Tài liệu bồi dưỡng HSG Toán THCS
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (338.11 KB, 36 trang )
n n
n n n n
a a a a a a a a
−
− −
= + + + +
!
"
#$%
&'%(#)*
+!
,
x x
= +
-
x N
∈
./
,0 !
"
#
1!(
2$%2
34 5*
6 *7
**
x
x
⇔ =
⇔ =
8
9
**
!
ab
(
/ :ab ba ab ba
+ +
M M
+
;
- / 6.ab a b a b Z a b
= + ∈ ≤ ≤
<#
=
- .ab ba a b
+ = +
>
?@AB-:.5
- . :
:
ab ba a b
a b
⇒ + = +
⇒ +
M
M
-?@AB-:.5.
C!
6a b
≤ ≤
( ) ( ) ( ) ( )
- . 7D D7 6E E6a b
⇒ =
8
9
7D/D7/E6/6E
"
#$
"
#%&'(#$
"
#)*
+$
"
#,-(.(/(0
- F1
"
G9
=
<
3
n
nthuaso
a =
3
n m m n
a a a
+
=
3
( )
m n m n
a a a m n m n N a
−
= ≥ ∈ ≠
- .
m n m n
a a
=
3H9$&
/ - .a a a a
= = ≠
3A$9
"
- . /- E. E/- . /- :. :
n n n n
x y x y x y x y
= = = =
3B$
=
I9
=
<J=
E/9
=
<
1
;
I/3B$
=
69
=
<J=
/9
=
<1
;
I/
,!
"
*
>
*
+
;
* * * * I
6 6
= = =
* E
* * D D - . D
= = = =
C!6K6
K
I : E E
6 D
⇒ < < <
8
9
*
K
*
!
*I
* *
−
M
*
I
5E
( )
*:
I
* *⇒ =
E
( )
:
* * : : : D *:
* * I I I I -I .
= = = =
*
*I
5-3*.
*I
5-
*I
3*I*
*
33*I*
*
3*
*I
.
L
*I
3*
*
33*
*
M
89 1
"
*
*I
5-*
I
.
:
E*
*I
E
*I
* *
⇒ −
M
1+$
"
#2%&3
4
#5
4
#
"
67
89#*5#
"
#*
"
:2
1. ;<
3,$
;
MNGOP2!Q>
;
Q!R
3G
;
!*
3G
;
(!E
3G
;
J=!D
3G
;
:!*
"
<6
4
62
. * *
n n
a a a a a a
−
⇔
M M
. : :
n n
b a a a a a
−
⇔
M M
.
n
n n i
i
c a a a a a
−
=
⇔
∑
M M
. 6
n
n n i
i
d a a a a a
−
=
⇔
∑
M M
*
. *:/I *:/I
. *:/D *:/D
n n
n n
f a a a a a a
g a a a a a a a
−
−
⇔
⇔
M M
M M
=<6
4
62&
@!S5
:
I
*
S
⇔
T-
3
*
3
I
3.4-
3
3
:
3.U
*
"
:
S5-
3
*
*
3
I
I
3.3-
3
3
:
:
3.
@V9
"
2W
*
5663
I
566663X
;
Y
"
*0
5(Q3!
54
54
:
54
X
;
Y
"
*03
5(1
"
4C!#
=
S5-(Q3
3
*
3
I
3.3
3-(1
"
4
4
4
:
.5(1
"
3-
3
*
3
I
3.4-
3
3
:
3.
B$>
9#Z0
>
#
;
#!
"
Q!
X
;
"
$
=
1
;
>
X
;
"
$
=
J=
;
#
=
!
@$
"
3
M
E
!@!7
7
37
M
6@$
"
7
D
3D
M
6-Đề thi cho
̣
n HSG
lớp 9 huyê
̣
n Văn Ba
̀
n năm ho
̣
c 2009 - 2010)
+
;
7
7
37
M
6[J
7
7
37
560
LJ
0
"
7
D
3D
457-7
7
37
4.3TD47-7.U
576046
56-70.
