THI TOÁN L1-2011(NGUYỄN TẤT THÀNH HN)

DAI Hoc su PHAIv{ riA NOt nE fm THU DAI HOC z0l0-201r (LAN r) rm/ouc rHpr NGU-yeN rar rliANH b,{oN TOAN'_ KHdI A '-^ ^' ' (lg? phfir, kh1ng ke thai gian pk6t d€i I. pgAN cHUNG cHo r{r cA cAc rHi srNH (T iridm) CAu I. 12 diiim) Cho him sd u = 1.t' - 3 ' + I -22 1. Khio sdt vd v€ dd thi (C) cria hdm s6. 2. Tim hodnh do cdc didm A thuOc (C) dd tidp tuy€h cria dd thi (C) tai A giao v6i (C) tai 3 didm ph0n biet. fr. (2 ilid@ l. Giai phuong trinh : *.r* = 8cosx. 2. Giaib{t phuong trinh: (0,25){-,' > (0,125):(zl'-rl-'} CAu ffi. (I ilidr4 Cho hinh ch6p trl gidc S.ABCD, hai rnit ch6o (SAC) r,i (SBD) cilng vu6ng gdc vdi ddy, ddy ABCD la hinh chfr nhAt c5 AB = o, BC = oJJ, didm I thu6c canh ben SC sao cho sI :2c{ vi th6a man Al l- sc. Hay tf.nh thd tich c'ia khoi chdp dd chc. Cdu IV. (2 ilidm)l. Tim nguy€n him t = [ ]e - J sin 2x + 4sinx 2.Haisdduong;r,ythayd<iith6amSn x+2y-r-v:0,h6ytimgi6trinh6nhatcliabiduthrlc P: ot * !' 4+8y 1+ "r il'PHAN nfSNC {3 didm) Tht sinh cht iluoc ldm mot trongftai phdn Qth,6n A hodc B) A" T'heo chuong trinh Chudn C&u V"a (2 didm) 1. Trong mat phang tga d0 Oxy, cho tam gii{c ABC, bidt toa do didm A(1;-3), phuctng trinh ducnig cao h4 t& B vi trung tuydn qua C ldn iuot ld (d):2x + 5y -21 = A, {d'};2x - 7y +8 =0. Hdy tim tga dQ hai dinh B vi C. 2. Trong khdng gian toa d0 Oxyz, cho tam gir{c ABC v6i A(- 1;l;2), 8(6; l; zl), C(t; l; -1). Hay lQp phucnrg trinh mlt cdu (S) c6 tdm I, bdn kinh bang 3 vi tiep xric v6i mat phing (ABC) tai C. Ddng thbi tinh rhd dch khdi tf dien IABC. CAu VI.a (1 didrnlTm rn dd phudng irinh sau c6 nghiOm .r e [-t; t0] 1+ 1og, {*t + l) - log, (x2 + 4x+ rn) = g - B. Theo chucmg trinh NAng cao CAu V.b (2 di€d 1. Trong mat phang toa dO Oxy, cho tam gidc ABC, bidt duong thing AB, AC ldn luot c6 phuong trinh ld (d): 8x+ 3y +l = 0, {d'): 2x - y-5 =0 vd X};l) ld trung didm cria canh BC. Hdy vidt phuong trinh ducrng thing tsC vd rinh di0n tich tam girdc ABC. 2. Trongkh0nggian toad0oxyz,chomatcdu (s): xt + y'+zt -zx+4y+Zz+2 =0 r'ihai didm A( 2;a;3), ry- 2;a;-1). Hey tim ioa d6 tidp didm M cria mar phing (p) di qua A, B vi riep xric v6i mdt cdu (S). CAu VI.b (ldiim)Giii phucrng rrinh (x+2) logl{-r+l)+ 4{x+i)log.