3log.mat. i bim
TRANSCRIPT
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LOGICOMATEMATICO I BIM.
TRILCE PRIMARIA
LOCUTORIO REN@TRIXCEL :992444616
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LOG. MATEMATICO
Í n d i c ePág.
...........Agrupando !"n#o$ % &or"a"o$ 'on(un#o$ )
.......*#r"+na'+,n d 'on(un#o$ por 'o"prn$+,n -#n$+,n
................................................................................. 9
.C!a$+/'a'+,n d 'on(un#o$: Un+#ar+o0 a'o0 un+r$a!0/n+#o0
............................+n/n+#o0 pr#n' - no pr#n' 11
............................Un+,n +n#r$''+,n d 'on(un#o$ 1)
.Rpr$n#a'+,n gr3/'a d n"ro$ % 5a!or po$+'+ona!
........................................................d$'o"po$+'+,n 19
..............................................Aprnd+ndo a!go "3$ 2)
......L'#ura - $'r+#ura a$#a 99 999 % Co"para'+,n 27
..........................An#r+or - po$#r+or % Apro+"a'+,n 81
COLEGIO TRILCE P3g+na 2
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LOG. MATEMATICO
1. R'or#a !a$ $+gu+n#$ /gura$ d an+"a!$ - agrpa!o$. Lugo pga!o$ n #u
'uadrno $gn una o ar+a$ 'ara'#r$#+'a$ 'o"un$.
COLEGIO TRILCE P3g+na 8
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LOG. MATEMATICO
R ' o r # a r ' o " o # + n d + ' a ! a p r o $ o r a .
COLEGIO TRILCE P3g+na 4
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LOG. MATEMATICO
&or"a"o$ 'on(un#o$1. Rpr$n#a !o$ $+gu+n#$ 'on(un#o$ u#+!+;ando d+agra"a$ d 5nn - !a$ !!a$.
& < = N " r o $ " n o r $ > u 6 ?
& < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
P < = 5 o ' a ! $ ?
P < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
A < = * a $ d ! a $ " a n a ? C < = C o ! o r $ 3 $ + ' o $ ?
A < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
& P
C < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
A C
R ' u r d a :
% E n ' a d a ! " n # o d ! ' o n ( u n # o $ ' o ! o ' a u n p u n # o n ! # r " o
+ n r + o r + ; > u + r d o .
% C a d a ! " n # o d $ ' r + + r $ ' o n ! # r a " + n $ ' u ! a .
COLEGIO TRILCE P3g+na )
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LOG. MATEMATICO
Ap!+'a"o$ !o aprnd+doI. C!a$+/'a !o$ o(#o$ >u n'un#ra$ n ! r'uadro - 'o!,'a!o$ n !o$ d+agra"a$
d 5nn.
1
23
4
5
< = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ? < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
< = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ? < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
COLEGIO TRILCE P3g+na 6
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LOG. MATEMATICO
B d # r " + n a p o r :
C u a n d o " n ' + o n a " o $# o d o $ ! o $ ! " n # o $
d ! ' o n ( u n # o .
C u a n d o " n ' + o n a " o $u n a ' a r a ' # r $ # +' a > u
d / n a a # o d o $ ! o $ ! " n # o $ d ! ' o n ( u n # o .
U N C O N J U N T O
E X T E N B I N C O M P R E N B I N
% O$ra a#n#a"n#:
A < = O a r +o 0 p + $ # +! o 0 g r a n o $ d p o ! n 0p # a ! o $ 0 ' 3 ! + ; ?
P o r e ! e n " i # n $
A < = P a r # $ d ! a D o r ?
P o r c o % & r e n " i # n $
o a r + o
p + $ # + ! og r a n o $ d p o ! n
' 3 ! + ;
p # a ! o $
A
Rpr$n#a !o$ $+gu+n#$ 'on(un#o$ por #n$+,n - por 'o"prn$+,n.
R < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
P o r e ! e n " i# n $
P o r c o % & r e n " i # n $
C o $ # a
B ! aB + r r a
M a r P r u a n o
R
R < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
COLEGIO TRILCE P3g+na 7
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LOG. MATEMATICO
N < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?P o r e ! e n " i # n $
P o r c o % & r e n " i # n $
d o
N
N < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?
r
" + a
$ o !
! a $ +
Ap!+'ando !o aprnd+do
1. O$ra $#o$ 'on(un#o$ d/n+do$ por 'o"prn$+,n0 !ugo dn!o$ por
#n$+,n o +'r$a.