M
6
8
97
D
3D
M
6
>@!7
7
37
M
@$
"
7
D
3D
M
-[Z!
,+
"
6O2$\J!
**.
2. *
?
4
@7
"
:5
%9
( )
( )
*
*
. /
- .
* - .
n
n n n n n
n n
n n
a n N a b a b a a b ab b a b Z
a b a b
n k k N a b a b
−
− − −
∀ ∈ − = − + + + + ∈
⇒ − −
⇒ = ∈ − +
M
M
( )
( )
*
*
. *
n
n n n n n
b k N n k a b a b a a b ab b
−
− − −
∀ ∈ = + + = + − + − +
( )
* /
n n
n k a b a b a b
⇒ = + + + ≠ −
M
@
"
>GMN
@$
"
2W*
3E
3
M
*
>89#*5#
"
#*
"
:A
"
- @$
"
Y9J
B9J
"
$
"
3]1
"
>^5
#V
3+
;
$
;
>^50#V
3_#X
;
$
"
>^503#V
<#
=
#$%
#Z
;
$
"
1
B
3
4
#C3
4
*
"
:%D
*
* *
. * 7- .
. * 7- .
n n
n n
a n N
b n N
+ +
− ∀ ∈
+ ∀ ∈
M
M
.
D 6
n
n
+ −
M
*
. * 7
n n
a
−
M
38^5/`#V
3+
;
$
;
50#V$
"
*
* 7
k k
−
M
[J
*
* 7
k k
q
− =
3]1
"
>^503
*- .
* 6- * . 6* ** 7-6 * . 7
k k k k k k k
q
+ + +
− = − + − = +
M
8
9503#V
a
*
* 7
n n
−
M
(.A
$%
.
D *7
n
n
+ −
M
38^5`#V>
3D45
M
*7
3+
;
$
;
50#V$
"
D *7
k
k
+ −
M
[J
D *7
k
k q
+ − =
3]1
"
>^503
[ ]
D- . - D . D D -D .
k k
k k k k
+
+ + − = + − + + − − −
( )
*7 *7 E *7- E . *7q k q k
= + − = − +
M
8
9503#V
a
D *7
n
n
+ −
M
EFG#CG<6H62
$
=
9#!
"
7 E : 7:x y M
!
$
=
9#!
"
I I:xyM
!
"
4
E
B
3
4
#A
"
*
a)
b) ,$
;
MN1
"
M$
c) ,$
;
MN9J
"
C121
d) ,$
;
MN#X
M$$
"
67
67I5
4
#
1FG#@J6?267
B!
"
0$
"
>Z99
?@AB
_@BB!
"
Q
"
O>Z
.BQ
"
!9
X
Q<
;
"
!
Y
;
B
!9
!
*.B
"
(!2!#!
"
(>
9
!
>
9
"
21!9
5
0
*
0*
0
-.
8
(!($
"
O
;
"
<9*>^
!
&%!J
(W!
;
"
<9#!
"
2!-.B$(>
9
(0X$
"
<9
!2!
"
<
*
C!#!
"
$
"
O
;
"
<
*
$
"
!
.B!>
!_@BB
;
>
>
9!>
(Q
;
>
!#!
"
!_@BB-.
Y
;
B!9
>
!
"
'KC
L
"
!!D3!7
+
;
@
"
D3
7
⇔
I3I3
7
⇔
I3
7
⇔
I347
7
⇔
I4I
7
⇔
I-4.
7
!
"
-I7.54
7
8
95703-0
∈
B.
@
"
* D3
7
⇔
D34*
7
⇔
DD
7
⇔
D-4.
7
!
"
-D7.54
7
8
95703-0
∈
B.
'3
4
/$
"
8
(&
"
(Q
;
72!
"
;
2W##Q
(`$
"
!7
%
;
#!
