THI THU HAI BA TRUNGCO LOI GIAI

Luyn thi THPT mụn Toỏn THI TH S 05 S GD&T THA THIấN HU TRNG THPT HAI B TRNG THI TH THPT QG LN - NM 2017 Mụn: TON Thi gian lm bi: 90 phỳt, khụng k thi gian phỏt Cõu 1: Cho mt tm nhụm hỡnh ch nht ABCD cú AD = 24 cm Ta gp tm nhụm theo hai cnh MN v QP vo phớa n AB v CD trựng nh hỡnh v di õy c mt hỡnh lng tr khuyt hai ỏy Tỡm x th tớch lng tr ln nht? A x = B x = C x = 10 D x = Cõu 2: Hm s no sau õy nghch bin trờn ton trc s? A y = x x B y = x + 3x + C y = x + 3x 3x + D y = x x+3 Tỡm tt c cỏc giỏ tr ca tham s m th hm s ch cú mt tim x 6x + m cn ng v mt tim cn ngang? A 27 B hoc 27 C D Cõu 4: Hm s no sau õy l mt nguyờn hm ca hm s f ( x ) = x x A F ( x ) = ln x + ln x B F ( x ) = ln x + ln x C F ( x ) = ln x ln x D F ( x ) = ln x ln x Cõu 3: Cho hm s y = Cõu 5: Tp xỏc nh ca hm s y = ( x 27 ) l A D = Ă \ { 3} C D = [ 3; + ) B D = ( 3; + ) D D = Ă Cõu 6: Cho log x = Giỏ tr ca biu thc P = log x + log x + log x bng A B 11 C 65 D 3 Cõu 7: Tớnh S = 1009 + i + 2i + 3i + + 2017i 2017 trờn on [ 2, 4] A S = 2017 1009i B 1009 + 2017i C 2017 + 1009i D 1008 + 1009i Cõu 8: Tip tuyn ca th hm s y = x + x + x + ti im A ( 3; ) ct th ti im th hai l B im B cú ta l A B ( 1; ) B B ( 1;10 ) C B ( 2;33) D B ( 2;1) Cõu 9: Hm s y = x x x + t cc tr ti x1 v x2 thỡ tớch cỏc giỏ tr cc tr bng A 25 B 82 C 207 D 302 Cõu 10: Phỏt biu no sau õy l ỳng x x x A e sin xdx = e cos x + e cos xdx x x x C e sin xdx = e cos x + e cos xdx x x x B e sin xdx = e cos x e cos xdx x x x D e sin xdx = e cos x e cos xdx Cõu 11: Cho a > 0, b > 0, a 1, b 1, n Ơ * Mt hc sinh tớnh: P= 1 1 + + + + theo cỏc bc sau: log a b log a2 b log a3 b log an b Trang Luyn thi THPT mụn Toỏn THI TH S 05 n Bc I: P = log b a + log b a + log b a + + log b a 3 n Bc II: P = log b ( a.a a a ) 1+ +3+ + n Bc III: P = log b a Bc IV: P = n ( n + 1) log b a Trong cỏc bc trỡnh by, bc no sai ? A Bc III B Bc I a Cõu 12: t I = x3 + x x2 + C Bc II D Bc IV dx Ta cú: a + 1) a + + 1ự B I = ộ ( ỳ ỷ a + 1) a + - 1ự C I = ( a + 1) a + + D I = ộ ( ỳ ỷ 3 Cõu 13: Tỡm tt c cỏc giỏ tr ca tham s m phng trỡnh x 3x log m = cú ỳng mt nghim A I = ( a + 1) a + - 1 < m< B m = C m = D < m < v m > 4 Cõu 14: Khng nh no sau õy l luụn luụn ỳng vi mi a, b dng phõn bit khỏc ? A a log b = bln a B a 2log b = b 2log a C a = ln a a D log a b = log10 b A Cõu 15: Tỡm mnh sai cỏc mnh sau: 10 A i ữ = B ( i ) + ( 2i ) ( + 2i ) + ( + i ) = 13 40i 2i i ( ) ( ) ( ) D ( 3i ) + 3i ( + 2i ) ( i ) = + + + i C ( + i ) ( i ) = 16 + 37i 3 Cõu 16: Cú bao nhiờu s phc z tho z = z + z A B C D Cõu 17: Khong cỏch gia hai im cc i v cc tiu ca th hm s y = ( x + 1) ( x ) A B C D Cõu 18: Gi z1 v z2 l hai nghim