matematika 8 - zbirka (krug)

Download Matematika 8 - Zbirka (Krug)

Post on 18-Dec-2015

148 views

Category:

Documents

16 download

Embed Size (px)

DESCRIPTION

Matematika 8 - Zbirka (Krug)

TRANSCRIPT

  • 1

  • 8

    8.

    '

    , 2 0 1 1 .

  • : , , ,

    8

    8.

    : , , 244,. 347 5576, -: .

    :

    : , . , , , ,

    : :

    : ,

    650-02-00299/2010-06 21. 07. 2010. , .

    1 - ,

    37.016:51 (075.2) (076)

    , , 1938- 8 :

    8. / , ; [ , ]. - 6. . - : ,2011 ( : ). - 157 . : . , ; 24

    10.000.

    18 978-86-7136-193-4 1. , , 1954- []

    138.8- 183736588

    18 978-86-7136-193-4 : 10 000

    : ,

  • 8. , 2009. . , 8. , . :

    1. ,2. , ,3. ,4. ,5. ,6. ,7. ,8. ,9. ,

    10. ,11. .

    , - . . , .

    , - .

    , 2010.

  • 7

    2

    V

    I 1

    N V

    2

    0 0

    7

    X X

    2

  • 1. .................................................................. ,1.1. .............................. .................................... 1.2. ................................................................. 41.3. ....................................... 61.4. I .......................................................... ................. 7

    2. , .................................................................. 92.1. , - ....................................... 92.2. .................................................................... 132.3. I I .............................. ............................................. 14

    3. -............................................................................................ 16

    3.1. ........................ 173.2. ........................ 233.3. .................... 273.4. II I ........................................ 31

    4. .................................................................................................. 364.1. .......................................................... 374.2. IV ........................................................................... 44

    5. ............................................................................................ 455.1. ..................................................... 405.2. V ........................................................................... 52

    6. ...................................................................... 556.1. = + ........................................................................... 556.2. - .............................................. 026.3. V I........................................................................... 55

    7. 67

    I

  • 8. . 718.1. ........ 728.2. -

    .................................................................................. 788.3. V I I I ........................................................................ 84

    9. ..................................................................................................... 879.1. ............................................................ 879.2. IX ........................................................................... 90

    10. ...................................................................................................... 9310.1. .......................................................... 9310.2. X ........................................................................... 96

    11. ........ ......................................................................................... 9911.1. ......................................................... 9911.2. XI......................................................................... 100

    12. .............................................................................................. 1031. ............................................................................. 1032. , ........................................................................... 1093. ..................... 1124. ................................................................................................... 1215. .............................................................................................. 1256. .............................................................................. 1307. ........ ..................... 1388. ................................ 1409. .................................................................................................... 14610. ...................................................................................................... 14911. .................................................................................................... 153

  • 1.

    - .

    1

    1.1.

    . , - :

    _ ~ ~

    1 _

    ^~~'

    1. , , 6 . , . : 6 = : , :

    ) = 3 , 6 = 4 , = 5 ;) = 7 , 6 = 5 , = 6 ;

    ) = 8 , 6 = 3 , = 5 .

    1 1 (1769-1821),

  • 2

    \(; 2 , 6, 1.

    :/ 2( ) : 6 = : ; ) = ;

    ) X = + 6

    ) = -; ) =

    6

    & &

    3. :) ; ) ;

    .

    /I 4.1 :^ ( ) 2 : 3 ; 6 ) 1 : 4 ;

    ... ) 2 : 3 : 4 ; ) 2 : 5 : 3 .

    ( (' . :

    ) ; )

    ) 3 :5 ;

    ( ) = /.\ :5

    ) = - 1 ; ' 3

    ) = - ;' 8

    ) = 1 - . 5

    6 . () [| > :

    ) ^ , = , = ;) 8 = 7 , 8 = 2 8 , = 1 4 ;) = , = 4 , 8 = 9 .

    . . 67. > . = 10 , = 2 = 15 , .

    8 . (). - :

    ) = 12 , = 4 , = 8 ;) = 15 , = 3 , = 25 .

    9. ) (> 6 , ) . :

    ) > = 8 , = 20 , = 6 ;) > = 2 0 , = , = 4 .

  • 1. 3

    . . 8 . . 10

    10. / ' ' ():

    ) = 12 , = , ' = 8 , ' = ;

    ) = 14 , = , ' = 7 , ' = ;

    ) = , = 15 , ' = 9 , ' ' = 8 ?

    11. . .

    0 1,5

    12. || .

    ) = 7 , = 2 1 = 1 0 , .

    ) = , = = 10 , .

    ) = 7 , 1V = 2 = 14 , .

    ) = 2 5 , / = = 4 , 1 .

  • 4

    1.2.

    1 1 1 , - :

    \ , /3 = /? 7 = 7 , : 6 : = : : 1

    : 1 11 ( ~ ^ 1!) :(1) (. = , /3 = /^);(2) - , - (. : = 6 : , 7 = 7^);(3) - (. : = : 61 = : \ );(4) - (. : 61 = : \ , 7 = 71, > 6).

    / = = = .1 &1 1

    13. :) 4 , 5 , 8 , 10 , 12 ;) , 4 , 9 , 1 5 , 1 8 ?

    14. 4 , 3,6 1,6 . 1,6 ( = 1,6 ).

    15.. = 20, = 16. &1 = 21, = 11,2 . 6 .

  • 1. 5

    16. / = 30 = 45 '^ ,

    . .

    17. = 18 = 12 32 , , . - .

    18. = 15 , 6 = 12 = 8 . - .

    19. = 25 = 12 , = 8 . .

    20. = 18 , 6 = 16 , = 9 . .

    21 . , :

    1 ;

    2 ;

    3 - .

    22. = 30 , = 24 , = 20 . 1 .

    23. = 12 , = 15 , = 18 5! = 60 .

    24. = 4, 6 = 6 = 8 .

    = .

    25. 2 : 5 : 6 . \ = . .

    26. I .

    ) 1

  • 6

    ) I ?

    ) I 1

    27. 8 . = 9 , = 4 , 8 = = 2 , 8.

    28. = 7 , 6 = 15 = 12 . 26 . ?

    29. = \ / 5 . .

    30. . .

    31. 8 . = 12 , 8 = 4 = 9 , .

    32. - 12 : 5. 60 , .

    1.3.

    , , = = = , , > . :

    = - , 2 = , 2 = .

  • 1. 7

    33. :) = 3 , 6 = 4 ; ) = 5 , 6 = 1 2 ;

    , .

    34. 6 , , , =

  • 41. = 12 6 = 4 . 0 , [). .

    42. = 8 = 4 , = . .

    43. ( = ) . . = 12 = 8 , .

    44. = 12 , 36 2 , . .

    45. . 5 52 , >. = 2 , = = , .

    46. . 1 . , 1 , = 4 = 9 , .

    47. .

    = 1.

    48. = 12 6 = 4 . .

    49. I) = 7 , .0(7 = 9 = . : .

    50. , .

  • 2. ,

    , 1 ( - )

    ()

    , . . . . . . , 1 .__________________________________

    2.1. , -

    51. . :

    ) 3; ) 4; ) 5; ) 8; ) ?

    52. , . : ) ; ) ; ) , ?

    53. , . ?

  • 10

    54. :

    ) 36; ) 66; ) 105 ?