4'- TRUoNG rHPr LE xoev Ot 1'fff 1'fftl DAI HOC - f,AN fff Nim hec z0t0-z0n MU*, ,oU*rlio\rfrort f::ryNurEN Cf,u 1: Cho him s6 y = -r' + 3x2 -4. (l) 1. Khio s6t sU bii5n thi€n vi v€ <16 thi (C) cua him sO (t). 2. 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. Ciu2z l. Giaiphuongtrinh: tanx.tan3x a3=-2 - . I + cos2x 2. Giii phuong trinh: !* * =2. x ,12-x' 3 . 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$c ph6n c6 the tich lcm hon), L oApAN + of rm rrffDAr HQc- r,AN ur rnrOr* itoii sAI'{ KiroA' HQc rV NrrrSN !=-x3 +3xz -4 TXD: R C6c gioi h4n: limy @;limY=+o '#6- J-+4 Xdt sg bi€n thi€n: Y'=-3xz +6x [x=0 ./'=0el*=Z Hdm s6 idng Ui6n tren (0; 2) vd nghich bi6n tren (-*; 0) vi (2; +o) \,/'\ Dths cit oy @l!lL tat 9X 0,25 0,25 qua I vdiTalild6c k:> Pt A: Y : k(x - 1) -2 Gqi A li tlulng th6ng qua I v0i he so goc l(:> pt a: y: K(x - r, - z phuong trinh hoinh <tQ giao iti€m cira (C) ve A: - xl + 3r2 - 4 = k(x-l) - 2. {Z) [i=l e (x-lXx' -2x + k -2)= 0 e l*, _2, + k -2= 0 (3) Xet(3)c6A: l+2-k=3'k Th"y-;=lvdo(3)=>k=3 Vflyvoi k < 3 thi (2) c6 3 nghigm ph6n biQt kh6c l' <=> (2) c6 3 nghiQm Phdn biQt l; xlx2 -> L cilt(C) tai 2 dilmphan biet A(xr;v');I$;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 cria AB. t.2 1.I 0,25 0,25 0,25 - lcosx * 0 Di0u ki9n: { ^ [cos3r + 0 Phucmg trinh: <+ tan x.tan 3x + 3 = I + tan2 x <+ tan x(tan 3x - tan x) + 2 = 0 sin2x 2sin2 <)tanx +2=0e -:- x +2=0el-cos2x+cos4x+cos2x=0 cos3xcosx cos3xcosx e cos4x - -l <+ 4v = (2k +l)n e t =4** 42 B6i ctri6u itiAu ki€n th6y thoi mdn. ,rTkr D6p s0: x =;+-; Giai b6t phuong trinh: I + x =2(t) Dk: x .FJ1;J7)vax+o D$ Jz-x'z = t;(/ > o) ft I l + - =2 Taduoc: { x t 'l lxz +t2 =2 0,25 0.25 <+ (logr(9' - 1))' - 4lo ftog, (9' - 1) > 3 el [log, (9' - l) < 1 [g'-r>8 [g'>g ol <+l le' -t<z L9' '3 DS : x e(0;/riv[;+o) Di€u kiqn: 9' -l > 0 c+ x > 0 Bpt elrog,ls' -t,{+)tor, ? =I*log,(e' -r)'[og,(e' -r) -tog, 16l> -3 Er(9'-1)+3>0 m 1.1 2tr 2"- [ /= J".G-;.ar= fisin tX tX X X ' - + cos' - + zsln-cos dr 2222 Det t= I+ ?-+ ax =2dt ' 24 OOi c4n: xl 0 I 2n t I rll4l 5ft/4 *:M'o;<;.? - r2 - x x\ srn-+cos- I 2 2) [l,intlat i'!r^0.) 5r/ /4 I =2J7 [lti"tlat =z % = rJt(- cos 4:/ * "o' tl'/') = 4Jl a,25 0,25 0,25 0,25 IV 1it 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- =2R+2p= r?o, = + R= all sinlSC Sin45" V$y mat cdu ngo4i tii5p S. ABCD c6 ban kinh: R= ali. \l l\ \ \ \ 4,25 0,25 0,25 0,25 c.5 1d ^,2;1.^. [(r*Jr'*rX y*.{y+ *t1=t (1) ulal ne: { Lz" yt + (1 +3xz)23.