TRUO]\G THPT I,N XOAY Ky thi khf,o srlt hi zOfi DE THI KHAO SAT LOP 12 M6n rhi: TOAN, Khtii A, AII Thdi gian ldm bdi i80 phut, khdng kd thoi gian t giao dd Cffu l. (2 di€rn) Cho lidrn s6 y =.Flf .t " 2(x+i)' r 1. Kh6o s6t vlr v€ dO thi ham sO 1c; 2. Tinr nhii'ng di6rn M trOn (C) sao cho titlp tuydn vcii (Cl) t4i M tao r,6'i hai truc toa c10 mdt tam gi6c c6 trong t0m nim tr6n duong thing 4x* y =' 0. Cf,u II. (3 di6m) 1. Giai phuong trinh 2. ciei h€ phuong trinh {y;,=\li::l (,'/ € R) x-3iV5-r3, 3. Tinh gi6i han: .I = lim x-1 Cf,u III. (2 di6m) Trong mpt phdng tga dQ Oxy cho tarn gi6c AI|C co dinh e(z;3), trong lAm C(0;2)vd irai dinh B,C lAn luot trdn hai dudng thing cl,:x +J/ + 5 = 0 vA ^ m\ I 1^ l d, :x+2y -7 = 0. Tim toa dQ t4rc tAm cua tam grdc ABC . CAu IV. (2 diern) Cho hinh chop S.ABCD c6 driy ABCD ld hinh vuOng cqrnh 2a. Cdc di6m M,N.P,]thv tu nim tr€n c6o canh AB.B(, D4,SCsao cho: AM =2M8, AP =2PD, 1VB = NC,4Sg= SC. Cho s,< vudng g6c vcii mflt phi$g c16y vii goc gifra hai mflt phing (.sBC) vd (ABCD)bing 600. t 1. Tinh di6n tich tam gi6c MNpvit khoAng c6ch tri di6m Qd6n mpt phdng (uw) 2. Tinh dg ddi dopn vuong goc chung ctsa MP vd sc. Cfiu V. (l di0m) * Cho c6c sO thqc duong x,!.2 thoa mdn diiiu ki€nt x+21t*; = 5. 'I'irn gi6 tri nhr) nh6t cua bieu thuc, -4x+2y+z *r-y -' 2xy+xz 4 FIp vd t6n thi sinh: : , ,. , , ,.S0 C6n bO coi thi kh6ng giai thich gi thdm. http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay rRU'oNG rHpr LE xoAy pAp AN - THANG DIfM Of t'ru KHAO SAl IAX t r 'l ',' - ':rr l- " ':''l'' t "' , i,:t :1tt*15 . Luu f : -Ddp dn g6m 04 trang ' ', ' ':'',1 ;'t;:,.|,r: ' -Hpi sinh-tdm il)ng thio cdch khdc'vdn cho didm tiit da. ' : : 1"'; Ciu Y Ndi duns trinh birv Di6m T 1 2 gh6 hirrr s6 r,= ,,II|(C). rcnao sdt vd ve dd th! hdrn sO(C) ' 2(x+l)' / 1.0 TXD: D = R\{*1} I chi€ubii5nthion: / =dD, >o,voi Vxe D =hdrn stl dong bi6n tr€n rnSi khodng :(-m;-l) vd (-l;+"o) Cqe tri: hdm s6 khdng c6 cpc tri Gi6'i h4n, ti0rn cdn : ,. I 1 linty=7, lim y=- ; lim y=-e , Iim !=+q .(+M / x+-a / x+(-l)' r+(-l)- I .^ ^ = y = - ld ti€nr cdn ngang; x = -l ld tiQm cQn ctfng '2 BAng bi6n thi€n: lrl ., I A*ll / l "l ,/-ll / L/ ll / l,/ ll,/ l" II',-* 7 l? DO thi: di qua c6c di€m (0; - Z I : GZ; i) ,l Nh{n,giao di6n crha hai tiqm c&n ICl; i) ldm tAm cl6i xfng I I I' It / llr ______; tl | , ll 'lv tA l,r 0.2s 0.25 0.25 0.25 ,'firn nhfing di€m M t'r€n (C) sao cho fiOp.tupi€n v6i (C) tgi M tpo vd'i hai trr,rc tpa d0 mOt tam gi6c c6 