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### Transcript of β΄ γυμνασίου...

• 2014-2015

• :

Page 1

1 ( )

.

, , , , x, y.....

.

.

.

.

.

:

:

i. ii. iii.

: = 3(x + 2y) 2(2x + y), x = 1, y = 2.

: = 3x + 6y 4x 2y = -x + 4y

= 1 y = -2 = -1 + 4(-2) = -1 8 = -9

:

(+) (+) = + (-) (-) = + (+) (-) = - (-) (+) = -

: = -3(2 3) + 5( 2) = 0,1 = -0,3

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......................................................................................................................................................

To

!!

x

3x!!

• :

Page 2

, x + = 0 ( 0).

:

1. ...

.

2. , .

3. .

4.

5. .

6. .

0x = 0 .(

x)

0x = 0

.( x)

x + = 0 , . ,

+ = 0 .

,

.

: ) 4x 3(2x 1) = 7x 42

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

) 2 : ) 4x 6x + 3 = 7x 42 4x 6x 7x = -3 42 -9x = -45 x = 5

) 6x 2 6x + 3 = 4 6x 6x = 4 3 + 2 0x = 3

) 3 2x 3 3 3 6x (5 x) = -5 + 7x 6x 5 + x = -5 + 7x 6x + x 7x = 5 5 0x = 0

• :

Page 3

1. .

2. x .

3. x.

4. .

5. .

: . ,

100 .

.

: x . ,

+ 100. :

+ + + 100 = x 12 + 12 + 12 + 12 100 = 12x

3x + 4x + 4x + 1200 = 12x

x = 1200.

:

......................................................................................................................................................

......................................................................................................................................................

: . 6

. ;

.....................................................................................................................................................................

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• :

Page 4

, < > . ( )

= < , . ( )

= >, . ( )

< , + < + < . ( )

< > 0, < . (/ )

< < 0, > . ( !!!!!!!)

< < , + < + . ( )

< < , > < . ( )

.

, x <

x > .

.

.

, :

1. .

2. .

3. ( ).

:

3 ! (1) 2 (2) : (1) 3x x < 5 + 1 2x < 6 x < 3.

(2) ( 2) 4 x 2x + 1 -2x x -4 + 1 -3x -3 x 1.

1 x < 3.

- 0 1 2 3 +

• :

Page 5

2 ( )

, ,

. "#. "\$ \$ 02 = 0.

1. :

"# = x 0, x 0 x2 = . 0, "# 0. 0, "# # "# #% x2 = , x = "# x = "#. x2 = 0, x = 0.

, 0, "# &'. , 0, "# &' '(#) "& *. ( )

2. , .

3. , .

: *2 &2 "+ = 2. :

*2 &2 "+ = &2 "2 2 = &2 "+ = "2 2 = "+ = 2.

:

................................................................................................................................ 21 x = ;

.................................................................................................................................

20

"2! ! (-5)2 = 25

!!!

• :

Page 6

- -5 -4 -3,2 -3 -2 - -1 0 1 2 3 " \$ 4 5 +

.

.

:

o

o .

: 0 1 2 3

: -2 -1 0 1 2

,-, , 0.

, - , -2 1,3 , 5,77

.

. "2, -"3 , , ... .

: :

) x2 + 5 = 9 ) 3x2 = 75 ) 105 x2 = x2 345 ) 2x2 5 = 5

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• :

Page 7

3 () x, y() x

y. y x.

.

.. y = 2x 1, y = -5x, y = x + 3 ..

.

.. y = 2x 1

(x, y) x y .

y

: y M(x, y)

x 0 x X

y

x 1 2 3 4

y 1 3 5 7

: f(x) = x2 2x + 3.

x -2 -1 0 5 10

y

• :

Page 8

.

xx yy .

xx (x, 0) yy (0, y).

4 () :

y

2(-,+) 1(+,+)

x 0 X

3(-,-) 4(+,-)

y

x y :

1 x > 0, y > 0. 2 x < 0, y > 0.

3 x < 0, y < 0. 4 x > 0, y < 0.

2

(x1, y1) (x2, y2)

:

() = &

: (3, -2) (5, -1) .

: () = & = &! 3 2 ="2 "!

: y

(-2, 3), (1, 0), (-3, -1), (0, 4), (2, -3)

x x

y

• :

Page 9

:

y

: y M(x, y)

x 0 x X

y

x, y

. x, y

. y = x

.

y ( > 0)

:

x 0 X

y ( < 0)

: .

= 2. y = 2x.

x 2 4 5 10

y 4 8 10 20

• :

Page 10

y = x +

y = x

yy M(0, y). .

!!!!

y

:

M(0, y)

x 0 X

y

:

xx y = 0

yy x = 0

xx y = yy, x = .

y = x + x + y = 0 0.

x, y , yx = . y =

. .

: 200 . ,

100 , .

) y x

.

) .

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