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T.inh the rJ tich khdi tu'di€n MAtBCt AB:BC:a,canh b€n... Theo chugng trinh nf,ng cao..[r]
(1)Tru'd'ng THPT LG Xoay Ndm hoc 2012-2013 DE THI THC D{HQC LAN I M6n: TOAN, KHOI D ('rhoi gian ldm bdi: 180 phut, khong k€ thoi giarr giii, PHAN CHUNG CHO rAr cA rui srNH 17di€m) Cdu l.(2 di6m) Gqi ((;,, ) le dO thi ham sd ,,= -rr +(zm+t)x2 _m_I (l) I Khao s6t s1r.bi6n thi€n vd v6 ao tni hdm s6 ( r (rn m:1 ldr rl.,;) tham s6) Tim m Ae OO thi (c,,,)ti6p xirc v6i O"*gifra"g) y=2mx _m _1 CAlu (2 di6m) l GiAi phucrng trinh: sin2x *cos2x +sin3x _cosx _2:0 Giei phucrng trinh: v_t- I + I = 4x2 * Jl" CAu 3.( I di€rn) cho ldng trr; dung AB('.AtBtcl co d6y ABC ld tam giric vu6ng v6i all, M le di6m tr6n AA,sao cho Vrt =l Zil T.inh the rJ tich khdi tu'di€n MAtBCt AB:BC:a,canh b€n ,,t,<, = Cdu 4.( I di€m) cho cdc sd thuc duong a,b,c thay d6i ru6n thoa m6n a*b+c:1 +c Chung minh.ing, 4:!*bz n+( c+a *r'*o a+b Cdu 5.( I di6m) Tinh gioi han sau: x' lim r+t -.6;L X_l PHAN RrtNG(3 di€m) (Thi sinh chi dugc ldm mQt rrong hai phAn A hodc B) A.Theo chu'crng trinh chu6n Ciu 6.a(2 di6m) : 1'Trong m[t phing oxy, cho hai duong thlng d,:2x*y*5:0, d,:3x+2y-r=g vri di6m G(1,3).Tim toa d6 di6m B thu6c d, vdc thu6c d, nh6n di6m G lirm tdm Bi€t A ld giao di6m c'a 2.Trong mat phing Oxy , cho duong thing: r/, :2x*y-3:0, ,/.:3x+4y*5:0 vd, d.: cho tam gidc d,va ABtl cr, 4x+]y+2:g Vi€t phucrng trinh duong trdn co tdm thu6c d, vati6p xuc yot cr,.cr z.?t I didm) 9al co hgc sinh nam va hoc sinh nfr chon em di lao dOng .l.inh xdc Ylr.l6 sudt d€ chgn dugc em nam vd em nft (2) B Theo chugng trinh nf,ng cao C0u 6rF(2 di€m) l.Trong rnpt phing sv vd Ys o*y, vi{it phuong trinh ducrng thing di qua goc toa dQ cit duong trdn (.r-l)'*(-v+:;'=zs tn.o mgt d6y Oai fi *.'}vq ,1"' ""un*.jaO : thing BDi ;;*;,n"i, 1".9P 1(1,g) :dyqs i".l*iil =u, im toa d6 c6c di6m A,B,C,D bi6t ring BD : zJl I J x-y+ ' r Cdu 7.b( l didm) cd) visn bi'mdu trfng,S vi6n bi vi€n bi miru xanh, r6y ng6u nhi6n -l bi Tfnh x6c sudt d€ vi€nlirl,vdngr bi l6y rJlrrong dri mdu 'i6n (3) nAp Au roAN 12- rH6r n CAul l.Vdi m:l | =-x3 +3x2 -2 r\ t' 'l Gioi h4n: lim=x'l -r* 7-',l=+o r+r \ Su bi6n thi€n Ta Co y' = -3x2 BAng bi6n thi6n X-) "f +6x 0,25 .!' = <+ X=0 hOdC X:2 I- l '*t .V'l , Lt tS -c + c - - '\ _ |l-+€ ,.1 I t c O //^ ,L \ \, _: -u/ ; ry: Hdrn s6 nghich bi€n trdn ( -*,0) vd (2,+ oo ) Hhm s6 ddng bi€n tr€n (0,2) Him so dat cuc dai t4i (2,2), cuc ti6u tpi (0,-2) Ddthi: 0,25 0,25 t,fH \"t" \tY\/ l- c lo00 l.Di€u kign d€ (C-)tiep xfc vdi y:2rnx-m-1 H [4 I-rt * (2m+l)r'- m-l=2mx-m-l 1-r"'+2(2m+l)x= e xt *u.6 net ,iC, 0,25 zm(t) +Zmx=0 -(2m+l)xr - 0) _' t sr[r'(2m+l)x+zm]=0<> Giai vrsr v 0,25 \ x-0,1;Zm Voi x:0 thay vAo (2) taduoc m:0 Voi x:l thay vao (2) ta duoc m:ll2 Voi x:2m thay vdo (2) taduoc m=0.112 Vdy m:0, I /2 0,5 0,25 1,00 Cffu2 l sin2x*cos2x*Jsiru(-cosx-2:2 e (2sinxcosx-cosx)*(r - 2sin2 x+3sin x- z) :6 e cosx(2sinx- I )-(sin x- I ).