6 đề thi thử Đh- hà nội-2011

DE THI TRU,ONG EHSP HA NOI rnu DAI HQC t AN I Narr ZOrt Mdn thi : TOAN TRTIONG THPT CUUVNTV - EHSP Thdi gian tdm bdi : IB0 phtit, kh6ng ke thdi gian phdt di Ciu ( 2,0 dilm ) Cho hAm I s6 y: 32 - 1**' + (*2 -3)x, m littham s6 Irt I(hAo s6t sg bi€n thiOn vi v€ d6 thi cta hdm s6 z = l Tim t6t cd cdc gi6 tr! oba m ae ham s6 c6 cuc d4i t4i x6p, c!.rc ti6u t4i xcr ddng thd'i xss, rcr lh dO diri cdrc canh g6c vudng cira mQt tam giirc vudng c6 dQ ddi c4nh huy€n birg F "{2 Cdu (2,0 diem) x2 Giii phuong trinh : : Gidi phuo-ng trinh -l z+^[s-x, +12-.,[s-*,1 sinal3x*|l * sinal3x -?=: CAu ( 2,0 di1m ) Tim nguyOn hdm cria hdm sO f1x; : tanx.tan(x + ];.tan1x 3" - l; 3', Tim c6c gi6 tri cta m d6 phuong trinh sau c6 nghiQm nh6t : g-lz-xl _ 43-|2-xl= p Ciu ( 1,0 didm, Cho, hinh ch6p ,tt6 tu gi6c ttdu S ABCD mdt b€n v6'i mdt d6y vi UU ddi canh ddy bing a, cgnh b6n bing t' '2 ttnn goc tao boi the tictr t0 s Eripsd =+ : t:9(dot>0) xell;f,1 0,25 4,25 0,50 lf [*i d(rnVTTF) lr"j#*=#r"z*1rrfra* d1 = - 1ntr1-52 0,50 Tas€tinh ,=Jrvt;;hox, d{t x=tant =+dt=fta,=(l t:l * Vdi x= I thi,=1,'*=y'3thi n tlT l=1f,at=,li 4raLL +tan2t)dt =* 0.50 tt=f-21n2+4 2J3 L2- E6ps6 ' o (0,50 diA@.Dr,rng thitit diQn c0a m{t phing di qua A, M vA song song v6i BD Gqi O=AC o BD, O'=A'C' n B,D' vd I=AM nOO' eual k€tluongthEngsong song v6i BD c8t BB', vd DD' lan lugr t4i K, N Khi d6 AKMN la tni6t diQn cAn dgng DAt Vr = , Ve.scrrx-f Va.oo"rN V2 = Vnaco.e,a'c,o'- Vr ff=#: I + DN=BK=Ot=;a"=; -^-^ ? c(0,50i1i6@.Tac6 oI AO Hinh ch6p A.BCMK c6 chi,iu cao AB = li I tl6y ld hinh thang BCMK U Q iIiAm) ^ Ot BC(BK+CM) -T =; Suy Ve.ecrpr = -AB.Ssgy* Ir0 a3 =i Hinh ch6p A.CDNM c6 chidu cao ld AD = B' a d6y lA hinh thang CDNM =T suyraveco*u=lRo.s"o"n 33t26 V6y, V, l V a3 =:r33Vz = a-, , cD(NP+cM) ={ _za3 a3 Q,0 ilidm) K B '1 Tirgiethi6tsuy la-blSB- s.aZ +(a-b)t< 4=r(a+b)2-4ab< 0,50 Q iliAm) Suy a* b< zr/ffi, tuongtgta cfing c6 : b + c S 2rlIEEE, a* c Docl6: a+b+c S VrT?E +Vr+:Ec+rma (1,0 iliiim) Tinh diQn tich tain gi6c - Duong tlrdng BC c6 vecto chi phuong il =(l; l) Phuongtrinh cta Bc : il (2 VI itiim) ' tu, [; : I ll [; : r*-?' Tac6: BC=fr Eudng thing BC viiit ve d4ng tdng qu6t Gei AH Vay Ii duong cao, ta c6 AH = Sasc = t9 IAH.BC= -# 0,r0 ld vecto ph6p t ph6ttirB n€ntgaclOthdamdnphuongtrinh:2(l ruong t6 phuong trinh AC szlffi (dpcm) : B(l+t ; 2+t) B thuQcduongcao xu6t +t)-2-t+ l=0=rt=- 0,50 L Vgy B(0; l) vd A(- 5; 5) x - y+ = # -0 0,50 \ ) Tim tqa d0 tdm vd b6n kinh IQ;- \8 I(hoangcrich.tir1-di5nmp(P)ldh=w=l o [x =O Ta c6 : /'(t) = 6xz -2x =2xQx-l)= r o I- -1 