cuadernillo_entrenamiento_secundaria_2011.docx
TRANSCRIPT
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SECRETARÍA DE EDUCACIÓN JALISCOCOORDINACIÓN DE EDUCACIÓN BÁSICA
DIRECCIÓN GENERAL DE EDUCACIÓN SECUNDARIA
DIRECCIÓN GENERAL DE PROGRAMAS ESTRATÉGICOSDIRECCIÓN DE PROGRAMAS DE ACOMPAÑAMIENTO
PEDAGÓGICO
SEGUNDA OLIMPIADA ESTATAL DE MATEMÁTICASEN EDUCACIÓN PRIMARIA Y SECUNDARIA
2ª OEMEPS 2011
CUADERNILLO DE ENTRENAMIENTONIVEL SECUNDARIA
Guaa!a"a#a$ Ja!%&'() *+,#+#( + 2011
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
2011
ÍNDICE
Pág.PRESENTACIÓN 3
JUSTIFICACIÓN 5
INSTRUCTIVO DE PROCEDIMIENTOS PARA LA APLICACIÓN YEVALUACIÓN DE LOS EXÁMENES
6
PROBLEMARIO 7
SOLUCIONES 11
FUENTES DE CONSULTA !
2
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2011
PRESENTACIÓN
L" S#$%#&"%'" (# E()$"$*+, J"-*$/0 " &%"2 (# -" C//%(*,"$*+, (#E()$"$*+, Bá*$"0 $/, #- %/+*&/ (# 4/%&"-#$#% #- (#"%%/--/ (#
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C/#,$*" "%" #- ",#?/ (# -" *,4/%"$*+,. S# %#-"$*/,", $/,@ -"9)#("0 *(#,&*>$"$*+,0 #"-)"$*+,0 #-#$$*+, *"&*8"$*+, (#*,4/%"$*+, #- #,"%0 %##=*/,"%0 "%g)#,&"% #=%#"% ?)*$*/ $%'&*$/","-*8"%0 *,&*8"%0 )&*-*8"% $/"%&*% *,4/%"$*+, #- $/,/$**#,&/ ",#?/(# (*&*,&" -+g*$" (# $/,&%)$$*+, (#- $/,/$**#,&/ #, (*#%" (*$*-*," #, -/ (*&*,&/ á9*&/ $)-&)%"-#. :SEP0 !!0 ág. !1<
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2011
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
2011
*/ )# 4)#%/, &/"(/ %*,$*"-#, (# -/ C"-#,("%*/M"á&*$/ !!7!!G !!!1!0 (# -/ 9/-#&*,# U, %#&/ á” 0 (# "-g),/ #=á#,# %/9-#"%*/ (# -" A/$*"$*+, N"$*/,"- (#P%/4#/%# (# M"á&*$" :ANPM
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
2011
JUSTI-ICACIÓN
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2011
INSTRUCTIVO DE PROCEDIMIENTOS PARA LAAPLICACIÓN Y EVALUACIÓN
DE LOS E.ÁMENES
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
2011
PROBLEMAS
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
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Fig. 1 Fig. 2 Fig. 3 Fig. 4
Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
2011
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
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2011
F#(#%*$/ 9"*-+ %#$*"#, $/, A-*$*" ,/ -/ H*8/ $/, C-"%"0 "' $//A-*$*" &"/$/ -/ )(/ H"9#% H#$H/ $/, )9#%&/. A(#á #, #-#g),(/ #,),$*"(/ # ">%" )# A-*$*" 9"*-+ $/, #- ,/*/ (# C-"%" $// A-*$*" 9"*-+ $/, F#(#%*$/0 #,&/,$# F#(#%*$/ # #- ,/*/ (# C-"%"
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2011
P/% -&*/ (# -" &"9-" # )#(# #% )# )9#%&/ +-/ )(/ H"9#%9"*-"(/ $/, C-"%" #% ,/*/ (# B#"&%*8. A' )# -" %#)#&" /,@)9#%&/ 9"*-+ $/, C-"%" -" "%#?" (# ,/*/ /,@ E()"%(/ D",*#-"0)&"/ A-*$*"0 F#(#%*$/ C-"%" )9#%&/ B#"&%*8.
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
2011
A' )#@$l rea del trin&lo AD$ es i&al a # &nidades - # &nidades . 2 = !2&nidades c&adradas/
$l rea del trin&lo B$0 es i&al a " &nidades - " &nidades . 2 =12/" &nidades c&adradas/
$l rea del trin&lo C0 es i&al a ! &nidades - ! &nidades . 2 =4/" &nidades c&adradas/
3nalmente el rea de la rein ris es i&al a 14 5 '!2 + 12/ " +4/"( = 14 5 4 = "" &nidades c&adradas/
T"9*2, /(#/ $"-$)-"% #- á%#" /-*$*&"(" # "'@ * &%"8"/ #-#g#,&/ F "%"-#-/ "- #g#,&/ DC #- á%#" (# -" %#g*+, g%* # *g)"-
" -" )" (# -" á%#" (#- $)"(%*-á%/ FD #- &%*á,g)-/ EF0 $//# "%#$*" #, -" >g)%" (# "9"?/@
7in embaro, res<a %&e el c&adriltero 80D es &n paraleloramo p&esto %&e9
1/ $l lado 80, por constr&ccin, es paralelo a s& lado op&esto D ) 2/ $l lado D8 tambi:n lo es a s& lado op&esto 0 por%&e los n&los
08 ) 08$ son correspondientes e i&ales entre s; 'ambos miden4"o (9 el n&lo 08 es alterno interno con el n&lo 0C entre lossementos paralelos 80 ) D cortados por el sementotransversal 8 por lo %&e son i&ales entre s;, con medida 4"o 'esfcil ver el n&lo 0C mide 4"o9 en el trin&lo C0,
pero
el n&lo C0 es &no de los n&los del rectn&lo ) C0 es eln&lo de rebote, es decir,
) entonces
( ) el n&lo 08$ es correspondiente al
37
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2011
n&lo D8 entre los mismos sementos paralelos cortados por elsemento transversal 0 ) entonces los dos tambi:n son i&alesentre s;, con medida 4"o 'tambi:n no es dif;cil observar %&e D8mide 4"o9 , pero el
n&lo 8DA es el n&lo de rebote ) el n&lo DA es &no de losn&los del rectn&lo, es decir, )
entonces (/
A*ora bien como los trin&los A$D, $B0 ) 0C son rectn&los eissceles 'A, B ) C son v:rtices de los trin&lo ) tambi:n delrectn&lo ) los n&los AD$, B$0 ) C0 son los n&los de rebote a4"o9 en el trin&lo A$D, por e
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Cuadernillo de Entrenamiento Nivel Secundaria 2ª OEMEPS
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2011
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2011
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2011
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2011
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