F
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LOG. MATEMATICO
R ' u r d a :
B + " p r d $ d
r p a $ a r n ' a $ + # a .
Con a-uda d #u "a$#ra d/n !o $+gu+n#:
MC o n ( u n # o u n + # a r +o
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
L C o n ( u n # o 1 a ' 2o
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
p r r og a # o
g a ! ! o
A
C
U
C o n ( u n # o u n + 1 r $ a !
A < = p r r o ? < = g a # o ?
C < = g a ! ! + n a ?
U < = A n + " a ! $ d o " 9 $ # + ' o $ ?
R'urda >u n un 'on(un#o !o$ !"n#o$ +gua!$ $ 'un#an $,!o una;. Por ("p!o:
A < =5o'a!$ d !a pa!ara p!an#a?
En#on'$: A $ un 'on(un#o un+#ar+o
COLEGIO TRILCE P3g+na 9
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LOG. MATEMATICO
2. Rpr$n#a gr3/'a"n# !a$ $+gu+n#$ a/r"a'+on$.
C o n ( u n # o / n + # o
E $ u n ' o n ( u n # o o r " a d o p o r u nn " r o d ! " n # o $ > u
p o d " o $ ' o n # a r.
E ( " p ! o
C o n ( u n # o + n / n + # o
E $ u n ' o n ( u n # o o r " a d o p o r u nn " r o d ! " n # o $ > u n o p o d " o $ # r " + n a r d ' o n # a r .
E ( " p ! o
8. E$'r+ a !a dr'a !a pa!ara /n+#o0 +n/n+#o0 a'o0 un+#ar+o o un+r$a!$gn 'orr$ponda.
O < =10 120 140 16?
P < =10 120 140 160...?
A < =A!u"no$ d! 8r grado >u p$an 2 Q+!o$?
R < =Pr$ona! do'n# >u 'onor"a Tr+!' pr+"ar+a?
B < =*+r'#or d! 'o!g+o Tr+!'?
T < =N"ro na#ura! "a-or >u ) - "nor >u 7?
COLEGIO TRILCE P3g+na 1
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LOG. MATEMATICO
5 < =N"ro na#ura! "a-or >u - "nor >u 9?
Pr#n' o no pr#n'
1. Car!o$ rpr$n#, !o$ a$#ro$ >u +n$#+gar3. R$pond $+ o no n#r !o$parn#$+$.
$ # o $ $ o n ! o $ d + u ( o $ d ! o $ a $ # r o $ > u + n $ # + g a r
P
aS pr#n' a !a +n$#+ga'+,n d Car!o$. S
S Lo$ an+"a!$ pr#n'n a !a +n$#+ga'+,n d Car!o$.
S
'S pr#n' a !a +n$#+ga'+,n d Car!o$.
S
dS Lo$ #ra#rr$#r$ pr#n'n a !a +n$#+ga'+,n d Car!o$. S
COLEGIO TRILCE P3g+na 11
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LOG. MATEMATICO
2. O$ra - ana!+;a ! $+gu+n# "apa:
B + u n ! " n # o ' u " p ! ' o n ! a ' a r a ' # r $ # + ' a d
u n ' o n ( u n # o 0 d ' + " o $ > u p r # n ' a $ ' o n ( u n # o
- u $ a " o $ ! $ " o ! o
C O N J U N T O
$ r ! a ' + o n a n ' o n
! " n # o $ ' ! a $ + / ' a d o $
" d + a n #
P r # n n ' + a N o P r # n n ' + a
B + u n ! " n # o n o ' u " p ! ' o n ! a ' a r a ' # r $ # +' a d
u n ' o n ( u n # o 0 d ' + " o $ > u n o p r # n ' a $ ' o n ( u n # o
- u $ a " o $ ! $ " o ! o
8. O$ra ! 'on(un#o d! (r'+'+o N 1 - 'o"p!#a 'on ! $"o!o∈
o∉
.
aS P dS P
S P S P
'S P S P
4. Mar'a 'on una S ! !"n#o >u no guarda r!a'+,n 'on !o$ d"3$!"n#o$ d 'ada 'on(un#o.
un $'o!ar?
COLEGIO TRILCE P3g+na 12
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LOG. MATEMATICO
R
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LOG. MATEMATICO
o r r a d o r $
# a ( a d o r $
, ! d r $
! a p + ' r o $
g o " a
' u a d r n o $
R B
O $ r a ' o " o! o p + n # a " o $ .
