UBNN riNs HA NAM or rru ruyEN sINH Lop 10 THpr NAnr Hec 20ts - z0t6 sO GrAo pUC vA DAo rAo M6n: To6n op cuiNu rHrlc c6u 1 (2,0 cti€m). Thdi gian ldm bdi; t20 philt, kh6ng ke thdi gianphdt d€ 2 2-rlx a) Gi6i phuong trinh 5x b) Giei hd phuong trinh Cf,u 3 (1,5 di€m). Trong mpt phing tga d6 Oxy cho parabol (p): ,- _ii y = 3mx - 3 (v6i m ld tham s6). ., ,l '-6x-8=0. I(. *3)(y* 2)=7 +xy [(**l)(v* t)=*y*2. a) Rut gon bi6u thric A = rA. - 7Ji + S",60 . b)Chobi6uthricB=^-G* -1 (v6i x>0 vd x +4). Riit ggn B Ciu 2 (1,5 tti€m). x-4 vdtimxdC B=1. i,i '1, ' ':' vd dubng thdng (d): a) Tirn m d6 ducrng thing (d) di qua di6m A(1; 3). b) Xdc dinh c6c giStri cua m 9i (d) cet (P) tq\:nitdi6m ph6n bi6t sao cho t6ng2 tung dQ cua hai giao di6m d6 bing -10. cho ducrng-lidn(o)^v?.dicm A ra- trdn duong trdn. 9qi o ld ti6p tuy5n cira (o) laiA, rr6n d l6ydi6m D (D kh6ngt*ns v6{ A), k6 ii6t66r r; .u, r.D (e iJdia;, B kh6ng trung v6i A). ;:' a) Chfng -j* ring tf gidc. AOBD n6i ti6p. b) Tr6n tia doi cria tia BA l6y di6m C. Ke bH vuong g6c v6i OC (H thu6c OC). Gqi I ld giao dicm cira ae ;5 oo. "ch;G -i"r, *"g oH.oc = oI.oD. c) Gqi M la.giao di6m cua DH v6icung nho AB cria (O). Chrmg minh ring CM Ia tiep tuydn cua 1O). + \ d).Gqi E l+ gi.uo. diem cria DH vd CI. Goi F ld giao di6m thf hai cira ducyng tron 9i"g. kinh oD.va dudng trdn ngoai ti6p tam gi6c oirra. chrmg minh rdng o, E, F thang hang. Ciu 5.(!1,0 Aiem1. ,. tt, , @ho x, y ld c5c s6 thuc duong thoa m6n x + 3y _< l0. ,.: rt-: : ' D6u ding thr. rayl;*I;J", HBT Girim thi tht nh6t: Gi6m thi thrl hai: HT.IONG OAX CAr Or-rWEN SINH LOP 10 THPT riNrr HA NAM NAM HQC 20ts _2016 Mdn: Todn. NQi dung A=2Ji -28J, +zsJ2 Ta co l': (-3)' - 5(-8) = 49 > O tr ,, prc6hainghiemph6nbi6t x, -3+7=z; i ''* 4. )55 I(^*3Xy +2)-z* [(**1)(V* l)=*y +2 -" l*r+x+y+l = xy+2 , ,:., 4:-i lZx +3y = I lZ* +3v = I al €1 <f< [x+y=1 l.:x+3y=3 ' ; lt';'. (u -) l/\-L r-r J \-,| lv=-1 w Vay h.g phuong trinh c6 nghi6m duy nh6t (x; y) : (2; _1). Dtrong thdng (d) di qua A( Phuong trinh hodnh d0 Siu -x' =3mx -3 <+ x2 +3mx-3 = 0 (*) Ta c6 L =9m2 +12 > 0, v6i moi m n6n phucrng trinh (*) c6 hai nghidm ph6n bi6t. Do d6 ducrng thing (d) vd parabol (p) c6t nhau tqihaidiCm (x,,y,) vd (*r,yr). fneo dinh ly Vi-6t ta c6 xr + x2 = -3m i Xr.Xz - _3 . Theo bdi ra ta c6 yr * yz= -10 o _^i _i = -10 e (", + *rl' - 2xrx, Dod6 9m2 +6=10<+m -*? DA vd DB te c6c ti6p tuy-6n@lO;,ren 6BDE Xdt tf gi5c AOB, :U' d"t5 * OD = 1g00, md hai g6c ndy 6 vi tri aOi aien n6n tir gi6c AOBpail,i tiep. b) Theo tinh clr6j.'hei figp ^ gi6c cria D . Do d6 tam gi6c ABD cdn taiD c6 Do re ducrng phdn gi6c n€n ddng thcyi ld ducrng trung tryc ,,, ic) usv.r. "xdt AoIC vd AOI{D c6 5id = ofu = 900; chung f6D n6n AOIC.,,AOFID(g.g) OI OC =OH.OC=OI.OD. (t) OH OD Xdt tam giSc AOD vu6ng tai A c6 AI ld (2) Ma OM = OA (ld b6n kinh (O). (3) Tt (1), (2) vd(3) suy ra OM2 = OH.OC = OM = OC OH OM. Xdt AOHM vd AOMC AOHM.,,AOMC(c.g.c) . + OMa - 6id = 900 n6n CM ld tiiip tuy6n cta (O). c6 chung Moa; gIuI = oc ,c, OH OM Do OMC = OIC = 900 n6n tri gi6c OIMC n6i ti6p ducrng trdn ducrng GF OC. ,o.,nia- l. Dudng trdn ngopi tiop tam gi6c cIM ld duong trdn ducrng kinh oc. ^ 1 suy ra OFC = 900. ,]:1||| , :.| Mpt kh6c ta c6 oFD = 900. Nhu v6y G-, m rc uisJv rabadiem C, F, '' .'t "a D thdng hdng. " ' a .:. Xdt tam gi6c ocD c6.ba dudng cao cH, oq di,md c6 E ld giao di6m cH, DI n6n ba di6m O, E,'F thing hdng. C6ch 1.Ap dung bgjtoet,i. 1 1 l1 r+ t-+a)l^:/ , ;.xe++x>3. (l) Vx Vx VVxJx Jx 2727^f2?n2.27 _++_L*3v > 3l_L.4.5 CQng cdc bdp d.tngthuc ( 1) vd (2) tadugc /\ ,[* -#)+(x +:v) >30 e r[# . #)>30-(x+3y) = 2e x +3:!r,'<10). 127 <]-/-+-/->10. D6u ding thtic xay ra khi vd chi *' t;=; C6ch 2. Ap dUng b6t tang thric Bunhiacopski , ta c6 I * 27 _ 1 _3:27 _- (t+e)' 1oo E-E=G- 3\EzG;m=F+\F' (r) (vi (, E #$y) = (r' + r'X* + 3y) < 100 = J* *3$y< 10. (2) Tir (1) va (2) suy ra ** +> 10. J* J:y -^ ryyrakhivdchithi I^=1 [Y=3 . ding thr. rayl;*I;J", HBT Girim thi tht nh6t: Gi6m thi thrl hai: HT.IONG OAX CAr Or-rWEN SINH LOP 10 THPT riNrr HA NAM NAM HQC 20ts _2016 Mdn: Todn. NQi dung A=2Ji. #$y) = (r' + r'X* + 3y) < 100 = J* *3$y< 10. (2) Tir (1) va (2) suy ra ** +> 10. J* J:y -^ ryyrakhivdchithi I^=1 [Y=3 . UBNN riNs HA NAM or rru ruyEN sINH Lop 10 THpr NAnr Hec 20ts - z0t6 sO GrAo pUC vA DAo rAo M6n: To6n op cuiNu