THI TOÁN L2-2011( LTV HN)

SO GD & DT HA I{OI DE THI THIJDAI HQC LAN ZNAru ZIII.I TRIiONG THPT LLrff\iG THE VItiH *6n thi: Todn Thoi gian litm bai: 180 phrtt, kh1ng ke thrli giun phcit cli Ciu I. (2,0 itiefl Cho hhm ro y, = # il) . i) Khdo sdt su bi€n rhi0n vi v€ d6 rh! crja hiirn sd ( 1). ' 7l Gqi I lh ,eiao di€m cua hai tifm can dd th! hnm s6 (l). Tim ciic gi/a tri cira tham so m dii cfuLong ihing td): I=x+2mcat dd th! hhm sd (l) taihai di6m A, B phdn bigt. Chrmg minh"dng khi cl6 ram .sidc L\B cdn tai I. ,? CAu ll. (2,0 tfliml l)Giiiphun,igtrinh:{tanx+cot2x)sin4x=2(cosx+2) '' '':, I i\ { ! {i*-r } Cflu III. (1,0 deil ! ' " ,/ .'; : -, .: huchphenI=J-sin?.{.e*h*dK-| Tin Ceu f1'. {1,0 ifrAm) : : : m1tphan-e(SBC)u*gT.Xdcdinh tem#tinhbrinkfnhm4tciungbaiti€phinhcht5p$ABC. ' ,',.:'.1'.] ':'''' ':. .'' ' ' 'l 1. - f x=l ',1 '' . . fI: r r-r : ix .1 I .,i 'Cho-xli.sd'4ucduong. Chungg,rintrring";,jl** > "[**'t . ,, i'', .'' ' '' - ' ' -i\i 2 2x - . : :: . : : ' - - . : . . :t:.: - li Tron.s *[i ple"S Oiy cho duonq rrdn (C]:(x -'2) . *t.1.,v+ 1): =.? nQrrti€p hinh vu6n-e ABCD, Biii I ' hinh tu0ng 136P l) Tmng.i.:hdng *s1an Oxlz cho cilc.di€m EtJ: l:0): F(0;f:0) vir Gt0;,g:-2). Vidq,pfriixg rrinh "' maiphingtPJdiquaoEsaochokhoingcdchtir:cricdi6mF"r'hGnJ5q.ntirphing.(P)bin frrhau.,. .: . ; Z*lcoslx-I linh $o' hiirl: L- lim= : - x_+o J*r+t_t : so Gp & ET HA:NQI .TRU.OT-G'THP'[ LU.OI{G THE VINH oAp Ar.t - TIIANG DIEM MoN ToAN of rm ruu'o4l Hec lAru r nAm 2077 t) Khno s6t vi Y6 d6 th!hlm s6 t =ffi. * i4p xi,c d!nh: D = R\{-1 }' : - Chii, bi6n thi€n: t'=#,), > 0 Vxe D . lim -+*. Iim =€' Di rhi (C) c6 tiQm cdn dtmg x = -1 vit tiQm c4n ngang v = I thi€ -CO -l *co t + + co 1 -co e do thi t) Gtai ph""Ig tnqh (tan x + coi 2x) sin'lx = Z(cos :t + 2)' Eiiuki€n: sinlx+0 o *+f sinx- * to'2k)*ir,-rx = 2(cosx + 2) <+ ++ = Z(cosx + 2) Phuung uinh <+ 1- . cos r sin 2x sin 2x ecosll=cosx+f <+ 3cos2 x-cosK-3=0 3 € cos* =i (loa) hoflg cosx=-l €] K=n+kn (kE Z) (thoamdn) .1'- bie $,23{l 0,25d 0.2sd :-: :'- - ;l- I drem 0.25d 0,25d 0,25d 0.25d I -;.^ I J OIENT I rli€nt 0.15tt 03scI 0,?511 0,15c'l 2) Tim cac gi6 11! cua thgrr,r sii m tI6 dutmg thnng (d): y = x * 2m cit ab th! .' """;"' Phuong trinh hol,nh d0 graq 6i6rn; xj =x+2m e g(x) = x2 + 2mx + 2m + 2=0 x+1 Duong thang td): y=xi2m qfi AO rhihhm sO (t) tqi hai di6m A, B phdn bi€t e phuong trinh -, I a'>o E gix) =0 c6 i nghiemphanbiet x=-l c+ i-,1;:o ol*t t +^.6 noac m<'i-'6 ( Y. +Y -+ rf =-:-rrr Tac6 I(-l: 1).GsiE ldtrungcti6mcuaABthi l*e =jfl-=-* = il-(-m+1; m-1) lYe =*e +2m= m ._+J Tir ua=(1:1) + IE'u4=0 <+ IErAB <+ ALA'B cdntail' 2) Gi[i bAt ptruung triirh: tog* 11r3 -3x+2)+log*13(i2 +x-2) > 5 ' Bit phuong uinh <+'log,-1(x-l)l(\ +2)+log.