Khao sat Toan 11D Le xoay 20122013

X6c dinh ttriiSt dien cta hinh ch6p cft b0i mat phang AMN... oAx cHAru,va rHANG prtnl.[r]

- so cD& Dr viNH PHUC on xnAo sAr \rnucrnc rHpr t t xo^q,v cnuytx of t Ax t nAru HeC r - 2012 - * 2013 M6ilioax ri xgOio Thdi gian ldm Ciu I Giii phuong trinh xz *l=.6.1 Gi6i b6t phuong trinh ciei he phuong,,,* CAU II l Giii cdc phucng b 180 phtit, kh6ng ke thdi gian phdt di (x'?-rr).F-lr-+ >0 {;,i]; rt:;::;rt=, rinh sinx+sin2x+cos'x cos bdi: x 4sin3 x + 4sin2 -0 r+ 3sin2x+6cosr =0 Cho phuong trinh 2(sino x+coso x)+cos4x+2sin 2x+m= Tim m d6 phuong trinh c6 it, nhAt t nghiem'.[o'f] * =b* , Nh0n dpng tam gi6c bi6t: Jih,"2 Ciu III.Mgt ttQng Tinh tO hgc sinh xic c6 l0 em d6 c6 nam vd nt su6t dii nh6m c6 ci nam vd Liy ramQt nh6m gOm em di lao nt Ciu IV _2 L Cho Elip co phuong trinh |+ Z * y' =l (E') X6c elinh tqa d0 M e (E) cho tj' sd ban kinh qua ti€u qua tti€m M bing Cho hinh ch6p S.ABCD c6 ddy ABCD li hinh binh hinh M la trung di€mcria SB N ld ili€m nim tren SD cho ND = 2NS X6c dinh ttriiSt dien cta hinh ch6p cft b0i mat phang (AMN) HET Cin Itp vd lhn thf sin r.' , bQ coi thi kh6ng gihi th{ch gi th€m ^Sfr.' HITONG oAx cHAru,va rHANG prtnl Ciu I D{p in Thang iIi6n r=-l r2l I TXD 0.25 '''., Phuong trinh tuong ducrng voi ("+l)(x' -x2 -t)= <+x(r+l)(x'?-x-t)=o {t' -t)' = x+1 <+ 0.2s o x=0 4.25 x=-l fx=0 <+lx=-l c? ,= Lt'-t-l=0 l*f t +.6 f6t hqp vdi diAu kign, phuong trinh c6 nghiQm x : -1, t = t +.6 3: 0.25 l[* -3x-4 > o BPT 0.25 ol[''-8x>o Lt'-3x-4=o 0.25 I[;::' l[*>s lL"=o [x=-l L'= o [r -t 0.25 el l-r>8 lx=-l lx=4 Viy tOp nghiQm (-*;-tl, {a} v[8;+o,) HQ phuong trinh cod4ng 0.25 a.2s * yt -3x+ 4y =l o Ir' tr(,,-3,)- z(f +ay)=t -3x,v = y' +4y,hQphucrng trinh c6 dang: e{lu +v =l e{lu =l D{t J u = xz -llr-2v=3-[v=o 0.25 :-Jil 0.25 €{eIxt-3x-l=o lf +4Y =s I *./i5 i 1l: Ir; Vfly hQ -4 phuqg trinh c6 nghiQm a.2s t-g''J'[-f ''),[t'f *),[*g l ' a DK cosr * PT <+sinx+sin2r+coslx=0 <+ sin <+ (l r(l + sinx) + cosx(l -sinx)(1+ + sin sinx) = x)(sin r + sosx -sin rcosx) = (l) [sinx=-l cll fsin x + cosr -sinxcosx = (2) Iu D- quy- $ g"q_F-: I 0ge) Dar r = sin x + cos x, [rl= -" -l= JT Khi d6 (2) c6 dang vJi t' -zt-l =0"" [t= Lr=l+Jitt> / E\ t -.8 J-z -z t =l-rl2 e sinl x+- t= :, o<+ \ 4) Jz |r*a=arcsin7+k2n I o J|-z -! Ji-z " +k2r I l-=-;+arcsin " €+l <+l J-'-+k2n | 3n lr*r=7r-arcsin!2=+k1tr + z L lt=T-arcsrn-2 fI, Vfly phuong tri'nh c6 nghi€m I = -;+ " .JV-t + k2n arcsin l- I l, Jz-z +k2r Lt=?-arcsrn-2 ,k b Phuong trinh tuong ducrng 4sin2x(sinx+l) + 6cosx(sinx+l) ez : I i:o :{-:! lsinx=-l o € for,n' x+6cosx = l-z.or' r+3cosx g-Qi11l 9(1"$n'" lsinr=-l +2 =0 0.25 f lsinx = -l 1""'^ ', lt=-f+rzn ,k eZ <+lcosx -el I lr=*2-o+k2n *3 [cost=2 L- Phuong trinh c6 dang r)+1- Z(t-zsin'?rcos2 e 3sin2 Zsinz 2x+2sin2x+ m=0 2x-ZsinZx= m+3 D{t t = sin2x, r = [o,i] e Thi phuong trinh tro thenh 2xe [o;z] <+ r e[0;1] e 3t2 Dd phuong trinh da cho c6 ft nh6t Xdt him s6 "f(r) =]t2 Theo yOu cAu gr4 Jl -2sin BsinC + jsin I c sin Bsin t- e sin r * f ,in B sin 2222 n( -f t [2 c> sin a(r €{ co bang biiSn thi€n c+!=b+c c+ fsin thi phuong trinh (*) c6 [o,i] 33m +3 s I <+ -T = * -i R.6 sin = bii to6n -: e e rc + 3(*) I nghiQm r -2t,t e[o;t] Tt gil thiGt ta c6 .ftarin -2t - sin f -sin(B ,in B cos c - € vf 2cos cl) * rin c([2 I (c + 30'))+ r(r -sin(c ['i'c(r = sin B +sin C c- ,in c - = R (sin B + sin c) sin +3oo))= o + roo o ))= rin.a rin c ,ir, B - c(r - sin(B + lo')) =o -! c sin l.o, rl ) cos B + sin =o c 0.25 =0 <+ifsin(c+3oo)=l 0.25 <+ B =C =600 [sin(r+3oo)=t Vay tam giric ABC dAu Iil 56 crich l6y rumQt nh6m em li C,l = 2tO iet;;'d;;; '*' h c,' = cdch lliy nh6m em nii li = s6;;h Sd Cn4 Suy s6 c6ch lAy mQt nh6m gdm V4y xdc sudt cen tinh ln w l (t) M(xo;yo) € Ta 15 ci Nam vd Nt h 210 - 16 = 194 g 210 c6 t M4 o*"0 'a2 =r*'of, 0.2s ,', -1 - 0,t5 MFr-o-'*o =2-xoJi a2 gii ois M4=7MFzhof;e MFr=7I,t4 (M4 *7 MFz)(ur, -7 MF,) = s Theo thidx € o -t (u42 + MF|)+50MF,Mr, =o e -t (u4 + MFr)' + atMF,MF, = s q-ldl=o <+-r rz+oq( ( 4l o_'q1 :l -o re d6 tac6 nFlt i,l/- x-n = *JI 4di€m rd [*,i),(-tt,;),(tr, j),(- 4) 0.25 Y'./ \ Y d'Gqi O=ACr:BD, 0.25 I=SOnMN 0i.ts K=,SCnAI Vfly thi6t diQn li tu gi6c ANKM 0,t5 0i:53