Justificacion de paes 2013 matematica 2 año

7/17/2019 Justificacion de paes 2013 matematica 2 año

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PROYECTO DE REFUERZO ACADÉMPARA ESTUDIANTES DE EDUCACI

JUSTIFICACIÓN DE LAS

OPCIONES DE RESPUESTA DE LAPRIMERA PRUEBA DE AVANCE

DE MATEMÁTICA

2 ° AÑO DEBACHILLERATO

PRAEM 2013

MINISTERIO DE EDUCACIÓN

DIR ECCIÓN NACIONAL DE EDUCACIÓNERENCIA DE SEUIMIENTO A LA CALIDAD

DEPARTAMENTO DE EVALUACIÓN DE LOS APRENDIZAJES

Númerode ítem:1

Enunciado:

S!"!##$%&' !" ()*+$&% ,!&!*'" -% ()*+$&% &. )/$+% ! #%**!/%&4! ' "'

/#!/$5&6 178 198 138:

Opciones de respuesta:

A; 17.2&

B; 19.2&

C; 19<2&

D; 1=.2&

Respuesta Correcta: D

D!(!*+$&' ('&(% !" >'"%* 4! "' 4$?!*!&#$' #%+% !" *%4#(% 4! 4-&.1#%**!#('+!&(!; Y /$ #%&%#! @ '"$#' #%**!#('+!&(! ;

Justifcación de las opciones. Posibles causas por la que los estudiantesseleccionaron una opción equiocada.

A; A" ($"$'* "' ?5*+"' @ #'"#"'* !" *%4#(% -&.14 %">$4' +"($"$#'* 4 %* .1;

B; C'"#"5 #%**!#('+!&(! !" >'"%* 4! "' 4$?!*!&#$'8 4 /$& !+'*,%8 !& !" *%4#(% 4!

-&.14 '"$#' $&#%**!#('+!&(! "' "!@ 4! "%/ /$,&%/8 .2-.1 .2;

C; I&>$!*(! "' +'&!*' 4! #'"#"'* !" >'"%* 4! 4G !/ 4!#$*8 17 198 19 13;

!ndicador de lo"ro: 1.# C'"#"'8 #%& /!,*$4'48 !" &.)/$+% ()*+$&% 4! &' /#!/$5&

'*$(+)($#'.

Justificación de las Opciones de Respuesta de la Primera Prueba de Avance de MatemáticaSegundo Año de Bachillerato PRA!M "#$%&

Númerode ítem:$

Enunciado:

U&' /#!/$5& '*$(+)($#' ($!&! !" /$,$!&(! ()*+$&% ,!&!*'"6 < 8

#K" 4! "'/ %#$%&!/ #%**!/%&4! '" /!,&4% @ (!*#!* ()*+$&% 4!

/#!/$5&

Númerode ítem:%

Enunciado:

S! $&(!*%"'& (*!/ +!4$%/ '*$(+)($#%/ !&(*! @.12 8 #K" 4! "%/ /$,$!&(!/

()*+$&%/ *!*!/!&(' &% 4! !/%/ +!4$%/ '*$(+)($#%/

&pciones de respuesta:

A; 9 @ 92

B; 0 @ 9

C; @ 72

D; 72 @ 7

Respuesta Correcta: '

U($"$' #%**!#('+!&(! !" ()*+$&% ,!&!*'" ! I4!&($#' ! *$+!*% 4!! //($($* '*'

& 2 @ "!,% '*' &38 @ '"$#' #%**!#('+!&(! "' *!,"' '*' %!*'* !&(!*%/ #%& $,'" %

4$?!*!&(! /$,&%;

Justifcación de las opciones. Posibles causas por la que los estudiantes

seleccionaron una opción equiocada.

B; C%&?&4! !" #K"#"% 4!" *$+!* @ /!,&4% ()*+$&% #%& "% /%"$#$('4%8 '&! "%/

#K"#"%/ &% ($!&!& !**%*!/;

C; A4!+K/ 4! #%&?&4$* !" *$+!* @ /!,&4% ()*+$&% #%& "% /%"$#$('4%8 /+' "%/ !&(!*%/

#%& 4$?!*!&(! /$,&% #'&4% !& *!'"$4'4 /! *!/('&;

D; R!#%&%#! ! 4!! #'"#"'* !" /!,&4% @ (!*#!* ()*+$&% 4! "' /#!/$5&8 /$& !+'*,%8

'"$#' $&#%**!#('+!&(! "' *!,"' '*' %!*'* !&(!*%/;

!ndicador de lo"ro: 1.( U($"$' #%& /!,*$4'4 !" ()*+$&% ,!&!*'" '" #'"#"'* #'"$!*

()*+$&% 4! &' /#!/$5& '*$(+)($#';

Númerode ítem:)

Enunciado:

S$ !" *$+!* ()*+$&% 4! &' /#!/$5& '*$(+)($#' !/ 1 "' 4$?!*!&#$' !/ 2

/+' 4! "%/ &G *$+!*%/ ()*+$&%/ !/ =008 #K&(%/ ()*+$&%/ /!'& /+'4%

4! !/' /#!/$5&

A; .10

Respuesta Correcta: *

D!(!*+$&5 #%**!#('+!&(! "' 4$?!*!&#$' '*' $&(!*%"'* +!4$%/ '*$(+)($#%/8

8 "!,% ,!&!*' "%/ (*!/ +!4$%/ '*$(+)($#%/6 38 .28 .7 .7 !/ &% 4! !""%/;

seleccionaron una opción equiocada.A; D!/#%&%#! #5+% %(!&!* "%/ +!4$%/ '*$(+)($#%/ !&(*! 4%/ &+!*%/ 4'4%/8 %* !/%

*!'"$' "' /+' !**5&!' 4! "%/ 4'(%/ *%%*#$%&'4%/;

C; R!/!">! '*#$'"+!&(! !" !!*#$#$% %*! /%"% 4!(!*+$&5 "' 4$?!*!&#$';

D; S+' #%**!#('+!&(! "%/ 4%/ &+!*%/ !&(!*%/ *%%*#$%&'4%/8 !*% 4!/#%&%#!

#5+% %(!&!* & +!4$% '*$(+)($#% 4! &' /#!/$5& '*$(+)($#'

!ndicador de lo"ro: 1.+ I4!&($#' @ #'"#"'8 #%& $&(!*)/8 (%4%/ "%/ +!4$%/ '*$(+)($#%/

!&(*! 4%/ ()*+$&%/ 4! &' /#!/$5& '*$(+)($#';

A; Q90

Repuesta Correcta: C

Númerode ítem:#

Enunciado:

D%*$/ 4!! /+'* #%**!#('+!&(! "%/ *$+!*%/ 1007 &+!*%/ $+'*!/8 !/

1 < 3 < 9 < 7 <: < 20138 #K&(% !/ !" (%('" 4! 4$#' /+'

S/($(@5 #%**!#('+!&(! "%/ 4'(%/ *%%*#$%&'4%/ ('&(% !& "' ?5*+"' '*' 4!(!*+$&'*

#'"$!* ()*+$&% 4! "' /#!/$5& #%+% !& "' ?5*+"' '*' /+'* "%/ *$+!*%/ ()*+$&%/

4! &' /#!/$5& '*$(+)($#';

A; D!/#%&%#! #5+% '"$#'* #%& *!#$/$5& "' ?5*+"' '*' 4!(!*+$&'* "' /+' 4! "%/

*$+!*%/ ()*+$&%/ 4! &' /#!/$5& '*$(+)($#'8 %* !/% 4$>$4! !&(*! 2 4$#' /+' %

'"$#' !" #K"#"% 4!" ()*+$&% ,!&!*'" 4! /+' /#!/$5& '*$(+)($#'8 !*% #%& !**%*!/;

B; C%&/$4!*' ! '*' %(!&!* =00 /! ' /+'4% 10 >!#!/ &%>!&('8 "% ! !>$4!&#$'

4!/#%&%#!* #5+% ($"$'* !" ()*+$&% ,!&!*'" 4! &' /#!/$5& !& #%+$&'#$5& #%& "'

?5*+"' 4! #K"#"% 4! "' /+' 4! "%/ *$+!*%/ ()*+$&%/ 4! &' /#!/$5&

D; D!/#%&%#! #5+% '"$#'* "'/ /#!/$%&!/ ' !/(! ($% 4! /$('#$%&!/8 *'5& %* "' #'"

#%&/$4!*' ! /! ' /+'4% = >!#!/ !" &+!*% 100;

!ndicador de lo"ro e,plorado: 1.- A"$#' #%**!#('+!&(! @ #%& *!#$/$5& "' ?5*+"'

'*' %(!&!* "' /+' 4! "%/ *$+!*%/ ()*+$&%/ 4! &' /#!/$5& '*$(+)($#';

A; 28 028 0=

B; 18 01Q8 0Q=

C; 303

D; 202=

Repuesta Correcta: *

R!/!">! #%**!#('+!&(! !" !!*#$#$% /%*! /#!/$%&!/ '*$(+)($#'8 %* !/% //($(@!