ca phng trỡnh z z + = bit ( z1 z2 ) cú phn o l s thc 2 õm Tỡm phn thc ca s phc w = z1 z2 A B C D Cõu 19: Mt ngi ln u gi ngõn hng 100 triu ng vi kỡ hn thỏng, lói sut 3% ca mt quý v lói tng quý s c nhp vo (hỡnh thc lói kộp) Sau ỳng thỏng, ngi ú gi thờm 100 triu ng vi kỡ hn v lói sut nh trc ú Tng s tin ngi ú nhn c nm k t gi thờm tin ln hai s gn vi kt qu no sau õy? A 232 triu B 262 triu C 313 triu D 219 triu b Cõu 20: Nu b a = thỡ biu thc xdx cú giỏ tr bng: a A ( b + a ) B ( b + a ) C b + a Cõu 21: Gii bt phng trỡnh: log 12 ( x + x ) D ( b + a ) A x < hoc < x B x < hoc < x < C x hoc x D x < hoc x > Cõu 22: Tỡm hp cỏc im M biu din hỡnh hc s phc z mt phng phc, bit s phc z tha iu kin: z + + z = 10 Trang Luyn thi THPT mụn Toỏn THI TH S 05 A Tp hp cỏc im cn tỡm l ng trũn cú tõm O ( 0;0 ) v cú bỏn kớnh R = B Tp hp cỏc im cn tỡm l ng elip cú phng trỡnh x2 y + = 25 C Tp hp cỏc im cn tỡm l nhng im M ( x; y ) mt phng Oxy tha phng trỡnh ( x + 4) + y2 + ( x 4) + y = 12 D Tp hp cỏc im cn tỡm l ng elip cú phng trỡnh x2 y + = 25 Cõu 23: Mt cht im chuyn ng trờn trc Ox vi tc thay i theo thi gian v ( t ) = 3t 6t (m/s) Tớnh quóng ng cht im ú i c t thi im t1 = (s), t2 = (s) A 16 B 24 C D 12 Cõu 24: Cho hm s y = x x + x cú th nh Hỡnh Khi ú th Hỡnh l ca hm s no di õy? Hỡnh A y = x x + x Hỡnh B y = x + x x 3 C y = x x + x D y = x + x + x Cõu 25: ng thng d : y = x + ct th hm s y = x + 2mx + ( m + 3) x + ti im phõn bit A ( 0; ) , B v C cho din tớch tam giỏc MBC bng 4, vi M ( 1;3) Tỡm tt c cỏc giỏ tr ca m tha yờu cu bi toỏn A m = hoc m = B m = hoc m = C m = D m = hoc m = Cõu 26: Trong khụng gian Oxyz , cho im A ( 3; 2;1) v mt phng ( P ) : x - y + z - = Phng trỡnh mt phng ( Q ) i qua A v song song mt phng ( P ) l: A ( Q ) : x y + z + = C ( Q ) : 3x + y z = B ( Q ) : x y + z = D ( Q) : x 3y + 2z + = Cõu 27: Hỡnh phng gii hn bi cỏc ng x = 1, x = 2, y = 0, y = x x cú din tớch c tớnh theo cụng thc: A S = ( x x)dx B S = ( x x)dx ( x x)dx C S = ( x x)dx + ( x x)dx D S = x x dx r r r Cõu 28: Trong khụng gian Oxyz , cho ba vect: a = (2; 5;3) , b = ( 0; 2; 1) , c = ( 1; 7; ) Ta vect r r 1r r x = 4a b + 3c l Trang Luyn thi THPT mụn Toỏn THI TH S 05 r 53 A x = 11; ; ữ 3 r 121 17 B x = 5; ; ữ 3 r 55 C x = 11; ; ữ 3 r 1 D x = ; ;18 ữ 3 Cõu 29: Trong khụng gian Oxyz , cho bn im A ( 1; 2;0 ) , B ( 1;0; 1) v C ( 0; 1; ) , D ( 0; m; k ) H thc gia m v k bn im ABCD ng phng l : A m + k = B m + 2k = C 2m 3k = D 2m + k = Cõu 30: Trong khụng gian Oxyz , vit phng trỡnh mt cu ( S ) i qua bn im O, A ( 1;0; ) , B ( 0; 2;0 ) v C ( 0; 0; ) 2 A ( S ) : x + y + z + x y + z = C ( S ) : x + y2 + z2 x + y 4z = Cõu 31: ( Q) : 2x y + = A Trong khụng B gian 