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Đề thi toán 11 - sưu tầm đề kiểm tra, thi học kỳ, thi học sinh giỏi tham khảo bồi dưỡng (31)

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Đề 1
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:



 
   

   
 
 
 
+
= = +
= =
− +
c
y y x
y y
x
!"#$%&!"'%(
)* 

π
 

 ÷
 
x



   += − +y
,-./!"

0
  1+ 0

+ =
x
2*
2*  *2
Câu II:
3.4!5!!!

6

"7

#%)+89:&"7

#%)+8
9:;!<=#"!>08?"7

6


"!@"8
0





 
+
 ÷
 
x
x
:(A!B
+
CD!#E<0=#F&G&3&H&I&J&,&K&L&M3=<.N!6OP
3Q!R7P;%8#%)"P7P<.NA"@S!"T!
76$A(!
Câu III:3<UFG3H<)#,Q3V#"!8(U36C#
8D!"7AUFW#X5!Y3VC6!!!6$G3ZUG&UHA
GV6[
!)\(UFG6U3H!8(F3V6$UGH
3C]B!CGV3V[#!
^6";(C8CGV3V[#
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a
3_ _)_`#A!#7\(D%D!_)
3%9

<
 +
 1
+
0
+ =



+ =

u u
u u
A!a6S!D3U[
Ubb#A!B%)
Câu V.a "!X5!.4! )2>*0&8F_
K?)-(F6c!d:#7\eB!906e\
f6e/
r
v
*_
-(32



 )

*>YeY)9g!<Y)>+
0

".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
1
Đề 2
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(
 = +y x


,j[&,[[(
  

π
= + −y x x
,-./!"
 
 
 >  0    *0
>
 + 1 *k     
− = +
+ − =
x
x c
c x x x
Câu II:
3B
1

 −x
x
;l!:(B"7
:(A!B0
A!@S!B(B
,fmZ96E!%
^@S!!R
;%8l!%#a!f#$/Xc!b
Câu III:3<UFG3H&)FG3H#&A&!<F<10

0
C&[#
8DAUF&UG


= =
SM SN
SA SB

!)\(UFG6U3H_UF36UGH
3B!C[nnU3H
,QW#X5!YC[6!G3\AoW6<\:
#!;:;(\:
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a
  HT!YAB!
 p
  1− ∀ ∈Mn n n N
^e;q!&!-6X(?)

\

=
+
n
n
u
n
A!a6S!%D!

 `
 > k
+
 
+ =


− + =

u u
u u u
l!(+A!a(D%D!\

*_
`
*r>
Câu V.a "!0)F__6.4!5!) *0?)-(F6Y
e\
We\
_>=
ur
u
_WeB!90
WeY)90!<Y)`0
0
We6d90&=@*
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
2
Đề 3
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN

Câu I:
(
 

=y
^e;s#P(

   = +y x x
,-./!"#.N!!
 *  
    0− − =x
>

 2

*
Sin
6
x + cos
6
x +sin
4
x + cos
4
x+ cos4x +


= 0
Câu II:
CDDd!k9)m69)m'&#%)!t79)m;%8#%)

9)m"!9)m?#%)"
A!u@S!B"!@"8
b


 −x
x
Câu III:3<UFG3H&FG3H#,QC&[&W#"!8(G3&
FH&UH
 ^!)\(UFG6U3H&UFC6UG3
 3"C[nnUFG
 !8(FC6UGH
^\:C[W6<&\:#!v
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a
3%D!
  
_ _
x x x
C C C
 .
 3?)

6$

*


3B!?)"7#D%9

UA!B%)(?)"7<!"0k
;l!0A!a(?)
Câu V.a "!g).4!5!2) +*06.4!"h<./!"3
 

 )2

*`
 -(.4!5!Ye\f6f/
_ = −
r
v

 -(.4!"h3YeY)9g!<`0
0

 -(.4!5!@d:#7\e\eB!
9g6e6d9gwc!
-(.4!"h3@d:#7\e\eB!"xg)6
eY)9g!<Y)>+
0

Đề 4
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
()*
 

  + +
x

x x x
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
3
,j[2,[[()*

 +x
,-./!"