#%**!#('+!&(! !" *$+!* @ "($+% ()*+$&% 4! "' /#!/$5&8 '/ #%+% "' #'&($4'4 4!

()*+$&%/ /+'4%/8 *!'"$' (%4%/ "%/ #K"#"%/ ($"$'&4%6

A; C%+*!&4! ! /%& !!*#$#$%/ 4! /#!/$%&!/ '*$(+)($#'/8 '&! "%/ #K"#"%/ !

*!'"$5 !/(K& #%**!#(%/8 %">$45 4$>$4$* !&(*! 4%/ "' #'&($4'4 4! ()*+$&%/ /+'4%/ 4! "'

/#!/$5&;

C; S+' (%4%/ "%/ 4'(%/ %/!*>'4%/ !& !" !&&#$'4%8 %/$"!+!&(! %*! 4!/#%&%#!

#%+% /+'* "%/ ()*+$&%/ 4! &' /#!/$5& '*$(+)($#';

D; S+' "%/ 4'(%/ ! %/!*>' !& "' /#!/$5&8 /$& '"$#'* &'4' *!?!*$4% ' "' /+' 4! "%/*$+!*%/ ()*+$&%/ 4! &' /#!/$5& '*$(+)($#';

!ndicador de o"ro: 1./ R!/!">!8 !!*#$#$%/ @ *%"!+'/ /%*! /#!/$%&!/

'*$(+)($#'/8 #%& $&(!*)/ @ !*/!>!*'&#$';

Número de ítem: 6

Enunciado:

U& '#$!&(! 4!" H%/$('" R%/'"!/ *!#$! !& / *!#!(' +)4$#' "' 4%/$/ 4! /

+!4$#'+!&(% '/6 100 +, -+$"$,*'+%/ !" *$+!* 4'8 @ 9 +, +!&%/ #'4' &%

4! "%/ /$,$!&(!/G; S$ !" (*'('+$!&(% 4*' 4%#! 4'/8 #K&(%/ +$"$,*'+%/ -+, ($!&!

! (%+'* 4*'&(! (%4% !" (*'('+$!&(%

A; Q9B; 199C; 70D; 11Q0

Respuesta correcta: C

L'/ *!/%&4!& #%**!#('+!&(! '!""%/ !/(4$'&(!/ ! '/%#$'& #%**!#('+!&(! #'4'&% 4! "%/ 4'(%/ #%& "'/ *!/!#($>'/ >'*$'"!/ 4! "'/ /#!/$%&!/ '*$(+)($#'/8 '/

Nú merode ítem:+

Enunciado:

CK" 4! "'/ /$,$!&(!/ /#!/$%&!/ !/ ,!%+)(*$#'

A; R!/!">! '*#$'"+!&(! #%**!#(' "' /$('#$5&8 !*% $&(!**!(' $&#%**!#('+!&(! "'*!,&('8 %* !""% /! !4'& !& !" #K"#"% 4! "%/ +, ! *!#$$*K !& !" 4%#!'>% 4';C'&4% /! "! !/(K $4$!&4% !" #%&/+% 4*'&(! (%4% !" (*'('+$!&(%;

B; E/(! ,*% 4! !/(4$'&(!/ !/ %/$"! ! *!#%&%#'& "' *!/!&#$' 4!" *$+!* ()*+$&%4! "' *%,*!/$5&8 !*% $&(!**!('& $&#%**!#('+!&(! !" >'"%* 4! "' 4$?!*!&#$' '" (%+'* "'%/$($>'8 @ "' *!,&(' 4! "' /$('#$5&8 @' ! /! $4! !" #%&/+% !& (%4% !"(*'('+$!&(%8 &% !" 4!" 4%#!'>% 4';

D; $!&!/ !"$,!& !/(' %#$5& 4!/#%&%#!& !" ($% 4! /$('#$5& ! /! "!/ *!/!&('8 %*!""% "% *!/!">!& '#$!&4% /% 4! / "5,$#'G8 @ $!&/'& ! %* /!* 12 4'/8 @ /$*!#$$!*' 100 +, #'4' 4'8 #%&/+$*K & (%('" 4! 1200 +, 4!" +!4$#'+!&(%8 !*%#%+% /! +!&#$%&' 4! 9 +, +!&%/8 #*!!& ! #'4' 4' *!#$$*K =9 +,8 !*% "'/$('#$5& !/ #"'*' '" 4!#$* 9 +, +!&%/ #'4' &% 4! "%/ /$,$!&(!/G; 1200 0 5 =9 12 11Q0

!ndicador de lo"ro: 1./ R!/!">!8 !!*#$#$%/ @ *%"!+'/ /%*! /#!/$%&!/'*$(+)($#'/8 #%& $&(!*)/ @ !*/!>!*'&#$';

A; 8 :

B; .8 .Q8 08 Q8 8 :

C; 18 28 Q8 8 18 :

D; 218 238 298 278 :

C%+*!&4! ! '" *!'"$'* "'/ *!/('/ #%&/!#($>'/8 /!,&4% ()*+$&% @ *$+!* ()*+$&%8

&% %($!&! &' 4$?!*!&#$' #%&/('&(!8 !*%8 / '" *!'"$'* "%/ #%#$!&(!/8 !/ 4!#$*8 * 28%* "% #'" #%&#"@! ! !/(' /#!/$5& !/ "' ,!%+)(*$#';

Númerode ítem:-

Enunciado:

E" ()*+$&% ,!&!*'" 2-31 '*'&6182838: 8 !*+$(! #'"#"'* &' 4! "'/

/$,$!&(!/ /!*$!/8 #K"

A; E/ %/$"! ! (!&,' &' $4!' !$>%#'4' !& *!"'#$%&' ! "'/ /#!/$%&!/ !

$&>%"#*' ?*'##$%&!/ #%**!/%&4! ' /#!/$%&!/ '*$(+)($#'/

B; P%/$"!+!&(! ($!&! 4$#"('4!/ '*' !&#%&(*'* "' 4$?!*!&#$' #'&4% '",&%/ 4'(%/ /%&

&!,'($>'/8 %* !/% '" >!* 4$#' >'*$'#$5&8 #%&#"@! !**5&!'+!&(! ! /! (*'(' 4! &'

/#!/$5& '*$(+)($#';

D; C%&?&4! !" #K"#"% 4! "' 4$?!*!&#$' #%& !" 4! "' *'5& 4! &' /#!/$5& ,!%+)(*$#'

!ndicador de lo"ro: 1.1$ E/('"!#!8 #%& #"'*$4'4 @ /!,*$4'48 "' 4$?!*!&#$' !&(*! &'

/#!/$5& '*$(+)($#' @ &' ,!%+)(*$#';

A; .8.8 38 218 :B; .8 .8 18.9Q :C; 28 .8 18 :D; 08.8.128 :

U($"$' #%**!#('+!&(! !" ()*+$&% ,!&!*'" @ 4%+$&$% 4! "'/ *%$!4'4!/ 4!

%(!&#$'#$5&8 @ !>'"'& #%**!#('+!&(! "' !*!/$5&

P'*'&1

P'*'&3

Númerode ítem:/

Enunciado:

S$ /! $ &(!*#'"'& Q ()*+$&%/ !&(*! Q @ =72 4! +%4% ! ?%*+!& &' *%,*

,!%+)(*$#'8 #K" %#$5& *!/!&(' &% 4! "%/ #'(*% ()*+$&%/ $&(!*#'"'4%/

A; A" !>'"'* !& !" ()*+$&% ,!&!*'" #%+!(! & !**%* 4! (*'&/?%*+'* !&

!>$4!&#$' (!&!* *%"!+' '" (*'('* &' %(!&#$' #%& !" !%&!&(! #!*%8 '/'*'

B; E& !" #K"#"% 4! "%/ ()*+$&%/ 4! "' /#!/$5& ($!&!& *%"!+'/ &$#'+!&(! #%& !"

