8° básico - matemáticas - 2010

download 8° básico - matemáticas - 2010

of 79

Transcript of 8° básico - matemáticas - 2010

  • 8/2/2019 8 bsico - matemticas - 2010

    1/79

  • 8/2/2019 8 bsico - matemticas - 2010

    2/79

  • 8/2/2019 8 bsico - matemticas - 2010

    3/79

    !"#$%&'((")*%+"#("(")(',-%.#%#'/%))0#' &)1('20"#%")%.'%"'1'%.' 3%!%'#4(*'( 5!""!!" '(#.."*0%& '(#.%'"(.(*6%'#.%"7(%+"/(0"%+" )"+"%.%#1'#%# ""!#$! ")%("'!%%!.%"7% ")%("'!%%.%1%.0%+" 8%"&'!$$"(#!

    )!!! 0%#('"+!)(#%!"#$%&''!%#(' * ') "#%#9:('/;.*% .#()('"')0")('00.%'

  • 8/2/2019 8 bsico - matemticas - 2010

    4/79

    ,-.

    .!(*%%#')0#((70"%!(!0')%!%%(*%"$%/(")%.)%%&(!#%*+*(

    #.%B( '(.%9')%!(!0')% )" ((!(!+')( !((1. .(*(# .(' &)1('20"#%")%.'@2A/.#'%(..(.('(")"#('6"('.*%)(('@AC0#7".%(00.%9%./#'!("C0%#%')%.")(!0#.%(%'0'!(!('!(*%%'#')0#(,!1%%!(%+"#.(''('!(!%)#."#09.!'")!(*%%("'))0/0"%!(!0')%!%%%C0..('')%.")('C0"(0")%"("!(*%%'!(!('9('!"!%.'(!("")'C0("7(%".%!(!0')%#.!(*%%'("? "%'!7%+"#.('%!"#$%&'C0'#".(*%!%%%.%"$%.('2/

    #.%(00.%,.(C0'>!'%%)%1D'#.(' "%(*%"$%+")!(%.#')('%!"#$%&'"'')'/0"#%#'9 "%!(!0')%#%)1#%#'#%!"#$%&/#1%.0%+",!'")%#%'%(#(#

    '0*"%9%"%%#("%.%')('(!("")','!'")%0"("&0")(#.")('C0'")*%"(".%7"%.#%##(")%.)%%&(!#%*+*(%.$%#(%!%)#.!(*%%/!((1..(*(#.('(&)1('C0D')!(!("9% )()%.#%# # .(' .")(' C0 (!("" . !(*%% ' (*%"$% # .% '*0")%"%? 9')%'+"!'")%("!)('70"#%")%.'C0')E"".%%'

    #.%(00.%/,% .%1$,("'))0/"0"%1'+"*"%.%%#.% 70"+"#.('%!%'#!(*'(9

    9 ("'')"" (")%("'

    .1%")'!%%)%%&%(".!(*%%/(*%"$%.)%%&(")("(%.'(9 ")*%"'0*"%'*"%.'!%%!("')('

    !('('%.'1(#..(*(#.('%!"#$%&'#7"#('".!(*%%9 9')%'+"!'")%'")D)%")

    .(' !(!+')(' / '")#(''(.(' C0 '%)0.%" .(' %!"#$%&' #.')( / .%'-%.#%#'%#'%(..%9%D"")*%%.*0"%'(")%("'!#%*+*%'.1%")'!%%!.")%.!(*%%".')(9

    !9 4'")% .% )()%.#%# # %!"#$%&' '!%#(' % #'%(..%

    #0%").%B(,(*%"$%#('#%0#(%0"#%#'9 "9F0")(("'!7%.('%!"#$%&''!%#('!(!('".%0"#%#,".0/"

    "#%#('#1%.0%+"/'0*"%'#%)1#%#'C0%!(/%"/(")%".)%%&(#')"%#(%!((1')('%!"#$%&'9

    # 9 .0')%" 7(%' # %!% . .(*( # .('

    %!"#$%&''!%#('/!'")%"')%)*%'#1'%'C0!0#"'0).$%#%'!%%')7"9

    $9)%)%#0'('.(*E7('/.)+"('C0!0#"'

    0).$%#('!%%!((1.('%!"#$%&'#.')(,#')"*0"#(")%C0..('!%%'("'0.)%#('!(.#(")#.('C0!0#"'0).$%#('!(.('')0#%")'9

    )(''0!('/

  • 8/2/2019 8 bsico - matemticas - 2010

    5/79

    ---

    /0"12&'!$

    ('%!"#$%&'C0'!(01.%(00.%/.('!(*%%'#')0#(%!0")%"%

    0"#'%(..( ")*%.# .('')0#%")'94%%')('7)(',')('%!"#$%&'"1(.0%"

    )%")(.#'%(..(#("(")('!(!('#.%#'!."%((-%.#%#'/%))0#'9

    0'%C0.('')0#%")'!("*%""&0*(')('("(")(',-%.#%#'/%))0#'

    !%% "7")%#1'('#'%76(', )%")(". (")>)( #. ')(#%!"#$%&((%.

    #'"1(.1'"'0")("(9')('0!("0"%(")%+"-%%..(*(# (!)"%',

    ")"##%' ')%' (( .% (1.$%+" # ("(")(', -%.#%#' / %))0#' !%%

    #'%(..%#%"%7)1%0"%%+"#)"%#%9

    )%)%#0"%"(+"#%!"#$%&".%C0')%'-%.#%#',("(")('/%))0#'

    '#'%(..%"#%"%")*%#%,"C0D"#('/!()"E"#('#%"%6!(%9

    %'-%.#%#',("(")('/%))0#'"('%#C0"'!(")E"%")%)%1D'#.

    ')0#(# .%'#'!."%'9C0"'!((1#%'#%"%)+#%/')%>!.6)%'

    ".('!(!+')('C0%)0.%".)%%&(#.('#(")'9

    ()*

    G.%!"#$%&"1(.0%"('(.(.'%,'"()%D".'%-%94(()%!%),.%

    (")"0%>!%"'+"/(!.&$%+"#.("(")(#%"#%")")%!%#%#'

    # !"'%")( C0 !)%", ") ()%' ('%', 0).$% . ("(")( # %"%

    %!(!%#%/*0('%H%#C0"01('("(")('H>%"%6)%").%#1'#%##

    70")'#"7(%+"#'!(".',/*"%"01('("(")('"7(%+"9

    ')% ')0%+" -% .1%") .% !((+" # #1'%' -%.#%#', (( !( &!.(?

    '(.1 !(.%', 7(0.% ("&)0%', %.$% E.0.(' " 7(% ")%. / ')% /

    17%!(!('("''!.',")()%'9

    +*

    *'*

    *)

    ,)

    (-

  • 8/2/2019 8 bsico - matemticas - 2010

    6/79

    !0')('9

    ()*

    G.('("!)('#.%'#'!."%'(')('#%!"#$%&"C0".%(!"'+"#.('

    ')0#%")''(.('7"+"('%.('C0'1""7")%#('9'!)".%("%'

    (".")("(,0).$%"#("(("'#0"%(!.%#/!(70"##%#C0(!.")%",#

    0"%%"%0%.,.'%()"#(#'#.'")#((:"/#.%>!"%()#%"%9

    #("%."), ')(' ("!)(' '(" 70"#%")%.' !%% .% ("')0+" # "01('

    %!"#$%&'!(!%)#.('')0#%")'9

    4(&!.(,''('1%0"%"7(%+""0"#%(C0(")"*%#%)('!'")%#('

    ")%.%'(*E7(',.')0#%")0).$%'0'("(")(''(')%#6')%!%%")!)%

    %'%"7(%+"9('("(")('!1('.%!%)%!%%!#'(.(C01%%.

    !%%.0*(17%'0'!#("'".%##%C0")"#.%"7(%+"/%'6("')0

    ')"01(("(")(9

    ()*

    G'(" 0"% ("#+" !%% . #'%(..( # .%' -%.#%#'9 ')%'"('#'%(..%" "0"

    1%6(,'"('(.%%'#)('("!)('(("(")('#)"%#('9

    ()*

    G.(' %!"#$%&' "( '(" .")(' C0 "1(.0%" :"%") .% #"'+" (*")1%9

    !')E"%'(%#('(".%'%))0#'/#'!('("'#.('')0#%")'9")(#.('

    !(!+')(' ')%.#(' !%% .% #0%+" ' (")!.% . #'%(..( " .(' E)('

    !'("%.,'(%.,D)(/0#%#%"(9')('"1(.0%"%'!)('#%E)%7)1(/,%.%

    1$,.#'%(..(#)%'#'!('("'9

    (#(#&!.(,.('%!"#$%&'"1(.0%"%))0#')%.'((!'1%"%,*(,

    7.>.#%#/(*"%.#%#%.'(.1!(.%'%)E)(',)%%&("C0!("%)1%

    !'("%.".%'(.0+"#!(.%'"(")>)('#1'('/'!)(!(#%'#')")%'%

    .%'!(!%'9

    (

    %

    %)

  • 8/2/2019 8 bsico - matemticas - 2010

    7/79

    8

    ()*G"0-(' %'(' C0"# .('("(")('/ -%.#%#' !%%'0#'%(..(9 ')('

    ("(")(' / -%.#%#' ")*%" -%")%' "'%%' !%% .%(% &0('

    "7(%#(', %"%.$% 6)%") #1'%' 0"')%"%', / !%% (")%')% )(' /

    #'("',")()('!('('"1(.0%#('".#'%(..(#%))0#'9

    .% 1$, .%' %))0#' (")%" . '")#( / . 0'( C0 %#% %.0"( ()(*% % .('

    ("(")('/ -%.#%#'%#C0#%'9 (", !( .( )%")(,0"%")#") "'%(!%%

    -%0"0'(("')0)1(#')('.")('9

    ()

  • 8/2/2019 8 bsico - matemticas - 2010

    8/79

    3

    3024!!546

    (" %!"#$%&'C0 )"" 0" %E) (!"'1(/ *"%., / C0 %!0")%" %.#'%(..(

    !'("%.,D)(,'(%.").)0%.# .('')0#%")'92(%"!%)("'))0)1%#.060.0

    "%("%./,!(.()%")(,.('')%.")('#"-%'%*(#!((1'0.(*(9

    ('2"('#'%(..%"%)%1D'#0"')(#%!"#$%&"!%)0.%,'"(C0#!"#"

    #.("&0")(#.060.09"".0*%)%")(%)%1D'#.%'#1'%'#'!."%'#.060.0

    ((#.%'#')")%'#"'("'#.C0-%#0%)1(@!(&!.(,%)%1D'#.!(/)(

    #0%)1("'))0("%.,.%!E)%#("),..%(*%"$%("%.,.%#'!."%(.%'("%'

    '(.%'A9

    (')%)%#(&)1('C0"1(.0%":"%")%))0#'/1%.('90!(".%")*%+"#

    ')('.")('(".#'%(..(#("(")('/-%.#%#'9

    !%) # .% %)0%.$%+" %.%( 00.% %.$%#% . %B( 5, ')(' (&)1(' ')E"

    (*%"$%#('%&(0"'C0%(:"!%%.%#0%+"E'%/.%#0%+"#%9%0#(

    (" ') 'C0%, .(' &)1(' 20"#%")%.' %"'1'%.' ' (*%"$%" " E)('?")(/%0)(%7%+"!'("%.,#'%(..(#.!"'%")(,7(%+"D)%,.%!'("%/

    '0")("(,/)"(.(*6%'#.%"7(%+"/(0"%+"9

    ('*

    #

    (.

    *)-

  • 8/2/2019 8 bsico - matemticas - 2010

    9/79

    5

    70""

    (" #'!("' *"%.' C0 'B%.%" # C0D %"% !(*'%" )6!%") .('

    %!"#$%&' " .%' E%' .%1 # 0" ')( #)"%#(9 )%)% # 7(0.%("'

    '")D)%'C0'")%"".('%'!)(''"%.'#%#%')(9!%)#')((7"

    0"%1'+"!%"(E%'(.("&0")(#.%!(*'+"#.%!"#$%&" .('%B('#'(.%#%#9

    ('%!%'#!(*'("(')%."%!"#$%&'%#("%.'%.('#7"#('".%(

    00.%/ .('!(*%%'# ')0#(9%!(*'+"C0#'"'0"%>!'+"E'

    *0'%/'")D)%#.('%!"#$%&'C0')('#('"')0")('')%."/,C0!(.(

    )%")(,'"'#")(#.(C0'!.%")%"..('90!%)0.%#%#("'')".%1'+"

    #("&0")(C0")*%"'(.%!(*'+"'!%#%%.(.%*(#)(#%.%%'*"%)0%9

    IJ0D0).#%#)"".('%!%'#!(*'(!%%.)%%&(#.('#(")'K

    (' %!%' # !(*'( !0#" ' 0" %!(/( !()%") )%")( !%% # 2 (( !%% %.$% . !('( # ! @1 (")%("' !%% .%

    !.%"7%+"/!%%.%1%.0%+"C0'!'")%"".!(*%%A9

    #("%."),.('%!%'#!(*'('("0"7"):).!%%!

    #')0#%")'#")(#.%0.%9

    - 4)" #% 0" !%'( C0 1% E' %..E # .% '!. ("')%)%+" # C0 >')"

    #')")('"1.'#%!"#$%")(#0"'(0'(9%"!!%%%%)$%

    #")7%("%/(!'+""C0D("'')"')%'#7"%',%!%)#'00'(

    !%%%"%.$%.('#'!B('#.('')0#%")'9

    - % !(*'+" C0 #'" !) ("( " C0D '")#( (")% .('%!"#$%&'# .('#')")('*0!('C0'%"7')%""0"'(0'(,)%")(#

    %C0..('C0"(-%".(*%#(."1.'!%#(!%%. 0'(,((!%%%C0..('C0

    /%.(-%"%.%"$%#(('0!%#(9

    >!'%" . !(*'( #. %!"#$%& " 0" E% .%1 #. ')( #%"% '")D)% /

    %."%#%%.%(00.%9

    ('%!%'#!(*'(#'""8"1.'.")()6!(#.%!"#$%.('')0#%")'"0"E)((.')(9%#%0"(#')('"1.'!'")%0"%>!)%)1%#%!"#$%&('!("#")%#('%B('#'(.%#%#94(&!.(,.1.('!("#%..(*(C0''!%!%%.%%/(6%#.('"B('/"B%'%.)D"(#*0"#(E'(H.1.('!("#%.)D"(#0%)(E'(,/%'6'0'1%")9.1.8#'.%!"#$%"%.0"((%.0"%C0%. *'%#.%#0%+"#%'L'('%.")M,'#,1%E' %..E#.%>!)%)1%!%%0%)(#(,C0#'.1.

  • 8/2/2019 8 bsico - matemticas - 2010

    10/79

    %1$.

    Nivel 3

    Reconoce que los nmeros naturales

    ,!""&$!

    ")%" .% .%( !#%*+*%,')%."#( !"#$%&''!%#(' C0 #%" 0")% # .('&)1(' 20"#%")%.' /(")"#(' 6"(', / .(' (*%"$%!(%.")%)%1D'#0"#%#'9

    1%345

    ) .

    Integrados en la

    formulacin del

    mapa de progreso

    !

