36 ĐỀ THI TOÁN 11 CB HK2

Mt s đ ôn tp thi hc k 2





 
  
 

→−
− + +
+


 
 
  

→
−
− −
 !"#$%$

&

'()*+, /+01+*,+#*234+5 !"+6
7898
:/0;/, /+01!
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+0523
12>,D(7E2>C#7E +/C2@=/F7G7E$G7$G@ 26HD7
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@=//>2@A7E(
 8I+,M/!/!/@A,D7G
 87⊥DK
2 />2/OD7@ ,DE(

(
E  !"
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G P
%
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+
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=
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

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
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8QR++H+S223 !"%+6
 = −

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E  !"
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E 12>,+:/C2XD(7EU2>7E$D7$G/BY +23I+C#(
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⊥
D(
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
^K_`Ya`bEc`
(+dGd<,e+
2C2/A6!



f g 
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  
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− +
− −



 
  d
(
 f

→
− +
−

 !"
( )

%    = − +
(
(;/5/W6 23 !"+0H+6
<
 =
(
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( )

%    = − +
+62> L;/(
12>,D(7EU2>C#7EU 1@=/GD7@=//>2@AI+,M/
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( JBKG`-h+ +0/DEGDU(:/
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
(/A62C2 !"!

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 
   g9  
 
+
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→
−
− +
−
(UV/5/WR++H+S223 !"

#   = + −
+6
<
 =
(
:/0;/, /+01
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  j <− + =
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9 − −
(

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 # ! = +
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 
# %    = = − + −
(
(J[k+, /+01
% l <<
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f 
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
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− + +
−
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#   = − − +
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m f #  <+ + =
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− −
>

−


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
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

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A. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH (7.0Đ)
I. TRẮC NGHIỆM: (2 Đ)
II. TỰ LUẬN: (5 Đ)
Câu 1:2k,!"2L/2C2!"6/ 2C2!"m /+[t
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B. PHẦN RIÊNG (3 Đ)
Thí sinh chỉ được làm mt trong hai phần (phần 1 hoặc 2)
1.Theo chương trnh Chuẩn
Câu 4a:12>,D(7EU2>C#7EU 1@=/+YG26(C226HD7$DE$
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2.Theo chương trnh Nâng cao
Câu 4b:12>,D(7EUG2>C#7EU 1++YG26G/>2
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I. TRẮC NGHIỆM: (2 Đ)
II. TỰ LUẬN: (5 Đ)
Câu 1:2k,!"

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Câu 3:16 232C2 !"
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Thí sinh chỉ được làm mt trong hai phần (phần 1 hoặc 2)

1.Theo chương trnh Chuẩn
Câu 4a:+:m?Y7E2>Y7GYEGYG=L+@=//>2@ Y7$YE$Y$G +0/
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2.Theo chương trnh Nâng cao
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2 Z2/O2C22I,-s/+M/D7@ UGD@ 7UG7E@ DUGD@ 7E
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A. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH (7.0Đ)
I. TRẮC NGHIỆM: (2 Đ)
II. TỰ LUẬN: (5 Đ)
Câu 1: !"
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Câu 2:12C2/A6!
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Câu 3: !"
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B. PHẦN RIÊNG (3 Đ)
Thí sinh chỉ được làm mt trong hai phần (phần 1 hoặc 2)
1.Theo chương trnh Chuẩn
Câu 4a::m?D7E2>7E +/C2@=/2‹E@ 7$G26D7@=//>2@A
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2.Theo chương trnh Nâng cao
g^12>,D(7E(∆7E@=/+67G/>2
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I.PHẦN CHUNG CHO TẤT CẢ THÍ SINH 
Bài 1 (12C2/A6!
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Bài 2.
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+
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 )*+,+++234+5 !"+62> L$&(
 )*+,+++234+5 !"*++*,+#*!/!/@Am#$
 

−
(
Bài 4. 12>,D(7EU2>C#7EU 1@=/26GD7@=//>2@AC#GD7$

(
:/0;/2C2I+H12>, O/+/C2@=/(
KTD7
⊥
DEU(
2/>2/OD@ ,D7E(
m/>2/OI+,M/DEU@ 7EU(

II.PHẦN RIÊNG
Thí sinh chỉ được làm mt trong hai phần (phần 1 hoặc 2)
1.Theo chương trnh Chuẩn
Bài 5a(


 
 x

  x
→−
+
+ +
(
Bài 6a(
 

#   d x

= − − −
(J[k+, /+01
8
# <≤
(
2.Theo chương trnh NC
Bài 5b(

 
  


