Bài soạn ĐỀ THI HỌC SINH GIỎI + DAP AN TOAN 9 HAY 16


a b c d+ + +
PHÒNG GD-ĐT HUYỆN LONG ĐIỀN KỲ THI CHỌN HỌC SINH GIỎI CẤP HUYỆN
------------------------------------------------ NĂM HỌC 2009-2010
-------------------------
MÔN THI : TOÁN
Thời gian : 150 phút ( Không kể thời gian giao đề)
Ngày thi: 16/01/2010
Ba
̀
i 1
 

a c
b d
=
 !"#$%&'()*+,)%)
Bài 2
-.+/"01' 2234
%'+
- -
- -
a b
a b
+
≥
−
 -5'617+8
abc
9:;


( )
-
-

-
abc n
cba n

= −


= −


<+)!8<-
Bài 3
-=>?
@

A
>
B

 C4
DDDDE
-:
−+−−−

@
+

D
≥
-F+
B
+G"?
A


H:DD:-ID
: -
=++++
Bài 4:-JK9G"5
 -  : Hx m m y m+ + − = −
 3LMN',JK+O)+,'=PQ
 L%'+"0R+'!+5JK)S)S+O)'T+,'
N
Bài 5-

∆
U.V)+,'C0'"
∆
U.UC
-
4.C
-
WC
-
9.CX
Bài 6 3 
YJ"ZJR.4-[>'\N]+,'U+T"^YJ

"ZF_+5+/)*+,'U8.F_+`abc5+/)*8UU.
%'+U..a.WU. a4U.
-

MNN"+,'U%+Ua`9+^<6X+^<6
9d[
PPPPePPPP

- - - -

L :L I: :ff
P
= + + + +
ĐỀ CHÍNH THỨC
a d b c
a d b c
+ − −
=
+ − −
ĐA
́
P A
́
N
Ba
̀
i 1('g++-+,'

- - - -


L :L I: :ff
P = + + + +
- - - -

:L LE Ef f-
= + + + +
       

: L L E E f f -
= − + − + − + + −
 
: -
= −
-
E
=

3L+,'
3L+,'
3L+,'


- -
a c
do ad bc ad bc
b d
 
= ⇒ = ⇒ =
 ÷
 

3L
+,'
Bài 2: -+,'
hi548
( ) ( )
( )
- -
- -
- -
-
a b ab a b
a b
a b
a b a b a b a b
− + − +
+
= = = − +
− − − −

h`2238G#.]Sj+-
9
( ) ( )
- -
-a b a b
a b a b
− + ≥ − ×
− −
ik!
- -
- -

a b
a b
+
≥
−

 -+,'
i+/c
-
-
33 3 
33 3  
abc a b c n
cba c b a n n

= + + = −


= + + = − +


l-9ffm4mL42mL
M
ff:3EL
CnR33
- -
 fff 3 333  :n n n≤ − ≤ ⇔ ≤ ≤ ⇔ ≤ ≤
:f  L fn⇔ ≤ − ≤
3EL
-

3L+,'
3EL+,'
3L+,'
3-L+,'
   
       
a d b c
a d b c a d b c
+ − +
=
   
+ + + + − +
   

   a d b c
=
+ + +
-  - 
a d b c
a d ad b c bc
+ − −
=
+ + − + +
- -
a d b c
a d ad b c bc
+ − −
=
+ + − − −


a b c d
+ + +
l:42mL4ff424-I
ik!b5'
IELabc =
3L
Ba
̀
i 3( 
-+,' C4
DDDDE
-:
−+−−−

@
+
D
≥
DDED
−+−−=
3-L


-L


DDD
−+−−−−−=
3L









−






−−−−=

-L
-

DD
-
3L
( )( )
-D:DD
+−−−−−=
3L
( )( )
-DD:D
+−−−−=
3-L

-F+
B
+G"?
A

H:DD:-ID
: -
=++++

>
o
>
@
!D4
A
+8
o
')
B
= 3EL
i
@
+
D3
<≤
?
A

H::-I:DD:-ID
: -: -

=++++<++++
p8=S+8
o
'
@
+
D3
<≤
3L
i
@
+D2?
A

H::-I:DD:-ID
: -: -
=++++>++++
p8=S+8
o
'
@
+D2 3L
i>
o
!=
@
+8
o
')!>
@

D4 3-L
Bài 4:-+,'
i5JK+O)=PQ8
 -   : H L H :m m m m m+ − + − = − ⇔ − = − ⇒ =
3L+,'
F_+
( )
3 3
Qx y
_T+,'N'+O)
9
3 3
 -  : Hm x m y m m+ + − = − ∀
3L
( )
3 3 3 3
3 3 3
3 3 3
  - : H 3 
 3 
- : H 3 -
x y m x y m
x y x
x y y
⇔ + − + − + = ∀
+ − = = −
 
⇒ ⇔
 
− + = =

 
ik!+,'N'+O)PQ-
Bài 5
iq'+V)Cp

+,'

'
- - -
AM BM CM= +
- - -
BN BM MN⇔ = +
BMN⇔ ∆
)Sr+C
·
·
·
3 3 3
f3 I3 L3BMC BMN NMC⇒ = + = + =
+,'
Bài 6:3
%'+U..a.WU. a4U.
-

%'+%+U`a5;k3
:
BCN ACM
BN AM
⇒ ∆ = ∆
⇒ =

U..a.4.
-

U. a4UU`4U
-
42]=C+,'
j
U`a
4U`Ua
≤

- - - -
- - -
AD AE DE AH+
= =
3EL
⇒
j
U`a

≤
- - -
- - -
AH AO R
≤ =
3EL
ik!CDj
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