    4'.('&)1('20"#%")%.'/(")"#('6"('.*%)(('C0)(#('.('')0#%")'#".(*%9

    &!.(?&)1(20"#%")%.3NE'(')%.')%)*%'!%%%.0.%0.)!.%("'/#1'("'#":('")('9(")"#(6"(.*%)((!.(#!(#")('#E.0.(!%%0.)!.%0"":("%)0%.!(0"":(")("*%)1(H/,>)"'+"##-('!(#")('%.%0.)!.%+"#":('")('9

    0

    ,.*

    ,.*, . 0 ). % . " '. - '

    , - ) #" 6

    Nivel 2

    Utiliza los nmeros naturales hasta1.000

    ".7888*

    """)*% 0"% 1'+" '")D)% #. !(*'( #.%!"#$%&"0"E%.%1#.')(,/'%&0')%%.%'>!)%)1%'#.%(00.%9

  • 8/2/2019 8 bsico - matemticas - 2010

    11/79

    -,-8,9-,9,9,8,

    %' (")%("' C0 ' !'")%" % (")"0%+" #')%%" %.*0"(' .")(' .1%")' %. (")( #

    !.")% . !(*%%9 .*0"%' # ')%' (")%("' ' 1"0.%" ')-%") (" %.*0"(' # .(' 2

    (")!.%#('".060.09

    /0*!!2

    ('#(")'#"!((1.&(#.%(0"%+"(%.,#.%.)0%/.%')0%

    ((!%)("'))0)1%#.)%%&(!#%*+*(('!("#")%%#%')(#%!"#$%&9

    ')('&0')7%!(C0.%'-%.#%#'#(0"%+"'("-%")%'70"#%")%.'C0

    .('')0#%")'#"!.%!%%%.%"$%.('%!"#$%&'!(!('#%#%')(9)%)%

    # -%.#%#' C0 "( ' #'%(..%" :"%") " . (")>)( #. ')( "*0%& /

    (0"%+",'"(C0'("'(.#%"%)%1D'#.&("#1'(''!%('/")("(%

    #1'(')%'/,!(.()%")(,"1(.0%".('()('')('#%!"#$%.060.09

    .(")(#0% .%.)0%,.%')0%/.%(0"%+"(%.,.('#(")'#"

    !(0%?

    )0%?

    - .% .)0% # #')")(' )!(' # )>)(' .1%")' !%% . ')( @)>)(' "7(%)1('!(!('#.')(,)>)('!(#6')(',"%%)1(',)%.%'/*E7('A

    - .% .)0% # )>)(' # ") (!.%# " .(' C0 ' 0)." ("!)(''!%.$%#('#.')(

    - .%#")7%+"#.%'#%'!"!%.'/.%.(%.$%+"#"7(%+".1%")- .% %.$%+" # ':"', '6")'' # .%' #%' / %*0")(' !'")%#(' " .('

    )>)('

    - .% :'C0#% # "7(%+" " 70")' ')%',#'"E"#(.%/ '.("E"#(.%#%0#(%'0!)""%- .%(!"'+"/#("(#"01('("!)('/!%.%%'9

    ')0%?- .% ')0% # )>)(' # #1'% >)"'+" / (!.%# @!( &!.(? !()',

    "'%/(',#'!("','!0')%'1'A- .%(*%"$%+"/!'")%+"#"7(%+"%)%1D'#'C0%'()%.%'- .%!'")%+"#.%'#%'#0"%%"%(-")/.%%- .0'(%!(!%#(#.1(%0.%(".(')>)('')('- .0'(()(#.%*%E)%/#.%()(*%76%9

    (0"%+"(%.?- .%%!%#%##>!("%")()%'!'("%'- .%>!'+"##%'/("(")('#%"%(*%"$%#%- .#'%(..(#.%%*0")%+"%.7(0.%#%'/(!"("'

    - 0" 0'( #. ."*0%& (" "1.' ")' # !'+", "(!(%"#( .(' ("!)('!(!('#.')(- . !.%")%")( # !*0")%' !%% >!'% #0#%', "C0)0#', / !%% '0!%

    #70.)%#'#(!"'+"- .% #'!('+" !%% '0-% "7(%+" # %"% (%., %")""#( .% %)"+"

    #0%").)!(C0#(- .%")%+"("()%'!'("%'!%%")%%#%',%"%.$%"7(%+"/.%(%

    (">("'".%+"%0")%"!%)0.%,(!%)!0")('#1')%/#'%(..%%0#('9

    9

    (

  • 8/2/2019 8 bsico - matemticas - 2010

    12/79

    30*!!(!#$56

    . #'%(..( # .%' %!%#%#' !%% 0).$% .%' "(.(*6%' # .% "7(%+" /

    (0"%+" @'A ')E (")!.%#( # %"% >!.6)% (( 0"( # .(' &)1('

    20"#%")%.'%"'1'%.'#.%(00.%9')(#%"#%C0.#("(/0'(#

    ')%' )"(.(*6%' '!(01% #%"% ")*%#%%. )%%&( %.$%#( %.")(#.('')('#%!"#$%&94%%')('#!(0%C0.%.%(#.('')0#%")'".0/%.

    0'(#.%''!%%?

    - 0'%,%#/(.)%"7(%+""!E*"%'O0()%'70")',/'.("%')%

    "7(%+",>%"%"#(6)%")'0.1%"%/%.#%#

    - !('% / (*%"$% #%)(', 0).$%"#( !.%")..%' # E.0.(, / %"!0.% .% "7(%+"

    '')%)$%#%"')%'!%%#")7%)"#"%',*0.%#%#'/!%)("'.%)1('%.('

    7"+"('')0#%#('".')(

    - #'%(..%/!'")%"7(%+"%)%1D'#.0'(#!('%#('#)>)(,!.%")..%'#

    !'")%+"@!(O!(")A,%'6((-%")%'/%!.%("'#%*",%0#(/1#(

    - ")%%"7(%+"%)%1D'# .%'-%")%'C0(7 ")")((.((

    .)+"(,-%),'!%('")%)1('"')('O,((0"#%#'1)0%.'- '!)%/%'0("'#%("'D)%'".0'(#.%'',((.0#%#(!'("%./

    . '!)( !( . ()( %. 0).$% ')%' -%")%'H 'B%.% .%' 70")' # #("# '

    ()" .% "7(%+", / '!)% .%' "(%' # 0'( / # '*0#%# # .(' '!%('

    1)0%.'9

    70!

    " . )%%&( !#%*+*(, . #(") # )(% " 0")% .% #1'#%# ") .('

    ')0#%")', /% '% " )D"(' 0.)0%.', '(%.', D)"(' ( .*('('H %'6 (( "

    )D"('#').('#%!"#$%&/#.('"1.'#("(")(9

    ')%#1'#%#)%("'*(#'%76('C0C0"'(")!.%#('!(.('#(")'9")

    ')('%'B%.%?

    - !((1 . '!)( % %#% 0"( # .(' ')0#%")', " 0" (")>)( # )(.%"% /

    %!)0%,1)%"#(.%'#')")%'7(%'##'"%+"

    - !(0%C0.('%!"#$%&''#'%(.."#0"%%"%'*"7%)1%".%+"%.

    (")>)(/.%%.#%##.('')0#%")'

    - !(0%C0)(#('.('')0#%")'.(*".('(&)1('#%!"#$%&'B%.%#('".

    060.0,!'%.%#1'#%#C0'%"7')%")..('9

    2

    #)""0")%C0%)"#%.%#1'#%##').('/)('#%!"#$%&"(

    !.%L>!)%)1%'E'%&%'M!%%%.*0"('')0#%")'94(.(")%(,.%"'#%##

    #0%" 7(%#7"%#%%!%0%"#("('#%('0")%#C0!%%C0 .('

    %.0"(' %.%"" %.)%' >!)%)1%', #(' ("( '0' "'#%#' ##E)%'

    9 ')

    % :# 0

    ( '

  • 8/2/2019 8 bsico - matemticas - 2010

    13/79

    !'("%.'9'!%('%C0)(#('.('')0#%")'%.%"".('%!"#$%&'#'!0')('!%%

    '0"1.(*%#(9

    "%)"+" % .( %")(, ' ("1"") C0 %.(")( # #'B% . )%%&( "0"%0"#%#, . #(") # ("'#% C0 !%% C0 %.*0"(' ')0#%")' .(*" ')('

    %!"#$%&' !'%E"E')!( (D)(#('#7")'9 4%%')( ##'%(..% 0"%

    !.%"7%+"").*")C0*".%'("#("'C0.!)%"?

    ("(.('#7")'"1.'#%!"#$%&/("(")('!1('#.('')0#%")'

    1%.0% / #%*"(')% " 7(% !%"") !%% ("( .%' "'#%#' #

    %!"#$%&

    #7".%>."%,("'#%"#(.!(*'("#1#0%.((!0")(#!%)#%

    ".0("%("'##E)%'@%*0!%")(', )%%&(*0!%.,"("'A/%)%.'

    #1'('@1'0%.',(&)('%"!0.%.'A

    1%.0%##')")%'%"%'%.('%.0"('/#%)%%'(":.)!.'(!("'

    !((1.%("7%"$%#.('%.0"('"'6'(' 4((10")%%&('')E)(!(!%)#.('')0#%")'/&)%+"%0"#%")9

    % )

    % )0 -

  • 8/2/2019 8 bsico - matemticas - 2010

    14/79

    ,-,94,:)9*,

    0 ,-,94,

    % !.%"7%+" ' 0" .")( ")%. " . '70$( !( !((1 / *%%")$% .('

    %!"#$%&'#.('')0#%")'94)%>$%.0'(#.)!(/#7".('!('('/

    0'('"'%('!%%C0')('.(*".('%!"#$%&'C0#"%.%"$%9

    ('!(*%%'#')0#(#."')(##0%+"("'))0/"0"%-%")%#%!(/(

    %.!('(#!.%"7%+"94%%')('7)('-%"'#(.%(%#('((0"%)%.7.>.

    C0 .('!(7'('!0#"%#%!)% % '0 %.#%# " .('#')")('(")>)('#0%)1(' #.

    !%6'9

    . !"!%. 7") C0 ")*% . !(*%% # ')0#( !%% !.%"7% '(" .('"12"9%"%%#("%.,.!(*%%%!(/%.%!.%"7%+"%)%1D'

    #.%!(!0')%#,#.%!"("(.+*(C0#("%#%

    0"%,/#.%!%%#'%(..%.('%!"#$%&'9

    !"!1!"!#

    % !.%"7%+" ' 0" !('( C0 ' ("#% %.$%, ("'#%"#( .(' '*0")'

    %'!)('?

    %#1'#%##"1.'#%!"#$%&C0-%"%.%"$%#(.('')0#%")'#.0'(,.(

    C0!.%!.%"7%,("'#%"#(#'%76('!%%#')")('*0!('#%.0"('9 .)!(%.("C0'0")%,#%"%#(!)$%.)!(#'!(".9

    %'!E)%'!#%*+*%'C0-%"#%#('0.)%#(''%)'7%)(('9

    (' 0'(' !%% . %!"#$%& (" C0 ' 0")%? )>)(' '(.%', %)%.'

    ##E)(', 0'(' .%(%#(' !( .% '0.% ( %C0..(' C0 ' "'%( #'B%,

    .%(%)((,%)%.'#'!(".'".")(#0'('#!"#$%&@A,")

    ()('9

    -"!""!#

    4%% C0 .% !.%"7%+" 7)1%") %/0# %. .(*( # .(' %!"#$%&', # ')%

    ")%#%")("(%')('/#'%(..%'%!%)#0"%1'+".%%#.(C0.('')0#%")'

    #" %!"#9 4%% .(*%.( ' ("#% .%(% .% !.%"7%+" " .(' '*0")')D"('?

    - 4%)!(0"%'!7%+"#.('%!"#$%&''!%#('C0"('.)%.')%.('9

    "% 1$ #")7%#(', ' "'%( #'%(..% 0"% #% .(E' .%% !('. # .%'

    >!'("'(")%'C0')('!0#%")"9')(!.%("(C0D#'!B('

    #.('')0#%")'#%"0")%#..(*(#.('%!"#$%&'9#!(#'!("#

    9

    %0

    (

    (*%0"%1'+".(E'.%%/(")%!('.'(.('#'!B('C0#%"0")%#.('%!"#$%&'G

  • 8/2/2019 8 bsico - matemticas - 2010

    15/79

    !*0")%' ((? IJ0D #6%" ' %!%' # #(')% .(' ')0#%")' C0 -%"

    .(*%#(0"#)"%#(%!"#$%&'!%#(K,IC0D-%6%C0('1%!%%'%C0

    0"%!"#$%&-%'#(.(*%#(K

    - !%)# .%' '!0')%' %')%' !*0")%', ## .%' 1%.0%("' % %.$%/ .%'

    ')%)*%' # "'B%"$%9 '!67%"), ' C0 #")7% C0D )%% #1%.0%+" ' E' !)"") !%% ('1% . #'!B( '!%#(, %'6 (( .%'

    (#%.#%#' # "'B%"$% C0 7%.)%E" %.%"$% ') #'!B(9 " %' % ')

    !('( ' #" #7" .%' 1%.0%("' 7(%)1%' / '0%)1%', .%' %)1#%#' #

    "'B%"$%,/.%'"')%"%'#)(%.")%+"9

    4%%..1%%%(')!('(,.('#(")'!0#"(!.")%.('!(*%%'(".('

    %!%'#!(*'(9')('")*%".")(':).'!%%("(.)!(##'!B(

    %'(%#(%.('%!"#$%&'9

    '0*C0.%7(%#!.%")%.%!.%"7%+"%%!(!0')%'%0).$%#%)%")(".%

    !.%"7%+"%"0%.((".%('!("#")%%#%0"#%#/%.!.%"#%#%.%'9

    9 "!# !1 " ') !('( . #(") # #')0 .(' %!"#$%&'

    '!%#('%.(.%*(#.%B('(.%("'#%"#('0(*%"$%+"!(0"#%#',')%.

    )!(C0'C0E!%%%#%0"#%#,/!($%.%'%("'C0("#0E"%.(*('

    %%#D(''*"7%)1('

    4%%')(.#(")#?

    - (*% 0"% 1'+" '")D)% #. ("&0")( # %!"#$%&' % .(*% #0%") . %B(,

    #"'("%"#(.)!(# %( C0 '#('1% ".('')0#%")'9 ')(#

    #'%(..%' % !%) # .(' %!"#$%&' '!%#(' '!7%#(' " .(' !(*%%'9#("%."),.('%!%'#!(*'(!0#"'0.)%0"%!(/(!()%")9

    - #")7%,")D"('*"%.',.)!(#1%.0%+"C0'C0E!%%17%.

    .(*( # .(' %!"#$%&'9 ')( !)E #'%(..% 0"% #% # .%' #%"#%' /

    C0")('%("'#%!%%%#%0"#%#9

    - (.%%'#')%1'+",%'*"%.(')!('%#')"%%%#%0"#%#94%%!(0%

    C0')%#')0+"'0.).(E'%.')%!('.'("#%%.$%.('*0")?

    ')% #6%' #. %B( / -(%' # .%' !( '%"% !%% ')% . )!(

    #'!(".9

    P%0"%%."#%$%+")")%)1%# .('%!"#$%&''!%#('!%%. %B((!.)(,("'#%"#(.('7%#(',.('#6%'#!0%,#!%'(,%'6((.%

    %.$%+"#1%.0%("'7(%)1%'/)(%.")%+"9

    P%0"%!.%"7%+"*0'%#.%'%)1#%#'%!%)#.%%."#%$%+"9

    &0')%!%"")").%%."#%$%+"(.%'%)1#%#'!.%"%#%'@1

    &!.(")%.%%#&0")%A9

    4".">('!'")%0"&!.(#%."#%$%+"%"0%.9

    G/"%'%')(##.%'1%.0%("',.%'')%)*%'#"'B%"$%,/.%#')0+")!(%.

    %.$%')!('(("'#%"#(0"%1'+"%.')%#.(')!('#'!(".'#0%").%B(

  • 8/2/2019 8 bsico - matemticas - 2010

    16/79

    !"%' #'%(..%#%' !%% 7)(' # !((1 '0

    %!"#$%&9

    %.$%')!('('"!##1')%.%)%#%!"#$%.%0"#%#

    4(0%C0.('')0#%")''!%"C0D/!(C0D1%"%%!"#,C0D%!"#("/#C0D%"%

  • 8/2/2019 8 bsico - matemticas - 2010

    17/79

    8

    0 ,-,9)9*.

    %1%.0%+"'0"!('(C07(%!%)("'))0)1%#.!('(#"'B%"$% 9('(.(

    #'0).$%#%((0"#(!%%(")(.%C0D'%".('')0#%")','"(C00!.

    0" (. ")%. " .% !((+" / #'%(..( #. %!"#$%&9 4%% C0 .% 1%.0%+"

    7)1%")0!.%("')%70"+"#)"(((&)1('?

