TRUC'NG THPT CHUY6N NGUYEN I]UE l<$. rm rnrl #4r F{qc lAw qrlU i*{HAr mAryr E{gc 201s - z01t DE THr nrOru' roAN xmox a,n Thoi gian liun bdi: 180 phrit, khdng te thO'i gian giao d€ Cf;u tr: (2,8 di€,m) Cho hdm s6 ! : x3 - 3(n +7)x2 + 9x * m , v\i nt Id tham sO thuc. l. Kh6o s6t su bi6n thi6n vd ve AO tni cria hlm sO Aa cho irng voi nt:7. 2. Xic dinh nt dd hem sO Oa cho dat'cuc tri tqi rr,)r? sao c.iro lx, - rrl=2. C6u X{: (.2,8 dihwe) 1. , Giai phuo'ng trinh: 2. Giai he phuong trinh: '.' I + 3 cosr; + cos 2x -2cos3x = 4sin x.sin 2x f:-ra ].'t * t). + Y- * 1 :J:-r-l' l.xy +:r +zv =1 (x' Ye R) Csu EEE: (f,8 di\m) T\tn f :f ox sinx.sinl " -t '. I \ 4,/ C6u EV: (1,8 di6mc) Cho lang tru tain gi6c ABC.ATBTCT c6 tdt ch cdc canh bAng a. g5c tao bdi canh bon rzd md'r phing d6y'oang 300. Flinh chieu H cira didin A tron mat ph&ng (ArBrCi) rhuOc dubng thing 8,C,. Tinh thd tich khdi 16ng tru ABC.ATB'C, vd tfnh khoang c6ch gir-r'a hai dubng thing AA, vlL B,C, theo a. C6u V: (I,ff dihree) ){et circ sd thqc <lucrng a, b, c th6a mdn didu kiOn a + b +c = 1 . Tim gi6 tri nho nh6t eri.a : r= Ciiu VI y2,t) *i6rte'S 1. Trong mat phing v6i h0 toa dd Oxy cho hai duo'ng trdn : , (lC1): x2 + f .:13 vi (C2): (x : 6)t + y2 :25 cit trirau tai A(Z:3). Vi€t phuong trinh duo'ng th6ng di qua A va ldn luryt c5t (C'), (Cz) theo irai dAy cung phAn bi6t c6 dQ ddi bdrrg nhau. 2. Trong kh6ng gian vo'i hQ toa dQ Oxyz cho tam giac i,uong cdn ABC c6 A(5 ; 3 ; - 1), C (2 ;3 ; - ilvd B ld ditim nirn tr6n rndt phing co phucng trinh : . -^ ;. lrm toa do cllern u. CAU VII Q,A diAwt) Giii phuong trinh : A (z-tog i-)iogn.3-; :- =l l- iog, x F{Ct Thf sinh kltong duqc sw dung tdi !f.€u. Cd"n bc coi tlti kltong giai thich gi thenr {r+-{+-)r:-l BA : tsC. Bi6t .x+y-z-6=4. www.VNMATH.com TR.IIONG TT{PT CI{UYEN NGUYEN HUE IITI$NG NAX CTTANN rrU rgtl DAI HqC LAN g'rr{I ror{Ar NAM FIQC 2010 - 20r 1 pg rril nnoN: ToAN KHoI A, ts t -6"t +9x_1. -12"r'f9:3(;r -4x+3) <0<=l<x<3. =JX Y6im=l tac6 y=a * T4p xiic dinh: D = R * Su bidn thiOn n Chidu'bidn thi6n: y', ^ ["r3 laco v'>(l€l ' | , 1 L.^ - -uo do: + Him sd ddng bidn trOn m6i khoing ( ,1) + FIdm sd nghich bidn tre-1 khoring- (1, 3), * Cuc tri: H)m sd dat cuc dai tai x:1 r,b va (3, + *). .''''' ''.'''''''''.''.'''''''''' '''' lcn: Y(1) = 3; dat ti0u 4"25 n ){ n ?5 4,25 o ?5 n ?( n-1 {1di6m) (Idrem) )cr:YG):-1- e Gi6i han: lirn ;r - -co, 'P : +oo. " BAng bidn thiOn: Ta c6 yl; 3x2 * 6(y+ l)x +- 9, Him sd dat cuc dai, cuc fid; di ;;, ;;; d,,*""g tii"r, t.= 0; i;";;hie* ;t ra ", , ", e Ft xt -21nt+1)x+3:0 c6 hai nghi€m phin biOt ld x1, x2. l-'uT .2 1\,= (m+ l)t - 3 > o +> | r/? > -r -f {r (l) 1,, < -l -",,5 V, - *rl = 2 e (x, +x, )' - 4r,r, - 4 e 4(m +t)' -12 = + T a(nt+l)2: ,ol'n=-' lm =l (2) q2s www.VNMATH.com 0 ?5 0,25 o)s 0 )s 0.25 n ?s 4,25 4,25 0.2 5 o ?i 4.25 o ?5 " ) <> 1 + 3cosx+ cos 2x *2cos(2r+ x) = 4sinx.sin2x 1 + 3cosx+ cos 2x - Z(cos x.cos 2r - sin x.sin 2x) =4sinx.sin 2x | + 3 co_s:r r, 9os2x _ 2cpS,r : 0.