đề thi thử môn toán THPT quốc gia 2016 có đáp án chi tiết

http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! DeThiThu.Net Truy cp http://dethithu.net thng xuyờn cp nht nhiu Thi Th THPT Quc Gia, ti liu ụn thi THPT Quc Gia cỏc mụn Toỏn, Lý, Húa, Anh, Vn, Sinh , S, a c DeThiThu.Net cp nht hng ngy phc v s t! Like Fanpage Thi Th THPT Quc Gia - Ti Liu ễn Thi: http://facebook.com/dethithu.net cp nht nhiu thi th v ti liu ụn thi hn Tham gia Group: ễn Thi H Toỏn - Anh cựng hc tp, ụn thi: http://facebook.com/groups/onthidhtoananhvan Thi Th K THI THPT QUC GIA MễN TON Web: http://dethithu.net Mail: dethithu.net@gmail.com Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Mc lc s 06 s 07 s 08 s 09 s 10 P N ỏp ỏn s 06 ỏp ỏn s 07 13 ỏp ỏn s 08 16 ỏp ỏn s 09 20 ỏp ỏn s 10 24 Cỏc thi th v ỏp ỏn s 1, 2, 3, , cỏc bn vui lũng xem ti: http://dethithu.net Nhng thi th ú website ó ng riờng r t trc nờn khụng gp chung vo thi th ny : http://dethithu.net/de-thi-thu-mon-toan-thpt-quoc-gia-nam-2016/ Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! thi th s http://dethithu.net THI TH I HC (THPT QG) MễN: TON thi th s Thi gian lm bi: 180 phỳt Cõu 1.(2 im) Cho hm s y = x x + a) Kho sỏt s bin thiờn v v th (C ) ca hm s b) Tỡm m phng trỡnh x x + = m cú ba nghim thc phõn bit Cõu 2.(1 im) http://dethithu.net a) Gii phng trỡnh: sin x + cos( x ) = b) Tớnh mụun ca s phc z bit z = + 2i + i + 1+ i Cõu 3.(0,5 im) Gii phng trỡnh: log 52 x + log x = ( )( ) y x + y y +1 = Cõu 4.(1 im) Gii h phng trỡnh: x 2 x + x y + xy = y ( ) Cõu 5.(1 im) Tớnh tớch phõn: I = + cos x dx http://dethithu.net Cõu 6.(1 im) Cho lng tr ng ABC.ABC cú ỏy ABC l tam giỏc vuụng ti A,AB=2a,AC=a,AA = 3a Tớnh th tớch lng tr v khong cỏch gia hai ng thng AB v BC Cõu 7.(1 im) Trong mt phng vi h ta Oxy cho hỡnh ch nht ABCD cú nh B thuc ng trũn x + y = 10 ,nh C thuc ng thng x + y = Gi M l hỡnh chiu vuụng gúc ca B lờn AC Bit rng cỏc im N ; ,P (1;1) ln lt l trung im ca AM ,CD ng thi B cú honh dng,C cú tung 5 http://dethithu.net õm.Tỡm ta cỏc nh ca hỡnh ch nht Cõu 8.(1 im) Trong khụng gian vi h ta Oxyz cho mt cu (S ) : x + y + z x y + z 15 = 0, mt phng (P): x y + z + 13 = Tỡm tõm v bỏn kớnh ca mt cu (S ) Vit phng trỡnh mt phng (Q) song song vi mt phng (P) ng thi tip xỳc vi (S ) http://dethithu.net Cõu 9.(0,5 im) Gi A l hp cỏc s t nhiờn cú ch s ụi mt khỏc c to t cỏc ch s 0,1,2,3,4,5,6 Chn ngu nhiờn mt s t A Tớnh xỏc sut s c chn cú cỏc ch s khỏc ch s v http://dethithu.net tng cỏc ch s l Cõu 10.(1 im) Cho ba s thc a,b,c tha món: log a + log b + log 32 c = Tỡm giỏ tr ln nht ca biu thc P = 1+ a + 1+ b + 1+ c2 3 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! http://dethithu.net THI TH K THI THPT QUC GIA s Mụn : TON Thi gian lm bi 180 phỳt x+2 x1 a) Kho sỏt s bin thiờn v v th (C) ca hm s ó cho b) Tỡm m ng thng d : y = x + m ct th (C) ti hai im phõn bit http://dethithu.net Cõu (1,0 im) cos 2x + (1 + cos2 x) tan x = + sin2 x a) Gii phng trỡnh cos x b) Tỡm hp cỏc im biu din s phc z tha |z i| = |2z 2i| Cõu (2,0 im) Cho hm s y = Cõu (0,5 im) Tỡm giỏ tr ln nht v giỏ tr nh nht ca hm s y = x (x2 x 1) trờn on [0; 2] http://dethithu.net 1 x =0 + +x x x3 y Cõu (1,0 im) Gii h phng trỡnh 3x + = y Cõu (1,0 im) Tớnh tớch phõn I = x2 ln (x 1) dx http://dethithu.net Cõu (1,0 im) Cho hỡnh chúp S.ABCD cú ỏy ABCD l hỡnh bỡnh hnh, mt phng (SBD) vuụng gúc vi ỏy, cỏc ng thng SA, SD hp vi ỏy mt gúc 300 Bit AD = a 6, BD = 2a v gúc ADB = 450 Tớnh th tớch chúp S.ABCD v khong cỏch t nh C n mt phng http://dethithu.net (SAD) theo a Cõu (1,0 im) Trong mt phng vi h ta Oxy, im M (2; 1) v hai ng thng d1 : x y + = 0, d2 : x + 2y = Vit phng trỡnh ng thng qua M v ct d1 , d2 ln lt ti A, B cho M l trung im AB http://dethithu.net x1 y+3 Cõu (1,0 im) Trong khụng gian vi h ta Oxyz, cho ng thng d : = = z3 v mt phng (P ) : 2x + y 2z + = Vit phng trỡnh ng thng nm (P ), ct v vuụng gúc vi d http://dethithu.net Cõu (0,5 im) Cú 14 tm th c ỏnh s t n 14 Chn ngu nhiờn tm th Tớnh xỏc sut tm th c chn cú tm th mang s l,4 tm th mang s chn ú cú nht mt tm th mang s chia ht cho http://dethithu.net Cõu 10 (1,0 im) Cho cỏc s thc dng a, b, c tha a + b + c = Chng minh rng : 2ab 3bc 2ca + + c + ab a + bc b + ca