phuong Dubng thrngBcc6 le trung rou uo.rrryIlS?.* "uotl.[r]
(1)www.VNMATH.com xoev z0t0-z0n Ot 1'fff 1'fftl DAI HOC - f,AN fff ,oU*rlio\rfrort TRUoNG rHPr LE Nim hec MU*, f::ryNurEN 1: 4'- (l) + 3x2 Cho him s6 y = Khio s6t sU bii5n thi€n vi v€ <16 thi (C) cua him sO (t) Cf,u -r' -4 Chrmg minh r6ng: Mgi duong thqg qua I(l; -2).v6ihp s6 g6c k < dAu cit gO thi (C) tei ba di6m ph6n bigt d6 mQt diiAm h trung dii6m cria ttoan thAng n6i trai tti€m cdnl4i Ciu2z l Giaiphuongtrinh: tanx.tan3x Giii phuong !* * x trinh: ,12-x' a3=-2 I + cos2x =2 Giai bAt phuong trinh: logo (9' - l).log* ,?, = j '22 Ciu 3: Tinh tich ph6n: f = Jd+sinr.* Cffu 4: Cho hinh vu6ng ABCD c6 cenh ld ali L6y H thuQc do4n AC cho ATI: a/2 Kd Hx *Qng g6c vqr (ABCD) vi 6y <Ii6m S thuQc Hx cho g6c ,lSC Uing 45o Tinh b6n kfnh mat cdu ngo4i ti€p S.ABCD ry, Ciu 5: ciai he phuong trinh: {f1 J7;)0 + '[v' +t) =t lzt' - yt +(l+3x212' +3x.22r * ! =2 CAU 6: l Trong mat ph6ng vdi hq trgc to4 tlQ Oxy cho iludrng trdn (C): x ' + y' - 4x + 6y =36 Dudng thang A qua f(-2:.0) vi cit duong trdn t4i hai <li€m P, Q Vi6t phuong trinh cria A cho doan PQ ngin nhdt Trong kh6ng gian v6i hQ tryc to4 ttQ axyz Cho A (-5; -3; 2); B(-2;0; -$;C(1; 0; -1) Lfp phucmg trinh mat phing qua OA vi chia tti di$n OABC ph,an c6 t1i s6 th€ tich bAng (DiCm B thu$c ph6n c6 the tich lcm hon), (2) www.VNMATH.com oApAN L HQc- r,AN ur HQc rV NrrrSN KiroA' sAI'{ of rm rrffDAr rnrOr* !=-x3 +3xz itoii -4 TXD: R C6c gioi h4n: limy @;limY=+o J-+4 '#6- Xdt sg bi€n thi€n: Y'=-3xz +6x [x=0 ./'=0el*=Z tren Hdm s6 idng Ui6n tren (0; 2) vd nghich bi6n \,/'\ Dths cit oy @l!lL tat 9X (-*; 0) vi (2; +o) + (3) www.VNMATH.com t.2 1.I : K(x - 1)r, 2z A: y: k:> pt he so goc l(:> vdiTalild6c Y k(x Pt a: Gqi A li tlulng th6ng qua I v0i phuong trinh hoinh <tQ giao iti€m cira (C) ve A: - xl + 3r2 - = k(x-l) e (x-lXx' -2x + k -2)= e [i=l l*, _2, + k -2= (3) Xet(3)c6A: l+2-k=3'k Th"y-;=lvdo(3)=>k=3 Vflyvoi k < thi (2) c6 nghigm - {Z) ph6n biQt kh6c l; 0,25 0,25 l' xlx2 <=> (2) c6 nghiQm Phdn biQt -> L cilt(C) tai dilmphan biet A(xr;v');I$;a);B(xz;lz) \* xz =2;!t = k(xt-1) - Z;Yz = k(xr-l)-2 ) fr * lz = k(xt * xz -2) - = Viv I li trune <ti€m lcosx * Di0u ki9n: { cria AB 0,25 ^ [cos3r + Phucmg trinh: <+ tan x.tan 3x + = I + tan2 x <+ tan x(tan 3x - tan x) + = sin2x +2=0e 2sin2 -:- x +2=0el-cos2x+cos4x+cos2x=0 <)tanx.cos3xcosx cos3xcosx e cos4x - -l <+ 4v = (2k +l)n e t =4** 42 0,25 0,25 B6i ctri6u itiAu ki€n th6y thoi mdn ,rTkr =;+-; D6p s0: x Giai b6t phuong trinh: I+ =2(t) x Dk: x FJ1;J7)vax+o D$ Jz-x'z = t;(/ > o) ft l-.+ I- =2 Taduoc: {x t 'l lxz +t2 =2 Di€u kiqn: 9' -l > c+ x > Bpt elrog,ls' -t,{+)tor, <+ (logr(9' - 1))' - =I*log,(e' 4lo Er(9'-1)+3>0 (9' - 1) > < [log, (9' - l) el ftog, ol ? [g'-r>8<+l[g'>g le' -t<z L9' '3 DS : x e(0;/riv[;+o) -r)'[og,(e' -r) -tog, 16l> -3 0,25 0.25 (4) www.VNMATH.com m 1.1 2tr 2"- [ X tX ' + cos'tX + zsln-cos-.dr /= J".G-;.ar= fisin -2222r2 x x\ srn-+cos- *:M'o;<;.? 2) X a,25 I I+ ?-+ Det t= OOi c4n: ' 24 ax xl I tI rll4l 0,25 =2dt 2n 5ft/4 5r/ /4 I =2J7 [lti"tlat =z [l,intlat i'!r^0.) 0,25 % = IV 1it rJt(- cos4:/ * "o' tl'/') = 4Jl 0,25 Dung tryc d cira dudng trdn ngo?i ti6p hinh w6ng ABCD (d qua tAm I cira hinh vudng vd vu6ng g6c voi (ABCD)) Vfly d song song vsi SH vi d thuQc m{t phdng (SAC) Trong tam gi6c SAC, dYng dudmg thdng trung truc atttt 54 c6t d tai O :> O litdm m{t c6u ngo4i ti€p S.ABCD Ap dUttg dinh l)t sin t.gi6c SAC: AC- + r?o, =2R+2p= Sin45" = sinlSC R= 4,25 0,25 0,25 all \l 0,25 V$y mat cdu ngo4i tii5p S ABCD c6 ban kinh: R= c.5 1d l\ ali y*.{y+ *t1=t \\ ^,2;1.^ ne: {[(r*Jr'*rX ulal Lz" -.yt + (1 +3xz)23.+3x.22' - f =2 Q) Nhan 2v6, cia(l) voi * *J *' *t + tadusc: - (y +,[y\l) = x -'{ ; Nhen 2vEctn(l)vdi y-Jfe+0 taducr.c: \ (1) -(x+ ,!.\l)-y-,tfi =) X: -y Th6 vdo (2): 23' + x' + (1 + 3x2 )2' +3x22' * x = e23' +3x.22'+3x22' +x'+ 2" +x=2 0,25 o(z'*r|*Q'**)-z=o 0,25 D{t r = 2' +x Ta c6: t3+t-2=0et=l Ydy 2'rx = I e2' =1-.r 0,25 (3) Vsi x = thi thon m6n (3) Voi x ) 0, x < dAu kh6ng thoimdn (3) (vi I vii > 1, I VAv nehi€m cria h€ (0: 0) vi5 < l) 0,25 c6.1 (C) c6 tam I(2; -3); ban kinh R=7 Jre :) A nim (C) =5<R Gqi H la hinh chiiSu cira I tr6n PQ AI = 0,25 (5) www.VNMATH.com c6 PQ=2PH =2Jm => PQ nhO nh6t IH ton nfr6t Khi dri: H trung voi A => A qua Ặ2; 0) vd nhfn ViY A c6 pt: 4(x + 2) - 3y:0 Hay 4x 3y + g - 0,25 frg;_Z) lim :0 Gii sri (o) Vnor, rapr 4,25 0,25 h mp can tim (o) -" ^ Soou, ffi=2effi=z BM fr=2+ BM =2MC Gii sri M(xoiloizo) fxo +2 = 2(l- xo) = Jro +o =2(o- yo) [xo ++ =2(-l-xo) =) M (0;0; -3) oM(a;0;-3);oA(-s;-3;2) r_ _1 ) n =lou,o,ll= (- l;rs;o) , 0,25 phuong vor ir= (-3; 5; 0) Mp (OAM) qua O vd nh6n ta- v6cto ph6p tuyi5n => pt (OAM) ld: -3x * 5y = g n cirng 0,25 i, 0,25 C\/ -atl (6) 4k_" rrl Dt rrrr rHU DAr Hgg;l'AN www.VNMATH.com \rnr-roNc ^^- NA- THPT r'fl xoaY hgc 2010-2011 Ciuf Thdi gian ldm bdi t' n'roo inii 1oful gian giaod€ ttti pntii'r'0"erc thdi +9x ' x3 dd thi him sO ! = -6xz vdvd i fnao tnAng d"v=-x'4'lfim *t +(m+Z)x-m co AO tfri (c')vd duong Cho d6i ximg €lua x+l t4i hai di0m phdn biet dvd dvir(c",)c6t ,, dC duong th6ngr dudngthing !=x' ta x'e' Ciu II TinhtichPhdn/ = o1,' lG*z)' -, A+B ar=L s6t I# J-+ ) Nhan dang Mncbi6t: J Tinh gioi h4n =lill *fi{) Ciu , Ban co oa"" )/ )r-q;;i , j *+&'T]t III trinh: Giai Phuong z.chohQphuonu, + atan A + b tan B = lo b)tan:l- *[i]-@ (.F *r)' x-1 *:i(r-'l {f7: F=o c6 nghiQmthgc' Tim ,, eC hQ dd cho phuong Dubng thrngBcc6 le trung rou uo.rrryIlS?.* "uotl rrong hg truc dinh/gr6m.tr€n dudng thdngx+zv -3 =o'Di0mM(z;o) 2' tigh c11n6 bhne trinhr- v - =o ; ro yl.'^,!i6iolen m[t phing (or) chira ^ di.m cuaAc Tim to11O "* 'vi6t;;;;;i'ior' hefruc rrong mflt phing * v +22 = am6t g6c oo0 ' Wi tu o*1"9 :*n d, g6c gifra trvc oxvd t4o vdi m{t nr'a"e z.a;,yg thang AB,CDbhng #:r i* ;il' ;;' Cho -f" ttl di€.n lncp|rJno*9:* eiui chirngb6nga'blftts=o'ci=l'ir"rtth€tichtirdiQnABCD' -HCt - """"""""':"": Hs vdt€n thi sinh: gi th€m' A;;O;;i thi khong gi6i thich """""'SO b6o danh:';""""""" (7) iy*: fri l{'a cs K*{ t) www.VNMATH.com ?6^?, +Ulr ' ryn- D=R _p fu'vt"ut = ,tt-ll rcI 7, , 5t>- j rc lLt<+3 ,!'=u e) f :;3, B{;t +oo+ - ws i9 t";+ \r.u t2+ ArJ ,/ -*, 4) ) (, u4, .