SGIODCVOTO TrngTHPTChuyờnVnhPhỳc (cú01trang) KHOSTCHTLNGLNTHII NMHC2013 2014 Mụn:Toỏn12KhiAưB Thigian:180phỳt(Khụngkgiao) I.PHNCHUNGCHOTTCTHSINH(7,0im) Cõu1(2,0im)Chohms y = x - 2mx + 2m +m4,vi m lthamsthc. a) Khosỏtsbinthiờnvvthhms m=1. b) Tỡmcỏcgiỏtrcamhmscúcci,cctiumcỏcimcci,cctiucathtothnhtam giỏccúdintớchbng1. - sin x - sin x + cosx = cos x - (1 + cosx). Cõu2(1,0im)Giiphngtrỡnh 2sin x -1 Cõu3(1,0im)Giibtphngtrỡnh x ( x+ 2) ( x + 1)3 - 1. x Cõu4(1,0im) Tớnhtớchphõn I = ũ(8x - 2x).e x dx Cõu5(1,0im)Chohỡnhchúpu S ABCD cúdicnhỏybng a ,mtbờncahỡnhchúptovimtỏy gúc60o.Mtphng ( P) cha AB viquatrngtõmtamgiỏc SAC ct SC ,SD lnltti M ,N.Tớnhthtớch khichúp S ABMN theo a Cõu6(1,0im)Choa,b,c lcỏcsthcdngthamón a + b + c = ( a + b + c )-2ab SGDưTVNHPHC TRNGTHPTCHUYấN THIKHSCLLNIINMHC2013 2014 HNGDNCHMTON12A,B. Hngdnchung. Mimtbitoỏncúthcúnhiucỏchgii,trongHDCnychtrỡnhbyslcmtcỏchgii.Hcsinhcú thgiitheonhiucỏchkhỏcnhau,nuývchoktquỳng,giỏmkhovnchoimtiacaphn ú. Cõu(Hỡnhhckhụnggian),nuhcsinhvhỡnhsaihockhụngvhỡnhchớnhcabitoỏn,thỡkhụngcho imcõu(Hỡnhhcgiitớch)khụngnhtthitphivhỡnh. imtonbichmchititn0.25,khụnglmtrũn. HDCnycú07 trang. Cõu Nidungtrỡnhby im a)(1 im) (2,0 im) ưKhi m =1 thỡ y = x - x +3 *)Tpxỏcnh D = R *)Sbinthiờn : 0,25 ộ x= Chiubinthiờn y ' = x - x = x( x -1), y ' = ờờ x= ờởx = -1 II.PHNRIấNG(3,0im): Thớsinhchlmmttronghaiphn(phnAhocphnB) ưHmsngbintrờncỏckhong(ư10)v(1 +Ơ ),nghchbintrờncỏckhong ( (-Ơ -1) v(01) ưCctr :Hmstcciti x = yCé =3 Hmstcctiuti x = yCT =2 ưGiihn lim = +Ơ A. TheochngtrỡnhChun ưBngbinthiờn : ổ Tỡm giỏtrnhnhtcabiuthc P = a + b + c+ 48ỗỗ + ữ b + c ữứ ố a + 10 Cõu7.a(1,0im)Trongmtphngvihta Oxy ,cho2ngthng d1 : x - y + =0, d : x + y - =0. Gi A lgiaoimca d1 v d2 Tỡmtoim B trờn d1 vtoim C trờnd2 saocho DABC cútrng xđƠ x y -Ơ +Ơ tõm G( 35). Cõu8.a(1,0im)Trongkhụnggian vihtaOxyz,chongthng d iquaim M ( -11) vcúvộct r chphng u = (1 0) im A ( -1 23).Vitphngtrỡnhmtphng ( P) changthng d saochokhong ư101 0+0 0+ ) +Ơ y ( +Ơ 0,25 cỏchtim A nmtphng ( P) bng x - x + Cõu9.a(1,0 im) Giiphngtrỡnh