( )
( )
      + = +x x x x
2+*
1

 +2k*0  
    − = −x x

Câu II:
CD#$Q<>0Q!E+&+y3<7Q>Q
3<&y W-<;%Dy
zOm#/@/+&Q!R7T!D#m
3<7Q\<m!D{6
;%8"!.NQ<;%D{X<;%D
A!@S!B"!@"8

 

x



Câu III: 3<UFG3Hi)#9g_FG*G3*!
UFG6S!AF_G*0
0

!)\(UF36UGH_UFH6UG3
i8[DAUF!8(3[6UGH
,Q,

&,

#a#.N#"Q!9(!UG36UGH3B!,

,

!!
FG3H
>i8CDAFH6$FC*0||CWYC!!UF63H^
\:(W6$<UFG3H;:;(\:<i8
:;)#$%
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a 3%D!&\"c!
  
 
1
 1
+ + =


=


u u u
u u
A!a6S!(%D!
;l!(kA!a7(%D!<^%D!&\
+
*`&
`
*
+
^%9!E1A!&\l!A!ac!1b&l!A!
c!
Câu V.a "!g)&2>)2*0&3

 )

  1) +*0-(
&3YeB!9L_
Đề 5
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
!"#$%(
  = + +y x
(
 
 
+
=

y

,-./!" 
      

π
π
+ − − =x x
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
4

    
1 1
π π
− = − −x x

 
     − + =x x x x
Câu II:
CDDd!>67'&+67"Z!&1676!&!.4Q">67zD
<K'<7Q8"!#%)"@S!(v
G\:(

"!@"8 

#`0A!B!!y"!@"8
Câu III:3<UFG3H&X)FG3H#!)#$FG&C#"!8
(3HCX5!WYC!!6$UF6G3
!)\(XX5!UFH6UG3_UF36UGH
\:(X5!W6<UFG3H#!v
!)\(X5!W6X5!UFH
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:

A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a CD%D!<A!B%#+&A!#

*>+6l!
A!#>00S!6
3__)_0#A!#7\(D%D!_)
3__#A!#7\(%9
Câu V.a "!X5!ADg)&.4!"hL&]6$L_&@;]*K?)
6\./!"-(.4!"hL&]YeE!A!<.Nc!d:
#7\e
v
T
6$
( )
>_ −=v
6
( )
&−O
V
.
Đề 6
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(


=
c
y
!"#$%6!"'%(

  = − +y c
,-./!"
[ ]
  
      0     > 
    > 0_ 0_
π
− + + = − − =
+ + = ∈
a x x b x x x x
c x x x
Câu II:
CDl"d<`Q6>Qy,67Q"Q
;%8
3-QT!!$;
3<;%Qy
A!Bq"!@"8
0

 +x
x
&"!@"8<}(!-a
Câu III:
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a "!%D!\   > ~~  b*++
%-!"(8 &

& #A!#7\(%
D!

".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
5
3%9

<
 +
 1
+
0
+ =


+ =

u u
u u
A!a7

6S!DY
l!(7A!a7c!01`v
Ubb#A!B%)(%9v
Câu V.a "!X5!).4!5!+) *0&C_0&
r
v
*_
-(8C6.4!5!YeE!A!<.Nz6:d:
#7\e\f
r
v
6eB!"xg

•\./!".4!"h-(.4!"h3<9C&@;c!Y
e\f
r
v
Đề 7
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
^e;s#P(


+
=
x
y
,j[6,[[(
 
  = +y x c x
,-./!"



   1 +   0
 
π
 
− = + =
 ÷
 
a c x b x x
Câu II:

3<7d7<+y"!<yB!-#$/yB!
".$
A!@S!B"!@"8




 

 ÷
 
x
x

Câu III:3<UFG3H&FG3H#!&L#!8.4!e&A
7FH6G3ZA{
!)\UFH6UG3_UFG6UH3
C#"!8UG!8CH6UF3
,Q#YL6!!UF&3HZFH&3G&U3&UH#a#.NACV&[&W&€3B!
"c!CV[W€#!6!8A7DU{
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a 3B!
> −
n
\6$Q
p
∈n N
3?)
    = −

n n
u u n

;A!B00
U`#A!B%)(?)
;l!(+0A!a(?)
Câu V.a "!g).4!5!2) +*06.4!"h<./!"3
 

 )2

*`
-(.4!5!@d:#7\e\eB!9g
6e6d9gw@*
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
6
-(.4!"h3@d:#7\e\eB!"xg)
6eY)9g!<Y)`0
0

Đề 8
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(
00
) *
 

!"#$%6!"'%(
 =y

,-./!"
 
