10 SUJETS TYPES DE BFEM CORRIGES ET COMMENTES, Lectures de Mathématiques

Télécharge 10 SUJETS TYPES DE BFEM CORRIGES ET COMMENTES et plus Lectures au format PDF de Mathématiques sur Docsity uniquement! M.CARRE MATHEMATIQUES LES AUTOROUTES DU BREVET 2006 REUSSIR VITE ET BIEN 10 SUJETS TYPES DE BFEM CORRIGES ET COMMENTES Illustrations nettes et précises. 
              
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 9  3 33_++++&,4 3 9  4 !  344 ,54 4  3=44 .+& ;;3 4 3, $434 4 3 33,
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 4 43  5:3 /:144; 1
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  J ''  '' K -  "' , '13  4; K  /= 3   4;1, J ''  '' K -  "' , J''F: . K . F( J! . J J!3J. 1%/:1J:  F'K/:K.1/:F1 1&3  %/:1 %/:1J:  F'K/:K.1/:F1 :FJ/:F'1 %/:1J/:F'1/:K'1K/:K.1/:F'1 :I'J/:F'1/:K'1 %/:1J/:F'1/:K'1K/:K.1 /:K.1



     
%/:1J/:F'1/:K'!1 :K'!J/:K!1 %/:1J/:F'1/:K!1  12 4 =   =  %/:1 %/:1J/:F'1/:K'!14  44;34 %/:1J:IK'!:F:F'! >   4; ;3 , %/:1J:IK':F'! 145: /:1J / 1 / '1/ .1 + & & &− + 1 4 43  5:3 /:144; $  5:3# /:1: /:'1/:K.1≠ + 4 45/:'1/:K.1J+    4 4  444/:15 ,  4 4  444/:1:, /:'1/:K.1J+ ⇔:F'J+:K.J+ ⇔:J':J. /:1:4  :≠ ':≠ . 4;3#  :≠ ':≠ .# / !1 / 1 . &  & & + = + 1$434 /:1 :J  :J'  :J  # /  !1 / 1  .  + = + ( 1!/ 1.1/./ 1.1/!/ . 1!/ 1/ − −− = −+ −+ = + + = . ((- . ((- 1/ + = − −− =  :J'# / ' !1 ' / '1  ' . -  − + − = = = − + / '1  − =
 4   # '1/%$21 *8 34  V%WV2$W4%J-3= 2$J 32J3,$434 45  3 *8
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4  4>= 4 4*   4,   /%14 3 3 454 7,   . 
::: 
 3 * 4:  # /:1J/:F1/:K!1F/F:1/F:1K:  F %/:1J:  F :K F/:F-1 '1
&3  /:1%/:1, /:1J/:F1/:K!1F/F:1/F:1K:  F /F:1JK/:F1 /:1J/:F1/:K!1K/:F1/F:1K/:1/:K1 /:1J/:F1V/:K!1K/F:1K/:K1W /:1J/:F1/:K'+1/:1J/:F1/:K'+1 %/:1J:  F :K F/:F-1 %/:1J/:F1/:F1F/:F1 %/:1J/:1V/:F1W %/:1J/:F1/:F!1 %/:1J/:F1/:F!1 12 4    /:1%/:1, /:1J/:F1/:K'+1 /:1J:IK'+:F:F+ /:1J:IK":F+ /:1J:IK":F+ %/:1J/:F1/:F!1 %/:1J:I!:F:K'+ %/:1J:IF.:K'+%/:1J:IF.:K'+ 1
$434 /+1/√1, /+1J+IK":+F+ /+1J+ /+1J+ /  1J ( ) "  ++ −
     - /  1J "  + '. " + − = − + /  1J '. " − + 1
/:14 ; /:1J / 1 / 1  & + & ,  44 4  :=/:15 U /:15  %/:1J+, %/:1J+ ⇔/:F1/:F!1J+ ⇔:FJ+:F!J+ ⇔:J:J! /:15  :J:J!, !12 3  4; /:1, /:1J / 1/ '1 / 1/ !1 & & & & − + − −   & ≠  !& ≠ #/:1J '+ ! & & + − /:1J '+ ! & & + −
