rRuoNc rHpr LE xoAy nt 1'ffr XSAO SAr CUAT I.{tgNC XHO1 tz Nim hqc 2010-201I M$W: 1OAN_ fH6t g, b Thdi gian: 180 phtit khdng kE thdi gian giaa di Cfru 1: Cho hdm sd y= x'-(m+3)x? +(2+3m)x-2m+l (l) 1. Khi n:0, vitit phuolg trinh tii5p tuy6n vdi dd thi hdm sO UiCt tii5p tuy0n ct6 1,. c6 he sO g6c nh6 nhdt. 2. Tim m d€ ao tni hdm sd cdt duong thing y: 1 tai 3 eli6m phan biQt c6 hodnh d0 l{p thinh "6p sO nhdn. Cdr 2l 1 . Giai phuong trinh: 6 tun 2* * 1 = -Z- . cos2x cot2 x- l' /\2 2. Giaib6tphucrng trinh: t rfuJ ='-r. Cdu 3: Cf,u 4: 1. Trong m{t phdng vdi he tryc top ctQ Oxy. Cho tam giSc ABC cdn tpi A, c6 phucrng trinh 2 c4nh AB, BC lan luqt ld 4x + 3y - 8 : 0; 2x- y - 4 : 0. LQp phuong trinh dudng cao BH cta tam gi6c ABC. 2. Cho hinh hQp clung ABCD.A'B'C'D' c6 ddy ld hinh thoi cqnh a; g6ca2o=60o Ducrng ch6o lcm cria d6y bing duong ch6o nho cira hinh hop. a. Tinh AA' 1;heo a. b. Gqi I ld trung didm cria AA'. Tinh khoing c6ch tt I tdi (BDD'). Cffu 5: Cho 2 s6 duong a,b: a+ b :4. Tim gi6 trinh6 nhAt cria bii5u thrlc: M =(r*o*!).+1r+r+j), l**L =, 1. Gi6i h€: ] J' ' lu*+= z l' ' J;-' 2. Tim c6c s5 hang khOng dm cria ddy {x,,} co sO hang t6ng qu6t: _ 30 AI.o n, -T- , (v6i n:1;2;3 ) r, rn+2 http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay Z- a;-r. ::-;iti :' i:Ft : .r: ,l;,i r.iJ nAp Ax or rru xnAo sAr cuAr rtIgNG rcH6r rz rvr6N: roAN- ru6r B;t Vdi m = 0. Hdm s6 trd thinh: y = x3 -3*z ,r2, -1 hs tpi ) -at (xo;/o)c6 hg s6 g6c k = y, (xJ. cAn tim c6 hO s5 k= -l vdi ti6p di€m M (1: -l Pt hodnh rtQ giao rliiim: x' - (m+3)x2 + (2 + 3m)x -2m = 0 e(x-l)(x-2)(.r -m)=0 0,25 0,25 0,25 0,25 y? l, ?,1-l0p thdnh c6p s6 nhdn, ta c6 c6c truong hgp: Cdp sd nhdn ld 1,2, m =) ln = 4. C6p s5 nhdn ld l, m,2 => m = *Ji Cdp sO nhdn ld 2, I, m =) m: Yz "0. /cos2.r * 0 lsin.r * 0 0,25 4,25 0,25 0,25 Phuong trinh: c+ .'6 t*?t + I cos2x cos2x 2sin2 x =% cosz x-sin2 x <+ r6sin2r = -cos2x etanZr=-* '13 1r kn C),I= +- 122 Thod m6n dlk 7t knt D/S: X = +- 122 DK:x>-4. )' > r-8 <+ xz {2::!r+ + it' ).r-8 ( : )' r r-8 <+ "'!3:: '2+tlx+4 x http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay <>(2-Jffiyz>x-8 €4-ala+x+4+x>x-g 9"{4'rra4 <> x<12 K6tlgp{iAu ki€n ta c6: - 4 < x < 12 