  
→
− −
− +
(
Bài 6b(

  
#
 
− +
=
−
(J[k+, /+01
8
# <>
(
X!"j
A. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH
(1
(
)

 g   − + −
g
( !"%$+G

/
 
=

−
(
% l<
/ l<
(
(12>,D(7EU2>C#7EU 12O+(E*+D7$G7E$GE$G26H
D7@=//>2@A%7EU(
/>2/O2C2I+,M/DE@ DU@A7EU(
JBY /23-s/2R7@ EU(Z[/2C2+\Y*%DU(
B. PHẦN RIÊNG CHO TỪNG BAN .
I.Ban cơ bản
1/A6

 <
  

 2!
→
− +
−
( !"
 
  g
#   
  
= + − −
2>4+5()*+, /+01+*,+#*234+5
*+0;/+*,+#*>!/!/@A-s/+M/m#$g'(
II .Ban khoa hc tự nhiên
(2k,!"

( )


+ut
  
 x
   d
  d<
− + =


+ =


1!"6/+H


@ 2=/LN232k,!">(
( !"
 2!  2! 
 + 
%   
!  

− π
<



= + ≤ ≤



− + +



2
nÕu 0 < x
6
nÕu -1 x 0
x nÕu x < -1
+0/>G +!"(
1G%H+S2+62C2$&@ $<(
X!"x
A. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH (7.0Đ)
I. TRẮC NGHIỆM: (2 Đ)
II. TỰ LUẬN: (5 Đ)
Câu 1:E"!"GG2Gm+6+ D2>+w/;/<<G+2;/&d(1g!">
Câu 2:12C2/A6!
(


  

 
→−∞
− +
−
(


 <
    


→
+ − + +
(
Câu 3::m?D7E2>+/C27E@=/+6EG7E$GE$GD7
⊥
7EGD7$(JBK
 +0/237E(
(/>2/OI+,M/DE@ 7E
(-s/27|23+/C27K
(/>2Œ/OI+,M/DK@ 7E
g(Z[/2C2+\7*DK
B. PHẦN RIÊNG (3 Đ)
Thí sinh chỉ được làm mt trong hai phần (phần 1 hoặc 2)

1.Theo chương trnh Chuẩn
Câu 4a: !"%$!y2!y
g 

+
(J[, /+01%}$<(
Câu 5a: !"#$

&'
)*+, /+01+*,+#*@A4+5 !"+5$
2.Theo chương trnh Nâng cao
g( !"#$


y

'
()*+, /+01+R,+#*23Z•+\7<9
(1+0H-s/+M/#$2C2+\>2>+Z•-h2+*,+#*@=//>2@A(
X!"f
A. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH (7.0Đ)
I. TRẮC NGHIỆM: (2 Đ)
II. TỰ LUẬN: (5 Đ)
Câu 1:D`+[
g 
 
  d<
  x<
+ =


+ =

(1
d g
 GD
Câu 2: !"% =

 
  
Z  
 
    Z  


+ −
<

−


+ + ≥

1+k+2[2C2/C+0523 !"H+S2+0HQ(
Câu 3:12>,D(7E(C# +/C27E2>7E$G7$xG
·
<
E7 d<=
(
6HD7@=//>2@AC#(E*+D7$E(
 mEGD7(
 12C2XgDG7GEG(
2 JBKG`+]+:+ 12*237+0HDEGD(/>2/OI+,M/7K`@ 
7E(
B. PHẦN RIÊNG (3 Đ)
Thí sinh chỉ được làm mt trong hai phần (phần 1 hoặc 2)
1.Theo chương trnh Chuẩn
Câu 4a !"#$2!

