Sat hạch T10-lần 1-Lê xoay-2012

\ Truong THPT L€ Xoay Nam hoc: 2Ol'1, - 2012 DE THI KHAO SAT CHUYEN DE LOP lO I,AN I Mdn:Tor{n-KhdiA+AB j' Thdi gian lim bii: 150 phrit (kh6ng kd thdi gian giao dd) ^ -t2 CAu I (2 ttidm): Cho Parabol (P) c6 phuong trinh: y = - '-vd didm MQ,-l). Gqi d li duong thing qua M '4 vi c6 hQ sd g6c li k. a. Chfng minh rlng vdi moi gLd tri crla k dudng rhing d lu6n cit (P) t+i hai didrn A, B phan biQt. b. Xdc dinh f*atictra k dd do4n AB ng6n nhflr. Cau II (3.5 tlidm): 1. Giii phuong trinh sau: xt +rl x' +I I =3I. .t (z 2. Giai he phuong trinh sau: lf^+ l'1+ 3x - 6v = 0 lx'+xy-3 3. Tim m dd phtrong trinh sau c6 3 nghiOm phan bi€t duong: x3 +2(m-x)(mx-l)=mx' CAu III (2.5 tlidm): Cho tam gi6c ABC bidt A(-2,3); B(4,3; vi C(1,0); Gqi G lii trgng tam cfra MBC vd I ld didm trOn canh AB sao cho L{=2IB a. Chrrng minh r[ng: MBC lb tam g!6c vuOng. ] b. X6c dinh tga dQ ctra didin D tren dudng thioe BC sao cho dulng thing ID song song vdi dudng thing AG. Cau IV (2 diim): r r sln2c cos'a ' 1. Unung intnn rang: I -:- = Sln d.cos a 1+cota I+tana (Vdi gii thi6t'cdc bidu thrlc dI cho ddu c6 nghla) 2. Cho a, b, c ld c6c sdthuc ducrng th6a mdn: a+b+c =J& Clrring nrinh rang: ab +bc + caZg(a + b + c) zags -___-__ I{o v} fdn thi sinh: . Sd bdo danh:. ( Cdn bQ coi thi kh6ng gitii thich gi th€m) oAp AN * THANG udvr Cdu v NOi dung Didm I a. 2 lho Parabol (P) c6 phuong trinh: y =+vi ttidm M(0,-t). Goi a li ttuong thing qua M rh c6 h€ so g6c li k. IMR: vdi moi gi6 tri cfia k tludng thing d ludn cit (P) tai hai diifn A, B phan bi6t. 1.0 - Phuong trinh dudng thang d li: y = lu-|. - Phuong tdnh hodnh d0 giao didm cira d vi (P) li: 2 -+ =/tx- 1 e x2 + 4lu- 4= 0 (l) 4 C6: A'=4k2 +4>0,VftelR. Do d6 phuong trinh (1) luOn c6 hai nghiQm phAn bi€t x,,xrv6i Vft e IR -+Duong thing d lu6n c6t (P) tai hai didm A, B phdn biOr v6i V& e IR 0.25 a.2s 0.25 0.25 b. Xdc ttinh gi6 tri cfia k dddogn AB ngin nhdt. 1.0 - Gii srl A(x,y,);B(x,yr) trong d6 x,,x, li hai nghi0rn ph0n biOt ctra ptr (1) t = .r;l"r-I; /" = fuz-l - Ap dgng dinh lf Vi- et ta c6: x,* x, = 4k;x,x, = -4 - Ta c6: AB2,= (*, - *r;' + (r, - yr)' = (t + tc,)(x, - ,r), = (t + k )[(", . *,,,)' - 4*,*,] =(t+k,)(an,+ro)>ro -+ AB24 DAu"-"xiy ra<+k=0 Vay vdi k=O,thi AB*,n = 4. 0.2s 0.25 0.25 0.25 il I rt+ ,f,'+1i=31. Giii phuong trinh sau 1.5 Dk: VxeR D+t Jr'z+f f = t, dk: r > 0 -+ xz =tz 11 Khi d6 phuong rinh:d6 cho tr6 rhlnh: tz + t - 42 = 0* [; = U' ,1,, , ^ v6it=6tac6: J7.lI =6+> x2 =25*[t=t. [x=-5 Vdy phuong trinh dd cho c6 hai nghi€m lh: x=5; x= -5 0.25 0.5 0.5 0.25 Giei h0 phuong trinh sau; Ta c6: (r) <+ {ff*+y)+ 3x-6y= o(l) \ / lx(x+ Y)=3(2) - Ta thdy x = 0 kh6ng ld nghi€m cira hQ. -XEt x* 0. Khi a6: (z) e x+ y =1 (3) The (3) vdo (i) ra dugc prr: U- *Z* - 6y = 0 <+ 3y, +3xz - 6ry = 0 ,-,8) o(t- !)'