2 ĐỀ THI THỦ ĐẠI HỌC MÔN TOÁN: NAM ĐỊNH - THANH HÓA


TRƯNG THPT TRC NINH B
ĐỀ KHO ST TRƯC K THI ĐI HỌC NĂM 2010
Môn: Toán !"#$%&'
Bài 1(2 điểm):
!' ()*+,&+-.&/00123&4'56+7
8 8
9 9 !' :9 9 !'y x x= + −
8' ;&</&<=5*>2?&@2?2ABC2DE5&.$&FG.$HI&2.':
Bài 2(3 điểm):
!' )I$DJ&<; 
8 8
!
8
8
 !' 8' K
x y
x y
xy x y x y

+ +
=

+ +


− − + + − =


Lx y R
∈

'
8' )$DJ&<; 
8 8
+ :& 5*+ 5*+8 :8 & 'x x x x x+ = −
L0M
x R
∈
'
N' ;&-52?$DJ&<;+F5AI&-5&<*2*O
P
QR
8
 
 
 


8 8
!S 8 !S8
!
 !':*  8' R P'* R R #
8
m x m m
x
− − + − + − =
−
Bài 3(1 điểm):
*&TUIV5A&,5V0FW5H2XVLVYQ5,55O
NSA SB SC a= = =
LZ#':

</5OLV[DE&\G2?L+*5*YVY:]&?&]5B75A$:V
&^*:
Bài 4(2 điểm):
!']&]5$H 
!
8 8
#
:! 'x x dx
+
∫
8'<*_&$`&*O2axy 5*2?NQ!':bc$$DJ&<;2D&`UdF05e&
5fFUDJ5,5&<=5&g2axLy&T&-&OhLi+*5*UI&]5&,5hij\&:
Bài 5(1 điểm):
<*BW0MI&g2akGl5*2D&`U
!

!
! 8 Q '
! 8
x t
y t t R
z t
= +


= + ∈


= +


L2D&`U
8

*&FG.56_&$`h' 8kmGm!Y#0i' 8knGn8lmPY#:g*2?56
U!0U
8
:o.&$DJ&<;2D&`U
N
dF8QNQ!'L23&5e&2D&`U
!
0U
8
[
DE&&OV0+*5*&,5V5H2X:
Bài 6(1 điểm):
*x, y, z
#≥
0
8 8 8
Nx y z+ + =
:T
N N N
8 8 8
N 8
8
! ! !
x y z
y z x
+ + ≥
+ + +

::::::::::::::::::.&::::::::::::::::::
!

TRƯNG THPT TRC NINH B
KHO ST TRƯC K THI ĐI HỌC NĂM 2010
Môn: Toán !"#$%&'
Đáp n vắn tắt:
V!
!'
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2?
aUF ?
pA+7 
8 8
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R
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8
n!'
pr sQ
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x x
y y
→−∞ →+∞
= +∞ = +∞
Q
N
t R R Q t # #Q !y x x y x x= − = ⇔ = = ±
pVV  #:8P

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po12%2&4 #:8P
8'
!
2?
pg #'
Ox∈
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pD&`U2dF0MI+7A5B5A$DJ&<; GYBkq'
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8 !  '
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pA
8
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k

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8
8
R  !'
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x x k
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x ax
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&.$&FG.$&M'5[026IV'$)5A8I$kQB'0MkB,5
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8 8
a a− ≠ < − ≠ >hoÆc
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pI
8 8
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⇔ − − − − − + − =
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p_&
[ ]
!S 8
P
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8
t x x t
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\F{k)G<B05XBkYGYlY!'
Sở GD & ĐT Thanh Hoá K THI KHO ST CHẤT LƯỢNG LP 12
Trường THPT Lê Văn Hưu MÔN TON KHỐI A
Tháng 03/2010
Thời gian:180 phút (Không kể thời gian phát đề)
PHẦN CHUNG CHO TẤT C CC THÍ SINH (7.0 điểm)
Câu I. (2.0 điểm)
*+7GY'
!:()*+,&+-.&/00123&4+7'

8:o.&$DJ&<;&.$&FG.0M23&4'L.&<{B*)5,5&@&H27kT5623&4'
2.&.$&FG.M\&:
Câu II. (2.0 điểm)
!:;I56$DJ&<;85*+Rkqq8'5*+8kY+8kn.&k∈u#Q
π
v:
8:)I$DJ&<;
N 8 N 8
8
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x y x x y
x y y y x y x
− −

− + =


− = + − +


Câu III. (1.0 điểm)
]&]5$H
N
!
R
8
#
 '
!

x
x
x e dx
x
+
+
∫
Câu IV. (1.0 điểm)
*kLGLl5,5+7&-5UDJMJ!0&*)y2fFBIkGnGlnlk≥8kGl
;,&<4M\&56?F&T5Ykq!'Gq!'lq!':
Câu V. (1.0 điểm)
*&TUIV.&VYYLYVYLYVY5:]&?&]556&TUIV:

PHẦN RIÊNG ( 3.0 điểm)
Thí sinh chỉ được làm một trong hai phần A hoặc B (Nếu thí sinh làm cả hai phần sẽ không được chấm điểm).
A. Theo chương trình nâng cao
Câu VIa. (2.0 điểm)
!:<*_&$`&*O2akG5*2D&`U
!
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8
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&H;0FW}}:],B]_&5[F2dF5,52?VL}LL:
Câu VIIa. (1.0 điểm)
)\&$DJ&<;
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N R
8
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#
P K
x x
x x
+ − +
>
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B. Theo chương trình chuẩn
Câu VIb. (2.0 điểm)
!:*^$~' Rk
8
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8
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!
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ĐỀ CHÍNH THỨC
kn8GnNlnNY#:bc$$DJ&<;_&$`h'2dFLV00FWA50Mi':
Câu VIIb. (1.0 điểm)
)\&$DJ&<;
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Sở GD & ĐT Thanh Hoá ĐP N K THI KHO ST CHẤT LƯỢNG LP 12
Trường THPT Lê Văn Hưu MÔN TON
Tháng 03/2010
Thời gian:180 phút (Không kể thời gian phát đề)
PHẦN CHUNG CHO TẤT C CC THÍ SINH (7.0 điểm)

CÂU NỘI DUNG
THANG
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