http://dethithu.net Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! http://dethithu.net THI TH K THI THPT QUC GIA s Mụn : TON Thi gian lm bi 180 phỳt Cõu (2,0 im) Cho hm s y = x3 + 3x2 a) Kho sỏt s bin thiờn v v th (C) ca hm s ó cho b) Tỡm m ng thng d : y = m (x + 1) ct th (C) ti ba im phõn bit M (1; 0) , A, B cho M A = 2M B http://dethithu.net Cõu (1,0 im) a) Gii phng trỡnh sin 2x + cos 2x cos 4x = 3i 3+i + b) Tỡm phn thc, phn o v mụ un ca s phc z = 1i 2i x+8 2x+3 Cõu (0,5 im) Gii phng trỡnh 3.243 x+8 = 32 x+2 Cõu (1,0 im) Gii h phng trỡnh 2x2 y + y = 2x4 + x6 (x + 2) y + = (x + 1)2 http://dethithu.net Cõu (1,0 im) Tớnh th tớch trũn xoay to thnh quay quanh Ox hỡnh phng gii hn bi th hm s y = sin x, trc honh v hai ng thng x = 0, x = Cõu (1,0 im) Cho hỡnh chúp S.ABCD cú ỏy ABCD l hỡnh thoi cnh a; gúc BCD = 600 ; cnh SA vuụng gúc vi mt phng (ABCD) Hai mt phng (SCB) v (SCD) vuụng gúc vi Tớnh th tớch chúp S.ABCD v khong cỏch t C n mt phng (SBD) Cõu (1,0 im) Trong mt phng vi h ta Oxy, cho tam giỏc ABC cú tõm ng trũn ngoi tip tam giỏc ABC l I(2; 1) v tha iu kin AIB = 900 , chõn ng cao k t A n BC l D(1; 1), ng thng AC i qua im M (1; 4) Tỡm ta cỏc nh A, B bit rng nh A cú honh dng http://dethithu.net x=1+t y = t Cõu (1,0 im) Trong khụng gian vi h ta Oxyz, cho hai ng thng d1 : z=2 y1 z x3 = = Chng minh d1 v d2 chộo Vit phng trỡnh mt phng (P ) v d2 : cha d1 v song song vi d2 http://dethithu.net Cõu (0,5 im) Gi A l hp cỏc s cú ch s khỏc c lp t cỏc ch s 1, 2, 3, 4, Chn ngu nhiờn ba s t A, tớnh xỏc sut ba s c chn cú ỳng mt s cú mt ch s http://dethithu.net Cõu 10 (1,0 im) Cho cỏc s thc x, y tha x2 + y + xy = Tỡm giỏ tr ln nht v giỏ tr nh nht ca biu thc P = x3 + y 3x 3y Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! http://dethithu.net THI TH K THI THPT QUC GIA s Mụn : TON Thi gian lm bi 180 phỳt 2x + x1 a) Kho sỏt s bin thiờn v v th (C) ca hm s b) Tỡm m ng thng d i qua A(2; 2) v cú h s gúc m ct th (C) ti hai im phõn bit thuc hai nhỏnh ca (C) http://dethithu.net Cõu (1,0 im) sin + cos a) Cho cot = Tớnh giỏ tr ca biu thc A = 2 sin cos b) Gii phng trỡnh z + 2z + z 18 = trờn hp cỏc s phc C Cõu (2,0 im) Cho hm s y = x+1 Cõu (0,5 im) Gii bt phng trỡnh log 2x1 > Cõu (1,0 im) Gii h phng trỡnh: http://dethithu.net x3 x2 + x = y y y + x3 + 4x2 + = y e x + ln x dx x2 Cõu (1,0 im) Tớnh tớch phõn I = Cõu (1,0 im) Cho hỡnh chúp S.ABCD cú ỏy ABCD l hỡnh vuụng cnh a Mt bờn SAD l tam giỏc u v SB = a Gi E, F ln lt l trung im ca AD v AB Gi H l giao im ca F C v EB Chng minh SEEB, CHSB v tớnh th tớch chúp C.SEB Cõu (1,0 im) Trong mt phng vi h to Oxy, cho tam giỏc ABC cú A(1; 4), tip tuyn ti A ca ng trũn ngoi tip tam giỏc ABC ct BC ti D, ng phõn giỏc ca ADB cú phng trỡnh x y + = 0, im M (4; 1) thuc cnh AC Vit phng trỡnh ng thng AB http://dethithu.net x y+2 Cõu (1,0 im) Trong khụng gian vi h ta Oxyz, cho hai ng thng d1 : = = x1 y6 z z+4 v d2 : = = Tỡm im A trờn d1 , im B trờn d2 cho ng thng AB 2 http://dethithu.net i qua im M (1; 9; 0) Cõu (0,5 im) Mt t cú hc sinh nam v hc sinh n Giỏo viờn chn ngu nhiờn hc sinh lm trc nht Tớnh xỏc sut hc sinh c chn cú c nam v n Cõu 10 (1,0 im) Cho cỏc s thc khụng õm a, b, c tha a + b + c = Tỡm giỏ tr ln nht ca biu thc : ca ab bc + + P = 3a + bc 3b + ca 3c + ab http://dethithu.net Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! http://dethithu.net THI TH K THI THPT QUC GIA s 10 Mụn : TON Thi gian lm bi 180 phỳt Cõu (2,0 im) Cho hm s y = x3 3x + a) Kho sỏt s bin thiờn v v th (C) ca hm s ó cho b) Tỡm im A thuc (C) cho tip tuyn vi (C) ti A ct (C) ti im B khỏc A tha 2013xB + 2014xA = 2012, ú xA , xB ln lt l honh ca A v B http://dethithu.net Cõu (1,0 im) a) Gii phng trỡnh sin 2x (2 cos x 5) + cos 2x + sin x cos x + = b) Tỡm hp cỏc im biu din mt phng phc Oxy ca s phc w = + i z +2 bit rng s phc z tha |z 1| http://dethithu.net Cõu (0,5 im) Tỡm xỏc nh ca hm s y = log2 + log (x2 + 3x) x + x2 2x + = 3y + y + x2 y 3x + 3y + = Cõu (1,0 im) Gii h phng trỡnh Cõu (1,0 im) Tớnh tớch phõn I = xe2x + xex + dx ex + http://dethithu.net Cõu (1,0 im) Cho hỡnh chúp S.ABCD cú SB = SC = SD = AB = BC = CD = DA = a v gúc gia hai mt phng (SAB) v (SAD) bng 900 Tớnh th tớch chúp S.ABCD Cõu (1,0 im) Trong mt phng vi h ta Oxy, cho hỡnh bỡnh hnh ABCD cú gúc ABC nhn, nh A(2; 1) Gi H, K, E