Đề thi học sinh giỏi cấp quận vòng 3 môn Toán năm 2012 - 2013

PHONG GD&DT KY THI HQC SINH GIOI CAP QUAN V ~ N G 3 
~ U A N LONG BZEN M6n : TOAN 
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 
b) ~ ~ + i i x + 3 = ~ - x - l - ~ i 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 
Bii 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 thohmh: abc = 3(a+b+c). 
b) Cho a;b la 2. s6 .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 HC' 
c) Ggi P 18 giao di&m cda d u h g t hhg MN va dubng thing BC. D v h g t h h g AP cht 
dubng trbn d u h g kinh AH tai di&m K (K + A). Tinh s6 do cua g6c BKC. 
d ) Cho AB=6cm; AC=8cm . Tinh bhn kinh cGa duhg 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 ..................................... 
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