    0"#((".0%.#('!(*'("..(*(#.('%!"#$%&'9

    4(!(("% "7(%+" C0 !)% ("( 7()%.$%' / #.#%#' # .('

    ')0#%")', / '( ')% %' )(%.")% .% "'B%"$% / !()"% .(' .(*('

    '!%#('#")(#.')(9

    0"%-%")%:).!%%.%!.%"7%+"9

    ;"!"12!.)%C0D'1%.0%E

    #")7%.(*('/#.#%#'

    7)(%.")%+"

    ('%!%'%!(/%"#1'('%'!)('#.!('(#1%.0%+"

  • 8/2/2019 8 bsico - matemticas - 2010

    18/79

    3

    .%7%.%>!)%)1%#%!"#$%&"%("%.,%.("(.%#'!+"#%#%"1.,

    '0' &!.(' # #'!B( / . )%%&( (")( # ')0#%")' C0 .0')%" ')%

    >!)%)1%9

    '1%.#'%(..(,!(*'+"(")(#.%'(!)"%'#0"%.0"(,%.

    ("')%)%+('0'#'!B(''1%"#'!.%$%"#(".%!%9

    (")%("(#.('#)%%'/!*0")%'C0!)"%%#%%.0"(1#"%'0'

    %!"#$%&'9

    ;!!=

    % 1%.0%+" # #'B%' % !%) # .(' %!"#$%&' '!%#(', (" . (&)( #

    ('1% . *%#( "C0 ')(' '(" .(*%#('9 4%% .(*% ')( ' ("#% #'B% .%

    1%.0%+"&0")(%.%!.%"7%+"/("'#%%.#'%(..%.%.%''*0")'!*0")%'?

    I0E.''(".('%!"#$%&''!%#('#.!(*%%C0%%%E.%1%.0%+"K

    @#!($%!"'"%C0..('%!"#$%&'C0'E"#0%#('/!C0')('

    !%% #'%(..% ()(' %!"#$%&'9 4%% ')( .(' %!%' # !(*'( !0#" ' #

    '!%.0).#%#A9

    IJ0D1#"%"')%6%C0'0'')0#%")'>-%"!%%#(')%C0#("%".('

    %!"#$%&''!%#('K@4%%')('("#%0).$%((%!(/(.('"#%#('#

    .(*(C0!'")%.!(*%%A9

    IJ0D D)(#( !.%E !%% 1%.0%K ' ("#%. 0).$% "')0")(' /

    ')%)*%'# #1'( )!(@&9,!0%'')%', *06%'#)%%&(,"7(', "'%/(',

    ")1')%',#%)',%!%'("!)0%.',"7('#.%(%)((,"1')*%("'A9

    " .( !('. ' #" !'")% ')0%("' C0 !0#" ' '0.)%' # #')")%'

    %"%'/("#7")*%#(#(!.%#,!%%C0.('#1'('')0#%")'!0#%"

    '(.1.%'1#"%"#('0'#')")('"1.'/').('#%!"#$%&9

    IJ0D!*0")%'".0E"'01%.0%+"K7(0.%!*0")%'*0('%'/%."%#%'

    (" .(' %!"#$%&' '!%#(' / C0 !)%" #(')% .% %. (!"'+" #.

    (")"#(1%.0%#(9

    I0E.''(".(')('#D>)(KI0E.''(".%'%%)6')%'#0"%'!0')%#

    %.)%%.#%#K

    ')('!0#'!("#0).$%"#(#')")%'')%)*%',((!(&!.(?o (!%% .%' '!0')%' #'0' ')0#%")'(" .%'&(' '!0')%' #()('

    %.0"('##%#'.%94%%')('!0#"0).$%.('&!.('!'")%#('"

    .('%!%'#!(*'(9

    o #")7%'!0')%'#1%.0%("'!1%")%.$%#%'C0>!'"."1.

    # #'!B( '!%#(, / 0).$%.%' (( (#.( !%% ()%' 1%.0%("'

    %.$%#%'")("(%.'(%!"#$%&9

    G/.0*(##C0D'C0!%%'01%.0%+"")D"('#1#"%',D)(#(',!*0")%'/)('

    4%)')%."#(.('%!"#$%&''!%#('%1%.0%G

  • 8/2/2019 8 bsico - matemticas - 2010

    19/79

    5

    o '%(..% :%' C0 "#C0" .(' '0.)%#(' >!.6)(' !%% 0" #'!B(

    '!67(/0')".('#7")'"1.'#%.#%#!%%#-(#'!B(9

  • 8/2/2019 8 bsico - matemticas - 2010

    20/79

    %"&?!$$"(#!

    . %!"#$%& # .% %)E)% %/0#% " .% (!"'+" # .% %.#%# / !(!(("% -%")%' !%%

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

    '(#%#9 " ("'0"%, .%%.#%#,!)""%/ %!.)0##' ("(")( %7)% .%' !('.#%#'/ .%%.#%##1#%#.%'!'("%',/%"1.#.%'(#%#%7)%.!()"%.##'%(..(#.!%6'9%%)E)%(7)%D".%!('.#%##)%%&%("")'%')%)('/'0'.%("',!!%%"#(%.('')0#%")'".%(!"'+"#.#(/#.%'(!.&%'.%("'C0'#%""0"'!%('+.(/76'(# (!.%# ")9 '!%(' " .(' C0 .% 0.)0%, .% )"(.(*6% / .%' "%' ' ')E" #7""#( /(!.&$%"#(" 7(%!%""),#("# .%'7"%"$%',.(''')%'# (0"%+", .%'").%("'")"%("'/0.)0%''.%("%"/'*.(%.$%"9?!

    ".%!"#$%.%'%)E)%''#'%(..%" competencias intelectuales del estudiante tales como el razonamientolgico, la visualizacin espacial y el pensamiento analtico,.E.0.(,.%$("%")(,.(#.%")(/.%'-%.#%#'

    !%%'(.1!(.%'9%)%.%'*0")!0#'0.)%:).,!(&!.(,!%%? '1%)%"'1'%.").%'-%.#%#'C0'#'%(..%"".')(9 2(%.$%'"0""1./#'B%%)1#%#'/1%.0%("'C0"7%)"#-%'-%.#%#'9 )0%'"."1./('1%.%'-%.#%#'C0'")"("%(".('%B('%")('/.%'C0

    ')%%&%E"E'%#.%")9 '1%#7"%'/'.)0#'".('D"7%''!(.('#"'B%"$%9

  • 8/2/2019 8 bsico - matemticas - 2010

    21/79

    ?!"

    @A BA CA DA EA A

    '(.1!(.%'"

    (")>)(''*"7%)1('C0C0".0'(#.('(")"#('#."1.9

    '(.1!(.%' "

    (")>)('#1'(','*"7%)1('9

    '(.0+" #!(.%' "

    (")>)(''*"7%)1('9

    '(.0+" #!(.%' "

    (")>)('#1'(' /'*"7%)1(',0).$%"#( .('(")"#(' #."1.9

    '(.0+" #!(.%' "

    (")>)('#1'(' /'*"7%)1('9

    "%.$%')%)*%'#

    '(.0+"#!(.%'#%0#((")('#7"#('9

    "%.$% .%1%.#$ # .('!(#")('0).$%#(' / #.(' '0.)%#('()"#('9

    1%.0% .% 1%.#$# .(' '0.)%#('()"#(' / .!.( ##-(''0.)%#(' !%%70"#%")%(!"("'/)(%#'("'9

    20"#%")%(!"("'/)(%#'("'9

    2(0.%("&)0%' /

    17%.%', !%%%.*0"(' %'('!%)0.%'9

    2(0.% /17%

    ("&)0%', "%'('!%)0.%'9

    #"% ":('/ 0%.(' " .%)%"0D%9

    #"%":(' /0%.(' " .%)%"0D%9

    #"%":(' /0%.(' " .%)%"0D%9

    %.$% E.0.('" 7(% ")%./')%9

    %.$%E.0.('" 7(%")%. /')%9

    %.$%E.0.(' "7(%")%. /')%9

    %.$%E.0.(' "7(%")%./')%9

    %.$% E.0.('" 7(% ")%./')%9

    !.%7(%''!.' #(#.%")(%)E)(

    !.% 7(%''!.' #(#.%")(%)E)(9

    !.% (#.('."%.' C0!'")%" .%.%+" ")

    1%%.'9 7%!(!('("''!.', !%%%'('!%)0.%'9

    7"% ")17%+" /#(')%+" #!(!#%#'9

    ')')(')E("#(((0"%(!()0"#%#!%%C0.('')0#%")'#'%(..""12"!,/%C0.%%)E)%("'))0/0"E%#.%0.)0%!(#('%".%(!"'+",>!.%+"/!#+"#')0%("'/7"+"('#.#(C0"('(#%9')('#'!"#.%!()%"%#.'70$(C0#"-%.('#(")'!%%C0)(#('.('')0#%")'""0')(!%6'%!"#%".('("(")('/#'%(..".%'

    %!%#%#'!(!%'#')%#'!."%9'0*""')('!(*%%'%.*0"%'(")%("'C0!0#"%/0#%%.('#(")'"'0!.%"7%+"/"'0'.%''!%%0!.("')(&)1(?

    9"%"#('')0#%")'#"#'%(..%/>!.(%.%'#%'%)E)%'"!(70"##%#/#"1.%'%)E)%'((0")(#(")*%#(,"(((7%*")('%'.%#('#.("(")(9.('')0#%")''.'#"7")%%1%%#%' >!"%' # %!"#$%& !%% %/0#%.(' % #'%(..%0"% (!"'+"!(70"#% # .(' ("!)('%)E)(', %'6 (( '0' (">("' / %!.%("', # )%. %"% C0 .'!)% !%)!% %)1%")/

  • 8/2/2019 8 bsico - matemticas - 2010

    22/79

    ()"%/(("7%"$%">!.(%/%!.%.%'%)E)%'9("#%'!%.")"..(E'(,.0'(#%)%.(")(,#)%%&('!E)('/.%!(/(#.%)"(.(*6%((!%)#')%'>!"%'#%!"#$%&9

    !!+

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

    !(".%'%!0%9("0"!('%#('+.(,*%"#'":('(":('0/!C0B('!0#"'%"%.$%#('/#()%#('#'")#(,/'!0#')0#%.(!()%")(#70"("',".0'(#%.)%(!.%#9")")(7:.)!.'%")'".('C0'!0#"(")%!'")%("'#"E%'#0"%*%"%")#%##(&)(' %)E)('9 (' !('%#(' *(D)(', " )%")(, !)" .% >!")%+" (" "(("' /.%("','%#.%*()6%0.#%"%,%)'%"%(1)(%.9(#(')(,"0"'!%(#%.)(")D'!%%.('')0#%")',/#%.)(!%)("0%")(%'07(%+"!%%0"%1#%%#%1$E'"7.0#%!(.%')"(.(*6%'#*)%.'9

  • 8/2/2019 8 bsico - matemticas - 2010

    23/79

    !$".!('(#"'B%"$%/%!"#$%.%%)E)%'#!(!%0"%")%)1(/6)(C07%1($%.%7(0.%+",17%+"(70)%+",#!%)#.C0%!"#,#("&)0%'".('!(.%'C0%(#%9"%")"C0.(,.%#0#%(!*0")%,'("("'#%#('!%)")*%")/1%.('%#.!('(#("')0+"#.("(")(,%")".C0.('%!()'#)(#(''("1%.(%#('/!0')('".(")>)(

    #0"%:'C0#%/("')0+"(.)1%9("'))0'"0"'!%(".C0'"%)0%..%"E.''#.%'%("'/!(#")(',#(#(#(!%%%"('%.)"%)1('9

  • 8/2/2019 8 bsico - matemticas - 2010

    24/79

    )-.8999F

    ""12"

    /A- 3A*/

    G$!*3

    8(*7

    $1*@!

    9 ')%.')%)*%'!%%%.0.%0.)!.%("'/#1'("'#":('")('9

    9 ).$%

    ')%)*%'!%%#)"%.1%.(#!()"%'#%'")%/

    >!("")"%)0%.99 )"%

    !(!#%#'#0.)!.%+"/#1'+"#!()"%'#%'")%/>!("")"%)0%.9

    9 7%C0

    !(!#%#'#!()"%'#%'

    ")%/>!("")"%)0%.'0!.""!()"%'#%'7%("%%!(')1%,#%.!(')1%/>!("")"%)0%.9

    9 '(.1

    !(.%'C0"1(.0".%'(!%("'("":('")('/.%'!()"%'#

    %'")%,7%("%%(#%.!(')1%/>!("")"%)0%.9

    9 %%)$%)%"'7(%("''(D)%'#7*0%'!.%"%'/("(.%'"#1'%'')0%("'/(")>)('9

    9 ("(%.*0"%'!(!#%#'#.%')%"'7(%("''(D)%'9

    9 ("')0)%"'7(%("''(D)%'#7*0%'*(D)%'!.%"%',

    0).$%"#(*.%/(!E'(!('%#('*(D)('99 '.%.!.%"(("

    !(.6*("('*0.%'0).$%"#(*.%/(!E'(!('%#('*(D)('9

    9 ).$%.%')%"'7(%("''(D)%'((-%")%!%%%.$%)'.%("'*0.%'/)'.%("''*0.%'9

    )('#1'(',#%").0'(###%'#)"#"%")%.,>)"#"#(%.%'(##%)('%*0!%#('"")1%.('9

    9 (!"#.("!)(#

    %.%)(#%#".0'(#0')%'/'0!()%"%".%%.$%+"#"7"%'9

    9 '*"%!(%.#%#')+%")%.%(0"%#1")(',">!")('%.%)(('("'0.)%#('7")('/C0!(%.',/(")%')%.%'("'0.)%#('

    >!")%.'9

    9 4.%")%0%("'C0!'")%".%.%+"")#('1%%.'"#1'('(")>)('9

    9 ("(

    70"("'"#1'('

    (")>)(',#")7%'0'.")('/!'")%#1'%'')0%("'%)%1D'#..%'9

    9 #")7%

    1%%.'.%("%#%'"7(%!(!(("%./"7(%"(!(!(("%.9

    9 "%.$%#%").0'(#

    '(7)O%'*E7('')0%("'#!(!(("%.#%#

    9 '(.1!(.%'"#1'('(")>)('C0!.%"!(!(("%.#%##)%/!(.%'C0!.%"!(!(("%.#%#"1'%9

    !(')%#(-(%'

    !(')%#(8-(%'

    !(')%#(

  • 8/2/2019 8 bsico - matemticas - 2010

    25/79

    --,/

  • 8/2/2019 8 bsico - matemticas - 2010

    26/79

    )"#. )%%&(("!()"%'#%''"%)0%.',7%("%%'/#%.'!(')1%', % %'' ")%' (" >!("")' "%)0%.'9 4%% .(*% ') !(!+')( ' %.$%" %)1#%#'(")%#%'%.%17%+"#.%'!(!#%#'#')%'!()"%'"%'('!%)0.%',%')%("'#..%',/%.%'(.0+"#!(.%'"(")>)('"0D('#("#..%'")1""9"!4()"%'#%'")%/>!("")"%)0%.Q!(!#%#'#.%'!()"%'9

    > #+"/'0')%+"#":('")('9 4()"%'#%'"%)0%.,7%("%%/#%.!(')1%(">!("")"%)0%.9"! 0.)!.%+"/#1'+"#":('")('9 4(!#%#'#.%0.)!.%+"/#1'+"#":('")('9 4()"%'#%'")%,7%("%%/#%.!(')1%(">!("")"%)0%.9 4(!#%#'#.%'!()"%'#%'")%,7%("%%/#%.!(')1%(">!("")"%)0%.9?!

    *0")%%%#.%1%.#$#.%'!(!#%#'#.%0.)!.%+"/#1'+"#":('")('9 ')%.')%)*%'!%%'(.1#1'("'#":('")('9

    ')%")%.").1%.(#%.*0"%'!()"%'9 ")!)%"7(%+">!'%#%"!()"%'9 ("&)0%,%*0")%,17%/%!.%!(!#%#'#.%'!()"%'9 %%&("C0!("%)1%!'("%.".%'(.0+"#!(.%'"(")>)('#1'('9

  • 8/2/2019 8 bsico - matemticas - 2010

    27/79

    8

    "12" -!

    ()1

    1

    /0 ! " !!