log = x 2.8x - 3.2 x + 2.16 x - 2.4 x +1 B TheochngtrỡnhNõngcao 0,25 th y Cõu 7.b(1,0im)Trong mt phng vi h to Oxy , chotam giỏc ABC vuụng ti A( 2),tõm ng trũn ổ 3ử ngoitiptamgiỏc ABC l I ỗ1 ữ vnh C thuc ngthng d : x - y - =0.Tỡmto cỏcnh B v C ố 2ứ Cõu8.b(1,0im)TrongkhụnggianvihtoOxyz,chomtphng(P):x+y+z=0.Lpphngtrỡnhmt phng(Q)iquagcto,vuụnggúcvi(P)vcỏchimM(12 ư1)mtkhongbng 2. Cõu9.b(1,0im) Giibtphngtrỡnh 4- x - x+ 0. log ( x -3) ưưưưưưưưưưưưưưưưưưHtưưưưưưưưưưưưưưưưưưưư 0,25 ư2 ư1 012 x b)(1 im) TpxỏcnhD=R x + x + - x ( x + 1) Ê ộ x = Ta cú y ' = x3 -4mx y ' = ởx = m Hmscúcci,cctiu y ' =0 cúbanghimphõnbit m >0 B ( - m m - m + m ), C ( m m - m + m ) DABC cõnti A , A ẻOxB,Cixngnhauqua Ox Gi H ltrungim ca BC 1 ị H m - m +2m ị S DABC = AH BC = m 2.2 m =m m 2 ( ) 0,25 (1,0 im) iukin 2sin x - sinx 0,25 0,25 0,25 1 2 Tacú I = ũ (8x - 2x).e x dx= ũ (4x - 1).e x 2xdx 0,25 t t = x ị dt =2xdx v x = ị t = x = ị t =1. 0,25 Tac I = ũ(4t - 1).etdt. ỡu = 4t - ỡ du = 4dt t ịớ t t ợ dv = e dt ợv = e - 2sin x - sin x + cosx = cos x - (1 + cosx) 2sin x- (1 - sin x ) (1 + 2cosx) = cos2 x - - (1 + cosx) sin x -1 2 0,25 ( ) -1 - 2cos x = cos x - - (1 + cos x ) 2cos x + - cos x - =0 0,25 1 ị I = (4t - 1).e t - ũe t dt = 3e + - 4e t = - e 0,25 0,25 0 ộ x = p + k2p cos x = ộ p x = + k 2p ( k ẻ Z) cosx= ờ ởờ p x = - + k 2p S (1,0 im) 0,25 N Kthpiukin sinx tacnghimphngtrỡnh l x = p + k 2p x = - p K A G 0,25 D M + k 2p ( k ẻZ ) I 600 O x0ị ( x + 1) - x >0 B 0,25 J C GiOlgiaoimca AC vBD ị SO ^( ABCD) Gi I ,J lnltltrungimca AB,CD G ltrngtõm DSAC Dovy x ( x+ 2) ( x + 1)3 - - (1,0 im) ỡ x ( x+ ) (1,0 im) ù ùù x iukin x x+ 1) ù( ù ùợ ( x + 1) - x 0,25 Kthpiukin x >0 tacnghim caphngtrỡnhóchol x = 2 2 Theogithit S DABC = ị m m = m =1 Vyỏpsbi toỏnl m =1 ) x ( x + 1) - Ê x ( x + 1) - = x ( x+ 1) = ộ -1 + x= x ( x + 1)= x + x- = ờ -1 - ờx = 0,25 Khi m >0 thhmscúmtimccil A ( 0, m + m ) vhaiimcctiul ( x ( x + 2) ( x + 1)3 - ỡSJ ^ CD Ta cú ị CD ^ ( SIJ) ợIJ ^ CD x x éSJI < 90 ị Gúcgiamtbờn ( SCD) v mtỏy ( ABCD) l éSJI ịéSJI =60 x + x x3 + x + x + - ( x + 1) x ( x+ 1) x3 + x + x + - ( x + 1) x ( x + 1) Ê ( x + 1) ộ x + x + - x ( x + 1)ự Ê ỷ 0,25 0,25 Tathy A, G,M thuc ( P) A, G,M thuc ( SAC) ị A, G,M thnghngv M ltrung im ca SC. SG = SO ltrungtuyntam giỏc SBD ịG cngltrngtõm G ltrngtõm DSAC ị SO tam giỏc SBD Lpluntngt ta cngcú ịB, G ,N thnghngv N ltrungim ca SD 7a ỡ2 x - y + = ỡ x= ị A(11) ợ4 x + y - = ợy = (1,0 im) TacaA lnghim cah 0,25 Gi K ltrungim ca MN ị K cngltrungimca SJ DSJI ucnh a G cngltrngtõmDSJI nờn IK ^ SJ Dthy SJ ^MN nờnSJ ^ (ABMN) ổ 2t+ 1ử B ẻ d1 ị B ỗ t ữ im C ẻ d ị C ( s5 -4s ) ứ ố 0,25 ỡ t + s + ù = ù G ltrngtõmtamgiỏc ABC 2t+ ù + - s + = ù ợ Thtớchkhi chúp S ABMN l: V = SK S ABMN DSJI ucnh a ị IK = 0,25 3a a SK = 2 1 ổ a a 3 3a2 a 3a2 a3 SABMN = ( AB + MN)IK = ỗ a + ữ = ịV = = 2 ố ứ 8 16 0,25 ỡ 61 ỡ 61 43 ùùt = ùù B( ) Giihnytac ịớ lỏpsbi toỏn ùs = -5 ùC ( -5 55) ùợ ùợ 7 0,25 (Hcsinhcú thdựngphng phỏp t sthtớch) (1,0 im) 0,25 0,25 Ta cú a + b2 + c = ( a + b + c ) - 2ab ( a + b ) + c = 5( a + b +c ) pdngbtngthcBunhiacopxkitacú 1 2 ( a + b ) + c ( a + b + c ) ị ( a + b + c ) Ê ( a + b + c )ị < a + b + c Ê10 2 pdngbtngthcCauchytali cú a + 10 a + 10 ổ a + 10 12 a+ 22 = = Ê ỗ + 4ữ = ị 3 4ố 12 a + 10 a + 10 a+ 10 a+ 22 ứ 3 b + c + + b + c+ 16 12 b+c = = ị ( b + c).8.8 Ê 4 12 b +c b + c+ 16 ổ ị P a = b + c+ 48.12ỗ + ữ ố a + 22 b + c + 16ứ pdngbtngthcCauchyưSchwarztac 1 2304 + ị P a + b + c+ a + 22 b + c + 16 a + b + c + 38 a + b + c +38 2304 2304 t t = a + b + c ị t ẻ ( 010]ị P t+ Xộthm f (t )= t+ trờn ( 010] t +38 t +38 8a (1,0 im) 0,25 Phngtrỡnh(P)cúdng: a ( x - ) + b ( y + 1) + c ( z - 1)= ax + by + cz + b - c =0 - a + 3b + 2c d ( A, ( P) )= 0,25 0,25 a + b +c = M a = -2b ị 5b + 2c 5b +c = 5b + 2c = 5b + c2 2 4b - 4bc + c = ( 2b - c ) = c =2b ( (4 0,25 0,25 0,25 ỡa= Chn b= -1ị Tac phngtrỡnh(P)l: x - y - z + =0. ợc = -2 x x 9a ùỡ4 - + > (1,0 im) Tathy "x ẻ R. x x ùợ2.16 - 2.4 + > Dovy x - x + log = x 2.8 x - 3.2 x + 2.16 x - 2.4 x + ( ( t - 10 ) ( t+ 86) ị f '(t ) Ê "tẻ 010 Ta cú f '(t ) = = ( ] ( t + 38 )2 ( t +38)2 ị f (t )nghchbintrờn ( 010 ] ị f (t ) f (10), "t ẻ ( 010 ] f (10) = 58 ị P 58 2304 0,25 ) ) ( ) ( ) ( ) + 1) + ( - + 1) = log ( 2.16 - 2.4 + 1) + ( 2.16 - 2.4 +1) ( 2) log x - x + - log 2.16 x - 2.4 x + = 2.16 x - 2.4 x + - x - x + log x -2 x x x x x x x 0,25 Xộthm f (t ) = log2 t +t trờn ( +Ơ) ỡa + b + c= 10 ùa + b = c ỡa= ùù ù ớb= a + 10 Dubngxyrakhivch ù = ùc= ợ ù ùợb + c = ỡ a= ù Vy P =58,tckhi ớb= ùc = ợ r ngthng d iquaim M ( -11) vcúvộct chphng u = (1 0). r Gi n = ( a b c ) ( a + b + c 0) lvộct phỏptuyn ca(P). r r Do ( P)cha d nờn: u.n = a + 2b = a = -2b Ta cú f '(t ) = + ị f '(t ) > "t >0 ị f (t ) ngbintrờn ( +Ơ) t.ln 0,25 Dovy ( ) 0,25 f (4 x - x + 1) = f (2.16 x - 2.4 x + 1) x - x + = 2.16 x - 2.4 x + 2.16 x - 3.4 x + x =0 0,25 ộ x = x = ộ x= 2x = -1 - ờ x = log - 2 ờở + x = ờở Vyphngtrỡnhó chocúhainghim x = x =log2 - ộ ỡù f ( x) ( I) ờớ ờùợlog ( x - 3) > - x+ log x - ỡù f ( x) Ê ớlog ( x - 3)< 0( II) ởùợ 4- x 0,25 ( I ) 7b (1,0 im) +TamgiỏcABC vuụngti A nờn I ltrungimca BC 0,25 + C ẻ d ị C ( 2t +1t ) I ltrungim ca BC ị B (1 - 2t 3-t ) uuur uuur AB = ( -2 - 2t - t ) AC = ( 2t - t- 2) ột = uuur uuur AB ^ AC AB AC = ( -2 - 2t ) ( 2t - ) + (1 - t ) ( t- )= -2 ờt = ỡù B( -1 2) +Vi t = 1ị ùợC ( 31) ỡ ổ 17ử ù Bỗ ữ -2 ù ố 5 ứ +Vi t = Vy ịớ ùC ổ -2ử ỗ ữ ùợ ố 5 ứ 8b (1,0 im) ỡ x ùỡ x ùỡ x ớ < x< ùợ0 < x - < ùợ3 < x < ợ3 < x < ỡ A + B + C = ỡù( P ) ^ ( Q) ù Tgithittacú: A + 2B - C = d M , Q = ù 2 ợù ( ( ) ) ợ A + B + C ỡ A = - B - C ù B - 2C = (*) ù 2 ợ B + 2C + 2BC 0,25 0,25 0.25 0,25 (*) B =0 hoc B + 8C =0. Nu B =0 thỡ A = -C Chn C = -1 ị A =1 Tacphngtrỡnhmtphng ( Q) l: x - z =0 0,25 Nu 3B + 8C =0 tachn C = B = -8 A =5 tacphngtrỡnh ( Q) l x - y + z =0 Vycúhaimtphngthomónbitoỏn,cúphngtrỡnhl: x - z =0 x - y + z =0 9b 0,25 Xộthm f ( x ) = 24- x - x +1. (1,0 im) Tathy f '( x) = -24- x.ln - ị f ' ( x )< 0"x ẻR ị f ( x)nghchbintrờn R M f (3) =0.Dovyf(x) x Ê3f(x) Ê x 3. 