Bi t_H fitfr Bsi hpc dfi j, ttrdly! - 20i3 TRIIO'NG DAr HQC S{.tPrrAM HA Ngr NE Tru THUSAI HOC SOT 1 ni *i giim ot trang MOw: ToAN Thdi gian kim bdi: 180 phtit I. PHAN Crrt]T{G cHO TAT CA rsi srNH g,0 iti\nl 'CAu 1 (2,0diim). Chohd.rn sdy:2x3-3(m+3)x2* lSmx-S (C",) a) Kh6o s6t sp bi6n thi€n vd v€ d6 thihdrn sO tctrl m= l, i b))Chr:ng n:inh rdng trOn parabol y :,t c6 hai di€m khdng thudc (c,,,) voi moi gid tr! cfia m. i.o).n*: n:inh ri tail{11,A diinfi" Gidi phuo'ng trinh , 2cos3x * cos2x * sinx : 0. CAu 3 (1,0 di€m). Giai phuongtrinh !f.:.ZlttlF+ 4x + 7+ 1) tx(./x, + S + 1) : 6 . \ ,-;;-" ,,:_ .i Cdu +\f,O di*m\. Tim t6t c,?it cin s6 hpng nguydn trong khai tri€n (rE +'r[1)n r' / rdpg S.4 : SB =.9C vd g<ic gita rlud'ng ihltng SA vd m{t ph[ng {ABC) b[ng 60'" T'fnh theo c th6 tich cira khOichOp S.AtsC. , CAu 6 {1,0 iliim}. C6c s5 thgc x, y thay dOi tliOa tmdny,+ y :7. Tirn gi6 tri 16n nhht cfiabi€u thfrc : \ '' P: (x'+ l)(y'+ l). II. PIIAN nffiroC {3,8 cti6nl: Th{ sinh chi dwqc ldne wQt trong hai phitn riilng {phfrn A hagic ptfin B) A. Theo chuong trinh Chu6n , Cdu 7.a (1,0 di6m). Trong m{t phdng v5'i hQ toa d$ Oxy, cho hai diOm A(-5; 1l), B(7;7) v}r hai <ludng thlng d1 : 2x-y- 1 :0, dz: x+3y -4 : 0. Tim toa d$ di€m C thu6c r{ vi di6m D ihudc d2sao cho tri gi6c AB;CD ld hinh binh hdnh. Cdu8.a (I,tldi\n\. Trongrnptphingv6'ih€tgadQ Oxy,chohaiduo'ngtron (C1): x2+y2-2x+2y-2:Avit (C2) : x2 + y' + 2x - 4y : 0. Ei€m A( 1; l) ld rnQt giao di6in cua hai du'ong trdn ndy. Vidt phu'o'ng trinh dudng thdng di qua A cfit(Cr), (Cz) l6n 1u9t tai B vit C kh6c phfa vd'i A saa cho AC : 2AB. Cdu 9.a (1,{} diAn$" Tim giS tri nhO nhSt cLia ft? sae cho tr€n d0 th! cira hdin s5 f(x) : * tOn tai cdp di6m nri tqri d6 cdc ti6p tuy6n cdra AO tni song song v6'i nhau vd khodng c6ch gifr'a cqip diOni ndy bing rr . li, Thro clru'e,ing trlrrh N*rrg eao 'ijf;.u 7"b {t,{} difwt}. T't"lingnirit phing.r,j!h0ica iffi C:ty,cttt:3 rlLi.i'nglhdnlr rr]r:x + \'-?:A;t!1)s. -\'+ l: (i vit $ :3x y - 5 : 0. Tini tga dQ c6c dinh hinh vudrrg ABCD, bi6t rang A. C €. c/t, B€ clz, Ce dz. Cflu 8.b {1,0 di1rn}" Trong mlt phdng v6i hQ tqa dQ Oxy, clto di€n M(- 1; 0) vi dud'ng trdn (Q c6 phtLong irinh rt * y'- 8x - 4y - 16: 0.Vi6t phu'o'ng trinh dudrrg thing di qua M cit(C) theo dAy cung AB ng*n nlfit. Cdu 9.b (1,0 di6*e).Tim ciic gi6 trl c&amde tr6n d6 tn1 cria hdni sd f(x) = x*2 *:l .O hai di€m -41r(x,; yr) va x_ ! Mz(xz y2) sao cho x1 * yr = x2 * lz = ri . Tu d6 chri'ng rninh ring iuft, M cirng thuOc m6t nhdnh cria dd thl ;. -* nam so da cno. V'lai sinlt kitdng dwqc sir dqrng titi liQw, cdn b$ coi thi kh0ng gidi tlr{t:h gi tltdm. Hq vi t6n thi sinh SO b:io danh; www.VNMATH.com