TRU'CNG EHSP i{A NOI TF,{{J'ONG T'i{PT', Ct+UVntE - &E{SF Dtr T'ixx rr+riB4x i{qc n-,AN,i\/ r"iAtof ztlll 1,,10n thi : TGlt Fi Thd'i gian ldnt bdi . iB0 phirt, kh6ng kA thdt giarc phit riA C6u tr. (2,0 di\m ) a\). uno naili so y: x- - x" + 1. t f . i{hio sd.i sii' bi0n thi6n va vd Cb ihi {'65 ctra hAm s0. ^ ,,,;. . , .,i i . ,;. ,, ,,^ , 'A ,A 7. ViOt phu:o'ng trintr tiOp tuydn cfra ii6 thi ('r'? , bitit tiep tuydn cht citc truc Cx, Oy iAn luct iai A, B vi.'iani gi6c AOts cAa tai C. CAu 2. (2,0 aii6nt) 1 L Giai phuong trirrli : Zi-ar,x+ coix =Zsin}x* ;_ . sin2;< 2, T'irl cAo gi|tri ^ ,t ,, + 1 LA:i J" \I,t-t 'lrcrn J Tinh ticir irliAn Cfiu 4" (1,0 diLm ) Trcirg i<ir*ng gian, cho r,ii;:rh chr5p S.ABCI) ca dA.y AEiCD iA hinh binh h.*.nh, AB : a1D" BC : a"7t vi d0 di.i cd.c canir bOn bdng aV5. Cpi. giao dirlm cira AC vd BD li H. T{nh the ilch kiioi cAu ngoai tidp hinh tii'ciiOr"r Si-laB, C6m 5. (i,0 iiiiru). Cho cdc sO dLrong a, b, c tir6a rn6n a + b + c: l. Chfiirg iniiri"l - .1 (x2 iox*g_<O cte n cie i,6 sau c6 nghi0nr : j '; 1x' - ittxv:,, -;- 12 = C 1,,["* *s; 'tl rl7 !o -'tl cix. cos3 x ['.t, i __- r_ !c+ab rX rr cr J L C[r: 5. i.?,G tiie ui) 1. Trcng m6.t piririg Oxy, ciro dud'ng ti'on (C) : x2 + y2 - 5>t'+ 2y r- 6 = 0 vd. digri p(i; 3). Vi6t phuo-rrg'cririh c6c ti€p triy6n FE, PF crlie dLl'dng h:dn (C), vo:i E, F iA c6c ti€p di€in. Tinli cii6n ticii tam giirc FEF. 2. Trong khOng giair Cxyz, cho tam giSc ABC vd'i di6rn h{(l; 0; 2) thuQc canir BC, duo.ng ph6n gi6c ilo:rg g6c B vi dud'ng cao kd til'ctinh A IAn luo-i c6 prru'ong irjnh : , x*2 y-I z-'J- x-1 v z ?. cit: *; :;= =-;-; dz.: li- = 3: , Tinir itiioAng c6ch tir di,5r:r Ir4 d6n dLLdn[ thing AB. CSu ?. {},i} cii€rn) ^ ,, Tlnr so pl-rirc z ci., rricci',rn nho irh,At vd thoa nifin i iz -,i l i- a 'l l-11 /-tl. 'S"cr*0i r v."rPac^, Hdt ,Dry ki6rc [ri,thi u56" fiigai isoc lfrm ilo{r 5 sd awp'c td cfufi,c vdo ngd3t 7.8/SiI$] t! vflia,. *Ap Arq * ?r{AFiG *rarvt arxi g't+ii Bn r,.4,rrr rnrr sc,- mana e*lt Fv i^o - i., j^o - Ndu xo = I ihi phu'ongtrinhti4p tu5,g1.' ), : x =+ O = A =ts (loaj). ._! 