(x+t)-16 = 0 Het Thi sinh khong duo'c sft dung tdi li|u. Ho r,i tcn hoc sinh: Ciu 1: 1. Hoc sinh tU li'rn z. x6t di6m A I 1 Lu';" tii5p tryi5n qua A: d : y: (zo'-eo|r-o)+lon -lo'+l ./\t22 ,l. ' giao di€m gifra (C) vir ti6p tuy6n qua A li nghiQm cia phuong tlinh L*o -3*, *I:Qo' -oo\r-a) *Loo'-3o'*|t*l E6 cho c6 3 giao cli6m thi (*) phii c6 3 nghiQm phdn biQt (*) € G-u)t (*'+ Zax+3*-6F0 (+ t ;;=.' + 2ax +l*- 6 :0 c6 2 nghiQm phdn biet kh6c I L'f(x): a' -(3a'-6) > 0 (+ tf(u):6a2-6*0 c+ I -Ji.o.Ji t aa r^+l I Cflu 2: 1. DK x+t?}tez) 2 (PT) () .6cosx*sinx:8cos2xsinx<>J3"o*t+sinx:8sinr-8sin3-r (} J3"o.o-" : 2sin3x o *io[i-r]:rir3t [3 ) do o<l<t) - -r,'*i) . (c) <+ ,x:L+k,, (kez) (t/m ilk) | -'u*ou 122 2.Dk x2 -2x>*ae ual tBpr)€ (;)'* =[;)"''-'r-') <+ '{IE<zF-rl- THI {) r> 2=2,{r'-2v <2(x-l)- toJ:l -2r.* f x>2 f x<0 (+ r,, -2,<2-3x ." t fii!e_3,I r( -2 (lu6n el""g) + T$p nghi€m 5-(-o;o] ,{2} Cflu 3: ACnBC:0 I (SAC)n (SBD):SO C6 , (SAC)I(ABCD) t +so r(ABCD) (sBD) r-(ABCD) AC:JBA' * BC' :2a * OA :OC:a f t rl \ r ,t F +*l r1 rl .rl -i'-1 :{+ - f; fr ** ,t * DAt SA:h >0 + SC: ___ r_^- ^SOt + oC2 :lht +a' Do SI : 2CI + IC : t.sc: 1 33 AAIC rrrdng tai I * AI: ,{AC' 1C' :! 3 c6 2S5a5A[.SC: SO.AC 4116;:17 3 (+ iu +za2lf -35aa:0€ (t, *1"=\lrt -5ot):g <+ ft: oJ5 ( h>0, t/m h<aJ3s ) Vs^eco:i so.snec*+ ,ns"'-t; pr n<a.€5) CSU 4: l. y:[ 2d'; :[ d- r sin?-r+4sin.r . J sin.r{cos : DAtt:c6x * dt:-sinxdx *I: -[ d' :[ d' r (l-r'?Xr+2) J (r? -tXr+2) /-:1 i A B C LJIaSU_-;= + - + - (r'-l)(r+2) t-l r+l t+2 Ddng nh6t thuc ta duo- c t A: I i ,::+ [ .:-l = 3 :J sinxak -l- ?\ {l:,cos2 x}(cos.r+2) t't'tB :-, - 8+4t- t+4t 5-5 + r:.1 [i|-!l!-*!l d, :! 6J t-l 2r t+l 3r t+2 6 "k - { - 1rr,lr + { +1n la + zl+ c -!hl*.r-tl' I 64"osx'+ { +1lol*r* + zl+ C (x+2y)2 2. Vot x,y )0, d{t e x+2y > 0 Tri gin thii5t: x+2y -2 {} rci*+r>8 (do t > 0) I P: t' *rt: t' *4Y'> 4+8y l+-:r 4+8y 4+4x Deng thric xdy ra € x4; y:2 Vdv minP : E ) 2 A.CT chuf,n 1. Cffu Y.a, ht +a h2 +a2 8+4(x+2y) [r: