨
٦)٨(
٧
١٠
)٩(
٣
٧
٨٥
)١٠(
٢
٣
١٧)١١(
٢
٩
٨)١٢(
٣
٤
١٦
‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaÍiaŠÛaÍiaŠÛaÍiaŠÛaÍiaŠÛa@Z@@Z@@Z@@Z@ñ†yë@lŠÓþ@kíŠÔnÛañ†yë@lŠÓþ@kíŠÔnÛañ†yë@lŠÓþ@kíŠÔnÛañ†yë@lŠÓþ@kíŠÔnÛa@@@@@@@@
‫ر‬

20. @}S@@{@ómdí@bß@wmbã@‡uëa@@
)١(٥٩,٥٦٨+٤٥,٧٣................................... =)‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﻷﻗﺮﺏ‬(
)٢(٢٤,٩٦+١٨,٧٣٥................................... =)‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﻷﻗﺮﺏ‬(
)٣(٥٣,٦٤+٨,٦٠١................................... =)‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﻷﻗﺮﺏ‬(
)٤(٣٦٢,٦–٢٩,١................................... =)‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﻷﻗﺮﺏ‬(
)٥(٤٢٨١٩÷١٠٠٠... =................................)‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﻷﻗﺮﺏ‬(
)٦(٧٥+٦٤,٣................................... =)‫ﺻﺤﻴﺢ‬ ‫ﻋﺪﺩ‬ ‫ﻷﻗﺮﺏ‬(
@}T@@{@ómdí@bß@Ýà×a@@
)١(٣٢‫ﻳﻮﻡ‬............. =‫ﺍﺳﺒﻮﻉ‬ ‫ﻷﻗﺮﺏ‬)٢(٣٩‫ﻳﺰﻡ‬............ =‫ﺍﺳﺒﻮﻉ‬ ‫ﻷﻗﺮﺏ‬
)٣(١٢٥‫ﺩﻗﻴ‬‫ﻘﻪ‬=,,,,,,,,,,,‫ﺳﺎﻋﻪ‬ ‫ﻷﻗﺮﺏ‬)٤(٤٠٦‫ﻗﺮﺵ‬......... =‫ﺟﻨﻴﻪ‬ ‫ﻷﻗﺮﺏ‬
)٥(٤٧‫ﻳﻮﻡ‬............. =‫ﺍﺳﺒﻮﻉ‬ ‫ﻷﻗﺮﺏ‬)٦(٥٤٦٨‫ﺳﻢ‬........ =‫ﻣﺘﺮ‬ ‫ﻷﻗﺮﺏ‬
)٧(٥٢٧٦‫ﻗﺮﺵ‬........... =‫ﺟﻨﻴﻪ‬ ‫ﻷﻗﺮﺏ‬)٨(١٣٠‫ﺩﻗﻴﻘﻪ‬........ =‫ﺳﺎﻋﻪ‬ ‫ﻷﻗﺮﺏ‬
)٩(٦٠‫ﻳﻮﻣﺎ‬......... =..‫ﺍﺳﺒﻮﻉ‬ ‫ﻷﻗﺮﺏ‬)١٠(٥٠‫ﻳﻮﻣﺎ‬........... =‫ﺍﺳﺒﻮﻉ‬ ‫ﻷﻗﺮﺏ‬
)١(‫ﺗﺴﺎﻭﻯ‬ ‫ﻗﺮﻳﺘﲔ‬ ‫ﺑﲔ‬ ‫ﺍﳌﺴﺎﻓﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬٤٦٢٥‫ﻣﺘﺮﺍ‬.‫ﻛﻴﻠﻮﻣﺘﺮ‬ ‫ﻷﻗﺮﺏ‬ ‫ﺍﳌﺴﺎﻓﺔ‬ ‫ﻫﺬﻩ‬ ‫ﻗﺮﺏ‬
)٢(‫ﺗﺴﺎﻭﻯ‬ ‫ﻣﺪﻳﻨﺘﲔ‬ ‫ﺑﲔ‬ ‫ﺍﳌﺴﺎﻓﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬٦٨٣٠‫ﻣﺘﺮﺍ‬.‫؟‬ ‫ﻛﻴﻠﻮﻣﺘﺮ‬ ‫ﻷﻗﺮﺏ‬ ‫ﺍﳌﺪﻳﻨﺘﲔ‬ ‫ﺑﲔ‬ ‫ﺍﳌﺴﺎﻓﺔ‬ ‫ﻓﺄﻭﺟﺪ‬
)٣(‫ﺍﺫﺍ‬‫ﺗﺴﺎﻭﻯ‬ ‫ﻗﺮﻳﺘﲔ‬ ‫ﺑﲔ‬ ‫ﺍﳌﺴﺎﻓﺔ‬ ‫ﻛﺎﻧﺖ‬٧٣٠٠‫ﻣﺘﺮﺍ‬.‫؟‬ ‫ﻛﻴﻠﻮﻣﺘﺮ‬ ‫ﻷﻗﺮﺏ‬ ‫ﺍﻟﻘﺮﻳﺘﲔ‬ ‫ﺑﲔ‬ ‫ﺍﳌﺴﺎﻓﺔ‬ ‫ﻓﺄﻭﺟﺪ‬
‫ﻝ‬ ‫اﺱ‬

21. ‫ﻣﺘﻨﻮﻋﻪ‬ ‫ﺍﻣﺜﻠﺔ‬)١(١٨,٣٧~١٨,٤‫ﻭﺍﺣﺪ‬ ‫ﻋﺸﺮﻯ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻭ‬ ‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬
)٢(٢١,٦٤~٢١,٦‫ﻭﺍﺣﺪ‬ ‫ﻋﺸﺮﻯ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻭ‬ ‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬
@@
@}Q@{@@éîmüa@†a‡Çüa@l‹Ó@l‹Óþ@ê‹“Ç@åß@õu@@
)١(٦٧,٢٩)٢(٥٦,٧١)٣(٩,١٦
)٤(٤٣,٩٥)٥(٧٤,٣٦)٦(٧٠,٠٧
)٧(٢٩٦,٠٤)٨(١٧٠,٥٩٧)٩(٢٨,٤٥١
)١٠(٤٩,٨٥)١١(٩٨,٥٤)١٢(٤٩,٨٥
@}R@{@@l‹Óþ@éîmüa@†a‡Çüa@l‹Ó@ê‹“Ç@åß@õu@@
)١(
٣
٤
١٨)٢(
٣٧
١٠٠
٥٠٢)٣(
٧
٥٠
٩٩
@}S@@{@ómdí@bß@wmbã@‡uëa@@
)١(١٤,٣٥٢+٢٥,٦٨٧................................... =)‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬(
)٢(٩٦,٨-٦٢,٣١................................... =)‫ﻋ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬‫ﺸﺮﻩ‬(
)٣(٤٢,٨٥÷١٠................................... =)‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬(
)٤(٤٥٣,٦٤–٧٢,٣١٧................................... =)‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬(
)٥(٥٢٧,٦٣+٣٢٧,٩................................... =)‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬(
)٦(١٥–٤,١٢٥................................... =)‫ﻋﺸﺮﻩ‬ ‫ﻣﻦ‬ ‫ﺟﺰﺀ‬ ‫ﻷﻗﺮﺏ‬(
‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†Ûaßb¨aßb¨aßb¨aßb¨a@Z@@Z@@Z@@Z@ꊒÇ@åß@õŒu@lŠÓþ@kíŠÔnÛaꊒÇ@åß@õŒu@lŠÓþ@kíŠÔnÛaꊒÇ@åß@õŒu@lŠÓþ@kíŠÔnÛaꊒÇ@åß@õŒu@lŠÓþ@kíŠÔnÛa@@@@@@@@
‫ر‬

22. ‫ا‬
‫ب‬
‫ج‬
‫ء‬
‫ا‬
‫ج‬
‫ب‬
‫ء‬
‫ا‬
‫ب‬‫ج‬
‫ء‬‫ا‬
‫ب‬‫ج‬
‫ء‬
‫ا‬
‫ب‬‫ج‬
‫ء‬‫ا‬
‫ب‬‫ج‬
‫ء‬
@}Q@@{@òßýÇ@Éš)√(@òßýÇ@ëa)×(@@@
)١(‫ﻓﻘﻂ‬ ‫ﻣﺘﺴﺎﻭﻳﻪ‬ ‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬ ‫ﺍﺿﻼﻋﻬﻤﺎ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬ ‫ﻣﻀﻠﻌﺎﻥ‬ ‫ﻳﺘﻄﺎﺑﻖ‬)(
)٢(‫ﺍﻟﺴﺎﻗﲔ‬ ‫ﻣﺘﺴﺎﻭﻯ‬ ‫ﻣﺜﻠﺚ‬ ‫ﻣﻊ‬ ‫ﺍﻻﺿﻼﻉ‬ ‫ﻣﺘﺴﺎﻭﻯ‬ ‫ﻣﺜﻠﺚ‬ ‫ﻳﺘﻄﺎﺑﻖ‬ ‫ﺍﻥ‬ ‫ﺍﳌﻤﻜﻦ‬ ‫ﻣﻦ‬)(
)٣(‫ﻣﺘﺴﺎﻭﻳﻪ‬ ‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬ ‫ﻭﺯﻭﺍﻳﻬﻤﺎ‬ ‫ﺍﺿﻼﻋﻬﻤﺎ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬ ‫ﻣﻀﻠﻌﺎﻥ‬ ‫ﻳﺘﻄﺎﺑﻖ‬)(
)٤(‫ﺍﻟﺰﺍﻭﻳﺔ‬ ‫ﻗﺎﺋﻢ‬ ‫ﺍﺧﺮ‬ ‫ﻣﻊ‬ ‫ﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺣﺎﺩ‬ ‫ﻣﺜﻠﺚ‬ ‫ﻳﺘﻄﺎﺑﻖ‬ ‫ﺍﻥ‬ ‫ﺍﳌﻤﻜﻦ‬ ‫ﻣﻦ‬)(
)٥(‫ﻣﺮﺑﻊ‬ ‫ﻳﺘﻄﺎﺑﻖ‬ ‫ﺍﻥ‬ ‫ﺍﳌﻤﻜﻦ‬ ‫ﻣﻦ‬‫ﺿﻠﻌﻪ‬ ‫ﻃﻮﻝ‬٧‫ﺑﻌﺪﺍﻩ‬ ‫ﻣﺴﺘﻄﻴﻞ‬ ‫ﻣﻊ‬ ‫ﺳﻢ‬٧، ‫ﺳﻢ‬٥‫ﺳﻢ‬)(
‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaÞëüaÞëüaÞëüaÞëüa@Z@@Z@@Z@@Z@@ÕibĐnÛa@ÕibĐnÛa@ÕibĐnÛa@ÕibĐnÛa@@@@@@@@
‫ﺷﺮﻭﻁ‬‫ﺍﻟﺘﻄﺎﺑﻖ‬
‫ط‬
)١(‫ﺍﻟﻄﻮﻝ‬ ‫ﰱ‬ ‫ﻣﺘﺴﺎﻭﻳﻪ‬ ‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬ ‫ﺍﻻﺿﻼﻉ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬
)٢(‫ﺍﻟﻘﻴﺎﺱ‬ ‫ﰱ‬ ‫ﻣﺘﺴﺎﻭﻳﻪ‬ ‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬ ‫ﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬
‫ط‬
‫ﺍﻻﻭﻝ‬ ‫ﺿﻠﻊ‬ ‫ﻃﻮﻝ‬ ‫ﻳﻜﻮﻥ‬ ‫ﺍﻥ‬=‫ﺍﻟﺜﺎﱏ‬ ‫ﺿﻠﻊ‬ ‫ﻃﻮﻝ‬
‫ط‬
‫ﺍﻻﻭﻝ‬ ‫ﺑﻌﺪﺍ‬ ‫ﻳﻜﻮﻥ‬ ‫ﺍﻥ‬=‫ﺍﻟﺜﺎﱏ‬ ‫ﺑﻌﺪﺍ‬
‫ﻣﻠﺤﻮﻇﻪ‬:‫ﺍﳌ‬ ‫ﻳﺘﻄﺎﺑﻖ‬‫ﺍﻟﻄﻮﻝ‬ ‫ﰱ‬ ‫ﻣﺘﺴﺎﻭﻳﻪ‬ ‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬ ‫ﺍﺿﻼﻋﻬﻤﺎ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬ ‫ﺜﻠﺜﺎﻥ‬
‫ر‬

23. @}R@{@@ómdí@bß@Ýà×a@@
)١(‫ﺍﺣﺪﳘﺎ‬ ‫ﺿﻠﻊ‬ ‫ﻃﻮﻝ‬ ‫ﻛﺎﻥ‬ ‫ﺍﺫﺍ‬ ‫ﺍﳌﺮﺑﻌﺎﻥ‬ ‫ﻳﺘﻄﺎﺑﻖ‬...................... =
)٢(‫ﻛﺎﻥ‬ ‫ﺍﺫﺍ‬ ‫ﻣﺴﺘﻄﻴﻼﻥ‬ ‫ﻳﺘﻄﺎﺑﻖ‬.........................................
)٣(‫ﻭﺯﻭﺍﻳﻬﻤﺎ‬ ‫ﺍﺿﻼﻋﻬﻤﺎ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬ ‫ﻣﻀﻠﻌﺎﻥ‬ ‫ﻳﺘﻄﺎﺑﻖ‬‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬.............
)٤(‫ﺍﻟﺸﻜﻠﲔ‬ ‫ﻳﻜﻮﻥ‬ ‫ﻟﺸﻜﻠﲔ‬ ‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬ ‫ﻭﺍﻟﺰﻭﺍﻳﺎ‬ ‫ﺍﻻﺿﻼﻉ‬ ‫ﺗﺴﺎﻭﺕ‬ ‫ﺍﺫﺍ‬...........
)٥(‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬ ‫ﺍﳌﻀﻠﻌﺎﻥ‬ ‫ﻳﺘﻄﺎﺑﻖ‬..........،.............‫ﻣﺘﺴﺎﻭﻳﻪ‬ ‫ﺍﳌﺘﻨﺎﻇﺮﻩ‬
@@
@}R@{@@éÇìàa@åß@ÝØ’@Ý×@Ý–)@‫ا‬‫ا‬‫ا‬‫ا‬@(@óÏ@éÔibĐí@ô‰Ûa@ÝØ“Ûbi@)@l@(@@@
)‫ا‬‫ا‬‫ا‬‫ا‬(
)‫ﺏ‬(

24. ‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaóãbrÛaóãbrÛaóãbrÛaóãbrÛa@Z@@Z@@Z@@Z@@éÜqbàn½a@ÞbØ‘üa@éÜqbàn½a@ÞbØ‘üa@éÜqbàn½a@ÞbØ‘üa@éÜqbàn½a@ÞbØ‘üa@@@@@@@@
‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻂ‬‫أ‬ ‫اﻝ‬ ‫اى‬ ‫ى‬ ‫اﻝ‬ ‫اﻝ‬ ‫ه‬
‫ﺍﳌﺘﻤﺎﺛﻠﻪ‬ ‫ﺍﻻﺷﻜﺎﻝ‬‫اآ‬ ‫او‬ ‫ﺙ‬ ‫ﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ا‬ ‫ه‬
‫ﺍﳌﺘﻤﺎﺛﻠﻪ‬ ‫ﻏﲑ‬ ‫ﺍﻻﺷﻜﺎﻝ‬‫ﺙ‬ ‫اى‬ ‫ﻝ‬ ‫ﻝ‬ ‫اﻝ‬ ‫ل‬ ‫ا‬ ‫ه‬
‫اﺱ‬‫اﻝ‬‫اﻝ‬ ‫ط‬ ‫د‬‫اﻝ‬ ‫اﺱ‬‫اﻝ‬ ‫ط‬ ‫د‬
‫اﻝ‬٤‫ف‬ ‫اﻝ‬‫ﺹ‬
‫اﻝ‬٢‫اﻝ‬ ‫وى‬ ‫ف‬ ‫اﻝ‬١
‫اﻝ‬٢‫ع‬ ‫ا‬ ‫وى‬ ‫اﻝ‬٣
‫ع‬ ‫ا‬ ‫ازى‬‫ﺹ‬‫اﻝ‬ ‫وى‬ ‫اﻝ‬١
‫ا‬ ‫اﻝ‬‫ا‬ ‫آ‬ ‫د‬‫ع‬ ‫ا‬ ‫اﻝ‬‫ﺹ‬
‫ﻣﻠﺤﻮﻇﻪ‬:‫ﲤﺎﺛﻞ‬ ‫ﺧﻂ‬ ‫ﻟﻴﺲ‬ ‫ﻭﻟﻜﻨﻪ‬ ‫ﻣﺘﻄﺎﺑﻘﲔ‬ ‫ﻣﺜﻠﺜﲔ‬ ‫ﺍﱃ‬ ‫ﻳﻘﺴﻤﻪ‬ ‫ﺍﳌﺴﺘﻄﻴﻞ‬ ‫ﰱ‬ ‫ﺍﻟﻘﻄﺮ‬

25. @}Q@@{@òßýÇ@Éš)√(@òßýÇ@ëa)×(@@@
)١(‫ﻟﻪ‬ ‫ﺍﳌﺮﺑﻊ‬٤‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬)(
)٢(‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﺍﺭﺑﻌﻪ‬ ‫ﻟﻪ‬ ‫ﺍﳌﻌﲔ‬)(
)٣(‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﺍﺭﺑﻌﻪ‬ ‫ﻟﻪ‬ ‫ﺍﳌﺴﺘﻄﻴﻞ‬)(
)٤(‫ﺍﳌﺜ‬‫ﻟﻪ‬ ‫ﺍﻻﺿﻼﻉ‬ ‫ﳐﺘﻠﻒ‬ ‫ﻠﺚ‬٣‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬)(
)٥(‫ﻣﺘﻄﺎﺑﻘﲔ‬ ‫ﺟﺰﺃﻳﻦ‬ ‫ﺍﱃ‬ ‫ﻳﻘﺴﻤﻪ‬ ‫ﺧﻂ‬ ‫ﻫﻮ‬ ‫ﻟﺸﻜﻞ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻂ‬)(
@}R@@{@ómdí@bß@Ýà×a@@
)١(‫ﻟﻪ‬ ‫ﺍﻟﻌﲔ‬.........‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬
)٢(‫ﻟﻠﻤﺴﺘﻄﻴﻞ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬.......... =
)٣(‫ﻟﻠﻤﺮﺑﻊ‬ ‫ﻳﻮﺟﺪ‬........‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬
)٤(‫ﺧﻄﻮ‬ ‫ﻋﺪﺩ‬‫ﺍﻻﺿﻼﻉ‬ ‫ﺍﳌﺘﺴﺎﻭﻯ‬ ‫ﻟﻠﻤﺜﻠﺚ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﻁ‬.......... =
)٥(‫ﺍﻟﺴﺎﻗﲔ‬ ‫ﻣﺘﺴﺎﻭﻯ‬ ‫ﺍﳌﺜﻠﺚ‬ ‫ﲤﺎﺛﻞ‬ ‫ﳏﺎﻭﺭ‬ ‫ﻋﺪﺩ‬.......... =
)٦(‫ﻣﺜﻠﺜﲔ‬ ‫ﺍﱃ‬ ‫ﻳﻘﺴﻤﻪ‬ ‫ﺍﳌﺴﺘﻄﻴﻞ‬ ‫ﰱ‬ ‫ﺍﻟﻘﻄﺮ‬.......‫ﺧﻂ‬ ‫ﻟﻴﺲ‬ ‫ﻭﻟﻜﻨﻪ‬.......
@@
@}S@@{@òßýÇ@Éš)√(@òßýÇ@ëa)×(@@@
)١(‫ﲤ‬ ‫ﺧﻄﻮﻁ‬ ‫ﺍﺭﺑﻌﻪ‬ ‫ﻟﻪ‬ ‫ﺍﻻﺿﻼﻉ‬ ‫ﻣﺘﻮﺍﺯﻯ‬‫ﺎﺛﻞ‬)(
)٢(‫ﺍﻻﺿﻼﻉ‬ ‫ﳐﺘﻠﻒ‬ ‫ﻟﻠﻤﺜﻠﺚ‬ ‫ﻭﺍﺣﺪ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻂ‬ ‫ﻳﻮﺟﺪ‬)(
)٣(‫ﻭﺍﺣﺪ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻂ‬ ‫ﻟﻪ‬ ‫ﺍﻟﺴﺎﻗﲔ‬ ‫ﺍﳌﺘﺴﺎﻭﻯ‬ ‫ﺍﳌﻨﺤﺮﻑ‬ ‫ﺷﺒﻪ‬)(
)٤(‫ﺍﻻﺿﻼﻉ‬ ‫ﻣﺘﺴﺎﻭﻯ‬ ‫ﻟﻠﻤﺜﻠﺚ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬=٢)(
)٥(‫ﻣﺘﻄﺎﺑﻘﲔ‬ ‫ﻣﺜﻠﺜﲔ‬ ‫ﺍﱃ‬ ‫ﻳﻘﺴﻤﻪ‬ ‫ﺍﳌﺴﺘﻄﻴﻞ‬ ‫ﰱ‬ ‫ﺍﻟﻘﻄﺮ‬)(
@}T@{@@@òßýÇ@Éš@@@ëa@@@ëa@@]@@
@ @‫ﻟﻠﻤﺮﺑﻊ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬‫ﻟﻠﻤﻌﲔ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬
‫ﺍﳌﺴﺘﻄﻴﻞ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬‫ﺍﳌﻌﲔ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬
‫ﻟﻠﻤﺮﺑﻊ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬‫ﻟﻠﻤﺴﺘﻄﻴﻞ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬
‫ﺍﳌﺮﺑﻊ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬‫ﺍﻟﺪﺍﺋﺮﺓ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬
‫ر‬

26. @}U@@{@µi@b¿@òzîz—Ûa@òibuüa@‚a@‘aìÓüa@@
)١(‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬‫ﺍﳌﻌﲔ‬........... =]‫ﻭﺍﺣﺪ‬ ، ‫ﺍﺛﻨﺎﻥ‬ ، ‫ﺛﻼﺛﻪ‬ ، ‫ﺍﺭﺑﻌﻪ‬[
)٢(‫ﺧ‬ ‫ﻋﺪﺩ‬‫ﺍﳌﺴﺘﻄﻴﻞ‬ ‫ﲤﺎﺛﻞ‬ ‫ﻄﻮﻁ‬.......]، ‫ﺻﻔﺮ‬٤،٢،٣[
)٣(‫ﻟ‬ ‫ﻳﻮﺟﺪ‬‫ﻠﻤﺮﺑﻊ‬..........‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬]‫ﻭﺍﺣﺪ‬ ، ‫ﺍﺛﻨﺎﻥ‬ ، ‫ﺛﻼﺛﻪ‬ ، ‫ﺍﺭﺑﻌﻪ‬[
)٤(‫ﲤﺎﺛﻞ‬ ‫ﳏﺎﻭﺭ‬ ‫ﻋﺪﺩ‬‫ﺷﺒ‬‫ﺍﻟﺴﺎﻗﲔ‬ ‫ﻣﺘﺴﺎﻭﻯ‬ ‫ﺍﳌﻨﺤﺮﻑ‬ ‫ﻪ‬.....]٠،١،٢،٣[
)٥(‫ﻟﻠ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﺰﻁ‬ ‫ﻋﺪﺩ‬‫ﺍﻻﺿﻼﻉ‬ ‫ﻣﺘﺴﺎﻭﻯ‬ ‫ﻤﺜﻠﺚ‬....... =]٠،١،٢،٣[
@}U@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬‫ﺍﻟﺪﺍﺋﺮﺓ‬ ‫ﲤﺎﺛﻞ‬........... =]١،٢،٣‫ﻋﺪﺩ‬ ،‫ﺟﺪﺍ‬ ‫ﻛﺒﲑ‬[
)٢(‫ﻋﺪﺩ‬‫ﺧﻄﻮﻁ‬‫ﺍ‬ ‫ﲤﺎﺛﻞ‬‫ﺍﻟﺴﺎﻗﲔ‬ ‫ﻣﺘﺴﺎﻭﻯ‬ ‫ﳌﺜﻠﺚ‬......]‫ﺍﺭﺑﻌﻪ‬ ، ‫ﺛﻼﺛﻪ‬ ، ‫ﻭﺍﺣﺪ‬ ، ‫ﺍﺛﻨﺎﻥ‬[
)٣(‫ﻟﻪ‬ ‫ﺍﻟﺬﻯ‬ ‫ﺍﻟﺮﺑﺎﻋﻰ‬ ‫ﺍﻟﺸﻜﻞ‬‫ﻫﻮ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﺍﺭﺑﻌﺔ‬......]‫ﺍﳌﻌﲔ‬،‫ﺍﳌﺴﺘﻄﻴﻞ‬،‫ﺍﳌﺮﺑﻊ‬،‫ﺍﳌﻨﺤﺮﻑ‬ ‫ﺷﺒﻪ‬[
)٤(‫ﺍﻻﺿﻼﻉ‬ ‫ﻣﺘﻮﺍﺯﻯ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬........ =]١،٢،٣،‫ﺻﻔﺮ‬[
)٥(‫ﺍﻻﺿﻼﻉ‬ ‫ﳐﺘﻠﻒ‬ ‫ﺍﳌﺜﻠﺚ‬ ‫ﲤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬....... =]‫ﺻﻔﺮ‬،١،٢،٣[