DK:x>0;y>0 Dat: Ji = o:Ji = bv6i(a, b > 0) ta dugc: at +! =z u, o) 6z aL-=2 He o) {"'o *t =2b (l) lb'a +l = Za (2) L6y (l) tru (2) theo v6 ta du_o. c : ab(a - b) +2(a * 6) = 0 fa=b <>l lab =-2 Vdi a = b, thi5 vdo (l) ta rtugc: at -Za+ t = O lo =' +)l -l+JJ (doa>0) x=y=l 1-t +.,6;, 3 -16 '42 V0y h€ c6 nghi€rn: 1,rry,11:f ,T, _ _ 30 Al.o -n, -7n+lg = " P" P nt >0c> n2 +7n-1gs0<+-g sn<2=lr=t Vfly dey d6 c6 2 s6 hanemdG6ll n=l c6 x1:10 n=2 c6 xr:g AB c6 vec to ph6p tuyiSn BC c6 vec to phrip tuyiln nnu(4;l Gin sri AC c6 vec to phii fi*(2';-t) ;b\fu2 +b2 *o http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay Do MBC c6'n+ AEC = Bel<+ cos(frrr, fiu") = "or1i*,41 o,[7* =lza-nl e3a2 -4ab=0 la=0 ol 4b lA=- L3 0,25 0,25 + khi a : 0 , AC c6 I vecto pfrap tuyfi co toq d6. (0;l). BH.L AC n9n BH qua B vd c6 mQt vecto ph6p tuyiin c6 to4 dQ(l;0). pt BH: x:2 +ldri a = 4b/3, AC c6 l vecto ph6p tuyiin.b tq oo(q;:).0oai vi ec'trtrng an;. D6p s6: Pt BH: x:2 a.Gid thi6t suy ra AI^BD ddu + BD = q ) B'D,= a Ap dgng dinh lf cos cho MBC ta co AC = all Do duong chdo lfn cria d6y bing dudrng chdo nho cria hinh hQp nen BD'- AC = alj - AA'- BB'= ^lBD,z -pt pr2 = ali 0r25 0,25 0,25 0,25 b. Ggi M ld giao cta A'C' vd B'D, A' M L (BDD') + d(A,,(BDD,)) = A, M Md AA' lt( Rlll)t\ r /l(I (/lf\r)t\\ - )lilt /Dnnr\\ tt t t lt ^t t^ OJj Md AA'//(BDD') + d(I,(BDD')) = d(A, ,(BDD')) = A,M = A,C,/Z = o!^t . 2 ddng thric C6si cho ba s6 duilgta co .(;)'.[;)' "T('*o*! ng ual t\' +-l a) Ap du [t* " 0,25 0,25 0,25 0,25 [' *' * ;)' .[1)' .(1)',' T('. u.*) 2+(a+b\+ z3 a2 + M +L>2.!- 24 ll4 M{t kh6c dE chung mrnn - *: 2 aba+b * M >343 4 D6u bing xiy ra khi vd chi khi a=b=2 vgy M ttat gi6 tri l6n nh6t Ld343/4 khi a=b=2. http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay . tuy6n vdi dd thi hdm sO UiCt tii5p tuy0n ct6 1,. c6 he sO g6c nh6 nhdt. 2. Tim m d€ ao tni hdm sd cdt duong thing y: 1 tai 3 eli6m phan biQt c6 hodnh d0 l{p thinh "6p. Minh Hải- THPT Lê Xoay Z- a;-r. ::-;iti :' i:Ft : .r: ,l;,i r.iJ nAp Ax or rru xnAo sAr cuAr rtIgNG rcH6r rz rvr6N: roAN- ru6r B;t Vdi m = 0. Hdm s6 trd thinh: y = x3. rRuoNc rHpr LE xoAy nt 1'ffr XSAO SAr CUAT I.{tgNC XHO1 tz Nim hqc 2010-201I M$W: 1OAN_ fH6t g,