c13 5to sec final

4
P-1 Quinto Grado de Secundaria 1. y p q p q V V F F V F V F F V F F p q p q V V F F V F V F F V V V [(p q) (p q)] (p q) A) FFFF B) FVFV C) VVFF D) VVFV 2. 80 lunes martes miércoles jueves viernes 120 180 200 240 soles (S/.) día A) 57,13 B) 53,17 C) 51,37 D) 57,31 3. A, B, C y D A; B; C; y D, A B C D 4. a n ) n 1 a 1 =1 y a a a n n n + = + - 1 2 2 3 2. n 1; a n n 1; a n a n a n A) FVFV B) VFFV C) FVFF D) VFVF Prueba Final - Quinto Grado de Secundaria Prueba Final - Quinto Grado de Secundaria

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EXAMEN DE MATEMATICAS PARA ALUMNOS DEL 5TO AÑO DE EDUCACION DE SECUNDARIA

TRANSCRIPT

Page 1: C13 5to Sec Final

P-1

Quinto Grado de Secundaria

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

(+.1+!%*!("*02&0("#!",!3#0#4"

p q p q

V

V

F

F

V

F

V

F

F

V

F

F

p q p q

V

V

F

F

V

F

V

F

F

V

V

V

" 50&&!"&0"*02&0"#!",!3#0#"#!

[(p q) (p q)] ! ( p q)" !" +%#+61!" &'("

,0&'3!("#!",!3#0#"#!"(1"/0*3+74

A) FFFF B) FVFV

C) VVFF D) VVFV

2. 8%" !&" (+.1+!%*!" .39$)'" (!"/1!(*30" &'"61!" 3!)01#0"1%0"

,!%#!#'30"#!"3':0":'3"#;04

80

lunes martes miércoles jueves viernes

120

180

200

240

soles (S/.)

día

" <!*!3/+%!"&0"#!(,+0)+-%"!(*9%#03"=0:3'>+/0#0/!%*!?4

A) 57,13 B) 53,17

C) 51,37 D) 57,31

3. @%" A1!.'" )'%(+(*!" !%" B0)!3" )'33!(:'%#!3" )10*3'"

)0(+&&!3'("A, B, C y D" =)'/'" (!"/1!(*30" !%" &0" .39$)0?"

)'%" )10*3'"$)B0(C" (!D0&0#0(" *0/2+E%" )'%"A; B; C; y D,

61!"!(*9%"!%"1%0"/!(04"F0#0"1%0"#!"&0("$)B0("!(*9"!%"

1%"('23!"#!"&0"/+(/0"0:03+!%)+0C"&'"61!"%'"%'(":!3/+*!"

(02!3" 61E" $)B0" (!" !%)1!%*30" !%" )0#0" ('23!4" !" .0%0"

G4HII"(+"(!"*+!%!"J"0)+!3*'(K" G4LI"(+"B0M"H"0)+!3*'(K" G4HI"

(+"('&'"B0M"1%"0)+!3*'"M"(!":+!3#!" G4LI"(+"%'"(!")'%(+.1!"

%+%.N%"0)+!3*'4" +"O%0":03*+)+:0"!%"!(*!"A1!.'C"P)19%*'"!("

&'"61!"!&&0"!(:!30".0%03Q

A B C D

O?" G4RICHL"

S?" G4TCUL

F?" G4RHCLI"

<?" G4RRCVU

4. !0"&0"3!)133!%)+0"=an)n !"1C"#'%#!"a1=1 y

a a an n n+

= + −1

22 3 2 .

" W%#+61!"!&",0&'3"#!",!3#0#"!%"&0("(+.1+!%*!":3':'(+)+'%!(4

" W4" X030"0&.N%"n #"1; an"%'"!("!%*!3'4

" WW4" X030"*'#'"n ! 1; an"!("(+!/:3!"!%*!3'4

" WWW4" Y'#'("&'("*E3/+%'("an"('%")10#30#'(":!3Z!)*'(4

" W[4" Y'#'("&'("*E3/+%'("an"('%"+/:03!(4

A) FVFV B) VFFV

C) FVFF D) VFVF

Prueba Final - Quinto Grado de Secundaria

Prueba Final - Quinto Grado de Secundaria

Page 2: C13 5to Sec Final

P-2

5. +"f =(!%x+cosx)\(!%Hx y 04

≤ ≤xπ

,

" #!*!3/+%!"!&",0&'3"#!",!3#0#4

" W4" f"!("+%M!)*+,04

" WW4" +"x $ RC"!%*'%)!("!&"30%.'"#!"f es 1 2 2; "4" WWW4" f"!("/'%-*'%04

" W[4" f"!("+%,!3(0

A) FFFF B) VVVV

C) FVFF D) VFVV

6. 8%"&0"(+.1+!%*!"!)10)+-%

(x+1)H+(x]H?H+(x+3)H]444]=x+99)H=yz ; z"^"RC"W%#+61!"!&"

