Đề thi HSG Toán 9 Diễn Châu 2017-2018

Trtcs Dtal<br /> <br /> t+;<br /> <br /> PHONG GIAO DUC VA DAO TAO OTEN CHAU<br /> <br /> pt rnr voxc r, cHeN Hec slrlH cr6<br /> <br /> HrryEN Lop<br /> NAnl Hoc zorT-20r8<br /> ivrONI: roAN 1 inat gian ldm bdi I50 philt)<br /> <br /> 9<br /> <br /> q1(3,0<br /> @<br /> <br /> .<br /> <br /> b)<br /> <br /> arcm1<br /> Tim mQt s6 chinh phuong c6 hai chfi s6 bitit ring sO OO bd"g binh phuong<br /> r<br /> cria t6ng c6c chfl s6 cria<br /> Chtmg minh ring: Voi n ld sd tU nhi6n thi n5 - n chia h6t cho t0<br /> <br /> n6.<br /> <br /> Cffu 2 (6,0 di€m). Giai c6c phuong trinh sau:<br /> <br /> a)<br /> <br /> .<br /> <br /> ^l,t+3<br /> <br /> +JA<br /> <br /> =2;<br /> <br /> b) (.,6.5 -6)(r*J7*z'*ro)=r;<br /> c)<br /> <br /> x2 +3x<br /> <br /> +l = (x +Z>Jf +t<br /> <br /> .<br /> <br /> CAu 3(8, 0 di€n)<br /> <br /> Cho tarn gi6c ABC vu6ng cdn tpi A (BC: a). Gqi M le trunq di6m cria BC;<br /> G ld mQt tliOm tr6n cpnh ABlsao cho GB :2GA. C6c dudng thing GM vd CA<br /> cit rfiau tai D. Dudrng thEng qua M vu6ng g6c v6i CG tai E cdt AC t4i K vA<br /> 'rZ<br /> thang<br /> AB tai I .<br /> ^dudng<br /> La) TinhCG theo a;<br /> Chirng minh: .<br /> tam gi6c BCD;<br /> Sj:J:3e.t6m<br /> BCID h hinh vudng;<br /> Ogc: DE.<br /> GK cit DE tpi P. Chimg minh tam gi6c PGE cdn.<br /> <br /> tb)<br /> <br /> '<br /> <br /> 7<br /> <br /> Ciu 4(3,0 diem)<br /> <br /> a)<br /> <br /> Tim gi6 tri lcrn nhdt ctra bi6u thirc:<br /> p 2or7 2-4x<br /> -L<br /> <br /> :<br /> <br /> Cho<br /> <br /> -'::!.<br /> x'+2<br /> <br /> x, y,<br /> <br /> H<br /> <br /> n<br /> 6,<br /> <br /> z ld 3 sti ducrng thoi mf,n *' + y' + z' < 6<br /> <br /> Tim gi6 tri nh6 nh6t cria biOu thrlc:<br /> H€t<br /> <br /> Q=<br /> <br /> L * L*<br /> xy yz<br /> <br /> I<br /> <br /> zx<br /> <br />