2 2 B ( S ) : x + y + z x + y z = D Oxyz , gúc C ( S ) : x + y2 + z + 2x y + 8z = gia hai mt phng D e k Cõu 32: t I k = ln dx k nguyờn dng Ta cú I k < e khi: x A k { 1; 2} B k { 2;3} C k { 4;1} ( P ) : x y z 11 = ; D k { 3; 4} Cõu 33: Hỡnh nún ng sinh l , thit din qua trc ca hỡnh nún l tam giỏc vuụng cõn Din tớch xung quanh ca hỡnh nún l l2 l2 l2 l2 A B C D 2 Cõu 34: Hỡnh phng gii hn bi y = x ; y = x ; y = cú din tớch bng 17 16 C D ( vdt ) ( vdt ) ( vdt ) 3 Cõu 35: Trong khụng gian Oxyz , cho hai mt phng ( P ) : x y + z = ; ( Q ) : x y z = A 13 ( vdt ) B V trớ tng i ca ( P ) & ( Q ) l A Song song B Ct nhng khụng vuụng gúc C Vuụng gúc D Trựng Cõu 36: Cho hỡnh chúp S ABC l tam giỏc vuụng ti A , ãABC = 30o , BC = a Hai mt bờn ( SAB ) v ( SAC ) cựng vng gúc vi ỏy ( ABC ) , mt bờn ( SBC ) to vi ỏy mt gúc 450 Th tớch ca chúp S ABC l: a3 A 64 B a3 16 C a3 D a3 32 r r Cõu 37: Trong khụng gian Oxyz , cho hai vộc t a = ( 2;1; ) , b = 0; 2; Tt c giỏ tr ca m hai r r r r r r vộc t u = 2a + 3mb v v = ma b vuụng gúc l: ) 11 26 26 26 + C D 18 6 Cõu 38: Trong khụng gian Oxyz , mt phng ( P ) qua im A ( 1;1;1) v vuụng gúc vi ng thng OA cú A 26 + ( B phng trỡnh l: A ( P ) : x y + z = C ( P ) : x + y + z = Trang B ( P ) : x + y + z = D ( P ) : x + y z = Luyn thi THPT mụn Toỏn THI TH S 05 Cõu 39: Hỡnh hp ng ABCD ABC D cú ỏy l mt hỡnh thoi cú gúc nhn bng , cnh a Din tớch xung quanh ca hỡnh hp ú bng S Tớnh th tớch ca hp ABCD ABC D ? 1 1 A a.S sin B a.S sin C a.S sin D a.S sin Cõu 40: Tỡm hp nhng im M biu din s phc z mt phng phc, bit s phc z tha iu kin z 2i = z + A Tp hp nhng im M l ng thng cú phng trỡnh x + y + = B Tp hp nhng im M l ng thng cú phng trỡnh x y + = C Tp hp nhng im M l ng thng cú phng trỡnh x + y = D Tp hp nhng im M l ng thng cú phng trỡnh x + y + = 2 Cõu 41: Trong khụng gian Oxyz , cho mt cu ( S ) : x + y + z x y z = Mt phng ( Oxy ) ct mt cu ( S ) theo giao tuyn l mt ng trũn ng trũn giao tuyn y cú bỏn kớnh r bng: A r = B r = C r = D r = Cõu 42: Trong khụng gian Oxyz , cho hỡnh hp ABCD ABC D cú A ( 1;1; ) , B ( 0; 0; ) , C ( 5;1; ) v D ( 2;1; 1) Th tớch hp ó cho bng: A 12 B 19 C 38 Cõu 43: Tỡm mnh sai cỏc mnh sau: A Mt cu tõm I ( 2; 3; ) tip xỳc D 42 vi mt ( Oxy ) phng cú phng trỡnh x + y + z x + y + 8z + 12 = B Mt cu ( S ) cú phng trỡnh x + y + z x y z = ct trc Ox ti A ( khỏc gc ta O ) Khi ú ta ụ l A ( 2;0;0 ) C Mt cu ( S ) cú phng trỡnh ( x a ) + ( y b ) + ( z c ) = R tip xỳc vi trc Ox thỡ bỏn kớnh mt cu ( S) 2 l r = b + c D x + y + z + x y z + 10 = l phng trỡnh mt cu Cõu 44: Mt mt cu ( S ) ngoi tip t din u cnh a Din tớch mt cu ( S ) l: a a B C a D a Cõu 45: Khi tr cú chiu cao bng bỏn kớnh ỏy v din