Đề, đáp án thi thử ĐH THPT Tam Dương



ĐỀ KHẢO SÁT CHUYÊN ĐỀ NĂM HỌC 2010 − 2011
MÔN: TOÁN 12 KHỐI A
Thời gian làm bài: 180 phút, không kể thời gian phát đề
I. PHẦN CHUNG CHO TẤT CẢ THÍ SINH (7,0 điểm)
Câu I (2,0 điểm). 
 

x
y
x
+
=
+
 !"#$%&'"%('))*+,"-./012
%&"345'6"78'"%&3"9:&'012+,"-./;$%&"7<'6"%&3"9:&'0!0+=92%+%> A.?@/;
B.−@?−/
Câu II (2,0 điểm ).
% %345'6"78'A

0  
0"  %' %' 
 "2' 
x
x x x
x
− = + −
+

% %B345'6"78'A

 
 
 @  C C  D
. ; /
@  D
x xy y x y
x y
x y xy y

+ + + + − =

∈

+ + + =


¡

Câu III (1,0 điểm). E'"E03F'A
C
D
C
C  C
x
dx
x x
−
+ + +
∫
Câu IV (1,0 điểm).

8'0G3S.ABCD+!:ABCDH8'"%I%&"SAJx;)K%
D Cx< <
)0!00L'0M'HL%0G
+NO%+=9$<'6E'">"E00128'0G3S.ABCD"Px
Câu IV (1,0 điểm). 0!0"#0O45'6a;b;c"2:+Q%H9R'" S'AaTbTcJ
U'6%'7<'6A
  

a b b c c a
b c c a a b
+ + +
+ + ≥
+ + +
II. PHẦN RIÊNG (3,0 điểm) Thí sinh chỉ được làm một trong hai phần (phần A hoặc B)
A. Theo chương trình Chuẩn
Câu VIa (2,0 điểm).
  7'6  V"  3W'6  )K%  B  "L  +N Oxy;  0  +%> A.?  C/  '<  '6%  +4X'6  "7M'  ./A
 
Y  Y Dx y x y+ − + + =
Z!0+-'"L+N+%>B;C"9N0+4X'6"7M'./20BH"79'6+%>
012+L'"W'6AC
7'6[R'66%2')K%B"\2+NOxyz;0V"3W'6.Q/AxTyTCzTCJD)2%+%>
A.?D?/;B.??/]^3345'6"78'V"3W'6.P/+%_922%+%>A;B))9R'66G0)K%V"
3W'6.Q/
Câu VIIa (1,0 điểm).B345'6"78'

C C
C



H6 H6 D

. /
D
x y
m
x y my

− =

∈


+ − =

¡

8m+>B345'6"78'0G'6%B"#0
B. Theo chương trình Nâng cao
Câu VIb (2,0 điểm)
7'6V"3W'6)K%B"L+NOxy;0+%>C.?−`/)+4X'6"W'6∆A
C @ @ Dx y− + =
8
"7('∆2%+%>A)B+%aU'6'29_92
`
?

I
 
 ÷

 
20O%B'"E0"26%!0ABC$<'6`
7'6[R'66%2')K%B"\2+NOxyz;00!0+%>A.−?D?/;B.??−/;C.−??C/S:
a!0+-'"L+N"F+4X'6"7M''6L%"%&3"26%!0ABC;
Câu VIb (1,0 điểm).% %$b"345'6"78'A
(
)
(
)
 
 ` C 
C `
H6 H6  H6 H6 x x x x+ + > + −
−−−−−−−−−−−−−c−−−−−−−−−−−−−
Cán bộ coi thi không giải thích gì thêm!
Họ và tên thí sinh: SBD:
HƯỚNG DẪN CHẤM VÀ THANG ĐIỂM MÔN TOÁN 12 KHỐI A
C©u Néi dung §iÓm
I
;ZAR\{−1}
T#$%&'"%('A
%K%L')"%B0^'A
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 
x x x x
x x
y y
x x

± ±
→±∞ →±∞ →− →−
+ +
= = = = ∞
+ +
m

0GHxJ−;HyJ
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D;`
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−f −
Tf
yg T T
y
Tf  
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−f
D;`

§å thÞ:
0,25
\%x
D
'+N"%&3+%>"%&3"9:&'H
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. /