    !"! $ G0

    %.0.%"0.)!.%("'#")('0).$%"#(.%')%)*%')%.#%9 %.0.%" #1'("' # ")(' 0).$%"#( .% ')%)*%

    ')%.#%9

    30 *!1"!!"$+"!0

    ).$%" ')%)*%' !%% #)"%" . '*"( #

    >!'("' #. )!(n)1( 0%"#( n ' 0" ":(

    "%)0%.9

    ).$%"')%)*%'!%%#)"%.1%.(#>!'("'

    #.)!(na)( 0%"#( na, '("":('"%)0%.'9

    ')%" ")%.") !()"%' # %' ")% # 0"#6*)(/>!("")"%)0%."(#94(&!.(,')%@8A((5R5,()""#(0"":("(%99

    70 "" !"! $ " $+"!0

    >!.%" .(' !%'(' %.$%#(' !%% #)"% .%'!(!#%#' # !()"%' # %' ")% / >!("")"%)0%.9

    %.0.%" !()"%' # %' ")% / >!("") "%)0%.0).$%"#(.%'!(!#%#'#)"%#%'9

    @0 )# > "" " $+" ! "! " #"& ! " $+"!0

    %.0.%"0.)!.%("'#!()"%'#%'7%("%%!(')1% / >!("") "%)0%., 0).$%"#( .% !(!#%#

    .%)1%%0.)!.%+"#!()"%'#*0%.%'")%/>!("")"%)0%.9

    7%" C0 !(!#%#' .%)1%' % .% #1'+" #!()"%'#%'")%/>!("")"%)0%.'0!.""!()"%'#%'7%("%%!(')1%9

    >!.%" # %"% ')% .(' !%'(' %.$%#(' " .%17%+" # !()"%' # !()"%' # %' #%.!(')1%/>!("")'"%)0%.'9

    B0 ,! "! > !! " G $ ! " & # !"$+"!0

    '0.1" !(.%' .%)1(' % 0.)!.%("' #")('9

    !.%"()%").%*.%#.(''*"('/.%!(#%## .%' (!%("' " .% '(.0+" # !(.%' #(!%)(%("%#%("":('")('9

    '0.1" !(.%' " (")>)(' ()#%"(' C0"1(.0"!()"%'#%'")%/>!("")"%)0%.9

    7%".(''0.)%#('()"#('"70"+"#.(")>)(#.!(.%9

    "%.$%" .(' !(#")('0).$%#('" )D"(' # .(''0.)%#('()"#('9

  • 8/2/2019 8 bsico - matemticas - 2010

    28/79

    3

    "12"!!4

    2>""!!!"!+0 4%)!%#%"%!(!(')1%"%)1#%#'*0!%.'9

    ''!("'%.".%)%%%'*"%#%9 (%"%)1%"%)1#%#'#%E)*0!%.9 4(!("%.)"%)1%'#'(.0+"%!(.%'%)E)('"%)1#%#'*0!%.'9

    "!*

    ')% 0"#%# %!.6% .%' (!%("' (" ":(' ")(' "(!(%"#( .%0.)!.%+" / #1'+", %.'!)('("#%%.#("))"0"%("'#%+"'.%%.)%)%")(#.%'(!%("'#%#+"/'0')%+"9%'*.%'!%%(!%("":('")('"('0."')%"7E.'#(!"#,!('#($%,.(0%.-%"'%("")1%.%:'C0#%#.%(!"'+"/1)%C0'(.('!(#0$%.%")"%.$%+"(6')%#.('!(#")('9 ("#%%.#(").%0).$%+"#)E7(%' ( %"%.(*6%' !%% %!(/% .% (!"'+" # .(' !(#")(' "1(.0%#(', !( '( .%&)%+"0)"%%9

    '!)(%.%'!()"%','.%(!()0"#%##%.$%%)1#%#'C0(")!."0")%%&(")*%#(")":('/E.*%,!(&!.(,".%#)"%+"#.1%.("*"%.#>!'("'#.)!(

    n)1( ,.%%!.%+"#')("(")(!%%)%%&%("!()"%'#. )!( na)( , a !)"")%

    .('"%)0%.'9((')%)*%,".%(!%)(%("!()"%''("#%."('(.(!%)#.(!%)0.%/..*%%.(*"%., '#, &!.7% / )%%&%("":('!%% .0*( *"%.$%H '"()%D", %.$% .!('("1'(,!(&!.(,0"%("#%+"!%%.('')0#%")'C0'0.#*%"0).#%#'7%C0 %#%1$C0 .%>!'+" %.*%% %$% #'")#(/ !(.( )%")(#70.) '0(!'+",L..1"M #-%' >!'("' %. )"( C0 .' ' 7%.%, ' #, ')0#" '0 (!()%")( !%%#')")(' 1%.(' "0D('9 %' %)1#%#' #%" !('.)% C0 .(' ')0#%")' (!"#%"

    >!'("'#.)!(? nn ba )()( ,(" nba ,, ".('"%)0%.'H0.)!.%("'#!()"%'>!'%#%'

    ((

    mn

    ba )()(

    (

    mn

    aa )()(

    H!()"%'#%'7%("%%#.%7(%

    n

    b

    a

    )(

    (" ba, ".('

    "%)0%.'H 0.)!.%("' # !()"%' (" %' 7%("%% # .% 7(% nn

    d

    c

    b

    a)()( (

    mn

    b

    a

    b

    a)()( (" nba ,, ".('"%)0%.'/!(:.)(("!()"%'.1%#%'%()%!()"%' mna ))(( ,

    (" na, ".('"%)0%.'9

    ".!('(#')%.*"%.$%("''"(%./'!%#(C0.('')0#%")'!'")")('#(!"'+"0/1%%#(',!(.(C0'("#%#'B%%)1#%#'C0(")!.".)%%&("C0!(".C0!0#%"%7.(%"%)0%.").6#'").)0%.'C0%!(/".%.%(#(")%.")(# %#% *0!(, !)"#( # ')% 7(% #1'7% .(' )(' # !(#0+", ()(*%"#( )!('#7"%#('%%#%')0#%")%#E'#!('.)%.#E.(*(/.%#'0'+"9

  • 8/2/2019 8 bsico - matemticas - 2010

    29/79

    5

    2"!

    /%!"!!!"!$G0/0H 2(0.%" ')%)*%' !%% 0.)!.% ":(' ")(' / .%' %!.%" !%% %.0.% 0.)!.%("' #("#")1""')('":('9.'!)(,7(0.%"')%)*%'!%%?

    %A0.)!.%":('#.%7(% )( ba

    A0.)!.%":('#.%7(% )()( ba !. #(") !0# '0* % '0' ')0#%")' C0 0)." .% !'")%+" # .(' ":(' ")(' " .% )%"0D%9

    ' !()%") C0 . #(") "("'B .%' *.%' # .(' '*"(' % '0' ')0#%")' %")'C0 .%(" ')%'')%)*%','"(C0%)%1D'#')%'%)1#%#'/"("&0")(("..('')%.$%"')%'*.%'9!.%"')%'')%)*%'!%%%.$%E.0.('#.)!(?

    A ))(( a

    #A )]()][()()[( badcba ++

    30H 2(0.%" ')%)*%' !%% #1# ":(' ")(' / .%' %!.%" !%% %.0.% #1'("' " ') (")>)("0D(94(&!.(,7(0.%"')%)*%'!%%?

    %A%.$%#1'("'#.%7(% )(: ba

    !

    .#(")!0#'0*%'0'')0#%")'C0.%#1'+"%")(.%>!'"".%7(% ba : 9

    A1'("'#.%7(% )(:)( ba (")"0%+".%0).$%"!%%%.$%E.0.('#.)!(?

    A )(:))(( ba

    #A )]([:)]()()[( badcba +

    70H '0.1"#1'("'#":(' ")(' 0).$%"#( .%'!(!#%#' # .%0.)!.%+"9 4( &!.(,!%%

    %.0.% )(: ba ,>!'%"')(")".%7(% )1

    (b

    a

  • 8/2/2019 8 bsico - matemticas - 2010

    30/79

    3%*!1"!!"$+"!0

    /0H ).$%" ')%)*%' !%% %.0.% >!'("' #. )!( )(.....)()()( aaaa ++++ , #("# ' -%'0%#(a 1' a ,("1)"#(')%'0%"7(%#!()"%'9

    30H ).$%" ')%)*%'!%% ')% !()"%' # %' ")% #0" #6*)(/ >!("") "%)0%.9 4( &!.(,')%"

    22)7()3( 9

    70H7%""%'('!%)0.%'C0 1)1(2

    =n

    / 1)1(12

    =+n

    0%"#( Nn ,/.(0).$%"!%%%.$%

    E.0.('#.)!(na)( /E.0.('#.)!(

    nab )( ,0%"#( Nn 94(&!.(, 5)3(2 @0H).$%"')(' '0.)%#('!%%'(.1E.0.('%'(%#('%>!'("' #("# ")1""!()"%'#. )!(

    nab )( 9

    4(&!.(, )5()5()5(3)5()5()5(2 +

    7%""!"!$" $+"!0

    ('')0#%")'0).$%"'0.)%#('%%#!()"%'#.)!(na)( /?

    /0H'0.)%#('()"#('"8S%B('!)(%0.)!.%("'#!()"%'#*0%.%'"%)0%./>!("")'

    "%)0%.'!%%#)"%!(!#%#''!)(%0.)!.%("'#.)!(mn

    aa ,#("#.%%''")%/.('>!("")''("":('"%)0%.'930H'0.)%#(' ()"#(' "8S %B( '!)(% !()"%' #!()"%','#%%#>!'("'#. )!(

    ( )mna #("# .% %' / .(' >!("")' '(" ":(' "%)0%.', !%% #)"% !(!#%#' '!)( %

    0.)!.%("'#.)!( ( )mna ,#("#.%%''")%/.('>!("")''("":('"%)0%.'9 @% )# > "" " $ +" ! "! "#"&!"$+"!0/0H7%"C0.%'!(!#%#'#0.)!.%("'#!()"%'#%'")%/>!("")"%)0%.'17%""0.)!.%("'#!()"%'#%'7%("%%(#%.!(')1%/>!("")"%)0%.,'#C0?

    mnmn

    b

    a

    b

    a

    b

    a+

    =

    .

    J0.%'!(!#%#'#!()"%'#!()"%'#")('#%'")%/>!("")'"%)0%.''17%""!()"%'#!()"%'#":('#%'7%("%%(#%.!(')1%/>!("")'"%)0%.','#C0?

    nm

    nmn

    m

    b

    a

    b

    a=

  • 8/2/2019 8 bsico - matemticas - 2010

    31/79

    30H7%"C0.%'!(!#%#'##1'("'#!()"%'#%'")%/>!("")"%)0%.'17%""#1'("'#!()"%'#%'7%("%%(#%.!(')1%/>!("")"%)0%.,'#C0?

    mnmn

    b

    a

    b

    a

    b

    a

    =

    .:

    J0.%'!(!#%#'##1'("'#!()"%'#%''")%'/>!("")"%)0%.'17%""#1'("'#!()"%'#":('#%'7%("%%(#%.!(')1%/>!("")"%)0%.,'#C0?

    nnn

    d

    c

    b

    a

    d

    c

    b

    a

    =

    :.:

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

    A % )!%)0% -% #'"0#( S .'0' %#% -(% #0%") -(%'9 I0E")(' *%#(' -% #'"0#( .%)!%)0%"')!(K@0H'0.1"!(.%''"..('C0C0"(!%)(%("":('")('#.)!(?4%%%.$%0">!")(,0"0$(!(7'("%.#'"#%)('#!(70"##%#,.0*('08)(',!%%!(')(")#'"#1'.#'"'("%.9IC0D!(70"##%#C0#+KB0H"1")%"!(.%'C0''0.1"(".%'(!%("'?

    %A )4()5(

    A )6(52:)10( +

    IC0H !.%" .%' !(!#%#' # .%' !()"%' # %' 7%("%% / #%. !(')1% (" >!("") "%)0%. "

    ')0%("'%.'?%00'00)000! ) ) 0 % ;8

  • 8/2/2019 8 bsico - matemticas - 2010

    32/79

    !

    "12"%

    *!1"!!"$+"!0

    !%

    ).$%"')%)*%'!%%#)"%".'*"(#>!'("'#.)!( n)1( 0%"#(n '0"":("%)0%.9

    ).$%" ')%)*%' !%% #)"% . 1%.( # >!'("' #. )!( na)( 0%"#( na, '(" ":('"%)0%.'9

    ')%"")%.")!()"%'#%'")%#0"#6*)(/>!("")"%)0%."(#94(&!.(,')%@8A((5R5()""#(0"":("(%99

    0

    9!0,"!"""0

    9 ')%,")%."),.1%.(#.%>!'+"1212 2)2( ++ +

    nn,!%%

    #')")('1%.('#n ,'%"#(C0!0#)(%'(.(1%.('"%)0%.'9')0')%+"".0%#(?

    9 %0"%*0")(C0%!(/.%1%.#$#.%'*0")!(!#%##.%'

    !()"%'%!.%#%".&(

    9 '")D"('#!()"%'?.%#7"%").%()%1%!%)#

    32 +n /.%)%## 12 +n 9.%>!'+"%")('!'")%!(A ,

    %.0.%.1%.("0D(#nA )1( !%%#')")('1%.('"0D('#

    ("'#%"#(C0!0#)(%'(.(1%.('"%)0%.'9

    )('#1%.0%+"?

    9')%".1%.(#!()"%'#%'0"#6*)(")(9

    9>!'%"((!()"%'!(#0)('"C0.('7%)(''("!()"%'#%'")%9

    9*0")%"%%#.%

    1%.#$#.%!(!#%##.0(")#!()"%'#*0%.>!("")9

    9!.%".%'!(!#%#'#.%'(!%("'#.%'!()"%'!%%'(.1!(.%'%)E)('9

  • 8/2/2019 8 bsico - matemticas - 2010

    33/79

    *38(

    "!

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

    ?! ("')0)%"'7(%("''(D)%'9 %.$%)'.%("'9 %%)$%.%0"7"%/.60.(((.0*%'*(D)('9 (!"#.":(!9 %.0.%.!6)(#.%0"7"%9 %.0.%E%'#.60.(/#.%'0!7#("(',."#('/!E#'9 %.0.%.1(.0"#("(',."#('/!E#'9 ))0#'#!'1%"%,*(,7.>.#%#/(*"%.#%#%.'(.1!(.%'%)E)('9 %%&("C0!("%)1%!'("%.".%'(.0+"#!(.%'"(")>)('#1'('9

  • 8/2/2019 8 bsico - matemticas - 2010

    34/79

    "12" -!

    ()1

    1

    /0 1 #)('#1'('9

    %%)$%".%)%'.%+"#7*0%'".!.%"(9 #")7%"E"*0.('/!0")(''!)(%.('C0'-%"

    7)0%#(()%("'9

    %%)$%" .(' &' # ')6% # 0"% 7.>+" #7*0%'".!.%"(9

    30 , ! "" !

