trêng THCS k× thi häc sinh giái cÊp trêng n¨m häc 2009-2010
xu©n lam M«n : To¸n 8 (Thêi gian : 120 phót)
Hä tªn häc sinh :............................................................................................................................................................................................ ...Líp................................
Sè b¸o
danh
Gi¸m
thÞ.....................................................................................................................................................................................
......................................................................................................................................................................................................
.......................
Sè ph¸ch
-------------------------------------------------------------------------------------------------
§iÓm b»ng sè §iÓm b»ng ch÷
...................................................................................................................................................................
...
Sè ph¸ch
Bµi 1: (6 ®iÓm) Ph©n tÝch ®a thøc sau ®©y thµnh nh©n tö:
1.
2
7 6x x+ +
2. x32 - 1
3. Chøng tá r»ng A = (x - 3)(x - 5) + 4 > 0 víi mäi gi¸ trÞ cña x.
Bµi 2: (2 ®iÓm)
a/ T×m a ®Ó ®a thøc x5 + 32 chia hÕt cho ®a thøc x + a
b/ T×m sè d trong phÐp chia cña biÓu thøc
( ) ( ) ( ) ( )
2 4 6 8 2008x x x x+ + + + +
cho ®a thøc
2
10 21x x+ +
Bµi 3: (4 ®iÓm)
a/ Chøng minh ®¼ng thøc sau:
yx
yx
yx
x
y
y
x
yxxy
yx
−=
−
+
+
+
−
+
22
2222
:
1
b/ Cho
cba
z
cba
y
cba
x
+−
=
−+
=
++ 4422
chøng minh r»ng:
zyx
c
zyx
b
zyx
a
+−
=
−+
=
++ 4422
víi abc # 0 vµ c¸c mÉu sè kh¸c 0
Bµi 4: (6 ®iÓm) Cho tam gi¸c ABC. ë phÝa ngoµi cña tam gi¸c vÏ c¸c tam gi¸c
vu«ng c©n t¹i A lµ AEC, ABD vµ h×nh b×nh hµnh ADIE. Chøng minh
a/ IA = BC
b/ IA
⊥
BC
c/ Gäi M, N theo thø tù lµ trung ®iÓm cña ®o¹n th¼ng BD, CE. Tam gi¸c ABC
ph¶i cã ®iÒu kiÖn g× ®Ó ba ®iÓm M, A, N th¼ng hµng.
Bµi 5: (2 ®iÓm)
a) Cho x, y lµ hai sè d¬ng tho· m·n x2+y2-xy = 8 T×m GTNN, GTLN cña
M=x2+y2
b) T×m gi¸ trÞ lín nhÊt cña biÓu thøc: A =
Bµi lµm
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Kh«ng viÕt vµo ®©y
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------