1 23 , 32 )l6u x^ = =+ r,^ = -; =r r,l:ricng iiinh t,€n tuvdli : ./ : ;r -:- - . i tlri,a. mAn ) " 3 27 ' ? "." -"-;- Lj ir$y ti6p tuy€r-r cAn iim lA : Zix*77y +- 32 = A. n'l{ 0,5# Phiiorrg trlnh i,E cl-lo tucng duoiig v6i i:t : ta;iy, * coix + taux : + t^w; *Zsin1r- -:- = 0 <+ 1 sin?,x qin?v a t^l.'n , - ,/ stit/-x r "* bIili,K sinx I it, /" I i I ,{f ; #"rcF12,t €" I * 2sin'x -2sin12x= A <'+ I 1- 1 ccs2x - * cos-Z)() = 0 k e Z (thda mdn fl"<) L'acd :<' 10x+!<g ++ i. (:i! 9. Sr-iy ra- hd c6 nghidrr er piluo'ng iiinh x2 - nrx-,& 1- 12:0 c6 ngiri6rr thudc doan i1; 9], IfX+ t: G * 4 cf 1':r L-t.:r.:, *.,-/-a a-:.+r^:-^r- 1 ,3 J^ ^ *,4+i2 #a 1 L-'vx + ','=ri;3]. I(hicr6piirontro'thdnh ia-n-,ti -,riz:0 <+ in= # {dctf 0). f4 t l') /\!L l\[/ - +i Ta.c6iii):13, rn, L - .a(-a tEli.tt -i +'/+\=-_-:_ vi fl(i)=0 (*i=r,f; c/1.?\ r Jl '"- I \Ll t+ _ * \,r _,i. ?1 /, (3)= +. i(',6)=+'sLiyra T= i(t)=rn:r. Vfly,J5 i-r3 c6 ngiii0in thi T = ,.,-r = .f f,-Arr *AP AN TI LF, \v t I {.trcfit i" t|,0 dia-n\. Floc sinh tii gidi. 2. {,1,ft diilm} . Vi€t phuo'ng trinh ti5p ruy6n .' Gii sri'ti6p diOm li ll(x"; y"). F:e sd gdc cria ti€p tuyCIn ld i< = y'(xo) = 3xo' -Zxo. Dli AAOB cAn tpi O thi hoEc tiilp tuydn vudng g6c v6'i Cuo'ng thdng y = x hodc vudng g6c v6i duong.il',ing!:-x. 0,5{} TI-i1 : Ti€p tuy6n vudng g6c. vdi duo'ng thing y = x. Suy ra k = - ! =+ 3xo2 -Zxo= - 1. Firr-Long trinh niy v6 nghidnr (loai) . TH2:Ti6ptu),An vu6-og6cvd'iduorgfl:Engy=-:t. Suyralt= 1 =+ 3xo2-2x"= 1 o l^o - ' , * ?q :1. ( J,r! di1wtS . GiAi phLrong trii.ii"l n r4 0,50 -11 1 s-,-ts - .ui. - l^ - u ccs'x . / * "r1- { .*t,r TTT 'L di€m) r\'/ $ sie*'* 1 di6m,\ t], {} Tinh i{ch phdn ^T .1 1-4^ 1: l5-* Jo coszx 1t :* I = Jo6 Vtanrx.d(tanx) = T. Vtansx -fI Ta c6 ASAC vd ASBD ld cdc ram gif"c,cdn n0n SH I (ABCD), SH2: SD2-Df{2: SA2 -AH2 + DH =AH =i AC: BD =+ T(LgiiicABCD lihinh ch* , :iit. AC2 : AB2 + BCz : Ba2 ,+ AC = 2atl7, =+ ./ilj = a:12. SIl2 = SA2 - AH? : 3a2 =i SH = ar6. a (0,50 diiwt). Do AHAB vudng t4.i H, n€n tAin O c&a m{t cAu ngcai tirip tri'diQn SI-LAB ld giao di€m cia iruc AHAB v6.i mdi phEng il'urrg tru'c cira canh Si-l" i lli io 1a c6 : R2 = oH2 = 89'* li-i1= l:.,G)t* tr3€\'= 4 !, 'tz) ,tzJ a a27a39Tta3 \/Av.V, :-aR.':+-: 3332 61; VJ 5 {s^\2 i*l \o/ ca- lca - _L - \ 1' I 'i e 1-c- '1/1r-a;1r-c; ' v' &,50 #,58 ut-)it r. lJ"{J Tn gi* l-a nA Turrng tq ta cfing c6 : ra 0<a,b,c<1. ;- leblatt \l i"-a-b + ab -r/{r-u){r-i) ' thi6t suy r; IdU l. 1 c.