!%&!&(! #!*% !& ; '*' &18 '*' &28 '*'&38 '*' &Q8 !(#;

D S%& "%/ !/(4$'&(!/ ! #%+!(!& !" !**%* 4! +"($"$#'* "' '/! %* !" !%&!&(!;

'*' &18 '*' &28 '*' &38

!ndicador de lo"ro: 1;1Q U($"$'8 #%& /!,*$4'48 !" ()*+$&% ,!&!*'" '*'#'"#"'* #'"$!* ()*+$&% 4! &' /#!/$5& ,!%+)(*$#';

A; 3Q B; 2Q3 C; 2Q2D; 10

Respuesta correcta: D

C%+*!&4! ! '*' $&(!*#'"'* 4!! 4!(!*+$&'* *$+!*% "' *'5&8 "' #K" !/ 3

8 A4!+K/8 '/'4% !&! /%& /!$/ ()*+$&%/ !& (%('" "%/ 4! "' /#!/$5& ,!%+)(*$#' -%*! /%& Q ()*+$&%/

"%/ ! '@ ! $&(!*#'"'* !&(*! Q @ =72; U($"$' "' ?5*+"' ,!&!*'" - @ !">'"%* 4! 8 '*' 4!(!*+$&'* "%/ #'(*% ()*+$&%/ $&(!*#'"'4%/8 !&(*! !""%/ 10 -

8 ! !/ &% 4! "%/ *!/!&('4%/;

&pcionesde respuesta:

Númerode ítem:10

Enunciado:

L' /+' 4! "%/ 4$! *$+!*%/ ()*+$&%/ 4! "' /#!/$5& ,!%+)(*$#'6 7

1=28;;; !/

A; D!/#%&%#!& #5+% $&(!*#'"'*8 %* !/% #%&?&4!& "' /$('#$5& #%& "' /+' 4! ()*+$&%/

4! &' *%,*!/$5& ,!%+)(*$#'8 '&! %($!&!& #%**!#('+!&(! "' *'5&4!

"' /#!/$5&8 #'"#"'& $&#%**!#('+!&(! "' /+'; %*! %">$4'&+"($"$#'* !" *!/"('4% %* !" *$+!* ()*+$&% 4! "' /#!/$5&;

B; D!/#%&%#! #%+% $&(!*#'"'* ()*+$&%/ !&(*! 4%/ 4'4%/ % "% /'! $&#%+"!(%8 %* !""%4!(!*+$&'& !& *$+!* ",'* !" >'"%* 4! "' *'5& -*8 @ "!,% *!'"$'& !" #%#$!&(! !&(*!!" "($+% @ *$+!* ()*+$&%8 %">$4'&4% ! !/ >K"$4% /$ "%/ ()*+$&%/ /%& #%&/!#($>%/-

C; T$!&!& 4$#"('4 '*' '%*4'* &' /#!/$5& ,!%+)(*$#' #'&4% /! 4!! $&(!*#'"'*()*+$&%/8 !*% #%+*!&4!& ! !" &+!*% /#'4% 4!! !/('* !&(*! Q @ =728!&(%&#!/ *!'"$'& "' *!/(' 4! "' +'@%* @ +!&%* #'&($4'4 -=72 Q8 "' #'" !/ =8 !/(!&+!*% "% 4$>$4!& !&(*! 8 ! /%& "%/ ()*+$&%/ ! 4!! $&(!*#'"'*8 %(!&$!&4%2Q2;

!ndicador de lo"ro: 1.1# I4!&($#' @ #'"#"' "%/ +!4$%/ ,!%+)(*$#%/ !&(*! 4%/()*+$&%/ 4! &' /#!/$5& ,!%+)(*$#';

C%+*!&4! ! '*' ($"$'* "' ?5*+"' '*%$'4' 4!! 4!(!*+$&'* "' *'5& -*8 !"

>'"%* 4! @ &8 "% #'" "! !*+$(! !" #K"#"% 4! "' /+' 4! "%/ ()*+$&%/ /%"$#$('4%/($"$'&4% "'

?5*+"' 8 //($(@! "%/ *!/!#($>%/ >'"%*!/

A; D!/#%&%#! #5+% '"$#'* "' /+' 4! "%/ ()*+$&%/ 4! &' /#!/$5& ,!%+)(*$#'

8 %* !/% /+' 4! "%/ 4'(%/ ! %/!*>';

B; U($"$' "' ?5*+"' '*%$'4' !*% '" ($"$'* O">$4' +"($"$#'* %* @*!'"$' * 1 4! ?%*+' $&>!*/' -1. *; Y /! *!4#! ' #'"#"'*

0;001=93129 1=93;129

D; A" '"$#'* "' ?5*+"' %">$4' 4$>$4$* %* *.1 . 0;98 @ *!'"$' !" #K"#"%7 -

!ndicador de lo"ro: 1.1( A"$#'8 #%& *!#$/$5&8 "' ?5*+"' '*' "' %(!&#$5& 4! "'/+' 4! "%/ ()*+$&%/ 4! &' /#!/$5& ,!%+)(*$#';

Número de ítem: 11

Enunciado:

U&' !+*!/' ($!&! 4%/ 4!5/$(%/ 4! ','8 A @ B; T%4%/ "%/ 4'/ "%/ !+"!'4%//'#'& #$ !*(' #'&($4'4 4! ',' 4! #'4' &%; D!" 4!5/$(% A /! !(*'% 9 "$(*%/

!" *$+!* 4' 108 !" /!,&4% 208 !" (!*#!*% @ '/ /#!/$>'+!&(!; D!" 4!5/$(%

B /! !(*'% 2 "$(*%/ !" *$+!* 4' Q8 !" /!,&4% 8 !" (!*#!*% @ '/

/#!/$>'+!&(!; E" "($+% 4' /! !(*'!*%& 4!" 4!5/$(% ' = "$(*%/ +K/ !

4!" 4!5/$(% *; CK&(%/ "$(*%/ 4! ',' /! !(*'!*%& !& (%('"8 4! #'4'

4!5/$(%

A; 110 @ 1Q

B; 12= @ 32

C; 10 @ Q

D; 319 @ 12

A"$#' "'/ /#!/$%&!/ '*$(+)($#'/ @ #%+*!&4! ! '*' *!'"$'* "' /+' 4! "%/ "$(*%/4! ',' !(*'4%/ 4! #'4' 4!5/$(% 4!! #%&%#!* !" "($+% ()*+$&% 4! #'4' &' 4! "'//#!/$%&!/8 "% ! $+"$#' #%&/(*$* !" ()*+$&% ,!&!*'" '*' #'4' &' #%&/$4!*'&4% "'#%&4$#$5&6 E" "($+% 4' /! !(*'% 4!" 4!5/$(% A = "$(*%/ +K/ ! 4!" 4!5/$(% BG;D!5/$(% A6 ($!&!& = < W8 * 28 ; D!! 4!(!*+$&'*/! WG @ &G;

A" //($($* !& 8 /! ""!,' ' (!&!* ! 8 @ '" 4!/!'* !&; S! ($!&! ! ;

Númerode ítem:1$

Enunciado:

CK" !/ !" >'"%* 4! G '*' ! .1 8 <18 2-<1 !/()& !& *%,*!/$5&

,!%+)(*$#'

D!5/$(% B6 ($!&!& W8 * 28 ; D!! 4!(!*+$&'*/! WG @ &G;

A" //($($* !& 8 /! ""!,' ' (!&!* ! 8 "!,%

Y '" /$+"$#'* ;

I,'"' '+'/ !*!/$%&!/ /! %($!&! ! Q;

E" '&(!*$%* 4'(% "% //($(@! !& 8 /! ($!&! ! &;A" 4!(!*+$&'* !" "($+% ()*+$&% 4! #'4' /#!/$5&8 /! !4! !&#%&(*'* #K&(%/ 4'/ /!!/(>% /'#'&4% ',' 4! "%/ 4!5/$(%/ -&; F$&'"+!&(! *!'"$' "' /+' '*' #'4'/#!/$5&;

L' /+' 4! "%/ ()*+$&%/ 4!" 4!5/$(% A !/ 3198 @ "%/ 4! B /%& 12;

A; D!/#%&%#! ! !/ &' /$('#$5& *!?!*$4' ' "'/ /#!/$%&!/ ,!%+)(*$#'/ %* !/% '"#%&('* "%/ "$(*%/ *!/!&('4%/ 4!" /!,&4% 4!5/$(% &%(' ! "' 4$?!*!&#$' !/ =;

B; A"$#' "'/ /#!/$%&!/ ,!%+)(*$#'/8 !*% '" *!'"$'* "' $,'"4'4 !&(*! @

%">$4' +"($"$#'* 2 %* #'4' ()*+$&% '/6 ""!,'&4% ' #%& "% ! #%&#"@! !**5&!'+!&(! ! !" "($+%

()*+$&% 4! "' %(*' /#!/$5& !/ 12=;

C; C%+*!&4! '*#$'"+!&(! !" *%"!+'8 %*! !&#!&(*' !" "($+% ()*+$&% 4! #'4'/#!/$5&8 !*% &% !/ "% *!!*$4% %* "' /$('#$5&;

!ndicador de lo"ro6 1.1+ R!/!">! #%**!#('+!&(! @ #%& $&(!*)/8 !!*#$#$%/ @

*%"!+'/ '"$#'&4% "' /#!/$%&!/ ,!%+)(*$#';

Repuesta Correcta: D

A"$#' "'/ /#!/$%&!/ ,!%+)(*$#'/ %* !/% *!'"$' 8 "' $,'"' ' 2!