tớch xung quanh bng Th tớch tr l: A B C D A Cõu 46: Cho hỡnh phng ( H ) gii hn bi cỏc ng y = x v y = x Khi trũn xoay to ( H ) quay quanh Ox cú th tớch l: A ( x x ) dx ( vtt ) C ( ) x x dx ( vtt ) ( ) B x x dx ( vtt ) D x x dx ( vtt ) ) ( Cõu 47: Trong khụng gian Oxyz , cho mt cu ( S ) : ( x 1) + ( y + ) + ( z ) = 49 v im M ( 7; 1;5 ) 2 Phng trỡnh mt phng tip xỳc vi mt cu ( S ) ti im M l: A x + y + z 15 = C x + y + 3z 55 = Trang B x y z 34 = D x y + z 55 = Luyn thi THPT mụn Toỏn THI TH S 05 Cõu 48: Trong khụng gian Oxyz , cho im A ( 2; 0; ) , B ( 3; 1; ) , C ( 2; 2;0 ) Tỡm im D mt phng ( Oyz ) cú cao õm cho th tớch ca t din ABCD bng v khong cỏch t D n mt phng ( Oxy ) bng Khi ú cú ta im D tha bi toỏn l: A D ( 0;3; 1) B D ( 0; 3; 1) C D ( 0;1; 1) D D ( 0; 2; 1) Cõu 49: Trong khụng gian Oxyz , cho im H ( 1; 2;3) Mt phng ( P ) i qua im H , ct Ox, Oy, Oz ti A, B, C cho H l trc tõm ca tam giỏc ABC Phng trỡnh ca mt phng ( P ) l A ( P) : 3x + y + z 11 = B ( P ) : 3x + y + z 10 = C ( P ) : x + y + z 13 = D ( P) : x + y + 3z 14 = Cõu 50: Cho hỡnh lp phng ABCD.ABC D cú cnh bng Tớnh khong cỏch gia hai mt phng ( ABD) v ( BC D ) A B C ỏp ỏn Trang D Luyn thi THPT mụn Toỏn 1-B 11-D 21-C 31-A 41-C 2-C 12-C 22-D 32-A 42-C THI TH S 05 3-B 13-D 23-A 33-B 43-D 4-A 14-B 24-A 34-D 44-B 5-B 15-D 25-C 35-B 45-B 6-A 16-A 26-D 36-D 46-D 7-C 17-C 27-B 37-A 47-C 8-C 18-D 28-C 38-C 48-A 9-C 19-A 29-B 39-A 49-D 10-A 20-B 30-C 40-C 50-A LI GII CHI TIT Cõu 1: ỏp ỏn B Gi I l trung im NP IA ng cao ca ANP cõn ti A AI = x ( 12 x ) = 24 ( x ) 1 din tớch ỏy S ANP = NP.AI = ( 12 x ) 24 ( x ) , vi x 12 th tớch lng tr l 2 a V = S ANP MN = ( 12 x ) 24 ( x ) (t MN = a : hng s dng) Tỡm giỏ tr ln nht ca hm s y = ( 12 x ) 24 ( x ) , ( x 12 ) : x + 24 12 ( 12 x ) + y = 24 ( x ) + = , y = x = ( 6;12 ) 24 ( x ) 24 ( x ) + Tớnh giỏ tr: y ( ) = , y ( ) = , y ( 12 ) = Th tớch tr ln nht x = Cõu 2: ỏp ỏn C Cỏc hm s trờn nghch bin trờn ton trc s y 0, x Ă + Hm s y = x x cú y = x x khụng tho + Hm s y = x3 + x + cú y = 3x + khụng tho + Hm s y = x + 3x 3x + cú y = x + x tho iu kin y = ( x 1) 0, x Ă + Hm s y = x cú y = x khụng tho Cõu 3: ỏp ỏn B iu kin cn (): th hm s ch cú mt tim cn ng mu s ch cú mt nghim hoc cú hai 4m = m = nghim nhng mt nghim l x = m = 27 ( 3) ( 3) + m = iu kin () x+3 x+3 + Vi m = , hm s y = y= : th cú TC : x = , TCN : y = ( x 3) x 6x + Trang Luyn thi THPT mụn Toỏn THI TH S 05 x+3 x+3 , ( x 3) th cú TC : x = y= y= ( ) ( ) x+3 x9 x x 27 x + Vi m = 27 , hm s y = , TCN : y = Cõu 4: ỏp ỏn A 1 Phõn tớch hm s f ( x ) = x x Cỏc nguyờn hm l ln x ln x + C mt nguyờn hm l F ( x ) = ln x + ln x Cõu 5: ỏp ỏn B y = ( x 27 ) l hm lu tha vi s m khụng