   0   + = + =x x x x
Câu II:
3&&&>&+3<7d7!Ey@
U<#s U<\
;
0    0 0
0 0 0 0
   = + + + +A C C C C
:(A!@S!B"!@"8B



b
  

&\
0   
   
3 3 3  3 +1=
Câu III:3<UFG3H<FG63H@S!!!&C#"!8U3
!8[(UH6CFG
,Qg#!8F36GH3CUg&FC&G[E!Y)
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a A!a6S!(%D!\
  +
  
 > 1

b
+1
+ + =



+ + =


u u u
u u u
3?)


 = −
n
n
u

^e;q!!-(?)
;l!+0A!a(?)
3B!"c!6$Q!)7./!<
 
   
 
   
>
+
+ + + + =
n n

n
Câu V.a "!X5!g)&
   0+ − =d x y
6
_ = −
r
v
-V(.4!5!Y
r
v
T

;@-!!y6V
,QCVV_)V#-(C_)Y
r
v
T
;CCV
Đề 9
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
^i(
)*
 
  
+
+
x
x
)*

 
 >
π
+
x
!"#$%6'%(
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
7
)*


> +x
 )*>2>> 
,-./!"

  

          +

+ = + + =a x x x x x x x
Câu II:
zy
0__ _ _ >_ +_1
<8#.N7d7<+y9:
@S!Zaov
3@"8
0




 

 ÷
 
x
x
A!B


;l!%-:(@"8
Câu III:3<UFG3H&!QC#D8D•"!(
∆SCD

!)\(UGC6UF3
!8(GC6UF3
\:(<ZoFGC
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a +#P#7\\l!(m!c!k+
3?)


k += −
n
u n

^e;X(?)
;
 1 ` ``
= + + + +S u u u u

;
0 0 00
= + + +S u u u
,-./!"
+0

2>`

 >b

2>k

 >1

2>+

 ~~ 

2

*+
Câu V.a "!X5!g)&L_>6.4!"h
 
    >  0+ − + + =C x y x y
&
  + 0+ − =d x y
-3V(.4!"h3YeB!9L
-V(.4!5!YeB!9L
^e6";./!(36z<)"6";./!!y3V6V
Đề 10

I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
^i(
)*

 +cosx
)*
 

π
−x
!"#$%6'%(
)* U )*3

 U


,-./!"
 
    0     > 

π
 
= + + =
 ÷
 
a b x x x
Câu II:
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
8

3\:(A!(@"8


 
+
 ÷
 ÷
 
n
x
x x
x
c!1K?)A!;
!y(@"8
,f#a#.NDmZ#a
;au(@S!!R
;%l!%(#a!f#+
Câu III:3<UFG3H<)FG3H#,QK&{#a#.N#"!
8(UF&UG
3B!K{nnU3H
3CDAU3!)\(K{C6U3H
!8L(H{6$UF33B!L#"Q!9(!UF3
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a 3B![\&&#%D!
 & &
a b c
#%9
A!a6S!D(%9\
 + >

 1 +
0
0
+ − =


+ − =

u u u
u u u

Câu V.a "!X5!g)&.4!5!
  > + 0
∆ + − =
x y
6
 
       `− + + =C x y

•\./!".4!"h3V#-(.4!"h3YeB!"x


•\./!".4!5!V#-(.4!5!
   + 0+ − =d x y
Ye
B!"x


;!<!y6


&z<)"!<!y6V
Đề 11
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(

  
=
+
y
x
b). y =
 
 
+
+
Cosx
Sinx
!"#$%6'%(
)* U )*
 
+   − Cos xSin x
,-./!"

        1  + = + =x x x x x x x
Câu II:
"7!<>Y)8Q&+Y)8•#‚6Y)8K<Q
j%)!R7>Y)8;%
 >Y)8#%)"<;%DY)8•#‚v
>Y)8#%)"<m!Y)8Qv

{"8B
1

 

 ÷
 
x
x
"!@"8(B


 
+
 ÷
 
n
x
x
\:(A!
Bf•!-a}(#6:(A!B
>

".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
9
Câu III:3<UFG3H<)FG3H#6$FG*&FH*CX7
UFG#9!6S!9AF"7AFH#%)8C6$FC*
0  ≤ <x a
CX
5!

( )
α
YC6!!UF&FGZG3&U3&UHA[&W&€
B!C[W€#!v
:;C[W€f6
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a 3B!
p
+  >   [
− ≥ ∀ ∈
n
n

3?)