!/ "' *'5&; D!(!*+$&'&4% 4! !/(' +'&!*' ! 3;

A; L% '%*4'& '",!*'$#'+!&(!8 %">$4'&4% ! 4!! 4!(!*+$&'* !" >'"%* 4! G @ &%

'*(! 4!" #%#$!&(! !&(*! !" /!,&4% @ *$+!* ()*+$&%; O">$4'& ! !/(K *!/%">$!&4%

& !!*#$#$% !& !" #'+% 4! "'/ /#!/$%&!/ ,!%+)(*$#'/;

B; A"$#' "'/ /#!/$%&!/ ,!%+)(*$#'/ !*% *!"'#$%&' $&#%**!#('+!&(! '",&%/ 4'(%/8%* !/% //($(@! !" >'"%* 4! 1 !& "' /!*$! 4! !*!/$%&!/ *!/!&('4'/8 !&#!&(*' "'

/!*$! 08 28 Q @ #%+% !&(%&#!/ !" *!/(% 4! ()*+$&%/ ! 4!/#%&%#! #+"$*K&#%& ! / *'5& !/ 2; P'/' %* '"(% ! !" #%#$!&(! !&(*! !" /!,&4% @ *$+!*()*+$&% &% !$/(!;

C; L' /!"!##$%&'& $!&!/ *!'"$'& !" #%#$!&(! !&(*! !" (!*#!* ()*+$&% @ !" /!,&4%82 #%&#"@!&4% ! !/ !" >'"%* 4! "' *'5&; C'&4% !/ !" >'"%* 4! ;

!ndicador de o"ro: 1.1+ R!/!">! #%**!#('+!&(! @ #%& $&(!*)/8 !!*#$#$%/ @

*%"!+'/ '"$#'&4% "' /#!/$%&!/ ,!%+)(*$#';

Enunciado:

E& & "%#'" 4! #%+$4' -#%+!4%* /! %?*!#!6 (*!/ ($%/ 4! #'*&!/8 #'(*% ($%/

4! !&/'"'4'8 #$&#% %/(*!/ @ /!$/ !$4'/; S$ & "'(% #%+"!(% #%&/$/(! 4! &'

%*#$5& 4! #'*&!8 &' !&/'"'4'8 & %/(*! @ &' !$4'8 D! #K&('/ ?%*+'/

4$/($&('/ !4! !4$*/! & "'(% #%+"!(%

Repuesta Correcta: D

A"$#' #%**!#('+!&(! !" *$&#$$% 4! "' +"($"$#'#$5&6 3Q9; E/ %/$"! ! "%/!/(4$'&(!/ ! !/#%,!& )/(' %#$5& #%+*!&4!& 4! "% ! #%&/(' #'4' "'(%#%+"!(%8 %* !""% '" !"!,$* !" ($% 4! #'*&!8 ($!&!& #'(*% %/$$"$4'4!/ 4! !&/'"'4'8 @! %* !" *$&#$$% 4! "' +"($"$#'#$5& /%& 3Q 12 ?%*+'/ 4$/($&('/ !& "'/ ! /!!4! !4$* !/(%/8 !*% %* #'4' )/('/ 12 %/$$"$4'4!/ ($!&! #$&#% %#$%&!/ 4!%/(*!8 @ %* !" +$/+% *$&#$$%8 ($!&! 129 0 %/$$"$4'4!/ 4! !/#%,!* /%"%$&#"@!&4% (*!/ 4! "'/ #'(*% %#$%&!/; P!*% /! $!*! & "'(% #%+"!(%8 !&(%&#!/($!&! (%4'>' /!$/ %#$%&!/ 4! !$4'/8 #%& "% #'" & >$/$('&(! ' !/(! "%#'" (!&4*K0 30 ?%*+'/ 4$/($&('/ '*' !4$* & "'(% #%+"!(%;

A; D!/#%&%#! #5+% '%*4'* !/('/ /$('#$%&!/8 %/$"!+!&(! #%&/$4!*' ! /5"% '@ (*!/

?%*+'/ 4$/($&('/ 4! & "'(% 4! #%+$4' %*! '@ /5"% (*!/ ($%/ 4! #'*&!;

B; S! !$>%#' '" #%&/$4!*'* ! "%/ !>!&(%/ /%& $&4!!&4$!&(!/8 @ /+' "'/ %#$%&!/

4!" +!&6 3<Q<9< 1;

C; D!/#%&%#! #5+% ($"$'* !" *$&#$$% 4! +"($"$#'#$5&8 @' ! "'/ #'&($4'4!/ "'/

M"($"$#' 3Q98 @ !/(! *%4#(% "% 4$>$4! !&(*! Q8 %*! "!! ! #'4' "'(% #%&/('

4! #'(*% #%/'/;

!ndicador de o"ro: $.$ R!/!">! *%"!+'/8 ($"$'&4% !" *$&#$$% 4! "'

+"($"$#'#$5& #%& /!,*$4'4;

Númerode ítem:1)

Enunciado:

U&' +K$&' '(%+K($#' ""!&' %"/'/ 4! "K/($#% #%& &' +!#"' 4

?*$%"!/8 *5#%"$ @ %(*'/ "!,+*!/; L' +'@%* '*(! 4! "'/ %"/'/ #%&($!&

!" !/% #%**!#(%8 !*% 4!$4% ' >'*$'#$%&!/ !&!" ('+'X% 4! "'/ >!*4*'/8

& '!(! !4! (!&!* & !/% "$,!*'+!&(! 4$?!*!&(!; U&' >!*$#'#$5

4! Q8000 '!(!/ ! /! ""!&'*%& !" +!/ '/'4% *!>!"5 "% /$,$!&(!6

P!/% E>!&(% N+!*%4!

P'!(!/

P*%'$"$4'4

M!&%* A 100 0;029

S'($/?'#(%*$% B 300 0;=00

M'@%* C 300 0;079

Q8000 1;000

&pciones de respuesta:A; Q00

B; 2;9

C; 0;090

D; 0;1

I&(!**!('& #%**!#('+!&(! !" "'&(!'+$!&(%8 '4!+K/ ($!&!& #"'*% ! !/ &' /$('#$5&#%& 4%/ !>!&(%/ +('+!&(! !#"@!&(!/ @ '#!& /% 4!" *$&#$$% 4! "' /+'8 %* "%

! *%#!4!& '/6 P-A U B P-A < P-B 0;029 < 0;079;

Númerode ítem:1#

Enunciado:

E& & /'#% /! ($!&!& 4%/ !"%('/ *%'/8 #$&#% >!*4!/8 (*!/ &!,*'/ @ #'(*%

'+'**$""'/; S$ /! !(*'! &' !"%('8 #K" !/ "' *%'$"$4'4 4! ! !/(' /!''+'**$""' % >!*4!

A; D!/#%&%#!& %">$4'& ! "' *%'$"$4'4 4! & !>!&(% %/#$"' !&(*! 0 @ 18 !

$&(!**!('& $&#%**!#('+!&(! "' /$('#$5& @' ! &% /! ' /%"$#$('4% 4!(!*+$&!& "'

#'&($4'4 4! '!(!/ ! #+"!& #%& ! (!&,' & !/% +!&%* % +'@%*;

B; E/(! ,*% 4! !/(4$'&(!/ /! 4!'& ""!>'* %* "% 4! & !/% +!&%* % +'@%*G @ %*

!""% !"$,!& 08029 @ +"($"$#'& %* 1008 +@ "!%/ 4! +%/(*'* #5+% #'"#"'* "'

*%'$"$4'4 4! 4%/ !>!&(%/ +('+!&(! !#"@!&(!/ ($"$'&4% !" *$&#$$% 4! "'/+';

C; E/(! ,*% $4!&($#' "%/ 4%/ 4'(%/ 4! "%/ ! '"' "' /$('#$5&8 !*% #%&/$4!*'& !

"' *%'$"$4'4 4! ! !/% /#!4!& /! !&#!&(*' !&(*! "%/ 4%/ 4'(%/ +%/(*'4%/ !& "'

('"'8 %* !/% *!'"$'& -0;079< 0;0292; E& *!'"$4'4 4!/#%&%#!& #5+% '%*4'* !/(!