ln lt l hỡnh chiu vuụng gúc ca A trờn cỏc ng thng BC, BD, CD Phng trỡnh ng trũn ngoi tip tam giỏc HKE l (C) : x2 + y + x + 4y + = Tỡm ta cỏc nh B, C, D bit H cú honh õm, C cú honh dng v nm trờn ng thng x y = http://dethithu.net x7 = Cõu (1,0 im) Trong khụng gian vi h ta Oxyz, cho hai ng thng : z1 x1 y+2 z5 y2 = v : = = Tỡm ta giao im A ca v Vit phng 2 trỡnh mt phng () cha v http://dethithu.net Cõu (0,5 im) Tỡm h s ca s hng cha x2 khai trin nguyờn dng tha 2Cn0 + 2n+1 n 6560 22 23 Cn + Cn + + Cn = n+1 n+1 x+ 24x n , bit n l s http://dethithu.net Cõu 10 (1,0 im) Cho cỏc s thc dng x, y tha x + y < Chng minh rng : + + x y 1xy 36 Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! ỏp ỏn thi th s P N THANG IM THI TH I HC (THPTQG) s Website: http://dethithu.net Mụn: TON (ỏp ỏn thang im gm trang) Cõu ỏp ỏn a (1,0 im) (2,0 +) Tp xỏc nh D = R im) +) S bin thiờn: Chiu bin thiờn: y ' = x x, y ' = x = x = Gii hn: lim y = + , lim y = x + im 0,25 0,25 x Bng bin thiờn: + http://dethithu.net 0,25 + Hm s ng bin trờn cỏc khong ( ;0) v (2;+ ) ,nghch bin trờn khong (0;2) Hm s t cc i ti x = 0, y C = ,hm s t cc tiu ti x = 2, y CT = +) th th hm s i qua cỏc im (0;1),(1;-1),(2;-3) th i xng qua im I ( 1; -1) 0,25 b (1,0 im) S nghim ca phng trỡnh x x + = m chớnh l s giao im ca th (C ) vi ng thng y = m T th suy phng trỡnh cú nghim thc phõn bit v ch m a (0,5 im) (1,0 Ta cú : sin x + cos( x ) = sin x cos x cos x = cos x(sin x 2) = im) ( sin x = khụng xy ra) cos x = x = + k , k Z http://dethithu.net 0,5 0,5 0,25 0,25 b (0,5 im) Ta cú z = + 2i + i (1 + 2i) (1 i ) + i 3i + i + = + = + 1+ i (1 + i) (1 i ) 2 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 0,25 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! =1 i vy z = 12 + (1) = 0,25 3 (0,5 im) (0,5 k: x > ,Pt log 52 x + log x = (log x 1)(log x + ) = im) x = log x = (TM ) http://dethithu.net x = log x = 25 0,25 0,25 (1,0 k: x im) Ta cú x + x y + xy = y ( x y )(x + xy + y ) = ( x y ) ( x + y )2 + y = [ ] x = y ( x + y ) + y = x = y = khụng tha mn 2 ( ] )( x + 1) = , x (0;1] x )( x + 1) = 3( x + 1) = ( x + + x ) (*) Vi x = y t phng trỡnh u ta cú ( [ x+3 x Khi ú x + Ta thy x = l mt nghim ca phng trỡnh (*) Vi < x < thỡ ( ) x + > cũn ( 0,25 ) x + + x < nờn (*) vụ nghim.Võy (*) cú nghim nht l x = t ú suy h cú nghim nht (x; y) = (1;1) 2 (1,0 Ta cú I = + cos x dx = dx + cos xdx im) 0 ( ) Trong ú: 0,25 http://dethithu.net 2 0 ( ) Xột K = cos xdx = cos x cos xdx = sin x cos xdx t t = sin x suy dt = cos x.dx , x = t = 0, x = (1 2t ) t + t dt = t t + Vy I = + 15 Th tớch lng tr l (1,0 V = AA S AA AB AC ' = ' ABC im) = 3a 2a.a = 3a = 0,25 0,25 dx = x = 0,5 0,25 (1 t ) dt t = ú K = 2 = 15 0,25 0,5 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Gi M v M ' ln lt l chõn ng cao h t A v A' cỏc tam giỏc ABC , A' B ' C ' ta cú B' C ' ( AA' M ' M ) nờn ( AB'C ') ( AA' M ' M ) Trong mp ( AA' M ' M ) h MH AM ' thỡ MH ( AB ' C ' ) Khi ú d ( AB ', BC ) = d ( BC ,( AB 'C ' )) = d (M ,( AB 'C ")) = MH 1 1 1 http://dethithu.net = + = + + 2 2 2 MH MM ' AM MM ' AB AC 1 1 49 6 => = + + = => MH = a Vy d ( AB ', BC ) = a 2 7 9a 4a 36a MH a m Gi Q l trung im BM thỡ PCQN l hỡnh bỡnh hnh nờn NP // CQ,mt khỏc Q l trc tõm (1,0 tam giỏc BNC nờn CQ BN suy BN NP im) Ta cú NP = ; l mt vộct phỏp tuyn ca ng thng BN nờn phng trỡnh ng 5 thng BN l x + + x = x + y + = Ta 5 5 B l nghim ca h x = x + y + = y = x x = 2 = y + = + + = 10 x y x x y = 13 suy B (1;3) vỡ B cú honh dng 0,25 0,25 0,25 0,25 Gi C (1 2c; c ) ta cú CB = (2c;3 c ) , CP = (2c;1 c ) CB CP nờn CP.CB = 4c ( + c )(1 c ) = 5c + 2c = c = c = C cú tung õm nờn C (3;1) Suy D( 1;3) , A(3;1) Vy A(3;1) , B (1;3) , C (3;1) , D( 1;3) http://dethithu.net 15 +1+ + =3 (1,0 Mt cu cú tõm I ;1;2 v bỏn kớnh R = 4 im) Do Mp (Q ) song song vi mp (P ) nờn phng trỡnh cú dng x y + z + D = 0, D 13 (Q ) tip xỳc vi (S ) nờn d ( I ,( Q ) ) = R => 11 + D =3 D = D = 13 D = , D 13 nờn ta ly D = vy phng trỡnh cn tỡm l 2x y + 2z = 0,25 0,25 0,25 0,25 0,25 0,25 Ký hiu abc l mt s bt k thuc A 0,25 Ta thy a cú cỏch chn (a 0) ,b cú cỏch chn (b a ) tng t c cú cỏch chn (0,5 http://dethithu.net Vy s phn t ca A l 6.6.5 = 180 im) Xột s abc cú cỏc ch s khỏc ch s v tng cỏc ch s l t cỏc ch s ó cho ta chon c c b s {a; b; c}l {a; b; c} = {1;3;4}v {a; b; c} = {1;2;5} T mi b trờn ta to c 3!