nguyờn nờn hm s xỏc nh x 27 > x > Tp xỏc nh l D = ( 3; + ) Cõu 6: ỏp ỏn A Ta cú log x = x = 3 Do ú, ( ) P = log 3 ( ) + log 3 3 ( ) =2 + log 3 3 3 + = 2 Cõu 7: ỏp ỏn C Ta cú S = 1008 + i + 2i + 3i + 4i + + 2017i 2017 = 1009 + ( 4i + 8i + + 2016i 2016 ) + ( i + 5i + 9i + + 2017i 2017 ) + + ( 2i + 6i + 10i10 + 2014i 2014 ) + ( 3i + 7i + 11i11 + + 2015i 2015 ) 504 505 504 504 n =1 n =1 n =1 n =1 = 1009 + ( 4n ) + i ( 4n 3) ( 4n ) i ( 4n 1) = 1009 + 509040 + 509545i 508032 508536i = 2017 + 1009i Cõu 8: ỏp ỏn C Ta cú y = x + x + , y ( 3) = Phng trỡnh tip tuyn ca th hm s ó cho l y = x + 19 Phng trỡnh honh giao im ca hm s ó cho vi tip tuyn ca nú l x = y = 33 x + x + x + = x + 19 x = Cõu 9: ỏp ỏn C x = y = Ta cú y = x x , y = x = y = 23 Cõu 10: ỏp ỏn A u = e x du = e x dx x x x t Ta cú e sin xdx = e cos x + e cos xdx dv = sin xdx v = cos x Cõu 11: ỏp ỏn D n ( n + 1) n ( n + 1) Vỡ + + + + n = nờn P = log b a 2 Cõu 12: ỏp ỏn C a Ta cú: I = Trang x3 + x x2 + a dx = (x + 1) x x2 + a dx = x + 1.xdx Luyn thi THPT mụn Toỏn THI TH S 05 t = x + t = x + t.dt = x.dx i cn: x = t = 1; x = a t = a + 2 Khi ú: I = a +1 1 t.tdt = t 3 ( ) = a2 +1 ( a +1 ) a + Cõu 13: ỏp ỏn D V th hm s ( C ) : y = x x 3 Ta cú phng trỡnh x x log m = x 3x = log m ( vi iu kin m > ) l phng trỡnh honh giao im ca th ( C ) : y = x 3x v ng thng y = log m Da vo th 0 m > Cõu 14: ỏp ỏn B Ta cú a 2log b = a log a b log a 10 =( a l og a b log 10 a ) =b log a 10 = b 2log a Cõu 15: ỏp ỏn D i 1 Ta thy: i ữ = i + ữ = = : ỳng 2i i i 2 ( i) 10 ( + i) + ( 2i ) ( + 2i ) + ( + i ) = ( 2i ) + 13 + ( 2i ) = 32i + 13 8i = 13 40i : ỳng ( i ) = + 11i ( 18 26i ) = 16 + 37i : ỳng ( 3i ) + ( ( 3i ) + ( ) ( ) ( ) 3i ) ( + 2i ) ( i ) = ( 3i ) + ( + ) + ( ) i ( 2i ) = ( + 3) + ( 3) i 3i ( + 2i ) ( i ) = + + + i : sai Vỡ 3 Cõu 16: ỏp ỏn A Gi z = a + bi vi a; b Ă Khi ú z = z + z ( a + bi ) = a b + a bi 2b + a bi 2abi = b = a = 2b + a = 2b + a = a = b = b + a = b ab = ) ( 2 1 1 Vy cú s phc z tha iu kin bi l z = 0, z = + i, z = i 2 2 Cõu 17: ỏp ỏn C Trang ( C) ta thy vi: Luyn thi THPT mụn Toỏn THI TH S 05 x = y = Ta cú y = x ( x ) ; y = x ( x ) = x = y = Ta hai im cc tr ca th hm s l A ( 2;0 ) v B ( 0; ) Vy AB = 22 + 42 = Cõu 18: ỏp ỏn D z1 = 2i Ta cú z z + = (do z1 z2 = 4i cú phn o l ) z2 = + 2i 2 Do ú w = z1 z2 = 4i 2 Vy phn thc ca s phc w = z1 z2 l Cõu 19: ỏp ỏn A Cụng thc tớnh lói sut kộp l A = a ( + r ) n Trong ú a l s tin gi vo ban u, r l lói sut ca mt kỡ hn (cú th l thỏng; quý; nm), n l kỡ hn Sau nm k t gi thờm tin ln hai thỡ 100 triu gi ln u c gi l 18 thỏng, tng ng vi quý Khi ú s tin thu c c gc v lói ca 100 triu gi ln u l A1 = 100 + ữ (triu) 100 Sau nm k t gi