THPT Qulnh C6i; D6ng Nfit Phqm Vdn Minh, llT, THPT chuyen Luong ThC Vinh; Btnh Phutrc: Cao Ydn TiAn, _118, THPT chuy€n Quang Trung; Btnh Dinh: iy'gryiz Quang HiL l2TN2, THPT Tang Bet H6,[r]
(1)XU{I Biil ilI1964 sd2012 419 NiM THO 49 oi\r,rx cso rnuruc ngc ex6 radruG va TRUNG TAP CHi BA HANG THANG - rgc co s6 Tru sd: 1878 Gianq V6 Ha NOi DT Bi6n taD: (04) 55121607: OT - Fax Phet hanh Tri sU (04) 35121606 Email: tapihitbanhoc_tuoitre@yahoo.com.vn Web: httb://www.nxbgd.vn/toanhoctuoitre tf;bi* g*, t??o - e.5.20t2) (2) CUOC THI uduur xreAvurraora Dot bn, mia Hi 4iiy Todn hoc vii -Tudi tr| xin mdi bun iloc cii nwic y1u thich todn hoc tham gia Cu6c thi D0VLI NeAV nE ZOIZ Cu6c th.i chia tint hai ia, daig tan htut t,n cdc sti bdtt 1t g (thdttg 5.20 t2l vii 420 (th(ing 6.201 2) DAi trrrtg df thi li ttir rii riJ ban 1.d:u roin tr€n cd nutic Ban hdy gt?i ldi giiri ba bdi iti vui Dot I vi Tda soan trwic ngiiy 3l.7.ZO i Z itneo aiu Bw di€n) vit ldi giiii ba hiii ilu t sE ilting THTT sO 123 (thring 9.2012) DAn hen lai Bdi I ^! BOIG IIOA DTGX IC Trong phong trdo thi duo chdo mJng Ngdy sinh nh6t Bdc Hd, mQt l6p hgc sinh dd ro m5i alidm l0 c0o m6t bdi rhi hoc ki ll dro iqng mgt b6ng hoo Nh5m c6c bon An, pinh,'D6ng, Nom, Hoo dd nh6n duoc 27 b6ng hoo Sd b6ng hoo nhdn m5i bon ndy ld kh6c nhou H6i c6 thd chon duo c bgn bgn ndy md c6 tdng sd bOng hoo didm I kh6ng it hon 20 kh6ng ? Gi6i thich vr'soo? duo c cOo THANH LOAN .) Bdi2.Tl(il OliA 00N TRAI NGIllit ltAN M6J ngudi ddn tham bon cOo minh sou m6t thdi gion xo c6ch, ho h6i hon nhou vd tinh hinh c6i Chrj nha 16 ldi cdu h6id6cOo kh6ch nhusou: - T6l c6 bo troi, cQu thri do6n xem ndm noy chOng l6n mdy, bidt tudi cOo ch0ng nh6n v6i nhou thl hSng tudi c0o t6i, tudi cOo ch0ng c6ng loi ld Kh6ch ng6m ngh; m6t h6i md v6n chuo thd tinh tudi cOo bo cdu troi mac di ala bidt tu6i ct]o cho nhd ld 36 Cudicung kh6ch n6i: duo c BEi3 - Bdi to6n cOo onh kh6ng x6c dinh Chti nhd cho bidt: D01g vqy, t6i dong ht vong rdng chdu l6n nhcit s6 duoc di dtr thi boi loi Thdnh Doan t6'ch0c vdo ngdy Qudc tdthidu nhi ndm noy Khdch n6i: Nhuvdy t6i c6 thd bidtduo c tudi c6c ch6u rdi! Theo bon ngudt kh6ch dd suy lu6n nhuthd ndo? TUAN MINH THI{NG TAM Dd chudn bi ki ni6m C6ch mong th6ng 8, ngudi to ldm hoi bdng, m5i b6ng c6 15 b6ng ddn xdp theo c6c vu6ng ihdnh hdng vd c6t nhu hinh ben O m5i bang, m5i ldn bd'm c6ng idc thi 6nh s6ng (sdng ddn chuydn thdi hooc tdi) ddi v6i tiit c6c d6n ndm tr6n m6t hdng, hodc m6t c6t, hodc tr6n m6t dudng thting ch0o dudng ch6o cOo vu6ng ndo d6 Bon ddu t€itc6 c6c ddn hoi bdng d6u ttit Bon hdy trinh bdy c6ch chon bcim c6ng tdc m5i bdng dd cudi c0ng c6c d6n s6ng xdp thdnh hinh T8 nhu trdn hinh v6 HOANGNGUYEN ooo ooo oao oao ooo .OO ooo aoa aoa oao (3) t- SffiT[Gre 1: \= -;.aa::\,mr UAO G]IUIIIE MIIUH (.,: l', -\ a\tiE@'S It* 1'.-\ HA VAN NHAN (GV THCS Hodng Xudn, Hodng H6a, Thanh Hoa) dudng thdng vu6ng goc vdi OP, cit OP tqi E vd cdt dtrdng trdn (O') tq.i I vd K (l niim gitia Q vd K| Goi.F la giao diem cia OQ va MN Chilmg minh rdng ndm diim P l F O K thuoc cirng gidi ctic bdi todn hinh hqc Ching ta nhing cd thd sri dtlng rinh chdt c a th gidtc p md cdn si d4ng ndi.quan hf giia cac i dwdng ndn ngoqi tiAp ni gidc dd g ii tdp.hinh hoc chuong lrinh ,odn viit xin gioi rhieu ki ndng gidi mAt hinh ioc dua vdo viQc chting nituh&i viQc mQt dmng trdn Lai gi,rti (h.2) , OBa,i to,in l Cho hinh.thang ABCD.c6 hai du'dng chlo AC vit BD bdng vd bdng da1, lln AB Goi M ld trung diim cia CD Cho bi€t g6c MBC = CAB Tinh s6 cdc goc ctiq hinh thang d6 Ldi Si,rti $.1) Ggi N li trung tli6m cria lD thi vi MNIICA= DE th6y QO Tir Q) co ABM rn MBC(gt) (2) DAC = ABM (1) Nfti Hinh I cAn^ sny BAD = ABC, mit CAB = lsdlN nln L,Q|N <oLQNK G.g >QN'=Qr.QK DAC=DNM (r) v\ AC = BD (gr) nln ABCD lit hinh than8 l^ INQ = NKQ = DMt[ nC,:, tA gig ANMB ndi i6p, s.u,y ANB = AMB Do AB: BD (gt) n6n tam gi6c BAD cdn t+i B' c6 DN = NA, suy ru ANB =90' = AW Lqi c6 MA = W itjnh chat d6i xung truc), tlo tam gidc AMB v$ngcint4i l|ne,n fus=GA=qS' Tam ei6c ABC cin tai A (AB = AQ nirr eCA = ,S,nC = l,[BA,+ MBC = 45' + WC Thay vio tting thuc BlC+ ACB + ABC =180' ta drocfu fi oo aa 6ib = ZEc = t s" , ( QNz 1) vd L (1) =QF.QO (2) tqi NF, md tam gi6c NOQ wdrlg srry Q QK (2) S.A -g-=4 -'A)q :> LQIF <nLQOK(c.g.c) >QFI =QKO, say tu giric 1FO,( n6i tiiip (3) Do tam giitc OIK cdnt?i O c6 OE L IK ndn IOE = KOE,n|KOE+EKO=9d, n& 6E +Eib =s0" tul "55f;l9=QFI; QFI+IFP=90', i6E = iFF * eiirc IF)P nQi 66p = Tn (3), (4) suy nem di6m P, 1, suy (4) F, O, K cing thu6c m6t tludng trdn Cl 1Di =6cD=rso' -iEc =ros".t OBii to,in Ti m6t di€m P d ngodi dudng rron lOl kd car tuyen P lt'lN voi Juong rron t ll4 ndm giia P vd M Coc tiip ruyin , ia durtng trdn tqi M vit N ciit tai Q Qua Q kA OBlri toin D.udng phdn gidc v€ ttr A c a tam giac ABC cdt dtdng trdn ngoqi tiAp tum gidc ct D Chfing minh ring AD> 47!9 Ldi gitii (W dqc lU vC hinh ) TrCn tia d6i cua tia C,4 liv tli6m E cho CE - AB Y\ AD lir tia phAn giric g,6c BAC (gt) suy DB = DC Lqi s,ii arg TORN HQC ts-zorzt * dudiu6 (4) dl gi6c ACDB n6i ncp nen ABD=mL ftt d6 LABD = L ECD (c.g.c) + AD = DE Trcngtam gi6c ADE c6 AD+N,>AE+AC+CE = AC + AB, suy oorB!^AC (rlpcm) QBii.torln Cho ttt giac ABCD c6 BC KD+MD=Ltr Suv tr : = EAF + BAD Mit khric, l4i c6 -4.- EAF = BCD BD, G.qi ,< h di6m voi ,4 noi fiAp duong trdn (O) Tr) C ke ti?p tuy,in vtri drdng trdn cdt dlrong thdng AB rqi E Goi F ld giao di€m c o hai dudng thdng AD vd BC Chimg minh rdng EF//CD d6i ximg Ldi siai b,.3) Ttt gi6c ABCD ECr(F n6i tiep n6nfr q!.pq ctrSt a6i xrmg; , Dan d6n ru giric =E,.ru bi "tti, =E fi =fuG6c cA c4nh tuong ring w6ng g6c) Suy et =6)R,finttt elac ADKC niti tiep Do i16 K e (O) V{y EF ld tludng trung truc suy E, O, F thnng hdng O ^ BCD = BDC(2) IyAtkh6c^ BDC = BCE I^ = lstlBC (3) Tt Hinh fu=fu=fu=fri ltintr BCD = FAE (I) Lqi c6 BC : BD sjrS qua EF thi ta c6 (1), (2) (3) suy FAE = BCE, d6 tb tiip + CFE =CAE lr.d, 6iE = 6Da = 6iD +GE =6eD srryruEFI/CD.A gi6c ACEF nQi cria ddy oung AK, Ofni toin Ti mQt ditim A ngodi iludng trdn (9) lG hai 6p uyin AB, AC vdi ttudng trdn (8, C ld cdc ridp didm) E ld m6t diim tin cung nhd BC tE khtic rA Q.Tiip uyin voi duong trdn (O) tai E cijt AB, AC theo tht tu o M, N G7i giao eliiim c a OM, ON voi BC lin laot ld P, Q Chtrng minh ring ba dudng thdng OE, MQ NP d6ng quy OBiri toin 5, Cho tam gidc ABC nQi tiip LN gi,ni (h.5) c6 ffiE = ffiB =!fiE, dudng trdn (O) Ctic duong cao AH, BI Chimg minh rdng OC vu6ng gdc HI Loi SiAi @t dqr tr.r ve hinh) Tt gia thi@ ta c6 AIB = AHB =90' n6n trl giric (1) ABHI rQiIiEp, wy ABC =HIC y61(O) K6 tia tiiip tuyiin Cx @i C ta c6 t^ ABC=ACx=t-sdAC (2) Ilinh Tu (l) ve md OC L (2) suy ru HIi Cx n0n OC O Biri toin Cho = I HI t* ACx = HtllCx (dpcm) giac ABCD tr nQi tiip dtrdng trdn (O) Dudng vu6ng g6c vdi AD tqi A cdt BC E Dudng vu6nq g6c vcri AB tqi A cdt Cq F Chimg minh rdng ba diAm E, O, F thdng hdng Lbi sirti G 4) Tt gie thi6t c6 180" I Eii diE = (EIF iii) (EiF FiD) TO6N HOC .cludi[e_t9_1eJ9-m1?_ l^ NOE = NOtr l^ =:COE N€n |ufil r ^ Suy =:BOC=+Si,BC=MBC )) = tuDE+ I{E nr gi6c OBMQ nli ti6p Lai co OBM =9C n}n OM lit duong kinh cria dudng trdn ngoai ti6p ru giric )BMQ + OQM =90'= MO LOQ Tuong t.u NP LOM md OE IMN (g!) nln OE, MQ NP ld ba tludng cao cua tam giric OW dod6 OE,MQ,NP d6ngquy O (5) Osii to{n G4i I ld mAt didm nim vd K ld m,t diim b€n nsoiti tt gidc li)i ABCD cho ABID, BICK b cac hinh binh hdnh vd CBI =CDI ch mgminhriing trdD=6d Ldi giai (Bqn dgc ttr vC hinh) Do ABID, BICK ln hinh binh hd, rh n6n ADIIBIIICK; AD: BI : Cl( n€n tu gihc ADCK li hinh binh hanh = frdn = 1Ts * 1/^ 5il = ;(67, dFn) l^ = 90'-:-ACB Tt (1) 2^ vi (2) suyra CFE=HOB (1) ACD= K4C Lqi c6 MBK = LDIC (c.c.c)+KAB=CDI * ^e6r=Gr=fr8 giAc laKC nQi ti6p.nln KAC=KBC=BCI (2) +fut fra rir (1) vi (2) suy 1iD = 6d (dpcm) tr to6n Tn di€m P d ngodi tlurtng tdn (M 10) vd cric riip nyin PM PN vni duong tdn PAB ruyin P kd cdt N ld cdc tiip diim'1 Qua U niim gifra P vd B) kh6ng di qua O Dudng thdng di qia A vd vuang 96" ia du ciit m'L W theo th* tu tqi C, D Ch*ng minh rdng CA = CD Liri gi,rti G 6) K€, oH LAB (HeAB),k€t hW v(i OM LPM,ONLPN, OHLPB, ta c6 nem di6m O, H, M P, N cing thuQc mQt <ludng trdn OBii ne, ffiF =ffiF Hinh Tt d6 tt? giirc OHFB rrQi n6p, fu=fu=N IAO Vi AO li ph6n gi6c c:ua 6, nlr c6 dinh, ma I c6 dinl suy H co aint vay EF lu6n di qua di6m c6 ainl ,n ld chdn tluong = BH w6ng g6c hq tu B xudng tluong ph6n gi6c cua gac A,.l ll OB;ri torin Cho tam gidc ABC c6 ba goc nhon n6i 6p dfing trdn (O) Gpi I ld mit ilidm trAn cung nhd AB" V? IM L BC, IN L AC Xic ilinh vi rri c a ili1m I d€ W c6 dA ddi lon nhdt tri giai (Ban tloc tU vC hinh) Yc IPMB (P e AB), k6t hqp v6i INMC, IMLBC, ta c6 cic tA gi6rc BIPM, ANIP vd INCM nii tt€p Lqic6 PM LOM;AD LOM n€nADllPM= ffiE =6tr8+ffiH =diu, suyratftgi6c ACHN nQi ti6P = AI{= Al'lC= ABM nin I IBM md HB HA (do OH L AB) srtY CH = CA: CD.A Osai to{n 10, Cho g6c vu6ng xAy, diam B cii dinh rrdn Ax didm C di ttQng tr4n Ay Dtdng trdn tdm O ndi li6p tam gidc ABC tidp xic vtti AC BC theo th* tr o E vd F Ch*ng minh rdng &fung thdng EF lu6n di qua mpt didm ci tlinh Lii sidi (h 7) Coi H ld giao di6m cria hai duoog thang EF vd AO De th{Iy CE - CF n€n GE so' )fcl Mlt l,*ric Tt t16 M[t Stty rir ta = BIM APN-_ AIN (1) c6 BPM k]r6c, tt gii$ ACBI -4: $i APN = BPM (1), (2), (3) suy (2) ri6p n€n IAN = IBM 'tpi (3) dFfu po da APM = BPM + APM = APB =18t MPN = NPA+ ndn ba didm M, P ,V rhing}ane ^ stty ru Ta lai c6 IAB = INM,IBA= IMN M'I IN AtAB <DAINM (s.s) >"'' =-'<1=lUN<BA &4A YQty o MN ftrc ltu nh6t vd chil<Jfli'N: =iii ttucrng trdn (OJ A,M: B e C1 li ttuong kinh cua =g0e d5i xr?ng vdi CqtaO.A e (6) HUoNG oAN on oE rnr ruyEN slNH vAo Lop l0 Niu ngc zou - 2or2 pi ni da ddng fiAn THTT si;418, thdng ndm 2012) Ciu Voi Q A .r.r, o"6 b) Ap dung hQ thuc luqng tam gi6c vu6ng AE$ v6!,{D li tluong cao, ta rtugc DK.DE = = d @ h dQ Mi cenh hinh wbng ABCD) AD Mlt EI?(DK + DE)2 >_ 4DKDE = 4Ad = v0yP- l Clu a) Phuong trinh tll cho c6 nghiQm kep klti vi cht lr:lri tr' =f -a=Qa',rr.=! b) Eidu kiCn dA phuong trinh tld cho c6 nghiQm ld A'= 3-zr > +m53 Theo *n hQ uu fi{rc Vi6te, tacb x, *r, x2 x1 4+x2=-\ )trxz=m*l (xr+ xr)' '2xrx, e EK> 2a Ding thftc xiy vi chl DK= eE=C ViV kh! 4l f DE: a tring voi tlinh C cua hinh vu6ng dii ngin nhit vi bdng 2a ABCD thl EK cb d0 CAU Ta c6 +/t =m+n+8 e 4Q* +rt)=4(m+n+8) 4tf -4tn+l+4r? -4n+l=34 (2m-l)z +(2n-1\z = 32 +52 (t) tt? e e <+z:z(trnat) Vi z,z e N, k6t hqp v6i (*) suy (zm-t=z l2m-t=s BDT dn cho tuong <luong vdi (x+y)2>4ry e l0 o (a)'-z(**t) =f m+l Clu kh6c, lai c6 {zr-r=s oot'[zr-r=3 - y)2 >0 (lu6n tlring) Ding thrirc xiy vd chi r : 1l lm=2, o{r=r ho6" Clu a) Yi AB = AD, BAF=DAK (cingphv voi g6c trEF=6R=90o Do d6 Vfy tim itugc hai cflp sii (z; n) th6a men de bai h (2; 3) ve (3; 2) Bi,IVANCHI MBF : K4F =W (x fra, L,ADK (g.c.g), suy ru AF , nCn bm gi c : AK, mit AKF w6ng cin tai ,4 lm=3 {r=2 (GY THCS La Lqi, Qry Nhot , Binh Dinh) suu tirn vi gioi thiQu (7) %O*rhrydru sinla uAa, b{" t 'rmiffiowrcff tfffi Qu,r60;noctrrlr6l,r,m-&e'[mil*"ffisffi Nitt ttgc zolr - 2012 (Thoi gian ldm bdi : 150 phtfrt) CAu l (2 didm) Giii hQ phuong hinh a).Gqi D h iliiim d6i ximg cria I qua tlu&ng thnng A Chimg minh ring t(r giitc BCDE nQi ti6p lx2+Y2-ry=19 [x]+y3+19=0 Ctu (1,5 tii1m) Cho parabol tluong th[ng (d): y = ca- a (P): y = x' Ya Ctt3.