%N/!3'"#!"('&1)+'%!(""#!")'/:'%!%*!("!%*!30(4

O?"+%$%+*0(" S?" H

F?"J" <?"I

7. F0&)1&!" !&" :3'#1)*'" #!" &'(" ,0&'3!(" #!" y" 0&" 3!('&,!3" !&"

(+(*!/0

ax by

b a

a b

x y

( ) = ( )=

log log

log log

;

,

" #'%#!"a; b; x; y"^"I4

A) a B) b

C) 1 D) b – 1

8. !0%" a "# b" %N/!3'(" 3!0&!(" #+(*+%*'(" M" :'(+*+,'(4"

<!*!3/+%!" !&" %N/!3'" #!" ('&1)+'%!(" #!" )'/:'%!%*!("

:'(+*+,0("#!&"(+(*!/04

x y ax by

x y a b

4 4

2 2 2 23

− = −

− = −

(I)

(II)

" O#!/9(C"a " b"$A'(4

O?"_" S?" H

F?"R" <?"T

9. <!*!3/+%!"&0"Z1%)+-%"+%,!3(0"#!"f *C"(+

f t t t*

;= − + −( )( ) < <{ }1 1 2 3 3 42

A) f x x x= − −( )

< <

; 21

21 1 3

B) f x x x= − + −( )

< <

; 21

21 1 3

C) f x x x= − − − −( )

< <

; 21

21 1 3

D) f x x x= − − −( )

< <

; 21

21 1 3

10. ̀ 0("/961+%0("M1; MH; M3"!&02'30%"H"*+:'("#!":3'#1)*'("

(P1 "#PH?C" #+(:'%+!%#'" #!&" *+!/:'" M" .0%0%)+0" 61!"

/1!(*30"&0"(+.1+!%*!"*02&0

M1 MH M3

a0%0%)+0

/9>G1%+#0#

P1 1 1 H G4HI

PH 3 1 1 G4bI

B'30(

#+(:'%+2&!(HJ RI RV

" F0&)1&!"&0".0%0%)+0"/9>+/04

O?"bRI" S?" HUI

F?"HJI" <?"HTT

11. 8%" 1%" *!*30!#3'" 3!.1&03"ABCD" (!" *3070" &0" 0&*130" BH y

!%"!(*0"(!"12+)0"P4"F0&)1&!"&0"(1/0"#!"*'#'("&'(",0&'3!("

!%*!3'("#!&" APDC" (+"P"!("/-,+&"0"*30,E("#!&"(!./!%*'"

BH4

O?"bVIIc" S?" JHIIc

F?"LJ_Ic" <?"VLUIc

12. <!&".39$)'C"A; E y T"('%":1%*'("#!"*0%.!%)+0K"0#!/9(C"&0"

!)10)+-%"#!"&0"3!)*0"L 1 !("Hx – y"d"H\I4"50&&!"&0"!)10)+-%"

#!"&0"3!)*0"L H4

L1

L2

E

T

A

Y

X

A) x y+ − − =2 5 5 0

B) 2 4 10 5 5 0x y+ − − =

C) 5 10 30 10 5 0x y+ − − =

D) 10 20 40 20 5x y+ − −

Page 3: C13 5to Sec Final

P-3

13. !"#!"$%&'()*(#+,-".%"(%!/*,"O"0".'1&%/*,"AB,"$%"#2'(3!"

P y Q %!"AB

-" /3+" 4#%"mPQ

= 45º5" 3.%&1$-" $%" /*363"PM

7%*7%!.'(#+3*" 3+" 7+3!," .%" .'(8," $%&'()*(#+,-" /3+" 4#%-"

AO

MO=

6

3

"9" :3+(#+%" +3" &%.'.3" .%+" .'%.*," %!/*%" %+"

$%&'()*(#+,"0"+3"*%;'<!"OMQ9

=>"?@A" B>" ?CA

:>"DEA" F>"G@A

14. !"#!"(#3.*3.,"ABCD, M y N"$,!"7#!/,$"&%.',$".%"AB

y BC-" *%$7%(/'H3&%!/%5" 3.%&1$" $%" /*363"PM" 7%*7%!.'I

(#+3*"3+"7+3!,".%".'(8,"(#3.*3.,5"AB = 2 5 y PM= 7 9

:3+(#+%"%+"1*%3".%"+3"*%;'<!"PDN9

=>"D" B>" 4 5

:>"E" F>"J@

15. !" #!" 7*'$&3" 8%K3;,!3+" *%;#+3*"ABCDEF"I"MNPQRS-" +3"

&%.'.3".%+".'%.*,"%!/*%"+3$"*%;',!%$"ANPD y ABCDEF es

G@A9":3+(#+%"+3"&%.'.3".%+"1!;#+,"%!/*%"AQsru

"0"%+"7+3!,".%"