thờm tin ln hai thỡ 100 triu gi ln hai c gi l 12 thỏng, tng ng vi quý Khi ú s tin thu c c gc v lói ca 100 triu gi ln hai l A2 = 100 + ữ (triu) 100 Vy tng s tin ngi ú nhn c nm k t gi thờm tin ln hai l A = A1 + A2 = 100 + ữ + 100 + ữ 232 triu 100 100 Cõu 20: ỏp ỏn B b 2 Ta cú xdx = x a = b a = ( b a ) ( b + a ) = ( b + a ) b a Cõu 21: ỏp ỏn C Ta cú: iu kin: x + 2x - > Êx - x (*) - ổử 1ữ ữ log x + 2x - Ê - x + 2x - ỗ = 16 ỗ ữ ỗ ữ ố2 ứ ( ) x + 2x - 24 x Ê - x Kt hp vi iu kin (*) ta cú: x Ê - x Cõu 22: ỏp ỏn D Ta cú: Gi M ( x ; y ) l im biu din ca s phc z = x + yi Gi A ( 4; 0) l im biu din ca s phc z = Gi B ( - 4; 0) l im biu din ca s phc z = - Khi ú: z + + z - = 10 MA + MB = 10 (*) H thc trờn chng t hp cỏc im M l elip nhn A , B l cỏc tiờu im Gi phng trỡnh ca elip l Trang 10 x2 y2 + = 1, a > b > 0, a = b2 + c 2 a b ( ) Luyn thi THPT mụn Toỏn THI TH S 05 T (*) ta cú: 2a = 10 a = A B = 2c = 2c c = ị b2 = a - c = Vy qu tớch cỏc im M l elip: ( E ) : x2 y2 + = 25 Cõu 23: ỏp ỏn A 4 ( ) ( Quóng ng cht im i c l: S = ũ v ( t ) d t =ũ 3t - 6t d t = t - 3t 0 ) = 16 Cõu 24: ỏp ỏn A th hm s hỡnh nhn lm trc i xng nờn l hm s chn Loi i phng ỏn B v C Mt khỏc, vi x = 1, ta cú y ( 1) = (nhỡn vo th) nờn chn phng ỏn A Cõu 25: ỏp ỏn C Phng trỡnh honh giao im ca d v th ( C ) : x + 2mx + ( m + 3) x + = ộx = x + 2mx + ( m + 2) x = ờj x = x + 2mx + m + = ở( ) Vi x = 0, ta cú giao im l A ( 0; 4) ( 1) d ct ( C ) ti im phõn bit v ch phng trỡnh (1) cú nghim phõn bit khỏc ỡù j ( 0) = m + ùớ ùù D Â = m - m - > ùợ (*) Ta gi cỏc giao im ca d v ( C ) ln lt l A, B ( x B ; x B + 2) ,C ( xC ; xC + 2) vi x B , xC l nghim ca phng trỡnh (1) ỡù x + x = - 2m C ù B Theo nh lớ Viet, ta cú: ùù x B xC =m + ợ Ta cú din tớch ca tam giỏc MB C l S = ìBC ìd ( M , BC ) = Phng trỡnh d c vit li l: d : y = x + x - y + = M d ( M , BC ) = d ( M , d ) = Do ú: BC = d ( M , BC ) = 1- + + ( - 1) = 2 BC = 32 2 Ta li cú: BC = ( xC - x B ) + ( yC - y B ) = ( x C - x B ) = 32 2 ( x B + xC ) - 4x B xC = 16 ( - 2m ) - ( m + 2) = 16 4m - 4m - 24 = m = m = - i chiu vi iu kin, loi i giỏ tr m = - Cõu 26: ỏp ỏn D Vỡ mt phng ( Q ) song song ( P ) : x - y + z - = nờn phng trỡnh ( Q ) cú dng ( P ) : x - y + z + m = ( m - 2) ( Q) i qua A ( 3; 2;1) nờn thay ta vo ta cú m = Trang 11 Luyn thi THPT mụn Toỏn THI TH S 05 Vy phng trỡnh ( Q) : x - y + z + = Cõu 27: ỏp ỏn B ộx = ( n) Gii phng trỡnh honh giao im x - x = ờ ởx = (n) 2 1 S = x x dx = x x dx + x x dx = ( x x )dx ( x x )dx Cõu 28: ỏp ỏn C r 1r r 4a = (8; 20;12) , b = 0; ; ữ , 3c = ( 3; 21;6 ) 3 r r r r 55 x = 4a b + 3c = 11; ; ữ 3 Cõu 29: ỏp ỏn B uuur uuur uuur AB = (0; 2; 1) AC = (1;1; 2) AD = (1; m + 2; k) uuur uuur uuur