= s nờn ta cú 0,25 10 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! t sin x + cos x = t |t| ọ sin x cos x = t2 , phng trỡnh (2) tr thnh : t2 = t2 + 2t = t+ ủ t=1 t = (loi) x = k2 ó Vi t = sin x + cos x = sin x + = x = + k2 (loi) 2 Vy phng trỡnh cú nghim x = + k, x = k2 (k Z ) Cõu 2b (0,5 im) Gi z = x + yi ( x, y R ), ta cú : http://dethithu.net |z i | = |2z 2i | | x + yi i | = |2 ( x yi ) 2i | ( x 2)2 + (y 1)2 = 4x2 + (2y + 2)2 3x2 + 3y2 + 4x + 10y = 10 x + y2 + x + y = 3 Vy hp cỏc im biu din s phc z l ng trũn tõm ; , bỏn kớnh R = 3 ầ Cõu (0,5 im) ủ x=1 x = (loi) Ta cú y(0) = 1, y(1) = e, y(2) = e2 , ú max y = y(2) = e2 , y = y(1) = e o hm y = ex ( x2 x 1) + ex (2x 1) = ex ( x2 + x 2); y =0 [0;2] [0;2] Cõu (1,0 im) iu kin x = 0, y = H ó cho tng ng vi : x + =2 x2 y 3x + = y x + Tr theo v (1) v (2) ta cú : x2 + ầ x 1 +2 = x x y y y http://dethithu.net x +2 = x y 3x + = y 2x + ồ2 (1) (2) x = = x y x y = x x = = x+ y x y x x = x thay vo (1) c 4x2 + = x = y = y x x Vi = x + thay vo (1) c 4x2 + = (vụ nghim) y x x http://dethithu.net Vy h cú hai nghim ( x; y) = (1; 1) v ( x; y) = (1; 1) Vi Cõu (1,0 im) Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 13 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! t đ dx du = u = ln( x 1) x1 , ta cú : x3 dv = x2 dx v= x3 ln( x 1) I= 3 = Vy I = 125 ln 3 http://dethithu.net 125 ln x3 dx = x1 3 x3 x2 + + x + ln( x 1) 124 ln 35 = 5ầ dx x +x+1+ x1 124 ln 35 http://dethithu.net Cõu (1,0 im) ữ = a 6.2a sin 450 = 2a2 Ta cú S ABCD = 2SADB = DA.DB sin ADB Gi H l hỡnh chiu ca S trờn BD SH ( ABCD ) (vỡ (SBD )( ABCD )) Khi ú H A, HD ln lt l hỡnh chiu ca SA, SD lờn ( ABCD ) ữ = SDH ữ ln lt l gúc ca SA, SD vi ( ABCD ) Do ú SAH ữ = SDH ữ = 300 H A = HD Theo gi thit ta cú SAH AD Suy tam giỏc H AD vuụng cõn ti H H A = HD = = a Trong tam giỏc SH A vuụng ti H cú SH = H A tan 300 = a = a 2a Vy th tớch chúp S.ABCD l VS.ABCD = S ABCD SH = 3 S http://dethithu.net I A B H K D C BD d( H, (SAD )) = d( H, (SAD )) HD Gi K l trung im AD HK AD AD (SHK ) Gi I l hỡnh chiu ca H trờn SK H I (SAD ) H I = d( H, (SAD )) a Tam giỏc H AD vuụng ti H nờn HK = AD = 2 1 1 a 15 Trong SHK cú = + = + HI = H I2 HS2 HK2 a 3a 2a Vy d(C, (SAD )) = d( H, (SAD )) = H I = 3 http://dethithu.net Cõu (1,0 im) Ta cú A d1 A(t; t + 2); M l trung im AB nờn B(4 t; t) Khi ú B d2 nờn t 2t = t = A (1; 3) , B (3; 1) AB = (2; 4) ng thng cn tỡm qua M(2; 1) v cú mt vect phỏp tuyn n = (2; 1) Vy ng thng cn tỡm cú phng trỡnh 2( x 2) + (y 1) = 2x + y = Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 14 Ta cú d(C, (SAD )) = d( B, (SAD )) = http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Cõu (1,0 im) Ta giao im A ca d v ( P) l nghim h x y+3 z3 = = 2x + y 2z + = x =0 y = z=4 A(0; 1; 4) http://dethithu.net Mt phng ( P) cú mt vect phỏp tuyn n( P) = (2; 1; 2) = (1; 2; 1) ng thng d cú mt vect ch phng u dợ ú = (5; 0; 5) lm mt vect ch phng n, u ng thng i qua A(0; 1; 4) v nhn ( P) x = 5t Vy cú phng trỡnh y = z = + 5t d Cõu (0,5 im) = 3432 Phộp th l chn ngu nhiờn tm th 14 tm th nờn ta cú || = C14 Gi A l bin c "trong tm th c chn cú tm th mang s l, tm th mang s chn ú cú nht mt tm th mang s chia ht cho 5", ta cú hai trng hp sau : TH1 : Chn th chia ht cho l th ghi s Ta cn chn thờm th ghi s l th ghi s l (tr th ghi s 5) v th ghi s chn th ghi s chn (tr th ghi s 10) Do ú trng hp ny cú C62 ì C64 = 225 cỏch chn TH2 : Chn th chia ht cho l th ghi s 10 Ta cn chn thờm th ghi s l th ghi s l (tr th ghi s 5) v th ghi s chn th ghi s chn (tr th ghi s 10) Do ú trng hp ny cú C63 ì C63 = 400 cỏch chn Do ú s kt qu thun li cho bin c A l | A | = 225 + 400 = 625 625 | A | = Vy xỏc sut ca bin c A l P( A) = || 3432 Cõu 10 (1,0 im) Bt ng thc cn chng minh tng ng vi : http://dethithu.net 2ab 3bc 2ca + + (c + a) (c + b) ( a + b) ( a + c) (b + c) (b + a) 2ab (1 c) + 3bc (1 a) + 2ca (1 b) (1 a ) (1 b ) (1 c ) ab + 4bc + ca 16abc 1 + + 16 a b c p dng bt ng thc 1 + x y 1 + + a b c c : x+y 4 + a b+c http://dethithu.net 16 = 16 a+b+c Ta cú bt ng thc cn chng minh Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 15 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net ỏp ỏn s Cõu 1a (1,0 im) http://dethithu.net