(2sinx- 1):g <+ (2sinx- ).(cosx-sinx+ | ;:g c+ sin x:l12 ho{c sin x-cosx:l Vdy x: 1+k2 n I t ; 4+ -'2 nr;!+ k2n;n '-'- + k2r 0,25 0,25 0,25 0,25 1,00 (4) e4x'-l+ 6i_ffi Didu ki€n: x>0 pt e(zx+t)(zx-r;+rffi=o !)=o +l ) ,l2x Ciu3 Tu gid rhi.!,, cqi H la trung di€m ,ii'ab vudng gdc v6i (ACc,,e,) 1,00 *iill uuong goc vdi AC vd BH Do dd BH ld duong cao cua hinh chop BM;,c,, 1'u gid thi6t suy MAt Ta co v0n,0,,,,, =!au 0r5 =*o,Act = alt sr^,, = j an.)aa,.e,c, t zJi - E Ydy * l -2 ' rr 'L',,,,, !J.it 1f , = o.1.-;a.rl2a j '/-2-^ o'Ji e BH _ 4,25 Ji 2- Nl - .t -\ 4,25 c ' 4,25 4,25 1,00 =:_:- Ciu4, Tuong tU BDT tro thdnh: 9,25 4,25 a+b b+c c+a ; f_r_>1 a+b b+c c+a .b+c c+a a+b-" b;;;; Ddu Lau5 = xily rao u:;": t/3 lyl$=u*ffi ={[l("'+x+r).1*1r_ffi b+a =l 0,25 I a,25 1.00 (5) Cf,u6a l.Toa d0 cua A 1l2x+v+5=0 l3x+2y-l=0 li nghiQm cria hg pt: (3 A(-n.17) Goi M ld trung ttitlm cria BC,M (7 Goi g e d, + B(x,.-2x,-5)ua Ce d, Ta c6 Eti =(7 - r,.2x, +l).cM ,-4) = c(r,1tt-r", , = )'J '.t [z -r _ j{: _ r, )j Do M ld trung di6m cua BC n€n l7-*,+7-xr=g =-35=-J.v, =65 aM+cfr=o*l + _2x, o{t, t -;(3 =0) = a9 = _73 ix [2x, lJ,, V0y B(-35,65) C(49,-73) 2.Ggi I e d, tdm cria dunng trdn, thi l(t,3-2tj -2t)+21 l:r + +(3 - 2r)+sl _lat Khi ld, $e s d6 .[-Sr <31 0,5 s + 17 = -2t +ll {t = c>{ [-5l+17=2r-ll 0.25 lr=4 Vqy duong trdn c6 pt hi (.r _ Z)' *(-r, + l)r = *(y *s)' = firu(r -a)' * f Ciu7a Chqn ngdu nhi6n em l0 em ns ar tuo AO.,,g co: (',i :252(cilch) Chon em nam vd em n& co (';C;:60(c6ch) VAy x6c sudt la 601252:15163 Cfiu6b l.(C)c6 I 15 t.00 0,-5 05 1.00 I(I,-im Ggi AB la d6y cung bi cit boi duong thing cAn vi€t vA duong tron (C ), ta c6 AB=8 Gqi M ldr trung di6m cua AB IM vu6ng g6c vdi An,1y4:,[14 - a14, Duong thing AB di qua gdc tqa d0 co dang ax*by:0 suy tM 0,25 0,25 =d(r 48)=-J$=: tlct' + b' 8al + 6uh= fl 4:p a = 0,4a = -3b Vdi a:0 chgn dudrng thang AB ld y:g V6i 4a:-3b chon b:4,a:3 duong thing AB le 0.25 C> b:l -3x+4y:g 0,25 1.00 (6) '{ I ld nehigm cta 0,25 4,25 U."T* tron tAm I,b6n kinh IB: ll} BD c6 pt: x' +(/ - 1)' = =tga dg B,D ld nghi€m cria h6 0,25 =2 J'' olr(r.2),D(-l.o) ["-J,+l = L;(-t.0),D(t,2) 0,25 f.,1 *(y-l)' Cflu7b Chgn ng6u nhi€n vi6n Goi A ld bien c6 : chgn bi c6 A,i I *au Ta co O cilch chgn ldct4c:c:-cjJ,'l; ""_:: 1.00 0,25 + c;c .l(,,1"=720(crlch) -ts4 = P(e1=J! 1365 273 Ta;6 cua A 0,5 chgn bi6n c6 chon bi kh6ng du mdu bi6n co aoi VAy xdc su6t cAn tim 4,25 154 Ile lA: -p(7)= \'-l - 273 ii r.00 I I rii 1f ":.t-rI f (7)