0 Cõu1(2,0im).Choh ms 3 2 3 2y x x mx m = + + + - ( m lthams)cúthl ( ) m C . a)Khosỏtsbinthiờnvvth cahm skhi 0m = b)Xỏcnh m ( ) m C cúcỏcimccivcctiunmvhaiphớatrchonh Cõu2(1,0im). Giiphn gtrỡnh: 2cos6 2cos4 3 cos2 sin 2 3x x x x + - = + Cõu3(1,0im). Tớnh: ( ) 2 1 0 x x x x e I dx x e - + = + ũ Cõu4(1,0im). a) Giiphn gtr ỡnh: 2 3 6 36 log log log logx x x x + + = b) Tỡmshngkhụngphthucvo x trongkhaitrinnhthcNiutn 2 3 2 n x x ổ ử + ỗ ữ ố ứ (vi 0x ạ ), bitrng * nẻ Ơ v ( ) 2 1 5 4 9 4 n n n n C C n + + + + - = + Cõu5(1,0im). Chohỡnh chúp .S ABCD cúỏy ABCD lhỡnh chnhtvi 3 2AB a AD a = = . Hỡnh chiu vuụnggúcca S lờnmtphng ( ) ABCD lim H thucc nh AB saocho 2AH HB = .Gúc gia mtphng ( ) SCD v mt phng ( ) ABCD bng 0 60 .Tớnh theo a th tớch khi chúp .S ABCD vtớnhkhongcỏchgiahaingthng SC v AD. Cõu6(1,0im). Trong mt phng ta Oxy cho tam giỏc cõn ABC cú ỏy BC nm trờn ng thng :2 5 1 0d x y - + = , cnh AB nm trờn ng thng :12 23 0d x y  - - = . Vit phng trỡnh ng thng AC b itnúiquaim ( ) 31M . Cõu7(1,0im). Trong khụng gian Oxyz , cho ( ) ( ) ( ) 100 , 020 , 003A B C .Vi t phng trỡnh mt phng ( ) P iqua ,O C saochokhong cỏcht An ( ) P bngkhong cỏcht B n ( ) P . Cõu8(1,0im). Gii h phngtrỡnh: ( ) 2 2 2 2 3 5 2 2 2 2 5 3 2 1 2 12 7 8 2 5 x xy y x xy y x y x y x y xy x ỡ + + + + + = + ù ớ + + + + + = + + ù ợ . Cõu9(1,0im). Chobasthcdng , ,a b c thamón 2 2 2 3a b c + + = . Tỡmgiỏtrinh nhtcabiuth c ( ) 1 1 1 8 5S a b c a b c ổ ử = + + + + + ỗ ữ ố ứ Ht Thớsinhkhụngcsdngtiliu.Cỏnbcoithikhụnggiithớchgỡthờm. Hvtờnthớsinh: Sbỏodanh: SGD&T TRNGTHPT CHUYấNVNHPHC KHOSTCHTLNG CCMễNTHITHPTQUCGIALN3NMHC2014 -2015 MễN:TONKHI12A+B Thigian180phỳt(Khụngkthigiangiao) thigm01trang 23 1 TRNGTHPTCHUYấNVNHPHC. (Hngdnchmcú 5trang) HNGDNCHMKSCL LN3 NM2015 Mụn:TON 12AB I.LUíCHUNG: 1)Nuthớsinhlmbikhụngtheocỏchnờutrongỏpỏnnhng vnỳngthỡchosim tngphnnhthangimquynh. 2)Vicchitithoỏthangim(nucú)tronghngdnchmphimbokhụnglmsai lchhngdnchmvphicthngnhtthc hintrongcỏcgiỏoviờnchmthihhosỏt. 3)imtonbitớnhn0,25im.Saukhicngimtonbi,ginguyờnktqu. II.PN: Cõu í Nidungtrỡnhby im 1 a Chohms 3 2 3 2y x x mx m = + + + - ( m lthams)cúth l ( ) m C . a)Khosỏtsb inthiờnvvthcahmskhi 0m = 1,0 ồ Khi 0m = hmstrthnh 3 2 3 2y x x = + - ã TX: D R = ã Sbinthiờn: +)Chiubinthiờn: 2 0 3 6 , ' 0 2 x y x x y x = ộ = + = ờ = - ở Hmsngbintrờncỏckhong ( ) ( ) 2 , 0 -Ơ - +Ơ ,nghchbintrờn ( ) 20 - 0.25 +)Cctr :Hmstcciti 2 ( 2) 