En#on'$ $u un+,n $ ! 'on(un#o:
R∪
B < =orrador$0 #a(ador$0 ,!dr$0 !ap+'ro$0 go"a0 'uadrno?
II. Aora pra'#+>u"o$.
B+: J < =agua0 a+r0 ana0 'arn?
F < =agua0 a+r0 ana0 'arn0 arro;0 "an;ana0 p!3#ano?
En#on'$ !a un+,n $:
J∪
F< = 0 0
0 0
0 0
?
T're' do%ici(i'ri'$
En #u 'uadrno ra!+;a 1 ("p!o$ d un+,n d 'on(un#o$. R'urda >u d$
gra/'ar!o$ - $o"rar!o$. YT pud$Z
COLEGIO TRILCE P3g+na 14
F
J
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LOG. MATEMATICO
In#r$''+,n d 'on(un#o$I. O$ra !o$ $+gu+n#$ ("p!o$:
La a"+!a Pr; #+n a!guna$ "a$'o#a$ 'o"o: Prro$0 ga#o$0 pr+'o$
- po!!o$V pro a!guno$ d $#a$ "a$'o#a$ pr#n'n a !a a"+!+a Ca$#+!!o0
pu$ !!o$ #nan: !oro$0 prro$0 pa#o$0 pr+'o$. WHu an+"a!$ $r3n
P < = 0 0 0 ?
C < = 0 0 0 ?
C
! o r o $
p a # o $
p r r o $
p r + ' o $
g a # o
p o ! ! o $
P
O $ r a d o n d $ o " r a " o $
En#on'$ !a +n#r$''+,n d P - C $#3 dado por: P
C < =prro$0 pr+'o$?
COLEGIO TRILCE P3g+na 1)
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LOG. MATEMATICO
II. Aora # #o'a a #+.
B+: M < ="an;ana0 naran(a0 pra0 ua?
[ < =p!3#ano0 $anda0 pra0 "an;ana?
En#on'$ !a +n#r$''+,n d M - [ $#3
dado por:
M [< = 0 ?
T're' do%ici(i'ri'$
Aora n #u 'uadrno ra!+;a 1 ("p!o$ d +n#r$''+,n d 'on(un#o$. YNo # o!+d$
d gra/'ar - $o"rarZ YT pud$Z
U # +! + ; a n d o ! " a # r + a ! " u ! # + 3 $ + ' o r p r $ n # a " o $! o $ " + ! ! o n $ 0 ! a $ ' n # n a $ 0 ! a $ d ' n a $ - ! a $u n + d a d $ d ! a $ +g u + n # " a n r a :
M + ! ! a r C n # n a * ' n a U n + d a d
E$'r+ !o$ n"ro$ >u $ $#3 rpr$n#ando 'on ! "a#r+a! "u!#+3$+'o.
COLEGIO TRILCE P3g+na 16
[M
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LOG. MATEMATICO
U M C * U
U M C * U
U M C * U
Lo$ n"ro$ na#ura!$
)*+, "on (o" n-%ero"
Bon +da$ d 'an#+dad >u $#3n n nu$#ra "n#: do$ a"+go$0 '+n'o
'o"para$0 #r$ r"ano$...
.
La or"a n >u rpr$n#a"o$ o $'r++"o$ $a +da r'+ ! no"r d
n+%er'(.
N u $ # r o $ n u " r a ! $ a ' # u a ! $$ o n d o r +g n i n d o ' r á / i g o .
E( "i"!e%' n+%,rico.
COLEGIO TRILCE P3g+na 17
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LOG. MATEMATICO
R'+ ! no"r d d'+"a! por>u a par#+r d $o!o 1 '+ra$ $ pud or"ar
'ua!>u+r nu"ra!. E$a$ '+ra$ $ 'ono'n 'o"o dg+#o$ - $on: 0 10 20 80 40 )0 60
70 0 9.
Para !r - $'r++r n"ro$ >u #ngan un+dad$ d "+!!ar0 $ n'$ar+o
ordnar!o$ d a'urdo a !a $+gu+n# #a!a:
U M C 0 U
U n + d a d $d " + ! ! a r S
C n # n a $ S * ' n a $ S U n + d a d $ S
L o $ n " r o $ $ + n + ' + a n ! - n d o ! a ' + r a d ! a
U M - $ a g r g a ! a p a ! a r a \ " + ! ] .