Tp xỏc nh : D = R S bin thiờn : + Gii hn ti vụ cc : lim y = ; lim y = + x + y x + Bng bin thiờn : y = 3x2 + 6x = x y + y 3x ( x 2); y 0 + 0 =0 ủ x=0 x=2 x O + U Hm s ng bin trờn (0; 2) Hm s nghch bin trờn (; 0) v (2; +) Hm s t cc i ti x = 2; yC = Hm s t cc tiu ti x = 0; yCT = th : http://dethithu.net + Ct Oy ti (0; 4) + Nhn im un U (1; 2) lm tõm i xng Cõu 1b (1,0 im) Phng trỡnh honh giao im ca d v (C ) l : 2 x + 3x = m( x + 1) ( x + 1)( x 4x + + m) = ủ x = x2 4x + + m = t f ( x ) = x4 4x + + m cú = m v f (1) = m + Do ú vi m < v m = thỡ d ct (C ) ti ba im phõn bit : M(1; 0), A( x1 ; m( x1 + 1)), B( x2 ; m( x2 + 1)) đ x1 + x2 = Trong ú theo nh lý vi-ột ta cú (1) x1 x2 = m + ằ Ta cú MA = ( x1 + 1; m ( x1 + 1)) MA = | x1 + 1|ằ + m2 MB = ( x2 + 1; m ( x2 + 1)) MB = | x2 + 1| + m2 ủ x1 = 2x2 + 2 Li cú MA = 2MB | x1 + 1| + m = | x2 + 1| + m x1 = 2x2 x1 = http://dethithu.net Vi x1 = 2x2 + thay vo (1) ta cú x2 = m = x1 = 11 Vi x1 = 2x2 thay vo (1) ta cú x2 = m = 81 Vy m = hoc m = 81 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 16 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Cõu 2a (0,5 im) http://dethithu.net Ký hiu phng trỡnh ó cho l (1) ta cú : ọ (1) sin 2x + cos 2x cos2 2x sin2 2x = sin 2x sin 2x + = (1 cos 2x )2 sin x cos x sin 2x + = 4sin4 x sin x sin xcos2 x + cos x 2sin3 x = sin x = 2sin3 x sin xcos2 x cos x = sin x = 2tan3 x 3tan2 x tan x = sin x = tan x = http://dethithu.net x = k (k Z ) x = + k Vy phng trỡnh cú nghim x = k, x = + k (k Z ) Cõu 2b (0,5 im) ọ ọ i (1 + i ) + i (i ) 2+ + = i Ta cú z = i2 2i2 2 2+ , phn o ca z l v |z| = Vy phn thc ca z l 2 7+4 ằ + = + 4 Cõu (0,5 im) iu kin x = 8, x = Phng trỡnh ó cho tng ng vi : 3 10x +15 x +8 = 32 2x +16 x +2 41x +68 4x +32 =3 x = 12 41x + 68 = 62 4x + 32 x+2 x= 41 12 x +2 62 41 http://dethithu.net Kt hp iu kin phng trỡnh cú nghim x = 4, x = Cõu (1,0 im) Xột h 2x2 y + y3 = 2x4 + x6 ằ phng trỡnh ( x + 2) y + = ( x + 1)2 ọ (1) 2x2 y x2 + y3 x2 2x yx y x2 ọ ọ + yx ọ3 ọ =0 ầ + y + x2 ủ y=x x=y=0 ồ2 ọ y2 + x y + x = ọ 2x2 + y2 + x2 y + x4 = y = x2 2x2 (1) , ta cú : (2) + x4 = http://dethithu.net Vi x = y = thay vo (2) khụng tha Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 17 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Vi y= x2 thay vo (2) ta cú ( x + 2) x2 + = x2 + 2x + () t x2 + = t, (t 1), phng trỡnh () tr thnh : ( x + 2)t = t + 2x t(t x ) 2(t x ) = (t x )(t 2) = ủ t=2 t=x Vi t = x2 + = x = y = http://dethithu.net Vi t = x x2 + = x (vụ nghim) ọ ọ Vy h cú hai nghim ( x; y) = 3; v ( x; y) = 3; Cõu (1,0 im) Th tớch trũn xoay cn tớnh l : sin xdx = 2 V= 0 (1 cos 2x ) dx = Vy th tớch trũn xoay cn tớnh l V = ầ x sin 2x 2 = http://dethithu.net Cõu (1,0 im) Theo gi thit ABCD l hỡnh thoi v ữ BCD = 600 BCD l tam giỏc u a2 Do ú BD = a; AC = a 3, suy din tớch ABCD l S ABCD = AC.BD = 2 BD AC http://dethithu.net Ta cú BD (SAC ) BD SC BD SA Gi O = AC BD, (SAC ), k OMSC, M SC SC ( MBD ) a Do ú BMD l gúc gia (SCB) v (SCD ) BMD = 900 OM = BD = 2 a 2a SA AC AC.OM a Ta cú SAC OMC = = SA = = 2 2 3a a OM MC OC OM a3 Do ú th tớch chúp S.ABCD l VS.ABCD = SA.S ABCD = S M H C B O A D Ta cú O l trung im AC nờn d (C, (SBD)) = d ( A, (SBD )) AH SO Trong (SAC ), k AH SO, H SO, ta cú AH (SBD ) AH = d ( A, (SBD )) AH BD 1 a Trong tam giỏc SAO vuụng ti A cú = + = + = AH = AH AS2 AO2 3a2 3a2 a2 a http://dethithu.net Vy khong cỏch t C n (SBD ) l d (C, (SBD )) = AH = Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 18 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Cõu (1,0 im) = 900 ữ Ta cú AIB ACB = 450 hoc ữ ACB = 1350 ữ = 450 , ú tam giỏc ACD vuụng cõn ti D nờn DA = DC T ú suy ACD Li cú I A = IC nờn ID AC hay AC nhn ID = (1; 2) lm mt vect phỏp tuyn Mt khỏc AC i qua M (1; 4) nờn cú phng trỡnh x 2y + = Ta cú A AC (2t 9; t) DA = (2t 8; t + 1) DA = 5t2 30t + 65 | + + 9| Li cú DA = 2d( D, AC ) = = 10 ủ t=1 T ú suy 5t 30t + 65 = 10 http://dethithu.net t=5 Vỡ im A cú honh dng nờn A(1; 5) ng thng DB i qua D (1; 1) v nhn DA = (2; 6) lm mt vect phỏp tuyn Do ú DB cú phng trỡnh 2( x + 1) + 6(y + 1) = x + 3y + = Ta cú B DB B(3m 4; m) IB = (3m 2; m 1); I A = (3; 4) = 900 nờn Vỡ AIB I A IB = 3(3m 2) + 4(m 1) = m = B(2; 2) Vy A(1; 5) v B(2; 2) http://dethithu.net Cõu (1,0 im) ng thng d1 i qua M1 (1; 1; 2) v cú mt vect ch phng u1 = (1; 1; 0) ng thng d2 i qua M2 (3; 1; 0) v cú mt vect ch phng u2 = (1; 2; 1) ợ ú ợ ú Ta cú u1 , u2 = (1; 1; 1) , M1 M2 = (2; 2; 2) u1 , u2 M1 M2 = = Do ú d1 v d2 l hai ng thng chộo (pcm) Mt phng ( P) cha d1 nờn i qua M1 (1;ợ1; 2).