ﻝﻮﻠﻌﻗ ﻲﺣ –
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א W
א F
م E
3ASSE 2011
א W و 3
د30 , - א د +*) א '( " # א $ %&א
ﻦﻳﺮﻤﺘﻟﺍ ) :
ﻥ (
ﺲﻧﺎﺠﺘﻣﻭ ﺪﻣﺎﻌﺘﻣ ﻢﻠﻌﲟ ﻖﻓﺮﻣ ﺀﺎﻀﻔﻟﺍ ﻥﺇ o, , ,
ﻦﻜﻴﻟ ﺔﻟﺩﺎﻌﳌﺍ ﻭﺫ ﻱﻮﺘﺴﳌﺍ
ﻭ ) (∆ ﻢﻴﻘﺘﺴﳌﺍ
ﻲﻄﻴﺳﻮﻟﺍ ﻞﻴﺜﻤﺘﻟﺍ ﻭﺫ :
1
y 2t
z t 2
-1 ﺔﻄﻘﻨﻟﺍ ﻞﻫ ﻱﻮﺘﺴﳌﺍ ﱃﺇ ﻲﻤﺘﻨﺗ
ﻞﻠﻋ ؟ .
-2 ﻢﻴﻘﺘﺴﳌﺍ ﻥﺃ ﲔﺑ )
(∆ ﻱﻮﺘﺴﳌﺍ ﰲ ﻯﻮﺘﳏ .
-3 ﻦﻜﻴﻟ ﺔﻄﻘﻨﻟﺍ ﻦﻣ ﺭﺎﳌﺍ ﻱﻮﺘﺴﳌﺍ
ﻢﻴﻘﺘﺴﳌﺍ ﺪﻣﺎﻌﻳﻭ )
.(∆
ﻱﻮﺘﺴﻤﻠﻟ ﺔﻴﺗﺭﺎﻜﻳﺪﻟﺍ ﺔﻟﺩﺎﻌﳌﺍ ﺪﺟﻭﺃ .
-4 ﺔﻄﻘﻨﻟﺍ ﺕﺎﻴﺛﺍﺪﺣﺇ ﺪﺟﻭﺃ
ﻱﻮﺘﺴﳌﺍ ﻊﻃﺎﻘﺗ ﺔﻄﻘﻧ ﻢﻴﻘﺘﺴﳌﺍﻭ
) .(∆
-5 ﻥﺃ ﲔﺑ
√3 .
-6 ﻦﻜﻴﻟ ﻭ ﻲﻘﻴﻘﺣ ﺩﺪﻋ
ﻢﻴﻘﺘﺴﳌﺍ ﻦﻣ ﺔﻄﻘﻧ )
(∆
ﻲﻘﻴﻘﺣ ﺩﺪﻋ ﻞﻛ ﻞﺟﺃ ﻦﻣ ﻪﻧﺃ ﲔﺑ :
M 6 12 9
.
-7 ﺑ ﻥﺃ ﻦﻴ ـﻟ ﻯﺮﻐﺼﻟﺍ ﺔﻤﻴﻘﻟﺍ ﻲﻫ
ﻦﻳﺮﻤﺘﻟﺍ ) :
ﻥ (
ﺮﺷﺎﺒﻣ ﺲﻧﺎﺠﺘﻣﻭ ﺪﻣﺎﻌﺘﻣ ﻢﻠﻌﲟ ﻖﻓﺮﻣ ﺐﻛﺮﳌﺍ ﻱﻮﺘﺴﳌﺍ
!", #, $%
ﻪﺗﺪﺣﻭ .
ﻂﻘﻨﻟﺍ ﻦﻜﺘﻟ ﺐﻴﺗﺮﺘﻟﺍ ﻰﻠﻋ ﻖﺣﺍﻮﻠﻟﺍ ﺕﺍﻭﺫ
.
&' 2( &) √3 ( &* √3 (
-1 ﺐﺘﻛﺃ
&' &) ﻭ
&* ، ﻲﺳﻷﺍ ﻞﻜﺸﻟﺍ ﻰﻠﻋ .
-2 ﺮﻄﻗ ﻒﺼﻧﻭ ﺰﻛﺮﻣ ﺞﺘﻨﺘﺳﺍ (r)
ﻞﻤﺸﺗ ﱵﻟﺍ ﺓﺮﺋﺍﺪﻟﺍ C,B,A
.
