ﻝﻮﻠﻌﻗ ﻲﺣ –
ﻱﺮﺤﺒﻟﺍ ﺝﺮﺑ -
ﺮﺋﺍﺰﳉﺍ
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2012
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2 V 30 ^‰
< < < < l^é•^è†Ö] <ì^Ú<»<oÖ^nÖ]<Ø’Ë×Ö<è†rjÖ]<<…^fj}÷] <
ﻦﻳﺮﻤﺘﻟﺍ ) :01
ﻥ05 (
-1 ﺔﺤﻴﺤﺻ ﺔﻠﻤﳉﺍ ﺖﻧﺎﻛ ﻥﺇ ﺔﻴﻟﺎﺘﻟﺍ ﺕﻻﺎﳊﺍ ﻦﻣ ﺔﻟﺎﺣ ﻞﻛ ﰲ ﺮﻛﺫﺃ ﻞﻴﻠﻌﺘﻟﺍ ﻊﻣ ﺔﺌﻃﺎﺧ ﻭﺃ
.
[ ] [ ] [ ]
152≡ 2 3 , 29≡ − 6 , 13− ≡4 5
-2 ﺔﻴﻌﻴﺒﻄﻟﺍ ﺩﺍﺪﻋﻷﺍ ﻞﻛ ﻦﻴﻋ ﻦﻣ ﺮﻐﺻﻷﺍ
ﻖﻘﲢ ﱵﹼﻟﺍﻭ 30
[ ]
4 7 . ≡
-3 ﻱﻭﺎﺴﻳ ﻭﺃ ﻦﻣ ﱪﻛﺃ ﻲﻌﻴﺒﻃ ﺩﺪﻋ ﻲﻌﻴﺒﻄﻟﺍ ﺩﺪﻌﻟﺍ ﻢﻴﻗ ﻦﻴﻋ ،2
ﻖﻘﲢ ﱵﹼﻟﺍ
[ ]
27≡5 .
-4 ﻖﻘﳛ ﺢﻴﺤﺻ ﺩﺪﻋ
[ ]
30757 10 ﺔﻳﺪﻴﻠﻗﻹﺍ ﺔﻤﺴﻘﻟﺍ ﻲﻗﺎﺑ ﻮﻫ ﺎﻣ ≡
ـﻟ ﻰﻠﻋ .10
-5 ﺔﺤﻴﺤﺼﻟﺍ ﺩﺍﺪﻋﻷﺍ ﻦﻴﻋ ﻖﻘﳓ ﱵﹼﻟﺍ
[ ]
27 ≡2 5 .
ﻦﻳﺮﻤﺘﻟﺍ )02
ﻥ07 :(
ﻰﻠﻋ ﺔﻓﺮﻌﻣ ﺔﻳﺩﺪﻋ ﺔﻴﻟﺎﺘﺘﻣ ( ) ﻲﻠﻳ ﺎﻤﻛ
:
3 4 5
= − +
-1 ﺩﻭﺪﳊﺍ ﺐﺴﺣﺃ
3, 2, ,1 0
.
-2 ( )
( )
ﻭ ﻲﻠﻳ ﺎﻤﻛ ﻥﺎﺘﻓﺮﻌﻣ ﻥﺎﺘﻴﻟﺎﺘﺘﻣ:
ﻲﻌﻴﺒﻃ ﺩﺪﻋ ﻞﻛ ﻞﺟﺃ ﻦﻣ :
4 5
= − ،
3 . =
ﺃ - ﻥﺃ ﺖﺒﺛﺃ
( )
ﺎﻬﺳﺎﺳﺃ ﺪﻳﺪﲢ ﺐﻠﻄﻳ ﺔﻴﺑﺎﺴﺣ ﺔﻴﻟﺎﺘﺘﻣ
ﻝﻭﻷﺍ ﺎﻫﺪﺣﻭ . 0
ﺏ - ﻥﺃ ﺖﺒﺛﺃ
( )
ﺎﻬﺳﺎﺳﺃ ﺪﻳﺪﲢ ﺐﻠﻄﻳ ﺔﻴﺳﺪﻨﻫ ﺔﻴﻟﺎﺘﺘﻣ ﻝﻭﻷﺍ ﺎﻫﺪﺣﻭ
. 0
-3 ﺔﻴﻟﺎﺘﻟﺍ ﻊﻴﻣﺎﺍ ﺐﺴﺣﺃ :
-1
1 = 0 + 1 +...+ -2
2 = 0 + 1+...+ -3
3 = 0 + 1 +...+
ا ا 2/1 ا
2
ﻦﻳﺮﻤﺘﻟﺍ ) :03
ﻥ08 (
ﻰﻠﻋ ﺔﻓﺮﻌﻣ ﺔﻳﺩﺪﻋ ﺔﻟﺍﺩ ـﺑ
: ( ) = 3 −3 +2
( )
ﺔﻟﺍﺪﻠﻟ ﻞﺜﻤﳌﺍ ﱐﺎﻴﺒﻟﺍ ﺎﻫﺎﻨﺤﻨﻣ ﺲﻧﺎﺠﺘﻣﻭ ﺪﻣﺎﻌﺘﻣ ﻢﻠﻌﻣ ﱃﺇ ﺏﻮﺴﻨﻣ ﻮﺘﺴﻣ ﰲ
(
, ,)
.