  4;  =%J'"MYJ'M$%J ! ,/Y14  34 > /%$1, '1
$434 4 4 :3 $ %$/%$J%YKY$1  $%J / " $J ' ' ! '!  ! / "+ × = = = $Y% $J'! %YIJ%IYI Y$IJ$IYI %YIJ'"I'I Y$IJ'!I'I %YIJ'"+ Y$IJ"' %YJ- ! Y$J( %$J%YKY$J(K- ! %$J(K- ! 1

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     . $Y% 44 * )4*# =%4 =&$44 =   " + = /&1HH/%$1   " + = 3&J  " + × &J ' '! '+ '" × = &J'+
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 >/$13/%17, '1
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 C      : 43  44 44 5    3 ,4  : *4# 
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 : *4  !+3 '1
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      '   .   .!6"F"679D-87 "?-9 '1
2 4 =    Y/ & 1J / & K  1  F   / & K  1K44; 4 ( )   (  ( (+ = + + J / & K &  K1F   &  ×K/ & K  1  J & K & √K J & K" &  K'F   & (44    # J & K &  KF   / & K  1JF   &  ×  43 3 # Y/ & 1J & K &  K  433 # Y/ & 1JK &  K & 0/:1J/ & K  1   44; 4 ( )   (  ( (+ = + + J & K &  K/:K  1  J & K &  K  43 3 # 0/ & 1J & K &  K  433 # 0/ & 1JK &  K & 1   ;3  Y/:1#    Y/ & 10/ & 14`;   ,  3#Y/ & 1J0/ & 1 25Q#Y/ & 1J/ & K  1  Y/ & 1J/ & K  1/ & K  1 1\/:1J√Y/:1# \/:1J ( ) & + J  & + 44; 4  = \/:1J  & + 1 45\/:1J√#   & + J   44; 4# ⇔    L L    &  &+ = + = −  L L (  (   (= ⇔ = = −    L L   &  &⇔ = = −    L L   &  &⇔ = = −
        1 45\/:1J   #   & + J   ⇔     L L     &  &+ = + = − ⇔     L L     &  &= − = − − ⇔       L L - - &  & − − − = = 312 *   4/==<1=   \/:1#, \/:1J  & +  & K√P+4 \/:1J & +  & K√P+⇔:P   −  & K√N+4 \/:1J  &− −  & K√N+⇔:N   −  & K√J+4 \/:1J+ & K√J+⇔:J   − D 79-87 ,-9C, 8B6*15*-    M   −∞ −   #\/:1J  &− −  :J   − #\/:1J+    M   − +∞   #\/:1J & +   #    M   −∞ −   #9J  &− −  :J   − #9J+    M   − +∞   #9J  & + : −∞    − +∞ \/:1  &− − +  & +
      ! $434  4  3 3S# $4344  B   3#BJ Z Z '+ ' +  0 0 = =  ' " =   -=    ' " −    . "     0 0π × × = J+3  . "  0 0π × × = × J:!+3J'++3  . + '++ !+++ "   π π× × = × =  !+++   π = $434  4  3 49  # $4344  B   3#BJ Z Z Z Z Z + ' +  0  1 0  1 = = = =  ' " =   -=    ' " −    . "      1 0× = @J +3  . "  1 0× = × J:!+3J'++3  . + '++ ' +++ "   × = × =  ' +++  = 3 4 : 4  : *4=4 ?4 *44 3,