($% 4! /$('#$%&!/;

!ndicador de o"ro: $.) C'"#"'* "' *%'$"$4'4 4! 4%/ !>!&(%/ +('+!&(!!#"@!&(!/ ($"$'&4% !" *$&#$$% 4! "' /+'8 #%& $&(!*)/ @ #%&'&';

&pciones de respuesta: A;

E/(! ,*% 4! !/(4$'&(!/ #%+*!&4! ! 4!! *!'"$'* !" "'&(!'+$!&(% 4! #'4'!>!&(% -A6 ''*!#! &' !"%(' '+'*$""'8 B6 ''*!#! &' !"%(' >!*4! @ %($!&! "'

*%'$"$4'4 '*' #'4' &' -P-A6 @ P-B 6 "!,%8 %* /!* "%/ !>!&(%/+('+!&(! !#"@!&(!/ P-A U B P-A < P-B8 #%& "% #'"

P-A U B "% #'" !/ "' *%'$"$4'4 ! "' !"%(' !(*'4' /!' '+'**$""' %>!*4!;

C%&?&4! "' *%'$"$4'4 4! 4%/ !>!&(%/ +('+!&(! !#"@!&(!/ #%& !" #K"#"% 4! "'*%'$"$4'4 #"K/$#' @ #'"#"'&

A; L' !"$,!& '!""%/ !/(4$'&(!/ ! *!/!&('& *%"!+'/ '*' "'&(!'* "' *%'$"$4'4

4! /%"% & !>!&(%; P%* !/% *!'"$'& !" #%#$!&(! !&(*! "'/ !"%('/ '+'**$""'/ @ "'/>!*4!/;

B; L' !"$,!& '!""%/ !/(4$'&(!/ ! *!/!&('& *%"!+'/ '*' "'&(!'* "' *%'$"$4'44! /%"% & !>!&(%; P%* !/% *!'"$'& !" #%#$!&(! !&(*! "'/ !"%('/ '+'**$""'/ @ "'/>!*4!/;

C; L' !"$,!& '!""%/ !/(4$'&(!/ ! (%4'>' &% (*'/#$!&4!& !" *%"!+' #"K/$#% 4!""'&'+$!&(% 4! &' +%&!4'8 @' ! #%&/$4!*' ' "%/ #%"%*!/ '+'*$""%/ @ >!*4!/ #%+%"%/ &$#%/ *!/"('4%/ %/$"!/8 @ #%+% /%"% & #%"%* /'"4*K8 *!*%4#! "' $4!' 4! "'+%&!4'

!ndicador de o"ro: $.) C'"#"'* "' *%'$"$4'4 4! 4%/ !>!&(%/ +('+!&(!!#"@!&(!/ ($"$'&4% !" *$&#$$% 4! "' /+'8 #%& $&(!*)/ @ #%&'&';

Enunciado:

S$ "'/ !+*!/'/ 4! (*'&/%*(! (!**!/(*! A8 B8 C8 D @ E %?*!#!& / /!*>$#$% 4$'*$%

!&(*! S'& S'">'4%* @ S'& M$,!" @ "'/ !+*!/'/ 4! '>$' #$5& P8 @ R ($!&!&

>!"%/ 4$'*$%/ !&(*! "%/ +$/+%/ 4!'*('+!&(%/; D! #K&('/ +'&!*'/

4$?!*!&(!/ /! !4! >$''* 4! S'& S'">'4%* ' S'& M$,!"

Númerode ítem:1+

Enunciado:

D! #K&('/ ?%*+'/ /! !4!& !"!,$* 4%/ "$*%/ 4! 4$?!*!&(!/ '/$,&'(*'/

#$&#% "$*%/ 4$/($&(%/ 4! #$!&#$'/8 (*!/ "$*%/ 4$/($&(%/ 4! +'(!+K($#'

"$*%/ 4$/($&(%/ 4! /$#%"%,'

Repuesta Correcta: C

S%& '!""%/ !/(4$'&(!/ ! #%+*!&4!& ! !/(! ($% 4! /$('#$%&!/ /! *!/!">!&%* !" *$&#$$% 4! "' '4$#$5&8 %* ! "'/ %!*'#$%&!/ ->$''* %* >' (!**!/(*! % ')*!'&% !4!& *!'"$'*/! /$+"(K&!'+!&(!8 /$&% ! % >$'' %* &' 4! "'/ #$&#% %#$%&!/4! >' (!**!/(*! % >$'' !& &' 4! "'/ (*!/ %#$%&!/ ')*!'/8 !/ 4!#$*8 /! ($!&!& 9 < 3?%*+'/ 4$?!*!&(!/ '*' >$''* 4! S'& S'">'4%* ' S'& +$,!";

A; S%& '!""%/ !/(4$'&(!/ ! #%&?&4!& !" *$&#$$% 4! "' +"($"$#'#$5& #%& !"

*$&#$$% 4! "' /+'8 /$& 4'*/! #!&(' ! "'/ 4%/ %!*'#$%&!/ /%& +('+!&(!!#"@!&(!/ -SOLO UNA DE ELLAS PUEDE OCURRIR; P%* %(*% "'4% &% '@ ! %">$4'*! /! !/(K $4$!&4% "'/ +'&!*'/ 4$?!*!&(!/ 4! >$''* 4! S'& S'">'4%* ' S'& M$,!";

B; S%& '!""%/ !/(4$'&(!/ ! #%&/$4!*'& $4' @ >!"(' !& (*'&/%*(! (!**!/(*! -10 ! $4'@ >!"(' 4! (*'/%*(! ')*!% -; A&! '"$#'& !" *$&#$$% 4! "' '4$#$5&8 &%$&(!**!('& #%**!#('+!&(! "% ! "' /$('#$5&;

D; S%& '!""%/ !/(4$'&(!/ ! 4!/#%&%#!& #%&4$#$5& 4! &% 4! "%/ *$&#$$%/ +K/K/$#%/8 #%+% "% !/ !" 4! "' !4$#$5&8 %* "% #'" #%&/$4!*'& ! /5"% !$/(!& 4%/ ?%*+'/4! >$''* % "% '#! %* '(%/ ->' (!**!/(*! % "% *!'"$' %* '$*! -'>$5&;

!ndicador de o"ro: $.# R!/!">! *%"!+'/8 ($"$'&4% !" *$&#$$% 4! "' /+' #%&

/!,*$4'4

A; 12 B; 31C; 0D; =0

Repuesta Correcta: *

C%+*!&4! #%**!#('+!&(! "% ! /! "! "'&(!' %* !""% '"$#' *$+!*% !" *$&#$$% 4!+"($"$#'#$5& *!/!('&4% "'/ #%&4$#$%&!/ 4! "' /$('#$5& /'! ! !4! !"!,$* 2"$*%/8 &% 4! #$!&#$'/ @ &% 4! +'(!+K($#'/8 4! 9 3 19 ?%*+'/;

Númerode ítem:1-

Enunciado:

CK" !/ !" *!/"('4% 4! /$+"$#'* 2 [

D! +'&!*' '&K"%,'8 !4! !"!,$* 2 "$*%/8 &% 4! #$!&#$'/ @ &% 4! /$#%"%,'8 4!9 2 10 ?%*+'/ @ !4! !"!,$* 4%/ "$*%/8 &% 4! +'(!+K($#' @ &% 4! /$#%"%,'84! 3 2 ?%*+'/; C%+% !/(%/ #%&&(%/ 4! /!"!##$%&!/ /%& '!&%/ %* '*!/8!4! ($"$'*/! !" *$&#$$% 4! "' /+' '*' #%&#"$* ! !$/(!& 19 < 10 < 31?%*+'/ 4! !"!,$* 4%/ "$*%/ 4! 4$>!*/'/ '/$,&'(*'/ !&(*! "%/ "$*%/ 4! #$!&#$'/8 "$*%/4! +'(!+K($#' @ "%/ "$*%/ 4! /$#%"%,';

A; $!&!/ !"$!& !/(' %#$5& 4!/#%&%#!& "' '"$#'#$5& #%+$&'4' 4!" *$&#$$% 4! "'+"($"$#'#$5& @ "' /+'8 /5"% "%,*' $4!&($#'* ! $&>%"#*' !" *$&#$$% 4! "'+"($"$#'#$5&;

C; E&#!&(*' !" *%4#(% 4! "%/ 4'(%/ ! /! "! *!/!&('&8 '"$#'&4% $&#%**!#('+!&(! !"*$&#$$% 4! "' +"($"$#'#$5& 2932 0;

D; T$!&! #$!*(' &%#$5& 4! #%+*!/$5& 4!" *%"!+'8 /! 4' #!&(' ! /%& 4%/ "$*%/ !/! !/#%,!*K&8 !*% #%+!(!& !" !**%* 4! /+'* (%4%/ "%/ "$*%/ -10 @ '"$#'& !"*$&#$$% 4! "' +"($"$#'#$5&8 10= =0;

!ndicador de o"ro: $.( R!/!">!8 #%& $&(!*)/ @ #%&'&'8 *%"!+'/ 4!" !&(%*&%! $&>%"#*!& "' '"$#'#$5& #%+$&'4' 4! "%/ *$&#$$%/ 4! +"($"$#'#$5& @ /+';

C%&%#! @ '"$#' #%**!#('+!&(! "'/ *%$!4'4!/ 4!" ?'#(%*$'" 4! #'"$!* &+!*%8%* !/' *'5& '"$#' ! 0[ @ !

