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

ﻝﻮﻠﻌﻗ ﻲﺣ –

ﻱﺮﺤﺒﻟﺍ ﺝﺮﺑ -

ﺮﺋﺍﺰﳉﺍ

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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 ﻦﻴ 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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ﺮﺋﺍﺰﳉﺍ

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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 ﻦﻴﺑ ﻭ

ﺪﻨﻋ ﻥﺎﻌﻃﺎﻘﺘﻳ

ﻭ .

-10 ﻂﻘﻨﻟﺍ ﺔﻋﻮﻤﳎ ﺪﺟﻭﺃ ﻖﻘﲢ ﱵﻟﺍ

|&| <Z √3 i< : .

-11 ﻥﺃ ﻦﻴﺑ 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_, ^D_F^E :

E

- ﺐﺴﺣﺃ C_A

.

-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 ﺮﺒﻋ 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! % ^QRS_S :

! 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 ﻦﻴﺑ 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 ﻦﻴﻋ 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 :

2

ا & 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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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 =4}

9 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

.

ﻝﻮﻠﻌﻗ ﻲﺣ –

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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 –

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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

0

ةر 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

 ; + 

 

 