(2,5 di€n) Giii phuong trinh x b) Tim^cric s6 nguyen t6p cho ha; s6 Z1,o + t1 vit 2Qt' + I ) ld hai s6 chinh phuong C0it (2 diiml Cho hai duong rrdn" (S) vd (7) S vi dQ dai canh , thoa ddng thoi l=8 vd x/ +xz+xt li mQt s6 nguy6n m6t? CAONGOCTOAN td A vit B Mot duong thang A ti6p xric voi tludng trdn (,9) t4i C, ti6p xric voi cat tludng trdn (I) t4i E, cho khoapg crich tu tlan A l6n hon khoing c6ch tir I il6n A cua Tim gi6 tri nh6 nhAt cta , b) Cho chin hinh vu6ng c6 cric tlQ dii c4nh tinh btrng mit lin luqt li n+l,n+2,n+3,n+4t n 5, n + 6, n + 7, n +.8,2 + 9, voi z ld s6 nguy6n duong Ggi S li t6ng diQn tich cia chin hinh w6ng niy C6 hay lih6ng mQt hinh.vudng diQn tich bing a) +2-2J-x+l =l+ b) G9iR5, R7 vir Ry lin luqt li b6n kinh cic tluong trdn (,S), (D V) Chting minh rang R3R = 4; cticdi6ukiQnx+y+z't +yz+yt+zt=18 I * I :, lx'l lx'l + Jx c mot tluong trdn ( Iu) Cit (2 tli6m) a) Xdt cric si5 th1rc.x, y, z, Xnc dinh tham sti a aE (A cit (P) tai hai <licm phin biQt c6 hoinh tlQ 4,x2 th6a x+2+2Jx+1 duo (GV THPT Tam Giang, Phong Di,in, Tkha ThEn - Hu€) ,4 stru tdm gioi thiQu Hinh inh Rdng qua cic thdi rlgi tluo c sip xiip nhu sau: 1a Th6 ki I b Th6 au lac bO citr.!fir lfinh tuqng x - XII,2c.Nhn L!,3b ki det nung Rdng tdn tl6 srl x I - x IV 2e Nha Trin 3a Rdng bing tc Th6 ki xtv - XVII, 2a Nhn L€.3d Ring dd o Ei6n Kinh Thi6n, Thing Long rd Th6 ki xvlll, 2d Nhi Tiy Son, 3e R6ng trdn mrli Dtn Vua Bi Eio Th6nh H6ng Nuong L6 Th! Yi5n, duo c sic phong nim I 796 le Th6 ki xlx trdnmiiDi€n - xX, 2b Nhri Nguy6n, 3c Rdng Ciic ban sauc6d6prin ddrng duoc nhin ting phdm: l\ Biti Einh Hi6u, 1lAl, THPT Qulnh Quj.nh Phu, ThiiBinh 2) Nguydn Quang Trong Hdi'Thr{iBinh' si6 l1Al, THPT Tiy Cdi Ti€n vAN KHANH TORN HQC 41e (5-2012) r crl,rdiue s (8) Ghudn eErysD,mmi![ G onr sd r(i HoP [i cho [i ilrl t6t nsni0r IHPr vi thiudo Oai hgc DANG THANH nA - rucuyEu THIANH THo (GV Hoc viCn PK - KQ Son Tey, Hd NQi) 1.-tdc bdi todn vi dqi s6 t6 hqp rdt da dqng vd ph , thdng co mlt cdc ki thi nyin sinh vdo Dqi hpc, Cao ildng vd cd cdc l*-, phong h thi hoc sinh giii ctic cdp NQi dung bdi viAt xin dd.cQp.toi mot s6 cdch lqip,nhdm dqa trin hai quy tdc dim co bdn ld quy tdc cQng vq quy tdc nhdn Cdc bdi todn ndy thdug dtgc chia thdnh ba dqng co bin sau tl6y DANG C6c phin tfr tham gia nh6m kh6ng l{p I4i ,OBti todn l.Ticdc chttsii0,1,2,3,4,5 c6 thd l\p du.oc bao nhiAu s6 chSn gim cht s6 ddi mAt khdc nhau? LOt gtat N6u ch[ si5 hirng v?n le, thi c6 ba cdch chqn tu criLc cht sO t, g-, S Do cht s6 hirng tlon vi li chin, n6n c6 ba c6ch cho n tu c6c cht s6 0, 2, Khi d6 c6c cht s6 hdng chuc, hdng trdm, hdng nghin dugc chon tt cht s6 cdn l4i, C6ch chgn tho6 m6n dlrh nghia chturh hgp vi 3.3.Ai = 216 (s6) N6u cht sti hang v4n chin, thi c6 hai c6ch s6 2, Tt d6 suy cht sd hang clon vj tlugc chgn tr: hai cht s6 chdn cdn lai Kii d6 c6c chir s6 hi,ng chuc, hi,ng trIm, chgn tr) c6c cht hiurg nghin tluo c chorr O chir s6 cdn lai c6ch chgn thoi mdn tlinh nghia chinh hgp vi c6 Al c6ch T\eo quy tdc nhdn, ta c6 2.2.A1 =96 (s6) Theo quy fic c\ng, ta c6 tilt ch 216 + 96:312 (sq A oBAi todn vdi cdc cht sii 1,2,3,4, 5, 6,7 8,9 c6 thd lqp ihr.oc bao nhi4u sd chin cd chrt s6 cl6i mdt khac vd kh6ng l6n hon 7892 Lfi gML l-ro soi,^,-,4 L: co J cnu so la so cban nen cht s6 hing tlon vi c6 c6ch chgn tu c6c chfr 2,4,6,,8 Do c6c s6 tluqc hp kh6ng lon hon 789, ndn chir s6 hang tr[m kh6ng th6 ld vd sd t ftratr-seeglgzgtz- Ung voi m6t c6ch chqn cht s6 hdng <lon vi: N6u chir s6 hang tram kbric 7, thi c6 crich chon ch[ s6 hang trlm (do cht sd hang tram nto h<vn vd khric chir s6 hdng don d) vA tuong fng c6 cflch chgn cht s6 hang chqc Theo quy tdc nhdn,Ia c6 7.5 =35 (s6) N6u.chf s6 hang mem ld 7, thi c6 crich chgn chri s6 hd,ng chuc (do cht s6 hang chuc nho hang) Theo quy tdc nhdn, ta o6 1.6= (s5) Theo quy chgn Viy cht dc voi m6i crich c6 35+6=41 (s6) cQng suy ung s6 hdng tram theo quy tiic nhdn c6 tAt cA 4.41= 164 (s6) D DANG Cr{c phAn tft tham gia nhrim kh6ng l{p l4i, song y6u ciu sg cd m4t cta mot s6 phan tfr theo mot tinh chat niro d6 OBlri toin Voi ctic cht s6 0, 1,2, 3, 4, 5, fip duqc bao nhi€u sii 4r nhiAn cd cd the chtt s6 d6i mQt khdc vd tl6 nhdt thi6t phdi cd mdt chfr sd 5? Ldi giAL o Cdch I - N6u cht st5 hang v4a h 5, thi cht s6 cdn lai ttuoc chgn ti cht s6 0, 1,2,3,4,6.Cbch chgn thoi mdn tIlnh nghia chinh hqp vd c6 At = 360 (c6ch) Tn d6 suy c6 360 G6) - N6u chii s5 hang v4n khric 5, thi c6 cdch chon cht s6 hdng v4n (do cht s6 hi,ng van khric 0) Do chi s6 c6 thd thmg o I v! tri hing nghin, hdng trim, hang chgc, hdng <lon vi vir ung voi m5i vi tri dd c6 A! c6ch chgn cht s6 cdn l4i, n6n theo nguy6n li nhdn c6 5.4.A1 = 1200 (s6) Y6'y lheo quy 'o dc cQng c6 3(.+12ff)=1560 G6) Cdch Chir s5 c6 th6 drmg d vi tri hdng v4n, hing nghin, hang trdm, hing chlc, hd,ng tlon (9) Trong t6t cd cric st5.di lap o tr6n, ta phrii lo4i bo c6c s6 c6 chr] s6 dung <r vj tri dau L{p lufln tucmg tU nhu trdn, ta phii 1o4i b6 vi vd img v6i m5i vi tri niy c6 Af c6ch cho.n vi tri cdn 1ai Theo quy fic nhdn, suy c6 5.Ae =1800 (s6) Trong cric s5 niy, ta ph6i lo4i b6 c6c si5 md chfr s6 O ermg d t tri haqg vpn Lfp luin tuong t.u, c6 4.Al = 240 (s6) , -, suy s6a c6c s6^ thoi mdn tli6u nhu v{y Tt d6 kign bdi to6n ld 1800-240 = 1560 G5) tr c1.-Il '3t2l = a2s (s6.) Tri tt6 suy stl c6c s,i thoa men didu kign bdi toillir 11760-420 = 11340 (s5) D 0nii Cho cdc ch* sd 0, 1,2,3, ,, , to{n ,: '^6.dryoc Hoi cd rhA @p bao nhiiu sd c6 c.hrt s6 fi nhrtng chfr s6 tr€n, d6.chir sd cd Onai to{n Voi ctic cht sii O, 1,2, 3, 4, 5, 6, 7, 8, c6 th€ lfip duo c bao nhiAu sii cd cht sii d6i mat khdc nhau, il6 hai chfr sii ,d g lu6n tlimg ki nhau? Ldi gini Tr) l0 cht s6 da cho, mdt d ng ba ldn, < ac chr) sd khdc cd mqt d ng not lan? lfp tlugc Cf Lli gini Xdttilt ca cec s6 itugc lflp (k6 ci c6c sO c6 cht s6 ilfng t tr{ tl6u) Do chii sd b0 gdm chir s6 kh6c nhau, d6 1u6n c6 m[t chp s6 rra g._oe cht s6 vd 1u6n dung kd thi m6i u6 gdm cht s6 kh6c d trdn lflp clugc 5!2! (s6) Theo quy tdc nhdn suy ru lip tluo c Cr4.5!.21 1sOl t c6 m1t dring ba 16n, c6c dung mQt c6c s6 Trong c6c si5 tluo c lflp, ta phii lo4i c6c sti c6 cht s5 dung iliu (hing chrc van) Lflp lu,in tuong tu c6 C?.4!.2! (s6) nhu vfly s<i O tir tham gia ' -.,*-.t 61 fheo quy td" nhdn, c6 ts6) $3! kiQn 3! Tu bai toin vi bii quriLt sau (s6 c6c toiin ta rut hoan vi lip): , -.1k6t qua ndy chung mini khri tlon gi6n, xin danh cho ban tlqc) BAI TAP T(I LUYEN Cho c6c cht s6 0, 1,2,3,4,5 H6i c6 th6 ldp tluoc bao nhi6u sii c6 chn s6 ru nhfng cht s6 tr6n tl6 chir s6 c6 mat dung hai ldn chii s6 c6 m{t dring ba ldn, cdn cric vi vi tri c6c cht sti cho thi si5 c6c si5 7! c3 " t!2! =ttz60 xlt l! hlk2t k,l' Ung v&i mOi U9 gOm chir s5 dugc chqn cung vdi hai ch[ s6 2, ba chir si5 lap du-o c 1l " (s6) (do horiLn vi c6c chrl s5 cho 3l2l- ' ' tt cic sii c6 cht ta ph6i lopi b6 cho tAp A={q, ar.- a"\ xa t6t ce c6c horin vi cria tdp B gdm z phdn tir <lugcl6y tntdp A, cho phAn tu c6 m{t tap B di:irrg ky lin (l = 1,2, ,2), vcri ttidu kien k,+kr+ +k =z Khi tt6 s6 c6c ho6n vi ld tit kh6ng fr,il ,rory 7l 6t h i :i = 720 (s6) quy tiic tdng chir s6 ddu ti6n <tu-o c fi mit dimg diu Lap luan tuong tU tu O Nh$n cd cric s6 gdm chir s6 ftii li 0) Do cht sii c6 mf;t hai 16n, cht si5 c6 mat ba lin, ndn phdi chgn.2 cht s6 nr chai s6 cdn hi (do cric cht s6 cdn l4i c6 m4t kh6ng qu6 mQt ldn) C6 Cfr c6ch chgn chfi s6 ndy lip du,c c 16p, bei toAn stj cdn lqi c6 m\t kh6ng qud mQt ldn? ci lin, ndn lip dusc Tir tt6 suy ra, sti c6c sti thoe -5n tlidu Onlri to6n Cd bao nhiau sd n nhi€n gim chtr sii, bi* riing chfr s6 co mqt &ing hai tin ch* sd c6 mdr dring ba ldn vd cdc chir Loi gidi.Xdt s6 cdn 1ei c6 (s6) nhu vriy Tir cl6 suy sii c6c sti thoa men didu kiQn bii toan li C$.5!.2!- C1.41.21.=15120 G6 A DANG Cfc phAn nhrim c6 l{p lli cht chir s6 k}6c co mAt dtng mdt lan? Tir c6c chr si5.l, 2.3, 4, 5.6, c6 th6 lap duoc bao nhi€u s6 g6m chn s6 d6i mQt kltdc nhau, tt6 phii c6 m{t c6c cht sd l, 2,3 <limg kC nhau? TO6N HQC Sti arg (s-zorz) t <[udiV" Z (10) 76rrol;zMffim DESOs llm bdi : 180 phrtt) psAN cnuNc (Thdi gran chut (2 dieficho hdm s6, =44 O Khio s6t su bi6n thi6n vi vE ad tfri 1c) cta him s6 tl5 cho 2) Viiit ptuong tioh tiep tuyen voi (q bi6r tiep 1) ary&r tso voi hai thiong tiern can cu4 tam giic co bdn kinh <lunng ron n$i ti6p (q tMnh ldrn nh6t Ctu II (2 diiim) 1) GiAi phuong trinh 2sinT.rsinx + Ssina 2.r + r6sin6r = 8sin2 2.r 2) Gi6i b6t phuong trinh 4zx -15.2tr+J-+ey < -16r",f*r C0u III (l diim) Tinh diQn tich hinh phing groi han boi cria tluong th[ng x = l; x = vd cdc dd ftihim s6 y = x3 -2x2*r-"or[r*]), y = sl1l a l:toc, x Cau IV (l didfi Cho hinh hng trs drmg ABC.AB{I, dly ABC ld tam giec vudng c6 : CA = CB o, g6c gita tluongihin e BAi viL m{t pheng (ACC/) bing 30' Gqi M lt trqng tli6m catth Ap1 Tinh khoring c6ch tir di6m M tl6n mlt phnns (AB A Ciu V, (1 Aanl "tim c6c sri thgc x,y,z thba mdn hQ phuong hinh l.l* +a+ 'tf -?xy + )P +1+,1)P -6y+lo =5 L,-,1)' llog &4zr = l0log, L*' z2 -l lqr!!: \'' v) PHAN RIENG (Tht sinh chi ihm c ldm milt hai phdn A ho,{c B) A Theo chucng trinh Chu6n CiuVIa Qdidm) 1) Trong m{t phin e toA 68 Oxy, cho c6c di&n A(l;2), B(4;3) Tim toa d0 tiiiim M g6c MAB c6 sii <lo b6ng 135" vi cho l'.*roang c6ch tt Mtl6n <tuong thing AB bing g B Theo chuong trinh Nflng cao Ciu VIb (2 diem) l) Trong m{t phing to4 dQ Oxy, cho A(2;3) li m6t hai giao di6m cria dudng trdn (C): x2 +y2 =13 vir dudng trdn (C): x2 + y2 -12x +ll = O Yi6t phuong fiinh ilu&ng thing rti qual cit (C,), (C :) theo hai d6y cung kh6c c6 d0 dni bdng 2) Trong kh6ng gian v6i hQ to1 dQ Oxyz, cho A(s;3;-2), 8(2;0;4), C(-l;0;1) LAp phuons trinh mit phing qua OA, ctt doqn BC tpi D cho ti sii ttr,3 tictr cua c6c kh6i tr! dien OABD vt OACDbing3 2) Trong kh6ng gran voi hQ toa dQ Oxyz, cho hinh lQp phuong ABCD.A;BTC1DT c6 A trtng g6c tga tlQ,.crlc tli6m B(l;0;0), D(0;1;0), lr(0;0;l) ViCt phuong hinh m4t phang (P) qua Ay'r bi6t (P) tAo voi BC vd ByD1 nhii::g Clu VIIa (1 didm) Tim t6t ce c6c si5 phrtc z thoi / r4 trinh I ' " | =1 Ctu VIIb (1 diiim) X6t khai triiin (l- x+ xz -x3)6 thdnh tla thric P(x) = a * d1x* a2x2 + a3-r3 + + a,6xl8 m?in phuong \z+i) g6c bdng llm ng SO 40 NGLYEN THANH GIANG (GV THPT chuyAn turng YAn) TORN HOC 'ctrdi[@J9a13l- (11) HrrdNe uAw erAr ofi s6 e I l) CAu Z1 narn Bpn ttgc t1t giai m tigm 4n sO y-m= " l(tn:m) PTTT t4i tfr?rg:r:;z; Gia str Mv6i (C,,) ( Ml \ ti6-m cQn ngng nP +l\ xo;m-I le(C) xoll) c6 dang +l xnl.tm mztl lxo+-m) )(n't m \xo + m)' ( 2m, +2\ suy ,{ | -m: m -:::: lvi B(2xo+m:m) xo+m ) \ m2 _y= - (r =21*' Tim ttusc tA *tl lxo+ml ; I B =2lxn + ml Tid6 Sr8 =!u.19=2lmz hoic m=Ji 1) DK.r < -1 hoflc x < PT tl6 cho CAu II tuong duong v6i 3) + 2(x + - i -r- { I e tx' + l).'