10 đề toán hay 2017 (2)

HNH TRèNH 80 NGY NG HNH CNG 99ER THPT HAI B TRNG TT HU LN THI TH THPT QUC GIA 2017 MễN: TON Thi gian lm bi: 90 phỳt H v tờn thớ sinh: S Bỏo Danh: S 39/80 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 3x Cõu 3: Cho hm s B y = x + x + y= C y = x + 3x 3x + D y = x x+3 x x + m Tỡm tt c cỏc giỏ tr ca tham s m th hm s ch cú mt tim cn ng v mt tim cn ngang? A 27 B hoc 27 C Cõu 4: Hm s no sau õy l mt nguyờn hm ca hm s D 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 ( )3 Cõu 5: Tp xỏc nh ca hm s y = x 27 l A D = Ă \ { 3} Cõu 6: Cho A B D = ( 3; + ) log x = Giỏ tr ca biu thc 11 B C D = [ 3; + ) D D = Ă P = log3 x + log x + log9 x 65 C K S H Hng Cung cp ti liu & thi THPT mi nht bng D 3 Trang 2017 [ 2, 4] Cõu 7: Tớnh S = 1009 + i + 2i + 3i + + 2017i trờn on A S = 2017 1009 i B 1009 + 2017i C 2017 + 1009i D 1008 + 1009i A ( 3; ) Cõu 8: Tip tuyn ca th hm s y = x + x + x + ti im ct th ti im th hai l B im B cú ta l A B ( 1;0 ) 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 B 82 A 25 C 207 D 302 Cõu 10: Phỏt biu no sau õy l ỳng e A C e sin xdx = e x cos x + e x cos xdx e B x sin xdx = e x cos x e x cos xdx sin xdx = e x cos x + e x cos xdx e x D sin xdx = e x cos x e x cos xdx x x * Cõu 11: Cho a > 0, b > 0, a 1, b 1, n Ơ Mt hc sinh tớnh: P= 1 1 + + + + log a b log a2 b log a3 b log a n b theo cỏc bc sau: n Bc I: P = log b a + log b a + log b a + + log b a Bc II: ( P = log b a.a a a n ) 1+ + 3+ + n Bc III: P = log b a Bc IV: P = n ( n + 1) logb 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: I= ộ a +1) a +1 +1ự ( ỳ ỷ B I= ộ a +1) a +1 ( D A I = ( a +1) a +1 - C I = ( a +1) a +1 +1 1ự ỳ ỷ Cõu 13: Tỡm tt c cỏc giỏ tr ca tham s m phng trỡnh x x log m = cú ỳng mt nghim x > Tp xỏc nh l D = ( 3; + ) Cõu 6: ỏp ỏn A Ta cú log x = x = 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 ) ( 4n ) i ( 4n 1) = 1009 + 509040 + 509545i 508032 508536i = 2017 + 1009i Cõu 8: ỏp ỏn C y ( 3) = Ta cú y = 3x + x + , 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 K S H Hng Cung cp ti liu & thi THPT mi nht Trang 11 x = y = y = x = y = 23 Ta cú y = 3x x , Cõu 10: ỏp ỏn A u = e x du = e x dx dv = sin xdx v = cos x e Ta cú t x sin xdx = e x cos x + e x cos xdx Cõu 11: ỏp ỏn D Vỡ + + + + n = n ( n + 1) nờn P= n ( n + 1) log b a Cõu 12: ỏp ỏn C a Ta cú: I = x3 + x x2 +1 a dx = (x ) + x x2 + a dx = x + 1.xdx t = x + t = x + t.dt = x.dx i cn: x = t = 1; x = a t = a + I= Khi ú: a +1 t.tdt = 1 a2 +1 t ) = ( a + 1) a + ( 3 Cõu 13: ỏp ỏn D V th hm s ( C ) : y = x 3x 3 Ta cú phng trỡnh x x log m = x x = 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 ( C ) ta thy vi: 0 m > thỡ tha yờu cu bi toỏn Cõu 14: ỏp ỏn B K S H Hng Cung cp ti liu & thi THPT mi nht Trang 