THI TOÁN L3 2011(TT TÔ HOÀNG)

T r{{;NG'rApr r,.T.$.H f& ro*Argg sd +* - tvco zg*t g, THANx{ NCr{I DT: 04.22453338 - 04.22011"t20 nS r*ls rrlr? *4r Hqc {sqr s; mCru TFII: rOAnq Ki tki ngdy: 30lQ4l20lI Thdi gian ldm bdi 180 phrtt :i prAN cHUNG cHo rAr cA cAc rnisrr"ls Cau I (2.0 didm) Cho hrri;r s0 y - x,-(rn+l)xZ+(m-l)x+l (l) l) KhAo sait & vO dO rhi hirrrr stj m = I 2)Tim circ gi6 tri thuc cira rn clc cld thi hlm so cirt Ox o ba diem phAn cho cdc tiep tuyen tai IJ ( song song CAu II (2.0 didm) l)cirii phuong ti'inh: 2tarif r - sin(2x ' -34* biei A( 1,0), B, C 2(cosx- sin") =I cosx+sinr '$ q (* *.*# 'r* \ , #" t*' I "S *''* Cau IV (1,0 ,*rt*.g' *.y ** s$ ;s.\k * Cho h.choP S.,'\IJCD c6 clay ABCD CAu V (1,0 didm) Cho x, pniin erENc ( thi sinh chi duoc A.Theo chutrng trinh chudn CAu VIa (2,0 diilm) \s €+J I $ *** a*n, &: *-y gl ditim) (sc,lnco):450,(sC.,,lsr)= \ ,,, sint x Tfrrh l- I" ""'^ 7r jcos'x.cos(x-") 6* III (1,0 dirim) CAu hlnh ch{t nh6t vdi AB=a, SA t (ABCD) 300 Tfnh rhei rfch hinh ch6p S.ABCD y c IR thay lim l) phein deii rim maxp, minp v6i p= x-y xt +-yu +6 A ho6c phdn B ) )Hinh chff nhat AtscD c6 ram t( :,: ), rrung didm AD la M(3,0), chu vi bang 10.,D 22 Tlm toa d0 A, B C, D 2)Trongh€oxyzchocdccl.rhiing y-1 z = l'^, z | =t 4,, -/ -z.n x-2 -r' "-l -J i t)m toa didm M e A,sao cho khoang c6ch tir M den a, bang khoing crich rri M den mit phing (xOy) CAu VIIa (1,0 Gi:ii phLrong rrinh rr€n : za +322 +4 = B.Theo chuong trinh nAng cao CAu VIb (2,0 didm) Chod.trdn (C): (x-4)'z+yt = 4&M(1,-2).Tim road6N thu6c Oy saochottttk.ooo hai tiep tuyen NA, NB den (C) ddng thoi duong rhing (AB) di quu M ( A, B li hai tidp didm) itidm) C l) 2) Trong h0 Oxyz cho cludng rhang A :{ = Z:-l = 1&mat phing (p): x+2y-Zz-2=0 212 tim toa didrn M e Ox sito clio khoAng cd, h tir M clen (P) bang khoing crich CAu VIIb (1,0 didm) Giii bdt phuong rrinh : (l r * *JE)^ +2(4- Ghi chti: - Cdn bd coi thi khhng gitii thfch gi th€m - Thi thft dot cudi 16/0612011 JG)' =, tt M ddn A t mi#ma m,{w v,& reAp Ars qsArs THT THU SAI HOC DOT III DAP AN Cffu I d _ a1 ' y=x3 -/.x nl=1, $i6*'; SBT: e y'=3x2 + + I (C); TXD: R (a) -4 x=x(3x-4):0ex.i0,;i JJ I 0.25 y c6 circ tri c lirn y=te x+t@ r i-o' BBT - O + rG; i* *\ ,.2 \-) '- ,I' I r i u I| I oo I 3- *- t' .t 0.5 J"l _- D6 