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Bộ đề thi thử đại học môn toán có đáp án năm 2014

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 Thời gian làm bài : 180 phút
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!&$Hn

k





+
y
dyy
ππ
=


+
k

π

n


∫ ∫


=−−=−=






3

3


y
ydydyy
πππ
k
3
π

nk

4
2
đvtt
π
+*2
+*2
+*2
%

 !
%
 !
i!%=EF$&C1n
N
4

3

aAAABCdt ==
i)7*)

k






ACAH
CAAAAH
ACAH
ACAH






+

=
→→→
→→
k




ACAH
CAAH
→→

+


+
4+*


3

3

3


3

3+
=→=== ACAH

aa
aa
ACAH
ACAH
nZA)7*)


k4+
+

nZA)7*)

k4+
+


( )( ) ( )
xxxxcbay 42

++=++++≤
eJo@k
N

xxxxx −++=++
o@k
4N
N
++− xx
*eJ
( )

*+*

∈= ttx
$k
N
3
+<4p4N
ff
=↔=+−=→++− ttgttgtt
,,!
P






P@$
3N
3

N
3
N
3

π
=→=↔== xxtkhi




2
3

2
3
N
3
42

≤≤−→≤ yy
O5(qkr@A&>
3
π
=x

c
x
b
x
a

==

A
cba 
3

4
==


+*2
+*2
+*2
+*2
+
+*2
+*2
777+5/5895*1
N

o
oo
+

N
3
+
i
l
N
3



o
o
o
+


N
3
+
i
l
N
3


!A1







−=
−=
−=








=
=

=
→=++
2
3+
2
2
3+
2
42

c
b
a
c
b
a
cba

%5$ !
 
iHds*>=tk
4

i
BABMA *T+
a
+
=
E.%(A&1
 === RMAMI

nZAP(M/;$&?ds>=t
f
k

P(MOP@*AH
LMIK1

( ) ( )





+−=
−=






−−=
=






=++

=−+−




+


y
x
y
x
yx
yx
nZAH%IA(W(HLM(&
*+%
XHd
*+* −J
>=tk3
iH.
** −

u
*[(U$$H8[Z

u
E.
[.[HO9$1
+ =+−+ Dzyx
i[\X]/;$&?H>&kOu*[k

2

=− rR
H1
2
3
+
=
+−−+ D





−−=
+−=

232
232
D
D
Y1HJ.6$1[

1
+232 =+−−+ zyx
[

1
+232 =−−−+ zyx
+*2

+*2
+*2
+*2
+*2
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 !
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abcd
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3
T
A
L**O
i`(k1
iv+1HpLH

p
A
L*O
ik+v1HwLwLO
ik+k1HwLO
nZAIA(W(E1
N+3wwwpw

p
3
T

=+++ AA
 !
_1
33<<N<
N


=→=−==→==→==+ cbacbbaay
x
ix.OC$E=U&$$b

`b

1

p

<
T
3
3
N

3
N


4+









+







==↔
=−=↔
−−+=↔
−+=
yx
caNFNF
NFNFNFNFNFNFFF
NFNFNFNFFF
nZAHN%IA(W(1
+*2
+*2
+*2
+*2
+*2
+*2
+*2

777+5/5895*1
2








−−



























3

*
3
N
<
3

*
3
N
<
3

*
3
N
<
3

*
3
N

N3
NNNN
+*2
$ !
ie/;$6$
*+*+
+
Mquađi∆
H.
+**

u
<
**N*<*+*
++
−=






−=
→→→
uAMAM
i$Q)