-1 ﺔﻟﺍﺪﻟﺍ ﺕﺍﲑﻐﺗ ﺱﺭﺩﺃ .
-2 ﻦﻴﺑ ﻲﻘﻴﻘﺣ ﺩﺪﻋ ﻞﻛ ﻞﺟﺃ ﻦﻣ ﻪﻧﺃ :
( ) =( +2)( −1)2
.
-3 ﻊﻃﺎﻘﺗ ﻂﻘﻧ ﻦﻴﻋ
( )
ﺕﺎﻴﺛﺍﺪﺣﻹﺍ ﻱﺭﻮﳏ ﻲﻠﻣﺎﺣ ﻊﻣ .
-4 ﺱﺎﻤﳌﺍ ﺔﻟﺩﺎﻌﻣ ﺩﺪﺣ )
(∆ ﲎﺤﻨﻤﻠﻟ
( )
ﺎﻬﺘﻠﺻﺎﻓ ﱵﻟﺍ ﺔﻄﻘﻨﻟﺍ ﰲ
0 =0 .
-5 ﻢﺳﺭﺃ ) (∆
( )
ﰒ .
ﻝﻮﻠﻌﻗ ﻲﺣ –
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ﻥﺎﺤﺘﻣﻹﺍ ﺢﻴﺤﺼﺗ ﺎﻳﺭﻮﻟﺎﻜﺒﻟﺍ
ﻢﻗﺭ ﱯﻳﺮﺠﺘﻟﺍ ﺓﺩﺎﻣ ﰲ 01
ﺕﺎﻴﺿﺎﻳﺮﻟﺍ
ﻲﺳﺍﺭﺪﻟﺍ ﻡﺎﻌﻟﺍ :
2011-2012
ﻲﺳﺍﺭﺪﻟﺍ ﻯﻮﺘﺴﳌﺍ :
3ASL-3ASLLE
:ﻝﻭﻷﺍ ﻦﻳﺮﻤﺘﻟﺍ ﺔﻟﺎﳊﺍ :01 ﻥﻷ ﺔﺌﻃﺎﺧ
[ ]
13≡ −2 5
ﺔﻟﺎﳊﺍ :02 ﻥﻷ ﺔﺤﻴﺤﺻ 29= (6 5) 1× −
ﺔﻟﺎﳊﺍ :03 ﻥﻷ ﺔﺤﻴﺤﺻ :
ﲏﻌﻳ
152 3= +2
-2 ﻷﺍ ﲔﻴﻌﺗ ﺔﻴﻌﻴﺒﻄﻟﺍ ﺩﺍﺪﻋ
ﻦﻣ ﺮﻐﺼﻟﺍ ﻖﻘﲢ ﱵﻟﺍ 30
[ ]
≡4 7
[ ]
≡4 7 ﲏﻌﻳ
:
7 4
= +
ﻞﺟﺃ ﻦﻣ
=1 ﻥﺈﻓ
= 4 ﻞﺟﺃ ﻦﻣ
=2 ﻥﺈﻓ
=18
ﻞﺟﺃ ﻦﻣ
=1 ﻥﺈﻓ
=11 ﻞﺟﺃ ﻦﻣ
=3 ﻑ
’ ﻥ
=25
ﻞﺟﺃ ﻦﻣ
=4 32 ﻥﺈﻓ
ﻢﻴﻗ ﻪﻨﻣﻭ ﺽﻮﻓﺮﻣ =
{
4,11,18, 25}
ﻲﻫ =ﱐﺎﺜﻟﺍ ﻉﻮﺿﻮﳌﺍ
3 152
2 50
-3 ﺔﻤﻴﻗ ﲔﻌﺗ
[ ]
ﺚﻴﺣ 27 5≡ﺎﻨﻳﺪﻟ
[ ]
27 5≡ ﲏﻌﻳ
: 27= × +5
27 5− =
ﻞﺟﺃ ﻦﻣ
= 2
=11 ﻞﺟﺃ ﻦﻣ
11 2
= − = = −
22=
ﻞﺟﺍ ﻦﻣ
=11 2
ﻞﺟﺃ ﻦﻣ = 22 n= 11
= −
ﻢﻴﻗ ﻪﻨﻣﻭ
{
1, 2, 2,11}
ﻲﻫ= − −
ﻢﻴﻗ ﲔﻴﻌﺗ
[ ]
ﺚﻴﺣ 2+ ≡2 5[ ]
2 ≡2 5
[ ]
≡1 5
ﻪﻨﻣﻭ
5 1
= +
-4 ﺔﻤﺴﻗ ﻲﻗﺎﺑ ﺩﺎﳚﺇ ﻰﻠﻋ
:10
ﻥﺫﺇ ﺔﻤﺴﻗ ﻲﻗﺎﺒﻓ 30757
ﻰﻠﻋ ﻮﻫ 10
7
10 30757
7 3075
ﻝﻮﻠﻌﻗ ﻲﺣ –
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ﺮﺋﺍﺰﳉﺍ
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ﺔﺤﻴﺤﺼﻟﺍ ﺩﺍﺪﻌﻟﺍ ﲏﻌﻳ ﻖﻘﲢ ﱵﻟﺍ
.
ﱐﺎﺜﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ ﺩﻭﺪﳊﺍ ﺏﺎﺴﺣ :
: ﺎﻨﻳﺪﻟ
3 4 5
= − +
ﺏﺎﺴﺣ 1 : 0
0
0 =(3) −4(0) 5 2+ =
ﺏﺎﺴﺣ 2
1:
1 =4:
ﺏﺎﺴﺣ 3 : 2
2
2 =(3) −4(2) 5 4+ =
ﺏﺎﺴﺣ 4 : 3
3
3 =(3) −4(3) 5 20+ =
ﺃ - ﻥﺃ ﺕﺎﺒﺛﺍ ( )
ﺔﻴﺑﺎﺴﺣ ﺔﻴﻟﺎﺘﺘﻣ :
) ( ) ﺔﻴﺑﺎﺴﺣ ﺔﻴﻟﺎﺘﺘﻣ (
ﲏﻌﻳ ) ﻲﻌﻴﺒﻃ ﺩﺪﻋ ﻞﻛ ﻞﺟﺃ ﻦﻣ
1 ،
+ − =
(
1 4( 1) 5 4 5
+ − = + − − +
1 4 4 7 4 5
+ − = + − − +
1 4
+ − =
ﻪﻨﻣﻭ ) ( ﺎﻬﺳﺎﺳﺍ ﺔﻴﺑﺎﺴﺣ ﺔﻴﻟﺎﺘﺘﻣ
=4
ﺎﻫﺪﺣ ﺏﺎﺴﺣ ﻝﻭﻷﺍ
0 = (0) 5− = −5 :
ﺏ - ﻥﺃ ﺕﺎﺒﺛﺇ
( ) ﺔﻴﺳﺪﻨﻫ ﺔﻴﻟﺎﺘﺘﻣ :
) ( ) ﺔﻴﺳﺪﻨﻫ ﺔﻴﻟﺎﺘﺘﻣ (
ﲏﻌﻳ ) ﻲﻌﻴﺒﻃ ﺩﺪﻋ ﻞﻛ ﻞﺟﺃ ﻦﻣ
+1 = (
1
1 3 3 3
3 3 3
+
+ ×
= = =
ﻪﻨﻣﻭ ( ) ﺎﻬﺳﺎﺳﺃ ﺔﻴﺳﺪﻨﻫ ﺔﻴﻟﺎﺘﺘﻣ
=3
ﻝﻭﻷﺍ ﺎﻫﺪﺣ ﺏﺎﺴﺣ
0 :
0 =3 =1
ﻊﻴﻣﺎﺍ ﺏﺎﺴﺣ :
ﺎﻨﻳﺪﻟ
1 = 0 + 1 +...+ :
) ﻷﺍ ﺪﳊﺍ ﲑﺧ + ﻝﻭﻷﺍ ﺪﳊﺍ
ﺩﻭﺪﳊﺍ ﺩﺪﻋ (
= S1
0
1( )
2
= + +
1( 5 4 5) 2
= + − + −
1( 10 4 ) 2
= + − +
( 1)( 5 2 )
= + − +
ﺏﺎﺴﺣ : 2
2 = 0 + 1+...+
( 1)
1
دو اد−
ﻝﻭﻷﺍ ﺪﳊﺍ −
2=
ﺏﺎﺴﺣ : 3
3 = 0 + 1+....+ ﻥﺃ ﻆﺣﻼﻧ
= −
0 0 0
1 1 0
= −
= −
. . .
