(1)

U )ﻝﻭﻻﺍ ﻥﻳﺭﻣﺗﻟﺍ3 (

ﺔﺑﺎﺟﻹﺍ ﻭ ﻝﺍﺅﺳﻟﺍ ﻡﻗﺭ ﻙﺭﻳﺭﺣﺗ ﺔﻗﺭﻭ ﻰﻠﻋ ﺏﺗﻛﺍ .ﺔﺣﻳﺣﺻ ﻁﻘﻓ ﺎﻬﻫﺍﺩﺣﺍ ﺕﺎﺑﺎﺟﺇ ﺙﻼﺛ ﻝﺍﺅﺳ ﻝﻛ ﻲﻠﻳ ﺔﺣﻳﺣﺻﻟﺍ 1 ﺔﺣﺟﺍﺭﺗﻣﻟﺍ ﻝﻭﻠﺣ ﺔﻋﻭﻣﺟﻣ-

6x−54x+1

ﻲﻓ ﻲﻫ 

ﺃ‌

(

]

^−∞^;3

[

(ﺏ

]

^{−∞ −}^{; 1}

[

(ﺝ

]

^3;^+∞

[

ﺔﻟﺩﺎﻌﻣﻟﺍ ﻝﺣ -2

2x=2

ﻲﻓ ﻭﻫ 

ﺃ‌

( 2

(ﺏ (ﺝ 2

2− 2

ﻥﺎﻛ ﺍﺫﺍ -3

ABCDEFGH

ﺙﻠﺛﻣﻟﺍ ﻥﺎﻓ ﺎﺑﻌﻛﻣ

CEH

ﺃ‌

ﻡﺋﺎﻗ (ﺝ ﻥﻳﻌﻠﺿﻟﺍ ﺱﻳﺎﻘﺗﻣ (ﺏ ﻉﻼﺿﻷﺍ ﺱﻳﺎﻘﺗﻣ ( ﻲﺗﻻﺎﻛ ﺕﻧﺎﻛﻓ ﻥﺍﻭﺟ ﺭﻬﺷ ﻥﻣ ﻉﻭﺑﺳﺍ ﻝﻼﺧ ﺔﻳﺳﻧﻭﺗﻟﺍ ﻥﺩﻣﻟﺍ ﻯﺩﺣﺎﺑ ﺓﺭﺍﺭﺣﻟﺍ ﺕﺎﺟﺭﺩ ﺕﻠﺟﺳ -4

31 32 , 31 , 34 , 31 , 34 , 33 , ﻭﻫ ﺓﺭﺍﺭﺣﻟﺍ ﺕﺎﺟﺭﺩﻟ ﺔﻠﺳﻠﺳﻟﺍ ﻩﺫﻫ ﻁﺳﻭﻣ

ﺃ‌

31 ( (ﺏ 32

(ﺝ 33

U)ﻲﻧﺎﺛﻟﺍ ﻥﻳﺭﻣﺗﻟﺍ 3

(

ﻥﻛﻳﻟ ﺙﻳﺣ ﺎﻳﻘﻳﻘﺣ ﺍﺩﺩﻋx

[

^{3; 1}

]

x∈ − −

ﺓﺭﺎﺑﻌﻟﺍ ﻭ

5 4 A x

x

= + +

1 ـــﻟ ﺍﺭﺻﺣ ﺩﺟﻭﺃ-

4 x+

ﻥﺃ ﺞﺗﻧﺗﺳﺍﻭ

4 0 x+ ≠

2 ﻥﺃ ﻥﻳﺑ-

1 1 A 4

= + x +

3 ﺓﺭﺎﺑﻌﻠﻟ ﺍﺭﺻﺣ ﺩﺟﺃ- ﺭﺻﺣﻟﺍ ﻯﺩﻣ ﺏﺳﺣﺃ ﻡﺛ A

U)ﺙﻟﺎﺛﻟﺍ ﻥﻳﺭﻣﺗﻟﺍ 5

(

1 ﺙﻳﺣ ﺓﺭﺎﺑﻌﻟﺍ ﺭﺑﺗﻌﻧ-

2 8 20

E=x + x−

ﺩﺩﻋ ﻲﻘﻳﻘﺣx

ﺃ‌

ــﻟ ﺔﻳﺩﺩﻌﻟﺍ ﺔﻣﻳﻘﻟﺍ ﺏﺳﺣﺃ ( ﻥﺎﻛ ﺍﺫﺍE

2 x=

ﺏ

‌

ﻥﺃ ﻥﻳﺑ(

(

⁴

)

