THI TOÁN L6 2011(SPHN)

rm rruu'DAr Hgc LAN vr Nann zorr Bfr TRU'ONG EHSP HA NQI TRUONG THPT CTTUVBN DHSF Mdn thi : TOAN Thdi gian tdm bdi : I 80 phfit, khong ki thdi gian phdt dd ' diem) Cho hdm so Y : x3-3mx2 + (nr- l)x+ C6u (2,0 Tim rr d6 hdm sO d3t cgc ti6u tai x = KhAo s6t sq' biOn thi€n vi a vE dO thi (C) cira hirm s6 ftng vdi gi6 tri cria m tirn dugc BiQn ludn theo ftsO nghiQm c[ra phuong trinh : )-_k x'-2x-2= ^ L^ ' :- lx-11 Ciu ' ' (2,0 di6m) l Ciei phLLong trinh : 6sinx - 2cos3x ciai hQ phuong tri'h : = 5sin2x.cosx F:r;.r;j; {_r_ ' Irrl,= ' nr I ' , : CAu (1,0 di|m ) l.€$x- Tinh tich phan r = -a CAu (1,0 di€m ) Cho tam gi6c cdn MBC c6 a EMe : l20ovd duo'ng cao MH : a^12 Trdn duong thing vudng g6c vdi m{t phing (MBC) tai M l6y hai di€m A vi D vC hai phia cria di6m M, cho ABC le tarn giilc dAu vd DBC le tam gi6c vu6ng cdn t4i D Tfnh th€ tfch kh6i cau ngoqi ti€p til diQn ABCD Cffu (1,0 diem ) Cho c6c sd duong a, b, c thay ddi ludn th6a m6n a + b * c = Chri'ng abbcca3 *'b+ca + +"b r*b minh ring : - Cdu (2,0 diim ) l Trong m4t phdng Oxy, cho hinh chir nhat ABCD phuongtrinh dud'ngthing AB ldx- 2y+2 ,1 c6 giao cli6m c0a hai duong chdo ld M(;; O), = vdAB = 2AD Tim toa d0 c6cdinh A, B, C, D biiit ring dinh A c6 hoinh d6 duo.ng Trong khdng gian Oxyz, cho mit phing (a) : 3x + 2y - z* 4:0 vA di€m d0 didm N cho MN vu6ng g6c vdi (a) clOng thd'i N c6ch dAu gOc toa M(2;2;0) dQ X6c dinh toa O vd rrrit phing (a) Cdu (1,0 diem ) -{3 * i, 22: eosloo- i,sin i Hiy bidu diSn sd ptiLlc z : (?\t'ou.di cl4ng ctai s6 Cho cdc si5 phirc z1: \L2/ tsqr ki6n ki tlri tfe# Bai leoc ldm fid-lk sE dwvte fA rh{pn ttAn n*}n, t p , a/K./rni t ; EAP AN _ TTIANG DIENI 2011 THI TI{TIDII LAN TH{T SAU - NAM -f*-.151^* -0,*;i,^irc 1iA,r l (+r v = ? d6,t'e,\: c+ m = rruu tni Didu:?:t ki€n cdn : Gi?t su nam so cl4' t'gu y' = 0 ^B:t^D A(2;2),8(-2;0), = C(4;a) vdD(3;0)' Thaya:2vitotgad6cacdi6m,tatimdu'-occ6cdinh *(* W ttidmJ GqiN(x; y; z), MN Ta c6 + ON2 = 72 Do ON: d(1V, 3t)2 (u)) ,'" ffi ' -re" 4td = i*a N rd [i=-lit;, \z: _t +(2+2t)2 +tz vikhoiLngc6chtilN d€n(ci) ld:d(t\ {2+3t)2 +(2+2t)2 +t2:14(t+ l)'? 3, vey N(- ;;;;1) (l,O aiiimj Bitlu di6n s6 phiic - 2(-* ir: 2(cos 11 + ;.sinT) vit z2 cos(- fl + ;ti" t- f) N€n a=ztcos(f *f l*rsin(f *ilt :z(cosff+i.r,nff) Ta w! I Arcfitl c6 siv,* J zt = i3) \a \L2 / , LrtL 13ft \ / -.t = ?':r'cns * i Sin- i = - ^1" :' (u)=lja lt+ t I ... kh6c SO nghiQm cira pt(*) bang se' voi dl thi hiin to I x-t l1x2 -zx-21' v: Tr) d6 thi tr6rr ta slry fa : - N€u k thi p1(*) c6 nghiOra phAn biQt - N€u -2... 2011 THI TI{TIDII LAN TH{T SAU - NAM -f*-.151^* -0,*;i,^irc 1iA,r l (+r v = ? d6,t'e,: c+ m = rruu tni Didu:?:t ki€n cdn : Gi?t su nam so cl4' t'gu y' = 0 1) = *f(x) n6u x ( - 1) = ('*) 1" : I x-l I (*t - 2x-2)tr0n midn R{l