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<span class='text_page_counter'>(1)</span>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. 1.. -r'. -4.. Chrmg minh r6ng: Mgi duong thqg qua I(l; -2).v6ihp s6 g6c k < 3 dAu cit gO thi (C) tei ba di6m ph6n bigt trong d6 mQt diiAm h trung dii6m cria ttoan thAng n6i trai tti€m cdnl4i.. 2.. Ciu2z. l.. Giaiphuongtrinh: tanx.tan3x. 2. Giii phuong 3. !* * 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.* 0. Cffu 4: Cho hinh vu6ng ABCD c6 cenh ld ali. L6y H thuQc do4n AC sao cho ATI: a/2. Kd Hx *Qng g6c vqr (ABCD) vi 6y <Ii6m S thuQc Hx sao 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 sao cho doan PQ ngin nhdt.. 2.. 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 thanh 2 ph,an c6 t1i s6 th€ tich bAng 2. (DiCm B thu$c ph6n c6 the tich lcm hon),.

<span class='text_page_counter'>(2)</span> 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). +.

<span class='text_page_counter'>(3)</span> 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 - 4 = k(x-l). e (x-lXx' -2x + k -2)= 0 e. [i=l. l*, _2, + k -2= 0 (3). Xet(3)c6A: l+2-k=3'k Th"y-;=lvdo(3)=>k=3 Vflyvoi k < 3 thi (2) c6 3 nghigm. - 2. {Z). ph6n biQt kh6c. l;. 0,25. 0,25. l'. xlx2 <=> (2) c6 3 nghiQm Phdn biQt -> L cilt(C) tai 2 dilmphan biet A(xr;v');I$;a);B(xz;lz). \* xz =2;!t = k(xt-1) - Z;Yz = k(xr-l)-2 ) fr * lz = k(xt * xz -2) - 4 = 4. Viv I li trune <ti€m lcosx * Di0u ki9n:. {. cria AB. 0. 0,25. ^. [cos3r + 0 Phucmg trinh: <+ tan x.tan 3x + 3 = I + tan2 x <+ tan x(tan 3x. -. tan x) + 2 = 0. sin2x +2=0e 2sin2 -:- x +2=0el-cos2x+cos4x+cos2x=0 <)tanx.cos3xcosx cos3xcosx e cos4x - -l <+ 4v = (2k +l)n e t =4** 42. 0,25 0,25. B6i ctri6u itiAu ki€n th6y thoi mdn.. ,rTkr =;+-;. D6p s0: x. Giai b6t phuong trinh:. I+. =2(t). x. Dk: x .FJ1;J7)vax+o. D$ Jz-x'z = t;(/. > o). ft l-.+ I- =2. Taduoc: {x t 'l lxz +t2 =2 Di€u kiqn:. 9'. -l > 0 c+ x > 0. Bpt. elrog,ls' -t,{+)tor, <+. (logr(9' - 1))'. -. =I*log,(e'. 4lo Er(9'-1)+3>0. (9' - 1) > 3 < [log, (9' - l). el ftog,. 1. 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.

<span class='text_page_counter'>(4)</span> 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 2) X. a,25. I. I+ ?-+. Det. t=. OOi. c4n:. '. 24. ax. xl 0 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 trong 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 + 0 tadusc: - (y +,[y\l) = x -'{ ; Nhen. 2vEctn(l)vdi. y-Jfe+0. taducr.c:. \. (1). -(x+. ,!.\l)-y-,tfi. 1. =) X: -y Th6 vdo (2): 23' + x' + (1 + 3x2 )2' +3x22' * x = 2 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 = 0 thi thon m6n (3) Voi x ) 0, x < 0 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 trong (C) =5<R Gqi H la hinh chiiSu cira I tr6n PQ. AI =. 0,25.

<span class='text_page_counter'>(5)</span> www.VNMATH.com c6 PQ=2PH. =2Jm. => PQ nhO nh6t khi 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) 1 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.

<span class='text_page_counter'>(6)</span> 4k_" rrl 7 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 2. Cho d6i ximg nhau €lua x+l t4i hai di0m phdn biet nhau dvd dvir(c",)c6t ,, dC duong th6ngr dudngthing !=x' ta x'e' Ciu II 1. TinhtichPhdn/ = o1,' lG*z)' -, A+B. ar=L. s6t. I#. J-+ .). 2. Nhan dang. Mncbi6t:. J 3. Tinh gioi h4n =lill. *fi{) Ciu. ,. Ban co oa"". )/.. )r-q;;i ,--j *+&'T]t. III trinh: 1. 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 - 4 =o ; ro yl.'^,!i6iolen m[t phing (or) chira ^ di.m cuaAc. Tim to11O "* 'vi6t;;;;;i'ior' hefruc 2. 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' ;;'. 3. 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:';""""""".

<span class='text_page_counter'>(7)</span> 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^$7t). rtFr**_tr,r; q;. i. t^.L. *. Lw+t)u. =. r+,1. €. t ). LtL'+ (rr^+))r +. t+-L. (, nd' t^' )i e ' 'l. I. _ rr_. v. +-tn a) (,t). r i u' ,pb r'1-; fT a' ' i'. \*Lyu. J. h' + Lu+ + rt r 7a. " qT L*,* d ' =. (v) f \er. ,. t4"+-fL. [*'; 'iiPrm A(k.tt yt) ) [t(',v V -). h,te G l{od I, <tt 4. , /\,1, +*. r -. +, I f "; 't. 1q+*u Z. 1* "+t' % = rq<)_ W1 4'ri; ,+g & f g '#f-)'-w -u)=^F+t)'ry -+). L4c*.. }( ry. cz). :U$ ='+4-q' €. m=4. atd.

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<span class='text_page_counter'>(9)</span> (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 ;. 5 ).. ?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 * 1 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. 4 42. (w { +e43 _-, we Lt, kl f-L-. *n, y qbr. ry4. 6.

<span class='text_page_counter'>(10)</span> 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 ; 7 3 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". 6 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.

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