L'=J *- JjL(r'' -"')= Bang biiSn thi6n : T € ,f'(r) f(') cit f(r)=2xt -x' t4iilirng mQt diOm nh6t' (l) lu6n c6 nghiQm nhitkhi a * ' =a He phuong trinh r ao thihim sd T{l, T'R{IffiG TE#T s}ao puv ,/ pm s's{x rmalo4r noc HA NOI x,AN rm, nndlol : Todn, xAla F{EC 2010 - 20Il m6i a Thdi gian ldm bdi : 180 phrit ( kh6ng te tn}i gian phdt d0 ) tsAi t (2 di}m) Cho hdm s0 ! = x3 +3x2 -mx+2 c6 AO mi (C*) 1" Kh6o sdt vd ve dd thi hdm s6 vdi m:0 ' Timm'd}hdm s6 c6 cgc d4i, cgc ti6u cho khoing-crlch tu trung di€m do4n thdng n,5i hai di6m cuc hoinh Eei elQ It ( diCm ) Giai c6c phucrng trinh, hQ phucrng trinh sau 4sin2x-cotx= 2losr(3x+5)+logo(lx+l)8 : fry-3xi, +y'-2x-4y+3=0 l*" 2y+6:A , Jj Bii III ( I diem ) Tim P(x)= Bni tri cria (C*) d6n tiiSp tuytin cria (C-) tai cii€m c6 bing le lorr nhdt L r' cfa - sd hang = 4logr(l2x+8) khdng chfta x khai triiSn nhi thric Newton cria (r*r-+l' \ r-l Iv ( di€m ) Trong m{t phing vdi hQ,fa dQ O*y , cho du}ng thing d : 3x - 4y +2011 = 0, vd duong trdn (C) : ,' + y' -6x -2y+1= ViCt phucrng trinh dudrng thing A song song v6i d vd cft (C) theo mQt dAy cung c5 dQ dni bing ChotudiQnABCD c6AB :a,AC- Za,AD= 3a vit A)C =C)n:fAn=600 Tinh th6 tfch tri di6n ABCD Trong kh6ng gian v6i hQ tga dQ Oxyz,cho m{t phing (P) : r+ 2yduong thing a c6ch tir tsni V" ' :4 * 2t-1 = + "-4 :0 duon vd Tim ditim M tr€n tnp oz cho cdc khodng M d6n m{t phAng (P) vd tludmg thdng d bing ( i diem ) Cho c6c sd thuc g a,b"c th6a m6n a+b +c =3 Chring minh ring : G.trh-b+c a6.111-rao +r.l,h-o+b.3 - Gi6m thi coi thi kh6ng gi6i thfch gi th6m TT{.['ONG TEXPT DAO DUY TTI &AF Ar{ - TETANG s[6M Tr{r rrurl DAr Hec rAN rrr (0e/01 /zstt'} nAdN : To:in, fniii.q, Bni/y Bii NQi dung cho tli6m Di6m 1.00 ! = x3 +3x2 +2 * TQp x6c dinh: D:R + SU bii5n thi6n: + Tac6: 0.25 !'=3xz +6x=3x(x+2) u':Q 4+ - [x=0 lx =-2 I Bang bi€n thi6n: 0.5 DO thi: A 'l -l i I "lI s.zs ! = x3 +3x2 -mx +2 + Ta c6: y'=3x'+6x-m + H?rm s0 c6 cpc d4i, cgc tiOu vd chi phuong frinh: y': 3x2 + 6x - m=0 i C6 hai nghiQm ph0n biQte A'= +3m> e m> -3(*) s5 dat cuc td tal 4, xr.Tac6 : y'(x,) = y'(xr) @ A li 0+1=i + (nt-9)' + nhO nh6t bdng d4t dugc m -9 = e 4.25 d l6n nh6t + Vfly 0.25 +3 = m= (thda man (*)) m:9 I BNiIVI Pr-3x-2Y+6=o [rt * y'-2x-4y+3=o €) Fr-3x-2Y+6=0 [ir-t)' +(y-2)' =2 + D{t fu=x-! HK: AK tan3Oo: _._:a- VJ 22 6 - 8i,, E :> BH : JEK' - I{K' = al - = a,i- * ::"8.