² ³⁶

E= x+ −

ﺕ

‌

ﻥﺃ ﻥﻳﺑﺗﻟ ﻙﻛﻓ

( (

²

)(

¹⁰

)

E= x− x+

ﺽﺮﻓ ﺩﺪﻋ ﻲﻔـــــﻴﻟﺄﺗ

2 ﺕﺎﻴﺿﺎﻳﺮﻟﺍ ﺓﺩﺎﻣ ﻲﻓ

ﻲﺳﺎﺳﺃ 9 ﻭ1

ﻭ2 5

ﺔﻳﺩﺍﺪﻋﻹﺍ ﺔﺳﺭﺪﻤﻟﺍ ﺱﺭﺎﻣ 20

ﺔﻴﻗﺎﻧﺮﻤﻟﺍ

ﺱﻷﺍ ﺓﺬﺗﺍ ﻱﺪﻴﺒﻌﻟﺍ ﻱﺩﺎﻬﻟﺍ : ﺐﻴﻄﻟﺎﺑ ﺔﻴﻣﺎﺳ- -ﻲﻨﻳﻮﺠﻟﺍ ﺔﻠﻴﻤﺟ–

2015/2016

(2)

ﺙ

‌

ﻲﻓ ﻝﺣ( ﺔﻟﺩﺎﻌﻣﻟﺍ 

0 E=

ﺝ‌

ﻲﻓ ﻝﺣ ( ﺔﺣﺟﺍﺭﺗﻣﻟﺍ 

E≤x2

ﺙﻠﺛﻣ ﻭﻫ ﻝﺑﺎﻘﻣﻟﺍ ﻝﻛﺷﻟﺍ -2 ABC

ﻲﻓ ﻡﺋﺎﻗ ﻭA

[ ]