0,25 ( II ) 0,25 ỡ ổ 17ử ù Bỗ ữ ỡù B( -1 2) ù ố ứ hoc ớ C 31 ( ) ùợ ùC ổ ùợ ỗố 5 ữứ ( Q) i quagctonờn ( Q) cúphngtrỡnhdng: Ax + By + Cz = 0( A2 + B + C ạ0). ỡ xÊ ùỡ x Ê ùỡ xÊ ù ộ x> x< -4 ợù x - > ợù x > ù x < -4 ợở 0,25 0.25 Tpnghimcabtphngtrỡnh óchol (-Ơ -4) ẩ(3 4) CmnthyNguynDuyLiờn(lientoancvp@vinhphuc.edu.vn)gitiwww.laisac.page.tl 0,25 SGIODCVOTO TrngTHPTChuyờnVnhPhỳc (cú01trang) KHOSTCHTLNGLNTHII NMHC2013 2014 Mụn:Toỏn12ư KhiD Thigian:180phỳt(Khụngkgiao) SGIODCVOTO TrngTHPTChuyờnVnhPhỳc (ỏpỏncú05 trang) HNGDNCHMTHI (Vnbnnygm05trang) A. PHNCHUNGCHOTTCTHSINH(7,0 im) - x + CõuI(2,0im).Chohms y= 2x +1 1) Khosỏtsbinthiờnvvth (C)cahmsócho. 2) Vitphngtrỡnhtiptuyncathhms(C)saochotiptuyniquagiaoimca ngtimcnvtrcOx. CõuII(2,0im)1)Giiphngtrỡnh: ( sin 2x + s inx )+ cos2x - cos x = x 2) Gii phngtrỡnh: e = + ln ( +x ). 2 + x CõuIII(1,0im) Tớnhtớchphõn : I = ũ dx 2x + CõuIV(1,0im). ChohỡnhchúpS.ABCDcúỏyABCDlhỡnhthangvuụngtiAvD, AB= AD=2a,CD=a,gúcgiahaimtphng(SBC)l(ABCD)bng 600 GiIltrungimca cnhAD.Bithaimtphng(SBI)v(SCI)cựngvuụnggúcvimtphng(ABCD).Tớnhthtớch khichúpS.ABCD. CõuV(1,0im) Cho a, b,c lcỏcsdngthomón ab + bc + ca =3.Tỡmgiỏtrnhnhtca biuthc: M = + abc ( a + b )(b + c)(c +a ) B.PHNRIấNG(3im) Thớsinhchclmmttronghaiphn(phn 1hoc 2) 1.TheochngtrỡnhChun CõuVIA(2,0im) 1) Trong mt phng Oxy, cho ng trũn ( C ): ( x - 1) + ( y + 1) =4 Gi ( C') l ng trũn cú tõm thucngthng ( d ) : 3x - y =0 vtipxỳcvitrcOyngthitipxỳcngoivingtrũn(C). Vitphngtrỡnh ngtrũn ( C'). I)Hngdnchung: 1)Nuthớsinhlmbikhụngtheocỏchnờutrongỏpỏnnhngvnỳngthỡchosimtng phnnhthangimquynh. 2)Vicchitithoỏthangim(nucú)tronghngdnchmphimbokhụnglmsailch hngdnchmvphicthngnhtthchintrongcỏcgiỏoviờnchmthi. 3)imtonbitớnhn0,25im.Saukhicngimtonbi,ginguyờnktqu. II)ỏpỏnvthangim: Cõu ỏpỏn im - x + Chohms y = 1,0 2x +1 1)Khosỏtsbinthiờn vvthcahms. ỡ -1ỹ Tpxỏcnh: D = R / ý ợ ỵ Sbinthiờn: y' = x-1 - Bngbinthiờn: x 1,0 0,25 + y y 0,25 -1 +à || -1 +à 0.25 || e + tan( x - 1) - CõuVIIA(1,0im).Tớnhgiihn lim x -1 2.Theochngtrỡnhnõngcao. CõuVIB(2,0im) 1) TrongmtphngvihtaOxy,chongtrũn ( C ): ( x - 1)2 + ( y + 2)2 =12. Vitphngtrỡnh ngtrũn(C)cú tõm M(51) bit(C)ct(C) tihaiim A,Bsaocho AB =2 3. 