ĐỀ THI Học sinh giỏi TỈNH ĐỒNG NAI 14-15

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: (-v3a-b~~)U3a-b +3~)=2-va(3a-b) -b. . .:. ., {6X + xy - 2 = 0 2)Tlmcacsothvcxvaythoa: 2-V(x+2)(3x~y) =y+6' Call 4. (3 diSm) Trong mQtm~t phing cho 10 dUOngtrim thoa cae diSu ki~n sau: { V&i2 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 Ii goc nhQn. Hai dUOngcao 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 dUOngtrim ngo:;1itiSp tam giac ABC t:;1idiSm Qkhac C. 1) ChUng minh MD la tiSp tuySn cua dUOngtrim ngo:;1itiSp tam giac CDE. . . CD PD 2) Chung mlnh CE = PE' 3) Xac djnh dUOngtrung trvc cua dO:;JllPQ. :HET " . 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 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 Ii goc. 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 dUOngtrim ngo:;1itiSp tam giac ABC t:;1idiSm Qkhac C. 1) ChUng minh MD la tiSp tuySn