ĐỀ THI Học sinh giỏi TỈNH ĐỒNG NAI 14-15

HE cHiNH TrnJC THI CHON HOC SINH GIGI L0, v&i mQi s6 thvc x.. Khong co 3 dUOngtrim cimg di qua 1 diem Hoi 10 dUOngtrim da cho chia m~t phing thiinh bao nhieu ph:ln.. 4,5 diSm Cho tam gia

sO GIAO DUC VA DAO TAO

TINH DONG NAI

HE cHiNH TrnJC

THI CHON HOC SINH GIGI L<1P 9

NAM riQC 2014-2015

Mon: Toan

Thai gian lam bai: 150 pMt

(D€ thi nay g6m 1 trang, co 5 cau).

Call 1 (5 diSm)

1) Giai phuongtrinh (} - 4x+ 3)(} - 6x+ 8)=3

2) ChUng minh x 4 - 5} + II} - 12x+ 6>0, v&i mQi s6 thvc x.

Call 2 (3,5 diSm)

Tim cae s6 nguyen x va y thoa: 3} + 5y2 = 255

Call 3 (4 diSm)

1) Cho hai s6 thvc a, b thoa a?: 0 va 3a?: b ChUng minh:

2)Tlmcacsothvcxvaythoa: 2-V(x+2)(3x~y) =y+6'

Call 4 (3 diSm)

Trong mQt m~t phing cho 10 dUOngtrim thoa cae diSu ki~n sau:

{V&i 2 dUOngtrim my y luon dt nhau t:;1i,2diSm phanbi~t

Khong co 3 dUOngtrim cimg di qua 1 diem

Hoi 10 dUOngtrim da cho chia m~t phing thiinh bao nhieu ph:ln.

Ciu 5 (4,5 diSm)

Cho tam giac ABC co ba goc ABC, BCA, CAB dSu Iigoc nhQn Hai dUOng cao

AD, BE cua tam giac ABC dt nhau t:;1idiSm H GQi M, N wong Ung la trung diSm

hai dO:;JllAB, DE DuOng th~ng CM cit dUOng trim ngo:;1itiSp tam giac CDE t:;1i diSm P khac C DuOng thing CN cit dUOng trim ngo:;1itiSp tam giac ABC t:;1idiSm

Qkhac C

1) ChUng minh MD la tiSp tuySn cua dUOngtrim ngo:;1itiSp tam giac CDE.

2) Chung mlnh CE = PE'

3) Xac djnh dUOngtrung trvc cua dO:;JllPQ.

:HET

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