[ %* ('&(% %!*'& '/6

Númerode ítem:1/

Enunciado:

CK&(%/ '**!,"%/ 4! #$&#% !"!+!&(%/ !4!& ?%*+'*/! #%& "'/ /$,$!

,*'/ ,!%+)(*$#'/8 /$ &$&,&' 4! !""'/ !4! *!!($*/!

A; D!/#%&%#! ! !" ?'#(%*$'" 4! #!*% !/ 18 '4!+K/ ! "' 4$>$/$5& !&(*! #!*% &%

!$/(!8 !/ 4!#$*8 %($!&! %*! %!*'& @ #%&#"@! ! '"

/$+"$#'* !" *!/"('4% !/ ;B; D!/#%&%#! ! !" ?'#(%*$'" 4! +G ($!&!& !" 4!/'**%""%

8 %* !/%*!'"$' !/ 4!#$* #'&#!"' ;

D; D!/#%&%#! [ !/ 4$?!*!&(! ' 4!#$* !" &+!*% +G8 '&! !/ %/$"! ! (!&,'#"'*% 8 !" >'#$% +%/(*'4% "% ""!>' ' &' *!/!/(' $&#%**!#(';

!ndicador de lo"ro: $.- S$+"$#'8 #%& *!#$/$5&8 !*!/$%&!/ ! #%&($!&!&

&%('#$5& ?'#(%*$'";

A; 21B; Q2C; 120D; 2920

S'! ! 4!! ($"$'* P k n n!

8 %*! %*4!&' "%/ !"!+!&(%/ (%+'4% ,*%/4! (n k )!

9 4! "%/ 7 ! %/!! !" #%&&(%8 %* !/% //($(@! @ %!*' '/ P 7

Númerode ítem:$0

Enunciado:

CK" !/ !" &+!*% 4! '**!,"%/ 4$/($&(%/ ! !4!& ?%*+'*/! #%& "'/ "!(*'/4!6 23 '3 43 &3 53 '3 3 '3 E3 53 C3 63 E3 3 '78 /$ (%4'/ "'/ "!(*'/ /%&

(%+'4'/ ' "' >!

5 2520;

A; D!/#%&%#! "' 4$?!*!&#$' !&(*! &' !*+('#$5& @ &' #%+$&'#$5& %* !/%#%&/$4!*' ! /! (*'(' 4! & !!*#$#$% ! /! *!/!">! %* #%+$&'#$%&!/ ;

B; A"$#' $&#%**!#('+!&(! "' ?5*+"' '*' #'"#"'* !" %*4!&'+$!&(% 4! "%/ !"!+!&(%/4!

n n! 8 %*!

*!'"$' & #%&&(% /$ /! (%+'* '*(! 4! !""%/ P k

(nk )!

D; C%&?&4! !" '"$#'* !" %*4!&'+$!&(% 4! "%/ !"!+!&(%/ 4! & #%&&(% (%+'&4%'*(! 4! "%/ !"!+!&(%/ #%& (%+'*"%/ (%4%/8 %* !/% *!'"$' 9[120

!ndicador de lo"ro: $.11 S%"#$%&'8 #%& '(%&%+' @ #%&'&'8 !!*#$#$%/ !$&>%"#*!& !" %*4!&'+$!&(% 4! & #%&&(% 4! %!(%/ 4$?!*!&(!/8 (%+'4%/ (%4%/ %'*(! 4! !""%/;

A; 328 0

B; 8108 0Q8000

C; 1830787Q838000D; 1818 21Q8Q00

Respuesta Correcta: *

R!#%&%#! ! ($!&! & !!*#$#$% ! *!$!*! *!/%">!*/! %* !*+('#$%&!/; N%(' !

' !/'* ! /! "! *!/!&('& 19 "!(*'/ '@ #'(*% "!(*'/ AG ''*!#!& 2 "!(*'/ SG @ "%

+$/+% /#!4! #%& "' "!(*' LG @ EG; C%& "% #'" 8108 0Q8000;

F%*+"'6 P'*' #'"#"'* !" &+!*% 4! !*+('#$%&!/ 4! !/(! ($% '/('*K 4$>$4$* !"

?'#(%*$'" 4!" &+!*% (%('" 4! /+%"%/8 #%&('&4% // *!!($#$%&!/8 !&(*! !" &+!*% 4!

>!#!/ ! /! *!$(! #'4' &%;

n x! y! z !...

A; S! !$>%#' '" #'"#"'* =[8 /$& #%&/$4!*'* "' #%&4$#$%&'&(! 4! "'/ !*+('#$%&!/

#'&4% "'/ "!(*'/ /! *!$(!&8 %* !/% #'"#"' !" ?'#(%*$'" 4! "' #'&($4'4 (%('" 4! "!(*'/

%/!*>'4'/8 !*% !"$+$&'&4% "'/ ! /! >'& *!$($!&4%;

C; C'"#"' 19[ %*! &% 4$?!*!&#$' !&(*! %(!&!* !" &+!*% 4! !*+('#$%&!/ 4! &

#%&&(% #@%/ !"!+!&(%/ /! *!$(!& 4! %(*% ! &%;

D; D!/#%&%#! #5+% *!/%">!* !/(! ($% 4! >'*$'&(! 4! "'/ !*+('#$%&!/8 %* !/% #!&('

/%"% &' >! "'/ "!(*'/ ! /! *!$(!&8 @ #%+$&' !" (%('" 4! "!(*'/ #%& "'/ = !

*!/"('*%& 4! / #%&(!% /$& *!!($#$5&8 %* !/% #'"#"' =19; C%& !/(% !/('*' $&4$#'&4%

! ($!&! &' $4!' !$>%#'4' 4! "% ! /$,&$#' 4!(!*+$&'* !" &+!*% 4!

!*+('#$%&!/ %/$"!/ (%+'&4% '*(! 4! "%/ !"!+!&(%/ #'&4% '@ *!!($#$5& 4! "%/

!"!+!&(%/ 4!" #%&&(%;

!ndicador de o"ro: $.1% R!/!">! *%"!+'/ '"$#'&4% !*+('#$%&!/ #%&

/!,*$4'4

Númerode ítem:$1

Enunciado:

E& &' #'**!*' 4! #$#"$/+% '*($#$'& 3 /'">'4%*!X%/8 2 ,'(!+'"(!#1

&$#'*',\!&/!8 3 '&'+!X%/8 2 %&4*!X%/ @ 1 !"$#!X%; E" &+!*% 4! ?

!& ! !/ %/$"! ! #"'/$!& (*!/ 4! !""%/ 4! '#!*4% ' / ""!,'4+!(' !/

D; 1320

C%+*!&4!& ! !/ &' '"$#'#$5& 4! !*+('#$%&!/ (%+'&4% '*(! 4! "%/

!"!+!&(%/8 %* !/% #!&(' !" &+!*% 4! '*($#$'&(!/ -12 @ #%+% /%"% !$/(!& (*!/

#"'/$#'#$%&!/ %

(*!/ "''/ '*' !/(! ,*% 4! !*/%&'/ #'"#"' %(*%/ 4$!*%& '"$#'*

121110;

A; N% #%+*!&4!& "' /$('#$5&8 %* !/% /%"% /+'& !" &+!*% 4! '*($#$'&(!/;

B; E+"!' !$>%#'4'+!&(! #%+% '"$#'* !& /$('#$%&!/ 4! "' >$4' #%($4$'&' "'/

!*+('#$%&!/ %* !/% #%&/$4!*' ! %* !$/($* !& &' #'**!' /%"% !" *$+!*8

/!,&4% @ (!*#!* ",'* !& "' #'**!*' '/('*K #%& %!*'* 312 3;

C; S%& '!""%/ !8 !$>%#'4'+!&(!8 '"$#'& 4! ?%*+' $&#%**!#(' !" *$&#$$% 4! "'

+"($"$#'#$5& !/ !?!#('&6 321321 3 @ !/(! *!/"('4% "% +"($"$#'& %*

!" &+!*% 4! #"'/$#'#$%&!/6 33

!ndicador de o"ro: $.1% R!/!">! *%"!+'/ '"$#'&4% !*+('#$%&!/ #%&

/!,*$4'4;

Númerode ítem:$$

Enunciado:

E" >'"%* 4! "' !*!/$5&39 C 5 3;9-C 5

B; 0C; 20

Repuesta Correcta: '

R!#%&%#! !" #K"#"% 4! "'/ #%+$&'#$%&!/ %* !/% *!#%&%#! "' !*!/$5& @ !?!#('

