rci rHr rnrl DAr Heqr,AN rHrI NnAl xAnn Hec 2010-_ zltt DE THI MON: TOAN xlr6t.L,n Thoi gian ldm bii: 180 phirt, kh6ng kC thoi gian giao d6 Cffu I: (2,0 itiAm) Cho him sd ! = x3 -3(nt+1)x2 +9x-m,vti m ldtharnsd thgc. l. Kh6o s6t sy bi6n thi6n vh vE OO ttri cria hdm sti ea cho ring v6i m =1. 2. XAc dinh m ee fram sO ea cho d4t cuc tri t4i xr,x2 sao cho la -*rl:2. Cflu II: (2,0 iti6m) l. Gi6i phucrng trinh: 1 + 3 cos x + cos 2x - 2cos 3x = 4sin x.sin 2x 2. Giai he phuong trinh: lxt +2x+y'+y:3-xy j ^ " (x,y€R) l*y+*+Zy-1 "' cf,uIII: (1,0ili0m) r\m J ff-;d. sinx.sinl x+: I \ 4) Cf,u IV: (1,0 ili6m) Cho l6ng tru tam gi6c ABC.ATBTCT c6 tdt ch cdc canh bang a, g6c tao b&i canh b€n vi mdt phing d6y bang 300. Hinh chidu H cfra didm A tr€n mat phftng (ArBrCr) rhuoc doong thing B,C,. Tfnh thd tfch khdi ldng tru ABC.ATBTC, vi tinh khoang cdchgifa hai dudng thing AA, vi B,C, theo a. Cffu V: (1,0 ifiAm)X6t chc sd thgc ducrng a,b, c thoa mdn di€u kiQn a+b+c=1. Tim gie d nh6 nh6t cria : ":m ? . h Cflu VI (2,0 iiidm) ' I 1. Trong mat phing vdi hQ tga ttQ Oxy cho hai dudng trdn : . (C1): x2 + f ,:13 vd (C2): (x: 6)'+ t' ,: ZS cit nhau tqi A(2;3). Vi6t phuong trinh ducrng thdng ili qua A vi 16n lugt cdt (Cr), (Cz) theo hai ddy cung phAn biQt c6 elQ dii blng nhau. 2. Trong kh6ng gian v6i h0 tqa d6 Oxyz cho tam gi6c vu6ng c0n ABC c6 BA : BC. Bi6t A(5 ; 3 ; - 1), C (2 ; 3 ; - 0vd B ld ditim nim tr6n m{t phing c6 phuong trinh : x+ y - z -6 :0. Tim tga c10 tli€m B. Cflu VII (1,0 iti6m) Gi6i phucmg trinh : (z - tog, x)logn,, -;ft; = t utlt TRUONG THPT CHUYfi,N NGUYEN HUE Thi sinh kh6ng duqc s* d4ng tdi li€u. Cdn bQ coi thi kh6ng gidi th{ch gi thent TRIIONG THPT cnuvnN NCUYNN HUE IIrtoNG uAx cHAvr rnr rnrt DAr Hec r,AN rntl unAr . NAnnFAC 2a!o - 2ott EE THI MON: TOAN KIIOI A, B CAU N( )I DT]NG D I-1 (tei6m) Ydi m= 1 ta cd y = xt -6x' +9x-1. * Tflp xdc dinh: D = R x Su bidn thiOn . Chidu-bidn thi€n: !'=3x2 -l2x+9:3(x2 -4x+3) [x>3 Tac6 _y'>0<+l ,t, _y'<0<+1< x<3. Lx. Do d6: + Him sd ddng bidn tr€n m6i khoAng (-*,1) vd (3, + oo) + Hdm sd nghich bidn trOn khoing(1, 3). 0,25 0,25 . crlc tri: Him sd dat cuc dai tai x=7 vd !co=y(1):3; dat cuc tidu tai x=3 vd !ct. = /(3) : -l . o Gi6i nan: "l]\/ - -co; 1im y - +a. o Biing bidn thiOn: 0,25 0,25 * Dd thi: }lA rhi .3t frrrn frrnd toi fiid* rsrr6 rllr ulvltl (0, -l). t-2 (ldi6m) Him sd dat cuc dai, cuc tidu tai xt, x2 <+ phuong trinh y,= 0 c6 hai nghi€m pb li x,, x, <+ R x2 -21m+l)x+3=0 c5hainghiOmphdnbi6t ld x1, x2. <+ A'- (m +1)2- 3 > 0 ol*> -t + '6 lm<-t-Ji (l) 0,25 0,25 0,25 0,25 +) Theo dinh lf Viet ta c6 x, + x, :2(m +1); xrxr: 3. Khi d6 1", -"rl - 2 e (x, + xr)' - 4*r*, - 4 e a(m +l)' -lz : 4 ^ f m:-3 e (m +l)' :1o | (2) Lm=l Til (1) vn (2) suy ra gir{ tri ctn m- - 3 ; m = I II-1 (1 di6m) PT e 1+3cosr+cos 2x-2cos(2x+x) = 4sinx.sin2r <+ 1 + 3cosx+ cos 2x -2(cosx.cos2x -sinx.sin 2x) = 4sin x.sin2x 4,2: 0,2: <> I + 3 cosx + cos 2x -2(cos.r.cos2x+ sin x.sin 2x) = 0 <+ 1 +3cosx+ cos 2x -2cosr = 0 <+ I + cos.r+ cos 2x = 0 e 2costx+cosx=0 [cosx = o ol l I cosx = -; 0,2 0,2 [": * l": 7r -+Klr 2 *?o *y2, J tt-z (l iliem) [*' *2x+ y2 t y :3- xy e[*t * xy + y2 +2x+y = 3 (1) lxy + x+2y :I l*y * * *2y =l (2) CQng (1) vn (2) theo vti dugc (*+ y)' +3(x+ y)-4 =0 0,2 0,2 0,2 0,2 Suy ra fx+y=1 l**r=u V6i x+ y:l thay vno (2) dugc -y2 *2y =g Iip {y".:(py)-: (l;o} (x;y) = (:l; 2) V6i x+ ! = -4 thay vdo (2) duqc -y2 -3y-5 :0 Phuong trinh vd nghiQm Hq c6 2 nghiQm (x;y): (l;0); (x;y): (-l;2) ilI (1 di6m) 0,2 0,2 -Jil"otI*t -ra(cotx) r cotx*l 0,2: 0,2: Ji (-*t r+ h lcot x + rl)+C IV (1 tti6m) Do AH L(A,B.C,) nOn g6c AAIH bang 300. 4H li g6c gifra AA, vi (A,B,C,), theo gii thidt thi g5c {\// / " 'i/ / =/y", 0,2 X6t tam gi6c vuOng AHA' c6 AA' = a, g6c 4H =30" =+ AH : I a a2 Jt o"li AtBtc 3 z 4 24 I 2 V ur"nrurr, : ! dn 's X6t tam gi6c vuOng AHAr c6 AA, = a, g6c AAtH=300 =+ AtH :+ Do tam gi6c AlBlCr lI tam gi6c ddu canh a, H thudc B,C, vlL AlH = { ^r^A,H vuong g6c vdi B,C,. MAtkhfc AH LB,C, nOn BtCt L(AA.H) 0,25 Ta c6 AAT.HK = ATH.AH + HK = AtH '!H = oJi Mt4 2 Tucrng tg c6: I-bc> 1-ca) , (r *").,(r *oXr*a) (r *r)u(r+"[r+a) 2 1r *a;n(r *"1r *"; b2 r'ra, [r.:)(r.;)[r.:) -[r.#)' = o' Do d6 min p : 8 d4t clusc khi a : b : c _l J V (1 ili6m) Ggi giao di6m tht hai cria duong thing cdn tim vdi (Cr) vi (Cz) ldn luqt li M vd N Ggi M(x; V)e (C,) + x2 + y2 :13 (l) Vi A h trung di6m ctra MN n€n N(4 - x; 6 - y). Do N e (Cr) = (2+ x)2 +(6- y)2 =25 (2) ouc"e itrins ;a; ti- aiq; A ;t M a6 ph;o"s tiintr : i - at + i : 0 Tri (l ) vd (2) ta c6 hQ {*' * v' ^=13 ' f(z* x)z +(6-!)2 :25 ciei hetadusc (x:2; y: 3) (lo4i vi trungA) vdC :# t r:: ). Vay*f { t !l VI- 1 (l tli6m) \ \ YT-2 (1 di6m) AC : 3J2 suy ra BA: BC : 3 l{*-s>' +(y -3)' +(z +t)' =9 1@-z)' +(y-3)' +(z+4)' =9 I L"*, -z-6:0 0,2: 0,2 0,2 0,2 lf*-s>'+(y-3)' +(z+t\' :9 l{*-s)' +(4-2x)2 +(2-x)2 :s <+jx+z-l:O o|t=l-x L"*y - z -6:0 ll =7 -2x Tim dusc: 8(2;3;-1) hoac B(3;1;-2) vII. (1rti6m) Dk:x)0,x+3,*+! 9 0,2: 0,2: Q -toerx)logr*, - *fu - | 4a (z- tog,.)G;- jr* =, 2 -los" x 4 aJ "' - -1 D{t: t:log3x ptthinh,? 4 =1, h+1't *-z ft =-l 2+t t-t *lt' -3t-4-geLi :o' 0,2 So siinh diAu kiQn duoc 2 nghiQm x =81 I J 0,2 ? . - 2ott EE THI MON: TOAN KIIOI A, B CAU N( )I DT]NG D I-1 (tei6m) Ydi m= 1 ta cd y = xt -6x' +9x-1. * Tflp xdc dinh: D = R x Su bidn thiOn . Chidu-bidn thi n: !'=3x2. - tog, x)logn,, -;ft; = t utlt TRUONG THPT CHUYfi,N NGUYEN HUE Thi sinh kh6ng duqc s* d4ng tdi li€u. Cdn bQ coi thi kh6ng gidi th{ch gi thent TRIIONG THPT cnuvnN NCUYNN HUE IIrtoNG. didm A tr€n mat phftng (ArBrCr) rhuoc doong thing B,C,. Tfnh thd tfch khdi ldng tru ABC.ATBTC, vi tinh khoang cdchgifa hai dudng thing AA, vi B,C, theo a. Cffu V: (1,0 ifiAm)X6t