(
(#ŽG#Ž}(
(/C+0523+:27$#}}}'d#}'d#yx(
2.Theo chương trnh Nâng cao
g

(2C2/A6!(

 
 
 
   
→
−
− −
(+w/D$
     g   <<f
<<f <<f <<f <<f <<f
( ( (  g(  ((( ( 
−
+ + + + +
X!"<
A. PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH (7.0Đ)
I. TRẮC NGHIỆM: (2 Đ)
II. TỰ LUẬN: (5 Đ)
d
Câu 1:D
( )


2>
 
g f
  g
  dd
+ =



+ =

(+w/gd!"6/+H23D
Câu 2: !"

 g
Z  
%
  
d Z  

−
≠

=
+ −


≠

(KT !"H+S2+6$(
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B. PHẦN RIÊNG (3 Đ)
Thí sinh chỉ được làm mt trong hai phần (phần 1 hoặc 2)
1.Theo chương trnh Chuẩn
Câu 4a !"%$
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+#*>!/!/@A-s/+M/#$−−
Câu 5a: 2C2/A6!
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→±∞
− +
− + −
2.Theo chương trnh Nâng cao
g !"#$
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Đ 31
Bài 1.
1/?+L26
•<9 ‘π
23, /+01
!  (2! 2! + =
(
J[, /+01
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!  2! !    g2! − + + = −
(
Bài 2.
1?!"23
g
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Bài 3.0/I+,M/+BLY#G2-s/+M/m2>, /+01y#'g$<()*+, /
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Đ 32 :
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Bài 1.J[, /+01
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Bài 3.KL+/-s2>21ZC-/2‹21F-h2ZC(`/-s>F+\/21L+2C2
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 
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Đ 33 :
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Bài 5. 12>,D(7EUC#7EU 1+/7E C#A(JB^G|-h+ +0/
237U@ E(
1/+#*23I+,M/D7E@ DU9I+,M/D7@ DEU(
:/^|!/!/@AI+,M/D7E@ DU
2JBJ +0B/++/C2D7E(QC25+*+m?2312>,@AI+,M/^|JG+*+
m?> 1/1v

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Đ 34 :
Bài 1.J[, /+01


!  2!    !    !  ! 
 <  
! (2!  
!   ! 
+ − + − +
= =
−
+
Bài 2.1Jp`@ J``*2>23 !"
# !  2!= −
(
Bài 3.
1?!"23
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#
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+0/Z+0y#
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(
J[, /+01
       

     
      <<
− −
+ + =
(
Bài 4. KL+A,B2/4d<B2!G+0/>g<B2!+2B2=+CG<B2!+2B2
=@„@ <B2!+2B22[=(2B/”HL+B2!(C2!k+232C2*
2"!
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E’B2!+2B2=@„’(
2’B2!+2B22[=’(
mU’B2!Z=/+2B22[=’(
Bài 5. 0/I+,M/+BLY#G27&9@ Ed9&(
1[23-s/+M/7EN,R,+5+*+]
@ 9=
r
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-s/+0—C
 
 g # d g− + − =
(1[23-s/+0—CN,R,4/m6/Z
+2?,R,H+*, ,R,":/+0S2Y#@ ,R,@5++7+‹!"Z$&(
Bài 6. 12>,  D(7EU2>C# 11  (  JB J@ ^  -h+ +0B/+
D7 G D7E∆ ∆
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1//O-s/+M/D7@A,JE(
2:/^J88D7U(
Đ 35 :
Bài 1.

81+,C2523 !"

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#
 + 
−
=
+
(
81Jp`@ J``23 !"#$!
g
'2!
g

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
+0H6•&π9π‘@ ,
[/*+H23 !"#$!

+0H6•&π9π‘(
Bài 2. J[, /+01
8

 !    !   <− + + =
8
 
 
2!   !  g! g
 
− − = −

8
!   2!  + = −
g8
  
2!  !  ! g
+ =
8

2! (2!(2! g(2!x
d(! 
=
Bài 3.
8:/'

'
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'
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
 

−
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8>„*/1--h2/+\*(pk#/–H*/1@ *,+]+:++\
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7’D"+6+  !"•Ž(\>G!#0C2!k+23*2"’!"+6+  !"2›Ž(
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Bài 4.
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f
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
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@
r
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8+/C27EX26@ -s/27^(KL+-s/+M/N^@=//>2@A7+6(
QC25,R,*1*+/C27^+ +/C27E^(
Bài 5.12>,D7EU2>C#7EU 11 (JBJ +0B/++/C2D7E@ 
 +0/7E(pk#K+0/67U!27U$7K(
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2>,D7EU(
Đ 36 :
Bài 1(1/C+05Ak+Guk+23 !"#$yg!
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Bài 2(J[2C2, /+0!
g2!'2!'2!g$&  !- 2!$
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, ∈<9π
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2! 
+ − =
Bài 3.
J[2C2, /+01!
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