    #("'9

    ("')0/".%("7*0%+"%'#0"%)'.%+"("E'#0"!(.6*("(*0.%0).$%"#()%"'7(%("''(D)%'9

    C0 1!#$!(!!!.%".("!)(#.0*%*(D)(9 >!.%" .%' #7"%' ") 60.( / 0"7"%,

    0).$%"#(.("!)(#.0*%*(D)(9

    D0 !! ! "( #

    $!!0

    !(>%"1%.('#.":( ,0).$%"#(.("*)0#'/#E)('#0"7"%'9

    %.0.%" !6)(' %!(>%#(' (" 1%.('%!(>%#(' #. ":( 9 4( &!.(, %.0.%" .!6)( # 0"% 0"7"% # %#( cm3 ("

  • 8/2/2019 8 bsico - matemticas - 2010

    35/79

    14,3= 9

    %.0.%"!6)('#%('#0"7"%'9

    E0 !!!!(!$

    0"'(.()D"(9

    J0 !! "# !& $ "& !1#!0

    (!%%"E%'#'0!7'#("('/!E#'9 !(>%" E%' # ."#(', ("(' / !E#' #

    %0#(%1%.('#')")('# 9 %.0.%"%#('/%.)0%'#("('")D"('#.E%

    #'0'0!79

    /K0 !!!G!$&!1#!0

    (!%%" 1(.:"' # '0!7' # ("(' /."#('9

    !(>%"1(.:"'#."#('/("(',!.%"#(#')")('1%.('# 9

    %.0.%"%#('/%.)0%'#("('/."#('"70"+"#'0'1(.:"'9

    //0,! "! +

    !!!% (#$

    (!0 "#!&$

    "0 )!G!$0

    '0.1" !(.%' " (")>)(' *(D)('.%)1('%.%#)"%+"#E%'#7*0%'"C0")1""60.('94(&!.(,%.0.%".E%#.%'0!7(!"##%")0"0%#%#(/0"60.("')("D.9

    '0.1"!(.%'%%#E.0.('#1(.:"'# ."#(' " (")>)(' *(D)('9 4( &!.(,%.0.%" . 1(.0" #. '!%( C0 >') ") #('."#('#%''#')")%'#*0%.%.)0%9

    '0.1" !(.%' .%)1(' % E.0.('# E%'#'0!7'# !E#'" (")>)('#.0"#( %.94( &!.(, 17%" E%' # .% '0!7 # .%'

    !E#'#*!)(9

    "12"!!4

    "&!+!$!!!"!0

    0')%0"D)(#(!%%%.$%.%')%"'7(%("''(D)%'9 4'1%".%%.$%+"#)'.%("'9 "%.%')%%'"%#%'.%)1%'%.(')%')%)%#('9 '%(..%)"%#%#7")%(')E0.('(#0#%'C0'.'!'")""!(.%'!(!0')('9

    2>""!!!"!+0

    4%)!%#%"%!(!(')1%"%)1#%#'*0!%.'9 ''!("'%.".%)%%%'*"%#%9 (%"%)1%"%)1#%#'#%E)*0!%.9 4(!("%.)"%)1%'#'(.0+"%!(.%'%)E)('"%)1#%#'*0!%.'9

  • 8/2/2019 8 bsico - matemticas - 2010

    36/79

    )('#1'(',!(&!.(,"(")>)('#.%)9

    30H%%)$%"7.>("'#7*0%'".!.%"(/.%'("(""(")>)('#1'('9.'!)(?

    %%)$%".('&'#')6%9

    (!"#"C0.%'7.>("'#7*0%'#.!.%"('%.$%"'!)(%&'#')6%9("("7.>("'#7*0%'#.!.%"("(")>)('#1'(',!(&!.(,"(")>)('#.0"#(#.('"')('9

    70H%%)$%"()%("'#7*0%'".!.%"(/.%'("(""#1'('(")>)('9.'!)(?

    (!"#"C0..%''%.$%"'!)(%0"!0")(/"0"E"*0.(#%#(9("("()%("'#7*0%'"(")>)('#1'(',!(&!.(,"(")>)('#.%76'%9

    I@0H("(")%"'7(%("''(D)%'"(")>)('#1'(',!(&!.(,("(")%"'7(%("''(D)%'"#7")')'.%("'#99'-@OOO9'-9(A9

    3%,!""!#E*("(''!)(%)%'#%#%'9!%'0*%.#(")C00')%'0'')0#%")'C0%')%(")%'.%#%.('1D)'#.%'7*0%'"0')+"!%%)%'.%#%.%7*0%(!.)%9#E''%("'&%%.#("))%%&%("'0'')0#%")'.%#)"%+"#.1)(#)%'.%+"0%"#(')""7*0%'C0-%"'#()%'.%#%#%'9

  • 8/2/2019 8 bsico - matemticas - 2010

    38/79

    3

    '0*%.#(")C0("')0/%("'0'')0#%")'0"7"%'("D")%'/C0.'0')C0%')%("()%.('1D)'#.(')E"*0.('"0')+"!%%C0')%7*0%C0#()%#%9%#(0")E"*0.(%.C0'%!.+0"%()%+",''0*("(.!0")(/E"*0.(#()%+"9'0*%.#(")C0!%'.%("')0+"#)%'!!"#0.%'9'0*%#E'C00')%'0'

    ')0#%")'C0%')%("7.&%.('1D)'#.('!(.6*("('"0')+"!%%C0')%7*0%C0#7.&%#%9')%'.%(%'+"C0)"".('')0#%")'##)"%.')6%#0"%7.>+"0%"#(')E""!'"%#7*0%'7.&%#%'9

  • 8/2/2019 8 bsico - matemticas - 2010

    39/79

    5

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

  • 8/2/2019 8 bsico - matemticas - 2010

    40/79

    D%!!!"(#$!!0

    /0H%.0.%"!6)('#0"7"%'##E)(("(#(930H%.0.%".%#(#0"%0"7"%("(#('0!6)(970H("(#%.%##%#0"%(#0"7"%%.0.%".E"*0.(%'(%#(%D.9E%!!!!(!$

    )0783

    30H#0"C0.%>!'+"

    360

    2 r'.E%#0"')(0.%#E"*0.( ,/.%(%"')%)*%'!%%

    %.0.%E%'.%)1%'% ')('0.%'%!.%"#(.%>!'+"*"%#%"(")>)('#1'('94(&!.(,.%(%"0"%')%)*%!%%#)"%.E%#.%'0!7(!"##%")#('60.('C01%.")'#%#(C0!%'%",%#%0"(,!(.")(#.()(60.(9J%!!"#!&$"!1#!0/0H).$%"#(.%'#'#.."#(,.("(/#7")'!E#',("&)0%""*0!('%%#.%'')%)*%'#E.0.(#.%''0!7'#')('0!('*(D)('94(&!.(?

  • 8/2/2019 8 bsico - matemticas - 2010

    41/79

    %.0.%".E%)()%.#0"."#((".('#%)('#.%7*0%?%'#%#(/%.)0%9

    ="%.$%.'0.)%#(!%%()"0"%>!'+"C0!'")%.E%)()%.#0"."#(930H%.0.%1(.:"'#7*0%'#("#")1""("('/."#(',#.)!(?

    "()%1(E'(,(".%7E"# 0"#"(,%.$%0"%1")%#&0*('#!B%94%%')(,2%"'(#'B%"1%''?0" "1%' (" 7(%# ("( # %.)0% / %#(5 / 0"% !E##%' 0%#%#% 0/%'##%''("?.%#(#.0%#%#(/%.)0%#.%!E#59!!%%("9#&0*(?%AIC0D"1%''"')%"('%")#%#!%%"1%'%)(#(.&0*(KAI0E")('"1%''#%#%)!('"')%"!%%"1%'%.&0*(K/K%!!!G!$!1#!0/0H7%"0'%"#(#1'%'')%)*%'C0.1(.0"#.("('0")(#.1(.0"#.."#(#.%'%%.)0%/%#(?

    30H)"%".%'#"'("'#)'."#('>!'E"#(.%'"(".('C0'!0#"1%'%)(:(#.6C0#(9

  • 8/2/2019 8 bsico - matemticas - 2010

    42/79

    //%,!"!+!!!%(#$(!0"#!&$"0)!G!$0

    /0H'(.1!(.%'C0"1(.0%"E.0.(#1(.:"'#."#('/("('#.)!(?)'

    30H '0.1" !(.%' .%)1(' % E.0.(' # .("*)0#' # 0"7"% " (")>)(' *(D)('9 4(&!.(?%.0.%".!6)(#0"%0"7"%"')%"0"0%#%#(#E%("(#%9)"%".%%")#%##%.%"'%%!%%%0"%'0!7#7(%0.%9

    70H.%(%"')%)*%'!%%#)"%.("*)0#'#%('#0"7"%/.('%!.%""(")>)('#1'('94(&!.(,%!.%".%'')%)*%'.%(%#%'!%%#)"%.%.("*)0##.%(#0"7"%C0#'0"7%(%.*%S%#('..%'%"%'#.7%(,#%#(C00"%..%%"%C01%.%93)('9@0H'0.1"!(.%'C0"1(.0%"E.0.(#E%'#0"7"%'#.)!(?% ' ) ))'3

    4.)%

  • 8/2/2019 8 bsico - matemticas - 2010

    43/79

    IB0H!.%".('("(")('7#('%E%'#'0!7'!%%'(.1!(.%'#.)!(?4%%')%0%0"%!E#,0"*0!(#>!)('##+!")%.%("0"(!0')('!%.9%!E#)"%'0%#%#%#.%#()('/'0%.)0%'#)('90")%(#.(!0')('!%.)".%%!%#%##!")%,I0E")(')%(''"')%"K

    !% '0* %. #(") C0 ')%.$% .% .%+" C0 >') ") . .%#( # 0" 0%#%#( / '0 #%*("%.9 '!()%")C0.('')0#%")'17C0"')%.%+""%'('!%)0.%'9

  • 8/2/2019 8 bsico - matemticas - 2010

    44/79

    !

    "12"%

    *!1 !#!.%".%'("#("'C0#"0!..('!(.6*("('"0")'.%#(9

    9"#%".%'("%("'!('.'#!(.6*("('"0")'.%#(9

    9#")7%".%')%"'7(%("''(D)%'%!.%.'!%%("')0.)'.%#(9

  • 8/2/2019 8 bsico - matemticas - 2010

    45/79

    --,3

  • 8/2/2019 8 bsico - matemticas - 2010

    46/79

    )(',0).$%"#(##%'#)"#"%")%.!%%#%)('%*0!%#('94(:.)(,'!(70"#$%".('("!)('#!(.%+"/0')%")(#0#('"!")%.' (" '0.)%#(' )+(', !( .( C0 'E !()%") . 0'( # -%")%')"(.+*%'C0!)%"'0.%0"*%"":(#1'0")(>!")(%.%)((/(")%')%.*E7( >!")%. (" . *E7( )+(9 4( :.)(, ' '!% C0 .('')0#%")' (!"#%" .('("!)('#'!%(0')%.,1")(/1")('C0!(%.'9"!%)('%*0!%#('"")1%.('Q70"%'##%)('%*0!%#('Q0')%'%.%)(%'QC0!(%.#%#Q'!%(0')%.Q(#.(#%!.%9> 4(.%+"/0')%9 20"%'%'(.0)%'/.%)1%'9 >!")(%.%)((9

    4(%.#%##0"1")(9 =E7('#70"%9"! ")1%.('9 !.)0##0"")1%.(9 %%#.%'#0"")1%.(9 %.%'#70"%("#%)('%*0!%#('"")1%.('9 #%%)D)%/(#%!%%#%)('%*0!%#('"")1%.('9 0')(%.%)(('!.9 C0!(%.#%##1")('9 4"!(0.)!.%)1(9 '!%(0')%.%'(%#(%0">!")(%.%)((9 4(%.#%#)+%#0"1")(9 (#.(#%!.%9

    ("#("'#.(#.(#%!.%?7")0##.'!%(0')%./C0!(%.#%#9?!

    '(.1 !(.%' " .(' 0%.' ' "'%( ")!)% "7(%+" % !%) # )%.%' #70"%("#%)('%*0!%#('"")1%.('9

    ("')0)%.%'#70"%("#%)('%*0!%#('"")1%.(',"7(%%"0%./#%")-%")%')"(.+*%'9

    # '( . )!( # 0')% " %.*0"(' >!")(' %.%)((' !%% "7 '( .%'

  • 8/2/2019 8 bsico - matemticas - 2010

    47/79

    8

    %%)6')%'#!(.%("',&!.7%"9 "%.$% . (!()%")(#0"%0')% ##%)(', 0'%"#(##%'# )"#"% ")%. /

    %*0")%+"%%#.%"7(%+"C0..%'")*%"9 #")7% . ("&0")( # .(' '0.)%#(' !('.' " >!")(' %.%)((' '!.' @'!%(

    0')%.A/.('1")('('0'('(('0("&0")('#%C0.9 ).$% . !"!( 0.)!.%)1( !%% ()" .% %#"%.#%# #. '!%( 0')%. / # .('

    '0'('(1")('9 7%'0">!")(%.%)((0!.(".%'("#("'#.(#.(#%!.%9 '*"%"7(%)+%.%!(%.#%##(0"%#0"1")("0">!")(%.%)((

    0).$%"#(.(#.(#%!.%9

    4'1%"%,*(,7.>.#%#/(*"%.#%#%.'(.1!(.%'%)E)('9 %%&("C0!("%)1%!'("%.".%'(.0+"#!(.%'"(")>)('#1'('9

  • 8/2/2019 8 bsico - matemticas - 2010

    48/79

    3

    "12" -!

    ()1

    1

    /0 "#"!#&$"!0

    #")7%")%.%'#70"%'("#%)('%*0!%#('9 (!"#" . '*"7%#( # .% 70"% # 0" ")1%.( " 0"%

    )%.%#70"%'("#%)('%*0!%#('9

    )"" "7(%+",# #1'('(")>)(',#%"). %"E.''##%)(' !'")%#(' " )%.%' # 70"% (" #%)(' %*0!%#(' "")1%.('9

    30 ,"&"#&!#"!0

    >!.%".%!)""%/1")%&%'#!'")%0"("&0")(##%)(',%)%1D'#0"%)%.%#70"%("#%)('%*0!%#('"")1%.('9

    !.%")(!%%##.":(#")1%.('%!(!%#('!%%%*0!%0"("&0")(##%)('9

    ("')0/" )%.%' # 70"%, ("#%)('%*0!%#(' " ")1%.(',"7(%%"0%./#%")-%")%')"(.+*%'9

    70 "$"#&+&!!&+!"!0

    )"%".%#%%!%)#0"%)%.%#70"%("#%)('%*0!%#('"")1%.(',/.%")!)%"#%0#(%.(")>)(9

    )"%".%(#%,%!%)#0"%)%.%#70"%("#%)('%*0!%#('"")1%.(',/.%")!)%"#%0#(%.(")>)(9

    >)%""7(%+"#'##%)('"0D('%*0!%#('"")1%.('/'0#('%)%1D'#.%#%((#%.%("%#('("0"%')0%+"(7"+"(9

    ")!)%""7(%+","#7")'(")>)(',%)%1D'#.0'(###%'#)"#"%")%.9

    1%.:%".%!)""%#.0'(#.%'##%'#)"#"%")%.,#%0#(%.)!(##%)('"1(.0%#('9

    (!%%""7(%+"'!)(%#('(E'("&0")('##%)(',0).$%"#(##%'#)"#"%")%./(0"%"'0'(".0'("'9

    @0 "!"!!$"!!1#0

    ')%."')%)*%'!%%'(*0')%'"7(%%.%)(%#0"#)"%#()%%B(,#'#0"%!(.%+"'!67%9

    ).$%"0"0'()"(.+*(,!(&!.(,0"%%.0.%#(%,!%%*"%":('%.%)(('/0'%.('!%%>)%0"%0')%#'#0"%!(.%+"'!67%9

    *0")%"%%#.%!()%"%#>)%0')%'"7(%%.%)(%!%%.%'(".0'("'C0'!0#%"%.$%%%#0"%!(.%+"9

    B0 "!!&+"!!#$>"!&$!!+"!0

    '" . '!%( 0')%. # 0" >!")( %.%)(( #%#( /()""'0%#"%.#%#9

    *0")%"%%#.%C0!(%.#%##%#%'0.)%#(!('."0">!")(%.%)((,%.$%"#(0"%'0.%+"("%!(/(#.%)"(.(*6%94(&!.(,%..%"$%0"#%#(9

    )"%" .%!(%.#%##(0"% #0" )( 1")("0"

    >!")(%.%)((,#%").(#.(#%!.%9 (!%%" . 1%.( # .% !(%.#%# # 0" )( 1")( " 0"

    >!")(%.%)((,()"#(#%").(#.(#%!.%,(".1%.(#.%70"%.%)1%()"#%%.'0.%.>!")(0"*%"":(#1'#%").0'(# .%)"(.(*6%,/(0"%"'0'(".0'("'9

    (!%%".*E7()+(#.(''0.)%#('#0">!")(%.%)((,()"#(%)%1D'#.(#.(#%!.%,/.*E7(#.%'70"%'.%)1%'#.'(>!")('0.%#(#%").0'(#)"(.(*6%,/(0"%"'0'(".0'("'9

  • 8/2/2019 8 bsico - matemticas - 2010

    49/79

    5

    "12"!!4

    &!+!$!!!"!0

    *0.('!%'('"#%#('-%')%(!.)%'0)%%&(9 4(!("")!)%("'(*"%.'#.('#%)('9 ')+#(()+#%".0'(#.%'70")'#"7(%+"92>""!!!"!+9

    ''!("'%.")%%&('*0!%.'9 4%)!%#%"%!(!(')1%"%)1#%#'*0!%.'9 (%"%)1%"%)1#%#'#%E)*0!%.9 4(!("%.)"%)1%'#'(.0+"%!(.%'%)E)('"%)1#%#'*0!%.'9

    "!*

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

  • 8/2/2019 8 bsico - matemticas - 2010

    50/79

    2"!