  3 *  4%$4%J!3M$J-3%$J. 3,44 V%$W, '1
$  0=43      4%$#
3    04  3    ,
      - 130K0%K0$J=   #   4=  K %K $J 0 0K0%K0$J ⇔0 K K0 K %K0 K $J ⇔0 K K %K $J ⇔ K %K $J0 0 J 0 ⇔ K %K $J 0
      . D 72C%& F72++! 4/'  0C1 : 33'  4:  # ;/:1J/:F!1I/:F'1I/:1J:IK/:K'1/!F:1F! 'G12 4 =     ;/:1/:1, G1&3  ;/:1/:1, G1/:1 / 1/! -1 /! 1/ 1 & & & & − − = − − 1
2 43  5:3 /:14; /:1, 1
  # / 1  & = , : 33
  539  3; >34 :9 5# #'!+&   54/ 1 3 4 +++&, #!+&45  54 , 'G1:4  5   44='/:1/:14 :; 3 3   3 := '/:1J'!+:K+++ /:1J!+:, G12` * /==<1=3  4    43 ;;',  #'3 '+++& 45:   '3  45:  3 G12    4 44 454  45    3 44 43434, G1  3     :34 5 ;; 9 4 4` :U : 33 'G113  3 34/1 3   9 3,% : /1  4, 43   /14 J 3, 31
\444   4 U 1
   4  454% , G1R4 5 3 4  34 >/%1 4 / 1, 1
@; % 4 34, 1
  3% J3R=3434 RR, G1
Y4 < 4   /%1, 1
3434 3%  :*  ;; , 1
:  %Y;3 3%    I+% +/ + = , G143 4 4[ ]4J3,
 44*4>/ 1 34[]&, \444   4&U  : 33 Y
3 5   4;  53S   4 /  ; 3 1#YJ'+3MYJ'+3MY43     ,
     !+ G12    4 44 454  45    3 44 43434,
54 >   '!   , $ 34 4  : 444'!+:K+++N!+:, '!+:!+:N+++ ⇔++:N+++ ⇔:P'! G1  3     :34 5 ;; 9 4 4` :U 2:34 5 ;; 4` :  '!   , : 33 'G113  3 34/1 3   9 3,% : /1  4,43   /1 4 J 3, 1\444   4 U J J 3J J  J 3 4   4 4 4, 31
   4  454% , %  4 , J-+G % J'"+G-+G % J'+G % J'+G G1R4 5 3 4  34 >/%1 4 / 1, 1
@; % 4 34, ∈/1 % 4 V%W *  /1 34 , 1
  3% J3R= 3434 RR, 3% J % + J '  3RJ  . J '   3RJ RJ× J" RJ"3 RIJRII RIJ- F'- RIJ " RJ  RJ  3
     !' G1
Y4 < 4   /%1, 1
3434 3%  :*  ;; , 24 4% Y 34Y, 3%J +/ +% 24 4%  34 , 3%J +% + 1
:  %Y;3 3%    I+% +/ + = , 3%J +/ +% 4 %YJ% ×3% %YJ% ×3% %YJ% × +% + %YJ +% + %YJ +% + G143 4 4[ ]4J3,
 44*4>/ 1 34[]&,\444   4 &U == 4 3  =&=4 3     %  % = = /) * )4*1 / 1HH/&1    %  = = 4 &J     × = × = &J3    % % = = 4 &J    %× = × = &J3 J&J&J34 & 4 4 4,
     ! : 33
3 5   4;  53S   4 /  ; 3 1#YJ'+3MYJ'+3MY43     , 'G1$434 4 4 33S, 64J L L    (  ×   64J I  / /π× × 64J '++ '+ '+++   π π× × = = 64  '+++     π π = = G1
    3 3:   5   3    ;44 3  '+3 3S>'+++&4;44,$434 4 4,  4 4J  π × × JYJ 9 $4344  3,  JJ  3 IJYIKYI IJ'+IK'+I IJ++ J'+   4 4J '+ '+  '++ π π× × =   5;44J3S×3S   5;44J'+×'+J'++
  ;443 J L L Z L        
  ;443 J '++   '++ π π=  π J='   '= ' = = # π ≈ = ((-/4 a 4>b1 N π N!  3  3=4     33 !;44, 24J!×'+++&J!+++&,