+3x.22' - f =2 Q) Nhan 2v6, cia(l) voi * *J *' *t + 0 tadusc: - (y +,[y\l) = x -'{ ; 1 Nhen 2vEctn(l)vdi y-Jfe+0 taducr.c: -(x+ ,!.\l)-y-,tfi =) X: -y Th6 vdo (2): 23' + x' + (1 + 3x2 )2' +3x22' * x = 2 e23' +3x.22'+3x22' +x'+ 2" +x=2 o(z'*r|*Q'**)-z=o D{t r = 2' +x. Ta c6: t3+t-2=0et=l Ydy 2'rx = I e2' =1 r (3) Vsi x = 0 thi thon m6n (3) Voi x ) 0, x < 0 dAu kh6ng thoimdn (3) (vi I vii > 1, I vi5 < l) VAv nehi€m cria h€ (0: 0) 0,25 0,25 0,25 0,25 c6.1 (C) c6 tam I(2; -3); ban kinh R=7 AI = Jre = 5 < R :) A nim trong (C) Gqi H la hinh chiiSu cira I tr6n PQ 0,25 c6 PQ=2PH =2Jm => PQ nhO nh6t khi IH ton nfr6t Khi dri: H trung voi A => A qua A(.2; 0) vd nhfn frg;_Z) lim rapr ViY A c6 pt: 4(x + 2) - 3y:0 Hay 4x - 3y + g :0 0,25 4,25 0,25 Gii sri (o) h mp can tim. (o) Vnor, -" ^ 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) , n cirng phuong vor ir= (-3; 5; 0) Mp (OAM) qua O vd nh6n i, ta- v6cto ph6p tuyi5n. => pt (OAM) ld: -3x * 5y = g. 0,25 0,25 0,25 C\/ a- tl \rnr-roNc THPT r'fl xoaY ^^- NA- hgc 2010-2011 dudngthing !=x' Ciu II 4k_" Dt rrrr rHU DAr Hgg;l'AN rrl 7 Ban co oa"" t' n'roo inii 1oful Thdi gian ldm bdi ttti pntii'r'0"erc thdi gian giaod€ Ciuf. i. fnao s6t vdvd dd thi him sO *t +(m+Z)x-m co 2. Cho ! = x3 -6xz +9x ' AO tfri (c')vd duong tnAng d"v=-x'4'lfim €lua ,, dC duong th6ng dvd x+l r dvir(c",)c6t nhau t4i hai di0m phdn biet d6i ximg nhau ar=L ta x'e' J-+ .) {) *fi 1. TinhtichPhdn/ = I# lG*z)' 2. Nhan dang o1,' -, A+B Mncbi6t: atan A + b tan B = lo + b)tan:l- *[i]-@ 3. Tinh gioi h4n J =lill Ciu III 1. Giai Phuong trinh: x-1 (.F *r)' *: i(r-'l , )/. )r-q;;i , j *+&'T]t z.chohQphuonu, {f7: F=o . Tim ,, eC hQ dd cho c6 nghiQmthgc' "uotl. rrong hg truc rou uo.rrryIlS?.* #:r. Dubng thrngBcc6 phuong trinhr- v - 4 =o ; dinh/gr6m.tr€n dudng thdngx+zv -3 =o'Di0mM(z;o) le trung di.m cua Ac. Tim to11O "* i* ro ^ yl.'^,!i6iolen tigh c11n6 bhne 2' 2. rrong mflt phing hefruc ;il' ;;' 'vi6t;;;;;i'ior' m[t phing (or) chira trvc oxvd t4o vdi m{t nr'a"e Wi tu o*1"9 :*n -f" * v +22 = am6t g6c oo0 ' 3. Cho ttl di€.n lncp|rJno*9:* eiui z.a;,yg thang AB,CDbhng d, g6c gifra chirngb6nga'blftts=o'ci=l'ir"rtth€tichtirdiQnABCD' HCt Hs vdt€n thi sinh: """"""""':"": """""'SO b6o danh:';""""""" A;;O;;i thi khong gi6i thich gi th€m' iy*: fri l{'a cs K*{ t) ?6^?, +Ulr ' ryn D=R _p fu'vt"ut = j rc I ,tt-ll rc 7, , 5t>- lLt<+3 ,!'=u e) f :;3, B{;t ws i9 t";+ .( -*, 4) ) K> rrrg la l+tt Re dd u) +,. 