-3 ﺓﺮﺋﺍﺪﻟﺍ ﺊﺸﻧﺃ (r)
ﻂﻘﻨﻟﺍ ﻢﻠﻋﻭ C,B,A
. ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ
ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ
ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ 3////1 ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ
1
ﻝﻮﻠﻌﻗ ﻲﺣ –
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+, U,./ 1 2 U,
-4 ﺔﺒﺴﻨﻟﺍ ﺐﺘﻛﺃ
01203 :
45246
ﻲﺳﻷﺍ ﻞﻜﺸﻟﺍ ﻰﻠﻋ ﰒ ﻱﱪﳉﺍ ﻞﻜﺸﻟﺍ ﻰﻠﻋ .
-5 ﺚﻠﺜﳌﺍ ﺔﻌﻴﺒﻃ ﺞﺘﻨﺘﺳﺍ .
-6 ﻟﻴ ﻦﻜ ﻭﺫ ﻥﺍﺭﻭﺪﻟﺍ ﳌﺍ
ﺰﻛﺮ ﺔﻳﻭﺍﺰﻟﺍﻭ
7
.8
ﺔﻘﺣﻻ ﻥﺃ ﲔﺑ ﺓﺭﻮﺻ
ﻥﺍﺭﻭﺪﻟﺎﺑ ﻲﻫ
&9: √3 ( :
-7 ﲔﺑ ﻥﺃ ﻭ ﺓﺮﺋﺍﺪﻟﺍ ﺮﻄﻗ ﻰﻠﻋ ﻥﺎﺗﺮﻇﺎﻨﺘﻣ .
-8 ﺔﻟﺩﺎﻌﻣ ﺪﺟﻭﺃ
ﺓﺮﺋﺍﺪﻟﺍ ﺓﺭﻮﺻ
ﻥﺍﺭﻭﺪﻟﺎﺑ .
-9 ﻥﺃ ﻦﻴﺑ ﻭ
ﺪﻨﻋ ﻥﺎﻌﻃﺎﻘﺘﻳ
ﻭ .
-10 ﻂﻘﻨﻟﺍ ﺔﻋﻮﻤﳎ ﺪﺟﻭﺃ ﻖﻘﲢ ﱵﻟﺍ
|&| <Z √3 i< : .
-11 ﻥﺃ ﻦﻴﺑ ﻭ
ـﻟ ﻥﺎﻴﻤﺘﻨﺗ .
ﻦﻳﺮﻤﺘﻟﺍ ) :
ﻥ (
ﺔﻳﺩﺪﻌﻟﺍ ﺔﻴﻟﺎﺘﺘﳌﺍ ﻦﻜﺘﻟ ﻰﻠﻋ ﺔﻓﺮﻌﻣ
ـﺑ ! :
?@A 1, @/ / U,. U,./ /BU,
-1 ﺐﺴﺣﺃ
ﺞﺘﻨﺘﺳﺍﻭ ﻥﺍ
ﺔﻴﺑﺎﺴﺣ ﻻﻭ ﺔﻴﺳﺪﻨﻫ ﺖﺴﻴﻟ .
-2 ﻦﻜﺘﻟ
"
ﺔﻳﺩﺪﻌﻟﺍ ﺔﻴﻟﺎﺘﺘﳌﺍ ﻰﻠﻋ ﺔﻓﺮﻌﳌﺍ
ـﺑ ! :
- ﺐﺴﺣﺃ +A
.
-3 ﻦﻋ ﱪﻋ +,./
ﺔﻟﻻﺪﺑ +, .
؟ﺞﺘﻨﺘﺴﺗ ﺍﺫﺎﻣ
-4 ﺐﺘﻛﺃ +,
ﺔﻟﻻﺪﺑ .n
-5 ﻦﻜﺘﻟ
!C,% ﺔﻳﺩﺪﻋ ﺔﻴﻟﺎﺘﺘﻣ
ﻰﻠﻋ ﺔﻓﺮﻌﻣ ـﺑ N
C, DFE :
E
- ﺐﺴﺣﺃ CA
.
-6 ﺓﺍﻭﺎﺴﳌﺍ ﻝﺎﻤﻌﺘﺳﺎﺑ W,./ ﻦﻋﱪﻋ U,./ V, /U, :
ﺔﻟﻻﺪﺑ U, V, ﻭ .
ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ
ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ
ﺔﺤﻔﺼﻟﺍ ﺐﻠﻗﺍ 3////2 ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ
ﻝﻮﻠﻌﻗ ﻲﺣ –
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ﺮﺋﺍﺰﳉﺍ
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-7 ﻥﺃ ﺞﺘﻨﺘﺳﺍ
W,./ W, 2
.
-8 ﻦﻋ ﺮﺒﻋ W,
ﺔﻟﻻﺪﺑ .n
ﻦﻳﺮﻤﺘﻟﺍ ) :
ﻥ (
ﻝﻭﻷﺍ ﺀﺰﳉﺍ :
ﻦﻜﺘﻟ I ﻰﻠﻋ ﺔﻓﺮﻌﳌﺍ ﺔﻟﺍﺪﻟﺍ J0 , ∞M
ـﺑ I! % 1 NO :
-1 ﺕﺍﲑﻐﺗ ﺱﺭﺩﺃ ﺔﻟﺍﺪﻟﺍ
I .
-2 ﺓﺭﺎﺷﺇ ﺞﺘﻨﺘﺳﺍ I! %
ﱐﺎﺜﻟﺍ ﺀﺰﳉﺍ :
ﻦﻜﺘﻟ P ﻰﻠﻋ ﺔﻓﺮﻌﳌﺍ ﺔﻟﺍﺪﻟﺍ J0 , ∞M
ـﺑ P! % QRSS :
! T% ﻭ ﺔﻟﺍﺪﻠﻟ ﱐﺎﻴﺒﻟﺍ ﲎﺤﻨﳌﺍ P
ﺲﻧﺎﺠﺘﳌﺍ ﻭ ﺪﻣﺎﻌﺘﳌﺍ ﻢﻠﻌﳌﺍ ﰲ
!U, , %
-1 ﺔﻳﺎ ﺱﺭﺩﺃ P
ﺭﺍﻮﲜ
؟ﻲﺳﺪﻨﳍﺍ ﲑﺴﻔﺘﻟﺍ ﻮﻫ ﺎﻣ ، o
-2 ﺔﻳﺎ ﺪﺟﻭﺃ P
ﺭﺍﻮﲜ +∞
ﻢﻴﻘﺘﺴﳌﺍ ﻥﺃ ﻦﻴﺑ ﰒ )
(D ﺔﻟﺩﺎﻌﳌﺍ ﻭﺫ ﻞﺋﺎﻣ ﺏﺭﺎﻘﻣ ﻢﻴﻘﺘﺴﻣ
.
-3 ﻖﺘﺸﳌﺍ ﺪﺟﻭﺃ PV! %
ﻞﺟﺃ ﻦﻣ J0 , ∞M
.
-4 ﺞﺘﻨﺘﺳﺍ ﺕﺍﲑﻐﺗ P ﺕﺍﲑﻐﺘﻟﺍ ﻝﻭﺪﺟ ﺊﺸﻧﺃ ﰒ .
-5 ﺔﻄﻘﻨﻟﺍ ﻦﻴﻋ A
ﲎﺤﻨﳌﺍ ﻦﻣ ﻥﻮﻜﻳ ﱵﻟﺍ T
ﺎﻬﻴﻓ ﺱﺎﻤﳌﺍ ) (∆ ﻢﻴﻘﺘﺴﳌﺍ ﻱﺯﺍﻮﻳ
!D%
.
-6 ﻢﺳﺭﺃ ) (∆
!D% ،
T ، .
ﻖـــﻴﻓﻮﺘﻟﺎﺑ
ﻖـــﻴﻓﻮﺘﻟﺎﺑﻖـــﻴﻓﻮﺘﻟﺎﺑ
ﻖـــﻴﻓﻮﺘﻟﺎﺑ 3////3 ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ ﺔﺤﻔﺼﻟﺍ
ﻝﻮﻠﻌﻗ ﻲﺣ –
ﻱﺮﺤﺒﻟﺍ ﺝﺮﺑ -
ﺮﺋﺍﺰﳉﺍ
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ــ ! ص#$%ا '!ر)*%ا +*,*%ا
ﻯﻮﺘﺴﳌﺍ 3ASS :
l^é•^è†Ö]<ì^Ú<»<è†rjÖ]<^è…çÖ^ÓfÖ]<xév’i l^é•^è†Ö]<ì^Ú<»<è†rjÖ]<^è…çÖ^ÓfÖ]<xév’i l^é•^è†Ö]<ì^Ú<»<è†rjÖ]<^è…çÖ^ÓfÖ]<xév’i l^é•^è†Ö]<ì^Ú<»<è†rjÖ]<^è…çÖ^ÓfÖ]<xév’i
ﻉﻮﺿﻮﳌﺍ :02
012*3%ا لو6ا
:
ا
ي ا
. نأ ي ا د ا ض 1
2 ا د ! ا " # ا ض ي
$ % &' $ أ
ي ا () *+ , ا
.