27. ٥
١
٤٣٢١ ٨٧٦
٥
٤
٣
٢
٦
٧
٨
٩
‫ا‬
‫ب‬
‫ج‬
‫ﻫﺎﻣﻪ‬ ‫ﻣﻼﺣﻈﺎﺕ‬
)١(‫ﻣﺮﺗﺐ‬ ‫ﺯﻭﺝ‬ ‫ﺑﻨﺎﻇﺮﻫﺎ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬ ‫ﻧﻘﻄﻪ‬ ‫ﻛﻞ‬
‫ﺍﻣﺜﻠﻪ‬
‫ﺍﻟﻨﻘﻄﻪ‬‫ا‬‫ا‬‫ا‬‫ا‬) =٤،٣(
‫ﺏ‬ ‫ﺍﻟﻨﻘﻄﺔ‬) =٥،٦(
‫ﺍﻟﻨﻘﻄﺔ‬‫ـ‬) =٢،٢(
)٢(‫ﺭﻗﻤﲔ‬ ‫ﻣﻦ‬ ‫ﻣﻜﻮﻥ‬ ‫ﻣﺮﺗﺐ‬ ‫ﺯﻭﺝ‬ ‫ﻛﻞ‬
‫ﻣﺜﺎﻝ‬‫ﺍﳌﺮﺗﺐ‬ ‫ﺍﻟﺰﻭﺝ‬)١،٤(
‫ﺭﻗﻢ‬١‫ﺍﻻﻭﻝ‬ ‫ﺍﻟﺒﻌﺪ‬ ‫ﺍﻭ‬ ‫ﺍﻻﻭﻝ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﻳﺴﻤﻰ‬
‫ﺭﻗﻢ‬٤‫ﺍﻟﺜﺎﱏ‬ ‫ﺍﻟﺒﻌﺪ‬ ‫ﺍﻭ‬ ‫ﺍﻟﺜﺎﱏ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﻳﺴﻤﻰ‬
@@
@}Q@@{@ómdí@bß@Ýà×a@@
)١()٣،) = ( ........،٥(
)٢(‫ﺍﳌﺮﺗﺐ‬ ‫ﺍﻟﺰﻭﺝ‬)٧،= ( ....‫ﺍﳌﺮﺗﺐ‬ ‫ﺍﻟﺰﻭﺝ‬.... )،٤(
)٣(‫ﻛﺎﻥ‬ ‫ﺍﺫﺍ‬)، ‫ﺱ‬٨) = (٥،٨(‫ﺱ‬ ‫ﻓﺈﻥ‬............ =
)٤(‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬)٤،‫ا‬‫ا‬‫ا‬‫ا‬) = (٤،٧(‫ﻓﺈﻥ‬‫ا‬‫ا‬‫ا‬‫ا‬........ =
)٥(‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬‫ا‬‫ا‬‫ا‬‫ا‬) =٣،٦(‫ﻟﻨﻘﻄﺔ‬ ‫ﺍﻻﻭﻝ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﻓﺈﻥ‬‫ا‬‫ا‬‫ا‬‫ا‬........ =
)٦(‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬‫ـ‬) =٦،٤(‫ﺍﻻﻭﻝ‬ ‫ﺍﻟﺒﻌﺪ‬ ‫ﻓﺈﻥ‬....... =‫ﺍﻟﺜﺎﱏ‬ ‫ﻭﺍﻟﺒﻌﺪ‬........ =
)٧(‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬‫ا‬‫ا‬‫ا‬‫ا‬) =٣،٥(‫ﺍﻻﻭﻝ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﻓﺈﻥ‬....... =‫ﺍﻟﺜﺎﱏ‬ ‫ﻭﺍﻻﺣﺪﺍﺛﻰ‬........ =
)٨(‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬‫ب‬‫ب‬‫ب‬‫ب‬) =١،٨(‫ﺍﻟﺴﻴﲎ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﻓﺈﻥ‬....... =‫ﺍﻟﺼﺎﺩﻯ‬ ‫ﻭﺍﻻﺣﺪﺍﺛﻰ‬........ =
‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛasÛbrÛasÛbrÛasÛbrÛasÛbrÛa@Z@@Z@@Z@@Z@@åí†ÈjÛa@ë‡@óqa†yüa@ôìnŽ½a@åí†ÈjÛa@ë‡@óqa†yüa@ôìnŽ½a@åí†ÈjÛa@ë‡@óqa†yüa@ôìnŽ½a@åí†ÈjÛa@ë‡@óqa†yüa@ôìnŽ½a@@@@@@@@
‫ر‬

28. @}R@@{@òßýÇ@Éš)√(@òßýÇ@ëa)×(
)١()٥،١٣) = (١٣،٥()(
)٢(‫ﺍﳌﺮﺗﺐ‬ ‫ﺍﻟﺰﻭﺝ‬)٢،٥= (‫ﺍﳌﺮﺗﺐ‬ ‫ﺍﻟﺰﻭﺝ‬)٥،٢()(
)٣(‫ﺍﳌﺮﺗﺐ‬ ‫ﺍﻟﺰﻭﺝ‬)٢،٧(}}}}‫ﺍﳌﺮﺗﺐ‬ ‫ﺍﻟﺰﻭﺝ‬)٧،٢()(
)٤(‫ﻛﺎﻧﺖ‬ ‫ﺍﺫﺍ‬‫ا‬‫ا‬‫ا‬‫ا‬) =٦،٥(‫ﺍﻻﻭﻝ‬ ‫ﺍﻟﺒﻌﺪ‬ ‫ﻓﺈﻥ‬=٦)(
)٥(‫ﻣﺮﺗﺐ‬ ‫ﺯﻭﺝ‬ ‫ﳝﺜﻠﻬﺎ‬ ‫ﺍﻟﺒﻌﺪﻳﻦ‬ ‫ﺫﻯ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬ ‫ﻧﻘﻄﻪ‬ ‫ﺍﻯ‬)(
)١(‫ﺍﻟﻨﻘﺎﻁ‬ ‫ﻣﻮﺍﺿﻊ‬ ‫ﺣﺪﺩ‬ ‫ﺍﻟﺒﻌﺪﻳﻦ‬ ‫ﺫﻯ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬‫ا‬‫ا‬‫ا‬‫ا‬)٢،١(‫ﺏ‬ ،)٥،١(،‫ـ‬)٥،٤(
‫ﺩ‬)٢،٤. (‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺳﻢ‬ ‫ﻣﺎ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫؟‬ ‫ﻟﻪ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬ ‫ﻭﻣﺎ‬ ‫؟‬ ‫ﺩ‬
)٢(‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻟﻨﻘﺎﻁ‬ ‫ﻣﻮﺍﺿﻊ‬ ‫ﺣﺪﺩ‬ ‫ﺍﻟﺒﻌﺪﻳﻦ‬ ‫ﺫﻭ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬‫ا‬‫ا‬‫ا‬‫ا‬)١،١(‫ﺏ‬ ،)١،٤(،‫ـ‬)٣،٤(
‫ﺩ‬)٣،١. (‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺳﻢ‬ ‫ﻣﺎ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫؟‬ ‫ﻟﻪ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬ ‫ﻭﻣﺎ‬ ‫؟‬ ‫ﺩ‬
)٣((‫ﺍﻟﻨﻘﺎﻁ‬ ‫ﻣﻮﺍﺿﻊ‬ ‫ﺣﺪﺩ‬ ‫ﺍﳌﺘﻌﺎﻣﺪﻳﻦ‬ ‫ﺍﶈﻮﺭﻳﻦ‬ ‫ﺫﻯ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬‫ا‬‫ا‬‫ا‬‫ا‬)٣،١(‫ﺏ‬ ،)٣،٤(
‫ـ‬)٥،٤(‫ﺩ‬ ،)٥،١. (‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺳﻢ‬ ‫ﻣﺎ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫؟‬ ‫ﻟﻪ‬ ‫ﺍﻟﺘﻤﺎﺛﻞ‬ ‫ﺧﻄﻮﻁ‬ ‫ﻋﺪﺩ‬ ‫ﻭﻣﺎ‬ ‫؟‬ ‫ﺩ‬
)٤(‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺭﺳﻢ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫ﺍﻟﺒﻌﺪﻳﻦ‬ ‫ﺫﻯ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬ ‫ﺩ‬‫ﺣﻴﺚ‬‫ا‬‫ا‬‫ا‬‫ا‬)، ‫ﺻﻔﺮ‬١(‫ﺏ‬ ،)٤،١(
‫ـ‬)٣،٣(‫ﺩ‬ ،)١،٣. (‫ﻣﺎ‬‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺳﻢ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫؟‬ ‫ﺩ‬
)٥(‫ﺍﳌﺜﻠﺚ‬ ‫ﺍﺭﺳﻢ‬ ‫ﺍﻟﺒﻌﺪﻳﻦ‬ ‫ﺫﻯ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫ﺣﻴﺚ‬‫ا‬‫ا‬‫ا‬‫ا‬)١،٥(‫ﺏ‬ ،)١،٨(
‫ـ‬)٥،٥. (‫ﺍﳌﺜﻠﺚ‬ ‫ﻧﻮﻉ‬ ‫ﻣﺎ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫؟‬ ‫ﻟﺰﻭﺍﻳﺎﻩ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬
)٦(‫ﺱ‬ ‫ﺣﻴﺚ‬ ‫ﺍﻟﺒﻌﺪﻳﻦ‬ ‫ﺫﻭ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬ ‫ﻝ‬ ‫ﻉ‬ ‫ﺹ‬ ‫ﺱ‬ ‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺭﺳﻢ‬)٥،١(‫ﺹ‬ ،)٧،٣(
‫ﻉ‬)٥،٥(‫ﻝ‬ ،)٣،٣. (‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺳﻢ‬ ‫ﻣﺎ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫؟‬ ‫ﺩ‬
)٧(‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺭﺳﻢ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫ﺣﻴﺚ‬ ‫ﺍﻟﺒﻌﺪﻳﻦ‬ ‫ﺫﻯ‬ ‫ﺍﻻﺣﺪﺍﺛﻰ‬ ‫ﺍﳌﺴﺘﻮﻯ‬ ‫ﰱ‬ ‫ﺩ‬‫ا‬‫ا‬‫ا‬‫ا‬)١،١(‫ﺏ‬ ،)٣،٢(
‫ـ‬)٥،١(‫ﺩ‬ ،)٣،٠(.‫ﺍﻟﺸﻜﻞ‬ ‫ﺍﺳﻢ‬ ‫ﻣﺎ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺏ‬‫ـ‬‫؟‬ ‫ﺩ‬
‫ﺍﻟﻠﻔﻈﻴﺔ‬ ‫ﺍﻻﺳﺌﻠﺔ‬

29. ‫ﺍﻟﻨﻤ‬‫ﻂ‬:‫ﻣﻌﻴﻨﺔ‬ ‫ﻗﺎﻋﺪﺓ‬ ‫ﻭﻓﻖ‬ ‫ﺍﺷﻜﺎﻝ‬ ‫ﺍﻭ‬ ‫ﺭﻣﻮﺯ‬ ‫ﺍﻭ‬ ‫ﺍﻋﺪﺍﺩ‬ ‫ﻣﻦ‬ ‫ﺗﺘﺎﺑﻊ‬ ‫ﻫﻮ‬
‫ﻣﺜﺎﻝ‬+ + :-+ +-+ +-
١،٤،٧،١٠،١٣،١٦،......‫ﺍﱁ‬
@}Q@@{@ómdí@bß@Ýà×a@@
)١(‫ا‬‫ا‬‫ا‬‫ا‬‫ﺟـ‬ ‫ﺏ‬‫ا‬‫ا‬‫ا‬‫ا‬‫ﺟـ‬ ‫ﺏ‬..........................
)٢(‫ﻉ‬ ‫ﺹ‬ ‫ﺱ‬ ‫ﻉ‬ ‫ﺹ‬ ‫ﺱ‬ ‫ﻉ‬ ‫ﺹ‬ ‫ﺱ‬..........................
)٣(▼▲▼▲▼▲.................................
)٤(■■■▲■■▲■■▲■▲.........................
)٥(١٠٠،٩٠،٨٠،.......،......،.........
)٦(٥،٨،١١،١٤،......،......،.........
@}Q@@{@ómdí@bß@Ýà×a@@
)١(ΟΟΟΟ▲ΟΟΟΟ▲ΟΟΟΟ▲ΟΟΟΟ▲...............................
)٢(‫ا‬‫ا‬‫ا‬‫ا‬، ‫ﺏ‬‫ا‬‫ا‬‫ا‬‫ا‬، ‫ﺏ‬ ‫ﺏ‬‫ا‬‫ا‬‫ا‬‫ا‬، ‫ﺏ‬ ‫ﺏ‬ ‫ﺏ‬‫ا‬‫ا‬‫ا‬‫ا‬، ‫ﺏ‬..........................
)٣(١٣,٢،١٣,٤،١٣,٦،.........،........،..........
)٤(١،٥،٩،١٣،.......،.......،.........
)٥(١٠٠،١٢٠،١٤٠،.......،........،.........
)٦(١٠،٩,٦،٩,٢،.......،.......،........
)٧(١٠٠،٩٩,٤،٩٨,٨،........،..........
)٨(× × ÷،÷ × ÷،...........،..........،...........
‫ة‬ ‫ا‬‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaÉiaŠÛaÉiaŠÛaÉiaŠÛaÉiaŠÛa@Z@@Z@@Z@@Z@@@ò튖jÛa@Âb¸üa@@ò튖jÛa@Âb¸üa@@ò튖jÛa@Âb¸üa@@ò튖jÛa@Âb¸üa@@@@@@@@
‫ر‬