uuur uuur AB AC = (5; 1; 2) AB AC AD = m + 2k uuur uuur uuur Vy bn im ABCD ng phng AB AC AD = m + 2k = ( ) ( ) Cõu 30: ỏp ỏn C Gi s phng trỡnh mt cu cú dng: ( S ) : x + y + z 2ax 2by 2cz + d = (a + b2 + c d > 0) Vỡ mt cu ( S ) i qua O, A ( 1;0; ) , B ( 0; 2; ) v C ( 0;0; ) nờn thay ta bn im ln lt vo ta cú d = d = 1 + + 2.1.a + d = a = 2 ( S ) : x + y + z x + y 4z = + ( ) + ( ) b + d = b = + + 2.4.c + d = c = Cõu 31: ỏp ỏn A r r n( P ) = ( 8; 4; ) ; n( Q ) = ( 2; 2; ) r r n( P ) n( Q ) 12 2 = r = Gi l gúc gia hai mt phng ( P ) & ( Q ) ta cú cos = r 24 n( P ) n ( Q ) Cõu 32: ỏp ỏn A Vy = t k e e k u = ln du = dx I k = x.ln ữ + dx = ( e 1) ln k I k < e x x x 1 dv = dx v = x e3 ln k < e e Do k nguyờn dng nờn k { 1; 2} ( e 1) ln k < e ln k < Cõu 33: ỏp ỏn B Do thit din qua trc l tam giỏc vuụng nờn r = Trang 12 l 2 Luyn thi THPT mụn Toỏn THI TH S 05 Vy din tớch xung quanh ca nún bng S xq = l2 Cõu 34: ỏp ỏn D Xột phng trỡnh honh giao im x = x = x2 = ; 4x = vdt x = x = 2 Din tớch hỡnh phng l S = x dx x dx = 16 ( vdt ) Cõu 35: ỏp ỏn B r r r r n( P ) = ( 2; 3;1) ; n( Q ) = ( 5; 3; ) n ( P ) k n ( Q ) ( k ) r r n( P ) n( Q ) Vy v trớ tng i ca ( P ) & ( Q ) l ct nhng khụng vuụng gúc Cõu 36: ỏp ỏn D S ( SAB ) ( ABC ) SA ( ABC ) Ta cú: ( SAC ) ( ABC ) ( SAB ) ( SAC ) = SA K AH BC SH BC ( SBC ) ( ABC ) = BC C A o ã SHC = 45 Khi ú: BC AH H BC SH B a a a o M AB = BC.cos300 = v AC = BC sin 30 = nờn AH = AB.sin 300 = 2 a Nờn SA = 1 a3 Do ú: V = S ABC SA = AB AC.SA = 32 Cõu 37: ỏp ỏn A r r r r r r Ta cú: u = 2a + 3mb = 2; 3m 2; + 3m v v = ma b = 2m; m + 2; 2m rr Khi ú: u.v = 4m + 3m m + + + 3m 2m = ( ( )( m 2 6m = m = ) ) ( )( ( ) ) 26 + Cõu 38: ỏp ỏn C uuur Mt phng ( P ) i qua im A ( 1;1;1) v cú vộc t phỏp tuyn OA = ( 1;1;1) Nờn: ( P ) : x + y + z = Cõu 39: ỏp ỏn A Ta cú: S = AB AA AA = A S 4a V S ABCD = S ABC = AB.BC.sin = a sin Vy: V = S ABCD AA = a.S sin Cõu 40: ỏp ỏn C Gi z = x + yi , ( x, y Ă ) Ta cú: Trang 13 D C B A B D C Luyn thi THPT mụn Toỏn THI TH S 05 z 2i = z + x + ( y ) i = ( x + 1) yi x + ( y ) = ( x + 1) + y x + y = 2 Cõu 41: ỏp ỏn C Mt cu cú bỏn kớnh R = + + = 14 v tõm I ( 1; 2;3) Khong cỏch t tõm I ca mt cu n mt phng ( Oxy ) l d = Bỏn kớnh ng trũn giao tuyn l r = R d = Cõu 42: ỏp ỏn C uuur uuur uuuur Th tớch hp a cho V = 6VABCD = AB, AC AD uuur uuur uuuur Ta cú: AB = ( 1; 1; ) , AC = ( 6;0;8) v AD = ( 1;0;5 ) uuur uuur uuur uuur uuuur Do ú: AB, AC = ( 8; 16; ) Suy AB, AC AD = 38 Vy V = 38 Cõu 43: ỏp ỏn D Cõu D sai vỡ phng trỡnh x + y + z + x y z + 10 = cú a = , b = c = , d = 10 nờn a + b + c d < Do ú phng trỡnh ó cho khụng l phng trỡnh mt cu Cõu 44: ỏp ỏn B Gi O l tõm ng trũn ngoi tip tam