ú Hn na ( P) song song vi d2 nờn nhn u1 , u2 = (1; 1; 1) lm mt vect phỏp tuyn Vy ( P) cú phng trỡnh 1( x 1) 1(y + 1) + 1(z 2) = x + y z + = Cõu (0,5 im) http://dethithu.net S phn t ca A l A5 = 60 S phn t ca A khụng cú ch s l A34 = 24 S phn t ca A khụng cú mt ch s l 60 24 = 36 = 34220 Phộp th l chn ngu nhiờn ba s t A nờn || = C60 Gi A l bin c "ba s c chn cú ỳng mt s cú mt ch s 4" C = 9936 Ta cú s kt qu thun li cho A l | A | = C36 24 9936 2484 | A | Vy xỏc sut bin c A l P ( A) = = = 34220 8555 || Cõu 10 (1,0 im) http://dethithu.net (x + y )2 ( x + y)2 x + y Khi ú P = ( x + y)3 3( x + y) xy 3( x + y) = ( x + y)3 3( x + y)( xy + 1) Hay P = ( x + y)3 3( x + y)[( x + y)2 2] = 2( x + y)3 + 6( x + y) Xột hm s f (t) = 2t3 + 6t trờn [2; 2] cú f (t) = 6t2 + 6; f (t) = t = Khi ú f (2) = 4, f (1) = 4, f (1) = 4, f (2) = Do ú max f (t) = f (2) = f (1) = 4; f (t) = f (1) = f (2) = T gi thit ta cú ( x + y)2 = xy [2;2] [2;2] Vy P t giỏ tr ln nht bng ( x; y) = (1; 1), ( x; y) = (2; 1), ( x; y) = (1; 2) V P t giỏ tr nh nht bng ( x; y) = (1; 1), ( x; y) = (2; 1), ( x; y) = (1; 2) Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 19 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net ỏp ỏn s Cõu 1a (1,0 im) Tp xỏc nh : D = R \{1} http://dethithu.net S bin thiờn : + Gii hn, tim cn : lim y = lim y = tim cn ngang l y = x + x lim y = ; lim+ y = + tim cn ng l x = x x + Bng bin thiờn : y = < 0, x D ( x 1)2 x y y y + + I 12 O Hm s nghch bin trờn (; 1) v (1; +) Hm s khụng cú cc tr th : ầ + Ct Oy ti (0; 1) v ct Ox ti ; x + Nhn giao im I (1; 2) ca hai tim cn lm tõm i xng Cõu 1b (1,0 im) ng thng d qua A(2; 2) v cú h s gúc m nờn cú phng trỡnh dng y = m( x + 2) + Phng trỡnh honh giao im ca d v (C ) l : http://dethithu.net đ 2x + x=1 = m ( x + 2) + mx2 + mx 2m = x1 t f ( x ) = mx2 + mx 2m cú = 9m2 + 12m ng thng d ct (C ) ti hai im phõn bit v ch : a =0 >0 f (1) = m =0 9m2 + 12m > = m>0 m< Gi s d ct (C ) ti hai im phõn bit cú honh x1 , x2 ( x1 < x2 ) 2m http://dethithu.net Theo nh lý vi-et ta cú x1 + x2 = 1, x1 x2 = m Khi ú d ct (C ) ti hai im thuc hai nhỏnh phõn bit v ch : x1 < < x2 ( x1 1) ( x2 1) < x1 x2 ( x1 + x2 ) + < 2m + + < m > (tha món) m Vy vi m > thỡ d ct (C ) ti hai im thuc hai nhỏnh phõn bit Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 20 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Cõu 2a (0,5 im) + cot = 13 = Ta cú A = cot 2 4+ Cõu 2b (0,5 im) Phng trỡnh ó cho tng ng vi : http://dethithu.net ọ z=2 z = i Vy phng trỡnh ó cho cú nghim phc z = 2, z = i (z 2) z2 + 4z + = Cõu (0,5 im) x+1 > x > Khi ú bt phng trỡnh ó cho tng ng vi : iu kin 2x x < http://dethithu.net x+1 < 0, t [0; +) Suy hm s f (t) luụn ng bin trờn (0; +), ú () f ( x ) = f (u) x = u Vi x = u y = x2 + thay vo (2) c x=0 ọ x4 x3 2x2 = x2 x2 x = x=2 x = (loi) http://dethithu.net Vi x = y = 1; vi x = y = Vy h cú hai nghim ( x; y) = (0; 1) v ( x; y) = (2; 5) ọ2 x3 + 4x2 + = x2 + Cõu (1,0 im) e Ta cú I = dx + x u = ln x dx = dx x2 t e ln x dx = ln | x ||1e + x = dx x x v = du ln x dx = + x2 e ln x dx x2 , ta cú : http://dethithu.net e e x3 I = 1+ ln x e x3 e3 x3 dx = + x e = 2e3 + 10 http://dethithu.net 2e3 + 10 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 21 Vy I = http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Cõu (1,0 im) a Tam giỏc SAD u cnh A nờn SE AD v SE = a Tam giỏc AEB vuụng ti A cú EB = AB2 + AE2 = Nhn thy SE2 + EB2 = SB2 nờn SEB vuụng ti E SE EB (pcm) SE EB Ta cú SE( ABCD ) SECH (1) SE AB http://dethithu.net = BCF Ta cú ABE = BCF ABE = 900 CH EB (2) ữ ữ ữ Xột BHF cú BFH + FBH = BFH + BCF T (1) v (2) ta cú CH (SEB) CH SB (pcm) S F A B H E D C 1 a = + = + = BH = BH BF2 BC2 a2 a2 a2 ằ a2 2a Trong tam giỏc HBC vuụng ti H cú CH = BC2 BH = a2 = 1 a a a2 15 Li cú din tớch tam giỏc SEB l SSEB = SE.EB = = 2 2 1 2a a2 15 a3 Do ú th tớch chúp C.SEB l VC.SEB = CH.SSEB = = 3 12 a3 Vy SE EB, CH SB v VC.SEB = 12 http://dethithu.net Trong tam giỏc FBC vuụng ti B cú Cõu (1,0 im) A E