Hướng dẫn giải đề thi HSG Toán 7 huyện Thái Thuỵ, Tỉnh Thái Bình, năm học 2010-2011
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (1.18 MB, 11 trang )
! "" "
= − − − − −
÷ ÷ ÷ ÷ ÷
#$%%&'()&*+%,-./0'/1%
2 -
-
−
=
−
3&'()&*+
41&$'(5&6&'()%,0'/1%78-9:-
;0-;%%'6%"∀-
∈<=8=0=%∈<9=#%%>?=0=%.@%'6%"
41&$'.1%-
; -;2A&%B&'>$
41&$'(5&6%BCD*E?05&
""
"
= = =
#
""
""
" "
+ + +
=
÷
+ + +
4%%.1%:-*FG-*
H-F
IJ:*
;F
41&$'(5&6-G*GF:"#KLJML'.1%.?'
!
N'=O=PMQMRSML(&.'/$%%%TJ4=4=J%,∆J4UV&L'
∆J4KW%%.TX&PYKLO%PYK&&B%KL05&P=OK&&B%KL
05&O
41&$'(5&IO;O;P;PY:J;4
Z∆YPKL∆O
41&$'∆YML$&'%K&%[
"
#$&'()M\]%,0'/1%
- ^- "
J
- -
+ +
=
+ +
!"#$%
&'(!
#$%&
! "" "
= − − − − −
÷ ÷ ÷ ÷ ÷
""_ "" ""_""
! "" " !"""
− − − − −
= × × ××× × =
"
=
'()*+,-.
8 9 8 9 8 9
! !
− −
− − −
= − − − − = =
÷ ÷ ÷ ÷
8`9
(#)%B
2 - 8- 9
- - -
− − −
= = = −
− − −
/3&'()&*+#Va'%B
- −
∈<⇔ ⋮8-G9⇔-G∈b8 9
c#b8 9:d±I± e=+M3V0X&
-H H H
- H 2
H!
8a$D9
8a$D9
H
8a$D9
"
8a$D9
c3*K\'-∈dHII I2e#3&'()&*+
(#)c#-∈<+./3&'()&*+#Va'%B
82G-9⋮8-G9⇒82G-;-G9⋮8-G9* ⋮8-G9⇔-G∈b8 9
Z.B'6Vf%&'a'R%%
c#78-9:-
;0-;%⋮"∀-∈<+
H c\'-:"#78"9:%⋮"
H c\'-:#789:;0;%⋮""⇒;0⋮"8K#%⋮"9
89
H c\'-:H#78H9:G0;%⋮"⇒G0⋮"8K#%⋮"9 89
g89KL89*(8;0;G09⋮"*⋮"
⇒⋮"8K#
M
"9 8 9
g89KL8 9*(0⋮"
c3*6&'()%,0'/1%78-9:-
;0-;%⋮"∀-∈<=8=0=%∈<9=
#%%>?=0=%.@%'6%"
'()*+,-.
6&'()%,0'/1%78-9:-
;0-;%⋮$∀-∈<=8=0=%=$∈<KL$
M
9=#%%>?=0=%.@%'6%$
(#)%B
- - 2+ +
_ _
- - - -
^ ^ ^ h
= + + + = + + +
÷ ÷
_
- - - - - -
! ! ^ h ! ! ! h
= + + + + = + + + +
÷ ÷ ÷
-
! h
= + +
÷
c#
- "
!
+ ≥
÷
∀-⇒
- "
! h
+ + >
÷
∀-
c3*.1%-
; -;2A&%B&'>$
(#)ij%%(Rk&SV
H ij-≥"#-
≥"KL -≥"⇒-
; -;2≥2`"
H ijH=2l-l"#-
`"∀-KL -`H!=2⇒-
; -;2`"=2`"
H ij-≤H=2#-l"KL-; ≤"
⇒-
; -:-8-; 9≥"⇒-
; -;2≥2`"
.B.1%-
; -;2`"∀-
c3*.1%-
; -;2A&%B&'>$
(#)m
""
"
A
= = = =
⇒
""
""
" "
A
= × ××× =
89
VCf&%]%,CD*E?05&=%B
"" ""
" "
A
+ + +
= = = = =
+ + +
⇒
""
""
""
"
A
+ + +
=
÷
+ + +
89
g89KL89*(
""
""
" "
+ + +
=
÷
+ + +
(#)m
""
"
A
= = = =
⇒
"" "
A = A == A= = =
⇒
""
"
A =
⇒
""
"
A
=
mA%=
"" "" ""
"" " "
" " "
A A A A8 9
+ + + + + + + + +
= =
÷ ÷
+ + + + + + + + +
""
A=
c3*
""
""
" "
+ + +
=
÷
+ + +
(#)c# -G*GF:"⇒-:*;F
%B :-8*FG*
GF
9:8*;F98*FG*
GF
9
:*
FG*
G*F
;*F
G*
FGF
:H*
GF
:HJ
.BKLJML'?.?'