^AH

ﺭﺩﺎﺻﻟﺍ ﻪﻋﺎﻔﺗﺭﺍ ﺙﻳﺣ ﻥﻣA

2 5 AH =

ﻭ

8 BH = +x

ﻭ

CH =x

ﻭ

0 x

ﺃ‌

ﻥﺃ ﻥﻳﺑ (

0 x

ﺔﻟﺩﺎﻌﻣﻠﻟ ﻝﺣ ﻭﻫ

2 8 20 0

x + x− =

ﺏ

‌

ﺙﻠﺛﻣﻟﺍ ﺩﺎﻌﺑﺃ ﺞﺗﻧﺗﺳﺍ (

ABC

ﺕ

‌

(

U)ﻊﺑﺍﺭﻟﺍ ﻥﻳﺭﻣﺗﻟﺍ 4

(

ــﻟ ﻎﻛﻟﺎﺑ ﻥﺯﻭﻟﺍ ﻲﻟﺎﺗﻟﺍ ﻝﻭﺩﺟﻟﺍ ﻝﺻﻭﺣﻳ ﺩﻳﺩﺟ ﺩﻭﻟﻭﻣ 100

ﻎﻠﻛﻟﺎﺑ ﻥﺯﻭﻟﺍ

[ [

^0;1

[ [

^{1; 2}

[ [

^2;3

[ [

^{3; 4}

ﻥﻳﺩﻭﻟﻭﻣﻟﺍ ﺩﺩﻋ 22

12 40

26 ﻲﻣﻛﺍﺭﺗﻟﺍ ﺭﺍﺭﻛﺗﻟﺍ

ﺩﻋﺎﺻﻟﺍ ﻲﻣﻛﺍﺭﺗﻟﺍ ﺭﺗﺍﻭﺗﻟﺍ ﺩﻋﺎﺻﻟﺍ ﺔﺋﻔﻟﺍ ﺯﻛﺭﻣ

1 ﻪﻠﻣﻛﺃ ﻡﺛ ﻙﺭﻳﺭﺣﺗ ﺔﻗﺭﻭ ﻰﻠﻋ ﻝﻭﺩﺟﻟﺍ ﻝﻘﻧﺍ-

2 ﺔﻳﺋﺎﺻﺣﻻﺍ ﺔﻠﺳﻠﺳﻟﺍ ﻩﺫﻫ ﻝﺍﻭﻧﻣ ﺩﺩﺣ-

3 ﺔﻳﺋﺎﺻﺣﻻﺍ ﺔﻠﺳﻠﺳﻟﺍ ﻩﺫﻫ ﻝﺩﻌﻣ ﺏﺳﺣﺍ-

4 ﻩﺫﻫ ﻁﺳﻭﻣﻟ ﺔﻳﺑﻳﺭﻘﺗ ﺔﻣﻳﻗ ﺞﺗﻧﺗﺳﺍ ﻡﺛ ﺔﻳﻭﺋﺎﻣﻟﺍ ﺔﺑﺳﻧﻟﺎﺑ ﺩﻋﺎﺻﻟﺍ ﻲﻣﻛﺍﺭﺗﻟﺍ ﺭﺗﺍﻭﺗﻟﺍ ﻊﻠﺿﻣ ﻡﺳﺭﺍ-

ﺔﻳﺋﺎﺻﺣﻻﺍ ﺔﻠﺳﻠﺳﻟﺍ 5 ﻱﻭﺎﺳﻳ ﻭﺃ ﻕﻭﻔﻳ ﻪﻧﺯﻭ ﻥﻭﻛﻳ ﻥﺃ ﻝﺎﻣﺗﺣﺍ ﻭﻫﺎﻣ ﺔﻋﻭﺟﻣﻟﺍ ﻩﺫﻫ ﻥﻣ ﺍﺩﻭﻟﻭﻣ ﺔﻳﺋﺍﻭﺷﻋ ﺔﻔﺻﺑﻭ ﺭﺎﻳﺗﺧﺍ ﻡﺗ-

ﻎﻠﻛ2

U)ﺱﻣﺎﺧﻟﺍ ﻥﻳﺭﻣﺗﻟﺍ 5

(

ﻥﻛﻳﻟ

ABCDEF

ﺙﻠﺛﻣﻟﺍ ﻪﺗﺩﻋﺎﻗ ﺎﻣﺋﺎﻗ ﺍﺭﻭﺷﻭﻣ ﻭEFD

ــﻟ ﻱﺩﻭﻣﻌﻟﺍ ﻁﻘﺳﻟﺍ H

ﻡﻳﻘﺗﺳﻣﻟﺍ ﻰﻠﻋB

( )

^AC

ﻭ ﻑﺻﺗﻧﻣI

[ ]

^AD

4 ﻭ

AB= cm ﻭ

3 BC= cm ﻭ

5 AC= cm ﻭ

10 AD= cm

1 ﺙﻠﺛﻣﻟﺍ ﻥﺃ ﻥﻳﺑ ﺭﻭﻏﺎﺗﻳﺑ ﺔﻳﺭﻅﻧ ﺱﻛﻋ ﺩﺎﻣﺗﻋﺎﺑ- ﻲﻓ ﻡﺋﺎﻗ ABC

B

2 ﻥﺃ ﻥﻳﺑ-

2.4 BH =

3 ﻡﻳﻘﺗﺳﻣﻟﺍ ﻥﺃ ﻥﻳﺑ (ﺃ-

( )

^EB

ﻱﻭﺗﺳﻣﻟﺍ ﻰﻠﻋ ﻱﺩﻭﻣﻋ

(

^ABC

)

ﺙﻠﺛﻣﻟﺍ ﻥﺃ ﺞﺗﻧﺗﺳﺍ(ﺏ ﻲﻓ ﻡﺋﺎﻗEBH

B

ﺏﺳﺣﺃ(ﺝ

EH