2)TrongkhụnggianvihtaOxyz,chobaim A(ư22 ư2), B(01 ư2)vC(22ư1).Vit phngtrỡnhmtphng ( P)iquaA,songsongvi BCvctcỏctrcOy,Oz theothtti M,N khỏcvigctaOsaochoOM =3ON. CõuVIIB(1,0im) Mtchichpng6cỏibỳtmuxanh,6cỏibỳtmuen,5cỏibỳtmutớm v3cỏibỳtmucỏnhst1n20.Lyngunhiờnra4cỏibỳt.Tớnhxỏcsutly c ớtnht2bỳtcựngmu. ưưưưưưưưưưHTưưưưưưưưưư x đ1 -3 ( 2x +1 )2 Hmsluụnnghchbintrờntngkhongxỏcnh CõuI.1 thhmskhụngcúcctr -1 -1 -1 lim y = lim y = thhmscú timcn ngang y = xđ-Ơ xđ+Ơ 2 -1 lim y = -Ơ lim y = +Ơ thhmscútimcnng x = 1 xđxđ- 2)TrongkhụnggiantaOxyz,vitphngtrỡnh ngthng ( D) iqua A ( -2 -4 ),songsong ỡ x = + 3t vimtphng(P): 3x - y - 3z - =0 v ctngthng(d): ùớ y = -4 - 2t ù z = + 2t ợ PNKHOSTCHTLNGLNTHII NMHC2013 2014 Mụn:Toỏn12ư KhiD Thigian:180phỳt(Khụngkgiao) -1 thhmscútõmixng I ổỗ -1 -1ửữ ố 2 ứ thhmscttrctungti A( 01),cttrchonhti B(10) Vitphngtrỡnhtiptuyncathhms(C)saochotiptuyniquagiaoim cangtimcnvtrcOx Phngtrỡnhtiptuynti M ( x0 y0)cúdng y = -3 ( x - x0)+ - x0 + (2 x0 + 1) x0 +1 CõuI.2 - 1,0 GiaoimcatimcncathhmsvitrcOxl N ( 0) 0.25 1,0 0.25 Tiptuyniqua N ( -1 0) - x + -3 -1 ( - x0) + = (2 x0 + 1) 2 x0 +1 0.25 Giiphngtrỡnh c x0 = 0,25 Phngtrỡnhtiptuynti M ( -1) l y = - x - 12 24 0.25 ịI= Phngtrỡnh óchotngngvi: CõuII sin x cos x + cos x - sin x + s inx - cos x = cos x +sin x ( ) 2,0 ộ s inx - cos x = s inx - cos x =0 ờở s inx - cos x = p ộ x = + kp ộ ổ pử sin x = ữ ỗ 6ứ p ố x = + k p ( k ẻ Z) ổ p ờ sin ỗ x- ữ = 6ứ ố x = p + k 2p ờở KL:Vyphngtrỡnhcúbahnghim: ( sin x - cos x ) -( ) 2 ( + t )tdt 1 = ũ ũ( + t - + t )dt 1+t 0.25 0.25 0.25 t ( + t - ln | t + 1|) = ( -ln ) 2 KL ChohỡnhchúpSABCDcúỏyABCDlhỡnhthangvuụngtiAvD,AB= AD= 2a, CD=a,gúcgiahaimtphng(SBC)l(ABCD)bng600 GiIltrungimca CõuIV cnhAD.Bithaimtphng(SBI)v(SCI)cựngvuụnggúcvimtphng(ABCD). TớnhthtớchkhichúpS.ABCD. = ( sin 2x + s inx )+ cos2x - cos x =2 1)Giiphngtrỡnh: 0.25 1,0 0.5 1,0 2)Gii phngtrỡnh: e x = + ln ( +x ). 