Đề thi thử đại học môn Toán lời giải số 26

Thầy giáo:Lê Nguyên Thạch ĐT:01694838727
ĐỀ THI THỬ ĐẠI HỌC SỐ 27
Ngày 16 tháng 1 năm 2013
PHẦN CHUNG CHO TẤT CẢ CÁC THÍ SINH ( 07 điểm )
Câu I 
  
 
 
y x mx m= − +
1.  !
2. "
#
$%&$$'$$()*+,(& +/+0!)1
Câu II1
123-4+567
 
8
9    :$   $ ; $

9
$
x x x x
x
π
+ + −
=
<
=
 > 
 
x

π π
∈
12&?@A3-4+56:





=−++
=+−+−

B9;

;
yxyx
yyxx
Câu III13-4+56
) ) ) 
8  = &8  = 
+
+ + − =
&23-4+56 &!8
"6&3-4+56$C$%D+E
Câu IV1 FG+5HIJ1IKJKK$%0IJF&+$(L+$M$'(0NIJ!

1
OP3/+IIKJ(L++%$<P3/+IJIIK!

12%$
·

QA AB
F+%$AP3/+
IKI'<P3/+IJD+%$9

1"RR$ FG+5HIJ1IKJKK
Câu V1
x y
SF$$$T-4+UN( E
x y z+ + =
1VU06+5W
X$Y&
  
   M
x y z
= + + +
1
PHẦN RIÊNG CHO TỪNG CHƯƠNG TRÌNH ( 03 điểm )
(Thí sinh chỉ chọn một trong hai chương trình Chuẩn hoặc Nâng cao để làm bài.)
A/ Phần đề bài theo chương trình chuẩn
Câu VI.a:1
1,"5+P3/+<E'DOxyU03-4+56$$$'$Y&&+$ABC5$M
>H
$M +$&'ZCBF
> K
5(+$'ABF
>M
1
2,"6E$Y&'+$*&
9
x

5+ &5


n
x
x
 
+
 ÷
 
5[+
 

; 9
n
n n
A C n
−
+
− = +
1
Câu VII.a:1 23-4+567
( ) ( )
 
:

;
F+   F+ ; F+ ;x x x
+ + = − + +
B/ Phần đề bài theo chương trình nâng cao

Câu VI.b: 11, "5+P3/+'D\)0$& +/+T

7;)]0]!T

7;)^
0]!1"6'DM R +5_D3&+$$%$'[5T

T

5H$\01
2,@F3`7
 
) 0

9 B
+ =
 +/+T

7

)^;0!
a)*+5[+ +/+T

$a@F3`'&3MEIJ1"6'D&%
<_&D$Y&IW4D$Y&$Y&J1
b)"6O)>0(D$`&$&+$OIJ$%TER$[+1
Câu VII.b:12E3-4+567

F+   : 9
:  1 1

x x y x y
y x
+
− + =



+ =


 Hết ]]]]]]]]]]]]]]]]]]]

b(0Ec'VA$:;c +b_("d"&V%&
Thầy giáo:Lê Nguyên Thạch ĐT:01694838727
HƯỚNG DẪN GIẢI ĐỀ 27
M(7!&$%
 
 
 
y x x= − +
.Tập xác định:
¡
Sự biến thiên
]2<''L$$7
F
x
y
→−∞
= −∞


F
x
y
→+∞
= +∞
]N(7"&$%

Q  y x x= −
>

Q 

x
y
x
=

= ⇔

=

J+
)
−∞

+∞
0K ^]^
0





+∞


−∞
V+5 +
( )
>−∞

( )
>+∞
V+$5 +
( )
>

]$57V'$$'')!