=0<)x=! Thay x - y vdo (2) ta duoc: 2y' =3 *> y' 3 E =t* Y:llt r.r=* V4y hq phuorng trinh d6 cho c6 hai nghiQrn li: (x,y) = [,E,1EJ,[ E ,rlz I; IJ - t_ ,rlz o.25 0.25 0.2s 4.25 m tli phuong trinh sau c6 3 nghi€m phfln biQt d Ta c6: (t) * x?(x-m)-2(x-m)(mx-t) = 0 T- _ <t (r- *)(*' -2mx+2)=o <+ l^;': lx'-2mx+2=A Q) Vdy phuong trinh (1) c6 ba nghidm phan biQt duong *, m > 0 vd phuong rrinh (2) c6 hai nghi€m phdn biOt duong kh6c m l*> o lo'to l. e{sto .'> I l"'o l*'-zm2 +2*0 Vay gi6 tri cdn tim cira mld: m, JZ . 0.25 0.25 Cho t1m gi6c ABC bidt ,4(-2,3); didm trdn canh AB sao cho IA = ZIB Ta c6: trB = (6,0), AC = (3, -3), gg = 1-3,-3) Khi d6: AC.BC = -9+9 = 0 *+ dC t gC . YQy MBC vuOng rai C. XD tga dQ cria diim D t.Cn f *^ _rn**u**, _=2+4+l _, l^c . ^ 1 ' r -+G(1,2) L, -le*la*lc =3*3*o =2 fto 3 3 - Vi t ttrugc cqnhAB mi IA = 2IB n€n ra c6: Vi lZW ( ^/ .l*, -xn=2(xu-x,) t 1 ly,-yn=2(yu-y,) - Goi toa dQ ctra didm D h: D(x,y) - Vi D tlruqc dqdng thing BC non 3_D ctrng phucmg vot Ee Mn BD=(x- 4;y-3); Ee =?3;-3) -+ x-i -+*"-y=l(l) '-3-3 - Theo gt h c6: ,ID cDng phuong vdi AG Md,,lD= (.r - 2; y - 3), 7G =(3; -l) - + = + -+, +3,y= I I (2) - Ta c6 tga dQ trgng tdfn G ctia tam gi6c ABC lh: Tu (1) vn (2) ta;c6 h€: 0.25 0.25 0.25 0.25 0.25 0.25 Chrrng minh rnng: , sin2 4 cos'a = Slll 4:COS 4 l+cota l+tana .1 1 . sln- 4 eos-a laco: vt -t _+ _r, sinl a + cos3a_, _ (sina+cosq)(sint a +eosta-sina.cosa) sina+cosa sina+cosa = t-(l-sina.cosa) = sina.cos a=VP (dpcm) Cho a, b, c Ii €6c sd thr;c duqng th6a m6n; a +b + c = Jobt Chung minh ringz ob +bc + ca) 9(a+b + c) Vdi moi sd thuc x, y, zta lu0n c6: x2 + y'.+ z' 2 xy + yz + zx +(x+y+z)' >3(xy+y+a) . Ap dqng BDT tr0n v6i x = ab; y = bc; z =ea ta duo. c: " (ob+be +c.a)i 23(,abzc+bcz a,t,+ce2b1=3abc:(CI+b+c) i -+ (ab + b c + ca) > Ji.J "b".J a + b + c = Jj.@ + b + clJi a a 111 :] rl l . Ir , 13 Mrt kh6c ta c6: a +b + c = mZ' lk,jjj,jf_ = (a +b * dW_ -+ Vc+b+p >3J3(2) Tt (1) ve (2) ta c6: ,ab + bc+ ca > g(a + b + c) (dpcm) Dau "-r' f6yrakhi vichilthi:,a= g=s-= !. :'' i' 0.25 0.25 ( Thf qinh lim theo c6eh khdc ddng v6n cho didm rfii da) tdtr g Ra ttd virlipr66- 5o 1 L= Nguydnfhi Hdng NgwydaThlEqnh so cD& ur viNn pHUC rnU$gc rHpr r,n xoav Ciu I. 't l. 3. Cdu II ri rnr. sAr n4crr LAN r NAM Hec z0tt-2012 on mu nnON roAlr L'Op ro- icnot o Thli gian ldm bdi 150 phrit, kh6ng t<e tnOi gian giao d6 __-_;__ ______ - 2. Tim m dd phuung trinh sau v0 nghiQm x-tit . x-3 I_ _., | _L x-l x cho phucrng trinh: zxz +Z(m+r)x+ mz +4nt+3=0 c6 2 nghiQm ",,x. Tim gi6 tri ldrn nh6t, nh6 nh6t cria bi6u rhric A:2( t * rl)_3*,*,. Gi6i phucrng trinh: Js,i + Jut = 4x -9 +zr,\f - 5, *2 (t i ciai he phucmg trinh: {o,l._rtiiiul:_;o=0 2. cho h6 phucng trinh: {.:T;::r=|!, rl_o*, Tim m ae ne c6 nghiQm duy nh6t ( x,y) th6a mdn r*t =z Cdu III. i. cho rarn gi6c a.BC, ,'€n BC l6y di6m D sao chorp =1ae. Gqi E Id di€m th6a mdn qEA+zEE +rfr :o . chrmg minh A, E, o driig rrang. - [ 1+cosC Za+b . 