2 CD CD x y y = - = - = Hmstcctiuti 0 (0) 2 CT CT x y y = = = - +)Giihn: lim lim x x y y đ-Ơ đ+Ơ = -Ơ = +Ơ 0.25 Bngbinthiờn: x -Ơ 2 0 +Ơ 'y +0 0+ y 2 +Ơ -Ơ 2 0.25 ã th:ct Ox ti ( ) ( ) ( ) 10 , 1 30 , 1 30 - - + - - thnhnimunU( 10 - )ltõmixng. ( Giỏmkhotv) 0.25 b b)Xỏcnhm ( ) m C cúcỏc imccivcctiunmvhaiphớatrchonh 1,0 ồ Phngtrỡnh honh giaoim ca ( ) m C vtrchonh l ( ) ( ) ( ) 3 2 2 3 2 0 1 2 2 0 1x x mx m x x x m + + + - = - + + - = 0.25 ( ) ( ) ( ) 2 1 1 2 2 0 2 x g x x x m = - ộ ờ = + + - = ở 0.25 2 ( ) m C cúhaiimcctrnmvhaiphớaivitrc Ox ( ) 1PT cúba nghim phõnbit ( ) 2 cú hainghimphõnbit khỏc 1 - ( ) 3 0 3 1 3 0 m m g m  D = - > ỡ ù < ớ - = - ạ ù ợ 0.25 Vykhi 3m < thỡ ( ) m C cúcỏcimccivcctiunmvhaiphớatrchonh 0.25 Chỳý hcsinhcú thgiitheocỏchphng trỡnh 0y  = cúhainghimphõnbit 1 2 ,x x v ( ) ( ) 1 2 0 Cé CT y y y x y x ì = ì < 2 Giiphngtrỡnh : 2cos 6 2c os 4 3 cos 2 sin 2 3x x x x + - = + 1,0 ồ PT ( ) ( ) 2 cos6 cos 4 3 1 cos 2 2sin cosx x x x x + = + + 0.25 ( ) cos 0 4cos5 cos 2 cos 3 cos sin 2cos 5 3 cos sin x x x x x x x x x = ộ = + ờ = + ở 0.25 ã ( ) cos 0 , 2 x x k k p = = + p ẻZ ã 3 1 2cos5 3 cos sin cos5 cos sin cos5 cos 2 2 6 x x x x x x x x p ổ ử = + = + = - ỗ ữ ố ứ 0.25 ( ) 5 2 6 24 2 5 2 36 30 6 x x k x k k x kx x k p p p ộ ộ = - + p = - + ờ ờ ẻ ờ ờ p p p ờ ờ = + = - + p ờ ờ ở ở Z Vyptcú ba hnghim ( ) 2 24 2 36 3 x k x k x k k p p p p p = + p = - + = + ẻZ 0.25 3 Tớnh ( ) 2 1 0 x x x x e I dx x e - + = + ũ 1,0 ồ ( ) ( ) 2 1 1 0 0 1 1 x x x x x x x e xe x e I dx dx x e xe - + + = ì = ì + + ũ ũ 0.25 t ( ) . 1 1 x x t x e dt x e dx = + ị = + icn+ 0 1x t = ị = + 1 1x t e = ị = + 0.25 Suyra ( ) 1 1 1 0 1 1 1 1 1 1 1 x x e e x xe x e t I dx dt dt xe t t + + + - ổ ử = ì = ì = - ì ỗ ữ + ố ứ ũ ũ ũ 0.25 Vy ( ) ( ) 1 1 ln ln 1 e I t t e e + = - = - + 0.25 4 a Giiphngtrỡnh: 2 3 6 36 log log log logx x x x + + = 0,5 ồ Phngtrỡnhxỏc nhvimi x R ẻ p dngcụngthc ( ) log log log , 0 , , 1 1 a a b c b c a b c a b = ì < ạ ạ 0.25 Phngtrỡnh 2 3 2 6 2 36 2 log log 2 log log 2 log log 2 logx x x x + ì + ì = ì ( ) 2 3 6 36 log log 2 log 2 1 log 2 0x + + - = ( ) * 3 Do 3 6 36 log 2 log 2 1 log 2 0 + + - > PT ( ) 2 * log 0 1x x = = Vynghimphngtrỡnhl. 