. /
x
y x x
x
x
+
= − +
+
+
8"%&3"9:&'0!0+=92%+%>A;B'('"%&3"9:&'+%_92"79'6+%>I012ABV0'6
'6V0"7h'6)K%AB
0,25
&9"%&3"9:&'+%_92"79'6+%>I.−?/012AB"8"20GA
D
D D


D
D
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.  /  

. /
x
x x
x
x
+
− − + = ⇔ =
+
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9:72345'6"78'"%&3"9:&'HA
 `
@ @
y x= +
0,25
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D

D
D
D



. /

x
x
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=

⇒ = ⇔
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K%x
D
JD"20G345'6"78'"%&3"9:&'HAyJxT
K%x
D
J−"20G345'6"78'"%&3"9:&'HAyJxT`
^:0G$2345'6"78'"%&3"9:&'A
 `
? ? `
@ @
y x y x y x= + = + = +
0,5
O
C
B
A
D
S
H
II

1. ®A
%'  D %'  D
%' 0 D "2' 
x x
x x x
≠ ≠
 
⇔
 
+ ≠ ≠ −
 


0 %' 0 0
%' %' 0
%' 0 %'
x x x x
x x x
x x x
−
⇔ = + −
+
 
0 %'
0 %' 0 %' %' 0
%'
x x
x x x x x x
x
−

⇔ = − + −
0,25
⇔
0 %' %' . %'  /x x x x− = −
⇔

.0 %' /.%' 0 %' / Dx x x x x− − − =
0,25
⇔
.0 %' /.%'  0 C/ Dx x x x− + − =
.0 %' /.  %'  C/ D
@
x x x
π
 
⇔ − + − =
 ÷
 

0 %' D
 %'. / C
@
x x
x
π
− =


⇔


+ =

(lo¹i)
0,25
⇔
0 %' Dx x− =

⇔
"2'xJ
. /
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x k k Z
π
π
⇔ = + ∈
."®k)
0,25
45'6"78'"U'b""45'6+45'6)K%A


. / C. /  D


x y
x y x y
x y
+ = −


+ + + − = ⇔


+ =

0,25
K%xTy J−"2:)345'6"78'"U"20GA

 C
 D
 D
y x
y y
y x
= ⇒ = −

+ − = ⇔

= − ⇒ =

0,25
K%


x y+ =
"2:)"U"20GA

  C 
@ @
i @ ` D
  C 
@ @

x y
x x
x y

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= ⇒ =
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
− + −
= ⇒ =


A
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0,5
III
V"9J

  x u x udu dx+ ⇒ − = ⇒ =
?+Q%0^'A
D 
C 
x u
x u
= ⇒ =


= ⇒ =


D;`
20GA
C   
C

D   
C  i 
. Y/ Y

C  C
C 
x u u
dx du u du du
u
x x
u u
− −
= = − +
+
+ + +
+ +
∫ ∫ ∫ ∫
D;`
( )




Y YH' 


u u u= − + +
D;`
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C YH'

= − +
D;`
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20G
.   /SBD DCB c c c SO CO∆ = ∆ ⇒ =
45'6"#"20GjJj
)^:"26%!0)9R'6"L%;

CA x⇒ = +
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     
AC BD AB BC CD AD+ = + + +

C . D C/BD x do x⇒ = − < <
 

 C
@
ABCD
S x x⇒ = + −
0,5
\%H8'0%&9012a9'6.I/8IJ'('IJ
⇒
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∈
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
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
x
SH
SH SC SA
x
= + ⇒ =
+
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

C . )""/
Y
x x d−

0,25

Ta cã: VT =
  
a b c b c a
A B
b c c a a b b c c a a b
 
 
+ + + + + = +

 ÷
 ÷
 ÷
+ + + + + +
 
 
D;`
[ ]
C
C
   
C . / . / . /

    k C
C . /. /. /C 
  
A a b b c c a
a b b c c a
a b b c c a A
a b b c c a
 
+ = + + + + + + +
 
+ + +
 
≥ + + + = ⇒ ≥
+ + +
D;`
  
 

 . / . /

 

a b c
a b c a b b c c a
a b b c c a
B B
 
= + + ≤ + + + + + + +
 ÷
 ÷
+ + +
 
⇔ ≤ ⇔ ≥
D;`
Tõ ®ã tacã VT
C 

 
VP≥ + = =
. DÊu ®¼ng thøc x¶y ra khi

C
a b c= = =
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