\x+l /1-j = t, _" r1.i'I r-t i -s=o , hodc (x + l)^ Ii -: !x+l = -4 =t - 2Ji: x =t + 2Ji 2) DK cos 3r + Dua PT tli cho vd d4ng sin2 x - sin r - = PT <li cho v6 nghi€m III Ta c6 AL t * a** '1 tin' ar = r, * 1, =1 j l-sin2x jl+sin2x DdD ' si I =L+1 42 -* 3b ' 2a+3c- 4a+3b+3c' suy P+11>16, hay P>5 Vfy minP:5 2a' CAu vra b= " =2 o r r B ( l? , 1'l ,a c[]?, -1) \s'sl q,l) \s's/ a(l?,_l),i l.s'sl [s'5] noa" cf vi I niim khric phia so voi (a) Ggi 81 ld tfi6m tt6i ximg voi B qua (a), / lA trung <1i6m BBr Tt didu Heo Bd cing phuong vafi vd Ie (a), tim ttuqc 4(0;3;1) Ta c6 2) Chrmg minh ilugc ,{ Ddp s6 x CAu o ) =(4a+3b+3clL*'* ' \2a 3b 2a+3c ) 1*1> , D6"6 2a 3b 2a+3b' 4416 \_ 2a+3b 2a+3c 4a+3b+3c 16 _.- *" I I tlat tluoc a1l=12 *=-Ji "ryru (x + l)1x *( r +4a+3c\+t2(b - c) +B =z*3(b*") 2al3b)2a+3c lud - wl:1ru - ua,l<.a, : Ja naxlud - wl= Ja tun u e\ q; -\ CAU VIIa (4; z2) = Q - t;l + i\, (21 ; z 2) = (-1 - i; I + i) Cffu VIb 1) Gai l1 h di6m d6i nmg cua I qua BE (A1 e BC) yf duongftingBc 3r+y + :0 Gqi l, la diin doi xrng vii A qn B bt AzC|/BM W ttr^nong thang Z2C: 7x-y+35 =0 Tim duSc .l q+ Ciu lV Ddp s6 Sas= trdn (BCD) 2) Ta tlriy A, B nim vE cing pbia AOi voi 1a1 Gqi 81 ld didm A6i xr?ng v6i I qua (a) Tuong t.u cAu VIa 2) tim dugc 81(2;2;0) Ta c6 Ggi ld trung.di6m cia CD M ld giao tli6m cira /B v6i mit cdu (S1 ngo4i ti6p hr diQn ABCD Duimg trdn lon cua (S) lir duong trdn (ABlu{) MAt phlr:re (BCD) cat (S) theo duong BM Luu a =-= sin 60' f tam tlttoc AM Y qura 6v v";,, gi6c M vd BM ld dutmg kinh, n6n ^l: la,,l ABI ddr, ftn 6fu :! AM "Ji oor 3nn' =E{1 162 Cf,uY.Tac6 P+11 = BC)=10(dvd0 cuen = AB + MA+ MB = J6 + MA+ Wr >Je +.q8, =Ja +zJi =60' Tim odp si5 rrrnC*o =JA +ZJi l<Jtt M(-L;z:l) CAu \iIIb D[t log3 ;r = / thi r = 3' /13 =a-i: ) R=-=- 2sin 60" I 12 2-BC/(A Ddp s6 PT 6a choc6 nghipm nh6t -x = I.J DuJNG CHAU D TH (Gl/ THPT chuyAn LA Qu!, D6n, Qudng Tri) - Sti ers HOC t ctdiua g (s-zorz)T06r{ (12) DAO TH! THU TH0Y (GV THPT chuyan Trdn Ph1, Hei phdng) oonucortnixoeycrdu r - cAcn4NcnArr4r Xdc dinh c6c ttpi lugng: tliQn trd thudn, cim khriag cuQn ddy, dung kh6ng crla tU diQn, t6ng tro cua m4ch tlien, di6n 6p, cuong d0 ddng diQn m3ch c6ng suit cira ddng tli6n xoay chi6u Vi6t bi6u thrlc tliQn 6p tuc thoi, culng ttQ ddng ttiQn tuc thdi Tim cyc tri cua di6n 6p, cuong d6 ddng tli6n, c6ng sudt cho R hoic L hoac C hoac ar bii5n thi6n theo th<ri gian X6c dinh su6t dign d6 ng cim rmg, tdn s6 ddng ttiQn cin mby phdt diQn, c6ng suAt ilQng co tliQn Bai ip va rxty bi6n 6p, sg tuy6n diQn ning - MOr s6 L[ru *Kril crArBAr rAp Cin xric djnh dunq cric phin tu cua m4ch rI tti6n, cdch mic c6c phan hr m4ch tliQn C6ng thrirc tinh t61S Sd $0 lQch pha z, i dtii voi mach R, l, C mdc n6i tiep tong bdi hQc chi tlung cho trudng hqp cuQn d6y ld thu6n cim CQng huong diQn xiy rrr4lch R, L, C mAc n6i ti6p li truong hqp gifr nguyCn gi6 diQn 6p hiQu dung hai tliu tlo4n m4ch vd thay tt6i fi dn si ddng diQn tong m4ch cho tr=! Ca C6ng thic tlnh c6ng su6t ddrg diQrr xoay chi6u P =[,[Lcos 9ld tmg v'6i c6ng suat fiung binh cua ddng tliPn Trong c6ch mic ddng ba pha hinh sao, chi c6c tai hoan todn d6i ximg, ddng diQn tr6n day fung hda moi.bing kh6ng C6ng su6t m4ch cli6n ba pha bdng t6ng c6ng suAt ddng di6n tr6n c6c pha Cdc c6ng thric cua m6y bii5n 6p bdi hoc chi ttung vcri m5y bi6n rip g6m hai cuQn d.iy c6 eti6n fd kh6ng tl6ng k6, mic chung tr6n mQt l6i sdt kin, b6 qua hao phi tliQn ndng m6y TORN HOC 10 cIudiEE_ ss 3Pg:39!2 rrr - BAr raP vi DU *Ceu t uhiiu hQp kin gi6ng mii hpp c6 hoi ch6t vni hai ddu c a m6t tu diin hodc m6t ('uon cdm o'tong nqp tdi mot doqm mqch g6m mQt tong cdc hpp dd noi tidp voi m6t di€n trd thuin c6 gid tr! 6}tl Khi ildt doan mach vdo m6r tlididp xoay chiiu in i6 50Hz thi ddng diQn mach nhanh pha -:29n so vdi didn dp H6o kin dd chra 90 A- tu dien cd C : 33,2StF B ttt di€n cd C -16,61tF C cuQn cdm c6 L =153mH D cu6n cdm cd L =306mH Hnlng ddn Do ttiQn 6p hai tlil mach tr6 pha so voi ddng tti6n n€n mach g6m R vd C n6i ti6p c6 ( zsn\ : I=-: tanl \ e0 *Cay / r -2ilRC = C= 33,2.104F z, Dot ma dien dp xoay chiiu co gia rri hiqu d4ng U vdo hoi ildu doqn mach g6m hai cu6n cdm c6 cac gia (R1, Lt) vd (R2, L2) J l tri ,: mac noi li4p Gqi U1 vd U2 lan ltrot la iliQn dp hiQu d4ng c a hai cuQn (R1, L) vit (R2, L) Diiu kiQn dii u: A.LtL't:RrR't tl + tiz lir B.lL=LL R2 Rr C.L+t-=R,+R, D.L=lL Rr R) Hrdng dfut" D6, U : Ut + U2 th\ 0r.v,v1, ahah SUV fa tan@, ,, =l.ano" / ' uztt tCau : hinh vd- = RI -=- R2 Cho mqch di€n xoay chiiu nhu effie (13) Aih : c,irc dien dp hi€u t00Y; U6 =100 dung J, V, n U6= : 200Y; U1y 50a, 7= 5sq,r Tim gi6 tri cria r A.50c) B.30c) c.2so D.200 Hwdmg ddn uo* un, = ,l(R+r)2 +(2.rE.f L)'z .l.Ceu Mtiry phtit r:25Q : l00J7cos(l00nr)V Bidt di€n dp hi€u IJ1:40Y: uc:120Y Tim hQ s6 c6ng suit cio mach ili6n d4ng 0,8 "ore = .i.cau ,! mac D 0,s n U -u')' o.u s Cho mOt doqn mqch R, L, C not tiAp, cuQn ddv thuin cdm cd c=]Ern "' didn hai ddu mach 6n a = t00cosfloor, \ Tiu diin rrn -12'lfvl 2) t1n iloqn mach ld tdn Xtic dinh Sid tri lon nhdt c a c6ng sudt R dd c6ng sutit tidu thu nhdt fiAu thq tr€n tloqn mech il6 B.404; 125W D.204;62,5W A.404; 62,5W C.204; 125w Hnimg ddn u'R ',- R2 +(Zr - Zr)' - uz **(2, Ap dmg BDT Cauchv r:rn kJliR=lzL-z(lsuy R - z")' aoq.L :40o t ="y- p"Jlizsfi *Ceu O MQt may ,ha dp c6 ti si5 gifia.s6 vdng day cuQn so.cdp vd cuAn th* cdp bdng k: Ngrui ta mdc vdo hai ddu cuQn diy th* cdp mQt dpng co l50W-25V, cd hQ sd c6ng 'k=1 = t OO A.3,5.10-3wb 8.2,8.1O-rwb c.5.10-3wb Hwimg ddn Tin D 12,5.10-3Wb s6 ddng tliQn mriy tgo :75-ốa "60 - ssy l, c6 r6to t6c it6.quay.crta r6to ld 750 vdng/ph t Phdn mg g6m b6n cuQn ddy gi6ng,nhau, m6i cuAn c6 50 vdng, *a" niii ii{p Bidt suiit diQn tl\ng hiQu dqng mdy_tqo ld 2Z0V Tinh tit th6ng cqc dai qua m6i vdng ddy y (u- l,Jtr diQn xoay chiiu mQt pha nam chdm g6m cQp clrc N-S xen kd, u ld : soq4 Su6t ttiCn tlQng hi6u dung m6y t4o /, r = (tn, /,i 0,6 C.0,7 =!-r = Jo' !ZU viy 12= 2' {.Cau l Cho mqch diQn xoay chiiu R, L, C mdc niii fiiip ihrqc tri bdi diQn dp B A Hmimg ddn dArL DQng co hoat ttQng trinh tlnlong n&r 150 = 25J2.0,8 E O+<z*ttf J, a turtng I Ueu (J M& mdt nd"ng lu.ong may bidn dp ld kh6ng ddng kA Ndu d6ng co hoqt dpng binh thudng thi cudng dQ hiQu dqng cuQn ddy so cdp ld A 1,254 B 1,6A C.0,8A D 1A sudr O,8 li =*'*r;'"', = oo ^! s.lor(wb) DAoDoNGvAs6uoprEwrr] I1 fi CACDANGBAIT+P x6c tlinh tAn s6 dao ttQng diQn tu tu do, gi6 dQ t1t cem, diQn dung cira m4ch Z Viiit Ueu thric cudng ttQ ddng trlc thoi, tliQn tich tren mQt ban tu alion SU bi6n thi0n diQn trudng ve tu truong m4ch, vfn dung s1r b6o todn nlng lugng tliQn tr) cira m4ch dao tlQng li tudng X6c dinh bu6c s6ng tliQn tu m4ch dao dQng c6 th6 ph6t hay thu ttu-o c tr- MQT S6 LUI, f IAil GIAI BAI TAP Khi tu ph6ng cliQn thi g giem, i tnng; i bi6n thi6n cung tin '2h ! s6 vir nhanh pha hon q DiQn truong gita hai bag tu vd tu trudng cria cuQn d6y mpch bi6n thi6n ctng pha voi nhau, nlng luqng cliQn trudng vd.neng lysng di6n truong cung bi6n thi6n v6i t6n s6 gdp tl6i trin s6 dao dQng c[ra m4ch vd ngugc pha (5-mP)TO6N H9C 'g[rdiw fl s6 41e (14) I(hi s6ng tliQn tu truyEn hr m6i trudmg sang m6i trudng lfi6c.thi tin s6 s6ng 1fi6ng tl6i nhung t6c d0 truyCn s6ng thay tl6i, c6ng thtrc A = 3.108.2rE{e dung voi m6i truong ch6n kh6ng (hofc g6n ttung kh6ng l,.hi) N6u mach dao ttQng c6 gi6 tri tliQn dung tu iliQn C vd d0 tU cem cuQn ddy Z thay il6i thi budc s6ng dien trl l6n nh6t ung va Crorvd L-*, bnic s6ng tliQn nh6 nh6t rmg v6i Cainvl L6in tt S6ng diQn tt c6 tAn sii cang 1on, budc s6ng cing nh6 thl mang nlng luqng cing l6n N6u m4ch dao ttQng c6 diQn.trd thi dao tlQng ri6ng cua m?ch sC t5t dan, de ri dp tlQng cAn cung cAp nlng luqng bir vdo ph0n nitng lugng hao phl tori nhiQt Voi tU phAng C - -d ru thay d6i 400 f n6n khodng c6ch hai ban hn li tutrng cd ndng Ittqng dao tlQng td W : 2.10-6J Ctl sau myt khodng thni gian td L,r:0,314.10-6s thi ndng lnong t4 lqi bidn thi€n qua gid tri 10-6! {.CAu S M6t mqch LC cia mqch A ar= 106 rad/s B ar:5.106 rad/s C o:5.107 radls D a;= 107 radls Tinh rdn s6 gdc cira dao dQng Hdng ildn gL =L I Cir sau mQt khoang thoi eran Ueng 611 -4 NhQn th6y rO-4J ntrng luqng diQn truong lai blng nlng luqng trr-BAr raPviDU *Cau f Trong mach dao itQng di€n ti, tu truong vd bing m6t nua ntrng luqng diQn ,2n2t mdc C1 n6i fiip voi C2 vdo mqch rhi in si trr, suy yy= Z!1= J!!- = 5.106(rad/s) ld Jil= lOOMHz Khi mdc Cr song song voi C2 vdo mqch thi tin sii mqch td f"" : 48MHz Hdi tin sii mqch bing bao nhiAu T mCch chi miic Cy vdo msch? (Biit Q < A.60MIIZ B 80MHz C.2OMJlz, C) D l40MHz Hudng dAn Tit dc c&rg thuc: Cs= C1+ C2; 1_1 ; ,"_= suy C* Ct Cz'2n,lLC t t I C1<C2 f,'+ f; =.fi:V* t,=E,chtn! 4Lt itiQn ti LC giim ttt 5pF uri cuQn cdm thuin Bid gid rri crc ilai cia di6n ap gifia hai ddu t4 didn ld Uo: l2V Tqi thoi didm dien dp gifra hai diu cu6n cnrn bdng u1 : 8Y ndng lu.ong W tnmng mqch bdng {'Ceu Mach dao itQng diAn c6 C: A.2.10 ',J B 1,6.1orJ 'J c.4,0.10 D.3,2.rc4J Hwdng il6n N[ng luqng diQn tt cua mach dugc b6o todn, suy w"= fi>f2 suyra, = 8oMltu '"22ry-9!:2.r0+(D *Cau Z MQt khung dao ttQng cd thd cQng {.Ceu s Mach dao dAns gin cuQn ddy cd hudng ddi buoc s6ng ti 100m d4n d0 A cam L = 30$1m0t tu di€n c6 C: 3000pF n€n 2OOOn Khung g6m mQt cuQn d,4y vd mQt fu phdng cd th€ thay tt6i khodng cdch gitia hai bdn tU l/oi ddi s6ng md khung cQng hudng duo c thi khodng cdch giita hai bdn tqt thay il6i ld A n= 120lin B.r:200 dn C n:2401dn D n:400 ldn Hrtng ddn sry ei6 Sri dung c6og thtc ti iliftr dnre t"v cor t =v.2nJIC [PT= Ilm/ c00 TO6N HOC cludi[e_s9 sq_g-2u?)_ 12 G" h DiQn trd thuiin cia mqch dao dQng lo D0 tri dgo tlgng tli(n mach vci hiiu diQn thd cuc ilqi tan tu dien h 6Y phdi cung cdp cho mach mQt ndng hrqng diQn cd conS sual ti A C 1,80W l.80mW 8.3,6W D.3,6mW rtn C6ng su6t cung c6p nlng luqng p =fa= 4* =9#*=1,8.r0-1(w") Hutng 22L (15) Gror THrEu ,rnOr s6 cHuol.to rniNn ffiffiffimmffimffiffiffiffim vrgT NAM oA rrruc Hrf,N uouyEru HA cuAu (Ph6 Vq tru1ng Vq Gi6o drlc Trung hgc, Gi6m ddc Chrtong tinh Phitt ti€n Gieo duc Trung hgc, B0 GD&DT) cra qutic gia vi qu6c ti5 h d6nh gi6 ngoiti tr6n diQn rQng tl6i voi c6c co sd 916o dgc E6nh gi6 ngodi ld kdnh th6ng tin quan treng xem x€t tlQ tin cfly cria tftimh gi6 rong; lim han ch6 tinh cht quan; tiing cudng tinh kh6ch quan cria d6nh grA fotrg g6p phan tti6u chinh ddmh gt6 trong; ld dQng l1rc ndng cao ch6t 1u9ng tl6nh gi6 nhim ndng cao hiQu qua hai chrlc n6ng co bAn cua drffi gi6: - Chric ndng xric nhfn: DQ tin cNy cao (chinh x6c, kh6ch q"an, c6ng bdng); - Chirc nlng tlidu khi6n: T6c tt$ng.vdo qu,i trinh day hqc (tao tt$ng lgc thfc ddy, ning cao cMt luqng d4y hoc) henh L) r clrtloNc TRiNH oAur crn QuOc crn Ddnh gi6 ki6t qun hgc tip cfra hgc sinh ldp ToinvdTi6ng Vi6t - Mdu hpc sinh: 60.000 em lop thuQc - Khdo sdtt m6n: 63 tinh, ph6 - De ddn khai ld vdo c6c n5rn 2001, 2N7,2011' + Ki khio set 2001: Chuy6n gia qu6c t6 Ng6n hang th6 gioi (WB) thUc hiQn, chuy6n gia ViOtNam chih6 ng + Ki kheo silt 2007: ViQt Nam thgc hiQn, chuy6n gia qu6c t6 h6 frq + Ki lfreo sdt 201 : ViQt Nam thuc hiQn hoan toelt2 Einh gi6 ki6t quf, hgc tlp cria hqc sinh It6p nnm 2009 - Mdu hoc sinh; 10.000 em l6p thuQc 25 tin\ thnnh ph6 - KhAo sdt man: ToAn vd Ngt van Dinh gi{ k6t qui hgc tip cfra hgc sinh ldp niim 2009 - Mdu h7c sirfr: 36.000 em lop thuQc 63 tinh, thdrh ph6 - Khao s6t m6n: Torin, Ti0ng Anh Ng[ Ver1 VAt H, Dinh gi{ kdt qun hqc l6p 11 t{p cria hgc sinh a) Mgtc tiAu - Gi6m s6t, d6mh gi6 k6t qud hgc tflp