2. Nhfln dang tam gi6c biCr I ri" c = G;-F lo'@+c-a)=bo +co -ao CSu iV" Cho 2 sti thUc a,b th6a mdn a+b>2 Chring rninh rAng: at +b3 < aa +bo H9 va tdn thf sinh: S0 b6o,danh: Cdn b.6 coi thi khing.giirti thfch gi th€m. (s Toa;tu - lfJ,lh'D r/ BL: f zL I 4 4 ltL+b ,Fr<4 @-*; r. * qx' i) (r-a) : Jic t J) t tL /rz.x- + lt 4t-+J = zzt-;,t_ _h1k -LX_= J tL(n+z/ = 3 inl NQj; nt*e=a qd h=*2- lRsn /1t"a7r*1t/"V/V NA ru +-L 7tr xts a' lV 1>r da- ct* riui n I #, : L3 J Dt 1n t,t I J K d 2. irt, h, le {rnc, tu+r-z= -(na) \ - z : taL+4tu +3 2 A : a(trrrn - )x,)(L = J(\n ) V /\ = *(kM)'- fr- { <n 2h= flvt"'+VVn+l+ L 4 => - 3,w'"'* A-0 w, (n\+n+)) - f au t{rru -Jl l* * tl a -,/ )ru aH ttl, l8 ,r,, 4{r=, (rrt{ &= b{ t4s LJ, = - t t\' - Lorn- 47 'htt LI, - 4J 141 frr *t -r0I ^4 ,/ +4 "/ ; (5 r Y .,t u:t- .t/' -la* : G't LTUZA = "'6 .l dzrlV/rl LA:C t:Ua' {il," th**A,a 6rN{ll=o tLhtor,'-,1 xL?. L l- + V t-,1 l' ':;''' I = )rt-t {-L-4 -6-t t.1 t trq/ PTt t tt- r / t- ='t-*6 + 14 t'-t-(:0 Vo' t=J -t* co, , ,l/ T;P f= - -( ho, t= 3 ll Tr__L + ll r_a $ re +( u i-f +,6 7ct '!=) L *6 -Jl x_+4x.> ; 2L= 2_ =a14 I L L^4t(Le",\ ,/ &di'tr I 1 fd) yt' tr- -;)44 + [y'= o (,{ } 4n-+21! ttr- //=o Q b'-Aq F=u 4 tL-o ) (o,cr) o _ U,r.,:a';V€, tUi-rf1l C./* ya F*l,= y "3 Lo l- L =4J L 1=.j XL ,, L- 'J +'_ '4(xa, tlVrr-, *l[;; =j H,Gb + -tlffin, =;! ll 5r s tt+ z- : .{ * LL- '<)' J 6-2_*_z"o ) 3*-_:fr._t, = qt /*u, -l ) )(1__4qx_+ Eq P1- uj l\, ,x -, ) oz{- Etf or3'- q zs- CI)zi- ry2f Drt ,z \ t- rl ,ll , O = (144 -4[ra ,-f2 i),. = vt,(vt"-4)( wwt1.) {\ I)Y = t'' -l) [v,,+r1 2 -*r'" t l\^ ".t tqL rcI; P) I LL= &t- 4 luk=4 €r f l* (O Lq7r4 Le { tu' +.Qf vq't-, / ?_ + (tur.4 V= zwrS )v+'l J t" + ,, I I I I I I I I I lq,r I I I I I I D,; I i i i I i I i I I iVse I i I i iqi{ j I t lo7,i' d 'a? .y,t+wGC*r"/\?-+1.' t tq e (ar+oo) v;,7t , e, €,) td .*)) \=/ ,e At E/ t) t/*-{* o 'fii /sT I cd C,- Xli, C-' 4t aflc 4 tuna o d 4 4n4 <- i-a -b = A+be s A) Qa-{o tl qd'-b- &:k-[')L t-pa'4" Ja+ b +2a-(12 H4 2- ze-b J A -]a.e+o q_ 4{ttnc- , #* T )1b,.e> gj{rarte t' za+ L -:-€- +=J {:, A) &\- tr, =- trt f't =b A r+D c- ,t.t: 0iLf 'r4- vtI- € v "7 r^ I .[tt t tG .h I I l,,2) n* I I 6\ +b +bJtLr-:/ € ^ 2c v," {,, +b-L2/ 0 \ I *) frl t,*, rtt tt0; lr : ).c € ill (A-dl r l,) ( b -t) r a <b-t * (a ^4) * (b-a1> o \? (. rf( 6L{A{,{) +tb-,r )'(t\+ lr4l) 4 4i+-z7rD U) l)D otrr,*,r= q.L)i4)u Va. b'+ b+ *&l L:I w *6 ,hfu.u, Pa v?) lp-4 . Truong THPT L€ Xoay Nam hoc: 2Ol'1, - 2012 DE THI KHAO SAT CHUYEN DE LOP lO I,AN I Mdn:Tor{n-KhdiA+AB j' Thdi gian lim bii: 150 phrit (kh6ng