DE48 THPT chuyên hưng yên _ ĐỀ THI THỬ THPT QUỐC GIA TOÁN NĂM 2015

TRNGTHPTCHUYấN THI TH K HNGYấN BANCHUYấNMễN THITHKTHITHPTQUCGIA2015 THI THPT QUC GIA 2015 - S 48 Thi gian lm bi 180Mụnthi:TON phỳt Thigianlmbi: 180phỳt,khụngkthigianphỏt oOo Cõu1(2,0im).Chohms y = x + 3mx +2 (1),vimlthamsthc. a) Khosỏtsbinthiờnvvthhms(1)khi m= 1. b)Tỡm mthhms(1)cúhaiimcctrA,Bsaochodintớchtamgiỏc OABbng2 (Olgcta). Cõu2(1,0im).Giibtphngtrỡnh log x + log x +1 - -log 2x ( ) ( ) Cõu3(1,0im). a)GiA,Blhaiimbiudinchocỏcsphclnghimcaphngtrỡnh z + z + =0.Tớnh dionthngAB. b)TrongkỡthiTHPTQucgianm2015,mithớsinhcúthdthitia8mụn:Toỏn,Lý,Húa, Sinh,Vn,S,avTinganh.Mttrngihcdkintuynsinhdavotngimca 3mụntrongkỡthichungvcúớtnht1tronghaimụnlToỏnhocVn.Hitrngihcú cúbaonhiờuphngỏntuynsinh? p sinx Cõu 4(1,0im).Tớnhtớchphõn I = ũ dx cos x + 3cos x + Cõu (1,0 im). Trong khụng gian vi h ta Oxyz, cho hai im A ( 2 ) , B( 007) v ngthng d : x - y - z- = = ChngminhrnghaingthngdvABcựngthucmt -2 mtphng.TỡmimCthucngthngdsaochotamgiỏcABCcõnnhA. Cõu (1,0 im). Cho lng tr ng ABC A ' B ' C'cú ỏy l tam giỏc cõn, AB = AC = a , ã =1200 Mt phng (AB'C') to vi mt ỏy gúc 600. Tớnh th tớch lng tr ABC.A'B'C' v BAC khongcỏchtngthng BC nmtphng ( AB ' C') theo a hoctoancapba.com Cõu7(1,0im).TrongmtphngvihtaOxy,chohỡnhvuụngABCDcú A ( -1 2).GiM, N lnltl trungimcacnh ADvDCK lgiaoimcaBNviCM.Vitphngtrỡnh ngtrũnngoitiptamgiỏcBMK,bitBNcúphngtrỡnh x + y - =0 vimBcúhonh lnhn2. ỡ(1 - y ) x + y = x + y + 3xy ù Cõu8(1,0im).Giihphngtrỡnh ( x,yẻ Ă) ùợ y + + x + y = 2y - x Cõu (1,0 im). Cho x, y,z l cỏc s thc dng tha x + y + z = ( xy + 2yz +zx ) ( Tỡmgiỏtrlnnhtcabiuthc: P= ) x y + z ( x + y +z )3 ưưưưưưưưưưưưưưưHtưưưưưưưưưưưưưưưư CmnbnMathLove(lovemaths.@yahoo.com.vn)ógitiwww.laisac.page.tl 295 PN Cõu Nidung a)Khosỏthms y = x + 3mx +2 Vim=1,tacúhms:y=x3 +3x2 +2 *)TX: Ă *)Sbinthiờn: +)Giihntivụcc: lim y = Ơ im 0,25 xđƠ +)Chiubinthiờn: y'=3x2 +6x ịy'=0 x=0hocx=ư2 Bngbinthiờn: x ưƠ y + 0 +Ơ + 0,25 +Ơ y ưƠ ịhmsngbintrờn(ưƠư2)v(0+Ơ)hmsnghchbintrờn(ư20) hmstccitix=ư2,yC =6hmstcctiutix=0,yCT =2 *)th: Nhnxột:thhmsnhnim I(ư14)lmtõmixng. 0,25 0,25 ư5 ư2 b)Tỡmmthhms(1)cúhaiimcctrA,Bsaochodintớch tamgiỏcOABbng2 Vimix ẻ Ă ,y'=3x2 +6mx ịy'=0 x=0hocx=ư2m hmscúcci,cctiuthỡphngtrỡnhy'=0cúhainghimphõnbit m ạ0 Khiú,tacỏcimcctrl:A(02)B(ư2m4m3 +2) ộm= SOAB =1 OA.d(BOA)=4 -2m = (thamón) ởm = -1 Vyvim= 1thỡhmscú2cctrthamónbi. log x + log x +1 - -log 2x ( ) ( 0,5 0,5 ) 0,5 296 log ( x + ) log ( x +1 - 3) + log 2x 2 log ( x + ) log ( 22 x +1 - 3.2x ) 0,5 x x + Ê 2 x +1 - 3.2 x - 3.2 x - ộ x Ê -1( L) x x ờở2 VyBPTcútpnghim:S= [ +Ơ) a)Xộtphngtrỡnh: z + z + = ( ) D'=1ư 3=ư2= i 0,25 Phngtrỡnhcúhainghim: z1 = -1 + i z2 = -1 -i ( ) ( ) ị A -1 B -1 - 0,25 AB= 2 b)TH1:TrngHchxột1trong2mụnToỏnhocVn: Cú: 2.C62 =30 (cỏch) TH2:TrngHxộtchaimụnToỏnvVn: Cú:1.C61 =6 (cỏch) 0,25 0,25 Vycúcỏctrnghpl:30+6=36(cỏch) p p 2 sin x sinx dx = ũ dx cos x + 3cos x + 2cos x + 3cos x + 0 I=ũ 0,25 tcosx=t ịdt=ưsinxdx Vix=0 ịt=1vix= 1 p ịt=0 dt dt ổ =ũ = 2ũỗ ữ dt 2 t + t + t + t + t + t + ( )( ) ố ứ 0 I =ũ 0,25 ổ 2t+ = ỗ ln ữ = ln ố 2t + ứ0 0,5 297 r ngthngdcúvộctchphng u ( -2 21) viquaM(361) uuur ngthngABcúvộctchphng AB ( -4 -25) uuuur AM ( -1 -1) r uuur r uuur uuuur Tacú: ộởu , AB ựỷ = (12612)ịộởu , AB ựỷ AM = -12 + 24 - 12 = 0,5 VyABvdngphng C ẻ d ị C ( - 2t + 2t 1+t ) TamgiỏcABCcõntiA AB=AC (1+2t)2 +(4+2t)2 +(1ưt)2 =45 9t2 +18t 27=0 t=1hoct=ư3 0,5 VyC(182)hocC(90 ư2) B C A H K B' C' A' +Xỏcnhgúcgia(AB'C')vmtỏyl ã AKA' ị ã AKA ' =600. a a TớnhA'K= A ' C '= ị AA ' = A ' K tan 600 = 2 3a VABC A ' B ' C '=AA'.SABC = hoctoancapba.com 0,5 +)d(B(AB'C'))=d(A'(AB'C')) Chngminh: (AA'K) ^(AB'C') Trongmtphng(AA'K)dngA'HvuụnggúcviAK ịA'H ^(AB'C') ịd(A'(AB'C'))=A'H a Tớnh:A'H= a Vyd(B(AB'C'))= 0,5 298 GiE=BN ầAD ịDltrungimcaAE DngAH ^BNtiH ị AH = d ( A BN)= A B 1 TrongtamgiỏcvuụngABE: = + = 2 AH AB AE 4AB2 5.AH ị AB = =4 H M 0,25 K D N C E B ẻBN ịB(b8ư 2b)(b>2) AB=4 ịB(32) 0,25 PhngtrỡnhAE:x+1=0 E=AE ầBN ịE(ư110) ịD(ư16) ịM(ư14) GiIltõmca(BKM) ịIltrungimcaBM ịI(13) R= BM 2 = 5.Vyphngtrỡnhngtrũn:(xư 1) +(y ư3) =5. 0,25 0,25 ỡ(1 - y ) x + y = x + y + xy(1) ù ùợ y + + x + y = - x + y ( 2) K:y ư1 Xột(1): (1 - y ) x + y = x + y +3xy t x + y = t ( t 0) 0,5 2 Phngtrỡnh(1)trthnh: t + (1 - y )t - x - y - x - y - xy = D=(1ưy)2 +4(x2 +2y2 +x+2y+3xy)=(2x+3y+1)2 2 ột = - x - y- ộ x + y = - x - y- ịờ ờ x + y = x + 2y ởt = x + 2y Vi x + y = - x - y -1,thayvo(2)tacú: ỡ ù y y +1 = 3y + y= ù9 y + y = ợ ị x = - x -1 (vụnghim) 299 0,25 ỡ -1 - ù x= ỡù y + = -2x ù Vi x + y = x +2y ,tacúh: ớ 2 ợù x + y = x + 2y ù y = + ùợ ổ -1 - + 5ử Vyhphngtrỡnhcúnghim ( x y )= ỗ ữ ứ ố 0,25 Tiukin:5x2 +5(y2 +z2)=9x(y+z)+18yz hoctoancapba.com 5x2 9x(y+z)=18yzư5(y2 +z2) 2 pdngBTCụsitacú: yz Ê ( y + z ) y + z ( y + z) ị18yzư5(y2 +z2) Ê2(y+z)2. Doú:5x2 ư9x(y+z) Ê 2(y+z)2 [xư 2(y+z)](5x+y+z) Ê0 ịx Ê2(y+z) x 2x P= Ê Ê 3 y + z (x + y + z) ( y + z ) ( x + y + z ) y + z 27 ( y +z ) ty+z=t>0,tacú:P Ê 4tư t 27 Xộthm ịP Ê16. ỡ ùù y = z= 12 VyMaxP=16khi ù x = ùợ CmnbnMathLove(lovemaths.@yahoo.com.vn)ógitiwww.laisac.page.tl 300 ... 3mx +2 Vim=1,tacúhms:y=x3 +3x2 +2 *)TX: Ă *)Sbinthiờn: +)Giihntivụcc: lim y = Ơ im 0,25 xđƠ +)Chiubinthiờn: y'=3x2 +6x ịy'=0 x=0hocx=ư2 Bngbinthiờn: x ưƠ y + 0 +Ơ + 0,25 +Ơ y ưƠ ịhmsngbintrờn(ưƠư2)v(0+Ơ)hmsnghchbintrờn(ư20)... +(4+2t)2 +(1ưt)2 =45 9t2 +18t 27=0 t=1hoct=ư3 0,5 VyC(182)hocC(90 ư2) B C A H K B' C' A' +Xỏcnhgúcgia(AB'C')vmtỏyl ã AKA' ị ã AKA ' =600. a a TớnhA'K= A ' C '= ị AA ' = A ' K tan 600 = 2 3a VABC