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Đề thi học kỳ II môn Toán 12 CB và đáp án

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  
A & / + + − >

)/QU0JRMRRN%&%8*+,%-./%>

O   A  X   ?
k  ?  A X   ? 
?k    A O ?
O  ?A  A O   A k
 &   & / 
 & /   & / &

 & /  & / /
 & /   &  
− − + = − + − = = −
  
  
+ − + + = − + + = =
  
⇔ ⇔
  
+ − − + = − = = −
  
  
− − + + = − − + = =
  

)CPV0Q*+,%-./%@
  
 X  k A !  !+ + − + − + =

fPV0Q=@b?LKL?'#!%F6%\


,-.
5>
( )
X

?
? X
X


 
  O   O O
    


 
 
 
+
+
+ = − ⇔ = ⇔ =
 
− −
 
 

f
( )


X  X     OA

    O O

   

 
+
+ + +

= = = =
− −

Q0.
?
X X X
X
 
    O
  

 

+
= = =

*

 !!"#$%&'()*+,
#
? ? 
 
@- @-  ? @-  A + − + ≤
?
al0F8%>mA
):l0F8%.&%>

[ ]
    
? @- @-  ? @-  A @-  ? @-    ⇔ − − − + ≤ ⇔ − ≥





 ?   A


   

≤ −

⇔ − ≥ ⇔ − − ≥ ⇔



$n*':l0F8%0.%-81#Y*+,%-./%e@
 ≥

,-/
Q=@bLK?L'#!%F6%@\
7
?
?'g,S*+,%-@
?
L L2 = −
ur

7

?'g,S*+,%-@


?L ?LA2 = −
uur

)/
α
%-%-':7
?
'7

%&%
α
?'g,*!*0$%@>

? 
LL? 2 2= ∧ =
r ur uur

N*+,%-./%
α
72%-EA

α
$*[':QF'SF>

 

  
 L   O k
?

  ?
/
/
 0 8 /
/
α
=
− + +

= ⇔ = ⇔ + = ⇔

= −
+ +


)CP*9%-je%&0V0@>

?
α
>EAL

α
>E?A
#BH

@+T%-9%-U0b''0G%--':
α
$*1
Q'
α

6%@-1

':
α



'0G%--':
α
%&%?'g,S*+,%-@>
LL?2 = =
r r

N

*+,%-./%@>

 
? 

 

! 
= +


= − +


= +



5D%-':-1Q'
?
α
@%-81*+,%-./%
K?A

kkA
?⇔ = −

Q0.$*1Q'
?
α
@>JALKL
5+,%-"$*1Q'

α
@ML?L
9/
:;</=>?/@/@/'23A/B/C/D2EF

 !!"#$%&'()*+,

×