trgng'tAt: nirn trdn dub'ng thang 4x + y = 6. * _l Gsi M(x";4 ) e (C) li di€rn cAn tirn 2(xo + l) ' Cqi A titlp tuy6n v6-i (C) t4iM ta c6 phuong trinh 0.25 http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay L: y = "f'Go)6-ro) + =lu -t,. ) | =t-f (x x^)+ ro -l ' 2(xn+l)' ' (xn + l)' t* *o' ' 21xo+11 coi A: Anox:)a1-r" -Zxt-t ;0) B: Anoy= ufo, {-)v -7 ' 2 )-)- 'zffil Ifti d6 At4o v6'i hai trpc toa dQ AOAB c6 trgng tdm ld: ^,( xl -zxo- I *ot - 2xo - 1) \irr ""_r. '1. 6 ' 6(xo +1)' ) :4x + Y = 0=) -O'4 -z:'-t* "i, tt',;t = Ol)o Ge dtrdng thing o o(.ro + r)- .t .3 4 = . tr (vi A, B *O ndn xo2 -Zxo-1*0) (.r, + l)- Voi xo =-)-uel;-|) ;v6i *o=-1-ueltll trt-t | *o *l=t I *o =-t el - <>l I I I .3 jxo+l= lr'= L z L'o z 0.25 4.25 0.25 II I GiAi phuong trinh s (1) =O'i"(;.") "(+-z')+z 1.0 / -\ Ddr rr=|**L lo"= r,-4,dodo: i, 6) 6' a / -\ (r) <> ,lsinl lL-2u+il*z = Dsin u o Jt;nz, +z = Jisinu \/ \3 3) (sinrr>o fsinr>o lfsina>o '- t: i ;'),i i r= 2 si n 2', o {i'r'i n r'.1r,, + 2 cos2 a = 0 € L}!:'r'= -l + Voi coszr = 0 e sin u =!l= sin u =1 e " =t,* kLn e, =!+ k2r,k e Z + V6i tatlu = -7 e u = -L + ktrk6thoo v6'i 4" sinu > 0= u = -L+Qt +t\, =?o +l2r a *=7o +l,n.l e z -4\'/4 12 Vdy PT co hai ho nghi€rn: *=!+k\n,keZvit x=?+l2n,l eZ 0.25 0.25 0.25 0.25 7 (x,y e R) Giai lrQ phuong trinn Jx{ = x +7 Y^+1 l"tYt =loYz -1 (1) (2) 1.0 riL (r)r f, = U+(do y = tttri (l)v6 nghi€rn), thay vdo \ / y-l "f7u*t)' (z) + ),tl *!+l = t0/' -t e y' (7 y+r)' =(roy, -r)(y-i)' '\Y-t) <* 39;,0 + 34rr3 *By' -2y.+l =o e (.v+l)(:y+t) =(tly'? *6y+t) = o Iv=*l:?x=3 * I ; = -i:; =, . vay hQ c6 hQ c6 trai nghidm: (";y)= (:;-t), (t'-i) 3-" 0.2s 0.25 0,25 0.25 3 x -3 + i.6.3t Tinh gi6'ihan: 1= lim - r+l x-l 1.0 http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay rl; 5 f _- 4 0.2s 0.25' ' :' 0.25 0.25 TII Trong m{t phing tga dQ Oxy cho tam gi6c hai dinh B,C lAn lugt tr6n hai tluo'ng thing tqa d0 trtlc ttn cila lam giitc ABC . ABC c6 dinh A(Zfi)treng ta; c(OJ+,d dr:x+y+5=0 vit dr:x+2y*7=0. Tim 2.0 t Xet B(h;-1, -5) e d,. C (t -Zc;c)e d". Theo cdng tlrrl'c trong r6m ta c6: i2+b-7-2c=3.0 lb-2c=-g Ib=l {e{e{ 1.3-r-5+c=3.2 lc-b=8 lc=-7 Do cto 3 =(-7;Z), C = (S;t) Cgi /1(r";"yr)ld trpc tdrn cira tam gi6c ABC .Taco ';7, = (* o * 2; yo - r,';'rt = (ro + 7 ; I o z),W = ( t z; - r),'ib = 1z; - z1 "l'iL tinh ch6t truc tdm r LlLnt Ll"I'l t , = I!r# trn: : * tlif *;l';[ -']) =i * I',1; - i;,==',',-('. ; v. ) =8 4) vi' rrLrc t.t,' H(6J'i&.1 ' (21'7 ) 0.2s 0.25 0.25 