<+^ ] + c,os x + c_os 2:: = -0 fcos": o 2costr+cos.t-0e I I I cosx = l2 P'f [-_, , {-t-1-l/-l Suv ra I - [-r *.v 4 VO'i ., i y -t thay vdo t2) duqc - r l- 2), =A Tiry dusc (x;;r) : (1;0); (x,y-) : ( 1;7) Vcvi :r * y = -{ thay vdo (2) duo'c -),2 *3),- Irhuong trinh ver nghi0m H€ c6 2 nghiim (x;y) : (1;0); (x,),) : (-1,2) f l/T lx:-*Kn lr | 'to I "r': + + K2tr L3 (t^)^t lt'' +2x +J'-+ f =J- ")tl lr,'-+)'l'rJ' +2.rt.v =3 (l) 1 €< ["ry+x+2y:l l-\.y+.\'*21,:l (2) CQng (1) vd (2) theo vC duoc (;,: + -1,12 + 3("r r 1') - 4 : 0 II-1 (1 tli6m) {H (1 eli6m) f cot-r l I / ci^' : Jt I .l 7T\ srnxsrnl"*, J cot -x ___d _ s inx (s inx + cos x) dx : Jt[ cot x sin2x(1+cotx) r:rCotx+l-l :-42lt4a(cotr) J cot-r+1 gifra AA, r')r (A,B,C,), theo giA thiet thi gdc AB J7 (- "ot :r + ln lcot x + rl) +C Do AH L(A.B.C,) nOn g5c A,4,H llgdc AA.H bang 30('. EI-? {n diem} IV {1 di6m} n')< www.VNMATH.com X6t tam gi6c vuOng AHArc6 AA, = a, g6c AA.H =30" = v :lor, -L.L.u'Jt-u'Jt 'ABL,l,B,cr-3tttt"uA,Br, -tt 4 - U AH:! 2 0 ?5 Xdt tam gi6c vuOng AHAr cd AA, = a, g6c AA,H=300 -> AtH :+ Do tam gi6c ArBrCr l) tam gir4c ddu canh a, H thu6c B,C, r'd Matkh6c AH J B,C, nen B{'t J (,4Afi) I^' AtI{ :$ nen A,H vudng g6c v6i 8,C,. ,) K6 du'dng cao HK- cfra tam g-1;l-c_ AA,H thi FIK cliinli ld khoing cdch gifr'a AA, rlh ts,C, A, H.AH orll Ta c6 AAI.HK = ATH.AH -) HK - "'' : 1A, 4 nhdn c6 : (t +a)](t + c) - ab)(r - bc)(t _(r '.; cQn -i)f 1) )\ca ) ;il;g bi"h .( a-p) -l 'i. At afig B 1-ab>7- (abc)2 trung binh [(t + a)+ - ro) 015 0 ?5 gva {z+a+u)(z*o*h} TuongtU c6: 1-bc>@ 2. (1 di6ma) n , ('1")J(!:Xl:b) Suy ra H,ra: [i.;)[t*-;Xt.:)- ?'.#-)' , o' Do d6 minp: B dardusckhi a:b: c Goi giao di€m thri'hai cira duong thing tirn vdi (Cr) vd (Cz) 16n luot id M vd N Ggi I\{(x: V)e (C,) = "'*-y2 :l j (1) vi A le truns di6* ;d ffi;d N(4:;; 6 : tj DoN e (Cr)+(2+ x)2 +(6-),)2:25 (2) ( z 2 ,^ lx +V :lJ Tn(l)ra(2)tacohd I " 'ftz*x)2+(6-1'l:=25 11 6 _17 Giai heladuoc(x:l:y:3)(loai vi trungA)va(x= ; ,V:] f Val M1 - 555 oucms thilg.in rir" oi q;; A id M io pn".ig rrinrr : i - iy I i-: a 0 ?5 0 ?5 0?5 vr- 1 (1 tli6m) 6 ^:) 5 www.VNMATH.com AC : 3J2 suy ra BA: BC: 3 n ?q a)5 0 75 0 ?5 o ?5 o ?{ 4,25 +(2* x)2 tqidoBi['gt'i6 iiinepii,,*'eiiilil' [{"-s)' + (y -3)2 +(z+l)2 = 9 lfr -r>' + (.y -3\2 + (z + 4)2 = e f"*, -z-6:0 [r"-sl;i6_i;l; ir,i i; =s '[r" -s;;;a;-;;;' o]" *z-1=0 olr=l-x l,.l ["*y-z-6:0 l:t=7-2x ':, . ::" VII. (1 tli6m) www.VNMATH.com . tron mat ph&ng (ArBrCi) rhuOc dubng thing 8,C,. Tinh thd tich khdi 16ng tru ABC.ATB'C, vd tfnh khoang c6ch gir-r'a hai dubng thing AA, vlL B,C, theo a. C6u V: (I,ff. +9x_1. -12"r'f9:3(;r -4x+3) <0<=l<x<3. =JX Y6im=l tac6 y=a * T4p xiic dinh: D = R * Su bidn thiOn n Chidu'bidn thi6 n: y', ^ ["r3 laco v'>(l€l ' | , 1 L.^ - -uo do: + Him. x sin2x(1+cotx) r:rCotx+l-l :-42lt4a(cotr) J cot-r+1 gifra AA, r')r (A,B,C,), theo giA thiet thi gdc AB J7 (- "ot :r + ln lcot x + rl) +C Do AH L(A.B.C,) nOn g5c A,4,H llgdc AA.H