E)7k
2
4

*
*
+
=






=∆

→→
u
uAM
Ad
i!$)_b'(
2
N
3

 ===→ AHAFAE
nZA_*b(MJW(d)*
,tk
2
N
/;$6$

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=+++−
=
=
=
2
3




zyx
z
ty
tx
+*2
+*2
+*2
k
2
 
(A&LM_bE1












=
+
=
+
=












=

=


=

2
N
2


2
N
2

z
y
x
z
y
x
+*2
%6

 !
i-L.cVk@iA
* Ryx ∈
7K






=
+=−+

NN

xyi
iyiyx






=
=








−=∨=
=

3
3

N


N

N
y
x
x
y
x
y
x
y
nZA.cW"E1
iz
3
3
N

N +=
+*2
+*2+
+*2
$

"#
 
 

x
y

x

=

777+5/5895*1
4
o

o
f

 n./0$&".(A*>$Q%s<.(A
G$


"#
 -./0$&"

w
  4  3  +  
  
x
x x x
π π
+ + = + +
 -K./0$&"1
N 3  
3 



x x y x y
x y x xy

− + =


− + = −


"#;!==.d1sk
N
+
 E 

x x
dx
x
π

"#%;
"H.X),HA),E$(U$9)8),k*JE
$d9yX7J.6$X),X)z$98J.6$A$H4+
+

!=U$H$#J.6$X),X,
"#%;**EO/0$I iikc$&G$1

3
a b b c c a
ab c bc a ca b

+ + +
+ + ≥
+ + +
&'  !"#
< )*+,) /0123/))#4/
"#%5
!&$J.6$LMD@A%)</;$6$

1@i3AiNk+
!"LM%,(M/;$6$

/;$6$),

S.8($H
N2
+

!&$>U$$8KLMD@AV*%P<l<
/;$6$

  1
  3
x y z
d
+
= =
− −

 N
 { 1

  2
x y z
d
− −
= =
c$1%P*O*O|z$G&MJ.6$n./0$&"J.6$
H
"#%5
-./0$&"1
 

N 
N  N 
E$ E$
x
x x x x
Log x x x
+
+ +
+ =

)*+,) /0123/)"/0,5+
"#%6
!&$J.6$LMD@A/;$&?
 
 1 C x y+ =
*/;$6$
  1 +d x y m+ + =
!"
m

%
 C
\
 d
9),OK=$),DE8
5
!&$>U$$8KLMD@AV*J.6$1
[1@jAiVik+*}1@jAiVi3k+*t1@iAj3Vik+
/;$6$


1



−x
k

+y
k
3
z
-L


E$(A[}
n./0$&"/;$6$O(U$$H8t\/;$6$


*




"#%6 -5./0$&"1E$
@
E$
3
T
@
jw


777+5/5895*1
w
$
"#=> ?@#/0 

~!Z.@1
{ }
h D = ¡
~!=


{ +
 
y x D
x

= < ∀ ∈


7$&>$
 <−∞

< +∞
~7>U$H&
~-89

+

= +∞
x
lim y

x
Limy


= −∞

x
Lim y
→+∞
=


x
Lim y
→−∞
=
eHKZc$1@k*KZ$$Ak

~,$
@
−∞

+∞
A| ll
A

+∞

−∞


~n
+2
+2
+2
+2

~!.(A9%
+ +
 <    M x f x C∈
H./0$&"

+ + +
{    y f x x x f x= − +
7A
 
+ + +
     +x x y x x+ − − + − =

~
~$Q%s<.(A~G$


+
N
+
 

  
x
x

⇔ =
+ −

$/S$K
+
+x =

+
x =
~.(AW"1
 +x y+ − =

2 +x y+ − =
+2
+2
+2
+2

 ~,•./0$&" /0$/0$8

 3   +   4 +
4
c x x c x
π
− + + + =

  2   3 +
3 4
c x c x
π π
⇔ + + + + =


    2    +
4 4
c x c x
π π
⇔ + + + + =
-/S

 
4 
c x
π
+ = −

  
4

c x
π
+ = −
E9
+2
+2
777+5/5895*1
p
~-

 
4 
c x
π
+ = −
/S$K


x k
π
π
= +

2

4
x k
π
π
= − +

+2
+2

~,•K/0$/0$8
  3
3 
  
  
x xy x y
x y x xy

− = −


− − = −


~eJ€.C

3
x xy u
x y v

− =


=


*/SK




u v
v u

= −

− = −

~-K&/S$K(<E<+l<l3
~!QH$/S$K@<AE<+l<+
+2
+2
+2
+2
3 ~eJk@
!=Okl@O@*•Z@k+"k*
N
x
π
=
"


t =
!QH




 