3
ي ا د
( )
ه :
2 3 0
− + − − =
4 23 ا
(0, 2,1)
5 6 ا 6 7 + ا و
:
2 2 2
1 1 1 3
= + + =
6 7 آ :
2ا & ا () ;' ا 7 :
$ :
7
2= > تاذ 'د ) اد
6A و
( )=6 2+12 +9
ق D 7 م
( ) 12 12
:
′ = −
( ) 0
′ =
ن
=0
;' 7
( )1 =3
$
2 1 =3
يا : $
+ ()
1'7#8%ا 012*3%ا :
1 !Fا 7 A ا :
3
2 2 π
=
5
و
2 2 π
=
و
2 6 π
=
2 نأ Gو :
= = =2
$
= = =2
6 ط ا يأ هIآ= ا ة=Kا ا
LM و
ه= N
=2
ﻝﻮﻠﻌﻗ ﻲﺣ –
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ﺮﺋﺍﺰﳉﺍ
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3 '=+ ا 7 A ا :
1 3
2 2
− = +
−
4
!Fا 7 A ا :
3
− π
− =
5 ةر + ا نا ( − )= π6 ( − ) :
نارود $ أ ل QIآ=
سأ= ا 'وازو
3 ه و π
(' ا
− 1
− =
6 N ا $ و
و 6 ' ) ا 'اوز ة
3 ه π
T(# ا $
عVWFا X' .
6 ه نارو ا ةر +)
( )
:
1 3
2 2
2 2
′ + = + +
أ + ا ;' 7
= − 3−
7 ا LM ب &7
[ ′ ]
:
2 0
′+
= =
8 نا
′ةر [
QIآ= نارو 7 $ 'واز و
3
π
ة=Kا ا د $ = ا LM ل 3 () \ &' نارو ا و :
(
+ 3)
2+( +1)2 =49 6 ا ;' 7 ناI' ناIآ= % ن =Kا ا و
ا % ا 6 =Kا ا د
6 =Kا ا .
10 ا ر & ] ا )
[ ′]
$ د :
2 3 +2 +4
11 د ا * & $ ا 6 ا ض
.
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9%#8%ا 012*3%ا :
2
1
3
= 4
ن ! ه ^ ا نا :
2 1
1 0
≠
نF 7 _ ^ ا نا :
2− 1≠ 1− 0
0 =1
2
3 نا ` '
1
:
1
+ = 2
$ %! !ا ! ه
1
=2
0 =1
و
4 م ا & ا
1 2
=
0 = −1
5
1 2
6
+ = +
7 *7 ا با ا 6
1 2
:
+ = +
$ %! !ا 7 _ 2
ﻝﻮﻠﻌﻗ ﻲﺣ –
ﻱﺮﺤﺒﻟﺍ ﺝﺮﺑ -
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8 ا & ا م
2 1
= −
+:ا2%ا 012*3%ا :
لو6ا ء<,%ا :
1 ل ا () ق DV (7 N اد
]0;+∞[
:
* b ا $
( ) 2 2−1
:
′ =
"Gأ 6
0ةر Dا
′(' آ ن A :
2
)
0; 2
$ ` ! * b ا نا
MN
) و
2; 2
+∞
* b ا نا
`G 6 ة 'اI .
2 ى=>M ا ' & ا ا
( )2 0
( ) 0
$
'7#8%ا ء<,%ا :
0 ( )
lim+
→ = −∞
$ د بر , ا ا "+ $ و
=0
( )
4
lim→+∞ = +∞
( )
و
( )
lim 0
→+∞ − =
$
="K بر , .
5 %g'= ل & () ق b( (7 N .
* b ا و :
( ) ( )
′ = 2
6 f ن ة 'اI
+G
1
7
; +