+3"*%;'<!"ABCDEF9

=>"?@A" B>" ?CA

:>"DEA" F>"G@A

16. L'" BC=5; ABMJN" 0" DA=DC-" (3+(#+%" %+" ('*(#!*3.'," .%+"

/*'1!;#+,"BDC9

A D C

B

=>"JGOPOQ" B>" JGOPDQ

:>"JGOPOG" F>"DQPJGO

17. L'

cos ; ,

π

2

2 2 2

2nn=

+ +∈

+ Z

" (3+(#+%"cosnπ

39

=>"JPN" B>" J

:>"R"J" F>"R"JPN

18. :3+(#+%" %+" &30,*" H3+,*" .%" +3" (,/3!;%!/%" .%+" 1!;#+,"

&'/3.".%"#!,".%"+,$"1!;#+,$"'!/%*!,$".%+"/*'1!;#+,"ABC9

A C

B

6 3

5

A) 8

7 B) 2 8

C) 2 14 D) 14

19. L'"x !"@5" PN#-"3.%&1$

coscos cos cos

,x

a

x

b

x

c

x

d=

=

=

3

4 2 4

" %!/,!(%$"$%"(#&7+%"4#%

A) a c

d

b d

c

+=

+

B) a c

d

b d

a

+=

+

C) a d

b

b c

a

+=

+ D)

a c

b

b d

c

+=

+

20. S2/%!;3"%+"%4#'H3+%!/%".%

π

arctan1

27

3

28+ arcsen

=>"JN" B>" G

:>"Q" F>"?

21. L'" 21

23 2

1

24 0

3 2

sen senx x+

− +

+ = .,

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

21

23 2

1

2

3 2

sen senx x+

+ +

,

-.%/0% 1.% 23

4.%22% 5.%26

22. 78% sen sen cotα α θ+( ) −( ) =1 12

,

% ($9$+'8:$%"!%&#'!%($%)!"*+$&%($;%&$: <&$:!,

A) 1 B) – 1

4.%3% 5.%2

Page 4: C13 5to Sec Final

P-4

23. 4!" #"$%$"%)!"*+%($%

arcsen2 2 6 3 2

4

− + +

,

A) 5"=/2% 1.% //"=/2

C) 7"=26% 5.%//"=26

24. 78%x !3>%"=2"?% 8:(8@#$%$"%:A'$+*%($%&*"# 8*:$&%($% "!%

$ #! 8B:,

sen sen

sen sencot2

1

2

1

22 2x x

x xx+ − − =

-.%/% 1.% 2

4.%C% 5.%6

25. 5$%"!%&8D#8$:9$%8D#!"(!(

% &$:2x%E%6F *&x%E%&$:x)=m,

% ($9$+'8:$%"*&%)!"*+$&%($%m,

A) − − ≤ ≤ +1 4 2 4 2 1m

B) 1 4 2 4 2 1− ≤ ≤ +m

C) 1 4 2 4 2 1− ≤ ≤ −m

D) − − ≤ ≤ −1 4 2 4 2 1m

26. 5!(!%"!% *:(8 8B:

2 3 2 2 4 32

− + =cos sen cosx x x ,

% !" #"$

sen º cos º

cos º.

2 60 3 2 60

2 603

x x

x

−( )− −( )

−( )

-.%2% 1.% E%2

4.%6% 5.%E%6

27. 78%x1; x 2; x 3 y x 6%&*:%&*"# 8*:$&%($%"!%$ #! 8B:

% &$:23x – cos26xG&$:25x – cos2Hx; x ∈ 02;π

,

% !" #"$%&$:2x1<&$:2x2<&$:

2x3<&$:2x6,

-.%C% 1.% I=6

4.%C=2% 5.%I=0

28. 7$!%1 2 23

24

3 3+ + =sen cos senx x x?%!($'J&%x ∈

π

π

2; ,%

4!" #"$%CF&$:2x< *&2x.<&$:Hx< *&Hx,

-.%E%2% 1.% 2

4.%C% 5.%6

29. K:%#:%9+8J:D#"*%! #9J:D#"*%ABC%&$% #'L"$%@#$

cos cos cos2 3 2 25

20A B C+ +( )+ = %,

% 4!" #"$%$"%)!"*+%($

sen sen sen .2 3 2 2A B C− +( )

A) 5

2 B) − 3

C) −3

2 D)

1

2

30. -"%+$&*")$+%"!%8:$ #! 8B:

2 2 3 0

4

sen cos; ; ,

x x x+ ≤ ∈

π

% M #J:9*&%)!"*+$&%$:9$+*&%!(*L9!%"!%$NL+$&8B:%16x

π

O

-.%/% 1.% 2

4.%C% 5.%6