    /%"#"!#&$"!0/0H%#%0"%)%.%#70"%'!(")1%.('/'0'70"%',%.0.%".('1%.('#%#%70"%.%)1%/.%)1%!(")0%.94(&!.(,%(")"0%+"'0')%".%'"()%'@!(#('A#.('')0#%")'#0"0'(%.7"%.$%.'*0"#()')".%%'*"%)0%#%)E)%?

    ")1%.(' #()%'

    40")(#(

    20"%

  • 8/2/2019 8 bsico - matemticas - 2010

    51/79

    '!("#"!*0")%'#.)!(? I0E")('"#1#0(''(")%"")%5"9K I0E.'.%(#%#.("&0")(##%)('K "!(#(,I0E")()!('(")%".%'!'("%'K

    3%,"&"#&!#"!0/0H)"""7(%+"#)(#('.('')0#%")'#.0'(("'!)(%'0')%)0%/%'0":(#-%"('9 !%) # ')(, . #(") >!.)% .% "'#%# # )%%&% (" )%.%' # #%)(' '!.' / )%.%' # #%)('%*0!%#('!(")1%.('930H*')%".%' ')%)0%'# .('')0#%")'"0"% .')%/ !'")%#%)('" )%.%'# 70"%(" #%)('%*0!%#('9!?'0*%.#(")%.$%')%%)1#%#"*0!(9'!0D'#*')%.('#%)('"0"%.')%,.('#')")('*0!('!'")%E".('#%)('()"#('")%.%'#70"%("#%)('%*0!%#('9

    %#%*0!(##E'(.":(#")1%.('%0).$%9' ("#%. C0 .(' ')0#%")' )"*%" .% (!()0"#%# # #'0) / ## 0E"#( ' %!(!%#( 0'%")1%.(',"70"+"#.)!(##%)('/.!(!+')(#.(C0'C0!'")%9'("#%.0).$%0"%!.%"..%.)+"%!%%'!.7%.('E.0.('#.('.")('#.%)%.%930H (!.%" #%)('# ")D' " .('#('# (0"%+"9 4( &!.(, "*'%" % .%!E*"% #.1('(.+*(#.%"1'#%##-.3/()"".%%)1#%#'6'%#.(':.)('#6%'?4'H'9! -! 9!TT8?3? ( 3Y%.#4-.0TT

  • 8/2/2019 8 bsico - matemticas - 2010

    52/79

    79 ("')0/" )%.%' '"..%' !( ")1%.(', 17%"#( C0 .% %")#%# # ")1%.(' # '!.7% .%!'")%+"#.('#%)('/"(##&%C0'!#%"7(%+"!()%")9!?

    P%"()%%.('')0#%")'C0.%1%%."0')+"('!("#% .%%*")0##.''(,/'(.%0%.'#"("')0.('")1%.('94%%.%("')0+"'"'%(#")7%.%%*")0#6"%/.%E>%97%"$"#&+&!!&+!"!0/0H!%)#0"%)%.%#70"%''!.()"#%%!%)##%)('#'0")D',%.0.%".%#%#.%0')%@!(#(!("#%#(A/'0(#%94(&!.(,''("'#%.("'0(.D)("'0%.#0"-(*%"]^P9

    ]^P 40")(#(5 20"%WQ8W

  • 8/2/2019 8 bsico - matemticas - 2010

    53/79

    C0H *')%" (".0'("' % !%) # #')")(' >!")(' / "0')%' ()"#(' # #')")(' #(' #(0"%+",#.('0%.''("(.%#%/T(.%(#%97%C0,"(%'("',')%'##%'!0#""('!'")%)1%'9D0H(!%%"#('("&0")('##%)('/%.0.%"")!)%"'0'##%'#)"#"%")%.,1'0%.$%"#(.%!()%"%#.%%.%)(#%##.%0')%94(&!.(,.%'%"0')%!%%#('0')%'#')")%'9

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

    @%"!"!!$"!!1#0/0H'""'00%#"(.%'("#("'"'%%'!%%%'*0%.%%.%)(#%##0"%0')%930H!%)#0"%.')%,.%'7%".%'0')%'"%.%)(%'/"(%.%)(%'970H >)%" "7(%+" / #%)(' # ')0#(' !:.(' # #7")' #(' # (0"%+" / ' .%''!7%("'#%#%0')%'(*#%9@0H4("""(:".('')0#('(!.%#('/.%"7(%+"#'0''!)1%'0')%'"*0!('9

    B0H"%.$%".(''0.)%#('##('"0')%'#')")%'"0"(")>)('*"7%)1(,0"%'(0"%0')%%.%)(%/.%()%"(9'""'00%#"(.%!()%"%#.%%.%)(#%##0"%0')%9!%'0*%.#(")!(!(("%%.('%.0"('%.*0"('>!")('("0')%'*0%#('!%%()".(''0.)%#('#'%#('9B% "! ! & +" ! !#$>"!&$!!+"!0

    /0H'"!(>)"'+""'0'0%#"('.('.")('# .(''!%('0')%.'##')")('>!")('94(&!.(?

    %A9B30H%"$%"0"#%#(1'%#%0"("*0!('#(%.0"('9'1%"/*')%""'0'0%#"('.%70"%.%)1%#%#%'0.)%#(@C0!(%.'A9

  • 8/2/2019 8 bsico - matemticas - 2010

    54/79

    79%.$%"..%"$%")(##('#%#('0"%*%"%")#%##1'/*')%".(''0.)%#('!%%.%'0%#.('!0")%&'#.%'%%'9).$%"%!(/(#.%)"(.(*6%/*%7%"9@9)"%".%'("%("'!('.'!%%. .%"$%")(# #('#%#('/*%7%".(''0.)%#('L)+('M!%%.%'0%#.%'%%'9).$%"0"*E7(#%%'!%%')(''0.)%#('#%.'9'!("#"%.%!*0")%?IJ0D'0%)"E'!(%.#%#'#'%.K

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

  • 8/2/2019 8 bsico - matemticas - 2010

    55/79

    !

    "12"%

    "!!&+"!!#$>"!&$!!+"!0

    !%

    '".'!%(0')%.#0">!")(%.%)((#%#(/()""'0%#"%.#%#9 *0")%"%%#.%C0!(%.#%##%#%'0.)%#(!('."0">!")(%.%)((,%.$%"#(

    0"%'0.%+"("%!(/(#.%)"(.(*6%94(&!.(,%..%"$%0"#%#(9

    )"%".%!(%.#%##(0"%#0")(1")("0">!")(%.%)((,#%").(#.(#%!.%9

    (!%%".1%.(#.%!(%.#%##0")(1")("0">!")(%.%)((,()"#(#%").(#.(#%!.%,(".1%.(#.%70"%.%)1%()"#%%.'0.%.>!")(0"*%"":(#

    1'#%").0'(#.%)"(.(*6%,/(0"%"'0'(".0'("'9 (!%%".*E7()+(#.(''0.)%#('#0">!")(%.%)((,()"#(%)%1D'#.(#.(#

    %!.%,/.*E7(#.%'70"%'.%)1%'#.'(>!")('0.%#(#%").0'(#)"(.(*6%,/(0"%"'0'(".0'("'9

    0#%#('%").%')0%+"#%#%9'!("#.%'!*0")%'!(!0')%'9

    "')(/('%&0*%"("("#%'9.&0*(("'')".%"$%0"%("#%#('1',!(.%"$%0"(,('%!(&!.(,/.0*(.()(&0*%#(,%.)"E"#('9"%('.%"$%")(''%."%%'("%(''..(,")("'*%"%('%,!(''%."#')")%'".!(%%/".'*0"#('..((11'%")("'*%"%"')(9

    4*0")%'?

    9"0"%"')%"%#.&0*(,I0%.'.'!%(0')%.KI0E")('.")(')"K

    9I0E.'.%!(%.#%#)+%#C0*%"('%K

    9 (' .")('#. '!%(0')%. I)"" *0%. !(%.#%# #(0"%K I4(C0DK

    9%.!)1'.&0*(,'()".%'*0"))%.%#70"%'?

    '0.)%#(' 20"%

    ' ' 3''

  • 8/2/2019 8 bsico - matemticas - 2010

    56/79

    4(!(("%.#%##)%"1'%9 !'")%+"*E7%.%!(!(("%.#%##)%"1'%9 '(.0+"#!(.%'C0!.C0"!.%")%/'(.10%("'#!*%#(("0"%"+*")%9"! )0%("'#1%%+"!(!(("%./"(!(!(("%.9 )0%("'#1%%+"!(!(("%.#)%"1'%9 ("!)(#70"+"/'0'#7")'!'")%("'9 ("(/(#(#70"("'9

    0%("'#!*%#(("E'#0"%"+*")%9?! #")7%')0%("'#1%%+"!(!(("%./"(!(!(("%.9 '(.1!(.%'C0"1(.0%"1%%+"!(!(("%.#)%9 '(.1!(.%'C0"1(.0%"1%%+"!(!(("%."1'%9 ("(70"("'"#1'('(")>)('9 #")7%#("(/(#(#70"("'"#1'('(")>)('9 '(.1!(.%'C0"1(.0%"70"("'"#1'('(")>)('9 4.%")%/'(.10%("'#!*%#(("#('"+*")%'9 %%&("C0!(/0')%"%)1%!'("%.".%'(.0+"#!(.%'"(")>)('#1'('9

  • 8/2/2019 8 bsico - matemticas - 2010

    58/79

    3

    "12" -!

    ()1

    1

    /0 ! > " !

    !! +0

    #")7%" .%' 1%%.' C0 ')E" "1(.0%#%' "')0%("'#.%1#%()#%"%9

    '!&%"0"%1%%."70"+"#.%()%"0%("'C0)""#('"+*")%'9

    1%.:%"0%("' !.%")%#%' " 70"+"#. (")>)(#.!(.%9

    30 , #

    +& # ! $")( #)"%#(, 1%%.' C0#!"#"!(!(("%.")#()%'1%%.'9

    #")7%" " 0" (")>)( #)"%#(, #!"#"%' "(!(!(("%.'9

    #")7%".%("')%")#!(!(("%.#%#"#!"#"%'!(!(("%.'9

    (!%%". 0(")") 1%.(' %'*"%#(' %1%%.'!%% #")7% 0"% .%+" # !(!(("%.#%# #)%")1%%.'9

    (!%%". !(#0)( ") 1%.(' %'*"%#(' % 1%%.'!%% #")7% 0"% .%+" # !(!(("%.#%# "1'%")1%%.'9

    ).$%".%("')%")#!(!(("%.#%#!%%%*0")%.%!(!(("%.#%##)%"1'%")1%%.'9

    @0 !1 ! #L

    #""!0

    #")7%", 0).$%"#( '(7)O%' *E7(', ')0%("'%'(%#%'%!(!(("%.#%##)%9

    ).$%" '(7)O%' *E7(' !%% #")7% ')0%("'%'(%#%'%!(!(("%.#%#"1'%9

    "%.$%",0).$%"#('(7)O%'*E7(',#%)('!'")%)1('#')0%("'!%%#)"%'')%''("!(!(("%.'9

    B0 ,! "! +> "!""! $ "! > "!""!0

    )"" 0%("' # ')0%("' %'(%#%' %!(!(("%.#%##)%9

    )"%" .% ("')%")# !(!(("%.#%# "#%)(' C01%6%"!(!(("%.")/.('0).$%"!%%%.$%E.0.('9

    !'")%", " )%.%' / *E7(', .%("' #!(!(("%.#%##)%"1'%")#('1%%.'9

  • 8/2/2019 8 bsico - matemticas - 2010

    59/79

    5

    "!*

    %0"#%##E.*%'!'")%!(!%1$".!(*%%#')0#(("#")#%#!(!%,')(C0#,("%0)("(6%#.(')%')%)%#('"":('9')--('!%)0.%").1%")0%"#('C0%"%.$%

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

    )%1D'#.%0%+"?T

    f1

    = 9

    % 0"#%# (7 )%D" .% !('.#%# # )%%&% "01%") )+!(' .%)1(' % !(!(("%.#%# #)% "1'%,(".%**%#(C0%.')%%&(.%.(#.E.*%'"C0'0)%%&(/'!()"%.("!)(#1%%+"!(!(("%.94(&!.(,.('')0#%")'!(#6%"(".0C0%.'. 0(")").!6)(/ .#E)(#0%.C00"7"%'!.'(":(,')%)%#0"%.%+"#)%")!(!(("%.,

    ")!)%"#(.%*0%.#%# PiD

    P= ((.%>!'+"C0!'")%#-%')0%+"9

    ')%'.%(!()0"#%#!%%")(#0.%'!'")%("'%.*%%'#0"%.%+"!(!(("%.,/%'%#)%("1'% /(')% '0' #7"%' (" !'")%("' # .%("' C0 "( 1%6%" !(!(("%."), %0"C00!.%" (" %.*0"% # .%' %%)6')%' # .%' !(!(("'9 4( &!.(, ' '!%. !%% . "1. C0 .('

    ')0#%")' #")7C0" .% >!'+" 12 += xy ((0"% .%+""(!(!(("%.,% !'%#C0 0%"#( 0"%

    1%%.%0")%)%D".(-%.%()%9.)%%&("C0!(7%.)%.%#'0'+"/%"E.''#')0%("'!(.%,7(")%"#(..#%$*(").)0%./.%E), %'6 (( .% %'*"%+" # (.'9 . )%%&( " E.*% ' !')% 7%1(%.") !%% %.)"% ")7.>+"/')0#(!'("%.("!.%")(/#'0'+"#')0%("'!(.E)%'9

  • 8/2/2019 8 bsico - matemticas - 2010

    60/79

    )('()#%"('%)%1D'#70"("'9

  • 8/2/2019 8 bsico - matemticas - 2010

    61/79

    !('("'*E7%'9

  • 8/2/2019 8 bsico - matemticas - 2010

    62/79

    '#'!.%$%'#)(!('*0"#(,#(E"#(' "0)(' / '*0"#(' "-% 0" 1%'#.7("#(#.%"%%.%'0!7("#'#.%'0!7%.7("#( # .% "%9 . .%!'( C0 )%"'0 ") . '%) # #('"('("'0)1(','#"0)('94*0")%'99 IJ0D )!( # .%+" >') ") . ":(, , # "(''%)%#(' / . )!(, ), C0 )%"'0 " . '%) # .(' "('KF0')7C099IJ0D.%+" >') "). )!( C0 )(%'%)%0""(@1%'#.7("#(#.%"%%.%'0!7A/.%1.(#%##'0#%# .%E!'0.%2D">K ("')0/% 0" *E7( C0 !'") .%.%+"").%'1%%.'99 '%")"" "1%%.' .('#%)(' ")*%#('" . "0"%#(,I0E")()!()(%6%.'%)#.('"('KF0')7C09

    )('#1%.0%+"9

    9#")7%".%'.%("'#!(!(("%.#%#").%'1%%.'9

    9!'")%"*E7%").%.%+"#!(!(("%.#%#")#('1%%.'