0.25 b Tỡmshngkhụngphthucvo x trongkhaitrinnhthcNiu tn 3 2 2 n x x ổ ử + ỗ ữ ố ứ vi 0x ạ ,bit * nẻ Ơ v ( ) 2 1 5 4 9 4 n n n n C C n + + + + - = + 0,5 ồ T githit ( ) ( )( )( ) ( )( )( ) ( ) 2 1 5 4 5 4 3 4 3 2 9 4 9 4 6 6 n n n n n n n n n n C C n n + + + + + + + + + + - = + - = + 15n ị = .Khiú ( ) 15 30 5 15 15 15 3 32 2 3 15 15 0 0 2 2 2 k k k k k k k k x C x C x x x - - = = ổ ử ổ ử + = = ỗ ữ ỗ ữ ố ứ ố ứ ồ ồ 0.25 Shngkhụng phthuc vo x tng ngvi 30 5 0 6 3 k k - = = Vyshngkhụngph thucvo x l 6 6 15 .2C 0.25 5 Cho hỡnh chúp .S ABCD cú ỏy ABCD l hỡnh ch nht vi 3 2AB a AD a = = TớnhtheoathtớchkhichúpS.ABCDvtớnhkhongcỏchgiahaingthng SC v AD . 1,0 ồ (Tvhỡnh).K ( ) HK CD K CD ^ ẻ .Khiú: ( ) CD HK CD SHK CD SK CD SH ^ ỹ ị ^ ị ^ ý ^ ỵ . Vygúcgia ( ) SCD v ( ) ABCD lgúc ã 0 60SKH = 0.25 Trongtamgiỏ cvuụng 0 : tan 60 2 3SHK SH HK a = = .Thtớchkhụi chúp .S ABC D l 3 . 1 1 . .3 .2 .2 3 4 3 3 3 S ABCD ABCD V S SH a a a a = = = 0.25 Vỡ ( ) ( ) ( ) ( ) , , .SBC AD d AD SC d A SBC ị = Trong ( ) SAB k AI SB ^ ,khiú ( ) BC AB BC SAB BC AI BC SH ^ ỹ ị ^ ị ^ ý ^ ỵ m ( ) SB AI AI SBC ^ ị ^ 0.25 Vy ( ) ( ) ( ) 2 2 . 2 3.3 6 39 , , 13 12 SH AB a a a d AD SC d A SBC AI SB a a = = = = = + 0.25 6 Trongmt phngta Oxy cho tamgiỏccõn ABC cúỏy BC nmtrờnng thng :2 5 1 0d x y - + = , cnh AB nmtrờnngthng :12 23 0d x y  - - = .Vit phngtrỡnh ngthng AC bitnúiquaim ( ) 31M . 1,0 ồ VTPTca ( ) : 2 5 BC BC n = - r ,VTPT ca ( ) : 12 1 AB AB n = - r , VTPTca ( ) ( ) 2 2 : , 0 AC AC n a b a b = + > r .Ta cú ã ã 0 90ABC ACB = < ã ã ( ) ( ) cos cos cos , cos , AB BC BC CA ABC ACB n n n n ị = = r r r r 0.25 4 2 2 2 2 . . 2 5 145 9 100 96 0 . . 5 AB BC CA BC AB BC CA BC n n n n a b a ab b n n n n a b - = = - - = + r r r r r r r r 12 0 9 8 0a b a b + = - = 0.25 Vi 12 0a b + = Chn 12, 1a b = = - thỡ ( ) 12 1 CA n AB AC = - ị r (loi) 0.25 Vi 9 8 0a b - = Chn 8, 9a b = = nờn ( ) ( ) :8 3 9 1 0AC x y - + - = : 8 9 33 0AC x y ị + - = 0.25 7 Trongkhụnggian Oxyz ,cho ( ) ( ) ( ) 100 , 020 , 003A B C .Vitphngtrỡnhmt phng ( ) P iqua ,O C saochokhongcỏcht A n ( ) P bngkhongcỏcht B n ( ) P . 1,0 ồ Do ( ) P cỏchu A v B nờnhoc ( ) P AB hoc ( ) P iquatrungim .AB 0.25 Khi ( ) P AB ( ) ( ) ( ) ( ) ( ) 000 : 2 0 , 630 2 10 qua O P P x y vtpt n AB OC n ỡ ù ị ị - = ớ ộ ự = - ị = - ù ở ỷ ợ uuur uuur r r 0.25 Khi ( ) P iquatrungim 1 10 2 I ổ ử ỗ ữ ố ứ ca .AB Ta cú : ( ) ( ) ( ) ( ) 0 0 000 : 2 0 3 , 3 0 210 2 qua O P P x y vtpt n IC OC n ỡ ù ị ị + = ớ ổ ử ộ ự = ị = ỗ ữ ù ở ỷ ố ứ ợ uur uuur r r 0.25 Vyphngtrỡnhmtphng ( ) ( ) : 2 0, : 2 0P x y P x y - = + = 0,25 8 Giih phngtrỡnh: ( ) ( ) ( ) 2 2 2 2 3 5 2 2 2 2 5 3 1 2 1 2 12 7 8 2 5 2 x xy y x xy y x y x y x y xy x ỡ + + + + + = + ù ớ + + + + + = + + ù ợ . 