{-alt ca _-+: b +ca ca (1-aX1-c) \; lT di€nr'1 Tiieo BET C0si ta co : i ,. I . Uorrg ve vor v0 cac bdi tr$n ta Ju'o-c iipcm. {,}"8 di6nz}. ilui;'ng tron (C) c6 t6:ri i i3; - t ) ttb6n k-Gh R- Cii sfr lvl(x; y) e (C) sao ciio pM lAtir5ptuy6n. Taco prt= (x_ 1; :t _3.)vA ll.A Khi d6 pfr t tpi e+ (x- i)( <-3)+(y-3Xy + i)=0 ++. x, +,.r, _ ttx_2y =A. Ta c6 Ir€ phLLoug trilrlr : a =u (x' i3) A - l.x2 *'yt Ly-io -oxf 5:r* _U *2x-ar {*' + y, * sx 4. z.y -,r 't^ {, x' -1- vt - lrx- Ztl -1 +v' 2v+6 ={x-3;y+l) o f"t'-yz - 6x*Zy*d = 0 1x=Zy*3 tx=2y*3 * tUOr*Zy_3=O =) Suy ra phuong irlr:ir duo.ng thEng EF : x_21r_ 3 : 0. Eat E(l; a Khi dd : EF :ing "U phrrong irinh liai ridpm f .r - < JX=1 [x:1*4t' ty=3"t Ya ly=Z-3t, {.1,8 ffi0nt}. Tfrih khoAng cach - figi Ir4:(;<; y; z) td Ut6' Goi H Idir''lirgdi€n cfia&'iM'tiri Hthu6c d1,tac6 'ii(2+2t;l -3i; 1 r-2t), vecio chiphirc.ngc.,ia drlit i(2: -3; Z) vd Mndix * 7; y; z_ Z). Tr) d,6 ra c6 ii6 : { i'rV.d = o jx+l =4Jr4-t I rr -:- !^l *. 'l /!- I Y I U *- /- - n, l"-"-t ' ^- ^ :-' nen ,48.',sdr=0 cr:(i -2t)_ 2(1_3i)+(_l +2f) =g =+ B(2; i: 1) vccto chi phuo*g c''ia AB id r 7.1146 = ?29: i; 5) ir6n AB c6 prrruong irinh : i(hodrrg cdcir iii M d€n dud.irg thirng AB : ,. - i[B=M.uot']l ^trtn lx I lx L d.lia !],50 {},25 ,3r58 i,0# l|t*;i ./sn {.!,# didm}" Tinl s6 ptruc ,- _ &xetrEj GiA s# z= x * yi; 1x,l:e nffi Sui,pu irz-Zl: lt-2-ii <+ Dodd lzl=$3lp :{;A 44,, * r: Gtu+ 5, +1 > i y.,. p 1 s - V5 Yr q/i' Biirg thilc;<Ay ia khi . sd.i sii' bi0n thi6 n va vd Cb ihi {'65 ctra hAm s0. ^ ,,,;. . , .,i i . ,;. ,, ,,^ , 'A ,A 7. ViOt phu:o'ng trintr tiOp tuydn cfra ii6 thi ('r'?. cAn tpi O thi hoEc tiilp tuydn vudng g6c v6'i Cuo'ng thdng y = x hodc vudng g6c v6i duong.il',ing!:-x. 0,5{} TI-i1 : Ti€p tuy6n vudng g6c. vdi duo'ng thing y. z ?. cit: *; :;= =-;-; dz.: li- = 3: , Tinir itiioAng c6ch tir di,5r:r Ir4 d6n dLLdn[ thing AB. CSu ?. {},i} cii€rn) ^ ,, Tlnr so pl-rirc z ci., rricci',rn nho irh,At vd