P o r ( " p ! o :
1 7 < ' + n # o $ + # .3 T r e " % i (
R$o!"o$1. )C+á( e" e( '(or de &o"ici#n
Ind+'a >u !ugar d! #a!ro po$+'+ona! ! 'orr$pond.O$ra ! ("p!o:
COLEGIO TRILCE P3g+na 1
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LOG. MATEMATICO
6 4 8 2
8 * ' n a $ .
6 U n + d a d $ d " + ! ! a r .
8 4 ) 6
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
4 ) 4
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
6 9 8
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
4 9 ) 1
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
9 4 9 2
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
) 6 4 6
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
9 6 4
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
1
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
7 9 2 1
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
YA p+n#arZ
COLEGIO TRILCE P3g+na 19
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LOG. MATEMATICO
P + n # a d ! " + $ " o ' o ! o r
! a ! ! a ' o n ! a p u r # a> u ' o r r $ p o n d a .
T n g o2 u n + d a d $
d " + ! !a r 04 ' n # n a $ 0
) d ' n a $- 1 u n + d a d .
B o - ! " + !n o ' + n # o $
# r + n # a- u n o .
T n g o6 n !
! u g a r d ! a $ ' n # n a $ .
T n g on u " + !
d o $ ' + n # a $' u a r n # a
u n + d a d $ .
T n g ou n ) n
! a $ u n + d a d $d " + ! !a r .
T n g o n ! !u g a r
d ! a $d ' n a $ .
T n g o1 u n + d a d d
" + ! !a r -1 ' n # n a .
1 9 8 1
4 6 8 2
1 9 1
9 2 4
) 8 2 2 4 ) 1
1 1
2. Co"p!#a:
• 1 'n#na < 1 d'na$ < 1 un+dad$.• 2 'n#na$ < d'na$ < un+dad$.
COLEGIO TRILCE P3g+na 2
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LOG. MATEMATICO
• ) 'n#na$ < d'na$ < un+dad$.
• 'n#na$ < 7 d'na$ < 7 un+dad$.
• 8 'n#na$ < d'na$ < un+dad$.
• 'n#na$ < 4 d'na$ < un+dad$.
• 'n#na$ < 6 d'na$ < un+dad$.
• 'n#na$ < d'na$ < 9 un+dad$.• 'n#na$ < d'na$ < un+dad$.
Ta!ro d a!or po$+'+ona!1. U+'a !o$ $+gu+n#$ n"ro$ n ! #a!ro d a!or po$+'+ona!.
U M C U0
1 1 9 1 6 8 1 47 1 7 )1 6 2) 1 28 4 1 21 9 1) 2 4 2
1 1 2
2. *$'o"pon+ndo 'ada uno d !o$ n"ro$ an#r+or$:
1 1 < 1UM ^ C ^ 1* ^ U9 168 < UM ^ C ^ * ^ U14 < UM ^ C ^ * ^ U7 17) < UM ^ C ^ * ^ U162 < UM ^ C ^ * ^ U) 12 < UM ^ C ^ * ^ U8 412 < UM ^ C ^ * ^ U191 < UM ^ C ^ * ^ U) 242 < UM ^ C ^ * ^ U1 12 < UM ^ C ^ * ^ U
COLEGIO TRILCE P3g+na 21
E $ ' r + n n " r o $ - ! # r a $ 0! u g o d $ ' o " p , n # u n " r o d ' a $ a 0 # u a o d n a ' + " + n # o - !
d 2 a " + ! + a r $ .
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LOG. MATEMATICO
[u!+a ra!+;, !a d$'o"po$+'+,n d! n"ro d 'arp#a$ >u a- n ! 'o!g+o.
P o r ! a ! o rd p o $ + ' + , n
1 U M
1
U M C 0 U
1 2 4 6C o " o n o # a ' +, nd $ a r r o ! ! a d a
^
^
2 C
2
^
^
4 *
4
^
^
6 U
6
B !: On' "+! do$'+n#o$ 'uarn#a - $+$.
P a r a ! r u n n " r o d ' u a # r o o ' + n ' o' + r a $ " p ; a " o $ ' o n ! a ' + r a d ! o $" + ! ! o n $ 0 a ' o " p a a d o d ! a p a ! a r a" + ! 0 !u g o ! " o $ ! n " r o o r " a d op o r ! a $ # r $ ' + r a $ $ + g u + n # $ .