thi (C)n gty = (A;\; (C) r ,tS L'2 n ox =1 (1, o;;11 - , orl 0.25 k X6t pt -/ = c> (x - 1)(x2 'mx-1)=0 m*0 Goi x',xc li nghiPm L=m2+4>0 Y€u cAu bdi toan cos'2x * 0; Ft c+ 2sin 2x- cosz2x+2(cosx-sinx)2 = cos2x +cos2x-2=0o ltotlt = -Z(loai) zy,*+,[r-Zy (a=3v - EiAu kign; D+t ' 0.5 >O 'thi phuong u trinh dAu tuong duong: r [A = "l*-Zy { a(az 0.5 +l)=b(b' +1)+ (a-b)(a'z+ab+b2 +1)=0 Do a2 +ab+b2 +1> vdi Va,b+a=b 0.5 ir'= o :9y2 +2y lo-4,'lY - l" HC iff.ry -" +5y ,pt Ddt t =9y2 III ld 0.5 =9y' +2y +3y -2 r it>Z +I-4.Do y>0=I =x-: eJt=t-2e1 it'-5t+4:0 r fr - r:2 tt tant xdx i=tl jcos"x(l+tanx) C6 DIt l=tanx:> =1165!d'I t'+1 0.5 = tv -'tllG -t Jz i liI +/+l,)dt = Ji(!t' '2 - r + rnir.tDl: Jitz-.6+mf, r 0.5 a LSAC vu6ng cdn cho SA= AC = h D4t BC- r =) x =,sc.sin3oo u! =+ 2=-!t.E=* MBC cho x2 +e'=lr'*L+a'=li o v v.oaco=lx.a.n=+ +h=all (dvtg 0.25 1it +122x2,ya.+l 2y2 vot Yx,y > (x- y)2 +4>al"- yl Ta c6 xa * lPl= xa +ya +6 =l=-l="=l 444 Ma cl(M,L2)= d(M,(xoy))c) fr-2)'+ {:}l[r=, _l7c>llu1+,i,r1 _17 -11 _) l'= lil i el 1t+ l,t - l,r) = lAM,io,f= it 2.-2,3 - t) =3lrl c+ j12 +10*n 0.5 -4 05 1,,r,*;, t +4=0 e(z'+2)' l r'+ z+2=0 +3zz za N z2 =0e(r'+'z+2)(22 -z+2)=Q 0.5 0.5 Lr'-t+2=0 vIb 2d (C) cb t6m 1(4, 0), 1/(0, b) ; gqi c6c ti6p di€m lit A(x,, (il1) tl,q.1i= =+ r,(xr * *16 ,=a =+ (rr 4)' + yl + 4x, - by, * I le ti6p tuy6n = y); B(x, yr) 4)+ y,(.r, -b) = - by,-16 = =+ 4x, - by, -12 = 0=> thuQc dugng thine 4x-by-12 = 0: 4+ = It l(x, - 4, y,); NA(x, , !, - b) tJ 4x, 0.5 O ,L Tuong tu thu6c dulng thdng 4x - by ,B -12= ; =+ (AB) : +* -ty -n Me(AB)+b:4+l/(0,4) M e Ox + M (t,0, A) ;,4(0, l, 0) e L;i {2,1,1 + vfr1l, l, 0) + lzu,i d(M,L)=d(M,P) c+ VIIb = U fn Jri)', t> dd bpt trcr thanh: e tt -3t+2 ... y=te x+t@ r i-o' BBT - O + rG; i* * ,.2 -) '- ,I' I r i u I| I oo I 3- *- t' .t 0.5 J"l _- D6 thi (C)n gty = (A;; (C) r ,tS L'2 n ox =1 (1, o;;11 - , orl 0.25 k X6t pt -/ = c> (x - 1)(x2 'mx-1)=0... +cos2x-2=0o ltotlt = -Z(loai) zy,*+,[r-Zy (a=3v - EiAu kign; D+t ' 0.5 >O 'thi phuong u trinh dAu tuong duong: r [A = "l*-Zy { a(az 0.5 +l)=b(b' +1)+ (a-b)(a'z+ab+b2 +1)=0... I le ti6p tuy6n = y); B(x, yr) 4)+ y,(.r, -b) = - by,-16 = =+ 4x, - by, -12 = 0=> thuQc dugng thine 4x-by-12 = 0: 4+ = It l(x, - 4, y,); NA(x, , !, - b) tJ 4x, 0.5 O ,L Tuong tu thu6c dulng