S& GL&O DVC VA DAO TqO KY THI HQC SlNH GTOT THANH P H ~ - LOP 9

NAM HQC 2012 - 2013

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HA NO1 ---------------------

1 DC C H ~ N H THOC 1

Man: Toan NgAy thi: 05/4/2013 Thlri gian Iirm bai: 150 phiit ( ~ e ' thi g&n OI trang)

a) Tim c i c s8 thuc a, b sao cho da thuc 4x4 - 1 Ix3 - 2ax2 + 5bn - 6 chia h i t cho

triciia P v6i a = 4 + & vB b = 4 - & .

Bai 2 (5 diem).

~ 6 ~ ~ - ~ ' - . r y + 5 ~ + 5 y - - 6 = 0

a) Giai h$ phumg trinh:

1 2 0 ~ ' - y 2 - 2 8 ~ + 9 = 0 .

b) Tim c l c s6 nguygn x, y th6a m2n:

Bli 3 ( 2 dikm). Cho ba s8 thqc a . 6 , ~ dumg thda m5n - + - + - = 3. C h h g minh:

l a L b 3 c

Bhi 4 (7 diin). Cho tam gihc AAC co ba g6c nhgn, noi tiip dubng trbn ( 0 ) va AB < AC. Cac duhg cao AD, BE, CF clia tarn giac ABC gap nhau tai H . Gpi I la giao diem hai dubng thing EF vB CB. D u h g t h b g A I tit ( 0 ) tai M ( M khhc A).

a) C h h g minh n5m diem A, M , F , H , E cung nim t r h rn+t d u h g tron. b) Goi N Il trung didm cua BC. Chirmg,minh ba di&m M , H , N t h k g Mng. c) C h h g minh BM.AC + AM.BC = AB.MC.

Bhi 5 (1 dikm). Cho 2013 diem 4,4, ...,A,, v8 d u h g trbn (0;l) tcy 9 c h g n k n trong mat p h h g . Chirng minh tren duimg trbn ( 0 ; 1) do, ta lu6n c6 the tim duuc mat diim M sao cho MX, + MA, + .. . + hQ,,, 2 20 13.

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