30. @}Q@@{@òjŽbä¾a@‘bîÔÛa@ñ‡yë@kn×a@@
)١(‫ﻣﻌﺪﻧﻴﻪ‬ ‫ﻣﻴﺎﻩ‬ ‫ﺯﺟﺎﺟﺔ‬ ‫ﳝﻸ‬ ‫ﻣﺎ‬ ‫ﻣﻘﺪﺍﺭ‬(................. )
)٢(‫ﺍﻟﻌﺎﺋﻠﻰ‬ ‫ﺍﳊﺠﻢ‬ ‫ﻣﻦ‬ ‫ﻋﺼﲑ‬ ‫ﻋﻠﺒﺔ‬ ‫ﳝﻸ‬ ‫ﻣﺎ‬ ‫ﻣﻘﺪﺍﺭ‬(................. )
)٣(‫ﳌﺎﺀ‬ ‫ﻣﻦ‬ ‫ﻛﻮﺑﺎ‬ ‫ﳝﻸ‬ ‫ﻣﺎ‬ ‫ﻣﻘﺪﺍﺭ‬(................. )
)٤(‫ﳌﺮﻳﺾ‬ ‫ﻃﺒﻴﺐ‬ ‫ﺎ‬ ‫ﻧﺼﺢ‬ ‫ﺩﻭﺍﺀ‬ ‫ﻣﻦ‬ ‫ﺟﺮﻋﻪ‬ ‫ﻣﻘﺪﺍﺭ‬(................. )
)٥(‫ﺍﻻﺳﺘﺤﻤﺎﻡ‬ ‫ﰱ‬ ‫ﺷﺨﺺ‬ ‫ﻳﺴﺘﻬﻠﻜﻬﺎ‬ ‫ﺍﻟﱴ‬ ‫ﺍﳌﻴﺎﻩ‬ ‫ﻣﻘﺪﺍﺭ‬.... )(.............
)٦(‫ﺑﻮﺩﺭﻩ‬ ‫ﺷﻜﻞ‬ ‫ﰱ‬ ‫ﺩﻭﺍﺀ‬ ‫ﺎ‬ ‫ﻳﺬﻭﺏ‬ ‫ﺍﻟﱴ‬ ‫ﺍﳌﻴﺎﻩ‬ ‫ﻛﻤﻴﺔ‬(................. )
)٧(‫ﺍﻟﻌﻤﺎﺭﺍﺕ‬ ‫ﺑﺈﺣﺪﻯ‬ ‫ﺧﺰﺍﻥ‬ ‫ﲤﻸ‬ ‫ﺍﻟﱴ‬ ‫ﺍﳌﻴﺎﻩ‬ ‫ﻣﻘﺪﺍﺭ‬(................. )
)٨(‫ﺍﻟﺰﻳﻨـﺔ‬ ‫ﻷﲰﺎﻙ‬ ‫ﺣﻮﺽ‬ ‫ﺑﺪﺍﺧﻞ‬ ‫ﺍﳌﻴﺎﻩ‬ ‫ﻛﻤﻴﺔ‬(................. )
@}R@@{òzîz—Ûa@òibuüa@‚a@‘aìÓüa@µi@b¿@@@
)١(‫ﺍﳌﺎﺀ‬ ‫ﻛﻮﺏ‬ ‫ﺳﻌﺔ‬..........]٣، ‫ﻟﺘﺮﺍﺕ‬٢٥، ‫ﻣﻠﻠﻴﻠﺘﺮ‬٢٥٠‫ﻣﻠﻠﻴﻠﺘﺮ‬[
)٢(‫ﺗﻘﺮﻳﺒﺎ‬ ‫ﺍﳌﻴﺎﻩ‬ ‫ﻣﻦ‬ ‫ﺑﻜﻤﻴﺔ‬ ‫ﺍﻟﻴﻮﻡ‬ ‫ﺍﺳﺘﺤﻤﻤﺖ‬.......]٥٠، ‫ﻟﺘﺮ‬
١
٢
، ‫ﻟﺘﺮ‬١٠‫ﻟﺘﺮ‬[
)٣(‫ﺳﻌﺘﻪ‬ ‫ﻟﻠﻤﻴﺎﻩ‬ ‫ﺧﺰﺍﻥ‬ ‫ﻋﻨﺪﻧﺎ‬........]٢٠٠، ‫ﻣﻠﻠﻴﻠﺘﺮ‬٥٠‫ﻟ‬، ‫ﺘﺮ‬٣٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬[
)٤(‫ﻣﻘﺪﺍﺭﻫﺎ‬ ‫ﻣﺮﻳﻀﺎ‬ ‫ﻛﻨﺖ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺣﻘﻨﻪ‬ ‫ﺍﺧﺬﺕ‬......]١، ‫ﻣﻠﻠﻴﻠﺘﺮ‬
١
٢
، ‫ﻟﺘﺮ‬١٠‫ﻣﻠﻠﻴﻠﺘﺮ‬[
)٥(‫ﻣﻦ‬ ‫ﻣﻜﻮﻧﻪ‬ ‫ﺍﺳﺮﻩ‬ ‫ﺗﺴﺘﻬﻠﻜﻬﺎ‬ ‫ﺍﻟﱴ‬ ‫ﺍﻟﻠﱭ‬ ‫ﻛﻤﻴﺔ‬٤‫ﺍﻓﺮﺍﺩ‬.......]٥٠٠، ‫ﻟﺘﺮ‬٢٠٠٠، ‫ﻣﻠﻠﻴﻠﺘﺮ‬٥٠‫ﻟﺘﺮ‬[
)٦(‫ﺳﻌﺘﻬﺎ‬ ‫ﺩﻭﺍﺀ‬ ‫ﺯﺟﺎﺟﺔ‬ ‫ﺍﳝﺎﻥ‬ ‫ﺍﺷﺘﺮﺕ‬..........]
١
٥
، ‫ﻟﺘﺮ‬٢، ‫ﻟﺘﺮ‬١٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬[
‫ة‬ ‫ا‬‫ا‬ ‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaÞëþaÞëþaÞëþaÞëþa@Z@@Z@@Z@@Z@éÈŽÛaéÈŽÛaéÈŽÛaéÈŽÛa@@@@@@@@
‫ا‬ ‫س‬ ‫ات‬ ‫و‬‫ـ‬
‫اﻝ‬=١٠٠٠
‫اﻝ‬=١٠٠٠‫ﺱ‬٣
‫اﻝ‬=‫د‬٣
‫ر‬

31. @}S@@{@ómdí@bß@Ýà×a@@
)١(٢‫ﻟﺘﺮ‬........... =‫ﻣﻠﻠﻴﻠﺘﺮ‬)٢(٤‫ﻟﺘﺮﺍﺕ‬............ =‫ﻣﻠﻠﻴﺘﺮ‬
)٣(٧٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬........ =‫ﻟﺘﺮ‬)٤(٣٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬....... =‫ﻟﺘﺮ‬
)٥(٣٥٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬...... =.‫ﻟﺘﺮ‬)٦(٢٠‫ﻟﺘﺮ‬......... =‫ﻣﻠﻠﻴﻠﺘﺮ‬
)٧(٩٧٥٠‫ﻣﻠﻠﻴﻠﺘﺮ‬....... =‫ﻟﺘﺮ‬)٨(٧,٥‫ﻟﺘﺮ‬......... =‫ﻣﻠﻠﻴﻠﺘﺮ‬
)٩(٤,٢٥‫ﻟﺘﺮ‬......... =‫ﻣﻠﻠﻴﻠﺘﺮ‬)١٠(٨٥٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬....... =‫ﻟﺘﺮ‬
@}T@@{@òßýÇ@Éš)√(@òßýÇ@ëa)×(
)١(‫ﺍﳌﻠﻠﻴﻠﺘﺮ‬=١‫ﺳﻢ‬٣)(
)٢(‫ﺍﻟﻠﺘﺮ‬=١٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬)(
)٣(٣‫ﻟﺘﺮ‬=٣٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬)(
)٤(٢٣‫ﻟﺘﺮ‬=٢٣‫ﺩﻳﺴﻢ‬٣)(
)٥(‫ﺳﻌﺘﻬﺎ‬ ‫ﺩﻭﺍﺀ‬ ‫ﺯﺟﺎﺟﺔ‬ ‫ﻧﺸﺘﺮﻯ‬ ‫ﺍﻥ‬ ‫ﳝﻜﻦ‬
١
٥
‫ﻟﺘﺮ‬)(
@}U@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(
١
٢
‫ﻟﺘﺮ‬....... =..‫ﺳﻢ‬٣
]٥،٥٠،٥٠٠،٥٠٠٠[
)٢(٤‫ﻟﺘﺮ‬........ =‫ﻣﻠﻠﻴﻠﺘﺮ‬]٤،٤٠،٤٠٠،٤٠٠٠[
)٣(‫ﺍﻟﻠﺘﺮ‬........ =‫ﻣﻠﻠﻴﻠﺘﺮ‬]١٠،١٠٠،١٠٠٠،١٠٠٠٠[
)٤(٧٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬...... =‫ﻟﺘﺮ‬]٠,٧،٧،٧٠،٧٠٠[
)٥(١٥‫ﻟﺘﺮ‬........ =‫ﺩﻳﺴﻢ‬٣
]١٥٠٠٠،١٥،١٥٠،١٥٠٠[
)٦(٣٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬........ =‫ﻟﺘﺮ‬]٣٠،٣٠٠،٣،٣٠٠٠[
)٧(١٠٠‫ﻟﺘﺮ‬....... =‫ﺩﻳﺴﻢ‬٣
]١٠٠،١٠٠٠،١٠،١[
)٨(٤٧٥٠‫ﻣﻠﻠﻴﻠﺘﺮ‬........ =‫ﻟﺘﺮ‬]٤٧٥،
١
٢
٤٧،
٣
٤
٤،
٣
٤
٣[

32. @}V@@{@@@òßýÇ@Éš@@@ëa@@@@@ëa@@@@@]@@
١
٤
‫ﻟﺘﺮ‬٢٤٥‫ﻣﻠﻠﻴﻠﺘﺮ‬٧٥٠‫ﻣﻠﻠﻴﻠﺘﺮ‬
٣
٤
‫ﻟﺘﺮ‬
٦,٥‫ﻟﺘﺮ‬٦,٥‫ﺩﻳﺴﻢ‬٣
٢,٧٥‫ﻟﺘﺮ‬٢٧٥٠‫ﻣﻠﻠﻴﻠﺘﺮ‬
‫ﺍﻟﻠﺘﺮ‬١٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬٥٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬
١
٤
‫ﻟﺘﺮ‬
٤‫ﻟﺘﺮﺍﺕ‬٤٠٠‫ﺳﻢ‬٣
٣٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬٣٠‫ﻟﺘﺮ‬
١,٢٥‫ﻟﺘﺮ‬١٢٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬١,٢٥‫ﻟﺘﺮ‬١٥٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬
@}W@@{@ómdí@bß@Ýà×a@@
)١(٢‫ﻟﺘﺮ‬........... =‫ﺳﻢ‬٣
)٢(
١
٢
‫ﻟﺘﺮ‬............ =‫ﺳﻢ‬٣
)٣(‫ﺍﻟﻠﺘﺮ‬........ =‫ﻣﻠﻠﻴﻠﺘﺮ‬)٤(٤٧٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬....... =‫ﻟﺘﺮ‬
)٥(
٣
٤
‫ﻟﺘﺮ‬....... =‫ﻣﻠﻠﻴﻠﺘﺮ‬)٦(٦‫ﻟﺘﺮﺍﺕ‬......... =‫ﻣﻠﻠﻴﻠﺘﺮ‬
)٧(٢,٥‫ﻟﺘﺮ‬....... =‫ﺳﻢ‬٣
)٨(٢٥‫ﻟﺘﺮ‬......... =‫ﺩﻳﺴﻢ‬٣
)٩(٤,٥‫ﻟﺘﺮ‬......... =‫ﻣﻠﻠﻴﻠﺘﺮ‬)١٠(٥‫ﻟﺘﺮﺍﺕ‬....... =‫ﺳﻢ‬٣
]٨[‫ﺗﻨﺎﺯﻟﻴﺎ‬ ‫ﺭﺗﺐ‬:٨,٧٥‫ﻟﺘﺮ‬٩٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬٥‫ﻟﺒﺘﺮﺍﺕ‬٦٥٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬
]٩[‫ﺗﺼﺎﻋﺪﻳﺎ‬ ‫ﺭﺗﺐ‬:١٠‫ﻟﺘﺮﺍﺕ‬٣٠‫ﻣﻠﻠﻴﻠﺘﺮ‬٢٠٠٠‫ﻣﻠﻠﻴﻠﺘﺮ‬٣٠‫ﻟﺘﺮ‬٣‫ﻣﻠﻠﻴﻠﺘﺮ‬
]١٠[‫ﺍﳌﺎﳒﻮ‬ ‫ﻋﺼﲑ‬ ‫ﻣﻦ‬ ‫ﺍﻟﻠﺘﺮ‬ ‫ﲦﻦ‬ ‫ﻛﺎﻥ‬ ‫ﺍﺫﺍ‬٤,٥‫ﺳﻌﺘﻬﺎ‬ ‫ﺍﻟﻌﺼﲑ‬ ‫ﻫﺬﺍ‬ ‫ﻣﻦ‬ ‫ﻋﺒﻮﻩ‬ ‫ﲦﻦ‬ ‫ﻓﻜﻢ‬ ‫ﺟﻨﻴﻪ‬٣‫ﻟﺘﺮﺍﺕ‬