cua hqc sinh sau mQt giai tlo4n hgc tgp vd rdn.luyQn Tri <16 cung cdp c6c th6ng tin g6p phin vdo vi6c chir:h li vd tli6u chlnh chuong trinh sacn 6ao khoa vi tao co sd cho vie; thi6t k6 chucrng trlnh - srich gi6o khoa THPT cho giai tlogn ti6p theo - Xem x6t mr?c ttQ dpt chudn ki6n thr?c, ki nlng theo chuong trbh hign hdnh d6i v6i c6c m6n To6,n, Ngt ven vd Ti6ng Anh cria hgc sinh tai thoi tli6m kh6o s6t - Cung c6p mQt md htnh lfi6o srit k6t qua hqc tfp cria hqc sinh cho cric Sd Gi6o dpc vi Ddo t4o tl6 thgc hjQn cdc cu$c khAo stit nrong qr voi quy m6 cdp tinh, ph6 C6c th6ng tin hr cic cuQc khdo s6t <16 c6 th€ girip cac tinh denh gi6 duo c chit lu-gng hgc 6p ilia phuong, tl6ng thoi c6 th6 grup viQc xiy dpng vd tti6u chtnh k6 h_oach pMt tri6n g16o duc cho phir hqp thuc ti6n tlia phuong - Cung c5p cho cdc nhi hoph itinh chlnh s6ch nhtng ngu6n th6ng tin vC crlc xu hu6ng diri han rut duo c tu k6t qu,i gr6m sit danlr gi6 th4nh tich hgc t{p cria hqc sinh E6 xu6t cric ki6n nsbi crrip B0 Gino dgc vi Dio t4o tlidu chinh cic chinh s6ch hiQn hinh vd xiy dqng nhtrng "chi6n luo c vi chinh srich moi nhem ph6t tri6n sU nghiQp gi6o dUc Trung hqc n6i ri&rg vi girio dgc ph6 th6ng n6i chung - Ndng cao ndng lgc ve trinh.dQ.dQi ngu chuy6n gia vd c6c linh qtc:.Thipt kE vi tliOu hanh c6c cuQc khdo s6t; Thi6t k6 c6c c6ng cu khio s6t; Chgn miu ltrdo srit; Xri ll vi phin tich k6t qud khrio s6t; Xdy dgng c6c b6o c6o gi6m s6t, d6nh gi6thnnh tich hoc 6p hpc sinh - _ TO6N HOC Sti arg (s-Porz) r G[.6iEC fa (16) - G6p phdn chu6n b| tam thi5 vd c6c cfidu ki6n cho ciin bQ quan li, gi6o vi6n vd hqc sinh tham gia Chuong trinh dbnh gi6 hgc sinh qu6c t6 (PISA) vdo nam 201 U Ddi tugng khdo stil Hgc sinh hgc krp I I nim hoc 2011-2012; Gi6o vi6n d4y c6c m6n hoc aluoc kh6o s6t lcrp 11; HiQu trudng c6c truong THPT c) NQi dung khdo sdt - Khno s6t kiit qua hoc tip cua hoc sinh hqc h6t chuong trinh hqc hj' lop 11 ndm hqc 201120 m6n To6n, Ngt van va Ti6ng Anh - Khio s6t vd c6c nh6n t6 li6n quan cli5n k6t qu6 hoc t6p cria hoc sinh tl) Chpn mdu khdo srit thb nghiQm - Miu ntdng: Chgn ngSu nhi€n 12 truong TTIPT tren toen qu6c thu6c tinh ; thdnh ph6 - Mdu hgc sinh' Chgn 1080 hgc sinh (90 hoc sinl/trudng tlu-o c khio s6t) - Miu gido viAn: HiQl trudng, Ph6 hiQu truong: girio vi6n dqy Torin girio vi6n dgy Ngri ven, girio vi6n d4y Ti6ng Anh e) Chgn mdu khdo stit chinh thtbc - Mdu mfing: Chon ngiu nhi6n 340 truong TIIPT thu6c 63 tinh/thefi ph6 - Mdu hqc sinh: Chgn 30 hoc sinh/trudng duoc kh6o s6t - Mdu HiQu truhng, gitio vldn: M6i trudng chon Hi6u trutmg, gi6o vi6n dqy Tohn, gi6o vi6n day Ngii vdn, glito vi6n day Ti6ng tuI J) Ctic cdng cg khdo sdt Cdc di khdo sdt &inh giti kdt qud m6n hoc + Eai khao sdt m6n ToAn, Ngri vin, bgc ki I lop I I g6m phrin: Tric nghidm vd Tu ludn +.De khao s6t m6n tieng Adr hgc h I - lop ll g6m phdn: Phan Nghe hi6u Ki6n thr?c ng6n ngii vd Eoc hi6u, phdn Vi6t - Cdc bQ phi6u h6i + Phitiu h6i HiQu truong truong THPT + Phi6u h6i girio vi€n d4y m6n Torin Ngri van, Tidng Anh lop l + Phi6u h6i hqc sinh lnp I l g) Thdi ifrAm kh,rto sdr tkfr nghi?m fi chtnh thtix' Kh6o s6t tht nghiQm lop 1 tlugc tiiln hdnh tu ngiry 3-5/1112011 TOAN HOC 14' cludi[A-se-1eJ!!9!2- Khao s{it chinh ttlrc lop 11 <luqc tii5n hdnh n*ty29-3UW2011 I cHrror.,{c rRiNH oAmr cn( Ou6c tt ro CEUONG TRiNH PASEC PASEC - Programme d'analyse des systdmes 6ducatifs de la CONFEMEN CIn ct tr6n Th6a thuQn vd Chuong trinh ph6n tich c6c hd th6ng girio dsc cua fiqi nghi SE trudng Gi6o duc ciic nu6c sri dung ti6ng Phrip giai tlo4n l0 (PASEC X) a) Mqc ti6u chung crta PASEC - Nh{n d4ng cdc m6 hinh nlri truong c6 hi6u que- it tdn k6m, bing crich ti6n hdnh cdc cu6c di6u tra_lheo miu lui chon tai cric truong, sau tl6 ti6n hinb so srfui trdn pham vi qu6c gia vi qu6c t6 - Ph6t tri6n tai m5i nu6c thdnh vi6n nenC luc bdn vd thuong xuydn ue aanfr gia cua ng th6ng girio duc nudc minh - pnO fi6n cric phuong ph:ip c6c c6ng cu d6nh giriL duoc 6p dung cfing nhu cric kiit qui tl4t duo.,c - N6ng cao vai trd quan s6t c6c hQ th6ng gi6o duc cria Ban Thu ki K thuat thudng trgc CONFEMEN b) Mltc fiAu riAng crta W8 Nam - Ddnh gi6 k6t qua hoc tdp cria hoc sinh lop vd lop linh v1rc To4n vd Ti6ng Vi6t vdo ddu vd cu6i ndm hoc, d6ng thoi thu th{p ciic tbdng tin v6 nitng nhdn t6 tric rlQng dtln kdt qud hgc tdp cua hoc sinh - HQi nghi B0 truong Girio dyc c6c nudc sri dung ti6ng.Phrlp tlua k6t quri phin tich vd d6nh giri vB chin} srich- gi6o dr,rc qu6c gia vd cl6 xudt nhiing thay d6i v6 chinh sdch girio duc cho cric qu6c gia - NAng cao ndng lgc cua.tfQi ngu can bQ quan li gttio_ duc vd girio vien v€ ki thuft dAnh gi6 ket qua hqc tap cua hgc sinh theo chu6n qu6c t6 - G6p phin d6i mdi phuong ph6p it6n} gi6 vi dua cdch tidp cdn moi v6 day, hoc ttinh gie vd rhi - TIng cuong hqp ric qu6c t6 linh vuc girio duc Q DiSi ugng kh,fio sdt - Hoc sinh ldp vd l6p n[m hoc 2011 - 2012 (17) HiQu tru&ng trudng Ti6u hqc vd gi6o vi6n day lop vd lop nim hoc 20ll - 2012 - d) COng cqt khdo stit - Oe n6m tra m6n Torin, TiiSng Viet lop vd lop - B0 phiiiu h6i hqc sinh lop vd lop - BQ phiriu h6i gi6o vi6n fuy lop lop - B0 phi6u h6i HiQu truong trudng Ti6u hgc d Mdu khao stit - Mdu hoc sizfi: Chon 2.700 em 1oP.2 vi 2.700 em lop T6ng miu khio srit qu6c gia cd kh6i lop ln 5.400 em - Mdu gido vi4n: Md khtli chon 180 gi6o vi6n T6ng cQng ld 360 girio vien - Mdu Hi€u truhng: Chqn 180 ngudi fl - Thoi diin tiin hdnh khiio stit Khao sdt tl6u vdo: Tudn thft hai th6ng 12 n[m 201 - Kh6o s6t dAu ra:Tn22-25/5/2012 CHT|ONG TRiNH PISA PISA - Progamme for Intemational Students Assessment (Chuong trinh d6nh gi6 hgc sinh qu6c t6) cia PISA Muc ti6u cia chuons trinh PISA nhim ki6m tra xem, Wri A6n tO tuOi kiit thric phin girio duc bit buQc, hgc sinh di duqc chudn b! d6 ilip ring cic thdch thr?c cta cuQc s6ng sau niy ,& mrtc tlQ nio Thu thdp vi cung cAp cho c6c qu6c gia c6c dr} liQu c6 *16 so s6nh ilugc O tAm qu6c tG ctng nhu xu huong cua d[ liQu qu6c gia v6 trinh t10 <lqc hi6u, to6n hqc vd khoa hgc cua hgc sinh alQ tu6i 15 a) M4tc fiAu Ei thi PISA - BO dd thi PISA bao g6m nhidu bdi tap ru-nit), m6i bai tap gdm m6t s6 ciu h6j (ltem) Mdi tl6 thi dAnh gi:i mQt s6 nh6m nlng lyc cua mQt linlr Wc nio d6 vd duo.,c d6ng thinl quydn D6 thi PISA (Booklet), day kholng 60 trang, khoang 60 ciu h6i Thoi gian dd hqc sinh lirm m6t tl6 thi lir 120 phut - C6c dpng cdu h6i dd thi PISA + CAu h6i tric nghiQm kh6ch quar nhiiiu llta chqn, don giin ho{c Phric t4P; b) + C6u h6i tl6ng ildi h6i tri ldi ngEn; + CAu h6i md ddi h6i tri 1di ngin hodc tri ltvi ddi - M6i ki ttanh gi6 t{p trung vio m6t linh vuc chinh (N[m 2000 ld Dqc hi6u; N[m 2003 li Torin hoc; Nem 2006 ld Khoa hgc, Nlm 2009 ld Dqc hi6u; Ndm 2012 ld To6n hgc) c) Chiim thi PISA (Md hda) PISA sri dpng thuit ngt coding (me h6a), kh6ng sri d\mg kh6i niQm chdm bii, vi m6i mQt ma cria cdu tri loi dugc quy dii5m s6 theo y6u cdu cria ciu h6i d) Ctic hoqt alflng cfuitth tham gia PISA - Drffi gi6 c6c cdu hdi thi PISA 2012 vit thyc hiQn c6c c6ng vi6c li6n quan <liin cho.n miu; tAp hu6n K thuat - Tij ch*c khdo sdt th{r nghi€m + D6i nrqng: Hgc sinh sinh ndm 1995 tqi cdc co sd giSo dgc du,o c chgn (35 hqc sinl/l truong) Tdng cQng L080 hac sinh d tudi 15 + C6ng cu khdo sdt Bdi khdo s6t (dd thi) gdm linh v.uc: To6n hgc, Khoa hgc vi Dgc hi6u B0 phii5u h6i hqc sinh BQ phi6u h6i danh cho Nhd trudng + Thdi gian: Tn 17 -19 I 12011 - T6 chtrc khdo sdt chinh thitc + D6i *ong: Hoc sinh sinh ndm 1996 t4i cbc co sd gi6o dgc clu-o c chgn (35 hgc sinh/l truong) 162 trudng thuQc 59 tinh T6ng cOng kho6ng 5.200 hgc sinh tu6i 15 + C6ng cu khdo sdt fii chinh thic, m6i hgc sinh ldm 01 dd thi 120 phrit C6c cdu h6i thi PISA 13 bO dA linh 4rc toan, Xhoa hgc, Dgc hi6u ttu-o c ti5 hqp thdnt 13 quy6n dA thi (booklet) khec Hgc sinh tlugc xric tl[n]r ngiu nhi6n dE ldm mQt 13 tlii 03 b0 phi6u h6i hqc sinh 01 bQ phiiSu h6i dd,nh cho nhd trulng + Thdi gian: Tn 12-141412012 - TOAN HQC Sd arg (s-zorz) r cfudite fS (18) \0t I Prl t& Bni T6/419, Clo a, b, c ld c6c s6 thuc duong Chung minh rdng M( > CAc LoPTHPT +cs) 6(a3 +b3 ruu +(:! atr4 (GV THPT cAc r,6p rncs Ncuvfilr soN nA (GV THPT chuyAn DHSP Hd NOi\ l Gri gi6c ABC sri tam giric c6 ttirlm Mth6amtn didu kiQn TitlhMA: MB: MC ffi)=fua=frd BAi T3/419 Tim gi6 tri nh6 nh6t cria cic tu nhi€n a, b, c th6a mtn a + (a +l) + (a + 2) + + (a + 6) = b +(b +t)+(b+2)+ +(b+8) + 2) (Ydi ct = si5 +(x'? + 6y1' DOAN VAN SOAN Li Thvimg KiQt ViAr rAn Adc Giangl m,*my.; o < m < p, p *0, m, p e N) o6rnaNnnAN (GY THPT chuyAn Bqc LiAu) trfN 16r oLYMPIC + + (c+10) Bti T9l419 Cho ba s6 thgc ToAN duong a, b, c thtm men <Iidu kiQn t*t I I rsfl* bz ]=tor + + l)+zorz c, bc T4l419 Giai phuong trinh 6(r-1)Gd - T8/4I9 Tim tit ca c* cip s6 "guy6n drong (n, &) th6a mdn ttiAu kti.n e"=!fi LE VAN TRACH tDing Na7 Bii "1, Bii (Gy THCS Hdng Bdng, Hdi phdng) (c+1)+(c 11 (GIt THPT chuydn Lam Son, Thanh H6a) Ncuyfiv rn,6.l.ttr NcuyEN =c+ + trdn ngoai ti6p tam giec ABC; D, E ldn luqt li,, ch6n <ludng cao hp tu cr{c ttinh A, B cia tartr gitc ABC Cric tluong thing OD vit BE cit tai K c6c tludng ,hine OE vit AD cit t4i L Goi M la tnrns di6m canh AB Chung minh rine ba tli6m Kl Z Mthine hdns vd chi kni bf,n di6m C, D, O, H cnignii tren m6t dudng trdn NCI'YEN VANNHIE.M t-* * vd r=l!1 1=L*J-* 12 22 32 502 101' So srinh I vd B vudng cin tai - ay Bili T7l4l9 Cho tam gi6c nhon ABC Lh6ng cd.n GOi ry 9W luqt id truc tirn, tam itudn! Bni TU419 (Lfp 6) Cho B.ii T2l4l9 (Lfip 7) Cho tam + al4c \a' a(G= -, = x(* + 2) ) Tim gi6 tri LA] QUANG THO (GV THCS Tan Duong, Wnh Ph c) J5a2 Bni T5/419 Cho nria dudng trdn Lem O tludng kinh AB M lit ttidm chinh gita cda g 78, C ld m6t di6m tren nta tludng lab l<rn nh6t cria bi6u ca) thric _L +2ab+2b2 J5b2 + 2bc + 2c2 JiA +zca+2o, "r rdn, AC cit MO tili g Chimg minh rnng 6m (GV THPT Aiq YiAn B Ninh Binh) tiudmg trdn ngogi ti6p tam gi6c MDC fu6n nam tren mQt dudmg thing c6 dinh kli C di tlQng tron nira <ludng trdn Bni T10/419 Tim rit c6 c6c ham s6./:R.-+lR cho v<ri moi r,y e IR ta c6 PHAMru{I\IKHAI @,iNai) NGUYENTIENTdN " f (d rol) + 11 1,1 + f o)) yf (x) + f (, + f 0)) rnAN Ncoc rsil.rc = (GIt THPT chuyAn linh Phic) TO6N HOC 16 'cludi!#J5-ml3l- (19) Bni T11/419 TrCn tlo4n la ; bl, ta lity k didm phan biQt xb xz; tich cr{c , , x1, Go1 d, ktoang c6ch hr tli ivm x, tn /r-1 di6m cdn lai; li n = 1,2,3 k Tim gi6 fti nh6 nhit crit I+ n=tdn PIIAM NGOC BOI (GV DH trhh, Nsh€ An) Bdi T72t4lg Cho tam giirc ABC vd didm M ki mdt pbang Chung minh rang b6t MA MB MC BC+CA+AB BC CA AB MA+MB+MC FOR LOWER SECONDARY SCHOOLS T1/419 (For 6tr grade) Let lttl165 A=i+ Zr+i+ + * Compare I and B NGUY6N VAN QLI.f CAC DE VAT LI Bni L1l419 MOt ngucri boi thing tr) di5riA b cqnh bd sdng d6n ati6m tl6i diQn ,B d bd b6n v6i vin t6c ban tl6u vo : 2ntls, A chch B mQt ruroangl, : 100 m Coi ddng nu6c chriy ttilu tr6n m{t s6ng vdi vAl t6c v, = I m/s Hdi ngudi tt6 boi qua s6ng mdt bao lau? Biet rang vfn t6c boi gidm cl6u theo khodng crich vd dOn B thi chi cdn lm/s fiII PHAM XTJAN 13cB38-bien Hda, Ding Nail mOt mach cAu nhu hinh v6 and 8= T2l4l9 (For 7th grade) LEt ABC be a right isosceles triangle with right angle at A lf therc exists a point (sv K56Arrl , DHKItN, DHSG Hd N4i) BliiL2t4lrg, Cho tffirilm M ffia = frd inside the triangle wilh GA= i41 : MB : MC T3/419 Find the minimum values of the Find the ratio natural numbers a, b, c satisfying a + (a + l) + (a + 2) + + (a + 6) = b + (b + l) + (b + 2) + + (D + 8) = c + (c +1)+ (c+ 2) + + (c+ l0) T4l419 Solve the following equation 6(r-l)J.r+l +(r'z +4(J,-]-3)- x@z +2) T5l4l9 Let M be the midpoint of the arc AB of a semicircle with center O and diameter AB AC meets MO at D Prove that the circumcenter of triangle ,,lDC always lies on a fixed line when C moves on the semicircle FOR UPPER SECONDARY SCHOOLS T61419, Let a, b, c be positive real numbers Prove that 6(a3 +b3 +c3) >tsou+({oO-"Y +{ic-aY +{a-4i)3 cho bi6t.Rr = x), Rz : TllAlg.I-EtABC 1tt, & = 13o., R4 = 4o., cua c6c ampe k6 a vi a'nh6 kh6ng ttr4ng k6; amp ek6 a ctu I 0,7 A l) Hny x6c tllnh c6c cudng tlQ ddng diQn qua c6c tliQn trd Rr, R2, R:, J?