Soal Olim Eko Tk Prov 2006

  ( ( ! ! " # (

  • ! ! $ % &

  ' / ! % % ( % (

  % 0120 !' ( % ( % (

  ( ) ( ( %

  % % (

  % ( -

  3

  4 5678 + ,

  −

  ( 5 6 +897 & %

  −

  # , % % ( %% ( +

  • % ( % %

  , 5 * ! % ( '

  & * ( ( ( (

  4 %

  ' (

  • 6 : +8,88 , ( ( 6 /8

  ( 6 : +88,88 * ,

  % ( ( - 6 /8 %

  ( 6 : + 888,88 , (

  • 6 /8 6 : +8 888,88 * , 6 /8

  . !

  • 6 : + 888,88 ,

  ( ' 6 /88

  • ; , % ( 388 / B ( '

  % ( , ' ( <

  ( C88 ((

  88 ( +3

  /8

  • 3

  88 7 ( , ( ( - ( ( '

  = 788

  5 (

  ! > % (

  ( ' 5 6 788 +8

  −

  5 6 788 /8 ( (

  −

  ( 5 6 788 9 +8 5 6 788 9 /8 % ( 5 6 /8 788

  −

  % (

  ? @ ( > A

  8 , , /88 C D ( , % ( ( % ( ( ( , % ( ( '

  ( ( (

  5

  5

  5 (

  ( (

  5

  5 8 @ EF G /

  ( ( (

  @ D , %

  , ( (

  $ ( ' * "

  , * % "

  ( @ ' (

  %

  • (

  3 * '

  A * : C8 888 H & " 1 * : 3 888, "

  I : 8 888

  ( # D

  ; (

  G: G

  !" 6 + 1 * 9 , &

  : 38 888,88 4 ,

  ' /8 *

  B 1 6 + 6 ?

  G:

  G, B 1 6 / 6 ?

  3/ * ( B 1 6 ; 6 ;

  • B 1 6 7 6 3 B 1 6 8 6 /

  : + ?88 888,88 : + 888 888,88

  • @ +

  : ?88 888,88 : 88 888,88 ( : 38 888,88

  ' = : @

  ? @ ( 2 (

  : +88 888,88 , . %

  @ * : .88 888,88

  • %

  4 '

  : . ;88,88 * , 0%

  : / 888,88 B B D 0%

  • ( A D

  J

  • 888 +38 +. ! % % 629 9 9 1 4 (

  −

  /88 +88 ( ( ( ( +3

  ' ( ( ( (

  7 A ( % , K ( ( ( ( K % % ' ( ( (

  > (

  • / D B# % ' > (

  M * ( > (

  • M > (

  ( M > (

  • C % % , ( M ( ( % '

  M ( ( *

  ( ( ( +3 D B" D#

  • ( ( ( ( $ '
  • ( ( , ( ( , * (

  % ( ( ( (

  • 8 @ ( $

  H

  2L ! '

  • ; %

  $ * '

  (

  • @ % B *

  ( (

  • @ " #

  , , # + ( % ( % '

  • ? * * & ( : 388,88

  ' * : + 388,88

  • 0K : / 888,88

  : : 838,88

  • A : ?88,88

  ( * : : 88,88

  • @ : + 388,88 2 % : / /38,88

  0K # : +88,88

  • 7 @ B @ ! % ( %

  K ( ' : . C88,88 : C +88,88

  ( : ?88,88 : 7 788,88 : ; .88,88

  # ( ( ++ % ( ( ( , ,

  % ( ( % ( 0120 !' % % %

  ( ( % ( ( ( ( ( % (

  ( ( % ( ( (

  • C % ( (

  ,

  • B *

  ( ./ @ B '

  ( B : (

  B (

  • .8 B B B N 4 * *
    • 4 .3 ! (

  • . (

  B @ (

  / * ( %

  3

  4 (

  % B

  • O .; ( , B , + . , /

  3 B @ , + / + , / 3 *

  3 * ( , . . B #

  ( , (

  ( % * ( * *

  4 B

  4 ( 4 ( 4 .? ( 4 *

  • , * .+ B @

  B * B @

  B (

  ( *

  • .7 ! = B .. ! B @ , ,

  , , ( , ,

  %

  • $ *
  • , , (

  , , * (

  42 % ( % * .C % ( & % ( '

  @ B

  • ( D * *

  /8 @ D @D D D

  • / B / * , ( '

  I # (

  I I $: ( I &

  I

  4 I D / B ( # D& AD:#D '

  : 788 888, A : ?88 888, @ : 888 888, B : 388 888,

  : / 888 888, & : + 888 888,

  : 8 888 888, B , ( '

  : 388 888, : 788 888,

  ( : + 888 888, : + 388 888, : . 888 888,

  /+ 4 : 88 888 888 4 : ?8 888 888 : 3 888 888, ,

  ' : : +3 888 888, I : +3 888 888,

  ( : : .3 888 888, I : .3 888 888, I : .8 888 888,

  /. ( , : 3?3 888 . +883 : .?3 888 4 F * +88;

  ' B @ : .?3 888

  " B @ : .?3 888 " B @ : .?3 888

  B @ : .?3 888 ( B @ : 3?3 888

  " B @ : 3?3 888 " B @ : 3?3 888

  B @ : 3?3 888 B @ : .?3 888

  " B @ : .?3 888 // F '