33. •‫ﻭ‬‫ﺍﻟﻮﺯﻥ‬ ‫ﻗﻴﺎﺱ‬ ‫ﺣﺪﺍﺕ‬
@@
@}Q@@{@òjŽbä¾a@‘bîÔÛa@ñ‡yë@‚a@@
)١(‫ﺍﻟﻔﺎﻛﻬﺔ‬ ‫ﺑﺎﺋﻊ‬ ‫ﻣﻦ‬ ‫ﻓﺎﻛﻬﺔ‬ ‫ﺷﺮﺍﺀ‬................]‫ﻛﺠﻢ‬ ، ‫ﺟﻢ‬ ، ‫ﻃﻦ‬[
)٢(‫ﺍﻟﺬﻫﺐ‬ ‫ﺑﻴﻊ‬ ‫ﳏﻞ‬ ‫ﻣﻦ‬ ‫ﻫﺪﻳﻪ‬ ‫ﺷﺮﺍﺀ‬..............]‫ﻛﺠﻢ‬ ، ‫ﺟﻢ‬ ، ‫ﻃﻦ‬[
)٣(‫ﺗﺮﻋﻪ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻘﺎﻡ‬ ‫ﻟﻜﻮﺑﺮﻯ‬ ‫ﲪﻮﻟﻪ‬ ‫ﺍﻗﺼﻰ‬.........]‫ﻛﺠﻢ‬ ، ‫ﺟﻢ‬ ، ‫ﻃﻦ‬[
)٤(‫ﺍﳌﺎﳒﻮ‬ ‫ﲦﺎﺭ‬ ‫ﻣﻦ‬ ‫ﲦﺮﻩ‬ ‫ﻭﺯﻥ‬......................]‫ﻛﺠﻢ‬ ، ‫ﺟﻢ‬ ، ‫ﻃﻦ‬[
)٥(‫ﺍﻻﺛﻘﺎﻝ‬ ‫ﺭﻓﻊ‬ ‫ﻟﻌﺒﺔ‬ ‫ﰱ‬ ‫ﺍﻻﻭﺯﺍﻥ‬ ‫ﲢﺪﻳﺪ‬...........]‫ﻛﺠﻢ‬ ، ‫ﺟﻢ‬ ، ‫ﻃﻦ‬[
@}R@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(‫ﻧ‬ ‫ﺳﻴﺎﺭﺓ‬ ‫ﲪﻮﻟﺔ‬ ‫ﺗﺒﻠﻎ‬‫ﻘﻞ‬..............]٢، ‫ﻃﻦ‬٢٠، ‫ﻛﺠﻢ‬٣٥٠٠‫ﺟﺮﺍﻡ‬[
)٢(‫ﻭﺍﻟــﺪﻯ‬ ‫ﻭﺯﻥ‬ ‫ﻳﺒﻠﻎ‬.............]، ‫ﻭﺍﺣﺪ‬ ‫ﻃﻦ‬٩٥، ‫ﻛﺠﻢ‬٨٠‫ﺟﻢ‬[
)٣(‫ﺎ‬‫ﻭﺯ‬ ‫ﺫﻫﺒﻴﻪ‬ ‫ﺍﺳﻮﺭﻩ‬ ‫ﺣﻨﺎﻥ‬ ‫ﺍﺷﺘﺮﺕ‬........]٢، ‫ﻃﻦ‬١٠، ‫ﺟﺮﺍﻣﺎﺕ‬٢‫ﻛﺠﻢ‬[
)٤(‫ﻳﻮﻣﻴﺎ‬ ‫ﺍﲪﻠﻬﺎ‬ ‫ﺍﻟﱴ‬ ‫ﺍﻟﻜﺘﺐ‬ ‫ﺣﻘﻴﺒﺔ‬ ‫ﻭﺯﻥ‬......]٣، ‫ﺍﻃﻨﺎﻥ‬٣، ‫ﺟﺮﺍﻣﺎﺕ‬٣‫ﻛﺠﻢ‬[
@}S@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(٢‫ﻛﻴﻠﻮﺟﺮﺍﻡ‬........ =‫ﺟﺮﺍﻡ‬]٢٠،٢٠٠٠،٢٢٠،٢٠٠[
)٢(
١
٤
‫ﻃﻦ‬......... =‫ﻛﻴﻠﻮﺟﺮﺍﻡ‬]٥٠٠،٢٥٠،٤٠٠،٥٢٠[
)٣(٦‫ﺍﻃﻨﺎﻥ‬........ =‫ﻛﻴﻠﻮﺟﺮﺍﻡ‬]٦،٦٠،٦٠٠،٦٠٠٠[
)٤(٤,٥‫ﻃﻦ‬........ =‫ﻛﺠﻢ‬]٤٥،٥٤،٤٥٠٠،٥٤٠٠[
‫ة‬ ‫ا‬‫ا‬ ‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaóãbrÛaóãbrÛaóãbrÛaóãbrÛa@Z@@Z@@Z@@Z@æ‹ìÛaæ‹ìÛaæ‹ìÛaæ‹ìÛa@@@@@@@@
‫ا‬ ‫اﻝ‬‫م‬=١٠٠٠‫ام‬‫اﻝ‬=١٠٠٠‫ام‬ ‫آ‬
‫ر‬

34. @}T@@{@ómdí@bß@Ýà×a@@
)١(٢‫ﻃﻦ‬......... =‫ﻛﺠﻢ‬)٢(٣‫ﻛﻴﻠﻮﺟﺮﺍﻡ‬........ =‫ﺟﺮﺍﻡ‬
)٣(‫ﺍﻟﻄﻦ‬.......... =‫ﻛﺠﻢ‬)٤(٥‫ﻃﻦ‬........... =‫ﻛﺠﻢ‬
)٥(٧‫ﺍﻃﻨﺎﻥ‬....... =‫ﻛﺠﻢ‬)٦(٦,٥‫ﻃﻦ‬........ =‫ﻛﺠﻢ‬
)٧(٤‫ﻛﺠﻢ‬....... =‫ﺟﺮﺍﻡ‬)٨(٦,٧٥‫ﻃﻦ‬......... =‫ﻛﺠﻢ‬
@}U@@{@@@òßýÇ@Éš@@@ëa@@@@@ëa@@@@@]@@
١
٤
٣‫ﻛﺠﻢ‬٣٢٥٠‫ﺟﺮﺍﻡ‬٦‫ﺍﻃﻨﺎﻥ‬٦٥٠٠‫ﻛﺠﻢ‬
٣,٥‫ﻃﻦ‬٣٥٠‫ﻛﺠﻢ‬٣‫ﻛﻴﻠﻮﺟﺮﺍﻣﺎﺕ‬٣٠٠٠‫ﺟﺮﺍﻡ‬
١
٢
٦‫ﻃﻦ‬٦٥٠٠‫ﻛﺠﻢ‬٥‫ﺍﻃﻨﺎﻥ‬٥٠٠٠‫ﺟﺮﺍﻡ‬
١٠٠‫ﺟﺮﺍﻡ‬‫ﻛﻴﻠﻮﺟﺮﺍﻡ‬٧٥٠‫ﺟﺮﺍﻡ‬
١
٢
‫ﻛﺠﻢ‬
)١(‫ﺍﳍﺪﻳﻪ‬ ‫ﻭﺯﻥ‬ ‫ﻛﺎﻥ‬ ‫ﻓﺈﺫﺍ‬ ‫ﺯﻭﺍﺟﻬﻤﺎ‬ ‫ﻋﻴﺪ‬ ‫ﰱ‬ ‫ﻟﺰﻭﺟﺘﻪ‬ ‫ﺫﻫﺒﻴﻪ‬ ‫ﻫﺪﻳﻪ‬ ‫ﺭﺟﻞ‬ ‫ﺍﺷﺘﺮﻯ‬٤٠‫ﻣﻦ‬ ‫ﺍﳉﺮﺍﻡ‬ ‫ﲦﻦ‬ ‫ﻭﻛﺎﻥ‬ ‫ﺟﺮﺍﻡ‬‫ﺍﻟﺬﻫﺐ‬
١٧٠‫ﺟﻨﻴﻬﺎ‬.‫؟‬ ‫ﺍﻟﺮﺟﻞ‬ ‫ﻫﺬﺍ‬ ‫ﻳﺪﻓﻊ‬ ‫ﻓﻜﻢ‬
)٢(‫ﺎ‬‫ﻭﺯ‬ ‫ﻣﺴﻠﻰ‬ ‫ﻋﻠﺒﺔ‬٥‫ﻛﺠﻢ‬.‫ﻣﻨﻬﺎ‬ ‫ﺍﻟﻜﻴﻠﻮﺟﺮﺍﻡ‬ ‫ﲦﻦ‬ ‫ﻛﺎﻥ‬ ‫ﺍﺫﺍ‬ ‫ﲦﻨﻬﺎ‬ ‫ﻳﻜﻮﻥ‬ ‫ﻛﻢ‬٧‫؟‬ ‫ﺟﻨﻴﻪ‬
)٣(‫ﺍﻟﻠﺤﻢ‬ ‫ﻣﻦ‬ ‫ﺍﻟﻜﻴﻠﻮﺟﺮﺍﻡ‬ ‫ﲦﻦ‬ ‫ﻛﺎﻥ‬ ‫ﺍﺫﺍ‬٣٥‫ﺗﺴﺘﻬﻠﻚ‬ ‫ﺍﺳﺮﻩ‬ ‫ﻭﻛﺎﻧﺖ‬ ‫ﺟﻨﻴﻬﺎ‬٢‫ﺍﺳﺒﻮﻋﻴﺎ‬ ‫ﻛﻴﻠﻮﺟﺮﺍﻡ‬.‫ﺗﻨﻔﻘﻪ‬ ‫ﻣﺎ‬ ‫ﺍﻭﺟﺪ‬
‫ﻣ‬ ‫ﻟﺸﺮﺍﺀ‬ ‫ﺍﻻﺳﺮﻩ‬‫ﻳﻠﺰﻣﻬﺎ‬ ‫ﺎ‬‫ﺫﻟﻚ‬ ‫ﻣﻦ‬‫؟‬ ‫ﺍﻟﺸﻬﺮ‬ ‫ﰱ‬
‫ﻝ‬ ‫اﺱ‬

35. •‫ﻗﻴﺎﺱ‬ ‫ﻭﺣﺪﺍﺕ‬‫ﺍﻟﻮﻗﺖ‬
@}Q@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(‫ﺍﻟ‬ ‫ﻋﻤﻞ‬ ‫ﺍﺳﺘﻐﺮﻕ‬‫ﺑﺎﻷﻣﺲ‬ ‫ﺍﳌﺪﺭﺳﻰ‬ ‫ﻮﺍﺟﺐ‬........]
١
٢
‫ﻳﻮﻡ‬،٣، ‫ﺳﺎﻋﺎﺕ‬٣، ‫ﺩﻗﺎﺋﻖ‬٣‫ﺛﻮﺍﱏ‬[
)٢(‫ﺍﻟﻌﺎﺩﻯ‬ ‫ﻟﻠﺸﺨﺺ‬ ‫ﺍﻟﻨﻮﻡ‬ ‫ﻓﺘﺮﺓ‬ ‫ﺗﺒﻠﻎ‬........]٥٠٠، ‫ﺛﺎﻧﻴﻪ‬٥٠٠، ‫ﺩﻗﻴﻘﻪ‬١٠٠‫ﺩﻗﻴﻘﻪ‬[
)٣(‫ﻃﻌ‬ ‫ﲡﻬﻴﺰ‬ ‫ﻓﺘﺮﺓ‬ ‫ﺗﺴﺘﻐﺮﻕ‬‫ﺍﳉﻤﻌﻪ‬ ‫ﻳﻮﻡ‬ ‫ﺍﻻﻓﻄﺎﺭ‬ ‫ﺎﻡ‬.......]
١
٢
‫ﻳﻮﻡ‬،
١
٢
، ‫ﺳﺎﻋﻪ‬٣٠‫ﺛﺎﻧﻴﻪ‬[
)٤(‫ﻗﺪﻡ‬ ‫ﻛﺮﺓ‬ ‫ﻣﺒﺎﺭﺓ‬ ‫ﺷﺎﻫﺪﺕ‬‫ﺍﺳﺘﻤﺮﺕ‬ ‫ﺍﻟﺘﻠﻴﻔﺰﻳﻮﻥ‬ ‫ﰱ‬........]٩٠٠، ‫ﺩﻗﻴﻘﻪ‬١٠٠، ‫ﺩﻗﻴﻘﻪ‬٣، ‫ﺳﺎﻋﺎﺕ‬
١
٤
‫ﻳﻮﻡ‬[
)٥(‫ﳌﻮﻇﻒ‬ ‫ﺍﻟﻴﻮﻣﻰ‬ ‫ﺍﻟﻌﻤﻞ‬ ‫ﻓﺘﺮﺓ‬ ‫ﺗﺒﻠﻎ‬........]٤٨، ‫ﺩﻗﻴﻘﻪ‬
١
٢
‫ﻳﻮﻡ‬،٣٦٠‫ﺛﺎﻧﻴﻪ‬[
)٦(‫ﺍﻟﺪﺭﺍﺳﻰ‬ ‫ﺍﻟﻴﻮﻡ‬ ‫ﻳﺴﺘﻐﺮﻕ‬.............]٦، ‫ﺳﺎﻋﺎﺕ‬١٢، ‫ﺳﺎﻋﻪ‬١٨، ‫ﺳﺎﻋﻪ‬١٥‫ﺳﺎﻋﻪ‬[
@}R@@{@ómdí@bß@Ýà×a@@
)١(‫ﺍﻟﺴﺎﻋﻪ‬......... =‫ﺩﻗ‬‫ﻴﻘﻪ‬)٢(
١
٢
‫ﺳﺎﻋﻪ‬........ =‫ﺩﻗﻴﻘﻪ‬
)٣(٣‫ﺳﺎﻋﺎﺕ‬... =...‫ﺩﻗﻴ‬‫ﻘﻪ‬)٤(‫ﺍﻟﺪﻗﻴﻘﻪ‬....... =...‫ﺛﺎﻧﻴﻪ‬
)٥(
١
٤
‫ﺳﺎﻋﻪ‬...... =..‫ﺩﻗﻴﻘﻪ‬)٦(
١
٣
‫ﺳﺎﻋﻪ‬........ =‫ﺩﻗﻴﻘﻪ‬
)٧(٣‫ﺩﻗﺎﺋﻖ‬.... =.....‫ﺛﺎﻧﻴﻪ‬)٨(٤‫ﺩﻗﺎﺋﻖ‬......... =‫ﺛﺎﻧﻴﻪ‬
‫ة‬ ‫ا‬‫ا‬ ‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛasÛbrÛasÛbrÛasÛbrÛasÛbrÛa@Z@@Z@@Z@@Z@@oÓìÛa@oÓìÛa@oÓìÛa@oÓìÛa@@@@@@@@
‫اﻝ‬=٦٠‫د‬
‫اﻝ‬=٦٠‫ﻥ‬ ‫ﺙ‬
‫م‬ ‫اﻝ‬=٢٤‫ﺱ‬
‫ر‬