  


=
+
n n
n
u u
n
^e;q!!-(?)
^e;X(?)
A!!)7(?)
3B!"c![\&&#3U3*


2&)*

2&
ƒ*

2}!A3U3
Câu V.a "!  X  5!  g)&    .4!  5! 
    0− + =d x y
6  .4!  "h
 
   > >  0+ − − − =C x y x y

•\./!"V#-(Ye
0
 _`0 O
Q

•\./!"3V#-(3Ye
0
 _`0 O
Q

;@-!zg\6V
Đề 12
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
^i(
 = +y x
!"#$%6!"'%(
 


π
 
= + +
 ÷
 
y x x
,-./!"
0 0
  0  b0    0         + + − + = + =x x x x x x
Câu II:
\
    
    
k
 3 3 3 * F +0 * F

CDBb67=@6•&"!<<+67&67'j%)
!R767z;%8.N
67
67'
Câu III:3B:FG3H&!QL&M#a#.N#"!8F36G3"7GH#%)8{
G{*{H
!8I(3H6LM{3B!HI*H3
!8J(FH6LM{3B!JF*JH
3B!J{nnLM
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
10
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a

Câu IV.a A!(%9!E+A!'
> 
+ 
k
>>
− =


− =

u u
u u
3?)

    >= − +
n n
u u n n
^e;q!!-(?)
A!'%(?)
;l!0A!a(?)
Câu V.a "!X5!g)&L_.4!5!
 >  k 0− + =d x y
 
       +− + + =C x y

•\./!"V#-(Ye
 _I
V

•\./!"3V#-(3Ye

 _I
V

;@-!zL\&)"@-!zL\V
Đề 13
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(


 
=

x
y
x
!"#$%6!"'%(
( )
   = + −y x x
,-./!"

 
      0+ + + =x x x x


     − =x x

 > 1*0
>3./!"


 x
 2*0
,-./!"@*0
^8./!"<!:
Câu II:
"!@"8
 0


 +x
x
K?):(
0
x

,fmZ9E!%;%8
l!X%:c!b
;X%:##P
Câu III:3B:FG3H,Q

G
6

G
#a#.N#"Q!9(!F3H6G3H
!)\(X5!3

G

G

6FGH
3B!"c!

G

G
!!X5!FG3
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a
•\7`A!f!y6k8.ND<A!;l!(
<
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
11
3
n
u
\
 +
` +
&
+ k+
= − =u u
;l!(bA!a
Câu V.a "!X5!.4! )2*0&8F&6.4!"h3
 
    >− + + =x y

K?)-(Y6:d:#7\eB!96e\
f6e/

r
v
*_
K?)-(3Ye6d9F
Đề 14
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(
  
= +
y x x
!"#$%6!"'%(
  >    = + = − −a y x b y x x
,-./!"


„
   + * 0_  @„& @    *
 
≠ ∈ Z b
>3./!"
      
1 1
π π
+ − + =x x m
,-./!"@*0
i8./!"<!:
Câu II:
 ,-./!"
  

k

+ + =
x x x
C C C x
 {"8B
+



 

 ÷
 
x
x
 3<k!.46!.4y&Q!R7!.4%<;
%!.4y
Câu III:3<UFG3H<)FG3H#9g,QC&[#a#.N
DAUG&U3
 
&
 
= =
SM SN
SB SC

!)\(X5!
 AMN
6

 SBD
&z<)"!8W(UH6
X5!
 AMN

^\:(<@ZoX5!
 AMN
6B!GH!
!6$\:<
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
 Câu IV.a A!a6S!(D3U3\
  >
 1


+ + =


+ =

u u u
u u
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
12
 A!a6S!D(D3U[\
> 
+ 
k
>>

− =


− =

u u
u u
 3B!"c!6$Q!)7./!<
 
   
 
   
>
+
+ + + + =
n n
n
Câu V.a
3
 
       >− + − =C x y
&-(3Ye6d9g=@*r
3r+) *0&-(Ye\f

_

 
= −
 ÷
 

r
v
-(Fr_YeB!9g6eB!"xg)
Đề 15
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(

 
=

x
y
x
!"#$%6'%(
    = − −y x x
,-./!"

   0− =x x

 
    0+ − =c x x
c).

   0− + − =x x
d).
 