1t, +); . fu-W' h"q'fr 1^$7t) (, u4, a ,14 (s,c) i rtFr** r; q; t^.L * Lw+t)u _tr, = _ rr_ v r+,1 € t LtL'+ (rr^+))r + +-tn a) (,t) ) t+-L r i r , , (, nd' t^' )i I ,pb r'1-; fT a' u' ' i' f I "; + 't e 'l \*Lyu (v) f t4"+-fL ' J " = h' + Lu+ + rt r 7a \er [*'; 'iiPrm qT L*,* d ' A(k.tt yt) ) [t(',v V -) h,te G l{od I, <tt 4 1q+*u Z , /\,1, +* L4c*. 1* "+t' % = rq<)_ W1 4'ri; ,+g & f g '#f }( ry )'-w -u)=^F+t)'ry -+) cz) :U$ ='+4-q' € m=4 +oo+ t2+ \r.u ,/. ArJ atd -t 4 oLu= r e-(( ,L+L) , \/= -J- x_+L 14 zri + Jr, rL Q- clL- ' In - lun uHu Zl t1 .Q- I tD Lk_ Ll= lt L =&__ (+e)' I = -_tc'aL ln u+) lL' _0 = ; tLt b 3 = a- +Q- t $ olr** * Afu^g : q{ +b1 lr.^ N /-" ew A t^'4 + 9r' *$to*$ = (9,n A+e;ng ) ta'-& t4 #;! "!,, L+A : )-9 J 4 e 9* A -9i,-U L gal - q^ B! __________J+ >o coa| . A,,. a-4 /> + hreA "C4^ ry @- t- lau'81 9", i- l^^n = h*g I L 9.u 4 -t9 , L *\cr* i") t*A 7 2- -"V *'rl ; 4Cul =o = ,!,-* l tq -+(" ryzD l-" (-L) g) =4L2 I a6- 02lrf o> 4^ It+ 4 7L, lr'- rI 3w'u L\4 A 1t^, (hn -t, TW. t)rk / '?, e) (ry'\ t(ry)"=n 94 Wl' (tro1 Fr!.d-y fr k =) \, t+ l'- t+f +4 ''o =c \2ju) L'd e t '4- lVt) € (ry/^- L I ?L = 4.,&, Lr' w ) TX\D ; 5 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? * l- W V .P"- {\, cui 'fr Y $" l,a J /v +L f @ /*"t ,tv 47ro Uv2 o +12. 4 42 (w { +- we Lt, kl L. QX* Lt -, t, ca) f 'ab- q4 qu{ e43 _ , ry4 6 f-L- *n, y qbr c6'N.*:; uk ro ct* Ac' + A('u' oQ =!dt+c'2 Jl' A(b-At t) l Jco ?ti 3 vc) =- t dttult)Y gbtrl= V" ; t=4 ?) 7 A=? rt) L u=-s/s r-AIE,i) e u.o; A (1,,t7 /+(\ t e . (-f ,I) 9,\a4. - ,l t*, B c) " l,c- = f*: oo cr.,- AC' ud, cft5r-a| d*e w 7, &t' t\.I *+z o i' g* )a,'rr- tt -+ =u (14; ) <") l) t =- 'l t ' Lt (t+)t= L,a 4, h( Lr t-+)'' ;* Bc'=L 'a 1t- b) 'vca\cl >"b oirYb'' n?:: tt:;-l'^ri ,!rY:j, b= ++B(+,0/ L t=L ] W-L/ fr!rr, 8,Y rct=rt vrI il^ = (0, 9,1 t *ho' ,d ry tvt W'"f" a 6 g" + lc 0c- - k' o - ar ,^f bv X* ir- [ ,!'rrtzo ,4 + )bzo (,9)'r/6 ! -6 z'a J'L =1t"clt^- 8-1V'c=4 LZ.Z u? e*4 C'-, . -y Th6 vdo (2) : 23 ' + x' + (1 + 3x2 )2& apos; +3x 22& apos; * x = 2 e23' +3x .22 '+3x 22& apos; +x'+ 2& quot; +x =2 o(z'*r|*Q'**)-z=o D{t r = 2& apos; +x -3 Er(9'-1)+3>0 m 1.1 2tr 2& quot;- [ /= J".G-;.ar= fisin tX tX X X ' - + cos' - + zsln-cos dr 22 22 Det t= I+ ?-+ ax =2dt ' 24 OOi c4n: xl 0 I 2n t I rll4l 5ft/4 *:M'o;<;.? -. AB. t .2 1.I 0 ,25 0 ,25 0 ,25 - lcosx * 0 Di0u ki9n: { ^ [cos3r + 0 Phucmg trinh: <+ tan x.tan 3x + 3 = I + tan2 x <+ tan x(tan 3x - tan x) + 2 = 0 sin2x 2sin2 <)tanx