1,0 /K x > -1 x Phngtrỡnh óchotngng e - ln ( + x )- =0 0.25 0.25 Xộthms f ( x ) = e x - ln ( + x ) - 1,x ẻ D = ( -1 +Ơ) ,x ẻ D x +1 f " ( x ) = e x + ,f " ( x )> 0"x ẻ D ( x +1) f ' ( x )= e x - 0.25 Suyra f ' ( x) lhmngbintrờn D Nhnthy f ' ( )=0 nờnphngtrỡnh f ' ( x )=0 cúỳngmtnghim x =0 Tacúbngbinthiờn X y Y 0.25 +à 0+ +à -Ơ 0.25 Tbngbinthiờntacú phngtrỡnhcúmtnghimduynht x =0 2 + x Tớnhtớchphõn: I = ũ dx + 2x CõuIII I = ũ 1,0 2+ x + 2x dx = 2 + 2x dx 2x ũ 1+ t t = 2x ị t = 2x ị dx =td x = ị t = icn: x = ị t =2 1,0 0.25 0.25 Nhnxột:SI ^ ABCD GiHlhỡnhchiucaIlờnBC. Ch éSHI =60 3a Tớnhc S ABCD = 3a IH = 3a 15 3a 15 Suyra SI = VS ABCD = (vtt) 5 0.25 0.25 0.25 Cho a, b,c l cỏc s dng tho ab + bc + ca =3. Tỡm giỏ tr nh nht ca biu CUV thc: 1,0 M = + abc ( a + b )(b + c)(c +a ) pdngbtngthccụsitacú: 1 0.25 M = + + 33 2 2 abc abc (a + b)(b + c)(c + a ) a b c ( a + b )(b + c)(c +a ) 2(ab + bc + ca) Cú abc( a + b)(b + c)(c + a ) = ( ac + bc)(ba + ca )(cb + ab) Ê =2 (1) 0.25 ab + bc + ca 2 (2) a b c = ab.bc.ca Ê =1 0.25 3 T(1)v(2)suyra M Dubngxyrakhi a = b = c =1 0.25 VygiỏtrnhnhtcaMbng a = b = c =1 1)TrongmtphngOxy,chongtrũn ( C ): ( x - 1) + ( y + 1) =4 Gi ( C') lng Cõu trũncútõmthucngthng d : 3x - y =0 vtipxỳcvitrcOyngthitipxỳc ( ) VIA.1 ngoivingtrũn(C).Vitphngtrỡnh ngtrũn ( C'). 1,0 ngtrũn ( C) cútõm I (1 -1),bỏnkớnhR=2 1,0 ngtrũn ( C') cútõm I ' ( a3a),bỏnkớnhR 0.25 Dongtrũn ( C')tipxỳcOynờnR=|a| Dongtrũn ( C') tipxỳcngoivingtrũn(C)nờn II ' = R '+2 ( a - 1) + (3a + 1) = (| a | +2)2 (1) -4 - 34 Giiphngtrỡnh(1)c a = hoc a = Vy :Phngtrỡnh ngtrũncntỡml: ( x ổ hoc ỗ x + ỗ ố ngtrũn (C)cútõm I (1 -2 ),bỏnkớnh R =2 Do(C)ct(C)tiA,Bnờn AB ^ IM GiEltrungimAB. DIAB u ị IE =3 , IM =5 NuEnmgiaIvM ị EM = 2,EA = ị MA = Phngtrỡnh ngtrũncnlpl: ( C ' ): ( x - 5) + ( y - 1) =7 0.25 0.25 0,25 2 ) + ( y - 2)2 = NuEnmgiaIvM ị EM = 8,EA = ị MA = 67 Phngtrỡnh ngtrũncnlpl: ( C ' ): ( x - 5) + ( y - 1) =67 0,25 + 34 ổ + 34 50 + 34 ữ +ỗ y + ữữ = ữứ ỗố 81 ứ ỡ x = + 3t 1,0 2) TrongkhụnggianvihtaOxyz,chobaim A ( -2 -2 ), B ( 01 -2 ) v 0.25 C ( 22 -1).Vitphngtrỡnhmtphng ( P)iquaA,songsongvi BCvctcỏc tiaOy,Oztheothtti M,NkhỏcvigctaOsaochoOM =3ON. uuuur