     − + =x x x x
e).
( )

       − + − =x x x x
Câu II:
CDD<067&!E67'6b67j%)!R767
;au(@S!!Rv
;%(\
F…3-•'†
G…3<;%D†
:(A!B

x
"!@"8B[f‡

+


 
+
 ÷
 
x
x

Câu III:3<UFG3H<)FG3H#&g#9(
,QC#"!8(AUG&[#8"7AG3G[*3[
3B!gC!!6$X5!U3H
^!)\(U3H6FC[
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a 3%D!
( )

n
u
6$S!&<

>= −u
&
+0
b0=u


u
6z<
A!l!Y(
( )
n
u

Câu V.a "!X5!QDOxy 
•\./!"ˆ#-(
  0− + =x y
YeB!9L_
•\./!"3ˆ#-(3
 
   > 1+ + − =x y
Ye6d9O=




".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi

13
Đề 16
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(
 



=
+
x
y
x
!"#$%6'%(

> > = − +y x x
,-./!"


   0
+ + =
x x
 
  
    
+ =
x x x

Câu II:

j%)!R7D67zDDBb67.Nz\b
%8#%).N!
n3s
njP6\
n\
 

> +
+
=
n n
C C

Câu III:3<UFG3H<FH6G3@S!!!,QC&[fBd#"!
8(AUG6U3
!)\(X5!UFH6UG3
3B!C[!!6$FG3H
!8(.4!5!UH6$X5!FC[
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a
%D!
( )
n
u
<+A!'?:B

  +
 +
>

0
+ − =


+ = −

u u u
u u

Câu V.a "!X5!QDg)&.4!5!
‰   ) * 0
6.4!"h
 
     > `++ =C x y

•\./!".4!5!

#-(YeB!"x
g

•\./!".4!"h3V#-(3Ye6d9
F_ −
=
@*2
Đề 17
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(
  
  

+
=

x
y
x
!"#$%()*>2
,-./!"
 
   +  * 


   *0

c x
Câu II:
zDDBqY-a"Z!6Y-a'&#%)!R7E!4>Y-;
%
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
14
GY-#%)"T!_
3<;%DY-a'
"!@"8(8B









6$
0&

Ơ
&?):(
1

\"c!
l!%-:"!@"8)c!`1b
Cõu III:3<UFG3H<)FG3H#B!#E,QI#D8D
"!(!U3H
!)\(X5!UF36UGI&)"!8(GI6X
5!UF3
^\:(<UFG3HZoX5!FGI
II. PHN DNH CHO TH SINH TNG BAN:
A. Thớ sinh theo chng trỡnh chun chn Cõu IV.a v Cõu V.a
Cõu IV.a
3?)u
n
) 6$
2 =
n
u n

3B!
( )
n
u
#%D!&\A!a6S!

;
+0
u
6
+0
S

A!a6S!D(%9

n
u
&\
> +
+ 1
+
0
+ =


+ =

u u u
u u u
Cõu V.a "!X5!QDg)&.4!"h9
( )
_I
&@;\./!
"-(.4!"h
( )
_I

YeE!A!<.Nc!d:#7\e6
d9O=6eB!Y"x Ox.
18
I. PHN CHUNG CHO TH SINH C HAI BAN
Cõu I:
(
+


=
+
x
y
x
!"#$%6'%(
) >>=
,-./!"

0 =x


> 0
+ =
x cotx
39LL
3<\P.N&&&>#%)!R7\P
CS-@S!!R
;%(\
F;%"7\P#s
Gl!%"7\P@S!e/1

:(A!uB

x
"!@"8
`




+


x
x

Cõu III:3<UFG3H<)FG3H#!6$)FG&3H
FG 3H

,QC#"!8(3H&

#X5!YC&!!6$UF6G3
".4!KW,h3S!iS!Bieõn soaùn : Tran Duy Thaựi
15
\:(<UFG3HZoX5!
‹
\:<#!v
!)\(X5!
‹
6X5!UFH).
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:

A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a
3%D!
( )



_ 1__ 1__
K?)A!


(%D!<&\"c!
l!(A!a7c!`k0
Câu V.a "!g)C>_&
 

= +


= − +

x t
y t
3

 )

 2>)2>*0
-(C&&YeB!"x )2*0
-3Ye6d9C=@*

Đề 19
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(
> 
) 
+ 
= +
x
!"#$%&!"'%(
  +
 
= +
x x
y
,-./!"

 +  0+ − =x x

  + = −x x

Câu II:
•\y___>_+_1_k_b_`#7`%\&<ZBd!R7`%
\<D!!!&.ND;%8.N#
nCDs
nCD#P
"!@"8B[/(

+
+

 

 ÷
 
x
x
:(A!B
>
x
.
Câu III:3<UFG3H<)FG3H#,Q,#"Q!9(
!UFG6L#"!8(FGj%)8C"7AFHFH*FC
ni.4!5!YC!!6$FGZ3LAM3B!i.4!5!M,
!!X5!U3H
n\:(<UFG3HZoX5!C,M#!v,-;
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.
 3%D!
( )
n
u
6$
 += −
n
u n
^qA!a7(%D!"7
^A!a76S!(%D!

k 

 k
b
 k+
− =


=

u u
u u
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
16
Câu V.a 3.4!"h3<./!"