M K B I M C D http://dethithu.net =ữ I ữ + CAI Gi AI l phõn giỏc ca gúc ữ BAC, ta cú : AID ABC + BAI, AD = CAD = CAI, ữ ữ nờn AID = I Li cú BAI ABC = CAD AD DAI cõn ti D DE AI Do ú AI cú phng trỡnh x + y = Gi M l im i xng vi M qua AI ta cú phng trỡnh MM l x y + = Gi K l giao im ca AI v MM ta cú K (0; 5), suy M (4; 9) Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 22 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Khi ú AB i qua A(1; 4) v nhn AM = (3; 5) lm vect ch phng Do ú AB cú phng trỡnh 5( x 1) 3(y 4) = 5x 3y + = http://dethithu.net Cõu (1,0 im) Ta cú A d1 A(3t1 ; + t1 ; + 2t1 ), B d2 B(1 + t2 ; 2t2 ; t2 ) Suy AM = (1 3t1 ; 11 t1 ; 2t1 ) , BM = (t2 ; + 2t2 ; t2 ) Do ú AM, BM = (12 + 6t1 + 3t2 + 3t1 t2 ; 5t2 + 5t1 t2 ; 9t1 + 13t2 7t1 t2 ) đ 12 + 6t1 + 3t2 + 3t1 t2 = t1 = ng thng AB qua M AM, BM = 5t2 + 5t1 t2 = t2 = 9t1 + 13t2 7t1 t2 = Vy A(3; 1; 2) v B(2; 4; 1) http://dethithu.net Cõu (0,5 im) Phộp th l chn ngu nhiờn hc sinh tng s 11 hc sinh = 165 Do ú s phn t khụng gian mu l || = C11 Gi A l bin c "ba hc sinh c chn cú c nam v n" chn hc sinh cú c nam v n ta chn nam n hoc nam n Do ú s kt qu thun li cho bin c A l | A | = C52 ì C61 + C51 ì C62 = 135 | A | 135 = = Vy xỏc sut ca bin c A l P( A) = || 165 11 Cõu 10 (1,0 im) Theo gi thit v bt ng thc AM GM ta cú : bc bc bc =ằ =ằ 3a + bc a ( a + b + c) + bc ( a + b) ( a + c) ca ca ca =ằ =ằ 3b + ca b ( a + b + c) + ca (b + c) (b + a) ab ab ab =ằ =ằ 3c + ab c ( a + b + c) + ab (c + a) (c + b) http://dethithu.net Cng theo v (1), (2) v (3) ta cú : P ầ bc 1 (1) + a+b a+c ầ ca 1 (2) + b+c b+a ầ ab 1 (3) + c+a c+b bc + ba ab + ac a+b+c ca + cb + + = = ( a + b) (c + a) (b + c) 2 Du bng xy a = b = c = Vy P t giỏ tr ln nht l a = b = c = Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 23 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net ỏp ỏn s 10 Cõu 1a (1,0 im) Tp xỏc nh : D = R S bin thiờn : + Gii hn ti vụ cc : lim y = +; lim y = x + y x + Bng bin thiờn : y = 3x2 = 3( x2 1); y = x = x y + y + + U + 1 O 1 Hm s ng bin trờn (; 1) v (1; +) Hm s nghch bin trờn (1; 1) Hm s t cc i ti x = 1; yC = Hm s t cc tiu ti x = 1; yCT = th : + Ct Oy ti (0; 1) + Nhn im un U (0; 1) lm tõm i xng http://dethithu.net Cõu 1b (1,0 im) ọ Ta cú A (C ) A x A ; x3A 3x A + ; y = 3x2 y ( x A ) = 3x2A ọ Do ú tip tuyn ti A l y = 3x2A ( x x A ) + x3A 3x A + Phng trỡnh honh giao im ca tip tuyn v (C ) l : ọ ọ ọ 3x2A ( x x A ) + x3A 3x A + = x3 3x + 3x2A ( x x A ) = x3 x3A 3x + 3x A ọ 3x2A ( x x A ) = ( x x A ) x2 + xx A + x2A ( x x A ) ọ ( x x A ) x2 + xx A + x2A 3x2A + = ọ ( x x A ) x2 + xx A 2x2A = ( x x A ) (( x x A ) ( x + x A ) + x A ( x x A )) = ( x x A )2 ( x + 2x A ) = ủ x = xA x = 2x A http://dethithu.net Vỡ tip tuyn ct (C ) ti B khỏc A nờn x B = 2x A Khi ú 2013x B + 2014x A = 2012 4026x A + 2014x A = 2012 x A = Vy im cn tỡm l A(1; 3) Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 24 x http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi.Cp nht hng ngy.Truy cp ti ngay! Cõu 2a (0,5 im) Phng trỡnh ó cho tng ng vi http://dethithu.net ọ sin x 2cos2 x cos x + + 2cos2 x cos x + = x = + k2 sin x = 21 x = 2cos x cos x + (2 sin x + 1) = cos x = (k Z ) + k2 x = + k2 cos x = ọ Vy phng trỡnh cú nghim + k2, x = + k2, x = + k2 (k Z ) 6 Cõu 2b (0,5 im) http://dethithu.net ọ w2 Ta cú w = + i z + z = 1+i w3i w2 Do ú |z 1| w i 1+i 1+i t w = x + yi ( x, y R ), ta cú w i x + yi i ( x 3)2 + y 16 ọ Gi (C ) l ng trũn tõm I 3; v bỏn kớnh R = Ta cú hp cỏc im biu din s phc w l phn mt phng nm ng trũn (C ), k c (C ) http://dethithu.net Cõu (0,5 im) x+1 > x > Khi ú bt phng trỡnh ó cho tng ng vi : iu kin 2x x < 1 x+1 < (tha món) Vỡ AB = DC D (4; 1) http://dethithu.net Vy B(4; 3), C (2; 1), D (4; 1) Cõu (1,0 im) x7 y2 z1 x=1 = Ta giao im A l nghim h x y = y+2 z5 = = z=5 Vy giao im ca v l A(1; 2; 5) ng thng qua im M(7; 2; 1) v cú vect ch phng u = (3; 2; 2) ng thng qua im M (1; 2; 5) v cú vect ch phng u = (2; 3; 4) ù ũ Mt phng () cha , nờn qua M(7; 2; 1) v nhn u , u = (2; 16; 13) lm vect = phỏp tuyn Vy () cú phng trỡnh 2( x 7) 16(y 2) 13(z 1) = 2x 16y 13z + 31 = Cõu (0,5 im) Xột khai trin (1 + x )n = n k =0 Cnk x k http://dethithu.net Ly tớch phõn hai v cn t n ta cú (1 + x ) n +1 n+1 Khi ú ầ n Cnk = k =0 x+ 24 x ồn x k +1 k+1 ầ n 2k +1 3n +1 6560 3n +1 Cnk = = n=7 n+1 k+1 n+1 n+1 k =0 1 = x + x 2 ồ7 = C7k x (7k) k =0 ầ 1 x ồk = C7k k x2 2k k =0 S hng cha x2 tng ng vi s hng cha k tha 27 34 k = k = Vy h s ca s hng cha x2 l 21 http://dethithu.net Cõu 10 (1,0 im) Vỡ x + y < nờn x y > 0, ú theo bt ng thc Schwarz ta cú bt ng thc cn chng minh Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 27 [...]