(#)c#-G*GF:"⇒-G*:F=-GF:*
ij;J :-*FG-*
H-F
;*
;F
:-*FG8-*
G*
9G8-F
GF
9
:-*FG*
8-G*9GF
8-GF9:-*FG*
FGF
*:*F8-G*GF9
:*F":"
c3*KLJML'?.?'
(#*)%BJ:*
;F
:*
8-GF9;F
8-G*9:-*
G*
F;-F
G*F
:-*
;-F
G8*
F;*F
9:-*
;-F
G*F8*;F9
:-*
;-F
G-*F:H
.BKLJML'?.?'
!
(R\%6=%1&$'.)M
n+$,-"&.,/#0
$$1,234,567
Chng minh
ij∆J4%BML(&.'/$%,J=OML(&.'/$%,4%Q%1&$'
OooJ4KL
O J4
=
(+'.?'%,'%,'OM]*.'/$P%O:OP
ij∆OPKL∆O4%B
O:O48&9
·
·
OP 4O=
8.?'.E9=
O:OP8%%Cp&9
+∆OP:∆O48%&%9⇒P:4=
µ
µ
4=
'&B%
µ
KL
µ
4
qK)(Mr(&05&+Poo4
ij∆PKL∆J4%B
:J8&9
·
·
P J4=
8.s&K)=Poo49
P:48%1&$'(+9
+∆P:∆J48%&%9P:J4=
µ
µ
J=
'&B%
µ
KL
µ
J
qK)(.s&K)05&+OooJ4
tT'%BP:O8%%Cp&9=J4:P8%1&$'(+9+
O J4
=
Tr li bi ton :
g&'a'6P:PJ=P:PY⇒P:PJ:PYRu&pO:O:O4
VCf&.)Mq(+%BO:
J
=P:
4
⇒P:O8:
J
9=O:P8:
4
9
.BO;O;P;PY:P;O;O;P:P;O:J;4
c3*O;O;P;PY:J;4
VCf&.)Mq(+%BOooJKLPoo4
Z*(
·
µ
JP =
8Mr(&9=
·
µ
4O =
8Mr(&9⇒
·
·
µ
JP 4O = =
ij0(Rk&SV
∆J4%B
µ
"
_"<
89⇒
·
·
"
JP 4O _"= <
Y'.B
H 'PJ5$&'v''PYKLP+
·
·
·
µ
"
YP YPJ JP _" = + = +
H 'O45$&'v''OKLO+
·
·
·
µ
"
O O4 4O _" = + = +
Z*(
·
·
YP O=
8:
µ
"
_" +
9
ij∆YPKL∆O%B
PY:O8:P9
·
·
YP O=
8%1&$'(+9
P:O8:O9
⇒∆YP:∆O8%&%9
∆J4%B
µ
"
_">
89⇒
·
·
"
JP 4O _"= >
Y'.B
H 'P5$&'v''PYKLP+
·
·
·
·
µ
" " "
YP YP P _" h" JP " = + = + − = −
H 'O45$&'v''OKLO+
·
·
·
·
µ
" " "
O O O _" h" 4O " = + = + − = −
Z*(
·
·
YP O=
8:
µ
"
" −
9
ij∆YPKL∆O%B
PY:O8:P9
·
·
YP O=
8%1&$'(+9
P:O8:O9
⇒∆YP:∆O8%&%9
∆J4%B
µ
"
_"=
8 9⇒
·
·
"
JP 4O _"= =
Z*(0.'/$Y=P=X&L&KL0.'/$=O=X&L&
Y'.BA&sT'%%$&'%YPKLO+A&/
c#OooJ+
·
·
PO JP=
8Mr(&9
U(Rk&SV=%B∆YP:∆O⇒Y:=
·
·
·
·
PY O=PY O= =
L
·
·
·
·
·
·
·
·
· ·
"
Y PY PO O PY JP PY PY YP PY _"= + + = + + = + + −
:
" " "
h" _" _"− =
∆Y%BY:=
·
"
Y _"=
+ML$&'%K&%[T'
U(Rk&SV=%B∆YP:∆O⇒Y:=
·
·
·
·
PY O=PY O= =
L
·
·
·
·
·
·
·
·
·
·
"
Y PO PY O JP PY PY h" P PY PY= − − = − − = − − −
:
·
·
·
" " " "
" 8YP PY PY9 " h" _"− + + = − =
∆Y%BY:=
·
"
Y _"=
+ML$&'%K&%[T'
U(Rk&SV =
Y P PY 84 J9
O O 8J 49
= + = +
⇒
= + = +
Y:
L
·
·
PO JP=
:_"
"
∆Y%BY:=
·
"
Y _"=
+ML$&'%K&%[T'
B$MT'=%B∆YK&%[T'
"
8- - 9
J
- - - -
+ + +
= = +
+ + + +
%B-
;-; :-
;-;-;;:-8-;9;8-;9;
:8-;9
;
c#8-;9
≥"∀-⇒8-;9
;≥∀-
]05&-a*(⇔-;:"⇔-:H
-
;-; :8-;9
;`"∀-+
J
$-
⇔
- - + +
$-⇔-
;-; $'
]*&'()w]%,-
;-; 05&⇔-:H
c3*&'()M\]%,J: ;
: =2⇔-:H
/$01203%45