"
;
(W
L
"
!@!(3I(!-(
∈
B.@$
"
2W3(
!
"
[J
3I(5 /3(59(
$
"
9
Ca
́
ch 1: 1
"
(`$
"
495-3I(.4-3(.53I(44(56(
B$>
9 49
C!
I9
,929
Ca
́
ch 2: ]1
"
_`$
"
I94 5I-3(.4-3I(.5I3I(4S4I(56
B$>
9I94
C!
I9
!
"
-I.59
Ca
́
ch 3 :]1
"
(`$
"
395-3I(.3-3(.53*(33(53(
B$>
9 39
C!
,929
Ca
́
ch 4: ]1
"
(`$
"
36953I(36-3(.53I(3636(563(
B$>
9 369
C!
69
!
"
-6.49
#$
%&
'
2!
"
"
;
2#
=
#$2
"
(`$
"
02
"
!
!
"
Q
(Q
;
0#!
"
$
"
-!
"
.!
(Q
;
;
%
;
I
;
%
;
9
1
"
(`$
"
49W0$
;
-$
"
!
;
(W. 1
"
(`$
"
39W
!2
;
(W
;
(%
;
I
;
(%
;
9
1
"
(`$
"
I94 W0$
;
( 1
"
(`$
"
369W
!2
;
((W
L
"
>@$
"
2W
9&%
-4.-3.
!*I
"
! !
"
-4.-3.
-.5
-4.-3.
-.
9&%
1
;
4>
3
J=
2!J=!
"
Q
(1
"
;
I
"
;
"
!D-*.
<-.>
-*.92-4.-3.!9
>
D
8
9-4.-3.
*I
;L
B
:E
4
E2
"
C
B
*%&#$
"
#
L
"
'O0!:
M$!7
M$:
"
+!
!:M$!7M$:
Ca
́
ch 18
0W!:!
"
M
:032-02
∈
B2K:.2!
#!
"
2:M$7M$:
,'%:!7M$:
:*6*E2!#!
"
;
!
"
*E
!:M$>
925*E
,'_O!
"
M
:03*E
*E
Ca
́
ch 2!
"
4
:
⇒
43
:
⇒
36-.!
"
4:
7
⇒
4:3I
7
⇒
36
7-*.<-.>
-*.9236
:
'_O!
"
"
_O2
5*E
Ca
́
ch 35: 35793:
⇒
: 5:93*93I
⇒
*-93*.
:
⇒
93*
:
+
"
2
'_O
;
9(W
"
2
'O
;
(W73:5*E
L
"
!
!
"
(Q$
=
!!!
M$*
!*
M$6D
"
Ca
́
ch 1:!
"
3*5*936D
⇒
59394I
⇒
94I
⇒
9503I-0
∈
B.
⇒
5*-03I.36D5*036IE
C!!
"
(Q$
=
0556IE
Ca
́
ch 2:< 59394I92
- 49.594IB b9
94I
≥
⇒
9
≥
I:
⇒
!
"
Z%(Q$
=
8
9 59M!#!
"
95I56IE
Ca
́
ch 3!
"
5 3*
*5* 3I7DI -.
LJ
0
"
5*936D
5*93*DD -*.
<-.>
-*.92*45*- 49.36IE
⇒
5*- 49.36IE
8
!
"
(Q$
=
56IE
MN'I1''
()*
+,-./
'
01234#
"
'
.!
L
"
(2WX
;
;
"
(WDI?@AB
;
"
(WE
+
;
+!
;
>
(-
≤
(.
!
"
-(.5E5Ec/(5E(c2!#!
"
-c(c.5-(c(/
∈
B.
C!3(5DIE-c3(R.5DI92c3(c5I
@!
J
c(c9
!
"
X
;
(WI-c
≤
(c.#$%
c : C!#!
"
E D
(c 6 ( 7D EE :I
L
"
!
!
"
"
(W?@AB(W:
"
+!
;
>
(-
≤
(.
!