12 a Ta cú 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 i ữ = i + ữ = = i i 2 Ta thy: 2i : ỳng (1 i) 10 ( + i) + ( 2i ) ( + 2i ) + ( + i ) = ( 2i ) + 13 + ( 2i ) = 32i + 13 8i = 13 40i ( i ) = + 11i ( 18 26i ) = 16 + 37i : ỳng ) ( 3i ) + ( 3i ( + 2i ) ( i ) = + + + i ( 3i ) + ( 3i ( + 2i ) ( i ) = ( 3i ) + + + i ( 2i ) ) ( : ỳng ) ( ) : sai Vỡ ( ) ( 3) + ( 3) i ( = 5+2 ) Cõu 16: ỏp ỏn A Gi z = a + bi vi a; b Ă z = z + z ( a + bi ) = a b + a bi 2b + a bi 2abi = Khi ú b = a = 2b + a = 2b + a = 1 a = b = b + a = b ab = ) ( 2 Vy cú s phc z tha iu kin bi l z = 0, 1 1 z = + i, z = i 2 2 Cõu 17: ỏp ỏn C x = y = y = x ( x ) = y = 3x ( x ) x = y = Ta cú ; Ta hai im cc tr ca th hm s l A ( 2;0 ) v B ( 0; ) 2 Vy AB = + = Cõu 18: ỏp ỏn D z = 2i z2 2z + = z2 = + 2i (do z1 z2 = 4i cú phn o l ) Ta cú Do ú w = z12 z22 = 4i Vy phn thc ca s phc w = z12 z22 l Cõu 19: ỏp ỏn A Cụng thc tớnh lói sut kộp l A = a ( 1+ r ) n K S H Hng Cung cp ti liu & thi THPT mi nht Trang 13 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 100 (triu) 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 100 (triu) Vy tng s tin ngi ú nhn c nm k t gi thờm tin ln hai l A = A1 + A2 = 100 + ữ + 100 + ữ 100 100 232 triu Cõu 20: ỏp ỏn B b Ta cú xdx = x a b a = b2 a = ( b a ) ( b + a ) = ( b + a ) Cõu 21: ỏp ỏn C Ta cú: iu kin: x + 2x - > x Ê - x (*) - ổử 1ữ ữ log1 x + 2x - Ê - x + 2x - ỗ ỗ ữ = 16 ỗ ố2ữ ứ ( ) 2 x2 + 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) Gi A ( 4;0) Gi B ( - 4;0) Khi ú: l im biu din ca s phc z = x + yi l im biu din ca s phc z = l im biu din ca s phc z = - z + + z - = 10 MA + MB = 10 (*) H thc trờn chng t hp cỏc im M l elip nhn A, B l cỏc tiờu im x2 y2 + = 1, a > b > 0,a2 = b2 + c2 b Gi phng trỡnh ca elip l a ( ) T (*) ta cú: 2a = 10 a = K S H Hng Cung cp ti liu & thi THPT mi nht Trang 14 AB = 2c = 2c c = ị b2 = a2 - c2 = x2 y2 ( E ) : 25 + = Vy qu tớch cỏc im M l elip: Cõu 23: ỏp ỏn A Quóng ng cht im i c l: ( ) ( S = ũ v( t ) dt =ũ 3t2 - 6t dt = t - 3t2 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 y ( 1) = Mt khỏc, vi x = 1, ta cú (nhỡn vo th) nờn chn phng ỏn A Cõu 25: ỏp ỏn C Phng trỡnh honh giao im ca d v th (C ) : x + 2mx2 + ( m + 3) x + = ộx = x3 + 2mx2 + ( m + 2) x = ờj x = x2 + 2mx + m + = ở( ) ( 1) A ( 0;4) Vi x = 0, ta cú giao im l 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= m2 - m - > ùợ (*) (C ) ln lt l A, B ( xB ;xB + 2) ,C ( xC ;xC + 2) vi xB , xC l nghim ca Ta gi cỏc giao im ca d v phng trỡnh (1) ỡù x + x = - 2m C ù B ù x x = m+2 Theo nh lớ Viet, ta cú: ùợ B C Ta cú din tớch ca tam giỏc MBC l S= ìBC ìd ( M , BC ) = Phng trỡnh d c vit li l: d : y = x + x - y + = d ( M , BC ) = d ( M ,d) = M BC = Do ú: + ( - 1) 2 = 8 = BC = 32 d ( M , BC ) 2 Ta