36. @}S@@{@ómdí@bß@Ýà×a@@
)١(‫ﻭﺭﺑﻊ‬ ‫ﺳﺎﻋﻪ‬......... =‫ﺩﻗﻴﻘﻪ‬)٢(‫ﻭﺛﻠﺚ‬ ‫ﺳﺎﻋﻪ‬........ =‫ﺩﻗﻴﻘﻪ‬
)٣(‫ﺳﺎﻋﺘﺎﻥ‬...... =‫ﺩﻗﻴﻘﻪ‬)٤(‫ﻭﺛﻠﺚ‬ ‫ﺳﺎﻋﺘﺎﻥ‬.......... =‫ﺛﺎﻧﻴﻪ‬
)٥(١٢٠‫ﺩﻗﻴﻘﻪ‬........ =‫ﺳﺎﻋﻪ‬)٦(١٥٠‫ﺩﻗﻴﻘﻪ‬........ =‫ﺳﺎﻋﻪ‬
)٧(١٣٥‫ﺩﻗﻴﻘﻪ‬......... =‫ﺳﺎﻋﻪ‬)٨(٢٧٠‫ﺩﻗﻴﻘﻪ‬......... =‫ﺳﺎﻋﻪ‬
@}T@@{@ómdí@bß@Ýà×a@@
)١(‫ﺍﻟﻴﻮﻡ‬......... =‫ﺳﺎﻋﻪ‬)٢(‫ﻳﻮﻣﺎﻥ‬........ =‫ﺳﺎﻋﻪ‬
)٣(
١
٢
‫ﻳﻮﻡ‬...... =‫ﺳﺎﻋﻪ‬)٤(٣‫ﺍﻳﺎﻡ‬.......... =‫ﺳﺎﻋﻪ‬
)٥(٤‫ﺍﻳﺎﻡ‬........ =‫ﺳﺎﻋﻪ‬)٦(
١
٤
‫ﻳﻮﻡ‬........ =‫ﺳﺎﻋﻪ‬
)٧(
١
٣
‫ﻳﻮﻡ‬......... =‫ﺳﺎﻋﻪ‬)٨(٧٢‫ﺳﺎﻋﻪ‬......... =‫ﻳﻮﻡ‬
)٩(٤٨‫ﺳﺎﻋﻪ‬...... =‫ﻳﻮﻡ‬)١٠(٣٠‫ﺳﺎﻋﻪ‬......... =‫ﻳﻮﻡ‬
@}U@@{@@@òßýÇ@Éš@@@ëa@@ëa@@@@@]@@@@@
٧٢‫ﺳﺎﻋﻪ‬٣‫ﺍﻳﺎﻡ‬
٣
٤
‫ﺳﺎﻋﻪ‬٥٠‫ﺩﻗﻴﻘﻪ‬
٤٨‫ﺳﺎﻋﻪ‬‫ﻳﻮﻣﺎﻥ‬١٢٤‫ﺛﺎﻧﻴﻪ‬‫ﺩﻗﻴﻘﺘﲔ‬
١
٣
‫ﻳﻮﻡ‬٧‫ﺳﺎﻋﺎﺕ‬‫ﻳﻮﻡ‬ ‫ﻧﺼﻒ‬١٥‫ﺳﺎﻋﻪ‬
٣
٤
‫ﻳﻮﻡ‬١٩‫ﺳﺎﻋﻪ‬١٢٥‫ﺛﺎﻧ‬‫ﻴﻪ‬٢,٥‫ﺩﻗﻴﻘﻪ‬
٨٤‫ﺳﺎﻋﻪ‬٥‫ﺍﻳﺎﻡ‬
٣
٤
‫ﺳﺎﻋﻪ‬٧٥‫ﺩﻗﻴﻘﻪ‬

37. @}V@@{@òßýÇ@Éš)√(@òßýÇ@ëa)×(
)١(‫ﺍﻟﺴﺎﻋﻪ‬=٦٠‫ﺩﻗﻴﻘﻪ‬)(
)٢(‫ﻳﻮﻡ‬ ‫ﺛﻠﺚ‬=٨‫ﺳﺎﻋﺎﺕ‬)(
)٣(٣‫ﺍﻳﺎﻡ‬=٧٢‫ﺳﺎﻋﻪ‬)(
)٤(‫ﻭﻧﺼﻒ‬ ‫ﺳﺎﻋﻪ‬=٩٠‫ﺩﻗ‬‫ﻴﻘﻪ‬)(
)٥(٢,٥‫ﻳﻮﻡ‬=٦٠‫ﺳﺎﻋﻪ‬)(
@}W@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(٧٢‫ﺳﺎﻋﻪ‬.......... =]٣، ‫ﻳﻮﻣﺎﻥ‬ ، ‫ﺍﻳﺎﻡ‬٤، ‫ﺍﻳﺎﻡ‬٥‫ﺍﻳﺎﻡ‬[
)٢(‫ﻳﻮﻡ‬ ‫ﺛﻠﺚ‬........ =‫ﺳﺎﻋﻪ‬]١٢،٣،٨،١٥[
)٣(‫ﻭﺭﺑﻊ‬ ‫ﺳﺎﻋﻪ‬...... =‫ﺩﻗﻴﻘﻪ‬]٦٠،٦٥،٧٠،٧٥[
)٤(‫ﻭﺛﻠﺚ‬ ‫ﺳﺎﻋﻪ‬...... =‫ﺩﻗﻴﻘﻪ‬]٧٥،٨٠،٩٠،١٢٠[
)٥(١٥٠‫ﺩﻗﻴﻘﻪ‬......... =‫ﺳﺎﻋﻪ‬]٣،
١
٢
٢،
١
٢
١،١٥[
)٦(
١
٨
‫ﻳﻮﻡ‬........... =‫ﺳﺎﻋﺎﺕ‬]٣،٤،٥،٦[
@}X@@{Š@bîÛŒbäm@km@bí‡Çb—më@ @@ @@@
٣‫ﺍﻳﺎﻡ‬٤٧٠٠‫ﺩﻗﻴﻘﻪ‬٧٥‫ﺳﺎﻋﻪ‬@@
٢٥٠‫ﺩﻗﻴﻘﻪ‬١٧٠٠٠‫ﺛﺎﻧﻴﻪ‬٣‫ﺳﺎﻋﺎﺕ‬
]٩[‫ﺑﺄﺟﺮ‬ ‫ﺑﺎﻟﺴﺎﻋﻪ‬ ‫ﻳﻌﻤﻞ‬ ‫ﻋﺎﻣﻞ‬٨‫ﻋﻤﻞ‬ ‫ﺳﺎﻋﻪ‬ ‫ﻟﻜﻞ‬ ‫ﺟﻨﻴﻬﺎﺕ‬.‫ﻋﻤﻞ‬ ‫ﻓﺈﺫﺍ‬١٢٠‫ﺍﻟﻌﻤﻞ‬ ‫ﺻﺎﺣﺐ‬ ‫ﻟﺪﻯ‬ ‫ﺳﺎﻋﻪ‬
‫؟‬ ‫ﺍﺟﺮﻩ‬ ‫ﻳﻜﻮﻥ‬ ‫ﻓﻜﻢ‬

38. -‫ﺍﻟﺘﺮﻣﻮﻣﺘﺮ‬ ‫ﺑﻮﺍﺳﻄﺔ‬ ‫ﺍﳊﺮﺍﺭﺓ‬ ‫ﺗﻘﺎﺱ‬
-‫ﻭﺣﺪﺓ‬‫ﻭﺭﻣﺰﻫﺎ‬ ‫ﺍﳌﺌﻮﻳﺔ‬ ‫ﺍﻟﺪﺭﺟﺔ‬ ‫ﻫﻰ‬ ‫ﺍﳊﺮﺍﺭﺓ‬ ‫ﻗﻴﺎﺱ‬١°
‫م‬
-‫ﻣﺜﺎﻝ‬:٣٩°
‫ﻣﺌﻮﻳﻪ‬ ‫ﺩﺭﺟﻪ‬ ‫ﻭﺛﻼﺛﻮﻥ‬ ‫ﺗﺴﻌﻪ‬
@@
@}Q@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(‫ﺍﳌﺎﺀ‬ ‫ﻏﻠﻴﺎﻥ‬ ‫ﺩﺭﺟﺔ‬........... =]‫ﺻﻔﺮ‬°
،٢٠°
،٣٧°
،١٠٠°
[
)٢(‫ﺍ‬ ‫ﺣﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬‫ﺍﻟﻌﺎﺩﻯ‬ ‫ﻻﻧﺴﺎﻥ‬....... =]٢٤°
،٣٧°
،٣٩°
،٤٠°
[
)٣(‫ﺣﺮﺍﺭﺗﻪ‬ ‫ﺩﺭﺟﺔ‬ ‫ﻷﻥ‬ ‫ﻟﻠﻄﺒﻴﺐ‬ ‫ﺑﺄﺧﻰ‬ ‫ﺫﻫﺒﺖ‬.......]٣٩°
،٥٠°
،٨٠°
،٩٠°
[
)٤(‫ﺍﳊﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬ ‫ﺗﻜﻮﻥ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺧﻔﻴﻔﻪ‬ ‫ﻣﻼﺑﺲ‬ ‫ﺍﺭﺗﺪﻯ‬.......]٤٠°
،١٥°
،٢٠°
،١٠°
[
)٥(‫ﺛﻘﻴﻠﻪ‬ ‫ﻣﻼﺑﺲ‬ ‫ﺍﺭﺗﺪﻯ‬‫ﺍﳊﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬ ‫ﺗﻜﻮﻥ‬ ‫ﻋﻨﺪﻣﺎ‬........]١٧°
،٣٥°
،٤٥°
،٥٥°
[
)٦(‫ﺍﳌﺮﻳﺾ‬ ‫ﻏﲑ‬ ‫ﻟﻠﺸﺨﺺ‬ ‫ﺍﳉﺴﻢ‬ ‫ﺣﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬......... =]١٧°
،٢٧°
،٣٧°
،٤٧°
[
)٧(‫ﺣﺮﺍﺭﺗﻪ‬ ‫ﺩﺭﺟﺔ‬ ‫ﺑﺎﺭﺩ‬ ‫ﻣﺸﺮﻭﺏ‬ ‫ﻧﺸﺮﺏ‬ ‫ﺍﻥ‬ ‫ﳝﻜﻦ‬.......]‫ﺻﻔﺮ‬°
،١٠°
،٤٠°
،٨٠°
[
)٨(‫ﻳﺴﺘﺤ‬ ‫ﺍﻥ‬ ‫ﳝﻜﻦ‬‫ﺣﺮﺍﺭﺗﻪ‬ ‫ﺩﺭﺟﺔ‬ ‫ﲟﺎﺀ‬ ‫ﺍﻧﺴﺎﻥ‬ ‫ﻢ‬..........]‫ﺻﻔﺮ‬°
،٣٥°
،٩٠°
،٩٩°
[
‫ة‬ ‫ا‬‫ا‬ ‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaÉiaŠÛaÉiaŠÛaÉiaŠÛaÉiaŠÛa@Z@@Z@@Z@@Z@@@ñ‰aŠ§a@òu‰…@@ñ‰aŠ§a@òu‰…@@ñ‰aŠ§a@òu‰…@@ñ‰aŠ§a@òu‰…@@@@@@@@
‫ء‬ ‫اﻝ‬ ‫ن‬ ‫در‬=١٠٠°
‫در‬‫ء‬ ‫اﻝ‬=‫ﺹ‬°
‫اﻝ‬ ‫اﻝ‬ ‫اﻝ‬ ‫ى‬ ‫ﻥ‬
‫ء‬ ‫اﻝ‬ ‫اﻝ‬ ‫اﻝ‬ ‫ى‬ ‫ﻥ‬
‫ﺹ‬ ‫اﻝ‬ ‫او‬ ‫اﻝ‬ ‫ن‬ ‫ﻥ‬ ‫ا‬ ‫ارة‬ ‫ﺡ‬ ‫در‬=٣٧°
‫ا‬ ‫ه‬ ‫ت‬
‫ر‬