B; D!/#%&%#! "' 4$?!*!&#$'#$5& !&(*! &' !*!/$5& *!?!*$4' ' #%+$&'#$%&!/ @ &' '!*+('#$%&!/ %* !/% 4!/'**%""' "' !*!/$5& 4'4' #%+% &' !*+('#$5&8

C; R!#%&%#! "' !*!/$5& @ !?!#(' 20, !$>%#K&4%/! '" &% 4$>$4$*%*

D; P"'&(!' "' !*!/$5& ;

3!2! 6!L%/ !**%*!/ %/!*>'4%/ /%& "%/ /$,$!&(!/6 "'&(!' #%**!#('+!&(! "' !*!/$5&8 !*% !"4!&%+$&'4%* "% !?!#(' $&#%**!#('+!&(!8 %*! 3[2[ "% "'&(!' #%+% [ !/ 4!#$*!?!#(' !" *%4#(% 4! 3 %* 2 @ "!/ #%"%#' !" /$,&% 4! ?'#(%*$'"; L!,% #%+!(! %(*%!**%*8 !" /$,&% 4! ?'#(%*$'" "% $&(!**!(' #%+% & ?'#(%* @ &% #%+% & %!*'4%*8 "!,%

"% /$+"$#' @ "! !4' &'"+!&(! ;

!ndicador de o"ro: $.1) I&(!**!('8 ($"$' @ !"$#' #%& /!,*$4'4 "' #%+$&'#$5&;

Númerode ítem:$%

Enunciado:

J'&8 L$/8 A&(%&$% @ P!4*% /%& '+$,%/ ! /! !&#%&(*'*%& !& &' !/

/'"4'*%& #'"*%/'+!&(!; CK&(%/ '*!(%&!/ 4! +'&% /! 4$!*%& !&(*! (

Repuesta Correcta: A

Comprende que la situación que corresponde a las combinaciones; la cual puede que la resuelva

al menos de dos maneras: Por un lado, que interprete que Juan saluda a sus tres amigos. Luis

saluda a Antonio y Pedro, porque antes se saludó con Juan y por ltimo Antonio saluda a Pedro,

obteni!ndose de esta manera " saludos.

#tra $orma de interpretar: %ay & personas y en un saludo intervienen dos de ellas, es decir

4 4! 432! 43

2 2!(42)! 2!21 2 6.

B; 'esconoce que la situación se re$iera a combinaciones por eso interpreta que Juan saluda a

sus tres amigos y a%( se terminaron los saludos.

C; )nterpreta saludos entre pares de amigos, Juan con Luis y Antonio con Pedro.

D; La con$unde con una permutación, considerando que el orden es importante, por eso obtuvo

4 que eran seis

saludos y luego multiplica por dos ó bien en la e*presión 2 no dividió por +&-/,

4 4! 432! resultando

2 2! 2! 4 x312.

Indicador de Logro: 2.15 0esuelve problemas aplicando las combinaciones con seguridad.

Enunciado:

U& /%*!(!*% ($!&! !& / #'**!(5& Q 4$/($&(%/ /'%*!/ 4! !"'4% -?*!/'8 >'$&$""'8

#%#% @ ('+'*$&4%; L%/ /%*!(!/ ! >'"!& ]0;90 !/(K& #%&?%*+'4%/ %* (*!/

##'*'4'/ 4! !"'4%8 4! "%/ /'%*!/ ! /! 4!/!!&; D! #K&('/ ?%*+'/

4$/($&('/ ! " /%*!(!*% !4! %?*!#!* / *%4#(%

A; 20B; QC; 12D;

Respuesta correcta: '

C%+*!&4! ! /! (*'(' 4! #%+$&'#$%&!/ #%& *!!($#$5& %* !/% #%&/$4!*' !!4! #%"%#'* (*!/ ##'*'4'/ 4! & /%"% /'%*8 4$)&4%/! 4'* #'(*% /%*!(!/

4$/($&(%/ 4! & /%"% /'%* -^?8 >>>8 ###8(((8 !4! %&!* (*!/ ##'*'4'/ 4! 4$/($&(%/'%*8 ,!&!*K&4%/! #'(*% >'*$!4'4!/ 4$/($&('/ -?>#8 ?>(8 ?#(8 >#(8 % $!& %&!* 4%/##'*'4'/ 4! & /'%* @ %(*' ##'*'4' 4! %(*% /'%*8 ,!&!*K&4%/! %(*'/ 4%#!>'*$!4'4!/ 4! *!/!&('#$5& 4!" /%*!(! -?##8 ?>>8 ?((8 >^8 >##8 >((8 #^8 #>>8#((8 (^8(>>8(##

B; D!/#%&%#! ! (*'(' &' /$('#$5& 4! %*4!&'+$!&(% #%& *!!($#$5& %* !""% /%"% (%+'

!& #!&(' ! !4! '#!* & /%*!(! %&$!&4% (*!/ ##'*'4'/ 4! & /%"% /'%* -^?8>>>8 ###8((( % $!& (*!/ ##'*'4'/ 4! 4$/($&(% /'%* -?>#8 ?>(8 ?#(8 >#(;

C; C%+*!&4! $&#%**!#('+!&(! "' /$('#$5& ! /! "! "'&(!' %* !/% /%"% (%+' !&#!&(' ! !4! '#!* /%*!(!/ 4! 4%/ /'%*!/ 4$/($&(%/ &' ##'*'4' 4! & /'%*@ 4%/ ##'*'4'/ 4! %(*% /'%* -?##8 ?>>8 ?((8 >^8 >##8 >((8 #^8 #>>8#((8 (^8 (>>8(##

D; C%+*!&4! '*#$'"+!&(! ! /! (*'(' 4! %*4!&'+$!&(% #%& *!!($#$5& %* !/% (%+'!& #!&(' "%/ /%*!(!/ 4! & /%"% /'%* -Q @ "%/ /%*!(!/ 4! (*!/ /'%*!/ -Q @/%&! ! !" >!&4!4%* !4! %?*!#!* %#% >'*$!4'4!/ 4$/($&('/ 4! / *%4#(%;

!ndicador de lo"ro: $.1- R!/!">! #%& /!,*$4'4 *%"!+'/ 4! '"$#'#$5& /%*! !"&+!*% 4! %*4!&'+$!&(%/ 4! %!(%/8 !&(*! "%/ #'"!/ '@ *!!($#$%&!/ % &% "'/ '@;

Númerode ítem:$#

Enunciado:

CK" !/ !" >'"%* 4! G !& "' !#'#$5&Q 3

&pciones de respuesta: A;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

B;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

C;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

R!#%&%#! ! !/(! ($% 4! /$('#$5& *!$!*! "' '"$#'#$5& 4! "' *%$!4'4 P'*'

4$?!*!&(! 4! #!*%8 !&(%&#!/ ' /$ @ /5"% /$ ' 8 %* !/% (*'&/?%*+'

#%**!#('+!&(! !& 8 "!,% ""!,'&4% ' %(!&!* ;

A; E**5&!'+!&(! #%&/$4!*' ! !/ !$>'"!&(! ' ; P%* !/%8 '&! ($!&! #"'*$4'4 4!

"' *%$!4'4 -P'*' 4$?!*!&(! 4! #!*%8 !&(%&#!/ ' /$ @ /5"% /$ ' 8 "'&(!'

$&#%**!#('+!&(! ! #%& "% #'" ""!,' ' 9;

B; A"$#' $&#%**!#('+!&(! "' *%$!4'4 P'*' 4$?!*!&(! 4! #!*%8 !&(%&#!/ ' /$ @/5"% /$ ' 8 %* !/% "% (*'&/?%*+' !& 8 ! $,'"' "%/ !%&!&(!/.3 38 %(!&$!&4% ;

C; D!/#%&%#! #5+% '"$#'* "'/ *%$!4'4!/ 4! "'/ ?&#$%&!/ !%&!&#$'"!/8 %* !/%$,'"' .3 Q @ %($!&! 7;

!ndicador de lo"ro6 %.$ I4!&($#' @ '"$#'8 #%& $&(!*)/ @ /!,*$4'48 "'/ *%$!4'4!/

4! "' ?&#$5& !%&!&#$'";

Númerode ítem:$(

Enunciado:

CK" !/ "' *!*!/!&('#$5& ,*K#' 4!@ 3

I4!&($#' #%**!#('+!&(! ! "% #'" !/ &' ?&#$5& 4!#*!#$!&(!

N úmerode ítem:$+

Enunciado:

E" >'"%* 4! "%,2 Q !/

A; S! !$>%#' '" #%&/$4!*'* ! %* (!&!* %*4!&'4' $,'" ' 3 !& "' ,*K#'8 !/(!