1. E$'r+ ',"o $ !n !o$ $+gu+n#$ n"ro$:
8 49 < .
1 126 < .
4 69 <
.
9 999 < .
6 84) < .
772 <
.
No#a'+,n d$arro!!ada
COLEGIO TRILCE P3g+na 22
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LOG. MATEMATICO
7 8 ) < 7 ^ 8 ^ )
$ ! : $ # ' + n # o $ # r + n # a - ' + n ' o
1. Co"p!#a:
N - % e r o 2 e d e " c o % & o n e 2 e ( e e $
4 6 8
1 ) 1
9 2 4
8 2
4 7 2 )
9 7
8 1
1 1 1
1 2 1 7
8 1 2 1
1 8 4
) 1 1 9
2 6 4
7 1 2
1 ) 1
9 6 2
4 ^ 6 ^ 8 C u a # r o ' + n # o $ $ $ n # a - # r $ .
E$'r+#ura d n"ro$ na#ura!$COLEGIO TRILCE P3g+na 28
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LOG. MATEMATICO
E $ ' r + ! o $ $ + g u + n # $ n " r o $ : U0CU M0 M
% M + ! d o $ ' + n # o $ ' a # o r ' .
% C + n ' u n # a - d o $ .
% H u + n + n # o $ + n # + $ + # .
% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ . % B $ n # a - o ' o .
% O ' o ' + n # o $ $ # n # a - $ + $ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ .
@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @% B # ' + n # o $ # r + n # a - # r $ .
% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ . @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @% O ' n # a - ' + n ' o .
% N u " + ! ' u a # r o ' + n # o $ n o n # a -$ + $ .
% C + n # o ' +n ' u n # a - ' u a # r o .
% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ . @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @% T r $ ' + n # o $ # r + n # a - # r $ .
% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ . @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @% B + # " + ! d o $ ' + n # o $ o ' n # a - # r $ .
% H u + n + n # o $ + n # + u n o .
% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ . @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @% @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ . @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @
9 2 1 4 8
4 4 2
2 9 ) 4 4
7 6 9 4 9
6 8 6 2 7
9
9 9 9 9 9
COLEGIO TRILCE P3g+na 24
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LOG. MATEMATICO
I. O$ra ! #a!ro po$+'+ona!.
0 M U M C 0 U
9999
1
1
^
II. E$'r+ ',"o $ ! 'ada n"ro: 5a"o$ a pra'#+'ar:
% 22 28 <
% 66 99 <
% 99 1 <
% 9 99 <
% 7 41 <
III. E$'r+ ! n"ro >u 'orr$ponda:
% C+n'un#a - $+$ "+! nu
% B$n#a - 'ua#ro "+! do$'+n#o$ 'uarn#a
% Cuarn#a - #r$ "+! +n#+do$
% Non#a - '+n'o "+! no'+n#o$ non#a - nu
% Tr+n#a - nu "+! #r'
Tara para #u 'a$a: E$'r+ ',"o $ !n !o$ $+gu+n#$ n"ro$:
aS 89 9 S 9 11 +S 69 28
S 4 79) S 9 1 (S 11 11
'S 99 1) gS 8 769 QS 49 79
dS 72 4 S )6 74 !S 2 42
COLEGIO TRILCE P3g+na 2)
R ' u r d a : ! a ! o r r ! a # + o d u nn " r o $ # 3 d a d o p o r ! ! u g a r> u o ' u p a .
L o $ n " r o $ " a - o r $ > u 1 - 1 $ $ ' r + n $ p a r a n d o! o $ " + ! ! a r $ ' o n ! a p a ! a r a " + ! .