. . .
. . .
= −
ﺪﳒ ﻊﻤﳉﺎﺑ :
3 = 2 − 1
1 3
3 1
( 1)( 5 2 ) 2
+ −
= − + − +
ﻝﻮﻠﻌﻗ ﻲﺣ –
ﻱﺮﺤﺒﻟﺍ ﺝﺮﺑ -
ﺮﺋﺍﺰﳉﺍ
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ﺚﻟﺎﺜﻟﺍ ﻦﻳﺮﻤﺘﻟﺍ :
-1 ﺔﻟﺍﺪﻟﺍ ﺕﺍﲑﻐﺗ ﺔﺳﺍﺭﺩ
:
ﺕﺎﻳﺎﻬﻨﻟﺍ •
3 : ( )
( )
3→−∞ →−∞
→+∞ →+∞
= = −∞
= = +∞
ﺔﻘﺘﺸﳌﺍ •
: ﺔﻟﺍﺪﻟﺍ ﻰﻠﻋ ﻥﺎﻘﺗﻺﻟ ﺔﻠﺑﺎﻗ
ﻲﻘﻴﻘﺣ ﺩﺪﻋ ﻞﻛ ﻞﺟﺃ ﻦﻣ ﻲﻫ ﺔﻘﺘﺸﳌﺍ ﺎﻬﺘﻟﺍﺩﻭ
ﻦﻣ
3 2
'( ) ( 3 2) ' '( ) 3 3
= − +
= −
ﺩ •
ﺭ ﻖﺘﺸﳌﺍ ﺓﺭﺎﺷﺍ ﺔﺳﺍ :
2 2
3 3 0
1
− = =
1 1
= −
=
ﺓﺭﺎﺷﻹﺍ ﻝﻭﺪﺟ :
1 +1 +
−∞ ∞
'( )
ﻝﺎﺍ ﻰﻠﻋ
] [ ] [
'( )≻0 −∞ − ∪ +∞, 1 1,
ﺔﻟﺍﺪﻟﺎﻓ ﻝﺎﺍ ﻰﻠﻋ ﺎﻣﺎﲤ ﺓﺪﻳﺍﺰﺘﻣ
]
−∞ − ∪ +∞, 1] [
1,[
+ +
ﻝﺎﺍ ﻰﻠﻋ
] [
'( )≺0 1,1−
ﺔﻟﺍﺪﻟﺎﻓ ﻝﺎﺍ ﻰﻠﻋ ﺎﻣﺎﲤ ﺔﺼﻗﺎﻨﺘﻣ
[
−1,1]
ﻝﻭﺪﺟ ﺕﺍﲑﻐﺘﻟﺍ :
1 +1 +
−∞ ∞
'( )
( )
3 3
( 1) ( 1) 3( 1) 2 4 (1) (1) 3(1) 2 0
− = − − − + =
= − + =
-2 ﻲﻘﻴﻘﺣ ﺩﺪﻋ ﻞﻛ ﻞﺟﺃ ﻦﻣ ﺕﺎﺒﺛﺇ :
ﺎﻨﻳﺪﻟ ( ) (= +2)( −1)2
ﺎﻨﻳﺪﻟ :
2 2
3 2 2
3
( 2)( 1) ( 2)( 2 1)
= x 2 2 4 2 = x 3 2
+ − = + − +
− + + − +
− +
ﻊﻃﺎﻘﺗ ﻂﻘﻧ ﲔﻴﻌﺗ ( )
ﺕﺎﻴﺛﺍﺪﺣﻹﺍ ﻱﺭﻮﳏ ﻲﻠﻣﺎﺣ ﻊﻣ
ﺐﻴﺗﺍﺮﺘﻟﺍ ﺭﻮﳏ 1 :
=0 (0) = 2
{ }
( )∩( ' )= (0.2)
ﻞﺻﺍﻮﻔﻟﺍ ﺭﻮﳏ ﻊﻣ ( ) =0
+ +
( 1)−
−∞
+∞
(1)
ﻝﻮﻠﻌﻗ ﻲﺣ –
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2
2
( 2)( 1) 0
2 0
( 1) 0
2 1
+ − =
+ =
− =
= −
=
{ }
( )∩( ' )= ( 2,0), (1,0)−
ﺱﺎﻤﳌﺍ ﺔﻟﺩﺎﻌﻣ ....
( ) ﺍ ﺪﻨﻋ ﻨﻟ ﺔﻠﺻﺎﻔﻟﺍ ﺕﺍﺫ ﺔﻄﻘ .0
'( )( ) ( )
'(0)( 0) (0)
3 2
= − +
= − +
= − +
( ) ر