#%**!/%&4' #%& "' '/! 4! @38 #'&4% !& *!'"$4'4 "' ,*K#' #%**!/%&4! '

B; S! !$>%#' '" #%&/$4!*'* ! @3 !/ $,'" ' @3;

D; S! !$>%#' '" #%&/$4!*'* ! @2 !/ $,'" ' @3

!ndicador de lo"ro: %.% S!"!##$%&'8 #%& /!,*$4'48 "' !/#'"' '*%$'4' '*'

*!*!/!&('* "' ,*K#' 4! &' ?&#$5& !%&!&#$'";

Númerode ítem:$-Enunciado:

L' !*!/$5&

"%, !/ !$>'"!&(! '

Respuesta correcta: 'I&(!**!(' ! !" "%,'*$(+% '/! 'G 4! & &+!*% G !/ & >'"%* G ('" ! /$ 'G /!

!"!>' '" !%&!&(! G8 /! %($!&! !" &+!*% G; P'*' "' /$('#$5& "'&(!'4'8 !"

!%&!&(! '" ! /! 4!! !"!>'* "' '/! 28 '*' %(!&!* Q !/ ;

"%,2 Q

2 2 !&(%&#!/ ;

B; D!/#%&%#! #%+% 4!(!*+$&'* !" "%,'*$(+% 4! & &+!*% %* !/' *'5& "% '/%#$' #%&

4!(!*+$&'* *' #'4*'4' 4! Q8 %* !/% /!"!##$%&' ;

C; I&(!**!(' $&#%**!#('+!&(! ! 4!(!*+$&'* !" "%,'*$(+% !$>'"! ' /$+"$#'* "%/ 4'(%/

%/!*>'4%/8 %* !/% %($!&! 32;

D; D!/#%&%#! #5+% '%*4'* "' !*!/$5& "%,2 Q8 %* !/% $&(!**!(' ! /$ +"($"$#' Q

%* 28 %(!&4*K 12 #%+% /%"#$5&;

!ndicador de lo"ro: %./ D!(!*+$&' !" "%,'*$(+% 4! & &+!*% 4'4' "' '/!;

A; log x

B; log

D; log 23 x z 3 3

Respuesta correcta: *

R!#%&%#! ! !/ !$>'"!&(! ' 8 '4!+K/ ! !/ !$>'"!&(! ' 8

'4!+K/ ! "' 4$?!*!&#$' 4! "%,'*$(+%/ !/ !$>'"!&(! '" "%,'*$(+% 4! & #%#$!&(!8

%* "% ('&(%6

log x3 3log x _ log x log z

_ log x log z 3

_ log3 x log z 3

_ log__ z 3 _

A; A"$#' $&#%**!#('+!&(! "' *%$!4'4 4! "' %(!&#$' 4! & "%,'*$(+% log x

3log z log x9log z log x

3 9 z 8

Númerode ítem:$/

Enunciado:

D! "' !#'#$5& 9-"%,11-"%,32-"%, 999 4_ 4 8 !" >'"%* 4! !/#*!#$+$!&(% 4!"

+!*#'4% &'#$%&'"

C; C%&/$4!*' ! "%, -"%,'*$(+% !/ & ?'#(%* @ '"$#' ?'#(%* #%+& log8 %($!&! "'

!*!/$5& *!/!&('4';

D; R!#%&%#! ! !/ !$>'"!&(! ' log3 x 8 '4!+K/ ! 3log z !/ !$>'"!&(! '

"%, 38 !*% 4!/#%&%#! ! "' 4$?!*!&#$' 4! "%,'*$(+%/ !/ !$>'"!&(! '" "%,'*$(+% 4!

& #%#$!&(!8 %* !/% "' 4$?!*!&#$' 4! "%,'*$(+%/ "' #%&/$4!*' #%+% "' 4$?!*!&#$' 4! "%/

'*,+!&(%/;

!ndicador de lo"ro: %.1+ R!/!">! !!*#$#$%/ '"$#'&4% "'/ *%$!4'4!/ 4! "'/?&#$%&!/ "%,'*(+$#'/;

Respuesta correcta: 'R!#%&%#! ! !/(K !& *!/!&#$' 4! &' !#'#$5& "%,'*(+$#'8 '"$#' !& !" +$!+*%

4!*!#%8 "' *%$!4'4 4! "' /+' 4! "%,'*$(+%/8 !4'&4% "' !#'#$5& 4! "' ?%*+'

log5(2 x 43)_log5(11_5)8 "!,% #%+% ($!&! &' $,'"4'4 4! "%,'*$(+%/ #%& "' +$/+' '/!8

$,'"' "%/ '*,+!&(%/ 2 x 43_558 "' #'" '" *!/%">!* "! !4' 2

B; A"$#' $&#%**!#('+!&(! "' *%$!4'4 4! "' /+' 4! "%/ "%,'*$(+%/8 %* "% ('&(% !& !"

+$!+*% 4!*!#% *!4#! log5(11) 4log5(5)_log168 "!,% $,'"' log5(2 x 43)_log5(16)8

%(!&$!&4% 2 x 43_168 %* "($+% !4' ;9

C; N% #%+*!&4! ! !/(K '&(! &' !#'#$5& "%,'*(+$#' @ *%#!4! #%+% /$ ?!*' &'

!#'#$5& '",!*'$#';

D; A"$#' $&#%**!#('+!&(! "' *%$!4'4 4! "' /+' 4! "%,'*$(+% @ "!,% *%#!4! #%+% /$

?!*' &' !#'#$5& '",!*'$#';

!ndicador de lo"ro: %.1+ R!/!">! !!*#$#$%/ '"$#'&4% "'/ *%$!4'4!/ 4! "'/

?&#$%&!/ "%,'*(+$#'/;

Número de ítem: 30Enunciado:

qo 22 3 1600 t *!*!/!&(' "' #'&($4'4 ! '@ !& +$"$,*'+%/ 4! *'4$%

-!"!+!&(% *'4$%'#($>% 4!/)/ 4! t G 'X%/ @ qo"' #'&($4'4 ! $&$#$'"+!&(!

'' 4! 4$#% !"!+!&(% *'4$%'#($>%8 ) !*!/$5& *!/"(' '" 4!/!'* t G

1600ln2 q

B; 2 1600qoq 2q

D; q2qo 1600

Respuesta correcta: '

C%+*!&4! ! /! (*'(' 4! &' /$('#$5& ! ($"$' "' ?&#$5& "%,'*(+$#' %* !/%

q 1600 t

'"$#' !" "%,'*$(+% &'(*'" !& '+%/ +$!+*%/8

22 3 8 qo q

1600tln 22 38 4!/!' (8 @ '/' ' 4$>$4$* '" +$!+*% $$!*4% ' "%/

4!+K/ ?'#(%*!/8 %($!&! lnqo t

1600ln2

B; T$!&! 4$#"('4 '*' $4!&($#'* "' '"$#'#$5& 4! "'/ *%$!4'4!/ 4! "%/ "%,'*$(+%/8

qo '" +$!+*% $$!*4% *!/"('&4% q

(2) 1600 t

%* !/% I&$#$' '/'&4% ' 4$>$4$*

1600 8 &%

$&(!**!(' ! "' >'*$'"! ' 4!/!'* !/ & !%&!&(! @ "' !*!/$5& 22 3 "' !&($!&4!

#%+% & ?'#(%* 4! t G 8 "% '/' ' 4$>$4$* '" +$!+*% $$!*4%8 @ %($!&! ! q 1600

qo t ; 2

C; E" '"+&% 4!/#%&%#! ! /$ & ?'#(%* 4! & ()*+$&% >' '/'* ' %(*% +$!+*% 4!!

'#!*"% 4$>$4$!&4% % +"($"$#'&4%8 4!!&4$!&4% #%+% !*' / /$('#$5& %*$,$&'"8

!*% !& !/(! #'/% "% '/' ' *!/('* #%+% /$ ?!*'& ()*+$&%/ ! /! /+'& % *!/('&

!& !" %(*% +$!+*% 4! "' !#'#$5&8 "!,% !" .100 /$ "% >! #%+% ?'#(%* 4! (G8 %* "%

('&(% "%

q 2q o_t '/' ' 4$>$4$*8 ""!,' ' %(!&!*

D; E& !/(! #'/% 4!/#%&%#! ! "%/ ?'#(%*!/ ! '#%+'X'& ' "' >'*$'"! (G8 "%/

$&(!**!(' #%+% ()*+$&%/ ! /! /+'& % *!/('& @ ! (*'/"'4' '" +$!+*%

#%&(*'*$%8 @ ""!,' ' q 2qo_ 1600t 8 "!,% '/' ' /+'* !" ?'#(%* .1008 @ %($!&! "'

!*!/$5& q 2qo 41600_t

!ndicador de lo"ro: %.1- R!/!">! #%& /!,*$4'4 @ #%&'&'8 *%"!+'/ 4!

'"$#'#$5& 4! "' ?&#$5& "%,'*(+$#'8 !& #%%!*'#$5& #%& %(*%/;

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