*'(x+ 2)(x -1) > 5' Eiiuki*n: x>l:x=l Bir phuong uinh <+ log*-1(x 1 1) + log.*2 (x - l) > ? ' 1 fli6nt 0.25tI 0.2-i6 0;2Sal r*l t>0 I ^ (r-l)r Dqr r=log*-1(x+?) = t+l > I e ::f>0 €+ Itog,-,G+4+l llog*-'(x+2t>0 I x>'l: x+z l(x -?)tx + 1,1> () fl ; Tinh tich phAn I = I sin 2.r.e-''ntdx. I 0 D4t t = sinx thi dt = cosxdx vi. x=0 =+t =0; L ?l Tac6 I =2isinx sinx cosxdx = 2 i te-tdt - J -_ J 00 D4t u = t + du = dt vit dv =e-tdt + t, I Khi d6 I =:(-te-'il 0 CAU IV Xdc dinh tim vi tinh bdn kfnh m{t hinh chdp SABC. t:= Gqi H h 1nm cua d:i-v ABC vd lvl lh trung didm BC. Ha .{K r Strl + AK I (SBC) ua eK = 9{P l 0,25d t1,256 -t .lr z - e-'l i =2(l - -) loe r ngoqi Szt D+t SA =.\ (x> 0). Trong tam siric S{t t111 SH'AII:IK.l]lvI (*) I^ t: l : I _ .,t Thav .L\I = tJ3 . AI{ = a{3 ' SH =,,1x: -f : S\t ='rl*= - 1- viio (*) tim ra ? ':-^ 3 ' y'- 3 y + r- rknh R=SH=T hinh chdp S.{BC r'i bfr r uJ6 r\- a J i r - -a m4t cdu ngoar tle H li. tim 0.25d 0.25ii 0.15.I 0.25it ' iir Cho x lir sii thEc ducrng; Chring'minh r'Ing ii. ,- Bdt ding thiic <+ irrr+ = [*J'. Dat >,= i:it= i in udt ding thfrc cin chung minh uo' thiurh ] rn y' ,l:1 € f (v) = t" 1' - 4:,n 2 6' I 4 - (v-1)- l0 Vy2l + tiy)d6ngbi$n Vy)l + f(y)>f(l)=O laCO I (y)= r 1 J-\ < r\r'lsvrre\vrvr' " Y (y+1)' Y1Y+l)- i . -(:iI Ciu V I tli6m Ciu VI 2 di6m t t ,f ,ec Oinn tqa dQ c6c ttinh A vlr C Do AB di qua M(l : - 2,r nOn AB c6 phuong trinh: Drrong trirn (C1c6 tim l(2'. -l) vir R =Ji = Ji=dil la+bl tr!;=-$ :? a=b = phuongtrinh AB:. x+Y+l =0 t- Gla su A(t; - I -t). Tu tl2 =2R2 =4 = (2-i)?'+rz =+ YFtl A(2;-3) = C(2:!t vir B(0; -l) + D(4;'-l) 4 Yiltphurng trinh m4t phing'(P) Mat phing (P; di qua O n€n c6 phuong trinh Ax + By + C2.10 ' . . j_. Do (P) qua E(2: l; 0) n€n. 2A+B=0 ++ B=-2A = phuqng trinh (P): At=ZAy *cz=Q Ttu d(F. (P)) = d(G. (Ptr Vdy phuong trinh (P): ax+by-u*26=0 <+ lzal=lcl :+t=0 (loai) hogc'l=2 l-+al l-zcl -: :- Jsaz + c2 Jsnz + c2 K-Zy *22=A ho{c x -2Y -Zz=O a2 +b2 I di€m 0,25d $2,sd 0J5d (1,25d I rti6m $zsd 025dl 025d 0,2,5aI 1 cti€m 05d 05d Cdu V,IIa Tinh gioi h4n: Tac6 L= lim (2*2 'x-r0 2*? cosl x - I lr# r-+o {*? +l -l . SO GD & DT HA I{OI DE THI THIJDAI HQC LAN ZNAru ZIII.I TRIiONG THPT LLrffiG THE VItiH *6n thi: Todn Thoi gian litm bai: 180 phrtt, kh1ng ke. Chii, bi6n thi n: t'=#,), > 0 Vxe D . lim -+*. Iim =€' Di rhi (C) c6 tiQm cdn dtmg x = -1 vit tiQm c4n ngang v = I thi -CO -l *co t + + co 1 -co e do thi t) Gtai. Chring'minh r'Ing ii. ,- Bdt ding thiic <+ irrr+ = [*J'. Dat >,= i:it= i in udt ding thfrc cin chung minh uo' thiurh ] rn y' ,l:1 € f (v) = t"