CÐ
y y= =
V'$$(')!
( )
 
CT
y y= =
1
Đồ thị:c$a5H$'


>

 
−
 ÷
 
>
( )
>
$a5H$(+'

>

 
 ÷
 
1ce(
 
>
 ;
U
 
 ÷
 
FM)*+1
Câu 1: 2"
#
$%&$$'$$()*+,(& +/+0!)1
"&$%0K!


 x mx−


Q 
x
y
x m
=

= ⇔

=

c$%$$'$$(
#

Q y =
$%&+E3ME
m⇔ ≠
1%+f$$$$'$$(F7

>

m
A
 
 ÷
 

( )

> B m
"&$%7

>

m
AB m
 
−
 ÷
 
uuur
>5(+g$Y&IJF7

>
 ;
m m
I
 
 ÷
 
"@0($h(IJ)*+<&(,(& +/+0!)
#
 +/+IJ(L++%$<
7 y x∆ =
5(+g$Y&IJ(D$ +/+
1 AB u
I
∆


=

⇔

∈∆


uuur uur






; 
m
m
m
m
m m

− =

=


⇔ ⇔


= ±



=


c$(N( E&$%
m = ±
Câu 2: 1,"&$%7
$ 

x x k
π
π
≠ ⇔ ≠ +
i< 3
⇔

( )
  
:$ 9      $  9$x x x x x+ + =



;$     :$x x x⇔ + =

$    ; x x
⇔ + − =

     x x⇔ − + =
( )


  
; ;
x k x k k
π π
π π
⇔ = + = + ∈¢
ie03-4+56G$$%+E
=
 > 
 
x
π π
∈
F
 B
>
; ;
x x
π π
= =
b(0Ec'VA$:;c +b_("d"&V%&
Thầy giáo:Lê Nguyên Thạch ĐT:01694838727
Câu 2: 2
⇔






=−++
=−+−

;


xyx
yx
⇔





=−−++−+−
=−+−
;
;


xyx
yx





=−−++−+−
=−+−
;

;


xyx
yx
Đặt



=−
=−
vy
ux



* "&0&$%E3



=++
=+
:;1
;

vuvu
vu

2CE&-j$




=
=


v
u
VP$



=
=


v
u
"&0+&$%



=
=


y
x
;




=
−=


y
x
;



=
=
=

y
x
;



=
−=
=

y
x

Câu 3 :

8  =
 

x
t
+
=
k&$%3

: t t a− + =

i<&!8&$%

: t t a− + =

  8⇔ = =
d-4+56$%&+EF
8  =

) ) F+ 8
+
= =
l+E$Y&3F+Ek$Y&3-4+56

:a t t= − +
F$(+$Y& +/+0!
&

:y t t= − +
<k

Fe3+$Y&%

:y t t= − +
<k F(e3$C$%D+E &!9P$
a ≤

Câu 472A1OF6$($Y&IK5IJI
$%7
⊥ ⇒ ⊥( ' ) ( ) ' ( )AA B ABC A K ABC
1 "&$%IKO
⊥
IO
⊥
I
·
=
0
' 60A MK


='A K x
1&$%
= − = −
2 2 2
' ' 3AK A A A K x
 O!
·
= −
2
2

sin 3 .
2
AK KAM x
OP $
= =
0
' cot 60
3
x
MK A K
e0&$%3
− = ⇔ =
2
2 3
3 .
2
3 5
x
x x

Λ
= = =
. ' ' '
1 3 5
. ' . . '
2 10
ABC A B C ABC
V S A K AC BC A K
Câu 57
      

   
x y z
M
x y x xyz
+ + +
= + + + =
1

;

;

;
 ;
 ;
 ;
x x x y z x yz
y y x y z xy z
z z x y z xyz
+ = + + + ≥
+ = + + + ≥
+ = + + + ≥
; ; ;
;
   