39. @}R@@{@òßýÇ@Éš)√(@òßýÇ@ëa)×(
)١(‫ﺻﻔﺮ‬ ‫ﺩﺭﺟﺔ‬ ‫ﰱ‬ ‫ﻭﻫﻮ‬ ‫ﺍﳌﺎﺀ‬ ‫ﻧﺸﺮﺏ‬ ‫ﺍﻥ‬ ‫ﳝﻜﻦ‬°‫ﻡ‬)(
)٢(‫ﺍﱃ‬ ‫ﺍﻧﺴﺎﻥ‬ ‫ﺣﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬ ‫ﺗﺼﻞ‬ ‫ﺍﻥ‬ ‫ﳝﻜﻦ‬٧٠°‫ﻡ‬)(
)٣(‫ﰱ‬ ‫ﺍﻻﻛﱪ‬ ‫ﻫﻮ‬ ‫ﺻﺤﻪ‬ ‫ﺍﻻﻛﺜﺮ‬ ‫ﺍﳉﺴﻢ‬‫ﺣﺮﺍﺭﺗﻪ‬ ‫ﺩﺭﺟﺔ‬)(
)٤(‫ﺻﺤﻴﺎ‬ ‫ﺍﻟﺴﻠﻴﻢ‬ ‫ﺍﳉﺴﻢ‬ ‫ﺣﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬)‫ﺍﻟﻄﺒﻴﻌﻰ‬= (٤٠°‫ﻡ‬)(
)٥(‫ﺣﺮﺍﺭﺗﻪ‬ ‫ﺩﺭﺟﺔ‬ ‫ﲟﺎﺀ‬ ‫ﺍﻧﺴﺎﻥ‬ ‫ﻳﻐﺘﺴﻞ‬ ‫ﺍﻥ‬ ‫ﳝﻜﻦ‬٨٩°‫ﻡ‬)(
)٦(‫ﻷﺧﺮ‬ ‫ﻣﻜﺎﻥ‬ ‫ﻣﻦ‬ ‫ﲣﺘﻠﻒ‬ ‫ﻻ‬ ‫ﺍﻻﺭﺽ‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﺍﳊﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬)(
)٧(‫ﻫﻰ‬ ‫ﺍﻟﺴﻠﻴﻢ‬ ‫ﻟﻠﺸﺨﺺ‬ ‫ﺍﳉﺴﻢ‬ ‫ﺣﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬٣٧°‫ﻡ‬)(
)٨(‫ﺍﻟﺼﻴﻒ‬ ‫ﰱ‬ ‫ﻋﻨﻬﺎ‬ ‫ﺍﻟﺸﺘﺎﺀ‬ ‫ﰱ‬ ‫ﺗﺘﻐﲑ‬ ‫ﻻ‬ ‫ﺍﳌﻌﺘﺎﺩﻩ‬ ‫ﺍﳉﺴﻢ‬ ‫ﺣﺮﺍﺭﺓ‬ ‫ﺩﺭﺟﺔ‬)(
@}S@@{@‘aìÓüa@µi@b¿@òzîz—Ûa@òibuüa@‚a@@
)١(‫ﻣﻼﺑﺲ‬ ‫ﻧﺮﺗﺪﻯ‬ ‫ﺍﻟﺼﻴﻒ‬ ‫ﻓﺼﻞ‬ ‫ﰱ‬.............]‫ﺛﻘﻴﻠﻪ‬ ، ‫ﻣﺘﻮﺳﻄﻪ‬ ، ‫ﺧﻔﻴﻔﻪ‬[
)٢(‫ﻣﻼﺑﺲ‬ ‫ﻧﺮﺗﺪﻯ‬ ‫ﺍﻟﺸﺘﺎﺀ‬ ‫ﻓﺼﻞ‬ ‫ﰱ‬.............]‫ﻣﺘﻮﺳ‬ ، ‫ﺧﻔﻴﻔﻪ‬‫ﺛﻘﻴﻠﻪ‬ ، ‫ﻄﻪ‬[
)٣(‫ﻣﻼﺑﺲ‬ ‫ﻧﺮﺗﺪﻯ‬ ‫ﺍﻟﺮﺑﻴﻊ‬ ‫ﻓﺼﻞ‬ ‫ﰱ‬.............]‫ﺛﻘﻴﻠﻪ‬ ، ‫ﻣﺘﻮﺳﻄﻪ‬ ، ‫ﺧﻔﻴﻔﻪ‬[
)٤(‫ﻣﻼﺑﺲ‬ ‫ﻧﺮﺗﺪﻯ‬ ‫ﺍﳋﺮﻳﻒ‬ ‫ﻓﺼﻞ‬ ‫ﰱ‬.............]‫ﺛﻘﻴﻠﻪ‬ ، ‫ﻣﺘﻮﺳﻄﻪ‬ ، ‫ﺧﻔﻴﻔﻪ‬[

40. @pbãbîjÛa@É»@kîÛbŽa@Z
)١(‫ﺍﳌﻼﺣﻈﺔ‬)٢(‫ﺍﻟﺘﺠﺮﻳﺐ‬)٣(‫ﺍﳌﻴ‬ ‫ﺍﻟﺪﺭﺍﺳﺎﺕ‬‫ﺪﺍﻧﻴﺔ‬
@pbãbîjÛa@Ýîr¸@Z
)١(‫ﺍﻟﺘﻜﺮﺍﺭﻯ‬ ‫ﺍﳌﺪﺭﺝ‬)٢(‫ﺍﳌﺰﺩﻭﺟﺔ‬ ‫ﺍﻻﻋﻤﺪﺓ‬)٣(‫ﺍﻟﺒﻴﺎﻧﻴﺔ‬ ‫ﺍﻟﺸﺠﺮﺓ‬
)١(‫ﺍﺑﺘﺪﺍﺋﻴﻪ‬ ‫ﻣﺪﺭﺳﺔ‬ ‫ﰱ‬ ‫ﺍﻻﻭﱃ‬ ‫ﺍﻟﺼﻔﻮﻑ‬ ‫ﺗﻼﻣﻴﺬ‬ ‫ﻋﺪﺩ‬ ‫ﳝﺜﻞ‬ ‫ﺍﻟﺘﺎﱃ‬ ‫ﺍﳉﺪﻭﻝ‬
‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻫﺬﻩ‬ ‫ﻣﺜﻞ‬‫ﺍﻟﺘﻜﺮﺍﺭﻯ‬ ‫ﺑﺎﳌﺪﺭﺝ‬
)٢(‫ﺍﳌﻌﺎﺭﺽ‬ ‫ﺍﺣﺪ‬ ‫ﰱ‬ ‫ﺍﻟﺴﺠﺎﺩ‬ ‫ﻗﻄﻊ‬ ‫ﻣﻦ‬ ‫ﺍﳌﻨﺘﺠﻪ‬ ‫ﺍﻻﺳﺮ‬ ‫ﻣﻦ‬ ‫ﳎﻤﻮﻋﻪ‬ ‫ﺑﻪ‬ ‫ﺍﺳﻬﻤﺖ‬ ‫ﻣﺎ‬ ‫ﻋﺪﺩ‬ ‫ﻳﺒﲔ‬ ‫ﺍﻟﺘﺎﱃ‬ ‫ﺍﳉﺪﻭﻝ‬
‫ﺍﻟﺘﻜﺮﺍﺭﻯ‬ ‫ﺑﺎﳌﺪﺭﺝ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻫﺬﻩ‬ ‫ﻣﺜﻞ‬
)٣(‫ﺍﳌﻌﺎﺭﺽ‬ ‫ﺍﺣﺪ‬ ‫ﰱ‬ ‫ﺍﻟﺴﺠﺎﺩ‬ ‫ﻗﻄﻊ‬ ‫ﻣﻦ‬ ‫ﺍﳌﻨﺘﺠﻪ‬ ‫ﺍﻻﺳﺮ‬ ‫ﻣﻦ‬ ‫ﳎﻤﻮﻋﻪ‬ ‫ﺑﻪ‬ ‫ﺍﺳﻬﻤﺖ‬ ‫ﻣﺎ‬ ‫ﻋﺪﺩ‬ ‫ﻳﺒﲔ‬ ‫ﺍﻟﺘﺎﱃ‬ ‫ﺍﳉﺪﻭﻝ‬
‫ﺍﻟﺘﻜﺮﺍﺭﻯ‬ ‫ﺑﺎﳌﺪﺭﺝ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻫﺬﻩ‬ ‫ﻣﺜﻞ‬
‫ﺍﻟﺼﻔﻮﻑ‬‫ﺍﻷﻭﻝ‬‫ﺍﻟﺜﺎﱏ‬‫ﺍﻟﺜﺎﻟﺚ‬‫ﺍﻟﺮﺍﺑﻊ‬
‫ﺍﻟﺘﻼﻣﻴﺬ‬ ‫ﻋﺪﺩ‬٨٠٦٠١٠٠٧٠
‫ا‬ ‫ة‬ ‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaëüaëüaëüaëüaÞÞÞÞ@Z@@Z@@Z@@Z@õb–yüaõb–yüaõb–yüaõb–yüa@@@@@@@@
‫ر‬
‫ﺍﻻﺳﺮ‬‫ﺍﻷﻭﱃ‬‫ﺍﻟﺜﺎﻧﻴﺔ‬‫ﺍﻟﺜﺎﻟﺜﺔ‬‫ﺍﻟﺮﺍﺑﻌﻪ‬‫ﺍﳋﺎﻣﺴﻪ‬
‫ﺍﻟﻘﻄﻊ‬ ‫ﻋﺪﺩ‬٣٥٢٥٥١٥٢٠
‫ﺍﻟﻨﺸﺎﻁ‬‫ﺭﻳﺎﺿﻰ‬‫ﺍﺟﺘﻤﺎﻋﻰ‬‫ﻓﲎ‬‫ﺛﻘﺎﰱ‬
‫ﺍﻟﺘﻼﻣﻴﺬ‬ ‫ﻋﺪﺩ‬٤٥٢٥٣٠١٥

41. ‫ا‬
)٤(‫ﰱ‬ ‫ﺍﲪﺪ‬ ‫ﻣﺪﺧﺮﺍﺕ‬ ‫ﻳﺒﲔ‬ ‫ﺍﻟﺘﺎﱃ‬ ‫ﺍﳉﺪﻭﻝ‬٤‫ﺷﻬﻮﺭ‬
‫ﺍﻟﺘﻜﺮﺍﺭﻯ‬ ‫ﺑﺎﳌﺪﺭﺝ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻫﺬﻩ‬ ‫ﻣﺜﻞ‬
)٥(‫ﺍﳌﻌﺎﺭﺽ‬ ‫ﺍﺣﺪ‬ ‫ﰱ‬ ‫ﺍﻟﺴﺠﺎﺩ‬ ‫ﻗﻄﻊ‬ ‫ﻣﻦ‬ ‫ﺍﳌﻨﺘﺠﻪ‬ ‫ﺍﻻﺳﺮ‬ ‫ﻣﻦ‬ ‫ﳎﻤﻮﻋﻪ‬ ‫ﺑﻪ‬ ‫ﺍﺳﻬﻤﺖ‬ ‫ﻣﺎ‬ ‫ﻋﺪﺩ‬ ‫ﻳﺒﲔ‬ ‫ﺍﻟﺘﺎﱃ‬ ‫ﺍﳉﺪﻭﻝ‬
‫ﺍﻟﺘﻜﺮ‬ ‫ﺑﺎﳌﺪﺭﺝ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻫﺬﻩ‬ ‫ﻣﺜﻞ‬‫ﺍﺭﻯ‬
)٦(‫ﺍﳌﻌﺎﺭﺽ‬ ‫ﺍﺣﺪ‬ ‫ﰱ‬ ‫ﺍﻟﺴﺠﺎﺩ‬ ‫ﻗﻄﻊ‬ ‫ﻣﻦ‬ ‫ﺍﳌﻨﺘﺠﻪ‬ ‫ﺍﻻﺳﺮ‬ ‫ﻣﻦ‬ ‫ﳎﻤﻮﻋﻪ‬ ‫ﺑﻪ‬ ‫ﺍﺳﻬﻤﺖ‬ ‫ﻣﺎ‬ ‫ﻋﺪﺩ‬ ‫ﻳﺒﲔ‬ ‫ﺍﻟﺘﺎﱃ‬ ‫ﺍﳉﺪﻭﻝ‬
‫ﺍﻟﺘﻜﺮﺍﺭﻯ‬ ‫ﺑﺎﳌﺪﺭﺝ‬ ‫ﺍﻟﺒﻴﺎﻧﺎﺕ‬ ‫ﻫﺬﻩ‬ ‫ﻣﺜﻞ‬
)٧(‫ﺍﻻﺭﻗﺎﻡ‬ ‫ﻣﻦ‬ ‫ﺗﻜﻮﻳﻨﻬﺎ‬ ‫ﳝﻜﻦ‬ ‫ﳐﺘﻠﻔﻪ‬ ‫ﺍﺭﻗﺎﻡ‬ ‫ﺛﻼﺛﺔ‬ ‫ﻣﻦ‬ ‫ﻣﻜﻮﻥ‬ ‫ﻋﺪﺩ‬ ‫ﻛﻢ‬ ‫ﺍﻭﺟﺪ‬ ‫ﺍﻟﺒﻴﺎﻧﻴﺔ‬ ‫ﺑﺎﻟﺸﺠﺮﺓ‬ ‫ﻣﺴﺘﻌﻴﻨﺎ‬١،٢،٣
)٨(‫ﺍﻻﺭﻗﺎﻡ‬ ‫ﻣﻦ‬ ‫ﺗﻜﻮﻳﻨﻬﺎ‬ ‫ﳝﻜﻦ‬ ‫ﳐﺘﻠﻔﻪ‬ ‫ﺍﺭﻗﺎﻡ‬ ‫ﺛﻼﺛﺔ‬ ‫ﻣﻦ‬ ‫ﺍﳌﻜﻮﻧﻪ‬ ‫ﺍﻷﻋﺪﺍﺩ‬ ‫ﲨﻴﻊ‬ ‫ﻹﳚﺎﺩ‬ ‫ﺑﻴﺎﻧﻴﻪ‬ ‫ﺷﺠﺮﻩ‬ ‫ﺍﺭﺳﻢ‬٢،٥،٧
‫ﺍﻟﺸﻬﺮ‬‫ﻳﻨﺎﻳﺮ‬‫ﻓﱪﺍﻳﺮ‬‫ﻣﺎﺭﺱ‬‫ﺍﺑﺮﻳﻞ‬
‫ﺍﳌﺪﺧﺮﺍﺕ‬
‫ﺑﺎﳉﻨﻴﻪ‬
٨٥٧٤
‫ﺍﻟﺜﻘﺎﰱ‬‫ﺍﻟﻔﲎ‬‫ﺍﻟﺮ‬‫ﻳﺎﺿﻰ‬
‫ﺍﻟﺮﺍﺑﻊ‬ ‫ﺍﻟﺼﻒ‬١٠١٥٣٠
‫ﺍﳋﺎﻣﺲ‬ ‫ﺍﻟﺼﻒ‬٢٠٢٥١٥
‫ﺍﻟﺴﺒﺖ‬‫ﺍﻻﺣﺪ‬‫ﺍﻻﺛﻨﲔ‬‫ﺍﻟﺜﻼﺛﺎﺀ‬‫ﺍﻻﺭﺑﻌﺎﺀ‬‫ﺍﳋﻤﻴﺲ‬
‫ﻭﻟﻴﺪ‬٣٤٣٦٤٢
‫ﻓﺆﺍﺩ‬٤٥٢٥٥٣