+, Rs (Rs gqi ld dign tro ciu) vd diQn 6p U,a3; Rs = 60, tliQn t& : nguy€n U,qa trhu cdu l, thay tliQn tro Rq beng ili€n tro R thi thay ampe kd a' chi s6 kh6ng (cAu cdn bnng) HEy x6c tlinh R vi s6 chi cria ampe kO a 3) CAu c6 cdn c6a blng khdng thay <t6i gi6 tri cta Uerho[.c cia I _ 2) Git ? be an acute triangle which is its orthocenter and not isosceles; and H, Obe let D, E be circumcenter respectively; respectively the foot ofthe altitude from A, B The lines OD and BE intersect at K, OE Lr.d lD intersect at L I,et M be the midpoint of AB Prove that K, L, M are collinear if and only if C, D, O, I/lies on the same circle edge T8i419 Find all pairs of positive integers (a &) satisf,ing Q,=?#, wherc Cg= ,,Pl ,,;o<m< p,p+0, rz,peN " ml(P-m)r NGUYEN QUANG HAU (Xem fiAp tuang 27) (Hd NAi) HQC ars (s-mP)TO6N r Grufiue s6 rz (20) Luu; Quing Ngnt Nguydn Tdn Trung,6H, THCS Hulnh Thic IQr6ng, DAng Luu liit Qui Phqm Thi Mi Hdng,- Ca9 Thi Thtiy 2ien Nguydn Th y Phuqng, Nguy€n Tdn Pltic, Nguyin Ihi W Chi, l/6 fuang Ph er&r Thoi, 6A Dd Thi Thanh Truyin, 6D, THCS HAmh Phuoc, Ngbia H th Trdn Thi Mj Ninh Vd Nguydn Hai, Nguyin Plan Tra My 64 I1!CS Nghia My Tu Nghiar TP H6 Chi Minh: Nguydn Dinh Duy,6A1 BRX KV rRudc THPT chuydn Tr.in Dai Nghia VIET HAI * *Bni T1/415 Cllo A-2o1l2ott ,i v' 20712or +2011 201220t2 +2012 So sdnh A vd B Ldi n: gi,rti Ta gi6i bii to6n t6ng qu6t DAt 2011, tt6 cAn so srinh .4=(n +11'*t "+'+ n+l " *i, B=(n +l)"1 ,, C = n(n +l)((n +l)' )Nh{n x6t l) Nhidu ban chung to -r*t ) > 0, cl6 A > t B > A D bofc chimg minh b6 dd sau: y'.'*1",.oi y +l a6t x =20112010,y =20122011 cfing suy k6t qu6 2) Cr{c b4n sau c6 loi giriLi tlfng: Yi€t Hda,-6A, THCS Vinh Lei, L6m Thao; Vinh Phircz Npy€n Khduh Ldm, !0 Anh Tudn, 6A, THCS Son DOng, LQp T\ryh, Ngayan fhi Dayan, Nguy4n Th! tu$ DuyAn B, Nguy€n Thi thtb Hda, L€ Thi Thiy Linh, Hoang Thi Minh NglttQt, Phqm Hoang Ly, Phqn thj Thtiy Nga,6Al, NguyAn Xudn Drong, Dlu Tudn Minh, NguyOn Hrong Qujnh, 6A3, Ltu Th! H6ng Nhung, 6A5, Chu_Mai.Anh,6E, IHCS YCn L4c; Thatrh H6a: Ng?yin Tudn Anh.6D.THCS Nht Be Sy TTr Brit Son Hoeng H6a; Nghe An HO Hnu Hdi.6A H6 Vdn Trung.6B THCS Hd Xudn Huong Quj,nh TORN HQC 18' " clgdi[e-t9 jPJI-2912- | l,q+a Ldi gidi Ta c6 Yu n I ttn A= J6 : > ) J4 = z=trls ,l=JơJợ +fi ,JarJq=z > {6 = B = A>z (t) B= i/ơVợ +Vọi {o*{/ợ *Vs = = {o*iE ={s =2 ,-1ddu cin )B<2 (2) Tri (1) ve (2) "v<ri cac sii dwng x, y md x < y thi Ph[ Thg: LA r -:;- Y,tin> thl _r/(n+lft +fln+lft -d(n+lft -(n+l'lrt (n+tf ((n+t)*t +n+1) Tri s6 cria phAn s it n - ,1 1va n > gaing o 6.(6rd6+ -V6 A vd B diu rc n ddu cdn Ki hi6u ll h s6 ngryOn l6n nhdt kh6ng I t-nf vuAt o o x HcN tim | _ 20122012 B= r : Bii Tzt4t' Cho,t=It -,,1a- -,1o *tyraA>B>A-B>0 Vil>0,8>0n€nA+B>0 M[t kh6c, (A + B) - (A- B) (3) = 28 > o - A+B>A-B>0 I B Tt (3) ve (4) ,uu.u o - ' A+ B (4) o '' Il-B"l=0 lA+B) vau >NhSn x6t l) MQt s6 b4n chimg minh ,4 > B bing c6ch nh{n xdt: Ndu a> I thi \G>IG C6 thii ching mtnh dtOC kel qud mqnh hqn - I < A_B< - (21) 2) C6c b4n sau tldy c6 toi gi6i t5t: (tia ni u,-{,rc.rucS S6ng Thao Cim NguyAn Dic Thudn,7A3, THCS L6m Thao; Hi Phrl Th{: Kh€, NQiz Tq Mai Anh,6C, THCS Tam Hrmg, Thanh Oai; Thanh H6a: Le Quang Ding.7D fHCS Nhir Bd Sy, Holng H6a; QuAng Ngai: Nguydn Thny Phlt.ottg, NguyAn Thi Hqnh Dqng Hq Vy Phqn Quang Nghia, NgODn lhi Lw fiet Qui Cao Thi fhiy Diim Vrt Thi Thi, A, THCS Hiath Phr6c, Ngay€n Tdn Trung, 6H, THCS Hulnh Thric Kh6ng, Nghia Hanh, Phqm Th! Vy I/y, Nguyen Phan Trd )uly, Tr,6n Thi lufi Ninh,74, THCS Nghia Ldi gidL o N6uy:0 thi PT (1) trd x2 -5x+ 6=o e * : T4l415 Chilmg minh biit d,ing thtlc [,.])[,.a) [,*!).r \ 2/\ 22) \ 2,) = o [' = ?r L.r (x;y) h (2;0),(3;0) -5x+4=O e (.r-lXr-4)=0 cap <+ l:='r nghi0m (.r;y) ld (l; 1),(a;1) x k}i chia cho Ni5ux = 3/r (fr e N) thi x2 -5x+7 PT (1) v6 nghiQm N6ux:3i+1(teN) s6 du cua o vdi z : t thi,l=l+1<3 (BDT (1) dnng cYoi n>2 th\ t ') (t-l) t=1(1a 12 ll 1nl ', I z\ Ctich l.NhQnx6t: V6i L ) \ z e N-, m>-2 ) tJtl _ I | 2.-ll+-<-.2,n 2*-t _l (2) Th{t v{y, x6t hiQu 12.-t ( l) 2^-r 1n-l I\ -r 2.l2*t 1Dt I ,/ 1M r "rn _1) Do tl6 suy BDT (2) tlu c chring minh /3 r6n thi -5*a7 =Qk+l')z -5(Jk+l)+7 =91? -gk$lg n6n PT (1) v6 nghiQm N6ur:3*+2 (fteN) (r) Ldi gidi G9i v6 tr6i cria BDT (1) Ul thAmh N6u y > thi 3/ = 3.3/-1 :9 Ta x6t VT (l) theo c6c truong hqp 1t *BAi thi (1) trd PT(l)c6hai 1z TRANHIIUNAM (x -2)(x -3) =o PT (1) c6 hai cip nehiQm N6u -y THPT chuy&r Trdn D4i Nghia M!, Tu Nghia NGUY6N XUAN BiN.H *Bti T3/415 Tim cdc sii g nhian x, y thda (l) mdn x2 _5x+.1=3y Doan Trang,8c, TIICS Xuan Di€u .Can LQtc, lhqn Hodng, Nguyin Thi Khdnh Linh Tdn Mai Hian, LA Trung Anh, 8B, THCS Hoang Xu6n Hi.n, Dtc Thg: Quing Ngfli: trdn Th! Mj Ninh.3A, THCS Nghia Mi, Nguyin Quang Tinh.9C THCS TTr S6ng Ve, Tu Nghiar TP H6 C-hi Minh: Do Nguyin Vinh Huy,8A3 Ap dlrng BDT (2) v6i m = 2,3, , n ta 6uo.c 22 -l\fl _.-23-r\1 tfl_.-2,-1 \ A<-t3(t_-2\2 2-t )12 2'z -t) 12 2*t -t) | _ (2' -t)(23 -1) (2, -r) - I)(22 - 1) (2*1 - 1) 2' 2n-t' (2 thi -5ya7 =Qk+21-\3k+2)+7 =9tP -Z,t+tll n€n PT (1) v6 nghiQm cip nghiqm tu nhi6n (x;y) th6a men Pr (1) ld (2;0),(3;0), (1;1),(a;1) D ''n =3.' Cdch ^ '<3.1=3 2.llhdn x6t: Voi (rtpcm) ze e N., m> thi VOy c6 b6n (3) 2^ >m2 -l Ta chimg minh nhAn x6t tr6n bing phuong )Nh6n ph6p quy nap to6n hoc x6t C6c ban sau c6 loi girii t6t: Ph6 Thq, Nguy4n Dtc Thu,An,1 Ai, THCS Lem Thag; Wnh Phtc:-N8ryer? Th! Thu Trang.6A5, DAn Tudn Minh Nguydn Th! Thanh.6A3, THCS YCD Lacl HAr NQi: Nguyin Chi Titng, 9A10 TH.CS Giang Vd, V Dinh; Bic Nintu Ta Thi Nga Nguyin lhi hin, Nguyin Thi Ph&ns,9A,T}lCS Y€n Phong; Nam Dinh: Phqm Quang Huy,7A4, THCS TIan DEng Nirh Thph IJdat Le Quang Dirg,- 7D, THCS Nht Bi Sy, Ho6ng H6a; Hi finhr Ngtyen Thi Khdnh Huyin, 1A, Trdn Tac6 22 >2-I; 2z =3'z-1 (1u6n tfting) Gii sri 2& > k2 -l (vai k >-3) ta sC chtng minh ring 2kn > (k +l)2 -1 viy 2k+t =2.2k >-2(kz -l) =(k, +2k+l)+(k, -2k-3) ThQt = (k +l)z + (k Sd 419 -l)2 -2> (k +t)2 +1 r cfrdiiEf (s-zor2)TORNHQC fg (22) da Theo nguyCn li quy ngp, suy BET (3) ttuqc chirng minh Tri (3)<) l+ I <l* I_l = -',_l 2n m2 m2 DHKcinqiD m2 e l+l< 2m (n-l)(m+l) (4) Ap d';ng BDT (4) vbi m = 2,3, , n, ta c6 n2 3n 322 32 (n-l)(n+l) 1.3 2.4 n+l l) 3(z + -, (ttocm) nl )Nhgn x6t l) V6i fuong t"r" gilo cin KAB, BCH, KDH c6 goc d bfng nhaa d6 chrmg d6ng dang D hqp z > ta c6 th6 ding 0<x<1, 0<y<1 thi 2) Tuy6n duong c6c b4n sau day c6 ldi giii t6t: Vinh Phric: Truong Thi Hodi Thu,.8A, t'tguyAn D*c Dqi,9Al, THCS YCn l,ec, Ng6 Twin Anh,8T, THCS D6ng Xu6n, TX Phfc Yen; Thanh H6a: LA Quang Diing,7D, THCS Nht 86 Sy, Hotug H6a; Qulng Cao fhi <triy )Nn6n x6t C6 r6t nhiau bau 16 giei drimg bni nAy Xitr tuyeD duong bai b4n hgc sinh lop tti cho nhtng ldi giai 6t: Thonh H6a: LA Ouans DAns,7D THCS E Da s6 bai giei cria c6c ban theo rtrOt kong hai c6ch trCu Tuy nhi€n, nhi€u ban lap tuen thiCu chtrt che ve khdDg chring minh nh{n xdt tlua Ng[i: B.u l+x<l l-x vd 0-xXl-y) >1-x-y d6dan, 9)6A<3 ntr{n x6t: Niiu b) Do hai hinh thane cAa AHCD vit ACKD nQi tiiip rtuqc n€n nem dtirm A, H, C, K, D nim tren mQt <ludng trdn Do d6 dtu =frE =dEE=6u 1l' : Tuong tU, vl AK = AB CD GnACA fir hinh thang cdn, suy AC = DK (2) Tt (l) ve (2) suy DH = DK hay tam gi6c Thny Diem, 8A, THCS Hdnh Phudc, Nghia Hrinh }{hE 86 Hodng H6a fi6n Ciaig: tfguyAn WguyAn -Sy, Minh Min, 7' , THCS L€ Nggc H6n, TP M! Tho PIIAN THI MINH NGIIYET *Bti T61415 Cho tan gidtc ABC voi a= BC, b: CA, c: AB Gqi A1 ld trung didm cqnh BC vit O, I tiin luqt td t,rm itudng trdn ngoqi iing fii5p, nQi fidp cfia tam gidc Chilng minh nAu AAlw6ng gdc voi OI thi mn(b,c)<a<max(b,c) Ldi giifi Y'htngnAttinh tllng qu.4{ gi6 su > c Tt A,\ IOI PHAM THI BACH NGOC OA2 *Bli *yn -OA? = IA2 (l) -14 15/415 Cho hinh binh hdnh ABCD drdng thdng AB vd BC lib cdc etiilm tuong ilng H vd K, cho ctic tam gidc KAB vd HC( cdn (KA : AB, HC : CB\ Chilmg minh rdng l) Tam gidc KDH cdn 2) Ctic tam gidc KAB, BCH, KDH ding dqng TrAn cdc voi Ldi gi,fiL Ta chimg minh cho trudng hqp hinh blnh heilt ABCD c6 dqng nhu d hinh vE bCn GInIm tto dovr AB, K ndm ngoai tloan BC), c6c trudng Gqi&r r theo thu tU oA2 li = R2; (p a) Do tu ghc ABCD h hinh binh hdrh ndn AD: BC,lai c6 HC: BC ndn AD: HC, wy r4 =rD +D4 =P *( li htnh thang cdn.Do d6 AC = TO6N HOC 20t Sd 41s DH (s-mP) (l) ban kffi dudng trdn o* =rc -1, uz = 12 +(p - a)2 hqp kh6c chrlng minh tuong tU LFICD h ngoar ue , nQi ti6p tam gi6c ABC Ta c6 nta chu vi tam C16c a ABQ; a+c-b\ b-=\ (2 ) - * -(\2) (23) rn (l) *, €r o c6 -(*, -t)=,, +et-4, -(r, +*f) a2 b+c-o\' ( 4\ (b ) -=l 4bc=2a(b+c1s - c), Thay 2=1*l Q) abc st l) D6 di d6n he thric (2) cbung ta ctng dung c6c hQ thric vecto cAe =@+b+ c)d; zM =78 +72 = (oE + oZ - zd) ve oi.7A q.Oi sina : cosa z si#or, y : z coi d, d6 x + y : z PT thri hai cria hO ta dugc z 49 : vio YAy@+y)z:492=24Ol.l > Nh{n ret I ) Do ss su6t ndn dd bAi phirn tiihg viet in nh6m (dC tdi ghi hong muc "Problems in this issue" in dung) Rat mong c6c b4n th6ng cdm Do tl6 min(D,c) < a < nax(b,c) (dpcm) O FNh{n x6t vd chi k.hi Ji _Ji _ c Suy ra.r )?2 >->TA(2) suvra ' min(D,c) a max(b,c) c6 the Eing thric xiy 2) Cdc b4n sau ttd sua lai tl6 bii vd c6 ldi gidi t6t: Htmg YCtr: Nguydn Trung Hier, l0 To6n l, T[{PT chuy€n Hrmg Y6n; Ht NQi: Ngay€n Duy Khdnh,ll1'l, THPT Ba Vi; Th[i Binh: Hodng Dinh Quang, l2Al, THPT Qulnh C6i, Qujoh PhU; Nghe An: Trdn Trung Eieu, + b.dE + I lAl, THPT Th6i Hod NCUY6].ITHAN}{ HdNC = o vi ggn hon c6: El NQi: Phan Ngpc Luiz, I I A l, THPT Lien Hi D6ng Anh; Wnh Phicz Hodng DO Kien.-llAl, THPT chuyen Vinh Phtc; Hulg YGtt Nguyin yiet Ha, l0 To6n l, THPT chuy&r Hmg Y€n; ThAi Binh: Iruarg Trung Quyit, I Torin l, THPT chuy€n Th6i Binh Bni Dnh Hiiu, I lAl, TI{PT Qujmh COi Qu}nh Phu: Thanh ll6a: Ii 77rj Lan Anh llT, TI{PT chuyen Lam 2) C6c ben sau c6 loi gi6i thing Son, LA Thi.Sar, 10C8, TIIPT Bim Son; NghQ An: Dwng Nt Diep Anh, 11A1, TIIPT chuy€n Phan BQi Chdr, LA Hodng Hi€p, I lA1, THPT Thii Hin' NguyAn Thi Qulnh Loan, 10'11 THPT D6 Luong I; Hi Titrh: Nguydn Hodng Ddng Trdn Vd Hodng, l0 To6n, THPT chuy6n Hd finh; Quing Ngni: rygd Thdnh Dqt, L0 Todn l THPT chuy€n t,€ I(hi€t; D6ng Nai: Phqn Ydn Minh,ll'loin,TllPT chuyen Luong Th€ Vinh H6 QUANG vrNH *Bni T8/4f Gidi hQ phwrng trinh llogrx=2t'z (1) (2\ lall+x+xy,,l++y'=o Ldi gidl Eidu kiQn ,>0 Tt (2) suy y<0 (n6u y>0 thivT(2) > 0) Ta biiin d6i phuong trinh (2) : a.,l1a, = -r.taa rz s, binh phuong hai vii ta tlu c 16(1+ x) = e e e x2 y'z (4 + y'z) -l6x + x2 ya -16 =0 (xy'z-4)(4x+xt'z++)=g 4x2y2 ry2-4=0 or=Vl (3) (Dox>0n6n 4x+ry2 +4>0) n o =4 Hdv rinh (x + y\.2 2' Ini gini Do r < d <4 Thay (3) vio n6n cosa < 0, sina < f 4.2v .