E Et t
I dt dt
t t
= − =
∫ ∫
~eJ


E <u t dv dt
t
= =

 
<du dt v
t t
⇒ = = −
X(A&




 
   
E E 
 


 
I t dt
t t t
= − + = − −

~B(

  E 

I = − −

+2
+2
+2
+2
N ~n"
~-L7E&($%,*c$
 SH ABC⊥
~•‚$$H$#J.6$X),*X)8JAE

+
4+SEH SFH= =
~R
HK SB⊥
*EZ.E(Z(A&$H$#J.6$X),X,
G$
HKA

~YZ.E(Z=/S)k),k*



a
HA =
*
+
3
 4+

a
SH HF= =
~!$X7(U$97H
  
   3
+
KH a
HK HS HB
= + ⇒ =
~!$)7(U$97H

+


3
3
+
a
AH
AK H
KH
a

= = =
+2
+2
+2
777+5/5895*1
T

3

3
AK H⇒ =

+2
2
~,•
 
   
a b c c
ab c ab b a a b
+ − −
= =
+ + − − − −
~!QH
  
        
c b a
VT
a b c a c b
− − −
= + +

− − − − − −
g**O/0$iik**(M>$+<kvl*l*l
O/0$
~.OC$56$cUO/0$/S
3
  
3  
        
c b a
VT
a b c a c b
− − −

− − − − − −
k3.
e6$c@A&>y>

3
a b c= = =
+2
+2
+2
+2
4
~

H./0$&"
 3
 
x t

y t
= −


= − +

H.
 3<u = −
ur
~)(M


 3 <   A t t⇒ − − +

~!H),<

kN2
+


 < 

c AB u⇔ =
uuuur ur





AB u

AB u
⇔ =
uuuur ur
ur


2 3
4T 24 N2 +
3 3
t t t t⇔ − − = ⇔ = ∨ = −
~%W"E
 
3 N  3
 < *  < 
3 3 3 3
A A− −
+2
+2
+2
+2
4
~OB(

+< <+M −
H.

< < 3u = − −
uur
O|B(


+<<NM
H.

<<2u =
uur
~!H
 
<  N< p<Nu u O
 
= − − ≠
 
uur uur ur
*
 
+<<NM M =
uuuuuuur
•ƒ
   
<  4 N +u u M M
 
= − + =
 
uur uur uuuuuuur
OO|$.6$
~-L[EJ.6$cOO|kv[H.
<< n = −
ur
B(
P


H./0$&"
  +x y z+ − + =
~g„5A%P<l<(Mo[*QHH.
+2
+2
+2
+2
w ~e'(>K1@v+
~!71@ƒ@kE$K
~!71@ƒ
x ≠
*•./0$&"/0$/0$8

  
 E$ N   E$ N  E$ N 
x x x
x x x
+ =
+ + + + +
eJ
E$  
x
x t+ =
*/S./0$&"

  
  t t t
+ =
+ +
$/Skklf3

~n8k
E$   
x
x⇒ + =
./0$&"AU$K
+2
+2
+2
777+5/5895*1
+
~n8klf3

E$  
3
x
x⇒ + = −


 3
N  x x⇔ + =
~
`Z5A

p
x =
E$K~
`(

p
x >

"n!~v
`(

p
x <
"n!~…*ZA~H$KO(A5

p
x =
~E(Z1$K./0$&" E@k

p
x =
+2
4 ~HdD+<+*>=tk
~O\9%.dK
 <  d O d⇔ <
~!H
  
  
  
OAB
S OAOB AOB AOB= = ≤
!QHOK=$)D,E85>y>
+
T+AOB =


 < 


d I d⇔ =

m
⇔ = ±
+2
+2
+2
+2
4
~


H./0$&"
 

3
x t
y t
z t
= −


= − +


=

~



H./0$&"

2 3
x s
y s
z s
= +


= +


=

~-†
 
<d A d B∩ ∆ = ∩∆ =
  <  <3 ,i<2i3<A t t t⇒ − − +
~
  <3 4< 3 AB s t s t s t= + − + −
uuuur
*otH.
<< 3n = −
ur
~
  ‡d R AB n⊥ ⇔
uuuur ur
z$./0$