giỏc BCD Trong mt phng ( ABO ) dng ng trung trc ca AB ct AO ti I Khi ú I l tõm mt cu ngoi tip t din ABCD a Ta cú: AO = AB BO = a , =a 3 Din tớch mt cu ( S ) 2 AB = AO R = IA = a2 2a 3 a l: S = R = a = 2 Cõu 45: ỏp ỏn B Gi h v R l chiu cao v bỏn kớnh ỏy ca tr Khi ú h = R Ta cú: S xq = R.h = R = h = Th tớch tr: V = R h = Cõu 46: ỏp ỏn D x = Xột phng trỡnh honh giao im x = x x =1 ( ) ( x) Suy V = x 2 Cõu 47: ỏp ỏn C Trang 14 1 dx = x x dx = ( x x ) dx 0 =a Luyn thi THPT mụn Toỏn THI TH S 05 uuur Mt cu ( S ) cú tõm I ( 1; 3; ) IM = ( 6; 2;3) uuur Mt phng cn tỡm i qua im M ( 7; 1;5 ) v cú vộct phỏp tuyn IM = ( 6; 2;3 ) nờn cú phng trỡnh l: ( x ) + ( y + 1) + ( z ) = x + y + z 55 = Cõu 48: ỏp ỏn A Vỡ D ( Oyz ) D ( 0; b; c ) , cao õm nờn c < Khong cỏch t D ( 0; b; c ) n mt phng ( Oxy ) : z = bng c = c = ( c < ) Suy ta D ( 0; b; 1) Ta cú: uuur uuur uuur AB = ( 1; 1; ) , AC = ( 4; 2; ) ; AD = ( 2; b;1) uuur uuur uuur uuur AB; AC = ( 2;6; ) AB; AC AD = + 6b = 6b = ( b 1) uuu r uuu r VABCD = AB; AC AD = b D ( 0;3; 1) b = M VABCD = b = Chn ỏp ỏn D ( 0;3; 1) b = D ( 0; 1; 1) Cõu 49: ỏp ỏn D Do t din OABC cú ba cnh OA, OB, OC ụi mt vuụng gúc nờn nu H l trc tõm ca tam giỏc ABC d dng chng minh c OH ( ABC ) hay OH ( P ) Vy mt phng ( P) uuur i qua im H ( 1; 2;3) v cú VTPT OH ( 1; 2;3) nờn phng trỡnh ( x 1) + ( y ) + ( z 3) = x + y + z 14 = Cõu 50: ỏp ỏn A Ta chn h trc ta cho cỏc nh ca hỡnh lp phng cú ta nh sau: A ( 0; 0;0 ) B ( 1;0;0 ) C ( 1;1; ) D ( 0;1; ) A ( 0; 0;1) B ( 1; 0;1) C ( 1;1;1) D ( 0;1;1) uuur uuur AB = ( 1;0;1) , AD = ( 0;1;1) , uuur uuur BD = ( 1;1; ) , BC = ( 0;1;1) Trang 15 ( P) l Luyn thi THPT mụn Toỏn * Mt phng ( ABD ) THI TH S 05 uuur uuur r qua A ( 0;0; ) v nhn vộct n = AB; AD = ( 1;1; 1) lm vộct phỏp tuyn Phng trỡnh ( ABD ) l : x + y z = uuur uuur r * Mt phng ( BC D ) qua B ( 1;0;0 ) v nhn vộct m = BD; BC = ( 1;1; 1) lm vộct phỏp tuyn Phng trỡnh ( ABD ) l : x + y z = Suy hai mt phng ( ABD ) v ( BC D ) song song vi nờn khong cỏch gia hai mt phng chớnh l khong cỏch t im A n mt phng ( BC D ) : d ( A, ( BC D ) ) = Trang 16 = 3 ... ln hai thỡ 100 triu gi ln hai c gi l 12 thỏng, tng ng vi quý Khi ú s tin thu c c gc v lói ca 100 triu gi ln hai l A2 = 100 + ữ (triu) 100 Vy tng s tin ngi ú nhn c nm k t gi thờm tin ln hai. .. Cõu 28: Trong khụng gian Oxyz , cho ba vect: a = (2; 5;3) , b = ( 0; 2; 1) , c = ( 1; 7; ) Ta vect r r 1r r x = 4a b + 3c l Trang Luyn thi THPT mụn Toỏn THI TH S 05 r 53 A x = 11; ; ữ 3... D cú cnh bng Tớnh khong cỏch gia hai mt phng ( ABD) v ( BC D ) A B C ỏp ỏn Trang D Luyn thi THPT mụn Toỏn 1-B 11-D 21-C 31-A 41-C 2-C 12-C 22-D 32-A 42-C THI TH S 05 3-B 13-D 23-A 33-B 43-D