3LOG.MAT. I BIM

8/17/2019 3LOG.MAT. I BIM

1/31

LOGICOMATEMATICO I BIM.

TRILCE PRIMARIA

LOCUTORIO REN@TRIXCEL :992444616


2/31

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


3/31

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$.



4/31

LOG. MATEMATICO

R ' o r # a r ' o " o # + n d + ' a ! a p r o $ o r a .



5/31

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 )


6/31

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

< = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ? < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?

< = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ? < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?



7/31

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 < = @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @

@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?



8/31

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


9/31

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



10/31

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?



11/31

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



12/31

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?



13/31

LOG. MATEMATICO

R


14/31

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


F

J


15/31

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)


16/31

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.


[M


17/31

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.



18/31

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:



19/31

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



20/31

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$.



21/31

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


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 $ .


22/31

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



23/31

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


24/31

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



25/31

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:



27/31

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 @ @ @ @ @ @ @ @ @ @ @ @ @ @



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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$:



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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.



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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 : @ @ @ @ @ @ @ @ @ @ @

3LOG.MAT. I BIM

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