Đề thi HSG môn Toán lớp 9 năm 2017-2018 - Phòng GD&ĐT Thái Nguyên

TI{A<br /> <br /> PUBND THANH PHO<br /> NGLIYEN<br /> <br /> PHoNG<br /> <br /> rci rnr cHeN Hec srNH cror Lop e<br /> Nim \Oc20lt -2018<br /> MON: TOAN<br /> <br /> GrAo.pWJADAo rAo<br /> <br /> Thdi gian ldm bdi: 150 philt, kh6ng ke thdi gian giao<br /> <br /> ON CHiIqH THITC<br /> <br /> Bei 1 @,0 di6m). Nhd 6ng An dr)ng kh6a sO AC kh6a nhd nhrmg 6ng An qu6n m6t<br /> mOt khAu gdm ndm chfr s6 d6 mcr kh6a. Ban hdy girip 6ng An tim ra mQt khAu vdi<br /> c6c di6u kiOn sau:<br /> a. Chfi s6 thir ndm c6ng<br /> <br /> b. Chir<br /> <br /> sO<br /> <br /> cht sd thri ba bing<br /> <br /> eau ti6n nh6 hcrn hai lAn<br /> <br /> c. Chfi sd thri tu 16n hon chfr<br /> <br /> cht<br /> <br /> d. Chfi s5 tnri hai c6ng<br /> <br /> sO<br /> <br /> cht<br /> <br /> st5<br /> <br /> 14;<br /> <br /> th,i hai 1 dcm vi:<br /> <br /> tnfr hai 1 dcm vi;<br /> <br /> s6 thir ba<br /> <br /> bing<br /> <br /> 10;<br /> <br /> e. TOng ndm chft sO ta:0.<br /> <br /> Biri 2 (2,0 di€m). Vitlt<br /> <br /> Bii<br /> <br /> sO<br /> <br /> ti6p theo cria ddy s6 8179;6399;6237;2294;<br /> <br /> 3 (2,0 di€m). cho *=1,1i*zJs<br /> <br /> *G-2{r,Jn<br /> <br /> Hdy tinh gi6 tri cria bi6u thuc A= ("' -<br /> <br /> x6 +<br /> <br /> .<br /> <br /> t)2018<br /> <br /> Bii 4 (j,0 di€m). Cho tam gi6c ABC vu6ng cAn c6 AB : AC :2018cm.<br /> ld<br /> <br /> cilc di6m tr6n<br /> <br /> ?<br /> <br /> G9 D vd E<br /> <br /> AB vd AC sao cho AD: CE. Tim giStrinh6 nhdt cria DE.<br /> <br /> Bni 5 Q,0 di€m). Cho tam giSc d6u ABC c?nh bdng a, geiO lir trung di0m ctra BC.<br /> DWng g6c xOy: 600 sao cho Ox cit cpnh AB tai M, Oy cht cqnhAC tai N. Chrmg<br /> minh:<br /> a. Tam gi6c<br /> <br /> b.<br /> <br /> BC2<br /> <br /> MBO d6ng dang v6i tam gi6c OCN.<br /> <br /> :4MB.NC.<br /> <br /> c. MO ld phAn giitc cl<br /> <br /> ;a<br /> <br /> g6c BMN.<br /> <br /> MN ludn tii5p xric v6i mQt duong trdn cO Ainn khi g6c xOy quay quanh O vd Ox<br /> .at ae tai M; Oy chtAC tai N.<br /> d.<br /> <br /> Bni 6 (,0 diAm). 6ttg Binh l5i chi6c xe m6i cria 6ng di trong m6t s6 nguy6n gid<br /> v6i t6c dO 55km/h. Lirc Uit eau di c6ng tcy m6t chi vdo s6 on, trong d6 abc ld sO<br /> ,.c6 3 chir sO v6i a>I;a+b+cs7. KOt thric chuy6n di c6ng to m6t chi vdo s6 cba.<br /> Hdy tinh gi6<br /> <br /> tri<br /> <br /> ctta a' + b2 + c2 .<br /> <br /> -----------HCt----------<br /> <br /> Hq t6n thi<br /> <br /> sinh.<br /> <br /> 56 b6o danh:<br /> <br /> di<br /> <br />