7/25/2019 Synoptiki Theoria B Gymnasiou

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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

1.

2.

3.

4. 1 ;

, ,

, .

1. 3x + x = x .

2. , .

3. 0x= 0 .

4. , .

5. 8x= 0 .

6. -5 > 15, > -3

7. .

8. 2 2 2x 1x .

9. (+)= + , ,,

10. .

(1-5)

(-),

.

1. x > 3

2. x 2

7/25/2019 Synoptiki Theoria B Gymnasiou

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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

3. 0x 2

4. 3 x

5. x

7/25/2019 Synoptiki Theoria B Gymnasiou

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5

. :

2 ( 1) 7 3 3 ( 2) 9x x x 1 2 3 1

2 6 12

x x

. :

3 4 ( 2) 10 2 (1 ) 7x x x

()

(); .

5.

. :

3 1 6 4

2 7

x xx

. :

6. (1) (2):

2 2 1 2 1

2 3 2 2 1 , (2)3 2 6

x x xx x x

. (1) .

. (2) .

. .

7.

. :

2 1 4 3

5 2

x xx

. :

2( 1) 4 1x x .

8.

. (1) (2):

3 1 6 2 2 3 12 (1)x x x 6 2 1 5 2 (2)x x

. (1) (2) .

4 2 5 4

5 3

x x

7/25/2019 Synoptiki Theoria B Gymnasiou

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9.

. N :

5 4 3 3 1 13 5x x x x (1) 3 5 1 2

16 4 8

x x x (2)

. N (1) (2)

10.

. :

3 1 2 10 5x x x 8

03

xx

. .

11.

:

2( 3) 4( 2) 8( 1)x x x 32x

2 3 54 12

12.

. 8-2(3x-1) 4(x-5)

. 3 (x 1) 2x 1

x4 3

. -2, -1, 2, 3,

. .

7/25/2019 Synoptiki Theoria B Gymnasiou

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1

1

, ,

, .

1. 5x -x = x .

2. 0x = 2 .

3. 8x= 0 .

4. -3 > 12, < -4

5. 2 2 2x

1x

.

2

:

3 2 5 1

4 3 6

x xx

.

3

. :

4(3 1) (5 2 ) 2x x (1) 3( 2) 2 9

5 10 2

x x xx

(2)

. (1) (2).

. , , < < ,

:

2( ) 3( ) ( 8 )A

.

7/25/2019 Synoptiki Theoria B Gymnasiou

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8

2

1

, , , .

1. 5x -x = 4x .

2. 0x = 0 .

3. 8x = 8 1.

4. 3 > -12, < -4

5. 2x=0 0.

2

4 3 2 ( 1) 2( 1)x x x x 2 4 3 1 4 1

6 3 3

x x x

3

. :

3 2 2 3 1K x x

. 4 5K x

. K 1x

. . :

100

2 3

x x

. ().

7/25/2019 Synoptiki Theoria B Gymnasiou

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7/25/2019 Synoptiki Theoria B Gymnasiou

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10

5

10E

3

1 = 35

2= 12

1.

.

2. ;

.

3. =8 , =13 , =9 .

4. , ,

.

, ,

, .

1. .

2. = 5 , = 8 = 3 .

3. =8 =15

=17.

4. =50

5. ,

3= 23

6.

,

, , .

. ()2= ()

2+ ()

2. ()

2= ()2()2

. ()2= ()2+ ()2

7/25/2019 Synoptiki Theoria B Gymnasiou

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11

. ()2= ()2()2

1.

0 90 , 0 30 2 3 .

5 11 ( cm )

. 2 4

. .

; .

.

.

2.

=10cm, =17cm =15cm.

. .

. .

3.

7/25/2019 Synoptiki Theoria B Gymnasiou

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12

= 10cm, = 8 cm = 45.

45

y

x

8 cm

10 cm

. x .

. y .

. .

4.

, =14 ,

=13 , =5. :

.

. . .

5.

: ==5m, =7m

=13m.

14 cm

5 cm

13 cm

7/25/2019 Synoptiki Theoria B Gymnasiou

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13

. x .

. .

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14

1

1

. =900

.

, :

.2=+.. . 2=- . 2=-

2

A. =x+2, =3x-2 =2x ,

xx=4.

B. (//) ,

=6 , =10

.

3

: ==5m, =7m

=13m.

. x .

. .

7/25/2019 Synoptiki Theoria B Gymnasiou

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