     !! G1$  4&4$&J%F$, $&J%F$ $&J$K$%F$ $&J$K$% $%K%&J$K$% %&J$ G1@; %44 V2&W, %&J$ 2%J%&4 %44 V2&W, 2%J$ : 33#'+/' 1 3 33 ;; 3 ,2 44 /61;/&1 <; ,
     !-  @;3 B1
: 4;4 F/:1 ;, & :;= :; /:1; 
41
4 4%$ 34% 4 J3$, 6 $34  1
-+ '!  = , 6 -+ '!  '! '!    × = = = 1
(+α β+ = ° 4 α β  4 , &  (+α β+ = ° 4 α β   34  1
  /!!!!!!1 /1 /""""""1+ = , & IK I≠ /K 1I 1
/F 1IJI K I, & /F 1IJ/'1I× /K 1IJIK K I 1
" ! 4 45 "F!:IJ+, & "F!:IJ+ !:IJ" :IJ " ! 1

  59J:K  4/'M!1, 6
,0 543;;;44 ;/:1J:K  4  3 'K , 1
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     !. <G<  H /%1HH/2$1/21HH/%$1 C %$2 4* I$WV%2W4`4%$2 444  C %J2$2J%$ <G H /%1⊥/%$1/%$1⊥/$21 /$21⊥/21/21⊥/%1 C
     -+  G  ++5"!*6",DB6K7, >8BK*5>9  3V%W 4 /   4 1 >     `4 ,    45 : =  3  , ) [4  I:1 34 3=   ` 4 4  I%91,
 44*4>I%91 34 V%W  4, ++5"!*6",DB-+,"D6B D!,D6 B987B"*D9     5 =   : 7 4 J 7,     5 7  %= 4 47%J%,
   5    3%,  %  :   47, 443 3: :  >   4 , J   %,
     -'  <      + +=+++ +=+++ '=+++ (+ ' +=+'. +=+'. !.=( '=+++ "(  +=+! +=+! "=- +=++( ""  +=+! +=+! '(=+" +=((( ". +=+.+ +=+.+ ' =+ +=((" "- ! +=+". +=+". ''=  +=((- "! - +='+! +='+! (=!' +=((! " . +=' +=' "=' +=(( " " +='( +=' ' .=''! +=((+ " ( +='!- +='!" -=' +=("" "' '+ +='. +='.- !=-.' +=("! "+ '' +='(' +='( !=' ! +=(" .( ' +=+" +=' =.+! +=(." ." ' +=! +=' =' +=(. .. ' +=  += ( =+'' +=(.+ .- '! +=!( +=-" =. +=(-- .! '- +=.- +=". = ". +=(-' . '. +=( +=+- =.' +=(!- . '" +=+( +=! =+." +=(!' . '( +=- += =(+ +=( - .' + +=  +=- =. . +=( + .+ ' +=!" +="- =-+! +=( -(  +=.! += + = .! +=(. -"  +=(' +=  =!- +=(' -.  += +. += ! = - +=(' -- ! +=  += -- =' ! +=(+- -! - += " += "" =+!+ +="(( - . += ! +=! + '=(- +="(' - " += -( +=! '=""' +="" - ( += "! +=!! '="+ +=".! -' + +=!++ +=!.. '=. +="-- -+ ' +=!'! +=-+' '=-- +="!. !(  +=!+ +=-! '=-++ +=" " !"  +=! ! +=- ( '=! + +="( !.  +=!!( +=-.! '= " +="( !- ! +=!. +=.++ '= " +="'( !! - +=!"" +=.. '=.- +="+( ! . +=-+- +=.! '=. +=.(( ! " +=-'- +=."' '="+ +=."" ! ( +=-( +="'+ '=! +=... !' + +=-  +="( '='( +=.-- !+ ' +=-!- +="- '='!+ +=.!! (  +=--( +=(++ '=''' '= - "  +=-" +=( '=+. +=.' . +=-(! +=(-- '=+- +=.'( - ! +=.+. '=+++ '=+++ +=.+. !     
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