(-"oro)* E)' NhQn th6y < (x +y + z)(si# a + co* a + 1) d- G >- -W +y+ / log2 = 2'.2 (4) T a co f ' ( +2locr(-y)-2=o y = -l X6t hdm s6 = 2(x + y + z\ Tri tl6 suy Ji.sina+.[co tluoc ta Vi y < , n6n PT(4) tucrng tluong v6i Srl d1mg BDT Bunyakovsky, ta th6y (G.(-rino;+ (l) li m6t nghigm cria PT (5) f (y)= c.z, +2tog,(-y)-2 y\ = 4.Tln (s) 2+ -2-, 1or r,, \-Y)h2 So TO6N HQC 41e (5-2or2) t sfudiUe Zf (24) ndn hdm si5,f (r) tirl y < o d6ng bi6n Do tt6 PT (4) c6 nghiQm nhdt y = Yu y = -1, suy i Ta c6 vcri x> 2,y> thl ry>x+y.Do d6 b[ng quy nap d6 th6y xt xh > xt + + x] voi xi 2 (i 1, 2, , k) YQry -t : r=-=4 v' Thri lai, ta fiAy (x;y)=(a;-l) th6a men he phuong fiinh ddu bdi V|yh0 tte cho c6 nghiQm duynh6t (x;y)= (+;-t) * *, = -r,[a * S /.r\ / \Vrl 4)= trl ffi vin = i-l Ta tluo c > 0, hem s6 /'r\ /l -= '\./xl /(4 tliing bi6n r > 2) C6c bsn sau diy cO toi giai tiit: Cao Bing: Hgdng Ngqc Dmn& 1lA THPT chuyen Cao Bingl Bic Nitrh: Lru Ngin 12 To6n THPT chuyen Bbc Ninh: Hdi DtaDlg: Vi Dinh ViCt, l2Al, THPT K6 Sit, Btnh ciang; NghQ An: Lttng Thi Mai Hvong, 1141, TIIPT chuyOn DH Vinh, LA Hodng HiQp, llAl, TI{PT Thei Hda; Quing NgLi, Huinh Nhdt Quang,_llToda l, THPT chuy€n L6 Khi6t; Binh Di.nh: Nguyin Qugng Hqi l2TN? THPT Teng Bat H6, Hodi Nhon; Ti6n Gizrg: Nguyin Tri l-lhdn.12Tin THPT chuy€u TiCn Giangr Ddrg ThAp: Au Anh Minh l/6 Hodi Bdo, I lT, THPT chuydn Nguyen Quang Di€ul BGn Tre: /d Thiln Khang ll ToAn THPT chuyen Ben Trc NGU16N ANH DUNC *Bti T9l415 Ta gei mQt bQ sii nguyEn i dgp tich cia cdc sii nguyAn d ndy biins l0lin tiing cila ching Hdy tim tk cdc b0 sii nguy1n d de p ndi tr€n (Cdc sii tong bQ kh6ng nhdt thiAt phdi phdn bi€t) O5 th6y bQ s6 nguy6n t6 de.p phei ch'ha s6 vd Gi6 sir pt< p2 < p,ld c6c s6 cdn 14i b6 Ta c6 10Pt P,=lO(7 + Pt+ + P,) TO6N lffCC 22 'c[rafi[#j5-mpl_ p"=3 this-l<4 = s<5 {pr, ,p,1i chic6th6 1d t2}, {3} Ki6m tra c6c b0 ndy a thAy bQ { } thda mEn ( I ) V{y bQ s6 nguydn t6 dep can tim ln (2 ; 3; ; 5) la c6o horin vi cua chung O FNn6n rtt C6c bai gui d6n tfAu co loi gia,i driurg Hoan nghenh c6c b4n TIICS sau dd tham gia giii vd c6 loi giaLi <lung: Thanh H6a: L? Quang D ns,7D, THCS NhE 86 SV Hodng H6a: Phn Tbg: Nguydn Tidn Dnng Nguyh Einh -Mfu, 8A3, THCS Ldm Thao; \tnh Fh[c: NguyAn Ti6n Thip,9C, THCS Vinh Tuong DANG HTNG THANG *Bti T10/4f5 Cho ndm ifiAm A, B, C, D vd E cirng nim tr€n mAt ihfing trdn (cdc tlidn ituqc liQt kA theo chiu kin ding.h6\ Cqi I,I, N, P vd Q.theo th* tr ld hinh chieu vu6ng goc cia E xu6ng aic ifudng tMng AB, BC, CD vd DA Chrimg minh riing biin iluing thing MN, Nl, A!( la ftp myin cia mQt parabot lO:: co teu cuem la li Liri gidi Trudc htit, ta cdn c6 hai b6 dd Ldi gidi, (Theo ban Trin Quang Todn, 1IT, THPT chuyCn Quing Binh) Bd e pr p"=7+A+ +p, nOn =se{2;3;4;5} Tir {p1, ,p,-,} chi c6 the ld {2}, {3}, {2 ;2}, {Z; 3} Ki6m tra c6c bQ ndy, ta th6y kh6ng c6 b6 nio th6a mdn (1) oYbi p, =5 thi s<3 + s e {2 ;3} Tr} 116 =r-, ),F-Fyf fCyl= a = -y = 13) -''' Jx e) Yoi p,=2 thi (1) vi6t thinh 2n+7 =7, vd li Y6i 't l= >_ e e (p"-1)(s-l)<8 o /(rl = 5l a a / z(t +z\ /'(r) + + Do s>2 n6n tu (2) suy pt -1<8 p e {2;3;5;7} n )nnA" rer 1) C6 thiS suy (3) blng c6ch kh6c Vdi ;r > 0; ), < 0, PT(2) c6 thi3 yii5t thdnh : !11 p, + = A p, (A + + p,_) p, s+pn+7>spn,dtl6.r=A * t p,_r A (l) I Cho ndm didm A, B C, D E c ng trdn Cdc didm M N, P, Q theo th r t$ ld hinh chi6u wbng g6c cia E ,:e,n.7d: duons thdng AB: BC: CD DA Khi hinh c"hieu w6ng gdc cua E trdn cdc itrdng rhdng NP, PQ, QM citng rhu6c m6t dtdng thdng dA thuQc mQt dudng W, (25) toln TTl 35l (TH&TT I chinh la ldi giai bei s6 355, th6ng 1.2007) Ph6p chrtng mturh b6 dd di Cho di6m F vd itudng thing @) kh6ng ili qua F Parabol (P) ryhQn F h fiAu Bd Hdy tim gioi hqn cila day s6 b, = a1+ a2 + + ar @) vdi Ldi giAi Nhdn xdt didm vd (L) ld duong chuiin N,fu M thuqc (L) thi dtdng trung Wc,aia FM tidp nic voi (P) Ph6p chimg minh b6 de kh tlon gian, b4n tlqc tu chimg minh o Tr0 lai gi6i bdi toAn T10/415 o Voi b6t N', V<ri n e b,+t = q + a2 ta c6 + L - Ji,a + + o, + o,., = ki.relR*,ta b" r+1>2 "6 chimg minh bing quy ouo l Do d6, ,*[o n ta thiiy >2-J2,VreN- D, oVoio<x< r<t l\ -r.,J= **!-( , x , o, ,cn i-(!-!)= r,-r,[,-!), \v x) \ ry) =(r- ,*!xy r r*1 > f(x) > f(y),trong d6 ta ki /(x) =v11-JZ 1r, x hieu Gpi X Y, Z, T theg thrl t.u h hinh chii5u cua E tr6n cdc duong thnnp MQ, MN NP P8 Theo b6 de I thi Y, Z, T cirn.g thuQc mQt duong theng, ki hi-Ou h (d) racit ,( li vi t\r tam E ti si5 Z CQl (P) parabol nhfln E li ti6u di6m vi (A) ld ituong chu6n DEt X' : EX n (q D,tongnhifln MQ ltr trung tr.uc cua W' Do tt6, theo b6 dd thi MQ n6p xnc vo1 (P) Tuong tu NP, PQ, NM cimgti'p xirc vdi (P) T6mlai MN, NP PQ,"QM cing ti6p xric voi G.qi (A) 6nh cua (d) qua ph6p parabol (P) (c6 ti6u tti6m ln E) FNhin Thanh HoAz LA Thd San, loc8, THPT Bim Scm, Nghe Ar; Chu Tv Tai, 1l{l2 TIIPT Di6n Cheu.2 Ar)i Quong D6ng, I I Al, THPT chuyen DH Vinb: B6n Tre: LA Thi Minh 71<io I lT THPT chuy&r B€n Tre NGU\tNMINHHA ) Arqc xac-dinh - Jl, n =1,2 Cho ddy sd @ bcri a, = l, ah,t = L al + + a ,(+)=+ fh)=z-Jr; f(b,)=2-Jr.lg-A =2-lr.T*-a=*)a = r[, \ -4) 2) rtr -0,7) = o,e < I = I bz tr x6t C6c ban sau c6 loi gi6i t6t: *Bni Tll/415 b,= b2= O; 7' Tr) c6c nhfn xdt tr6n suy ru h = fh).b, = f(k), t, bt <no (r) b, <$; fli)=i'u I b,rhrl "'12 Nhuvflyta c6 b, < bo < s6 41e bu j, TORN HQC (5-2012) 'qndiuezet (26) h>k>bsr rl ' Jr' Ki hiQu p = lim b2", q = lim b2, y Ta suy t'l o = n, b,-, = 6,+1- J2,z i= Cho n chin, n > +co ta duoc ) N' ,=o*!-Ji p pq=p2-Jip+t Choz16, n-)+@ = e (1) > o=r*!-Ji q (2) vd (2) suy (p'-q')-Ji@-q)=o e @-d(p+q-Jr)=o f, Thay vio (1) ta c6 4{, - o) = *Ao .' n6u (trzr-r)' =o o qui li lim Ldi ld ham don gi,AL Nhda thi x6t ring q=Ji-p /(x) fa;pl.Ttilt vfy, l,*ri cti6u tdng tr€n tloSn f(x)- f(x)=?!21-41 4+l xl +l (xz - n)(t(xz + n) - 2xrxz + +l) nen him s6 X.r; U him doan la;Pl (xr'z +1 o e 2f -2.1-p +t = o =i=, =nI i=+ = - v- 2), O +1)(x] ctc,n itiQu tr -i ,lz Ngpc Lrim" llAl,TtjfllT NCIJYEN MTNH *Bti I e( t\ = f ( 6\ - +ll +' t2 r, o, - r0 - a)(t@ (d2 Li€n Hd, D6ng DIT f t2 + h - 2ttp + z) +lxlg, +l) I SJt2 +l(2t'z + 5) ,< Anh; Hung YCtz Nguy€n Thi Viet Ha, 10T1,_THPT chuyEn Hrmg Y6n; V-rnh Phitc: Hodng D6 KiAn, Drong Phudc Tho, llAl, THPT chuydg \tnh Phic; Nghe Ar: Li Hoang Hi(p, )1A1 Nguyen NgpcMinh 1142, TI{PT Th6i Hda; D6 Bd D*c, l1Al2, TT{PT Di6n Chdu Il; Luong Thi Mai Huong, 114'1, TTIPT chuydn DH Vinh; Binh Phur6'c: Cao ltdn Tiin, llA1 THPT chuy€n Quang Trung; Ddng Nai: Phqn Vdn MrrI, I lT, THPT chuy6n Luong Th€ Vinh 16tz + 25 +:1 t6 Vi v{y g(tan a) = SJtan'oi(2tarr'o+s) 16tan2 a + 25 L[-1-.r) COS4\COS'4 ) t6 ^ cosz a +> - = 16 +z4"o"o cosa l6+9cos% zJlo'u rcJa > ' l6+9cos2a 76+9cos2a Do d6 e(tana) T12l415 Gqi d, ld hai nghiQm thuc phdn bi€t cda phuong trinh 4x2 -4tx-l=0 Cring voi hai BDT tuong lu, ta tluo c (t td tham s6 th+?c) vd hdm s6 f xdc dlnh tuAn doqn fa ; pl g(tana) g(tanb) TOfiN HOC 24 tlng tr6n a+B=1'ap=-rnit Jt2 D" = )Nh$n x6t Ddy B bdi ror{o gi6ri h4n d4ng co bdur L&i giei tr6n kh6ng phrii dung tl6n c6ng cU tlao hnm d€ khdo sdt him sd CdLc ban hqc sinh sau c6 loi girii t6t: F{tNii: Phqn g(tana) g(tanb) g(tanc) Theo <linh ll Vidte ta c6 Nhu vdy ta ltudn cb p = q H0 llt-3J6 . ] .r- _ p+q-Ji=o Chir mdn sina+s;nb+snc =1 ta cd biit diing thilrc d1\1h<p,tacb pq=q2 -.12q +t Tt (l) xithdnsij s@= ff$tf@)- I*rt<O chilng minh ring voi o,t,".(o;!) *ao 'cfqdil$ so ru @=2:-t: x2 +l tffil_ 111 s I +C(tan r) j ,- (16.3 + 9(cos2 a + cos2 b + cos2 c)) l6J6' (27) =;[trt a + sin2 D+sin2 -rOin2 Q C6 c)) dab /\ Ti o-b.c [ 0,1 I ue sina * sinb + sinc: I | '2) 3(sirf a+sin2 b + sin2 Ldi trd vd vi tri ban diu Diiu ki€n dd ldgt2 thA quay gi,rti =l c) > (sina+ sinD + sinc)2 *'g(tanc).*o ' C$ana) S(tanD) FNhgn x6t D6y ld mot bAi to6n vd b6t eling thric hdm thuoc dang kh6ng quen thuQc o b$c phd th6ng, n€n c6 nr China ben tham gia giai Dey ld bni Mathematical Competition, Problem 15 Dem 2004 Da s6 c6c bpn tl6u girid nrong tu nhu crch da trinh bdy d t6n C6c bgn sau d6y co loi gidi durg: liy it vtrh Ph(c: D(ng Quang Tuiin, Dmns Viii Tha, I 1A1, THPT chuyen Vinh Phric; Hd N0it Phqn2 Ngoc Ldm, llA1, THPT Li6n Hd, D6ng Ar:/l', NgryAn Duy Khdnh, llAl THPT Ba vi; YutgYGn: hntg Mqnh Cudng, Ngay€n Tnmg Hieu, l0Tl, THPT chuy6n Hung Y€nr Th{i Blnb: Hodng Di4h Quang, Biti Dinh Hidu llAl THPT Qulnh C6i; D6ng Nfit Phqm Vdn Minh, llT, THPT chuyen Luong ThC Vinh; Btnh Phutrc: Cao Ydn TiAn, _118, THPT chuy€n Quang Trung; Btnh Dinh: iy'gryiz Quang HiL l2TN2, THPT Tang Bet H6, Hoii Nhqn; Nghf An: Le Hodng Hiip Trdn Trung HiEa, l l A l, THPT Th6i Hda NGUYENvANMAU LU415 MQt vitng ti trudng tliu vdi cAm mg t* B : 2.rc4T nAm tong mi€n gitri hqn boi hai mfit phdng song song vtri cdc dudng s*c tir vd cach iloqn b :15cm Ti v! tri cdch m(t gioi hqn v ng ti tnmng itogn a : 3crn" mAt electron duqc bdn vi phia vimg lv co phrong wong goc It ffircng vot vqn toc vni aic dudng stic nr vd hqp voi mQt gitti hqn ,-o vitng ti trudng gdc a : 45" nhr hinh vd BiAt kh6i lrqng vd diQn tich cua electron kin lrqt *Bni a ld m vd 9,l.10atkg ng tnnrng , d0 lon vdn t6c a) D6 electron kh6i vimg tr: trudng theo phuong ru6ng g6c mpt grcri han thi n6 pMi chuy6n tl$ng theo cung f,.dn CD c6 tlim li Or nhu hinh v€ Brin kinh qui dao cria electron b = cosa cosd khid6h R,=4C=CE Q) Tri (1) vd (2) suy vfln uic cua eleckon ld lelat mcosa Thay si5 tinh tluo c v: 7,46.106(n/s) b) D6 electron trd vA vi tri ban ttdu thi qu! <lao phrii tl6i xring, nghia ld n6 phAi chuydn tlQng theo cung trdn CFG c6 thm li O2 nhu Tt da a) Ra khdi vilng ti trudng theo phuong vw6ng g6c voi mdt (1) a ldk=o2c=ozH-aHcosa cosa cosa Tinh electron alii n6: R = ,^' ,-r-'U-R >- -' vls -,'-' ' dinh bcri l"l su = hinh v6 Brim kinh quy tlAo cria electron tl6 e: -1,6.lo*1eC qua tirc dqng da Bd tro Khi electron vio vung tu truong n6 s6 chuy6n tl$ng theo quy dao trdn voi lUc hu6ng t6m li luc Lo-ren-xo Bdn kinh quy ateo trdn x6c B ( ) vri (3) suy vfn ttic cria electron (3) h lelna mcosd Thay s6 tinh <luqc v = 1,49.106(n/s) gini hqn ving ti D6 electron c6 th6 chuy6n dQng theo cung trdn CFG nhu th6 thi D phii kh6ng nhd hon trudng tloan CF, tuc li TOfiN HOC So 4re (5-2012) r sTtrdi[eZS (28) b>CF=qF+qA= " *o=o(r*' ) ( cosa/ wa b) So dd mach diQn tluqc mic bi Dhu hinh vC Thay s6 ta tluoc b>7,24(cm) D >Nhan x6t C6c b4n sau c6 loi giii <ting; Tt hinh vd ta c6 {[(&,t&) / (& ntnu)] nt (& // R )\ // & D6 ddng tinh NGLA'EN XUAN QUANG *B i Ch9 R,,, L2t4t5 bay diQn trd 112.s R+0,5R R Ru, 0,6n mdc theo so d6 AB nhu hinh vd Gqi 1' Edt gifra A va B mAt di€n dp U cd gid t/! ta c6 a) Miic gifra C vd B mQt v6n kii l2Y ti tudng thi kA bdng mQt ampe kA H *ong thi ampe k€ chi A Ldi gi,fii a) Tr) hinh vE cua n,^ =2R dA bdi vd c6c dt li '-UU3U RAD+RDB 2R*R 5R' = ua=lu*=l^-=l# Suy 2RU -) n:Y.n=! 