"
-(.5:5:c(5:(c2!#!
"
-c(c.5
C!(5*:c(c592c(c5*5I
@!
J
c(c9
!
"
"
(W*-c
≤
(c.#$%
c C!#!
"
: :
(c * I ( E *
3
'
0
'
,5
.6
7
3##
"
'
+,89234#
"
'
.!
L
"
>
(2W?@AB
;
"
(W_@BB
;
"
(W6
"
+!
"
;
>
(
;
$
;
≤
(
!
"
-(.55c(5(c-c(c.5/c
≤
(C!#!
"
(5c(c-.
LJ
0
"
(5T(U-(.5656 -*.
<-.>
-*.92c(c56!
"
"
2$\%
c * : 6 C!#!
"
* : 6
(c 6 I: D ( 6 I: D
)*
234#
"
+,0:.$
'
;
L
"
O@!>
(-b(.
.@$
"
2W!(
-(.5(
(.@$
"
2W0X!(
?@AB
;
(W?@AB
;
'>
M$2!1
"
&!'
.C
"
1
"
2#!
"
?@AB-7*:E.
"
<
.L!
$&
;
>
(`
$&
;
([
;
!
M!
!((
$&
;
>
(8
9-(.5(
(.+!
2
M$2!1
"
!(-b(.!
"
5(032-0
∈
B.
$
"
2W-(.5-(2.
>
9>
(
!M
2!MM!#!
"
$&
"
;
>
(!
$&
;
(>
2-.
[
;
!
(>
2
!M
!MM!#!
"
$&
;
(
>
2!
$&
;
>
(-*.
<-.>
-*.92
%
"
$&
;
>
(>
%
"
;
(
>
2(WC!#!
"
&O2!
%
#!
"
!
(W$
"
-(.5-(2.
.7*:EM$E67*:E.5-:EE.
:EEM$D-:EE.5-ED./
E!D-ED.5D8
9-7*:E.5D
B
1
"
+
;
$
;
0X!(>
!(M$2
(!
2
M$2
*
2
!2
*
M$2
2
4*
!2
M$2
c
2
!2
M$-M
=
9(
2
2
*
2
M
=
9
;
M
1
"
$
=
M!#!
"
Y
"
2
2
;
0
"
>^QM$(W.1!$
"
%
;
>
"
MN2!
"
-(.5-(2
.5-2
2
*
.55-2
c
2
.52
->
2
!2
.
B$>
9?@AB-(.
2!M
=
9
"
1
"
!(/(!2
/2
!2
*
/2!#!
"
2
2
*
M$2!
"
1
"
1!$
"
2
2!
$#J
"
$
7* :E
:E E
E D
*
8
QM
=
91
"
$2#$%
!
!
"
d4
2$\%
?@AB
;
(
?@AB
;
2X
?@AB
;
0
Y
;
>^$
"
(
O0676
B
6
9
!
"
?@AB(WB!
"
"
0
"
"
;
!
"
$&M9O
L
"
@$
"
2W
.-0
"
.
9
(.1
;
9
.*3>
3-
∈
B.
9
"
<
.+!
M
∈
?@-*3*3.
⇒
-*3.4-*3.
M
⇒
*
M
⇒
M
∈
e/*f
B$M≠*>
M
$&
;
1
;
8
9M5
.+!
M
∈
?@-*33.
⇒
-*3.4*-3.
M
⇒
M
⇒
M5
L
"
!
#!
"
"
63*I>
3I
"
9
"
+
;
$
;
63*I>
3I
!9M
63*I4-3I.
M
⇒
*
M
⇒
M
∈
e*/f
[Z0
#Z-63*I3I.5
M≠*>
M≠`M≠>
3I
0X!LM≠*
;
!
"
"
OQ2!63*I>
3
I0X!*O9
63*I
1
;
⇔
61
;
⇔
1
;
3I
1
;
⇔
1
;
⇔
1
;
8
9#Z0
#!
