S GIO DC V O TO

NG THP K THI CHN HC SINH GII LP 9 THCS
CP TNH NM 2011 THI MễN: TON
Ngy thi: 13/3/2011
Thi gian lm bi: 150 phỳt (Khụng k thi gian phỏt )
( thi gm cú: 01 trang)
Cõu 1: (3 im)
a) Thu gn biu thc: A =
4 10 2 5 4 10 2 5
+ + + - +
.
b) Chng minh rng s B di õy l s chớnh phng:
B
{
2011 sụ' 1
11 1
= x
{
2010 sụ' 0
1 00 0 5
+ 1.
Cõu 2: (4 im)
Cho biu thc:

+
.
c) Tỡm giỏ tr ln nht ca Q.

Cõu 3: (5 im)
a) Gii phng trỡnh : ( x
2
+ x + 1)( 2x
2
+ 2x + 3 ) = 3( 1- x x
2
).
b) Gii h phng trỡnh :
ù
ợ
ù
ớ
ỡ
=+-+
=-++
0441
511
yx
yx

c) Cho a, b, c l di 3 cnh ca mt tam giỏc. Chng minh rng:

( )( )( )
abc a b c b c a c a b
+ - + - + -

a) Chng minh rng: Ba im C; M; D thng hng.
b) Chng minh rng: CD l tip tuyn ca ng trũn tõm O.
c) Xỏc nh v trớ ca im M sao cho tớch AC. BD ln nht.
HT

H v tờn thớ sinh: ________________________ S bỏo danh: ___________________________

Ch ký GT1:_____________________________

Ch ký GT2:____________________________
THI CHNH THC