li cú: 1- + 2 BC = ( xC - xB ) + ( yC - yB ) = 2( xC - xB ) = 32 K S H Hng Cung cp ti liu & thi THPT mi nht Trang 15 2 ( xB + xC ) - 4xB xC = 16 ( - 2m) - 4( m + 2) = 16 4m2 - 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 - 3y +2z - 2= nờn phng trỡnh ( Q) cú dng ( P ) : x - 3y +2z + m = 0( m - 2) ( Q) i qua A ( 3; 2;1) nờn thay ta vo ta cú m = Vy phng trỡnh ( Q) : x - 3y + 2z +1= Cõu 27: ỏp ỏn B ộx = (n) x2 - 2x = ờ ởx = (n) Gii phng trỡnh honh giao im 2 1 S = x x dx = x x dx + x x dx = ( x x)dx ( x x)dx Cõu 28: ỏp ỏn C 1r r b = 0; ; ữ r 4a = (8; 20;12) , 3 , 3c = ( 3; 21; ) r r r r 55 x = 4a b + 3c = 11; ; ữ 3 Cõu 29: ỏp ỏn B uuu r uuur uuur AB = (0; 2; 1) AC = (1;1; 2) AD = (1; m + 2; k) uuur uuur uuur uuu r uuur AB AC = (5; 1; 2) AB AC AD = m + 2k uuur uuur uuur AB AC AD = m + 2k = Vy bn im ABCD ng phng ( ) ( ) Cõu 30: ỏp ỏn C Gi s phng trỡnh mt cu cú dng: ( S ) : x + y + z 2ax 2by 2cz + d = (a + b + c d > 0) K S H Hng Cung cp ti liu & thi THPT mi nht Trang 16 Vỡ mt cu ( S ) i qua O, A ( 1;0;0 ) , B ( 0; 2;0 ) v C ( 0;0; ) nờn thay ta bn im ln lt vo ta cú d = d = + + 2.1 a + d = a = + ( ) + ( ) b + d = b = 2 2 + + 2.4.c + d = c = ( S ) : x + y + z x + y z = Cõu 31: ỏp ỏn A r r n( P ) = ( 8; 4; ) ; n( Q ) = ( 2; 2;0 ) ( P ) & ( Q ) ta cú Gi l gúc gia hai mt phng Vy = r r n( P ) n( Q ) 12 2 cos = r = = r 24 n( P ) n( Q ) Cõu 32: ỏp ỏn A t k e u = ln du = dx e k x x I k = x.ln ữ + dx = ( e 1) ln k dv = dx v = x x 1 Ik < e ( e 1) ln k < e ln k < e3 ln k < e e k { 1; 2} Do k nguyờn dng nờn Cõu 33: ỏp ỏn B Do thit din qua trc l tam giỏc vuụng nờn Vy din tớch xung quanh ca nún bng S xq = r= l 2 l2 Cõu 34: ỏp ỏn D Xột phng trỡnh honh giao im x = x = x2 = 4x2 = x = ; x = vdt Din tớch hỡnh phng l 2 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 ) K S H Hng Cung cp ti liu & thi THPT mi nht Trang 17 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 ) ( SAC ) ( ABC ) H ( SAB ) ( SAC ) = SA B Ta cú: K AH BC SH BC ( SBC ) ( ABC ) = BC ã SHC = 45o BC AH BC SH Khi ú: a a a AB = BC.cos300 = AC = BC.sin 30o = AH = AB.sin 300 = v nờn M C A Nờn SA = a 1 a3 V = S ABC SA = AB AC.SA = 32 Do ú: Cõu 37: ỏp ỏn A r r r r r r u = 2a + 3mb = 2; 3m 2; + 3m v = ma b = 2m; m + 2; 2m Ta cú: v rr u.v = 4m + 3m m + + + 3m 2 m = Khi ú: 26 + m= 9m 6m = ( ( ) ) ( )( )( Cõu 38: ỏp ỏn C ( P ) i qua im A ( 1;1;1) Mt phng ( P) : x + y + z = Nờn: A v cú vộc t phỏp tuyn ( ) ) uuu r OA = ( 1;1;1) D C B A B D C Cõu 39: ỏp ỏn A K S H Hng Cung cp ti liu & thi THPT mi nht Trang 18 Ta cú: S = AB AA AA = S 4a S ABCD = 2S ABC = AB.BC.sin = a sin V Vy: V = S ABCD AA = a.S sin Cõu 40: ỏp ỏn C ( x, y Ă Gi z = x + yi , ) Ta cú: 2 z 2i = z + x + ( y ) i = ( x + 1) yi x + ( y ) = ( x + 1) + y x + y = 2 Cõu 41: ỏp