)

 1)>*0Œ(3Y#7\
e6d

 & 

−O
V

6eY)g&`0
0
#.4!"h3V&./!"(3V
Đề 20
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:

(
 
)
 

=
+
x
x
!"'%(

 

π
 
= − −
 ÷
 
y x

   = − +y x x
,-./!"

  − =x
 
 
+    1 0
+ − =
x x x
Câu II:

zy0&&&&>&+&1&kK'<7s<qySD@
#%)zy"7v
 CDB1676$k67"Z!&167f667'j%)!R7>
67;%8#%)m!67"Z!
3B!"c!
0  > 00   00`
00 00 00 00 00 00 00
 + + + + = + + +C C C C C C C

Câu III:3<
S ABCD
<)#!&AD#)#$,Q I#"!8CD&
M#8T)‚"7ASI
!)\(X5!
( )
SAD
6
( )
SBC
_
^\:(<6$X5!
 ABM

II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a A!a6S!(%D!
( )
n
u
\

 0
 k
+ 
 +
+ = −


− = −

u u
u u
Câu V.a "!X5!ADg)&.4!"h3

 )

2 >)2>*0
-(3Ye\f6f/
_ = −
r
v

-(3Ye4.Nd:#7\oe\f6f/
_ = −
r
v
6eB!Y"xg
Đề 21
I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(


)  
 
=
+
!"#$%6'%(
  = +y x
 ,-./!"

  0+ =x

 k b 0− + =x x

   
   >  +  1
− = −
x x x x
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
17
Câu II:
"!DDd!+67'&b67"Z!6k676!3Q!R7E!4+
67
;au(@S!!R
;%8
n3-+67#%)"•<6!v
n+67#%)"<;%D67"Z!v
:B
0
x
"!@"8B[/

+




 

 ÷
 
x
x

Câu III:3<UFG3H<)#,QC&[#a#.N#"!8(
U3&G3W#D8%@•"7AUFW@S!"T!6$U6F
n!)\(UFG6$C[W
n!)\(C[W6$UH3U)"\:(<UFG3H@
Zo[CW
II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a 3%D!
 
n
u
-?
{
k 
> 1
+
0
− =

+ =
u u
u u
&A!a

u
6S!(%D!"7
&G\
+=
n
S

Câu V.a "!  X  5! 
Oxy
   .4!  5! 
 0∆ − =x y
 6 .4!   "h
 
    > > 0+ + − − =C x y x y
./!".4!"h
 

C
#-(
 C
Ye
B!"x


Đề 22

I. PHẦN CHUNG CHO THÍ SINH CẢ HAI BAN
Câu I:
(
 
) 
 
+
=
!"#$%6'%(

  
)  
>
+
=
,-./!"

    0+ =x

   + 0− =c x c
2

 

*2>


Câu II:
zDDd!>Y-a"Z!61Y-afj%)!R7Y-a;%


nGY-a#%)"<f"Z!
n3-Y-a#%)"•#"Z!
nŽ%#%).NY-af
:(A!B
k
"!@"8


x

k
".4!KW,h3S!iS!Bieân soaïn : Traàn Duy Thaùi
18
Câu III:3<UFG3H<)#DB!#E,QC&[#a#.N#"!8(U3
63H,Q
α
#X5!YC&[6!!6$.4!5!F3
n!)\(
α
6$FG3H
n!8(.4!5!UG6$
α

n\:(<@ZoX5!
α

II. PHẦN DÀNH CHO THÍ SINH TỪNG BAN:
A. Thí sinh theo chương trình chuẩn chọn Câu IV.a và Câu V.a
Câu IV.a
3%D!


&
p
∈ Νn
6$

*6
+
*+>
nS!(%D!<
n;l!(+A!a(%D!<
Câu V.a
"!X5!QDg).4!5!) +*0&8C_
n-(.4!5!Ye\f
_=
r
v
n-(8CYeE!A!<.Nc!d:#7\e
6d9gw6eB!"xg
K\
“Mọi thành công đều nhờ sự kiên trì và lòng say mê”
".4!KW,h3S!iS!Biên soạn : Trần Duy Thái
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