5R5 Do 66 ugs =(ra +(ror ZA' Do + RDu R+0,5R n f5 2R & =& =R n}n Iz=It l7=+-+=+=4(A),suy RR R s(o) D ht6n xOt C6c b4n sau tt6y c6 lai giai t6t: R= =1.T =T DLag D4o, Nguyi-n Vdn Long I I A4, NguyAn yiet Anh, Truong Dic Id, I lAl, THPT Thudn ThAnh 56 l; HA Nam: Dizi Nggc Hdi.l2 Li, THPT chuy6n Bien Hda" Phi Lj; Nam Dith: Biti Xudn Hiin, t, Li, Trdt Thi Thu Huong.l I To,in THPT cbuy€o L€ Hdng Phong: Htmg YGo: Nguyin Trung Hie 12 Li, THPT c-huy6n Hung Y€n; Thii Binh: Nguyin Vdn Minh Nguydn Vdn Son, 11A2, THPT Bic D6ng Quan; Thatrh H6a: Za Thqnh-Hdi lOA3 THPT Luqng Dic Bing; Nghe Atr; yid larin I0A5 THPT chuydn DH Yilh, Chu ryCuyAn -O, U=15(V) TORN HQC RAD 10 VItrh Phi-c; Biri Vdn Vinh,gA THCS Li€n Hda Lip Thgch; Bilc Ninh: Vi Si C6ng l0Al THPT NguyEn J Ddng diQn qua mgch chinh u^, cuong ilQ ddng tliQn qua m9 ch ADB , v1,y IG = t - Hdy xdc itlnh U vd R riid6 li R ,,u15 khdng d6i li€u tld cho ta c6 1,5.R ,u152s fii,ld R, drnt b) Thay.v6n c Rn = R; RD, = 0,5R Cuong dQ ddng tti€n qua mach chinh bdng gi6ng hCt nhou, m6i cfi cd giti v6n k€ chi <Iuo clqdi[6 Q0_!eJ!aq?i_ nr.Tdi, llAl2, THPT Di6n Chdu 2, Nguyd'n htng Hi?u, Nguyin Hdi Hdu 10A1 THPT NguyEn Xudn Ou D6ng Th pl Hujtnh Thanh D4 II Li, THPT chuydn Nguy6n Quang Didu; Quing Binh:.Vgaye:z Hodng Duy Thdnh,l I Li, THPT chuy€n Qudng Binh NGUYEN VAN T}TUAN (29) @ *Trong hai ngiy 14 - l5/4/2o-12, ri TP Nha Trans tinl Khrffi Hda tl6 di6n HQi thdo khoa-'hpc bii drdng hgc sinh gi6i Torin THPT cric tinh puyAn hdi Nam Trung bQ vd Tdv Nsuydn liin thti ftai S& GD-DT Kia*?iti""a HOi TorlLn hec He NOi ph6i hqp ddng t6 chr?c Tham d1r HQi thio c6 ldnh tlao cAc Sd GD-ET, tt4i di6n Ban Gi6m hiQu, gi6o vi6n Torin c6c trudng TIIPT chuy6n thuQc khu vyc Duydn h6i Nam Trung bd vi TAY Nguyen g6m tinh Binh Dinh, Phi Ydn, xialnn aIaa, Ninh rhugn, Ldm Ding, Ddk Ldh Ddk N6ng, Gia Lai, Kon Tum Ong LA Xudn Thdn Ph6 Chi tich UBND tinh Kh6nh H6a de toi du vd phrit bi6u chig mtrng HQi thdo HQi th6o chia lim hai phdn' Phdn I g6m nhtrng b6o c6o cira c6c crin bQ quan li v6 phrit tri6n nang luc dQi ngu gitio vi€n ciic truong chuy6n, ph6t hiQn vd b6i duong ndng khiilu cria hoc sinh chuydn; cricb thric quan li chi tlao, CranC d?y vi hqc t4p d ctic lop chuydn; tl6ng thoi thdo lu6n v6 li6n k6t b6i dud'ng hgc sinh gi6i Torin THPT khu Wc DuyC; hai Nam Trung bQ vi Tdy NguY6n Phin gdm nhtmg b6o c6o vC Chuy6n iI6 bgi dudns hoc sinb ei6i Torim TIIPT vi c6c vin aE tie-n quan cua- ciic nhi khoa hqc vi girio vi6n To6n ciic truimg TIIPT chuyen' PROBLEMS.- (riip tans 17) TOWARD MATIIEMATICAL OL}MPIAD T9t419 Let a, b, c be three positive real numbers satisfoing | 1')=,0[l*l*l)+zorz rsf r + * [r, b2 c2 ) \ab bc ca ) Find the largest possible value of ' cntc'ipi ngii *noo _t J5o'+2ab+2b2 I J5c') + zca + 2a'? J5b2 +2bc +2c2 hgc Ctic chuyai id Todn hgc bdi dwdng hgc sinl gi6l pey V hoi thio diu ti6n theo tinh than ki k6t ph6i hgp hoat tlQng bim uA li6n k6t b6i duong-hgc sinh gi6i, ttdc biQt ln b6i du6ng hgc sinh gi6i Tortur TIIPT vd THCS HQi thdo vinh du d6n ti6p TS I/ri Dinh Chudn, VU Truong VU GiAo dpc Trung hqc, BQ GD&DT, cic nhd khoa hgc, nhi gi6o 16o thdnh, c6c nhi quan Ii, c6c chuy6n gia gi6o duc," c6c nhi Todn hqc brio c6o t4i phi6n toan th6 va c6c gi6o vi6n tlang trsc ti6p b6i duong hgc sinh gi6i Toen bAg crio tpi phi6n chuy€n d6 Sing 2714, Ban Ttt chuc HQi rhdo da tdng ket Ki thi HOMO 2012 vi tuydn duong ktren thu&ng c6c hqc sinh <loqt gidi: L*a tudi Junior 112 gidi,Nhdt, 29 crai Nhi, 41 gii,i Ba, 16 gi6i Khuy6n khich) L*a tu6i Senior (l l giei Nhat, 28 giei Nhi, 48 gini Ba, 14 giii Khuy6n ldich) Tap chi TH&TT dA tham fir cri hai hQi theo, tang t?p chi vi tl[c san cho cic tlai bi€u tlng qui cho c6c em hgc sinh doat giai NheL Nhi crla Ki thi HOMO 2012 rnArr,rNcQc rr+UE (HOi Todm hoc Hd NAi) T10Al9 Find all functions /:lR-+lR that for all x,y e IR we have f ({ @) +.f ("f (*) + f 0) = such yf (x) + f (* + f U\) - Tllt4l9 On the interval la ; bl, prck k distinct points xr, xz, -o x1, l-et d, be frrc product of the distances from x, to the t-l remaining ponts; n =1,2,3 ,/r Find the lr smallest value expression ' the 'f' Trong hai ngdy 26 - 27 /412012, t4iTntdng THPT Chu- VIn An, TP Hi NQi, So GD-DT Ha NOi ph5i hqrp vdi HQi Toin hoc Hn NQi t6 of I l a=ld" "ll2l4l9 Given a niamLgle ABC arld an arbitrary point M Prove that MA MB MC BC+CA+AB BC CA AB W+ W+ MC Translated by LE MINH IIA TO6N r clirdiwzz e (5-2012) Sd 41s s5 ts-zor2) HQC (30) ffiwffiffiffiw hinh hgc kh0ng gian ttCUVEtt tr,ttrun nA (GV Tntitng THPT chuyen DHSP He NOi) fI cAc sAI ToANHiNH HeC KHONG GLAN cua V.V PMXOI,OV vi I.F SARYGIN trang 25, Nhd xu6t ban Dd NIng, ntrm 1997 c6 mQt bdi torin Wc fi hinh hoc kh6 hay rone^cuonsacn OBei todn l Xit C6 hai ti duo c Ta c6 S = San r.,ro = gioi thiQu loi gi6i Bdi + SHnH,u, + Sn,arsr) Trudng hW Hinh chi6u vu6ng g6c cua ktr6i tu diQn ddu AA.ly44 tr6n m{t phing to6Ln (P) ld mot tam Cho tit di6n Alfila vd m{t phdng (P), ta ki hiQu diQn tich cic tam giirc AzAlq, Al+4t, Aq4d2, A/2A3 theo thir tU h S,, Sz, S:, S+i giic, kh6ng m6t H2 tinh t6ng qu,it gia sri tam girl.c tl6 li mH|r-L(h.2) diQn tich hinh chi6u ru6ng g6c cria c{ic tam Al+4r Aq,4/2, AdzAt trdt mlt phing (P) theo thr? t.u h s;, si, sl, Si; diQn tich hinh chiiiu w6ng g6c cira trl diQn AAzAy4a, ffin Ntphang (P) h S Tru6c hiit, ta cin c6 ba bO t16 gi6c AzAy4+, Tac6 =]Is; I SHoHrH, + SHfi2li) tcn".l B6 dA N€u (P\.tac6s=1ls^ Hinh S = Sa,arn, =1(Surnrxo*SnrHoH, B6 dd Cho t* di€n AAzAla vd mdt phing o ld tdm c*a t* di€n diu A|A2A3A4 vd M ld di€m bh ki khdc o thi I Chfing minh Gqi H1, H2, ru, h theo thrl tU hinh chi6u ru6ng 11+ + SHrHnH, 2L""' c6 cqnh biing a vd mfit phiing (P) S ld di€n tich hinh chiiu vu6ng g6c cua A /2Ala tr4n (P) Tinh gid tri nhd nhat c a S theo a sE )\Snrnra, : ls"' tffit OBiri todn Xdt tti di€n diu AlA2Ala Bdi b6o niy o Tnrdng hqp Hnlr, chi6u vu6ng g6c cria nrOi tu Agn dd,a ArAr.errEo h€n m4t;h-eng (p) li mQt trl gi6c ldi, kh6ng m6t tinh trirng qu6t gi6 srl tn gi6c ldi d6ld Hfl2ruII4(h.1) di€n ctiu ArAzAy4q c6 canh bdng a vd mil phdng (P) S ld di€n tich hinh chidu vu6ng gdc ctia AtAzAy4a, tr€n (P) Tinh gid tri l6n nhtit c a S theo a MQt c6ch t.u nhi6n, bdi todn sau trulng hgp xiy "os'(o.+.oil\=! ,?.or13 fl, goc ci;o A1, A2, 4, A4 fil rll,lt pheng(P) TO6N HOC 11 H3 Hinh I 28' cludifie- te-1!9J! al2- Ch*ng minh Ift6ng m6t tinh t6ng qtult gia $i kh6i tu dienl /2Alac6 c4rttbing 2Jr Gqi Ad7AlsAlu[yLt -lir hinh lfp phuong ngosi ti6p khtii trt di€n ddu AtA2AlA(hA - (31) Ding thric xiy vi chi ba s6 b6t ti bi5n s6 q(l<r<4) hoflc cirng kh6ng 6m ho[c cr)ng kh6ng.duong, vd chi hai s6 ndo tl6 b6n s6 a, (1 < i < 4) blng kh6ng vi hai sti cdn l4i mQt s6 beng E mOtsObang ^ r.: -{,E._ (<tpcm) {:, Trd lqi gidi Bdi todn $ D6 thdy Hinh D6 th6y binh lfp phucmg niy c6 c4nh bdng Gqi O lir tam cua tu diOn ddu I lzAyLq, X, Y, Z theo thfi tu le trung <li€m cria AzAt, Alu A/2 Lap h0 toA tl$ Descartes Oxyz cho c6c tia Ox, Oy, Oz tuong fng chinh circ tia OX, oY, oz li Ta thiy At( - l; l; l), Az0; * l; 1), At\; 1; l), Aq(- 1; * 1; - 1) Gin st M(r; y; z), ta c6 I I<i<4 - I.,I "o"'(oZ-oil\ _(-x + y + z)2 +(x - y + z)' +(x + y - z)' +{-x - y - r)' ' \Jt'!i +f +*) 4(x2 +1P +22\ 4.(dDcml '' 3(f +f +2'z) -3 -\2 \a,=0 lata4 vd \ai =!J lri<4 (Al 4A ), (A 4A /2), (A /2$), t_, S=; ) S, (heo86tt6 l) I l<i<+ ta c6 l, I S lcos(Ol-OM)l =:I t<i<t I = f ,,,2 l.o< -,-)l (theo (1)) Ul AtA2Ay44l titdiOn itdu n6n ! Dort6 Z : OAz >[n.r.il r,,ll zl +tz r,rl= *'[ *"[ "li J fP I e a) =Ae = OAt = OAq, cosQZ.ofi)=o (3) l<i<4 theo 86 dd 2, ta c6 *:=i (4) ,?**"'(dl,dfr)=: Dlng tlrlc xiy <+ OM :lia 2@ =r O4.OM=0 Tn (2), (3), va (a) theo g6 d,i 3, = ,?*OA (2) tni > pll [ >r.rT =[ zur][ zr-r]= 1994\ lEiel \tsr<4 ,/ \r<34 /\KEl ,/ ) +lqll-cl) voi c6c m[t phing (AzAli, vu6ng g6c suyra Chtns minh.Tathdy =,I(a (1) Gqi OhtAmcua tir ilQn ddt AtAzAy4qvir Mlit hinh chi6u ru6ng g6c cia O t6n m[t pheng (P), chit ! fing OAt OAz, OAt, OAq rheo thf nt Tr! t16, chri y dng OA1 ,l*^loPzfr = "A -=a2 l<i<4 B6 da Niiu ctic sii a1(1<i<4) thod mdn cdc tliiu kiQn =S2 =S3 =5:4 = *y' ru S>$ 2.12 v:udng g6c v6i hai hong b6n ctuimg thnng OAt OAz, OAt, OAt e" OM :rtring g6c v6i mQt sru mflt phlng (oA/), (OA\4), (oA/4), (oA24), (OA2Aj, (OAl4) a OM song song voi mQt cpnh nio tl6 qia tu di6.n AdzAy4t, e Nt phing (P) vu6ng g6c v6i mQt c4nh ndo <t6 cua t& diQn AdzAy4+ T6m lai girl tri nh6 nhit cria U ,U :i 2J2 O HQC (s-zop)TOAN t cTudiEf Zg Sti 41g (32) LTS Tap chi THTT si 416, 417 ild gidi.thigu din bgn dltc r\i Q CuAc thi gidt thi,u Sdch thum khiio cis NXBGD YiCl Nam vd Danh mqrc mQr si ofin ,;ticlt Trung si ndy ,vd sA sau, chfing fii xin gidi thiQu ti€p Danh mltc cric cuAn sdch cia NXBGD Vifl Num di trgtii clq'thi viAt gidi thiQu sI,cE TEAM Kfiio THEo cAP L6P Bdi dudng natrg luc nghe n6i ti6ry Anh trip Etrslish for me) - kCm dia Bdi du8ng naDg tuc trghe n6i ti6ng Anh top 'Enelish for me - teche/s zuide) 3im thu vi phan tich tiic ohAm virl hoc l0 - TaD Tap 3iAns vIn KiCn thtc bd ho Nstr vEn Kren tltuc llo tro Nsu van / Kittn tlruc b6 trq ) Trc sii- dich Ten s{ch bd stch STT VAr hoc Vi6t Nam Net Neuy6n Qu6c Hung, Nguy6n Qudc Tu6n 6n Van Lone Irdn vnn TAn En 13 30 16 sie v6n chuons t4 B6c H6 d Ph6D (s6ch l5 Bdi hoc ld ei ? C6c rhd H6a hoc tluoc siei thu&ne Nobel T{c sia dich sia Manh S[v V[ Ou]n Phuons H6ne Hd - Nsuv6n Thi Tini Hii Ndoc Eai 6n Ou6c Tin '6n 6!h) Ctu vi drns dau kirh thini Thens Lons (ThC ki xU-XVIn ) 3ev c6 c6 ich vi6t Nam - Tdo l T6o Shan &ms ve bft tich nhn vnn Vi6t Nam - Tdo l Tip 20 3hAn dunp vA rhAn dinh cria nhi vin v6 t6c ohim trone nha trudre Tao 2t :huven b va thi cu cua ViCt \am thoi Dhons kien 22 36ns nsh6 si6o duc - TeD LTaD2 23 3u6c rloi L,i C6ne Uan 24 Dpy hd c6 chi ti6n thu ) Khlc Phi (CB) Hoine Thdnh ChwE sich b6 s6ch 100 bei toi{n Khic Phi (CB 6n vui vd tdc nshiem chi s6 cAm xirc EQ t2 l6 ltli Irin Dinh ttrfc bO to NsE vnn 9 Ki6n thfc b6 tq Ne[ vhn 1l nhns cao - T6o Tdo l0 Ki6n thtc b6 trqNst vtu 12 naru cao - TaD TaD ll \lhEns chuv& da hav vd kh6 H6a hoc THCS STT (CB) An Phan Hiv Dine Su { CB) frdn Dinh Si {CB) Neuv6n Vtu Lotrs (CB) 6n Vin Lone (CB) oHCS) Ki6n sii Nguytu Qu6c Hung, Nguytu Quoc Tuan 17 )u6c Ch6n l8 l9 Yd VIn Chi Tiin HoD Irer Thanh Phuqns I '6n Vnn Tune Than Phuqne Thu Thi Hanh Th6i Neoc Tu&ns a6 Nggc D4i LC DiDh Hd n frieu Anh Ba, Nggc Linh 'suu tam-bi6n soan) 25 26 27 28 29 D?y Vt Hoa My, Duong Quirh Hoa tlc c6 tr6i tim yeu thuong n vqi iic phArn vin chuons :suu tam-bieo soan) Dhuons E6ns (Trutre QuOc - Nh6t Ban - Afl D0) Nzuv6n Thi Bich HAi Done Duons xua Em di them det nudc - TAD l TeD eD Em tim hi6u vi thgc htuh ph6p luft Iap 1: Ph6p tu4t t ong Duims C6ns Minh Xuao vinh V[ Xuan ViDh tloi stiog gia dtnh Iap 2: Ph.lp luat tong Dha tluong Iap 3: PhAp luat nqi c6ry cong I4p 4: Ph6p 1u6t tham gia giao th6rg IaD 5: Ph6o luat voi c6c te nart xA h6i 30 Evo Heritase: M6t thion dudne SDa 31 Vi hei oh6o siao duc TORN HOC ZO' cltrcnfie-:9ileJlf9sl- Ih6i Quane Trune (CB) HA Nsoc Dai (33) 46 41 Giai thoai da su Vi6t Nam Guons mit nzudi thdv HuA - Lane man Viet Nam GIue - The romance ofvietnam) Huv Cin - nson lrta thi€ne kh6ns tit K6 chuydn cdc nhi vdn ViCl Nam th€ ki XX - Tdp l T6p Kinh pui cric b6c cha me Lich si quan h6 qu6c td hien dai N6 oi (t6o truv6n nein v6 nhd