ur Tgithittacú M ( 0m0) v N ( 00n) trongú mn ạ0 v m = 3n ị MN = m.u thng(d): ùớ y = -4 - 2t 1,0 uuuur Gis ( D) ct(d)ti M ( + 3t -4 - 2t1 + 2t ) ị AM = ( 3t - -2t - 22t + ) r Mtphng(P)cúvtpt n = ( -2 -3 ) r uuuur ( D) //(P) n.AM = ( 3t - 1) - ( -2t - ) - ( 2t + )= t =2 uuuur Khiú AM = ( -69 ) uuuur ngthng ( D) iqua A ( -2 -4 )cúvtcp AM = ( -69 ) ỡ x = + 5t Suyraphngtrỡnh ( D) l: ùớ y = -2 - 6t ù z = -4 + 9t ợ x-1 x đ1 lim x đ1 x đ1 3 x đ1 2 3 0,25 2,0 = + 3= 2 1)TrongmtphngvihtaOxy,chongtrũn ( C ): ( x - 1) + ( y + 2) =12.Vit phngtrỡnh ngtrũn(C)cú tõm M(51)bit(C)ct(C) tihaiim A,Bsaocho AB =2 Cõu 1,0 ỷ KL: Mtchichpng6cỏibỳtmuxanh,6cỏibỳtmuen,5cỏibỳtmutớmv3cỏi bỳtmucỏnhst1 n20.Lyngunhiờnra4cỏibỳt.Tớnhxỏcsutly cớtnht2bỳtcựngmu. Scỏchlybnchicbỳtbtkỡt20chicbỳtóchol: n ( W )= C20 =4845 1,0 0,25 0,25 0,25 0,25 1,0 0,25 0,25 ( ) n A = C61 C61 C51 C31 =540 0,25 1,0 GiAlbinclycớtnhthaibỳtcựngmu Scỏchlyc4bỳttrongúkhụngcúhaicỏinocựngmul: 0,5 Cõu VIB 7B ổ e - x + x + tan( x - 1) ( x + 1)( x + x+ 1)ử = lim ỗỗ + ữữ x - x +1 x + ố x -1 ứ x-1 VIIA 0.25 1,0 x-1 e + tan( x - 1) - r r uuur r r ỡùn ^ BC Gis ( P)cúvtpt n 0.Do ( P)iquaM,NvsongsongviBCnờn r r suy ùợn ^ u r uuur r n//ộở BC ,u ựỷ r r uuur r vi u ( -13 )ị ộở BC , u ựỷ = ( -46 2),chn n = ( -3 -1)ị (P): 2x - 3y - z + = r r uuur r vi u (0 -1 -3 ) ị ộ BC , u ự = ( -6 2),chn n = (1 -31)ị (P): x -3y + z +10 = 0.25 ổ e -1 tan( x - 1) = limỗ + ữ ( x - 1)( x + 1) ố ( x - 1)( x + 1) ( x - 1)( x + 1)ứ x -1 Cõu r vi u ( -13 ) hoc u (0 -1 -3 ) 0,25 e + tan( x - 1) - Tớnhgiihn lim ( x - 1)( x +1) 0,25 hoc ( C ' ): ( x - 5) + ( y - 1) =67 A ( -2 -4 ),songsongvimtphng(P): 3x - y - 3z - =0 v ctng Cõu VIA.2 0,25 KL :Cúhaingtrũnthamón ( C ' ): ( x - 5) + ( y - 1) =7 2) TrongkhụnggiantaOxyz,vitphngtrỡnh ngthng ( D) iqua ù z = + 2t ợ 0,25 ( ) Scỏchlyc4bỳtmcúớtnhthaibỳtcựngmul: n ( A) = n ( W ) - n A =4305 0,25 Xỏcsutlyc4bỳttrongúcúớtnhthaibỳtcựngmul: n ( A) 4305 287 P ( A) = = = n ( W) 4845 323 0,25 CmnthyNguynDuyLiờn(lientoancvp@vinhphuc.edu.vn)gitiwww.laisac.page.tl