... http://dethithu.net thng xuyờn cp nht nhiu Thi Th THPT Quc Gia, ti liu ụn thi THPT Quc Gia cỏc mụn Toỏn, Lý, Húa, Anh, Vn, Sinh , S, a c DeThiThu.Net cp nht hng ngy phc v s t! Like Fanpage Thi Th THPT Quc Gia - Ti Liu ễn Thi: http://facebook.com/dethithu.net cp nht nhiu thi th v ti liu ụn thi hn Tham gia Group: ễn Thi H Toỏn - Anh cựng nhau hc tp, ụn thi: http://facebook.com/groups/onthidhtoananhvan... http://facebook.com/groups/onthidhtoananhvan Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 11 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net ỏp ỏn s 7 Cõu 1a (1,0 im) Tp xỏc nh : D = R \{1} S bin thi n : + Gii hn, tim cn : lim y = lim y = 1 tim... http://facebook.com/dethithu.net 15 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net ỏp ỏn s 8 Cõu 1a (1,0 im) http://dethithu.net Tp xỏc nh : D = R S bin thi n : + Gii hn ti vụ cc : lim y = ; lim y = + x + y x + Bng bin thi n : y = 3x2 + 6x = x y + y 3x ( x 2);... http://facebook.com/dethithu.net 23 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net ỏp ỏn s 10 Cõu 1a (1,0 im) Tp xỏc nh : D = R S bin thi n : + Gii hn ti vụ cc : lim y = +; lim y = x + y x + Bng bin thi n : y = 3x2 3 = 3( x2 1); y = 0 x = 1 x 1 y + 0 3 y 1... Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net ỏp ỏn s 9 Cõu 1a (1,0 im) Tp xỏc nh : D = R \{1} http://dethithu.net S bin thi n : + Gii hn, tim cn : lim y = lim y = 2 tim cn ngang l y = 2 x + x lim y = ; lim+ y = + tim cn ng l x = 1 x 1 x 1 + Bng bin thi n : 3 y = < 0, x D ( x 1)2 x y 2 y y + 1 + ... y 5 = 0 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 14 Ta cú d(C, (SAD )) = d( B, (SAD )) = http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! Cõu 8 (1,0 im) Ta giao im A ca d v ( P) l nghim h x 1 y+3 z3 = = 1 2 1 2x + y 2z + 9 = 0 x =0 y = 1 z=4 A(0; 1; 4) http://dethithu.net Mt phng ( P) cú mt... 2x2 3 x1 = 3 http://dethithu.net Vi x1 = 2x2 + 1 thay vo (1) ta cú x2 = 1 m = 1 x1 = 11 Vi x1 = 2x2 3 thay vo (1) ta cú x2 = 7 m = 81 Vy m = 1 hoc m = 81 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 16 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! Cõu 2a (0,5 im) http://dethithu.net Ký hiu phng trỡnh... http://dethithu.net Vỡ tip tuyn ct (C ) ti B khỏc A nờn x B = 2x A Khi ú 2013x B + 2014x A = 2012 4026x A + 2014x A = 2012 x A = 1 Vy im cn tỡm l A(1; 3) Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 24 x http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! Cõu 2a (0,5 im) Phng trỡnh ó cho tng ng vi http://dethithu.net... 2 a Trong tam giỏc SAO vuụng ti A cú = + = + = AH = AH 2 AS2 AO2 3a2 3a2 a2 2 a http://dethithu.net Vy khong cỏch t C n (SBD ) l d (C, (SBD )) = AH = 2 Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 18 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! Cõu 7 (1,0 im) = 900 ữ Ta cú AIB ACB = 450 hoc ữ ACB =... (1) = f (2) = 4 T gi thit ta cú ( x + y)2 3 = xy [2;2] [2;2] Vy P t giỏ tr ln nht bng 4 khi ( x; y) = (1; 1), ( x; y) = (2; 1), ( x; y) = (1; 2) V P t giỏ tr nh nht bng 4 khi ( x; y) = (1; 1), ( x; y) = (2; 1), ( x; y) = (1; 2) Ht Like Fanpage cp nht thi th nhiu hn qua Facebook : http://facebook.com/dethithu.net 19 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy ... http://facebook.com/dethithu.net http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! http://dethithu.net THI TH K THI THPT QUC GIA s Mụn : TON Thi gian lm... http://facebook.com/dethithu.net 11 http://dethithu.net - Website Thi Th THPT Quc Gia - Ti Liu ễn Thi. Cp nht hng ngy.Truy cp ti ngay! THI TH K THI THPT QUC GIA Mụn : TON Thi gian lm bi 180 phỳt http:/ / dethithu.net... nhiu Thi Th THPT Quc Gia, ti liu ụn thi THPT Quc Gia cỏc mụn Toỏn, Lý, Húa, Anh, Vn, Sinh , S, a c DeThiThu.Net cp nht hng ngy phc v s t! Like Fanpage Thi Th THPT Quc Gia - Ti Liu ễn Thi: http://facebook.com/dethithu.net