c13 5to sec final
DESCRIPTION
EXAMEN DE MATEMATICAS PARA ALUMNOS DEL 5TO AÑO DE EDUCACION DE SECUNDARIATRANSCRIPT
P-1
Quinto Grado de Secundaria
1. !"#!$%!%"&'(")'%!)*+,'("&-.+)'(" y "/!#+0%*!"&0("
(+.1+!%*!("*02&0("#!",!3#0#4"
p q p q
V
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F
F
V
F
V
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F
F
p q p q
V
V
F
F
V
F
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V
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V
" 50&&!"&0"*02&0"#!",!3#0#"#!
[(p q) (p q)] ! ( p q)" !" +%#+61!" &'("
,0&'3!("#!",!3#0#"#!"(1"/0*3+74
A) FFFF B) FVFV
C) VVFF D) VVFV
2. 8%" !&" (+.1+!%*!" .39$)'" (!"/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
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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
P-2
5. +"f =(!%x+cosx)\(!%Hx y 04
≤ ≤xπ
,
" #!*!3/+%!"!&",0&'3"#!",!3#0#4
" W4" f"!("+%M!)*+,04
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" 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?"+%$%+*0(" S?" H
F?"J" <?"I
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(+(*!/0
ax by
b a
a b
x y
( ) = ( )=
log log
log log
;
,
" #'%#!"a; b; x; y"^"I4
A) a B) b
C) 1 D) b – 1
8. !0%" a "# b" %N/!3'(" 3!0&!(" #+(*+%*'(" M" :'(+*+,'(4"
<!*!3/+%!" !&" %N/!3'" #!" ('&1)+'%!(" #!" )'/:'%!%*!("
:'(+*+,0("#!&"(+(*!/04
x y ax by
x y a b
4 4
2 2 2 23
− = −
− = −
(I)
(II)
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O?"_" S?" H
F?"R" <?"T
9. <!*!3/+%!"&0"Z1%)+-%"+%,!3(0"#!"f *C"(+
f t t t*
;= − + −( )( ) < <{ }1 1 2 3 3 42
A) f x x x= − −( )
< <
; 21
21 1 3
B) f x x x= − + −( )
< <
; 21
21 1 3
C) f x x x= − − − −( )
< <
; 21
21 1 3
D) f x x x= − − −( )
< <
; 21
21 1 3
10. ̀ 0("/961+%0("M1; MH; M3"!&02'30%"H"*+:'("#!":3'#1)*'("
(P1 "#PH?C" #+(:'%+!%#'" #!&" *+!/:'" M" .0%0%)+0" 61!"
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!)10)+-%"#!"&0"3!)*0"L 1 !("Hx – y"d"H\I4"50&&!"&0"!)10)+-%"
#!"&0"3!)*0"L H4
L1
L2
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T
A
Y
X
A) x y+ − − =2 5 5 0
B) 2 4 10 5 5 0x y+ − − =
C) 5 10 30 10 5 0x y+ − − =
D) 10 20 40 20 5x y+ − −
P-3
13. !"#!"$%&'()*(#+,-".%"(%!/*,"O"0".'1&%/*,"AB,"$%"#2'(3!"
P y Q %!"AB
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AO
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:>"DEA" F>"G@A
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y BC-" *%$7%(/'H3&%!/%5" 3.%&1$" $%" /*363"PM" 7%*7%!.'I
(#+3*"3+"7+3!,".%".'(8,"(#3.*3.,5"AB = 2 5 y PM= 7 9
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=>"D" B>" 4 5
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16. L'" BC=5; ABMJN" 0" DA=DC-" (3+(#+%" %+" ('*(#!*3.'," .%+"
/*'1!;#+,"BDC9
A D C
B
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:>"JGOPOG" F>"DQPJGO
17. L'
cos ; ,
π
2
2 2 2
2nn=
+ +∈
+ Z
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39
=>"JPN" B>" J
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18. :3+(#+%" %+" &30,*" H3+,*" .%" +3" (,/3!;%!/%" .%+" 1!;#+,"
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A C
B
6 3
5
A) 8
7 B) 2 8
C) 2 14 D) 14
19. L'"x !"@5" PN#-"3.%&1$
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
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