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LOG. MATEMATICO
Co"para'+on$: +gua! a u `S
1. O$ra - ! !a$ r!a'+on$ >u # pr$n#a"o$:
% 81 82) ` 81 8)2 $ !: 182) $ "nor >u 18)2
% 81 8)2 _ 81 82) $ !: 18)2 $ "a-or >u 182)
2. E$'r+ ',"o $ ! !a d$+gua!dad:
aS 2 91 2 19 $ !: 291 $ "a-or >u 2 19
S 82 99 84 7) $ !:
'S 14 748 14 744 $ !:
dS 42 268 42 26 $ !:
S 29 8 29 8 $ !:
8. Co!o'a ! $"o!o _0 ` o < $gn 'orr$ponda:
)4 72 ) 72 72 )6 27 )6
92 7 92 7 9 7) 97 )
)8 14 48 )4 99 1 99 1
89 9 89 9
4. En'+rra 'on un 'r'u!o &S $+ $ a!$o o 5S $+ $ rdadro:
COLEGIO TRILCE P3g+na 26
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LOG. MATEMATICO
5 &a S ) 2 7
S 7 1 9
' S 7
d S 9 1 1 7
S 7 7
`
`
_
_
`
8 ) 2
9 1 7
7
7 1 9
6 9 7 1
5 &
5 &
5 &
5 &
Ap!+'o !o aprnd+do
I. 5a"o$ a 'o!o'ar _0 ̀ o
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LOG. MATEMATICO
Y M u - + n
! o ! o g r a $ # Z
1. Co"p!#a $gn 'onnga:
1 9 9 9
8 4 ) 9
1 6 7
9 9 9 9
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
8 4 ) 6 7
7 6 ) 4
1 8 9 7 1
6 9 8 9
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
1
1 8 2 6 9
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
1 8 9 7 2
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
2 1
8 4 6 1
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
2 1
8 9 ) 6
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
@ @ @ @ @ @ @
4 7 8 8
2 7 9
2 6 @ @ @ @ @ @ @ @ @ @ @ @ @ @
COLEGIO TRILCE P3g+na 2
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LOG. MATEMATICO
Apro+"ando n"ro$ W'r'a o !(o$
1. O$ra ! $+gu+n# 'a"+no:
2 1
2 1 1
2 1 2
2 1 8
2 1 4
2 1 )
2 1 6
2 1 7
2 1
2 1 9
2 2
2 1 2 6 $ # 3 " 3 $ ' r ' ad 2 1 8 > u d 2 1 2 .
2 1 4 $ # 3 " 3 $ ' r ' ad 2 1 > u d 2 1 9 .
2. &(a# n !a /guraV n#r >u d'na$ $#3n 2 1260 2 1)7 - 2 140 !ugo
'o"p!#a.
aS 2 126 $#3 n#r 2 12 - 2 18 - !a d'na "3$ pr,+"a $ 2 18.
S 2 14 $#3 n#r - 0 - !a d'na "3$ pr,+"a $ .
'S 2 1)7 $#3 n#r - 0 - !a d'na "3$ pr,+"a $ .
8. En 'ada $r+0 n'+rra !a$ d'na$ "3$ 'r'ana$ d !o$ n"ro$ >u $#3ndn#ro d !o$ 'uadrado$:
COLEGIO TRILCE P3g+na 29
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LOG. MATEMATICO
4 2 4 1 4 2 4 8
4 7 6 4 ) 4 7 4
1 6 1 2 8
1 2 4 2 1 2 8 1 2 4 1 2 )
2 7 1 2 8
7 2 8 7 1 7 2 7 8
a S
S
' S
d S
S
S
4. O$ra !a $+gu+n# r'#a nu"r+'a - 'o"p!#a !o$ 'uadro$.
1 2 8 4 ) 6 7
N - % e r o
2 4 8
8 7 2
) 9 9
1 1 2
) E n ! r e + ,c e n ! e n ' "
" e e n c + e n ! r '
) C + á ( e " ( 'c e n ! e n '
% á " & r # i % ' N - % e r o
1 7 2
6 8 9
8 2 7
2 1
) E n ! r e + ,c e n ! e n ' "
" e e n c + e n ! r '
) C + á ( e " ( 'c e n ! e n '
% á " & r # i % '
). Apro+"a !o$ $+gu+n#$ n"ro$V d a'urdo a !a +nd+'a'+,n d #upro$oraS.
COLEGIO TRILCE P3g+na 8
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LOG. MATEMATICO
8 6 9 : @ @ @ @ @ @ @ @ @ @ @ 1 1 : @ @ @ @ @ @ @ @ @ @ @
4 6 7 : @ @ @ @ @ @ @ @ @ @ @ 8 8 6 4 : @ @ @ @ @ @ @ @ @ @ @
9 9 9 9 : @ @ @ @ @ @ @ @ @ @ @ 7 9 9 : @ @ @ @ @ @ @ @ @ @ @
8 2 9 9 : @ @ @ @ @ @ @ @ @ @ @ 4 9 9 9 9 : @ @ @ @ @ @ @ @ @ @ @