1,0 ồ iukin: 2 2 2 2 5 2 2 0 2 2 5 0 2 1 0 2 1 0 x xy y x xy y x y x y ỡ + + ù + + + + ớ ù + + ợ . Khihcú nghim ( ) ( ) 1 0x y x y ắắđ + 0.25 Tathy ( ) 2 2 5 2 2 2 *x xy y x y + + + dubngkhi x y = thtvy ( ) ( ) ( ) 2 2 2 2 * 5 2 2 2 0x xy y x y x y + + + - luụnỳngvimi ,x y ẻĂ Tngt ( ) 2 2 2 2 5 2 **x xy y x y + + + dubngkhi x y = T ( ) ( ) ( ) ( ) ( ) 1 1 2 2 2 2 * & ** 5 2 2 2 2 5 3VT x xy y x xy y x y VP ị = + + + + + + = Dungthcxy rakhi x y = ( ) 3 0.25 5 Th ( ) 3 vo ( ) 2 tac: 2 3 3 1 2 19 8 2 5x x x x + + + = + + ( ) 4 iukin 1 3 x - ( ) 4 ( ) ( ) ( ) 2 3 2 1 3 1 2 2 19 8 0x x x x x x - + + - + + + - + = ( ) ( ) ( ) ( ) 2 2 2 2 2 3 3 2 2 0 1 3 1 2 2 19 8 19 8 x x x x x x x x x x x x - - - + + ì = + + + + + + + + + 0.25 ( ) ( ) ( ) ( ) 2 2 2 3 3 0 1 1 2 2 0 1 3 1 2 2 19 8 19 8 x x x x x x x x > ộ ự ờ ỳ ờ ỳ - + + ì = ờ ỳ + + + + + + + + + ờ ỳ ờ ỳ ở ỷ 144444444444424444444444443 ( ) ( ) 3 2 3 0 0 0 1 1 x y x x x y ộ = ắắđ = - = ờ = ắắđ = ờ ở . Tha móniukin Vyh phng trỡnh cúhainghim ( ) ( ) ( ) ( ) 00 & 11x y x y = = 0,25 9 Chobasthcdng , ,a b c thamón 2 2 2 3a b c + + = . Tỡmgiỏ trinhnhõtcabiuthc ( ) 1 1 1 8 5S a b c a b c ổ ử = + + + + + ỗ ữ ố ứ 1,0 ồ Nhn xột: ( ) 2 5 3 23 8 , 1 2 a a a + + vimi 0 3a < < dubngkhi 1a = thtvy ( ) ( ) 2 2 3 2 5 3 23 8 3 16 23 10 0 1 3 10 0 2 a a a a a a a a + + - + - Ê - - Ê luụnỳng vimi0 3a < < dubngkhi 1a = 0.25 Tngt ( ) 2 5 3 23 8 , 2 2 b b b + + dubngkhi 1b = ( ) 2 5 3 23 8 , 3 2 c c c + + dubngkhi 1c = 0.25 T ( ) ( ) ( ) ( ) ( ) 2 2 2 1 , 2 & 3 3 69 1 1 1 8 5 39 2 a b c S a b c a b c + + + ổ ử ắắắắđ = + + + + + = ỗ ữ ố ứ Dubngxyrakhi 1a b c = = = 0.25 Vygiỏtrnhnht ca 39S = tckhivchkhi 1a b c = = = 0,25 Chỳý: tỡmravphica(1)ta sdngphng phỏp tiptuyn . = + + + + + ỗ ữ ố ứ 1,0 ồ Nhn xột: ( ) 2 5 3 23 8 , 1 2 a a a + + vimi 0 3a < < dubngkhi 1a = thtvy ( ) ( ) 2 2 3 2 5 3 23 8 3 16 23 10 0 1 3 10 0 2 a a a a a a a a + + - + -. Ê - - Ê luụnỳng vimi0 3a < < dubngkhi 1a = 0.25 Tngt ( ) 2 5 3 23 8 , 2 2 b b b + + dubngkhi 1b = ( ) 2 5 3 23 8 , 3 2 c c c + + dubngkhi 1c = 0.25 T ( ) ( ) ( ) ( ) ( ) 2 2. phngta Oxy cho tamgiỏccõn ABC cúỏy BC nmtrờnng thng :2 5 1 0d x y - + = , cnh AB nmtrờnngthng :12 23 0d x y  - - = .Vit phngtrỡnh ngthng AC bitnúiquaim ( ) 31M . 1,0 ồ VTPTca ( ) : 2 5 BC BC