    9'0.1"!(.%',0).$%"#(.%'

    .%("'#!(!(("%.#%#")1%%.'9

  • 8/2/2019 8 bsico - matemticas - 2010

    63/79

    (,=0!(#)(%.(%%"%,,558,b

    #+"9 ;,2"%"#(9%%)E)%%!.%#%%.%1#%()#%"%9%.("%,#)(%.=%+,559 ],9,^,9,/=,9.%!"#$%.%'%)E)%'9%.("%,#)(%.%(99,

    559 =a, F('D/ ()('9 %$("%")( %)E)(9 D>(, ")"%("%. -(!'("#)(', 558, b

    #+"9

    =P, "%0.%#%, =a;a, F('D 0' / ()('9 :(' ")('9 %)E)%'? 0.)0% /!"#$%&9%##,#)(%.6")'',55 ^,P9,4P],9)1#%#'!%%!.")%.('&)1('20"#%")%.')%"'1'%.'9(

    #("',9 ]],99("')0("'=(D)%'#%")0"(!E'9(':,#)(%.,539 /()('9=()6%.")%.9%")%*(,#("'"1'#%#%)+.%#-.,559 9,=-/Y%9.":(#((9)((?(')('H)(((')('90"('',#)(%.4('#+",

    5(,2("#(#0.)0%

    ("+%,9 ,F('D9"(,(','G=()6%()%1$9*")"%,#)(%.J,9 =, 9 L"% ")(#0+" % .% ##E)% # .% %)E)%M, " "'B%"$% # .% %)E)%9

    .+".(*E7%,)%#0+"!%%.42,/559 FP, 9, 4, F9 @A9 ")(#0+" % .%##E)% # .%' "%'/ .%%)E)%,0"(' ',

    (.-09 ], 9, ]=, 9, , / ()('9 %%)E)%? '0 (")"#(,D)(#(' /

  • 8/2/2019 8 bsico - matemticas - 2010

    64/79

    )('#%)E)%?

    =()6%?-))!?TTOOO9Y/!''9(T>539>.@%!6)0.('#.("'"'!%B(.A;.*%-))!?TTOOO9Y/!''9(T>5839>.@%!6)0.('#.("'"'!%B(.A

    >)('!%%.#(")/.')0#%")#0%+"'0"#%%D>(?-))!?TTOOO97(%'0"#%%9'!9*(9>T%)%)%'T##%)(9-).-))!?TT).'0"#%%9#*9'!9*(9>T%)[#T%)[#[9!-!

    ,!!M%

    !'!%-))!?TTOOO9#0%-.9.T4()%.9%'T^T1(")"#(9%'!>KV3

  • 8/2/2019 8 bsico - matemticas - 2010

    65/79

    T%)[#T%)[#[9!-!

    ,!!M%

    $&'!%B%%

    -))!?TT0'(')9#0%("9'T#'%)'TOT%!.%("'9!-!

    !!"!)!&%!!.)'#.%"1'#%##P%.".%*"D('-))!?TT".190'09#0T'T"%1,("!0#'(*.('".%'#)('?HG$"%

    -))!?TT".190'09#0T'T"%1T%)*(/[*[[)[9-).H!%

    -))!?TT".190'09#0T'T"%1T%)*(/[*[[)[9-).H8(%

    -))!?TT".190'09#0T'T"%1T%)*(/[*[[)[9-).-))!?TT".190'09#0T'T"%1T%)*(/[*[[)[9-).H!$!%

    -))!?TT".190'09#0T'T"%1T%)*(/[*[[)[9-).

    !'!%-))!?TTOOO9#0%-.9.T4()%.9%'T^T1(")"#(9%'!>KV39!-!K)V'0[!%*'g%)V9!-!K)V'0[!%*'g%)V9!-!K)V'0[!%*'g%)V

  • 8/2/2019 8 bsico - matemticas - 2010

    66/79

    (,%%'&%,

  • 8/2/2019 8 bsico - matemticas - 2010

    67/79

    ')0"("&0")(#"')0")('00.%'C0.('#(")'!0#"0).$%#%"%("&0")%/(!.")%%(".!(*%%#')0#(9')('!0#"'0'%#('#%"%7.>.!%%%!(/%. #'B( !.")%+"#')%)*%'##E)%'/!%%1%.0%.('%!"#$%&'9

    " "9 7" 0" %( *.(%. !%% ("( +( !(*'%" .('%!"#$%&'.%1%.(.%*(#.%'(.%#%#940#"'0'%#(',")()%'!('.#%#',((0"%!(/(!%%%(#%.%#1'#%##%!"#$%&'C0'>!'%%.")(#0"0'(,/%C0!)"?- %%)$%.('#')")('"1.'#%!"#$%&".('C0'"0")%".('')0#%")'

    #0"0'(9- ("(#C0D%"%#"(")"0%!(*'%"#(.('%!"#$%&'#.('*0!('#

    ')0#%")'C0'"0")%""')('#')")('"1.'9

    + !9 '%(..%" .(' &)1(' 20"#%")%.' / .(' (")"#(' 6"('.*%)(('!%%%!(/%.)%%&(#.('%.0"('".%0.%/70%#..%,/.'")*%">!.%("'/%)1#%#'!%%7%1('0%!"#$%&/'0%0)(1%.0%+"9

    (' #(")' !0#" "C0 .% !.")%+" #. 060.0, -%"#( )%D" 0'( # .(' 0'('")*%#('!(."#0%)%1D'#? (',"!"125,6/.('%)%.'!'(',%0#(1'0%.',#*)%.'/

    (")('")*%#('%)%1D'#')('9 . !, / .%' -%")%' )"(.+*%' C0 ') -% !0')( % #'!('+" # .('

    ')%.")('9

    " .%!E*"%O#."')(##0%+"'"0")%#'!(".. #(0")( !"#/()('%)%.'C00'%"%!(/%.)%%&((".('%!%'@-))!?TTOOO9060.0"#09.T%/0#%T#(0")('TA9"0"%!E*"%#'""8"1.'.")()6!(#.%!"#$%.('')0#%")'"0"E)((.')(%.(.%*(#.('%B('#'(.%#%#(.*%)(%9%#%0"(#')('"1.'!'")%0"%>!)%)1%#%!"#$%&('!("#")%#('%B('#'(.%#%#94(&!.(,.1.('!("#%..(*(C0''!%!%%.%%/(6%#.('"B('/"B%'%.)D"(#*0"#(E'(H.1.('!("#%.)D"(#0%)(E'(,/%'6'0'1%")9.1.8#'.%!"#$%"%.0"((%.0"%C0%.*'%#.%#0%+"#%'L'('%.")M,'#,1%E'%..E#.%>!)%)1%!%%0%)(#(,C0#'.1.

  • 8/2/2019 8 bsico - matemticas - 2010

    68/79

    ISTERIODEEDUCACIN

    UNIDADD

    ECURRCULUMY

    EVALUACIN

    DICIEMBRE2010

    68

    O

    3%!#!

    EPQ

    ("'#%"!")%.'9

    /

    #")7%1%%.'

    .%("%#%'"7(%

    !(!(("%./"

    7(%"(!(!(("%.

    3

    ).$%')%)*%'!%%

    #)"%.1%.(#

    !()"%'#%'")%/

    >!("")"%)0%.9

    B

    &)%+"9

    3

    1'+"#.%1%.0%+"

    B

    '*"%!(%.#%#'

    )+%")%.%(0"%

    #1")(',"

    >!")('%.%)(('("

    '0.)%#('7")('/

    C0!(%.',/

    (")%')%.%'("'0.)%#('

    >!")%.'9

    3

    &)%+"9

    7

    ).$%')%)*%'!%%

    #)"%.1%.(#

    !()"%'#%'")%/

    C

    &)%+"9

    7

    !%'(

    C

    '*"%!(%.#%#'

    )+%")%.%(0"%

    #1")(',"

    7

    &)%+"9

  • 8/2/2019 8 bsico - matemticas - 2010

    70/79

    ISTERIODEEDUCACIN

    UNIDADD

    ECURRCULUMY

    EVALUACIN

    DICIEMBRE2010

    70

    >!("")"%)0%.9

    >!")('%.%)(('("

    '0.)%#('7")('/

    C0!(%.',/

    (")%')%.%'("'0.)%#('

    >!")%.'9

    @

    ).$%')%)*%'!%%

    #)"%.1%.(#

    !()"%'#%'")%/

    >!("")"%)0%.9

    /

    &)%+"9

    @

    !%'(

    /

    '*"%!(%.#%#'

    )+%")%.%(0"%

    #1")(',"

    >!")('%.%)(('("

    '0.)%#('7")('/

    C0!(%.',/

    (")%')%.%'("'0.)%#('

    >!")%.'9

    @

    &)%+"9

    B

    ).$%')%)*%'!%%

    #)"%.1%.(#

    !()"%'#%'")%/

    >!("")"%)0%.9

    3

    ("')0)%"'7(%("'

    '(D)%'#7*0%'

    *(D)%'!.%"%',

    0).$%"#(*.%/(!E'

    (!('%#('

    *(D)('9

    B

    40%*.(%.

    3

    '*"%!(%.#%#'

    )+%")%.%(0"%

    #1")(',"

    >!")('%.%)(('("

    '0.)%#('7")('/

    C0!(%.',/

    (")%')%.%'("'0.)%#('

    >!")%.'9

    B

    "%.$%#%").

    0'(#'(7)O%'

    *E7('')0%("'#

    !(!(("%.#%#

    C

    &)%+"

    7

    ("')0)%"'7(%("'

    '(D)%'#7*0%'

    *(D)%'!.%"%',

    0).$%"#(*.%/(!E'

    (!('%#('

    *(D)('9

    C

    40%*.(%.

    7

    4(%.#%#'

    C

    "%.$%#%").

    0'(#'(7)O%'

    *E7('')0%("'#

    !(!(("%.#%#

    /

    &)%+"

    @

    ("')0)%"'7(%("'

    '(D)%'#7*0%'

    *(D)%'!.%"%',

    0).$%"#(*.%/(!E'

    (!('%#('

    *(D)('9

    /

    '(.1!(.%'"

    (")>)('#1'('

    .%)1('%E.0.('#?

    46)('#

    0"7"%'/E%'

    #60.('9

    ;%'#'0!7'#

    ."#(',("('/

    !E#'9

    (.:"'#."#('/

    ("('9

    @

    '*"%!(%.#%#'

    )+%")%.%(0"%

    #1")(',"

    >!")('%.%)(('("

    '0.)%#('7")('/

    C0!(%.',/

    (")%')%.%'("'0.)%#('

    >!")%.'9

    /

    "%.$%#%").

    0'(#'(7)O%'

    *E7('')0%("'#

    !(!(("%.#%#

    3

    &)%+"

    B

    ("')0)%"'7(%("'

    '(D)%'#7*0%'

    *(D)%'!.%"%',

    0).$%"#(*.%/(!E'

    (!('%#('

    3

    &)%+"9

    B

    &)%+"9

    3

    &)%+"9

  • 8/2/2019 8 bsico - matemticas - 2010

    71/79

    ISTERIODEEDUCACIN

    UNIDADD

    ECURRCULUMY

    EVALUACIN

    DICIEMBRE2010

    71

    *(D)('9

    7

    (")(.

    C

    &)%+"9

    7

    &)%+"9

    C

    &)%+"9

    7

    &)%+"9

    @

    )"%!(!#%#'#

    0.)!.%+"/#1'+"#

    !()"%'#%'")%/

    >!("")"%)0%.9

    /

    &)%+"9

    @

    &)%+"9

    /

    &)%+"9

    @

    &)%+"9

    B

    )"%!(!#%#'#

    0.)!.%+"/#1'+"#

    !()"%'#%'")%/

    >!("")"%)0%.9

    3

    &)%+"9

    B

    &)%+"9

    3

    &)%+"9

    B

    &)%+"9

    C

    )"%!(!#%#'#

    0.)!.%+"/#1'+"#

    !()"%'#%'")%/

    >!("")"%)0%.9

    7

    '.%.!.%"(("

    !(.6*("('*0.%'

    0).$%"#(*.%/(!E'

    (!('%#('

    *(D)('9

    C

    (")(.

    7

    &)%+"9

    C

    '(.1!(.%'"

    #1'('(")>)('

    C0!.%"

    !(!(("%.#%#

    #)%/!(.%'

    C0!.%"

    !(!(("%.#%#

    "1'%9

    !

    /

    &)%+"

    @

    '.%.!.%"(("

    !(.6*("('*0.%'

    0).$%"#(*.%/(!E'

    (!('%#('

    *(D)('9

    /

    ")!)%"7(%+"%

    !%)#)%.%'#

    70"%,0/('#%)('

    ')E"%*0!%#('"

    ")1%.('9

    @

    &)%+"9

    /

    '(.1!(.%'"

    #1'('(")>)('

    C0!.%"

    !(!(("%.#%#

    #)%/!(.%'

    C0!.%"

    !(!(("%.#%#

    "1'%9

    3

    &)%+"9

    B

    '.%.!.%"(("

    !(.6*("('*0.%'

    0).$%"#(*.%/(!E'

    (!('%#('

    *(D)('9

    3

    ")!)%"7(%+"%

    !%)#)%.%'#

    70"%,0/('#%)('

    ')E"%*0!%#('"

    ")1%.('9

    B

    &)%+"9

    3

    &)%+"9

    7

    &)%+"9

    C

    &)%+"9

    7

    &)%+"9

    C

    &)%+"9

    7

    &)%+"9

    @

    &)%+"

    R

    /

    &)%+"9

    @

    &)%+"9

    /

    &)%+"9

    @

    &)%+"9

    B

    &)%+"

    3

    &)%+"9

    B

    !'")%#%)(',

    !(1"")'##1'%'

    70")',")%.%'#

    3

    &)%+"9

    B

    &)%+"9

  • 8/2/2019 8 bsico - matemticas - 2010

    72/79

    ISTERIODEEDUCACIN

    UNIDADD

    ECURRCULUMY

    EVALUACIN

    DICIEMBRE2010

    72

    70"%'("#%)('

    %*0!%#('"")1%.('9

    C

    1%.0%+"

    7

    ).$%.%'

    )%"'7(%("'

    '(D)%'((

    -%")%!%%%.$%

    )'.%("'*0.%'/

    )'.%("'

    '*0.%'9

    C

    !'")%#%)(',

    !(1"")'##1'%'

    70")',")%.%'#

    70"%'("#%)('

    %*0!%#('"")1%.('9

    7

    !%'(9

    C

    &)%+"9

    /

    1%.0%+"

    @

    ).$%.%'

    )%"'7(%("'

    '(D)%'((

    -%")%!%%%.$%

    )'.%("'*0.%'/

    )'.%("'

    '*0.%'9

    /

    &)%+"9

    @

    1%.0%+"

    /

    &)%+"9

    3

    1'+"#.%1%.0%+"

    B

    &)%+"9

    3

    &)%+"9

    B

    1'+"#.%1%.0%+"

    3

    &)%+"9

    7

    7%C0!(!#%#'#

    !()"%'#%'")%/

    >!("")"%)0%.'0!."

    "!()"%'#%'

    7%("%%!(')1%,

    #%.

    !(')1%/>!("")"%)0%.9

    C

    1%.0%+"9

    7

    &)%+"9

    C

    4.%")%0%("'C0

    !'")%".%.%+"

    ")#('1%%.'"

    #1'('(")>)('9

    7

    &)%+"9

    @

    7%C0!(!#%#'#

    !()"%'#%'")%/

    >!("")"%)0%.'0!."

    "!()"%'#%'

    7%("%%!(')1%,

    #%.

    !(')1%/>!("")"%)0%.9

    /

    1'+"#.%1%.0%+"9

    @

    &)%+"9

    /

    4.%")%0%("'C0

    !'")%".%.%+"

    ")#('1%%.'"

    #1'('(")>)('9

    @

    &)%+"9

    B

    7%C0!(!#%#'#

    !()"%'#%'")%/

    >!("")"%)0%.'0!."

    "!()"%'#%'

    7%("%%!(')1%,

    #%.

    !(')1%/>!("")"%)0%.9

    3

    %%)$%.%

    0"7"%/.60.(

    ((.0*%'*(D)('9

    B

    &)%+"9

    3

    4.%")%0%("'C0

    !'")%".%.%+"

    ")#('1%%.'"

    #1'('(")>)('9

    B

    1%.0%+"

  • 8/2/2019 8 bsico - matemticas - 2010

    73/79

    ISTERIODEEDUCACIN

    UNIDADD

    ECURRCULUMY

    EVALUACIN

    DICIEMBRE2010

    73

    C

    &)%+"9

    7

    %.0.%.!6)(#

    0"7"%'/#%('

    #..%'9

    C

    1%.0%+"

    7

    &)%+"

    C

    1'+"#.%

    1%.0%+"9

    /

    &)%+"9

    @

    %.0.%.!6)(#

    0"7"%'/#%('

    #..%'9

    /

    1'+"#.%1%.0%+"

    @

    &)%+"

    /

    '(.1!(.%'"

    #1'('(")>)('

    C0!.%"

    !(!(("%.#%#

    #)%/!(.%'

    C0!.%"

    !(!(("%.#%#

    "1'%9

    3

    &)%+"9

    B

    &)%+"9

    3

    ")!)%/!(#0

    "7(%+","(")>)('

    #1'(',#%").0'(

    ###%'#)"#"%

    ")%.,>)"#"#(%.

