β΄ γυμνασίου...

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    15-Apr-2017
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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

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

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

    To

    !!

    x

    3x!!

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    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

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    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 +

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    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

    !!!

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    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

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    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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