Đề thi thử đại học môn Toán có đáp án số 55

ĐỀỬĐẠỌĐẲĂ.
Môn thi : TOÁN
Bài 1(2 điểm):
  !"#$%&'(
 
#) )  *#) ) y x x= + −
 +',,-$./ 0''1 0' 234 56$&7897:; #*
Bài 2(3 điểm):
 ;75</,+=
 



# #  >
x y
x y
xy x y x y

+ +
=

+ +


− − + + − =

#
x y R
∈

 75</,+=

 
 *& $ $ *# & x x x x x+ = −
#?
x R
∈

@ +''$ 075</,+&8$2/;'$,/ A
B
CD

 
 
 
=

 
E  E 

# *F/ #  D# BF/ D D 

m x m m
x
− − + − + − =
−
Bài 3(1 điểm):
GH;IJ$2&'/$J8K/$: LJJM&C$$$A
@SA SB SC a= = =
#&N
*,$AIIJFOF56FP9 0'&$IMJM&*Q0Q$3($27
*JR&*

Bài 4(2 điểm):
QQ$7:=

 

*F# x x dx
+
∫
,/'S7T/A Uxy $ 0'#@C*VW775</,+ 5X/T/HY8&$Z
$[8H5</$$,-$\& UxyGA]^&$H;Q$&'/$]^_P*
Bài 5(1 điểm):
,/3K//&?;\& U`9a$ 5X/T/H
=


  C# 
 
x t
y t t R
z t
= +


= + ∈


= +

 5X/T/H


F
/&89$%&&'S7T/#]=`b9bM#^=`c9cabBM*\F/& 0'
$%&HH

*d75</,+ 5X/T/H
@
Y8&#C@C !/X$Z& 5X/T/H


H

FOF56AJ&$&'/$J$: L*
Bài 6(1 điểm):
x, y, z
≥

  
@x y z+ + =
*G/'=
@ @ @
  
@ 

  
x y z
y z x
+ + ≥
+ + +
************************************


Đáp Án ĐỀỬĐẠỌĐẲĂ.
Môn thi : TOÁN
J=


0'
UH8/ e0'
f2'(=
 
#) )  *#) ) y x x= + − ⇔
9M`
D
g`

c#
fhe=iC
F' C F'
x x
y y
→−∞ →+∞
= +∞ = +∞
C
@
j D D C j  C y x x y x x= − = ⇔ = = ±
fJJ= *B
fe\$ k/3/ C$$," *B
fd k/ " *B


0'

f\#&=
Ox∈
'134 56$ #&7897:;*
fe5X/T/H Y8&?;(/2$3$275</,+=9M3#`g&
fHF$%&#3$L3;7&8$2/;'=
D 
@
  # 
# 
D D
x x k x a
I
x x k

− + = −

− =

*B
f2


#  # 
 
k
I A
x
=

⇔


− =

S$


D # 
# 
@ D  #
x x k
B
x ax

− =


− + =


*B
f1;#$L$&'U789H89PFH=9M*dW9 0134 56$@7
897?#$O %F;#J7$2/;'7#`C3?`3$

±
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75</,+#7$2/'7`3$

±

*B

^=
@ @
 
 
a a− ≠ < − ≠ >hoÆc
*B
J=
UH8/ e0'


0'
f;
 
#  #  B
# # l#  # m >
x y
x y x y

− + − =
⇔

− − − + − =

*eS


u x
v y
= −



= −

8 56$;
 
B
#  >
u v
uv u v

+ =

+ =

*B
f,& 56$=
@
* 
u v
u v
+ =


=

Cf,& 56$=
 
 
u x
v y

= − =


= − =

S$
 
 
u x
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= − =


= − =

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@

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
⇒

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
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fe=
$ x ≠
*]
@ @
 $ $  *#$  x x x x x⇔ + = −
*B
# $ *$ *# $  x x x x x⇔ + − =
*B
 $ C $ x x x x⇔ + = − =
*B

C &,$& C#  
D 
x k x l k l Z
π
π π
⇔ = − + = + ∈
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E  E 
# *F/ #  # BF/ #   m x m x m
⇔ − − − − − + − =

feS
[ ]
E 
B
F/ #  CD C

t x x t
 
= − ∈ ⇒ ∈ −
 
 
*B
8 56$7=
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D D
j#  C j#   
# 
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fQ 56$
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a
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*J *
o o @D
*
q r
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a
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fQ
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feS

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@
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u x
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dv x dx
v x


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
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= +
 
+
⇒
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=


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
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@ @ 
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x
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+
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fQ
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D
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 
l  m ***
  @ D
x
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x x
π
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∫ ∫

*B
fdW9
 D
*F 
@ q >
I
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fH$27=
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x y
a b
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*B
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@  @
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f2

* * @
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OPQ
S a b
∆
= ≥
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