  & + F":#DI 0#0: 4DD# D@ ! : %

  4

  • @ @ " 83 *

  ! D ..8 888 8 ;?8 888 888 888 3 + 888 888 + 888 888

  • ! 2 .88 888 C ?88 888 8 888 888
  • ?8 888 7 ?.8 888 C 888 888
  • 3 * +8 888 888 +8 888 888 .8 @ . 888 888 . 888 888
    • 4 +883 '
    • , : C88 888,

  • , : ;/ 88 888, . , : ;/ 88 888, / @ , : 3 888 888, 3 * , : +8 888 888, ; " , : .8 888 888, ? B , : + 888 888, 7 4 , : . 888 888,

  : .8 888 888, @ * +883 : 3 888 888,

  @ : +88 888, " B : + ?88 888, 4 # ! : / C88 888,

  " : /88 888, @ : 888 888,

  /; B ( ! F +883 ' : 3 888 888,

  ( : 7. 888 888, : C+ 888 888, : 3 888 888,

  4 : ? 888 888, : +8 888 888,

  : + 888 888, (

  7

  7 ,.,3,;,?

  7 ( ,/,3,;,?

  ' ,+,.,/,3 ? ,+,/,3,;

  F"4ID& C88 888 ;/ 88 888 3 888 888 +8 888 888 .8 888 888

  4

  ? !

  • ,.,/,3,; ? /3 B E@ @ G ' 4 +883 :
  • 8 888 888, +883 : ?+ 888 888,

  ! * F +883 '

  ! . F +883 ' : ;88 888 !

  8 . . 3 888 . 3 888 / ;73 888 /88 888 ;88 888 +88 888 + .73 888 / 388 888

  / /88 888 /88 888 /88 888 +88 888 + ?88 888 / C88 888 8 . . 3 888 . 3 888 / 873 888 /88 888 /88 888 +88 888 + .73 888 / C88 888

  4 F 3 888 888 /88 888 888 888 +88 888 + ?88 888 / C88 888 . ;88 888 ;88 888

  " B

  ! " @

  8 . . 3 888 .88 888 3 888 / ;73 888 /88 888 /88 888 +88 888 + /88 888 / +73 888

  4 F 3 888 888 /88 888 888 888 +88 888 + ?88 888 / C88 888 . ;88 888 ;88 888 3 888 888 /88 888 /88 888 +88 888 + ?88 888 / .88 888

  " B

  ! " @

  4 F 3 888 888 /88 888 888 888 +88 888 + ?88 888 / C88 888 . /88 888 /88 888 3 888 888 /88 888 ;88 888 +88 888 + ?88 888 / 388 888

  8 F +883 ' 4 ( ( : .88 888, : 3 888, , '

  " B

  ( ! " @

  8 . . 3 888 .88 888 3 888 / ;73 888 /88 888 ;88 888 +88 888 + /88 888 / /73 888

  4 F 3 888 888 /88 888 888 888 +88 888 + ?88 888 / C88 888 . /88 888 /88 888 3 888 888 /88 888 ;88 888 +88 888 + ?88 888 / 388 888

  " @ " B

  8 . . 3 888 .88 888 3 888 3 +73 888 /88 888 ;88 888 +88 888 + /88 888 / 773 888 !

  4 F 3 888 888 /88 888 888 888 +88 888 + ?88 888 / C88 888 . /88 888 /88 888 3 ;88 888 /88 888 ;88 888 +88 888 + ?88 888 / C88 888

  " B

  ! " @

  /? D +883 : +/ 888 888,

  • 88; * ' B @ : + 888 888,

  @ K < ,888 @ K < ,888

  " : .8 888 888 : .8 888 888 ! 4 * F " @ *

  7$/$83 : +C /88 888 " " : +C /88 888

  : +C /88 888 " : .8 888 888 ! 4 * F " @ *

  ! 4 * F " @ * 7$/$83 " " : .8 888 888 : +C /88 888

  7 D +883 : .8 888 888 +$ 8, $.8 " @ * ! ( '

  3 D +883 ! 4 * F ( %

  D(( < ,888 /C !

  ( @ < ,888 2 < ,888 @ < ,888

  @ < ,888 @ K < ,888 2 < ,888

  4 F .8 OO @ K < ,888

  %

  @ : 8 888 888, /7 4 0 < ,888 % % F & F ! *

  B @ : 8 888 888, B @ : 8 888 888,

  B @ : / 888 888 @ : 8 888 888,

  @ : / 888 888 ( @ : / 888 888,

  @ : + 888 888 B @ : / 888 888,

  • : ;88 888 * : ;88 888
  • : ;88 888 * : ;88 888

  ( 7$/$83 " " : +C /88 888 : .8 888 888 : ;88 888 * : ;88 888

  : .8 888 888 " : +C /88 888 ! 4 * F " @ *

  7$/$83 " " : .8 888 888 : +C /88 888

  • : ;88 888 : ;88 888 : +C /88 888 " : .8 888 888

  ! 4 * F " @ * 7$/$83 " : .8 888 888 : +C /88 888

  • : ;88 888 : ;88 888 * : +C /88 888 " " : .8 888 888 38 @ "

  4 . +883 ' : + ;88 888,

  " : 7 +88 888, B : .38 888,

  ! : ; 888 888, ! : /8 888 888, " " : C /88 888, 4 : /. 838 888

  : * +8 888 888, : /+ ;88 888, : 8 888 888, * : / .88 888,

  B D : / +88 888,

  • B : +/ 888 888 B : . 888 888, B : 388 888,
  • D
    • 883 : 8 /38 888,

  • 883 ' : ;7 /88 888, : /. /88 888,

  ( : .? /88 888, : 38 +88 888, : / ;88 888