    %'(##%)('%*0!%#('

    "")1%.('9

    B

    &)%+"

    3

    !%'(

    7

    &)%+"9

    C

    &)%+"9

    7

    ")!)%/!(#0

    "7(%+","(")>)('

    #1'(',#%").0'(

    ###%'#)"#"%

    ")%.,>)"#"#(%.

    %'(##%)('%*0!%#('

    "")1%.('9

    C

    &)%+"

    7

    !%'(

    @

    '(.1!(.%'C0

    "1(.0".%'(!%("'

    ("":('")('/.%'

    !()"%'#%'")%,

    7%("%%(#%.!(')1%

    />!("")"%)0%.9

    /

    %.0.%.!6)(#

    0"7"%'/#%('

    #..%'9

    @

    ")!)%/!(#0

    "7(%+","(")>)('

    #1'(',#%").0'(

    ###%'#)"#"%

    ")%.,>)"#"#(%.

    %'(##%)('%*0!%#('

    "")1%.('9

    /

    &)%+"

    @

    40%')%.

    B

    '(.1!(.%'C0

    "1(.0".%'(!%("'

    ("":('")('/.%'

    !()"%'#%'")%,

    7%("%%(#%.!(')1%

    />!("")"%)0%.99

    3

    %.0.%.!6)(#

    0"7"%'/#%('

    #..%'9

    B

    ")!)%/!(#0

    "7(%+","(")>)('

    #1'(',#%").0'(

    ###%'#)"#"%

    ")%.,>)"#"#(%.

    %'(##%)('%*0!%#('

    "")1%.('9

    3

    (")(.

    B

    40%')%.

  • 8/2/2019 8 bsico - matemticas - 2010

    74/79

    ISTERIODEEDUCACIN

    UNIDADD

    ECURRCULUMY

    EVALUACIN

    DICIEMBRE2010

    74

    C

    '(.1!(.%'C0

    "1(.0".%'(!%("'

    ("":('")('/.%'

    !()"%'#%'")%,

    7%("%%(#%.!(')1%

    />!("")"%)0%.9

    7

    &)%+"9

    C

    ")!)%/!(#0

    "7(%+","(")>)('

    #1'(',#%").0'(

    ###%'#)"#"%

    ")%.,>)"#"#(%.

    %'(##%)('%*0!%#('

    "")1%.('9

    9

    7

    ("(70"("'"

    #1'('(")>)(',

    #")7%'0'.")('/

    !'")%#1'%'

    ')0%("'%)%1D'#

    ..%'9

    C

    !%'(

    /

    '(.1!(.%'C0

    "1(.0".%'(!%("'

    ("":('")('/.%'

    !()"%'#%'")%,

    7%("%%(#%.!(')1%

    />!("")"%)0%.9

    @

    &)%+"9

    /

    &)%+"9

    @

    ("(70"("'"

    #1'('(")>)(',

    #")7%'0'.")('/

    !'")%#1'%'

    ')0%("'%)%1D'#

    ..%'9

    /

    !%'(

    3

    &)%+"

    B

    &)%+"9

    3

    &)%+"9

    B

    &)%+"9

    3

    >%"2"%.

    7

    &)%+"9

    C

    (")(.

    7

    &)%+"9

    C

    &)%+"9

    7

    >%"2"%.

    *Lashabilidadesdelrazon

    amientoMatemticoseesperaque

    seandesarrolladasatravsdetodo

    sloscontenidos

  • 8/2/2019 8 bsico - matemticas - 2010

    75/79

    MINISTERIO DE EDUCACINUNIDAD DE CURRCULUM Y EVALUACIN

    DICIEMBRE 2010

    75

    O7%24!"-$*

    -/ -3*% *%24!/ 3 7 @

    9 ')%.')%)*%'!%%%.0.%0.)!.%("'/#1'("'#":('")('9 >

    9 ).$%+"')%)*%'#E.0.(C0!.%".0'(#!()"%'# %' ")% / >!("") "%)0%., #)"% / %!.% '0'!(!#%#' / >)"#.%' % !()"%' # %' 7%("%% (#%.!(')1%/>!("")"%)0%.9

    >

    9 ("( 70"("' " #1'(' (")>)(', #")7% '0'.")('/!'")%#1'%'')0%("'%)%1D'#..%'9

    >

    9 #")7%1%%.'.%("%#%'"7(%!(!(("%./"7(%"( !(!(("%. / '(.1 !(.%' " #1'(' (")>)(' C0!.C0".0'(#.%.%+"#!(!(("%.#%#9

    >

    9 %%)$% / 7)0% )%"'7(%("' '(D)%' # 7*0%'*(D)%' !.%"%', ("( %.*0"%' # '0' !(!#%#' #")7% ')0%("' " (")>)(' #1'(' C0 ('!("#" %%!.%("'##-%')%"'7(%("'9

    >

    89 ")!)%"7(%+"%!%)#)%.%'#70"%,0/('#%)('')E"%*0!%#('"")1%.('/0).$%'))!(#!'")%+"!%%(*%"$%#%)('!(1"")'##1'%'70")'9

    >

    39 ")!)%/!(#0"7(%+","(")>)('#1'(',#%").0'(###%'#)"#"%")%.,%!.%"#(%.%'(##%)('%*0!%#('"")1%.('9

    >

    59 (!"#.("!)(#%.%)(#%#".0'(#0')%'/'0!()%"% " .% %.$%+" # "7"%',/ 0).$%##%' #)"#"%")%.!%%%"%.$%.(!()%")(#0"%0')%##%)('/%*0")%%%#.%"7(%+"C0')%'##%'")*%"9

    >

    9 )"%)+%")!(%.#%#'# (0"%#1")(',

    ">!")('%.%)(('("'0.)%#('7")('/C0!(%.',/(")%')%.%'("'0.)%#('>!")%.'9 > 9 !.% 7(%' '!.' # (#.%")( %)E)(, 17%

    !(!('("''!.',!%%%'('!%)0.%',/%!.%-%.#%#'E'%' #. !('( # '(.0+" # !(.%' " (")>)('#1'(' / '*"7%)1(', 1%.0% .% 1%.#$ # .(' '0.)%#('()"#(' / . !.( # #-(' '0.)%#(' !%% 70"#%")%(!"("'/)(%#'("'9

    > > > >

  • 8/2/2019 8 bsico - matemticas - 2010

    76/79

    MINISTERIO DE EDUCACINUNIDAD DE CURRCULUM Y EVALUACIN

    DICIEMBRE 2010

    76

    O@%(!"-$*

    -/ -3*% *%(!/ 3 7 @

    S,-% 9 !.( # !(#")('# E.0.( !%%0.)!.% 0"":(

    "%)0%. !( 0" ":( ")( "*%)1( / >)"'+" # #-('!(#")('%.%0.)!.%+"#":('")('9

    >

    9 >)"'+"#.%.*()(#.%#1'+"#.('":('"%)0%.'%.%#1'+" # ":(' ")('9 '0'+" / %!.%+" # #-(%.*()(9

    >

    9 ).$%+"#')%)*%'#E.0.(")%./')(C0!.%".0'( # !()"%' # %' ")% / >!("") "%)0%.,#)"%+" / %!.%+" # !(!#%#' .%)1%' % .%0.)!.%+" / #1'+" # !()"%' C0 )"" %' ")% />!("")"%)0%.,/>)"'+"%!()"%'#%'7%("%%(#%.!(')1%/>!("")"%)0%.9

    >

    9 '(.0+"#!(.%'"(")>)('#1'('/'*"7%)1('C0"1(.0%" .%' (!%("' %)D)%' (" ":(' ")(',!()"%' # %' ")%, 7%("%% ( #%. !(')1% /

    >!("") "%)0%., "7%)$%"#( " . %"E.'' 6)( # .('!(#")('#'(.0+"/#.(''0.)%#('()"#('9

    >

    98,% 9 4.%")%")(#0%("'C0!'")%".%.%+"")#('

    1%%.'"')0%("'(7"+"('#.%1#%()#%"%/%"E.''#. (!()%")( # #-(' 7"+"(' % )%1D' # )%.%' /*E7('9

    >

    89 ("(")( / !'")%+" (( 0"% 70"+" # .%'.%("'#!(!(("%.#%##)%"1'%")#('1%%.',"(")>)(''*"7%)1('9(!%%+"("1%%.'.%("%#%'"7(%"(!(!(("%./%*0")%+"%%#.%#7"%(".%'(!(!(("%.9

    >

    39 "E.''##1'%'')0%("'C0!'")%")%")(%*")0#'!(!(("%.' (( "( !(!(("%.', #%") . 0'( #'(7)O%*E7(9

    >

    59 '(.0+"#!(.%'"#1'('(")>)('C0!.%".0'(#.%.%+"#!(!(("%.#%#(((#.(%)E)(9

    >

    8,% 9 %.$%+" # )%'.%("', 7.>("' / ()%("' # 7*0%'

    *(D)%'!.%"%'%)%1D'#("')0("'("*.%/(!E'/ !.%"#( 0" !('%#( *(D)(, #'0'+" %% # .%'"1%%")'C0'*"%"%.%.$%')%')%"'7(%("'9

    >

    9 ("')0+" # )'.%("' *0.%' / '*0.%' /%*0")%+" %% # .%' )%"'7(%("' '(D)%'0).$%#%'"#-%')'.%("'9

    >

    9 %%)$%+" # .% 0"7"% / . 60.( (( .0*%'*(D)(' / '0 !'")%+"#%") ."*0%& ("&0")')%

    #")7%+"#'0'.")('?%(,0#%,'%")/)%"*")9

    >

    9 7"+"#.":(!/'0.%+"(".#E)(/.%.("*)0##0"%0"7"%9E.0.(#.%.("*)0##0"%0"7"%/')%+" #. E% #. 60.( !( #(#!(.6*("(' *0.%'"')('".%0"7"%9

    >

    9 2(0.%+"#("&)0%'.%("%#%'(". E.0.(#.1(.0"#.."#(/("(HE.0.(#.E%#.%'0!7#.."#(/("(,/17%+","%'('!%)0.%',#%").0'(#0"!('%#(*(D)(9

    >

    9 '(.0+" # !(.%' " ')0%("' '*"7%)1%' C0 >

  • 8/2/2019 8 bsico - matemticas - 2010

    77/79

    MINISTERIO DE EDUCACINUNIDAD DE CURRCULUM Y EVALUACIN

    DICIEMBRE 2010

    77

    "1(.0%".E.0.(#.%.("*)0##.%0"7"%,.E%#.60.(,.%'0!7#.."#(,("(/!E#'/.1(.0"#.."#(/("(9

    -:T,% !")('("0')%'9

    >

    89 ("')0+" # )%.%' # 70"% (" #%)(' %*0!%#(' "")1%.(',"7(%%"0%./#%")-%")%')"(.+*%',% !%) # #1'(' (")>)(' / #)"%+" # .% #%%)D)%/(#%"')('%'('9

    >

    39 '0'+"'!)(#.%!()%"%#)(%0')%'%.%$%"%.*0"(' >!")(' %.%)((' !%% "7 '( .%'%%)6')%'#!(.%("',&!.7%+"#%'('9

    >

    59 "E.''#.(!()%")(#0"%0')%##%)(',"#1'('(")>)(', 0'%"#(##%'# )"#"%")%. / %*0")%+"%%#.%"7(%+"C0..%'")*%"9

    >

    9 "E.''#&!.('"#1'%'')0%("' #("# .(''0.)%#(''(" C0!(%.', % !%) # .% '0.%+" # >!")('%.%)(('#%").0'(#-%")%')"(.+*%'9

    >

    9 #")7%+" #. ("&0")( # .(' '0.)%#(' !('.' "

    >!")(' %.%)((' '!.' @'!%( 0')%.A / # .('1")('( '0'('(('0("&0")('# %C0.,0'(#. !"!(0.)!.%)1(!%%()".%%#"%.#%##.'!%(0')%./#.(''0'('(1")('9

    >

    9 '*"%+""7(%)+%#.%!(%.#%##(0"%#0"1")( " 0" >!")( %.%)((, (" 0" ":( 7")( #'0.)%#('!('.'/C0!(%.',0'%"#(.(#.(#%!.%9

    >

  • 8/2/2019 8 bsico - matemticas - 2010

    78/79

    MINISTERIO DE EDUCACINUNIDAD DE CURRCULUM Y EVALUACIN

    DICIEMBRE 2010

    78

    OB%,!"12"&24!546$

    (!56-/%"12" 4 */%G$!

    9 ')%.')%)*%' !%%%.0.%0.)!.%("' / #1'("'#":('")('9

    / /H3

    9 ).$% ')%)*%' !%% #)"% . 1%.( # !()"%' # %'")%/>!("")"%)0%.9

    3 7

    9 )"%!(!#%#'#0.)!.%+"/#1'+"#!()"%'#%'")%/>!("")"%)0%.9

    3 7

    9 7%C0D!(!#%#'#!()"%'#%'")%/>!("")"%)0%. ' 0!." " !()"%' # %' 7%("%% !(')1%,#%.!(')1%/>!("")"%)0%.9

    3 7

    9 '(.1 !(.%' C0 "1(.0" .%' (!%("' (" ":('")('/.%'!()"%'#%'")%,7%("%%(#%.!(')1%/>!("")"%)0%.9

    /H3H// /H3H7H@

    *3%8( 9 %%)$% )%"'7(%("' '(D)%' # 7*0%' !.%"%' /

    ("(.%'"#1'%'')0%("'/(")>)('9

    B /K

    9 ("(%.*0"%'!(!#%#'#.%')%"'7(%("''(D)%'9

    B /K

    9 ("')0)%"'7(%("''(D)%'#7*0%'*(D)%'!.%"%'0).$%"#(*.%/(!E'(!('%#('*(D)('9

    B /K

    9 '.%.!.%"(("!(.6*("('*0.%',0).$%"#(*.%/(!E'(!('%#('*(D)('9

    B //

    9 ).$% .%' )%"'7(%("' '(D)%' (( -%")% !%%%.$%)'.%("'*0.%'/)'.%("''*0.%'9

    B //

  • 8/2/2019 8 bsico - matemticas - 2010

    79/79

    -3"12" 4 *7%$1 9 ")!)%"7(%+"%!%)#)%.%'#70"%,0/('#%)('

    ')E"%*0!%#('"")1%.('9

    D /C

    9 !'")%#%)(',!(1"")'##1'%'70")',")%.%'#70"%'("#%)('%*0!%#('"")1%.('9

    D /D

    9 ")!)%/!(#0"7(%+","(")>)('#1'(',#%").0'(###%'#)"#"%")%.,>)"#"#(%.%'(##%)('%*0!%#('"")1%.('9

    E /DH/J

    9 (!"#.("!)(#%.%)(#%#".0'(#0')%'/'0!()%"%".%%.$%+"#"7"%'9

    J /EH/J

    9 '*"%!(%.#%#')+%")%.%(0"%#1")(',">!")('%.%)(('("'0.)%#('7")('/C0!(%.',/(")%')%.%'("'0.)%#('>!")%.'9

    /K 3KH3/H33

    *@%! 9 4.%")%0%("'C0!'")%".%.%+"")#('1%%.'"

    #1'('(")>)('9

    @ B

    9 ("(70"("'"#1'('(")>)(',#")7%'0'.")('/!'")%#1'%'')0%("'%)%1D'#..%'9

    7 C

    9 #")7%1%%.'.%("%#%'"7(%!(!(("%./"7(%"(!(!(("%.9

    @ D

    9 "%.$%#%").0'(#'(7)O%'*E7('')0%("'#!(!(("%.#%#9

    @ E

    9 '(.1!(.%'"#1'('(")>)('C0!.C0!(!(("%.#%##)%/!(.%'C0!.C0!(!(("%.#%#"1'%9

    @ J