"
-63*I3I.5
1
;
=)*
234#
"
'
0>6
'
+,
L
"
?@AB
;
*>
63I-
∈
B.
+!
M
∈
?@-*463I.
⇒
*-63I.6-*4.
M
⇒
7
M
⇒
M
∈
e/7f
!
"
*4
7
⇔
*4D
7
⇔
*-46.
7
⇔
46
7
⇔
⇔
57036-0
∈
B.
B57036
*4
7>
63I56-7036.3I57603D:
7M!#!
"
-*463I.57
B≠7036
*4
0X!7M!#!
"
-*463I.5
L
"
!
?@AB
;
*
.-
+
nn
>
*n 3-∈Bg.
"
<+!
M∈?@
+
+
*
*
.-
n
nn
n-n3.
M>
*n3
M
,92n-*n3.4n-n3.
M$
"
n
*
M
<n-n3.
M>
n
*
M92n
M
!
"
*n3
MM!#!
"
MM5
8
9?@AB
;
*
.-
+
nn
>
*n3(W
@*5
4
"
*P6
:9,Q0
BM
"
2<9
;
QS5
(
9
h
$%
"
$&
;
S(W- 3.-93.-h3.
>
9$&
;
S
!
"
M
2!#!
"
!
"
3
"
!
-
*
.
!
"
93
"
!
-
((
*
(
9
.
!
"
h3
"
!
-
*
h
.
C!#!
"
$%
"
$&
;
S(W- 3.-93.-h3.
L
"
'O!
"
*$&
"
F
"
;
21!9
B5
(
9
h
!
"
- 3.-93.-h3.5*
-
≥
9
≥
h
≥
≥
.
,*!
"
(Q
"
>
Q
"
;
Q9Z1!&%
*5*5E*5I5**
]1
"
"
2$\%
.$
"
Q1!9a#!
"
35* 5@!
1!
9'O
*!
"
'O2!2$\%
9
*
(.$
"
<9
a#!
"
- 3.-93.5E*!J
- 3.-93.5IM!#!
"
5:95!J
5
95*[`'O!
i9'$
"
>^&!
"
5*
:
56E!J
5*
*
57*,'O2!2$\%
9
7*
.$
"
(<9
a#!
"
- 3.-93.-h3.5** 5*95h5,'O
*
*
:5E
,!
"
(*
7*E2!(2$\%
O9'O!
"
*$&
E
;RS=TUVWUNWX;
=
Y
79
]1
"
"
M
=
9
.C
=
9*
(.C
=
91
;
:7.C
=
9
"
!M$I7
2!
"
M
=
92X=
0<
$
"
#Z&%
#$
"
!
2$&!
"
Q#%>
#%>
9
%
;
M
=
9./
*%
;
M
=
9
(./
%
;
M
=
9.!
"
M
=
92
M
=
9Q
]1
"
M
=
9QI7E6
$
=
;
M
=
9
,
$
"
E
;
M
=
9
9
6(WI3-E4./
$
"
;
M
=
9
9
I3-4.5
X
;
Y
"
QM
=
9Q!
"
#
>
$
=
M
$
"
;
M
=
9Q#!
"
-0
"
.(W
5
3-.M -.
&
"
L
"
Z
"
4
6
Y
79
I37333*:3*D3-X
.
>S5I3733*:3*D3
S53*D3*:33373I
*S5-I3.3-73*D.33-*D37.3-3I.5-I3.
C!#!
"
S5
-I .
7:
*
+
=
X
;
Y
"
QM
=
9Q!
"
#
X
;
;
#!
"
#$%
"
$
*
.-
naa
S
n
+
=
-*.-g.
2$\%
#J
(
X
;
;
(J
"
#
<(W
3*3335
- .
*
n n +
-.
"
Y
7A
"
L
"
$
"
;
"
M
=
9#$%
>1!Y9
.D:*I: -.
(.*IE*6: -*.
.E: -.
M.*:7*E -I.
