ĐỀ THI VÀ HƯỚNG DẪN ĐỀ HSG TỈNH NGHỆ AN - Năm học 2013-2014

so cnsor NcuD lN on csiNs rstJc i' Tt+cs Vil, L3: xV rHt cHQN HQC THI GIol LoP e Ndm Hgc 20.13-2014 Mdn Thi: TOAN - Bing A Thoi gianr 150 phut (khong kA thoi gian giao d€1 CAu 1 (4.0c1i6m). a, Chung minh rdng t6n t4i s6 tq nhidn frsao cho 20130 -l chia het cho l0 b. Tim mgi sO nguyOn x sao t1's )c2+28 ld s6 chinh phuong Cdu 2 (6.0 tli6m). a. GiAi phuong trinh: ^t+r'-;y1: -2'[7 - -+1 =9x-3 b. ciai hQ phuong trinh: \''l':*: =t .r'::' I x zxY-Y =z Cdu3(3.0eli6m).ChocdcsdthucducrnEX,l'zth6amlnxy+yztzx=t' Tim rnin c6a P: ::-n r- * x+y y+z z+x rron tai c, D(c nam gioa M vd D) cung CAD nho hon curtg CBD' Gqi /J ld giao dicnt gba AB vsi OM. a. Chung minh 5Eb = zSnc b, Tir o ke tia or vu6ng goc voi cD cattia BA o K' Chu'ng minh KC vi KD la tiilr tuy6n cua dudng tron O C6u 5 (2.0 rli6m). Cho ducrng gAp khuc khep l<in co clQ dai bang l 'Chung nrinh rAng lu0rr t6n t4i mQt hinh trdn c6 b6n kinh p: I chua todn b0 cluirng gAp khuc dti 4 Ho v2r tOn thi sinh Sd b6o danh . CLr. trut !! - 0, o, b. t'fce r.r. f{ tc=o 'h.J ' 2n3o -,, =o.: ,f05 ) 1l.eV p.*J* lDl}f,-r i rol t'+I8 {ot }6' otnr\ Pf.}ix. * t,a $,i' lt *rl = v,,8 o C* eNx) \ui : i.t-+ 1.t r^i- <a v"P=p' =2A et Q"r-rc)(vu+r) =2-8' nit + rn,?L e.L -) P*-'"); t^tn) € E ; vA *= *+8 ) n4r I c"\ -l*11 h^Y' \!; ?le-Dl .n;/b+r.)1,(, )s' c.ld.,,nd*^t^ . Tli, S -D (**d =-t8 l,A"l. J+e -,6^-rXa^*rc)/ n32F" ,rL!, 1l;l =='!^, " I )=-i o f u^ -" -r4 [ -nr. > -r- v^ f+2s ,'8q ri'cX{ CUN >) vnn'uilt \ N^ *A \{/ q q^-T L Ct^r-= tr ( ^*r:rq "l n=, (D ",{I=;'a [:;l='l "l;=; 5x-3 (s _\fr_t) =o \Ta rdrl C Erc ; ea Q,t-l) r ) =O 'ia^,i, ttril AC" \ffi1 +r'Iffi =o (/9. b -J t6 = izt-uf 0 il'q lr"i &r+16 *zvFi -? : Q' (4.)PI n-r,.,1 -y.=2- o u,@-,') (w-[rr)=o a (Dd I o"t = L' ., \ o.t ' \t'-:-rtt1 -1-=l- {n"-'tr(T G E. r{* rfia^h-fr1nozal-lt p= L *s'- , + a Sgtr-\' : ?({112 ' b 1* ?{L t@t1+r) L h^;t \&,[ l"d. [:,\-,\utrz)' (S'-d.fl (t.,t'*9 e) ft1"tz' ] rt? tte +e] vE \w \ Ch t- 'l\d MA'= rqo'_u-p/ |^k" tl(- nD U$ t a lre\\^NMAo Ct-y) )Nq MK h.q DZc =+ ^., ) Pet r-Dai. M b. n*, A AMo \^ a Etso (tt) ) Ao = $o :; frsL= Mo.eo Eo fto DOL T\S.' -\ /^"1 lqO OH.OE= (v U *'rL Kterq G L"r (oi rr '.4 'u") ( ro\ ["1" o ]i ' *l,l (t* i e r'.,. ) 0e.0*:6rf.0?=t G) o!'o t' = cot (=J or e :) {p-iq -_ xoo TUvJf 0r'oK = oc'eA) =) , ,t" = %o' c L\< l* t-d(oj . Ci E. "- >) coIBK el 0 b Li V b) (rl\ x;a *A) U a uA!=uE.Mo MO 00 - z1- OK = D ol< ) b 0I0.^LgDl< . c.ld.,,nd*^t^ . Tli, S -D (**d =-t8 l,A"l. J+e -, 6^-rXa^*rc)/ n32F" ,rL!, 1l;l =='!^, " I )=-i o f u^ -& quot; -r4 [ -nr. > -r- v^ f+2s ,'8q ri'cX{. &apos ;-: -rtt1 -1 -= l- {n" ;-& apos;tr(T G E. r{* rfia^h-fr1nozal-lt p= L *s&apos ;- , + a Sgtr-' : ?({112 ' b 1* ?{L t@t1+r) L h^;t &,[ l"d. [:, -, utrz)'. -J t6 = izt-uf 0 il'q lr"i &r+16 *zvFi -? : Q' (4.)PI n-r,.,1 -y.= 2- o u, @-, ') (w-[rr)=o a (Dd I o"t = L' ., o.t ' &apos ;-: -rtt1