ỏn C I ( 1; 2;3) Mt cu cú bỏn kớnh R = + + = 14 v tõm ( Oxy ) l d = Khong cỏch t tõm I ca mt cu n mt phng 2 Bỏn kớnh ng trũn giao tuyn l r = R d = Cõu 42: ỏp ỏn C uuu r uuur uuuu r V = 6VABCD = AB, AC AD Th tớch hp a cho uuur uuur uuuu r AB = ( 1; 1; ) AC = ( 6;0;8 ) AD = ( 1; 0;5 ) Ta cú: , v uuu r uuur uuur uuur uuuu r AB, AC = ( 8; 16; ) AB, AC AD = 38 Do ú: Suy Vy V = 38 Cõu 43: ỏp ỏn D 2 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 K S H Hng Cung cp ti liu & thi THPT mi nht Trang 19 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 Ta cú: AO = AB BO = a a =a 3 , R = IA = AB = AO a2 2a =a a 2 S = R = a = ( S ) l: Din tớch mt cu 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 = x2 = x x =1 Xột phng trỡnh honh giao im Suy V = ( x2 ) Cõu 47: ỏp ỏn C ( S) Mt cu cú tõm ( ) 0 uuu r I ( 1; 3; ) IM = ( 6; 2;3) Mt phng cn tỡm i qua im phng trỡnh l: x dx = x x dx = ( x x ) dx M ( 7; 1;5 ) v cú vộct phỏp tuyn uuu r IM = ( 6; 2;3) nờn cú ( x ) + ( y + 1) + ( z ) = x + y + z 55 = Cõu 48: ỏp ỏn A Vỡ D ( Oyz ) D ( 0; b; c ) , cao õm nờn c < K S H Hng Cung cp ti liu & thi THPT mi nht Trang 20 Khong cỏch t D ( 0; b; c ) n mt phng ( Oxy ) : z = bng c = c = ( c < ) D ( 0; b; 1) Suy ta Ta cú: uuu r uuu r uuu r AB = ( 1; 1; ) , AC = ( 4; 2; ) ; AD = ( 2; b;1) uuu r uuu r uuu r uuu r AB; AC = ( 2;6; ) AB; AC AD = + 6b = 6b = ( b 1) VABCD = uuu r uuu r AB; AC AD = b D ( 0;3; 1) b = VABCD = b = b = D ( 0; 1; 1) Chn ỏp ỏn D ( 0;3; 1) M 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) H ( 1; 2;3) i qua im v cú VTPT uuur OH ( 1; 2;3 ) nờn phng trỡnh ( P) l ( x 1) + ( y ) + ( z 3) = x + y + 3z 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; ) 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) , uuu r uuur BD = ( 1;1; ) , BC = ( 0;1;1) * Mt phng ( ABD ) Phng trỡnh ( ABD ) qua A ( 0; 0;0 ) uuur uuur r n = AB; AD = ( 1;1; 1) v nhn vộct lm vộct phỏp tuyn l : x + y z = r uuur r uuu m = BD ; BC = ( 1;1; 1) ( BC D ) qua B ( 1;0;0 ) v nhn vộct * Mt phng lm vộct phỏp tuyn Phng trỡnh ( ABD ) Suy hai mt phng l : x + y z = ( 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 ) ) = K S H Hng Cung cp ti liu & thi THPT mi nht = 3 Trang 21 ...2 2017 [ 2, 4] Cõu 7: Tớnh S = 100 9 + i + 2i + 3i + + 2017i trờn on A S = 2017 100 9 i B 100 9 + 2017i C 2017 + 100 9i D 100 8 + 100 9i A ( 3; ) Cõu 8: Tip tuyn ca... = 2 Cõu 7: ỏp ỏn C Ta cú S = 100 8 + i + 2i + 3i + 4i + + 2017i 2017 = 100 9 + ( 4i + 8i + + 2016i 2016 ) + ( i + 5i + 9i + + 2017i 2017 ) + + ( 2i + 6i + 10i10 + 2014i 2014 ) + ( 3i + 7i +... tin thu c c gc v lói ca 100 triu gi ln hai l A2 = 100 + ữ 100 (triu) Vy tng s tin ngi ú nhn c nm k t gi thờm tin ln hai l A = A1 + A2 = 100 + ữ + 100 + ữ 100 100 232 triu Cõu 20: ỏp