si6o) Nsuoi hoatrs tudnp s6 (tao auvCn nsiin vA nhd ei6o) Nhdr tho Nsuv6n Khoa Di6m vi trudns ca "Mat dudns kh6t vons" Nhd vin Nsuv6n Truns Therh vi truv€n nein " Rir.ns xa nu" Srirls danh nhans anh hins hio kiet ViCt Nam Stc rudc rgdn ntrm: Ddn ld g6c - Tinh hu6ng cuQc s6ng hdng ngdy Quy6n l: D6n sinh Quy6n 2: Y t5, girio dgc, vnn h6a Quy6n 3: Ar ninh -trat tu OUYCn 4: Tu DhdD- Chinh s6ch x5 hdi Suy ng6m vd 1ga chgn Idp I: Nhtng &du xd hQi kh6ng mong muiSn Ifo tr: Gita hai ddng - duc IeD lll: Con duone ali d6o nhDne vdns nzuva que Iim li hoc day hoc Iheo Bec Hd di ktdns chi6n 41r Ihi 32 33 35 3',7 38 39 40 41 42 43 44 45 ,lsuv6n Pham Ih6i Ouans Tnms- Hi Blch Li6tr - gi Minh Dlic Pham Dlnh An t6 Nsoc Dai fran Nam TiCtr Vt Xuen Vinh V[ Xuan Vinh n C)uans Trune- Mai 7l '72 '73 '74 75 '76 Var Hoan Vd Thi Kim Nstur Vt XuAn Vinh Iruotrg MiDh Tuan,Tr.inh Van Son tl6ng CB) Bni Ti6n 116 Quf Nsoc Dai Irinh Ouanp Phri ph6p hqc d ViCt Nam ),lguy6n Deng DiCp, Nguy6n Van 49 Iinh hoa v5n h6a ohuons D6ns 50 Iinh hoa vdn hoc Nsa - KhAm ohri vd thudns thtic 51 16 Holi - Sric sens tao clla m6t ddi vdn In\ chuv&r v6i nhi vtrn c6 t6c ohim trons s6ch ci6o kloa ti6u hoc 53 Iruvcn c6 dan eian (ddnh cho HS ti6u hoc) 54 fruvetr c6 detr eian c6c dAn ldc Vier Nam - Truv€n c6 Bana 55 Truv€n c6 dan sian c6c dan t6c Vi6t Nam - Truven c6 dan t6c Gi6y 56 Iruvcn c6 dan sial c6c dan 6c viet Nam - Truv6n c6 H'm6ns 5'7 IruyCn cii dan siar c6c dan t6c Viet Nam - TruyCn c6 Khmer 58 IruvCn cii der sian c6c detr tdc Viet Nam - Truycn c6 Ti Oi 59 IruvCn cai dan sian crc d.etr t6c vi6t Nam - Truy€n c6 thugng ngu6l s6ng Thao 60 I ruven co lne s10l ve loal val - I aD I 61 Iruv6n dao dtc xua vd nav - Tdp 1: Tinh cim sla dinh - Quv€n I 62 IruvCn dao dtc xua vd nav - T6o l: Tinh cim gia dinh - Quy6n 2, Quv6n 63 IruvCr dao drrc xua vd r.av - TeD 64 IruvCn alao dfc xua vd nav - TaD 65 Iruven dao afilc xua vd nav - T6p 4: T6n su trone dao 66 fruvdo dao altrc xua ve - TaD 5: Quao h€ driv tro 67 Truv6n dao dric xua vd nav - TaD 6: Ouan hE sia dinh - Ouv6n I 68 Truven dao drirc xua vd nav - Tdp 6: Ouan hC eia dilh - Quv6n 69 70 Kiec Thuan Vi6t Hotus ki3 vd crtu danh hoa tr€n th6 si6i - TaD l TaD rruv6n k6 vd lane ou6 nsusi Vi6t Vin hoc truns dai ViCt NaIn duoi s6c nhin vtrn h6a ViCt Nam drt nusc nzuoi Vi6t Nam Edrte Nam A - nedn uctr vd vtrn h6a ViCt Nam Dhtns su kiOn lich sti (1975-2000) Iruv6n tirog hrvell cnon) Dins Dtc Si6u \,lsuv€n HAi Hl l{l Minh Drlc IhAn Phurms Thu 3hu Thi Hao (CB) lsuven Trons B6u Isrvefl Trons Bru fCB) Itrsuv6n Tronp B6u (CB) lsuv6n Trons B6u Xua[ Mai \lcuvdn Kh6trh Phone Le Ouinh Tuoos L€ Ou6c Hins fsuu tAm-bien soan) n M&rs Hrme (suu ti'm-bien soan) \,IsuvEn Vtur Liv Bii Nsoc Son fdn Ver Thinp NeuvEn Veo Liv Bid Neoc Son NzuvEn Vtu Liv Biri Neoc Scm Nsuv6n Vtrn L[v Bui Npoc Son han Vln Thins (CB) IrAn VIn Thine Vf, Thi Lan Nsuv6n Vtu L[v Bui Nsoc Son Nsoc Phuons Nsuvet Minh Ns6n Ha Chu Huv DIns Thiom 116o Nho Thin [,€ Th6ns (CB) Pham Dtc Duons 6n Hilu Dao Eodne Thi6u Scm en K.nac I hllan Vi6t Nam non xanh nu6c bi6c Vict srt eiai tloai (8 taD) BAN TO CH(IC CUOC THI s,6 41e HOC & cfudiue (5-2012)TORN ar (34) xuir aiNrduot s6119 (5.2012) Ioa $ :1t 8,D[f sttu!r0,[a]tat 0I8lan ED: 01351zlllr, 0I Irr Ptfl Emalt natr cs cdiiN xuoe, ngc rsrn mAN vAN Chi tich Hoi ddng Thenh vien kiem Tdng Gi6m ddc NXB Gi6o duc Viet Nam xcur Nc,6 TRAN fu rrnxo rs.NGuYfovANvo NG Ph6 Tdng Gi6m ddc kiem Tdng bien tap Nt(B Gi6o d\rc Viet Nam cd DoAN eUYNH FGS S 14 su:0{.35l2t00t cill0'lri0G_tldhr@t$m.com.m curu rnAcu Nutpa xa.tTB;N rsrlr rcuvftr c,{xn roAN as l lfflr rs NGt Yh{ euYTHAo TRANVAN IIAO uQrodtre nfiN rAr Tdry bitn t$p : TS.PEAM TIII BACH NGQC Thtt HTds soqn : rrrS nd QUAXC VrXg rs rn iN oixn cnAu, ras NcuyEN eNH DONG, Ts rn iN rau DirNc, rs Ncuy6ll vrNs o(t, rs t.tcw6r.t MrNH H^A" rs rcurEN vrEr nA, pcs rs LE qu6c nAr.r, rrs pHAM vAN HirNG, pcs rs vO rgarr xruEr, cs rsra NcurEN vAN M4u, 6ng NcuvEN xH.{c rtamlr, rs TRiN H0U NAM, pcs rs NcuyEu oANc puAr, pcs rs TA Dlry pHLDNc, z,s NcuvEu rd rnacn, Gs rsKlr DANG Ht NG ruiNc, lcs rs PHAN DoAN THoAI, ras vO rru rnriv, pcs rs vO DrroNc rHUy, cs ?sffi ttcd vrEr rnwc TRONG SO NNY Q Lower @ NSwa Hdi Ctuau - Gi6i thi6.u mQt sd chuorrg hinh danh gi6 audc gia;e a;6t td h9c sinh phd thong de thlc hien Vi6.t Nam Hd Vdn Nhdn - Srl ng td gi6c nQi iidp vio vau uuu,,E chitng ,'u.,uur minh hinh hoc ,vu' ;11 Dd n^ _ra r_: ki _! ney - Problems in This Issue Gl v Hrr6ng d6n giai Dc'thi tuydn sinh vAo lfu 10 Tt/+tg , Tt2l41g,Ltl4tg,L2l4tg Tnrdng THPI chuy6n I€ Quf - D6n, Binh ki trudc - Solutions to Previous Dinh, iam hoc zol't - 20L2.' @ -Cili r",H,*j ni,rt "t o Trung hgc Co s& lecorxrary Dcnqr For du TIIPJ Dc'thituydn sinh v3o 16p_10 Trrrong chuy6n Qu6'c hoc Hud,' Thta Thi6n - Hu6, ne; hgc iOu -'2012 ciJUai ars ",ia "A Khut - HQi ihio khoa hgc c6c Ngoc @ thirii - chuy6n "":'{l ttd b6i dudng hqc sinh gi6i toan @ cauqcuo-Mathclub cn,cn bi thi vho ira hqc - university @ f,fi:Xfrn;.;J:$;ff;T;t#;""n" @ Entrance Preparation td hinh hoc kh6ng gian frrE Ihanh H,ni" Nquvdn lhi AnL ThdMOi"o'uxt"a""'0d;i;6'tdhdp @ !3n!_muc s"acn !!qm khio.cria NXBGD thi-D€s6E in giiti E€ td O Thr? srfic trrrdc Hntnr t ki .- Oa, Thi Thu Thrty ^- H llhng ddn 6n tAp @ m6n Vat H thi tuvdn sinh Dai hoc Cao tting nim 2012 - vict Nam dd neudi du thi vidt gi6i thi0u' ;ffi Li6n, huvfn Nam Dirn, tinh NghdAn Ngudn: www.google.com Bla2' Cudc thi D6 vui Ngiv hi 2012' (35) trild;firffiililffiailffffit i6p tuo ph:it tridn lfiirr rfn4l ' trh nhri hu si tdn vi6c dn 5i Gin dlch k.wl.ttti il6i llys nanai siizrhin(hulrinh,Hilinriii, ttililt) hool d6ng I lm zott, phdn ldn crir doonh I \hnh Mt dong sdn vd ltii chinh g{p khti khtn vi vlin, nghiGp vu.c de!'i,'kuiil:if;Til:f iii"lfii,;r'illlo 'oinsoo,itiil4i crio cric chrj ildu lu lrong linh diii vtiidoonh nghidp cri mft voy nu lin thiEtlvdn ti ndy, diiin hinh drrm ilnh tdi rhinh dn dinh vd ldnh monh Vi dring tiiin, ttl khoi thdr tod nhd tru srlldm dic biQt vin tri duo.c ti l4 tidn mdt, ctic khodn duong fidn vd ttic vu.c vdn hdnh, khoi thrir, qurin kinh doonh B0S (6ng ty v6n khoi [i (Ong ty dd ki vift aio Sd'Gioo dch fiting khodn Hd fiuong hi6u vd tim ki6m fi6m khdch hdng lrong linh vuc nriy bdt ilrrqt nhring cs h6i muo dum ldi sdn gid rd (6ng chinh vd b6t d6ng sdn (BES) sul gidm s0u fii ming ldi kh6ng cti no ry ll6i (llNXl loi Sii Phon (hu Trinh, Hodn l(i6m, Hri l{6i Trong nim tidn rhidm fi rong lin co cdu tdng tdi stin: rhi6m 54% tdng 20lll dd tri vu.c k6t duo.c th6m hon diing qudn li vd 2012, (6ng thd sdn sring drin li vd firir vri mri r6ng ilrror linh khodn ddu trr fionh khotin nhonh cri thC chuydn hrio dum thdnh tdi sdn (theo Brio crio kidm todn ndm rr, ly s6 fi6p tuc ndng coo chdt luong dirh vu, mri r6ng .i.Hoot ddng ildu i, B0S: Oi6m ti trqng 3M0% lrong dng ldi sdn Trong ndm 2012, (6ng ly s6 tdp trung ddu u, khoi firit cric BDS dd hodn thtinh l(hdng ddu tuddn trdi vdo cric durin quy m6 kiq kdo xdu, rocdu no trdn tdng ldi srin vd tr6n v6n thri stt hriu ld r6t thdp: ddi, khong rhi6m ldn lrrqt tl7% vd t47% thom gio cdc drr dn B0S c0ng Nhd xudt bdn Gido duc Vi6t Nom dd Bon ldnh iloo t6ng ly ttl xdc dinh ndm 2012 vdn crin nhiiu khrj khdn thdch thric rrio ndn kinh t6 M th6, muc li6u crio [6ng linh hoot phri hon rho cric cd il6ng vrii ti 16 vrtifirp t6 Drim btio ctitrit hop li, k6 hoqch doonh thu ndm 2012 ld 36 d ddns vd loi nhudn trurk fiu6 ld lt2 Oul lndm 2012 (6ng ty do- dfl iluqc 5,95 ti diing thu6, bdng 39J% k6 hoqch lql nhuin cilng ki ndm 2011 Dq ki6n mit ndm rtng ruing lin dinh, 2012 ld girl vring iin dinh stin xu6t kinh doonh, diiu chilh k6 hoqd ty noy v6, dq dn rri quy m6 ftin, ndm ri v! trf ildt dio vd hrio hen fidn vong khd quon lrong luong loi .i.lloq dqq fi6p tc (6ng ly ddu vtdi dirft fti6n luqt nio torg I ld fi0n ur: ti6n muc li6u dn illnh, tdng curing kidm sorit rqng nii ro: l6p tr to ld ll% lld bdng fdn ly ltp vdo cdc doonh nghi6p ui ngdnh nghi kinh doonh dn khrii cdc doonh nghiOp kdm hi0u quti TQn dqng uu th6 vd ddng ti6n hian crj, rim ki6m co h6i ddu tu fii mrdng tiit, d{c bi6l ld tim ki6m co hqi muo doonh nghiQp, muo du rin thuQt linh vqc Gitio dqc Hi0n (6ng ry ilong xem xdl ddu fir vdo linh vu.t Mdm non chdt ly hOn tt ildy monh lrrong oo, ddy ld linh vu.c tiim ning, hth vd iin dinh trrong hen dem loi loi nhu6n coo loi 2011, nhung vrii il6i ng0 l/d fnh srr vdn hdnh crj kinh nghiQm, duo.c ildo loo vd lrrm phdt fidn tong ndm 2012 vd lrong luong loi, }IDOT C6ng $ip nhiiu khti ki 187 Gidng cii tric roo Ti6p tuc csc6u loi donh muc ddu fir, nit viin qurin li vd khoi thdc B0S: (6ng ctin b6 qutin li, il6t diii ddq truric mdt ld Du dn d1nh, mdc phrit ridn tim kidm thi tnning vdo linh vu.c tidm ndng ndy Mdc d0 rrrrtdng gion ddu trr Ti6p tuc ftung ildu nhudn trung chri ydu vdo cric mdng rhinh sou: rfi ftdi turtt ld Phuong huring hoqt d6ng nim 2012 crio (6ng .lHool il6ng tdn dung qu,i hieu qud vd ri diing linh d6n h6t tri ndm vd bdng 300% so vrii di tric nim kiim sodt drrm khdn nim hinh k6t qud kinh doonh iluo.c cdp cdc chdng chi hdnh nghi 0udn li dg dn, gidm sdl thi 6ng, ttl kinh doonh BDS, (6ng ty (d fid ddp dng duq( nhfng yOu cdu coo ndm 2012 mri iloi h6i lin tudng (Ong ly sE ila d6 ilrrm Ouy l, chi6n ly dqt vd vuo k6 hooth stin xudt kinh doonh c6' dong gioo cho (36) ,.A NHA XUAT BAN GIAO DUC YIET NAM I I - ^t coltc Ty (0 pHAr Dlffi uu xu[T rlr ono ouc lll nol Oio chi: l87B Giing U5, e D6ng Do, Hti teb (Utl ll6i 35t22058 - rox (04) 35r2322s 3tNN47746; qffiilAl?z,l?stu/" rAr LtEu cHUytN roAN rHpr a "Tdi liQu chuyonTodn" l6p 10, 11, 12c6i/jrtcd 12 cu6n, m6i tdp c6 cu6n q6m cu6n ti thuy6t (Dai s6 - Gidi tich vd Hinh hoc) vdr cu6n bdi t6p NQi dung m6i cu6n deu b6ir s6t chuong trinhcho hgc sinh cdc trudng.THpr chuy6n md B0 Gi6o ouc vd Daolao oE ban hdnh d m6i cu6n ii th.uyet gidi thiCu c5c chuyen dA bit bu6c crla chuong.trinh chuyCn duoc trinh bdy khd s6u vdr chdt ch6, c6 kh6 nhi6u cdcvidq, baitQp lanhi?ng bai thi cia kh6-ichuyEn To6n, thi hocsinh gi6iTodn eu6cgia, thi To6n Qu6cte Trong m6icu6n b2ritQp, ngo?ri huong d6n gi6i khd dAyd0 cdc bditQ-p cu6n tit-huy6t, cdn c6 mQts6 bditQp b6sung d6 hec sinh tham khJo cai tacgid cri"oO ir,b-yliio co nnieu kinh nghiQm vicc b6i duongtrgc sinh gi6i.Todn, ocu oE noac dang "j"niatZ" truc ti6p g;'ni dav tai cac trudng THPTchuyon, kh6ichuy6n To6n, cdciruong Dai hqc, ViQn'nghi6n-crlu, 'trEn rn'ap ia nuoc, nhu : GS Dod'n Qu/nh, cs.TS vdn Nhu cuong, pGS TS Nguy6n Ding ph6t, PGS.TSKH va Dinh Hdai, _o.s,r![u aa ruuy Khoei,Ts Nguyan Minh H.i, cs rsKH Da ng mng rnang, pGS.TS Nguy6n vrt Luulgt, ThS D6 rhanh S on, T S TrAn N a m D fin g, T S L6 B d Kh nn iri n h, i hS Ni uva n irq t'llvqlg ring b0 s19!39 d6p rlng duoc phan tdn y6u cdu hoc tQp cia hoc sinh, viQc gidng day cia gido vi6n d c6ctrudng THPTchuy6n; c[ng nhu nhu cdu doc cria nhirng nguoiyeu ihiin ioanl BQ s6ch igii6i, -***.*.-*u*=l r^l rEU cfiuYAi rolx HINH HQC *ifrxlit *eg '*a"ra, t*',.,**,*l r^l r+u cllUYA, xiruH rolx ugc 10 Il, utu c'tuyCl rol IAI TAP FIAI S( ' -*t*rr*l '.,, ,,,-a,,t.,.1 TAI { DArs6lO '{( UfU CHUYETT TOAX TAP HiNH HgC 10 #al &- -_ _ E - E*-,-**-,* E- *** I rAr E ,*-* !4, crirvair rolx (37)