+ 2a.3a.sin6o') veecn : \an a,acD V+ T2 VT ="'{t M eOz =M(0,0,t) + Dudng thang d di qua di6m A(1,0 ,-2) vitc6 vecto chi phuong i, = q2;,-11 0.25 l- l +Tac6 : AM =(-1,0,1 +2)fu,AMl=(t+2,-2t-3,1) + Khoang c6ch tu M d6n mpt pheng e) li ''*al d, = d(M,(P)): lI J6 0"5 + Khodng cdch tu M tt0n ctudrng th5ng d ld tk' t_ ' *2 = _Y.',_ d, _ d(M,a1=t' ,1Yl l;l d, = d =^[*t:'** J6 r4:- e I +l6t +1a =lt + al ^l5f I I e2t2 +4t-1=0 I I ! i t_ -z+J6 ^l vt I I ! I l,_-z-Je lr:- L2 0.2s A | I I I I I I I I I I + Vty c6 hai di€m th6a mdn dO bAi ld : M1 I -2-J6 Mz (0,0,&=) *,[',',=*) o.o.& -2 BAi V I ! I i.8s Ap i+ne U6t Oang thric Cauchy cho ba sti kh6ng 6m ta c6 a.-.[r.(:r + c) = < o.t - 2*' J (1) - 3-c+a b-_ a (2) U-5U -1 c i[.r{ : -a + [) = r.' - 1.*' (3) \ + Tir (1), (2), (3) suy ra: *{-1-b+c a6.{1- as +c.{l-a+b =o.3-2*t *b-3-'^*o 333 | - b + c + t.{t - t + o * ".{1 - o'16 0.25 a + b + c =3 OA=b=C=1 *''t-1*u 0.25 \ rci rHr rnrl DAr Heqr,AN rHrI NnAl TRUONG THPT CHUYfi,N NGUYEN HUE xAnn Hec 2010-_ DE THI MON: TOAN zltt xlr6t.L,n Thoi gian ldm bii: 180 phirt, kh6ng kC thoi gian giao d6 Cffu I: (2,0 itiAm) Cho him sd ! = x3 -3(nt+1)x2 +9x-m,vti m ldtharnsd thgc l Kh6o s6t sy bi6n thi6n vh vE OO ttri cria hdm sti ea cho ring v6i m =1 XAc dinh m ee fram sO ea cho d4t cuc tri t4i xr,x2 cho la -*rl:2 Cflu II: (2,0 iti6m) l Gi6i phucrng trinh: + cos x + cos 2x Giai he phuong trinh: - 2cos 3x = 4sin x.sin 2x " "' jlxt +2x+y'+y:3-xy (x,y€R) ^ l*y+*+Zy-1 cf,uIII: (1,0ili0m) r\m J -ff-;d sinx.sinl x+: \ I 4) Cf,u IV: (1,0 ili6m) Cho l6ng tru tam gi6c ABC.ATBTCT c6 tdt ch cdc canh bang a, g6c tao b&i canh b€n vi mdt phing d6y bang 300 Hinh chidu H cfra didm A tr€n mat phftng (ArBrCr) rhuoc doong thing B,C, Tfnh thd tfch khdi ldng tru ABC.ATBTC, vi tinh khoang cdchgifa hai dudng thing AA, vi B,C, theo a Cffu V: (1,0 ifiAm)X6t chc sd thgc ducrng a,b, c thoa mdn di€u kiQn a+b+c=1 Tim gie d nh6 nh6t cria ":m : -? Cflu VI (2,0 iiidm) Trong mat phing vdi hI ' tga ttQ Oxy cho hai dudng trdn : (C1): x2 + ,:13 vd (C2): (x: 6)'+ t' ,: ZS cit tqi A(2;3) phuong trinh ducrng thdng ili qua A vi 16n lugt cdt (Cr), (Cz) theo hai ddy cung phAn biQt Vi6t c6 elQ dii blng Trong kh6ng gian v6i h0 tqa d6 Oxyz cho tam gi6c vu6ng c0n ABC c6 BA BC Bi6t A(5 ; ; - 1), C (2 ; ; - 0vd B ld ditim nim tr6n m{t phing c6 phuong trinh : x+ y - z -6 :0 Tim tga c10 tli€m B Cflu VII (1,0 iti6m) Gi6i phucmg trinh : hQ f : (z - tog, x)logn,, -;ft; =t utlt -Thi sinh kh6ng duqc s* d4ng tdi li€u Cdn bQ coi thi kh6ng gidi th{ch gi thent rnr rnrt DAr Hec r,AN NAnnFAC 2a!o - 2ott EE THI MON: TOAN KIIOI A, B IIrtoNG uAx cHAvr TRIIONG THPT cnuvnN NCUYNN HUE CAU rntl unAr N( )I DT]NG Ydi m= ta cd y = xt * Tflp xdc dinh: D = R D -6x' +9x-1 x Su bidn thiOn Chidu-bidn thi€n: Tac6 !'=3x2 -l2x+9:3(x2 -4x+3) [x>3 _y'>0