( la l+tt Re dd u) +, 1t, +); a ,14 (s,c) K> rrrg fu-W' h"q'fr 1^$7t) rtFr**_tr,r; q; i t^.L * Lw+t)u = r+,1 € t ) LtL'+ (rr^+))r + t+-L (, nd' t^' )i e ' 'l I _ rr_ v +-tn a) (,t) r i u' ,pb r'1-; fT a' ' i' \*Lyu J h' + Lu+ + rt r 7a " qT L*,* d ' = (v) f \er , t4"+-fL [*'; 'iiPrm A(k.tt yt) ) [t(',v V -) h,te G l{od I, <tt , /\,1, +* r - +, I f "; 't 1q+*u Z 1* "+t' % = rq<)_ W1 4'ri; ,+g & f g '#f-)'-w -u)=^F+t)'ry -+) L4c* }( ry cz) :U$ ='+4-q' € m=4 atd (8) t4 Lk_ Ll= lt L #;! "!,, I = = oLu=www.VNMATH.com r e-(( ,L+L) , \/= -J=& x_+L (+e)' -_tc'aL 14rL Q-zriclL+ ln Jr, u+) lL' uHu _0 ; tLt lun ' In - b Zl t1 .Q- I tD = a- L+A : +Qt )-9 J $ olr** * Afu^g : q{ +b1 lr.^ N/-" ew A t^'4 + 9r' *$to*$ = (9,n A+e;ng ) ta'-& gal -9i,-U 9* A - q^ B! L e + hreA "C4^ @- t- lau'81 9", i- l^^n = h*g L 9.u -t9 , (-L) g) ry I J+ >o coa| A,, a-4 /> ryzD l-" i") t*A L *\cr* 2- -"V It+ 7L, 1t^, lr'- rI 3w'u *'rl ; a64Cul tq -+(" l ,!,-* = L\4 A =o =4L2 I 02lrf o> 4^ (9) (hn w www.VNMATH.com t)rk -t, / TW '?, e) (ry'\ t(ry)"=n 94 Wl' (tro1 Fr!.d-y fr k =) \, t+ l'- t+f +4 ''o L'd =c \2ju) e t '4- lVt) € (ry/^- L I ) TX\D ; ) ?L = 4.,&, Lr' tt), Lf ,1 z,,t q u',ffi ) v - W ('',Vzra) IP;i.&or4 iHrv,I ' lurL-tv'=brv-t_ ( *+ V = I * u-v=u? lL QX* W V P"- {\, cui 'fr Y $" l,a J /v +L f @ 47ro Uv2 Lt -, t, /*"t ,tv ca) q4 f 'ab- o qu{ +12 42 (w { +e43 _-, we Lt, kl f-L- *n, y qbr ry4 (10) w c6'N *:; uk ro ct* www.VNMATH.com Ac' + Ắú oQ =!dt+c'2 Jl' A(b-At t) l Jco vc) =- t dttult)Y gbtrl= V" ?ti A=? rt) t=4 ; L u=-s/s ?) r-AIE,i) cr.,- AC' ud, u.o; e A /+(\ t 9,\a4 d*e &t' t\.I *+z o cft5r-a| e (-f (1,,t7 ,I) 7, - ,l <") t*, c) B l) " l,c- = t =- 'l t ' h( Lr t-+)'' ;* 4, 'vca\cl oirYb'' Bc'=L >"b t *ho' rytvt (14; ) g* )a,'rr- tt -+ =u i' ,d 'a n?:: f*: oo fr!rr, W'"f" g" + lc 0c- (,9)'r/6 Lt 1t- b) tt:;-l'^ri 8,Y rct=rt a - k' o - -6 z'a J'L =1t"clt^- 8-1V'c=4 LZ.Z u? e*4 C'-, ar ,^f ! bv X* ir- [ ,!'rrtzo ,4 + )bzo .- b= ++B(+,0/ (t+)t= L,a L t=L ] W-L/ ,!rY:j, vrI il^ = (0, 9,1 (11) (' C'& lv www.VNMATH.com b A4T.l,4 nrutrN FcFo ryy' ? h.'.4,0; U-z l/o*r, f A 1., t3 gr-{) I 4-(nor='ulle^4 llrl 'lrl l-' : W W W= ' ic'L * -'"- ?o./,.1 Fl Iro -\ c*{ 1,, r I ) (12)