9;
x y z
x y z
M
xyz xyz

+ + +
= ≥
1mX(!)05& )!0!S!n
Câu 6a7^c +/+AC (L++%$<HK e
 > HK = −
uuur
F3AC,(&K
  7  ; 1AC x y− + =
"&$o+Tp$%7
  7   BK x y+ − =
1
^m
A AC B BK∈ ∈
+f
 ;>   >   1A a a B b b− −
OP $
>M
F
5(+$Y&AB&$%E7
 ; 9   ;
1
     
a b a b a
a b a b b
− + = + = =
  
⇔ ⇔
  
+ − = − = =
  

l(05&7
;> ; > 1A B −
b(0Ec'VA$:;c +b_("d"&V%&
Thầy giáo:Lê Nguyên Thạch ĐT:01694838727
^l(05&7
 > 9AB = − −
uuur
(05&7
  7 : AB x y− − =
1
^c +/+BC,(&B(L++%$<AHe
> ;HA =
uuur
(05&7
  7 ;  1BC x y+ + =
b7ie07
  7  ; − + =AC x y
  7 : − − =AB x y

  7 ;  1+ + =BC x y
Câu 6a:23-4+56
 

; 9
n
n n
A C n
−
+
− = +

>Điều kiện7q>∈r1
d-4+56-4+-4+<
 s
  ; 9
s s
n
n n n
n
+
− − = +
−
⇔
 
  ; 9

n n
n n n
+
− − = +
⇔

tt!⇔!]b'P$!1
i<!&$%*$r(47
( )

; 
 


 

 
 

  1 1 1
k k
k
k k k
k k
x C x x C x
x
−
−
−
−
= =
 
+ = =
 ÷
 
∑ ∑
l'+0$*&
9
x
 
  
;
;  
k N k
k
k

∈ ≤ ≤

⇔ =

− =

1ie0E$Y&'+$*&
9
x
F7
; :

C
Câu 7a7
( ) ( )
 
; :

F+   F+ ; F+ ;x x x+ + = − + +
cN( E7
 
; ;
; 

; 
x
x
x
x
x

+ ≠

− < <


− > ⇔
 
≠ −


+ >

( ) ( )
( )
( )

    
 
 
 F+   F+ ; F+ ; F+   F+ 9
F+ ;  F+ 9 ;  9
x x x x x
x x x x
⇔ + + = − + + ⇔ + + = −
⇔ + = − ⇔ + = −
^i<
 ;x− < <
&$%3-4+56

;   x x+ − =

>
( )
 9x x⇔ = = − lo¹i
i<
; x− < < −
&$%3-4+56

;  x x− − =
;>
( )
 ;  ;x x⇔ = − = + lo¹i
ie03-4+56%$$%&+EF
x =
P$
( )
  9x = −

Câu 6b72AIF+&T

T

&$uI>
2AJF+&T

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
<\0&$%>;
2AJgF +3M+$5++%$J<g(D$\I %&$%g;n>v!;n(05&3 +5_
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 

) 0

9 B
3x 4y

+ =



+ =

ie0T

$a`'3ME
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I  >
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 
−
 ÷
 
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J  >
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−
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 
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∈
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∈
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π
x
uy7IJ!
= 
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∆
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= 
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
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= 
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=
+
!
$ 
;
π
−


⇒
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$ 
;
π
−
!
⇒
!
π
n;>!=
π
n;
ie0$%OUF7
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 
O  >

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 ÷
 


 
O  >

 
− −
 ÷

 
Câu 7b7dh(
⇔
0t)^:!
( )
9

y x⇔ =
3*&&-j$7
 
:  1 1
x x x x
+ =
: : 18
x x x
⇔ + =
: :

8 8
x x
   
⇔ + =
 ÷  ÷
   

 

 
x x
   

⇔ + =
 ÷  ÷
   
cP7!


x
 
 ÷
 
 k
&$%37
( )
( )
 
    t t t t t+ − = ⇔ − + + =



x
t
y
=

⇔ = ⇒

=


b(0Ec'VA$:;c +b_("d"&V%&

Thầy giáo:Lê Nguyên Thạch ĐT:01694838727
b(0Ec'VA$:;c +b_("d"&V%&