0.25 0.2-s 0.25 0.25 0.25 cho hinh clrop S.ABCD co d6y AIICD ld hinh vudng canh 2o. c6c di6m A'{,N,P,Othil ttt' nim tr0n circ c4nh AB,BC,DA,SCsao cho: .41'{ = 2ll47, .4P = ZPD, NB = NC, 4,\Q =,9c . cho ,!l vudng g6c v6'i rn{t phing d6y vd goc giil'a hai rndt phing (SAC)va (anCn)bdng 600. l. Tfnh di€n tich tam gidc MNPvit, khoirng c6ch tir di€rn Qd0n m4t phing (urvr) 2. T(nh dO ddi doan vudns c6c MP vd SC . 2.4 IV C 'fir gii thi€t suy ra: Sool,ri, = Srr,r, -Sn,,o* -So*, -S*.rn R . i I 4a 4a I 2a t(2a ) - toaz /i\\ =4o l -+al)o /i\\ ,??": 1: : e li\\ Ta c6 (SBl) t nc + SBA= 600Id g6c giira hai m4t phi{ i iO \ (sBC) va (ttnco)=.TBr = 6o0 I i , 'l\ \ = rar 60o = l{ * sA=Zalj I i' I \t, \ AB I :i I \', \ , a (O,e,wn)) _,t (o.(,a.nur)) ec 3 I .,' i I \',, \ Matl<hr{c: \-' '1 - \4\ /'' =-, i , I \,', \ rvr(r.r\rraL';6@il- sr =n=ol ,- i I V". \ , . \\ 3 1 - 2-r^ ltio,\, | "':i:\,,tif- ,,,,\ =rt(e,(uur'))=]sa=iryJi'W f , '.,. |4li"" "\, /, l {.:',,,, ,,,,., ' 1, ''t'''. \ N 0.2s 0.25 0.25 0.25 http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay Goi / = A[p olC. Dlrng // r sC (l), (/ e SC). Ta co MP / I BD = MP L AC tlit MP L SA* MP f (S/C) :> Mp -L IJ (Z) "l"ir (t),(Z)= l/ Id ctoqn vudng goc chung crta Mp vd SC. Mdt l<hirc: )- i.zalz.talt J ffi .h/_. IJ SA IJ stnJL.4-_=_e.:_= rc .sc ') : AC -1 Clro c6c s6 thLlc duo:rg x,1t,z lhba rr:rfin cli , ,.; - 4x+2v+z x-v z cua bten tlluc /'= ' Zxy+xz 2 4 Nguy€n Thi Hanh -q'./fu 4s x(zy+z) z + x(s-x) 'z 4 Ll clLrq.c ]!qt qud tu'ong trr. T6 tru6'ng chu5,Qn rndn thim tlinh 4 I ix 5 ( 4 5-x\ (t \ s +_+___ _l _+__ l+l _+x l__ 5-x .r: 4 4 \5-x :_* ) 2 'r'rreo BDr c6-sita co r ) ,E+.2x[1 -]=+-i=i Dirr cling rhflc xay ,u Lni {t = ] - c ( x =1 lx +2y * z = 5 t \r, +, = 4(*'!'t t o) . ( vdy rnin ,=Lo{;;l ,=4(*,y,2>o) Luu y: co thc clirng ilao hdm: X6r f (*)=+x{s x) a a - 5-x x(s-x) 'z 4 ki€n: x+ 2y + z = 5 . Tim gi6 tri nh6 x e (0;5)ta cfing l4nh I'udng, ngdy I9 thdng 07 ndm 201I Girto vi€n ra tld vi lgp ttr{p rin BiliHAi Quang 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay . giai thich gi thdm. http://www.violet.vn/haimathlx Sưu tầm: Nguyễn Minh Hải- THPT Lê Xoay rRU'oNG rHpr LE xoAy pAp AN - THANG DIfM Of t'ru KHAO SAl IAX t r 'l ',' -. 'l ',' - ':rr l- " ':''l'' t "' , i,:t :1tt*15 . Luu f : -Ddp dn g6m 04 trang ' ', ' ':'',1 ;'t;:,.|,r: '. ' (xn + l)' t* *o' ' 21xo+11 coi A: Anox: )a1 -r" -Zxt-t ;0) B: Anoy= ufo, {-)v -7 ' 2 )-)- 'zffil Ifti d6 At4o v6'i hai trpc toa dQ AOAB