t * cho. n vtcp 4':(0;1 ;O)*(dX y: I +t(r e [z=-l f, Tt gi6 thitit c5 I e d vd IC:3 + I ::' Ir: -3 X6t F3 <+ I(1;4;-1) * (S): 1x-t;2 +1y+;2 Ir5+ r:-?d\ l(1 ) 1\* fS\' fv-l\ 2+(w+)\ /LVLL -Jt'^\rrk) Ltt -\J 2. B(xs;yu) * {: "ol , D _ lhangdiemAB e(d') lLx"+5t,r-21:0 3. {+ Jr.t*r, -7 3*r', +8=o tBC2;5) lz2 C6 i.nc :4or : (5;-2) > AC : 5x-21:-1 1 :'0., C[n, : 5x- 2-r' - I I : o e c(3;2) f(d'), 2x -7 Y-Y$:g ZJ(6t tludmg theng (d) vu6ng g6c voi (ABC) t?i C ca<-2;0:3) CB:(5;0;5) )lpa,cE1:(0;25;0) v,.or.= 1 IC. seec- | t QIc a; c e|: +( dvtt) Cflu Vf.a. DK: x2+4x*mX) (PT) e5(xt+1;: 12 +4x*m € m:4x2-4x+5 X6t f(x):4x2-4x+5 d€ pt c6 nghiQm xe[-l;10] thi m phii thuQc t+p gi6 tr! cria {x) voi xe[-l;10] f("): 8x-4; f (x):S {) 1:1 Bang biiin thi€n l1 Tt BBT * 4s ms365 B. CT ne.ng cao Cf,u Vb. l.B(xs;ys); C(xc;yc) Ta c6 ft)j +(z+1)?:9 2+(z+l'l2:9 8x" +3_r'o +1=0 2]:. t,c -5:0 xu+x. _ I *{r(-z;s) 2 2 lc1:;t; -lrB +_1'a a 2 = l(l;-3) (d'):2x-7y+$:g B Tdrn I(1;-2;-1), R:2 in eg1 {ce1a.'; <+ [i iu ,r*g diem BC *BC:4x+Jy-17:0 A:ABnAC*{4x., +3r', +l =o L2*.0-r'.r-5=0 M le ti6p di€m gifra (P) r'd (S) lw.u:a [{*-r)t 2)+(-r, +2)t;+(z+l)(z-3):g ) ]w.aE -o <> {-+(*-t)-a(z+t):s [rn.1s) [fr-rl, +(_i,+ z\2 +(z+t)? :4 laa(t;o;-i) *l'(;'#,*) Cffu Vf.b. DK: x> -l *80 81 -2 t: 5y-21:0 d(A;BC) :#; BC:J+I * Soec:l4 (dvdt) 2, (S): (x-l)2+(y+2)2 +12+1)' 4 EAt {'::*t. , + (u + l). u'+ 4,rro -16:0 {+ (v+4)[(u+1)v-4] :0 ' [u:logr(x+t) - \- v*4:0 s log(x+l):-4 o *:-#(ft dk) (u + 1).v - 4-0 (} v (3"+ 1)==4 OE tfr6y VT la him il0ng bi6n vi cd v:l ld nghiCm * nghi€m duy nh6t v:l {+ log (x + 1) : 1 C) x:2 vay . 1.t' - 3 ' + I -22 1. Khio sdt vd v€ dd thi (C) cria hdm s6. 2. Tim hodnh do cdc didm A thuOc (C) dd tidp tuy€h cria dd thi (C) tai A giao v6i (C) tai 3 didm ph0n. bidt duong thing AB, AC ldn luot c6 phuong trinh ld (d): 8x+ 3y +l = 0, {d'): 2x - y-5 =0 vd X};l) ld trung didm cria canh BC. Hdy vidt phuong trinh ducrng thing tsC. f(x):4x2-4x+5 d€ pt c6 nghiQm xe[-l;10] thi m phii thuQc t+p gi6 tr! cria {x) voi xe[-l;10] f("): 8x-4; f (x):S {) 1:1 Bang biiin thi n l1 Tt BBT * 4s ms365 B. CT ne.ng