PHONG GD&DT KY THI HQC SINH GIOI CAP QUAN V ~ N G 3
NIm hqc 2012-2013
Nguy thi: 31/01/2013
Thui gian lam bai: 150 phzit
a) Rut gon biku thirc: A = 2\j4-\/5+\/21+480
0-Ji
b) Tim chc gil tr/ ciia x d i bi6u thirc sau c6 giii tri nguy&n M = 6
X + ? & + Z
Bai 2 (6 diim)
1 Giai cac phumg trinh sau:
a) J Z Z T + x + l = ~ j x - 2
2 T i m c l c s 6 n g u y ~ n x v a y t h o ~ m h : x2+xy-2010x-2011y=2012
B i i 3 (2 di&) Cho a > 0, b > 0 v h a + b 5 I Tim giP tri lim nhAt cua bi&u thirc:
a2b2
A =
a4b2 + u2b4 i- a* + b2
a) Tim tit cachc b6 ba sanguydnta khbnhau a, b, c t h o h m h : abc = 3(a+b+c)
b) Cho a;b la 2 s 6 .guyen Chimg minh r h g 5(a+b):+ab chia h6t cho 441 thi ab
ciing chia hkt cho 44 1
Biii 5: (6 di&) Cho tam giac ABC vuBng tai A, (AB<AC) co dubng cao AH vB 0 la bung didm cGa BC Duhng trbn t h I dubng kinh AH cht AB, AC la11 luqt tai M v i N
a) Chimg minh : Tu giL BMNC nGi tiip
1 1 1
b) Goi D II giao di&m clia OA va MN C h h g minh - = - + -
AD HB H C '
c) Ggi P 18 giao di&m cda d u h g t h h g MN va dubng thing BC D v h g t h h g AP cht
d ) Cho AB=6cm; AC=8cm Tinh bhn kinh cGa d u h g tron ngoai tikp tam g i b BMN
Ch ti Ji: Gidm fhd coi fhi klr 8ng giai thich gi thin
Tkisinh n@p 11pi d$ thi srru klti tlii .vo~~g
Hr, ten thi sinh: SBD
I