.C
=
9-.!
"
`>M$&M
/*I/:/IE/:7
LX=
;
M
=
9-.
Q
"
;
1!1!$
"
&%
1!$
"
O
*#%>
@
"
1!$
"
O
M
=
9*I:M
=
9
9!
"
$
"
C!#!
"
$
"
;
M
=
9-.(W*5*
(.C
=
9-*.!
"
`>M$&M
IE76*:
,
$
"
;
M
=
9I7
3665*6D
,
$
"
;
M
=
9-*.(W*6D5D6I
.C
=
9-.!
"
`>M$&M
* * I I: :E
/ / / / /
* * * * *
,
$
"
;
M
=
9-.(W
::
*
=
M.C
=
9-I.!
"
`>M$&M
3
*
3*
*
3
*
3I
*
3:
*
,
$
"
;
M
=
9-I.(W3
*
5
1[;X+
$
=
$
"
0>Z
"
;
M
=
91
;
:7
*.
"
X
;
"
1
;
!
"
$
=
(.
"
X
;
"
J=!
"
$
=
@!
"
!
;
M
=
9
(W*90Wj
/3*/3*3/ 3*33I/
I.8
"
;
M
=
9<#
!
QS
"
X
;
"
$
=
;
S
(.@k'$2><#
:a
"
2<9l$
"
<97&
(W(!j
E
"
S5*:
(W(!$
=
j
7.
"
_5D6I7I!
"
(!1!*0
"
2<9
j
(.
"
@5*6!
"
(!<0
"
21!
9j
D@!
"
(!#X
\
"
;
;
M
=
9
7:I7 -.
*6E*76 -*.
62!M
=
9*66!
"
`!
#$%
ZO(!#!
"
X
;
(O0^#$%
!
!Dj
@M
=
90
<!
"
-
"
!
"
#$%
#J
2!MO!J
.
-.-*.-I:E.-7D6.-*I:.
.
#
;
!
"
$
"
(.
"
X
;
"
Q!
"
$
"
@!,
53*
,
*
53I3:
,
5E373D36
,
I
533*33I
"
,
*
"
$
"
:
;
"
M
=
9
.E/*7/D/
(.I/I7/7/
@!S533
*
3
33
*
_5
*
*
"
_4S
I@!S53I3I
*
3I
33I
66
_5I
@$
"
2WSK
B
:
"
"
2
;
(`$
"
.S56366366633666
:$
=
(._56366366633666
*$
=
=TU\+]'^;;RSVWUNWX;
C
=
9
"
>1!Y9
#
=
#$%
2
(
9%
;
;
#Zm@
"
k
J
"
$
;
>
n
;
"
#$%
>1!
"
Y9
O#
L
"
"
D*
++++=
A
!
"
7*
++++=
A
-.
D7*
++++=
A
-*.
AO9-.2<-*.#$%
*S5
E:E
E:E
E:E
D
=−=
C!#!
"
E:E
*D
=
A
L
"
!
"
X
;
#
;
"
M
=
9
.
⋅⋅⋅
:I
I
*
*
(.
⋅⋅⋅
E
7E
EE
E
.
"
9
"
2R
.-
*
*
*
*
+
=
+
−⋅⋅⋅=−=−
nnnn
C!#!
"
=+⋅⋅⋅++
*
*
=−+−+⋅⋅⋅+−+−=
66
*
*
=−=
(.2$&>
"
nEEE7EEM$&M
E/E/E/
E*/
$
"
;
M
=
9!
"
M
-:4I.-:3.
@
"
X
;
S5
:I6E
E
E
E
+⋅⋅⋅+++
#$
%&
'
<
: : :
/ / /
E E E E I6E : I6E:
− = − = ××× − =
X
;
Y
"
.:.-I:-
:
:
I:
+−
=
+
−
−
nnnn
C!#!
"
:
:
:
:
I6E
E
E
:
=−=−+⋅⋅⋅+−+−=
A