 3 4 3

  3
s t s t s t+ − + −
⇔ = =


3
N
t⇒ =
~OB(
  3
 < < 
  p
A
H.
<< 3n = −
ur
kvOH./0$&"
3
 
p
 
  3
z
x y

− −
= =

+2
2

+2
+2
777+5/5895*1

w
~e'(>K1
3
+
E$ T w +
T w +
x
x
x >


− >


− >

$/S
T
E$ w3x >
n"
T
E$ w3x >
v. /0$/0$8

3
E$ T w

x
x− ≤

T w 3
x x
⇔ − ≤

3 p
3 T
x
x

≥ −







x
⇔ ≤
~E(ZZ.$K1
T
E$ w<ˆT =
+2
+2
+2
+2


(
AB/;
(Thời gian làm bài 180 phút, không kể thời gian phát đề)
!
"#( 2,0 điểm):
 N


x
y
x

=
+


$!"&%@c$(B(/;$6$P`Pl3<+`l<l
"#(2,0 điểm)1
-./0$&"1


 3 
 3
x x
x x
= + + −
+ + −

$-./0$&"1
 3 N  3 N

       x x x x x x x x+ + + = + + +
"#(1,0 điểm)1!==.d1


E
E
 E
e
x
I x dx
x x
 
= +
 ÷
+
 

"#%(1,0 điểm):"H.X),gX|),gH($AE"(U$),g9
7yXX|G'z$M.=8J.6$),g*H"((U$$HEAEWE/S
E&($%7)g&($%,!=%=.W($"H.*&G$X7
kX|k
"#%(1,0 điểm):@*A*VE#$O/0$ @AVk!"$&I5%(c1

T T T T T T
4 3 3 4 4 3 3 4 4 3 3 4
x y y z z x
P
x x y y y y z z z z x x
+ + +
= + +

+ + + + + +
&'!
  !" #
<)*+,) /0123/),)#4/
"#%5(2,0 điểm)
!&$J.6$8K9MD@A*/;$&?H./0$&"1
 
N 3 N +x y x+ + − =

!DA\9)YZ../0$&"/;$&?|*>=t|k.@‚$89)
777+5/5895*1

$!&$>U$$8K9MD@AV*%)<<l*,w<l<3/;$6$OH./0$
&"
 3
  t
N 
x t
y t
z t
= +


= − ∈


= +

!"&O#$%P•$>$QP),EI5
"#%5(1,0 điểm)1-./0$&"&$Z..c1


+z z+ =
9)*+,) /0123/)/"/0,5+
"#%6(2,0 điểm):
!&$J.6$8K9MD@A*"#Z),gH9),1@lAlk+*/;$ƒ,g1
@lwAiNk+/;$ƒ)B(%P<!"9My"#Z
$!&$>U$$8K9M(U$$HD@AV*/;$6$1

  + 3 3 +
  < {
 +   +
x y x y z
x y z x y
+ + = + − + =
 
∆ ∆
 
− + − = − + =
 
c$&G$/;$6$


{∆
\(
n./0$&"=\J./;$6$.d$$H9:


{∆

"#%6(1,0 điểm)1-K./0$&"1

  
3 3 3
E$ 3 E$ E$
E$  E$ E$
x y y x
x x y y
+ = +


+ = +


llllllllllllllllllllllllllllllllC1llllllllllllllllllllllll
(
"# ?@#/0
$

 !
"# %
!•e1gkth‰lŠ
'(1

4
{ + @ g
 
y
x
= > ∀ ∈
+


kv$&^>$
 < −∞ −

 < − +∞
*>U$H&
%
&
-891
 
E * E * E
x
x x
y y y
− +
→±∞
→− →−
= = +∞ = −∞

kveHKZc$@kl*KZ$$Ak
,,!
@ l

li

A| ii
A

i



l


&
%
&
ie1
e\&C9%
( )
<+
*&C($9%+<lN
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3
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N   +
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 
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x x y y
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1
3 ++ =x y
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3

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