42. ‫ﺍﻻﺣﺘﻤﺎﻝ‬ ‫ﺍﻧﻮﺍﻉ‬
)١(‫ﺍﳌﺆﻛﺪ‬ ‫ﺍﳊﺪﺙ‬ ‫ﺍﺣﺘﻤﺎﻝ‬=١
)٢(‫ﺍﳌﺴﺘﺤﻴﻞ‬ ‫ﺍﳊﺪﺙ‬ ‫ﺍﺣﺘﻤﺎﻝ‬=‫ﺻﻔﺮ‬
)٣(‫ﻣﻦ‬ ‫ﻭﺍﻗﻞ‬ ‫ﺻﻔﺮ‬ ‫ﻣﻦ‬ ‫ﺍﻛﱪ‬ ‫ﺍﳌﻤﻜﻦ‬ ‫ﺍﳊﺪﺙ‬ ‫ﺍﺣﺘﻤﺎﻝ‬١
)١(‫ﺑﻪ‬ ‫ﺻﻨﺪﻭﻕ‬٣، ‫ﲪﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬٤‫ﺧﻀﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬.‫ﻓﺄﻭﺟﺪ‬ ‫ﻋﺸﻮﺍﺋﻴﺎ‬ ‫ﻭﺍﺣﺪﻩ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺒﺖ‬ ‫ﻓﺈﺫﺍ‬:
١–‫ﲪﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﺧﻀﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
)٢(‫ﺑﻪ‬ ‫ﺻﻨﺪﻭﻕ‬٤، ‫ﺻﻔﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬٣، ‫ﲪﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬٢‫ﺯﺭﻗﺎﺀ‬ ‫ﻛﺮﻩ‬.‫ﻋﺸﻮﺍﺋ‬ ‫ﻭﺍﺣﺪﻩ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺐ‬ ‫ﰎ‬‫ﺍﻭﺟﺪ‬ ‫ﻴﺎ‬:
١-‫ﺻﻔﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﺯﺭﻗﺎﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
)٣(‫ﻋﻠﻰ‬ ‫ﳛﺘﻮﻯ‬ ‫ﻛﻴﺲ‬٣، ‫ﲪﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬٥‫ﺑﻴﻀﺎﺀ‬ ‫ﻛﺮﺍﺕ‬.‫ﺍﻭﺟﺪ‬ ‫ﻋﺸﻮﺍﺋﻴﺎ‬ ‫ﻭﺍﺣﺪﻩ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺐ‬ ‫ﰎ‬:
١-‫ﺑﻴﻀﺎﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬‫ﲪﺮﺍﺀ‬
)٤(‫ﺑﻪ‬ ‫ﺻﻨﺪﻭﻕ‬٥، ‫ﲪﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬٣، ‫ﺯﺭﻗﺎﺀ‬ ‫ﻛﺮﺍﺕ‬٧‫ﺍﳊﺠﻢ‬ ‫ﻣﺘﺴﺎﻭﻳﺔ‬ ‫ﺧﻀﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬.‫ﻭﺍﺣﺪﻩ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺐ‬ ‫ﰎ‬
‫ﺍﻭﺟﺪ‬ ‫ﺍﻟﻌﻴﻨﲔ‬ ‫ﻣﻐﻤﺾ‬ ‫ﻭﺍﻧﺖ‬ ‫ﻋﺸﻮﺍﺋﻴﺎ‬:
١-‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬‫ﺯﺭﻗﺎﺀ‬
٢-‫ﺧﻀﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٣-‫ﺍﳌ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬‫ﲪﺮﺍﺀ‬ ‫ﲪﺮﺍﺀﻟﻴﺴﺖ‬ ‫ﺴﺤﻮﺑﺔ‬
‫ا‬ ‫ة‬ ‫ا‬ @÷‰†Ûa@÷‰†Ûa@÷‰†Ûa@÷‰†ÛaóãbrÛaóãbrÛaóãbrÛaóãbrÛa@Z@@Z@@Z@@Z@@Þbànyüa@Þbànyüa@Þbànyüa@Þbànyüa@@@@@@@@
‫ر‬

43. )٥(‫ﺑﻪ‬ ‫ﺻﻨﺪﻭﻕ‬٥، ‫ﲪﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬٣، ‫ﺯﺭﻗﺎﺀ‬ ‫ﻛﺮﺍﺕ‬٤‫ﺧﻀﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬‫ﺍﻭﺟﺪ‬ ‫ﻋﺸﻮﺍﺋﻴﺎ‬ ‫ﻭﺍﺣﺪﺓ‬ ‫ﻛﺮﺓ‬ ‫ﺳﺤﺐ‬ ‫ﰎ‬:
١-‫ﺯﺭﻗﺎﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﲪﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٣-‫ﺧﻀﺮﺍﺀ‬ ‫ﻟﻴﺴﺖ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٤-‫ﺍﺣﺘﻤﺎﻝ‬‫ﺧﻀﺮﺍﺀ‬ ‫ﺍﻭ‬ ‫ﲪﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬
)٦(‫ﻋﻠﻰ‬ ‫ﳛﺘﻮﻯ‬ ‫ﺻﻨﺪﻭﻕ‬٤، ‫ﺯﺭﻗﺎﺀ‬ ‫ﻛﺮﺍﺕ‬٢، ‫ﲪﺮﺍﺀ‬٣‫ﻣﻨﻬﺎ‬ ‫ﻭﺍﺣﺪﺓ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺒﺖ‬ ‫ﻓﺈﺫﺍ‬ ، ‫ﺍﳊﺠﻢ‬ ‫ﻧﻔﺲ‬ ‫ﳍﺎ‬ ‫ﺧﻀﺮﺍﺀ‬
‫ﺍﻭﺟﺪ‬ ‫ﺍﻟﻌﻴﻨﲔ‬ ‫ﻣﻐﻤﺾ‬ ‫ﻭﺍﻧﺖ‬:
١-‫ﲪﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﺯﺭﻗﺎﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٣-‫ﺯﺭﻗﺎﺀ‬ ‫ﻟﻴﺴﺖ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
)٧(‫ﻋﻠﻰ‬ ‫ﳛﺘﻮﻯ‬ ‫ﺻﻨﺪﻭﻕ‬٤، ‫ﲪﺮﺍﺀ‬ ‫ﻛﺮﺗﲔ‬ ، ‫ﺯﺭﻗﺎﺀ‬ ‫ﻛﺮﺍﺕ‬٣‫ﺍﳊﺠﻢ‬ ‫ﻧﻔﺲ‬ ‫ﳍﺎ‬ ، ‫ﺧﻀﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬.‫ﻛﺮﻩ‬ ‫ﺳﺤﺒﺖ‬ ‫ﻓﺈﺫﺍ‬
‫ﺍﻭﺟﺪ‬ ‫ﻋﺸﻮﺍﺋﻴﺎ‬ ‫ﻭﺍﺣﺪﺓ‬:
١-‫ﺯﺭﻗﺎﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﲪﺮﺍ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬‫ﺀ‬
٣-‫ﺧﻀﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٤-‫ﺯﺭﻗﺎﺀ‬ ‫ﻟﻴﺴﺖ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٥-‫ﲪﺮﺍﺀ‬ ‫ﻟﻴﺴﺖ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
)٨(‫ﺑﻪ‬ ‫ﺻﻨﺪﻭﻕ‬١٠‫ﻣﻨﻬﺎ‬ ‫ﻛﺮﺍﺕ‬٤، ‫ﲪﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬٦‫ﻣﻐﻤﺾ‬ ‫ﻭﺍﻧﺖ‬ ‫ﻋﺸﻮﺍﺋﻴﺎ‬ ‫ﻭﺍﺣﺪﻩ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺒﺖ‬ ‫ﻓﺈﺫﺍ‬ ‫ﺑﻴﻀﺎﺀ‬ ‫ﻛﺮﺍﺕ‬
‫ﺍﻟﻌﻴﻨﲔ‬.‫ﺍ‬‫ﻭﺟﺪ‬:
١-‫ﲪﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﺑﻴﻀﺎﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬

44. )٩(‫ﺑﻪ‬ ‫ﺻﻨﺪﻭﻕ‬٥، ‫ﻪ‬‫ﻣﺘﺸﺎ‬ ‫ﻛﺮﺍﺕ‬٢‫ﻣﻨﻬﺎ‬، ‫ﺯﺭﻗﺎﺀ‬٣‫ﲪﺮﺍﺀ‬.‫ﻋﺸﻮﺍﺋﻴﺎ‬ ‫ﻭﺍﺣﺪﺓ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺒﺖ‬ ‫ﻓﺈﺫﺍ‬.‫ﺍﻭﺟﺪ‬
١-‫ﲪﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﺍﳌﺴﺤ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬‫ﺯﺭﻗﺎﺀ‬ ‫ﻮﺑﺔ‬
)١٠(‫ﻣﻨﻬﺎ‬ ‫ﻛﺮﺍﺕ‬ ‫ﻋﺸﺮ‬ ‫ﺑﻪ‬ ‫ﺻﻨﺪﻭﻕ‬٤‫ﲪﺮﺍﺀ‬.‫ﺑﻴﻀﺎﺀ‬ ‫ﻭﺍﻟﺒﺎﻗﻰ‬.‫ﺍﻭﺟﺪ‬ ‫ﻋﺸﻮﺍﺋﻴﺎ‬ ‫ﻭﺍﺣﺪﻩ‬ ‫ﻛﺮﻩ‬ ‫ﺳﺤﺐ‬ ‫ﰎ‬:
١-‫ﺑﻴﻀﺎﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
٢-‫ﲪﺮﺍﺀ‬ ‫ﺍﳌﺴﺤﻮﺑﺔ‬ ‫ﺍﻟﻜﺮﺓ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬
@}QQ@@{@ómdí@bß@Ýà×a@@
)١(‫ﺍﳌﺆﻛﺪ‬ ‫ﺍﳊﺪﺙ‬ ‫ﺍﺣﺘﻤﺎﻝ‬............. =
)٢(‫ﺍ‬‫ﺍﳌﺴﺘﺤﻴﻞ‬ ‫ﺍﳊﺪﺙ‬ ‫ﺣﺘﻤﺎﻝ‬........... =
)٣(‫ﺍﳌﻤﻜﻨﻪ‬ ‫ﺍﻻﺣﺪﺍﺙ‬ ‫ﺍﺣﺘﻤﺎﻻﺕ‬ ‫ﳎﻤﻮﻉ‬........ =
)٤(‫ﻭﺍﺣﺪﺓ‬ ‫ﻣﺮﻩ‬ ‫ﻣﻌﺪﻧﻴﻪ‬ ‫ﻗﻄﻌﺔ‬ ‫ﺍﻟﻘﺎﺀ‬ ‫ﻋﻨﺪ‬ ‫ﺻﻮﺭﻩ‬ ‫ﻇﻬﻮﺭ‬ ‫ﺍﺣﺘﻤﺎﻝ‬.......... =
)٥(‫ﻭﺍﺣﺪﺓ‬ ‫ﻣﺮﻩ‬ ‫ﻣﻌﺪﻧﻴﻪ‬ ‫ﻗﻄﻌﺔ‬ ‫ﺍﻟﻘﺎﺀ‬ ‫ﻋﻨﺪ‬ ‫ﻛﺘﺎﺑﺔ‬ ‫ﻇﻬﻮﺭ‬ ‫ﺍﺣﺘﻤﺎﻝ‬.......... =
@@
@}QR@@{µi@b¿@òzîz—Ûa@òibuüa@‚a@‘aìÓüa@@@
)١(‫ﺍﳌﺆﻛﺪ‬ ‫ﺍﳊﺪﺙ‬ ‫ﺍﺣﺘﻤﺎﻝ‬............. =]، ‫ﺻﻔﺮ‬١،٢،
١
٢
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)٢(‫ﺍﳌﺴﺘﺤﻴﻞ‬ ‫ﺍﳊﺪﺙ‬ ‫ﺍﺣﺘﻤﺎﻝ‬.......... =]، ‫ﺻﻔﺮ‬١،٢،
١
٢
[
)٣(‫ﺍﻟﺸﺮﻕ‬ ‫ﻣﻦ‬ ‫ﺍﻟﺸﻤﺲ‬ ‫ﺗﺸﺮﻕ‬ ‫ﺍﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬.........]، ‫ﻣﺆﻛﺪ‬ ، ‫ﳑﻜﻦ‬‫ﻣﺴﺘﺤﻴﻞ‬[
)٤(‫ﻣﻌﺪﻧﻴﻪ‬ ‫ﻧﻘﻮﺩ‬ ‫ﻗﻄﻌﺔ‬ ‫ﺍﻟﻘﺎﺀ‬ ‫ﻋﻨﺪ‬ ‫ﺻﻮﺭﻩ‬ ‫ﻇﻬﻮﺭ‬ ‫ﺍﺣﺘﻤﺎﻝ‬...... =]١،٢، ‫ﺻﻔﺮ‬ ،
١
٢
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)٥(‫ﺍﻟﻌﺪﺩ‬ ‫ﻇﻬﻮﺭ‬ ‫ﺍﺣﺘﻤﺎﻝ‬٣‫ﻭﺍﺣﺪﺓ‬ ‫ﻣﺮﻩ‬ ‫ﻧﺮﺩ‬ ‫ﺯﻫﺮﺓ‬ ‫ﺍﻟﻘﺎﺀ‬ ‫ﻋﻨﺪ‬......]، ‫ﺻﻔﺮ‬١،
١
٢
،
١
٦
[
)٦(‫ﺍﻟﺮﻗ‬ ‫ﻇﻬﻮﺭ‬ ‫ﺍﺣﺘﻤﺎﻝ‬‫ﻢ‬٧‫ﺍ‬ ‫ﻋﻨﺪ‬‫ﻭﺍﺣﺪﻩ‬ ‫ﻣﺮﻩ‬ ‫ﻧﺮﺩ‬ ‫ﺣﺠﺮ‬ ‫ﻟﻘﺎﺀ‬......]، ‫ﺻﻔﺮ‬١،
١
٢
،
١
٦
[