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6 ON LUY'N THI THPT QUOC GIA MUC DQ (DJ thi6 05 trang) (DJ c6 ldi giai) Mon: Toan Thai gian lam bai: 90 phut, khong k€ thai gian phat dS Caul: Ham s6 y = -x3 + 3x2 + c6 bao nhieu di€m eve tri? A B C D Cau2: Trong khong gian Oxyz, cho hai diSm A(1;1;-1) va B(2;3;2) Vecta AB co tQa d()la Cau 3: s6 phuc z = a+ bi (a, b E D (3;4;1) Jll) la s6 thu~n ao va chi B a* 0, b = A a= 0, b * Cau 4: Ham s6 y c (3;5;1) B ( -1;-2;3) A (1;2;3) C a = D b = f (x) c6 d6 thi nhu hinh ben la m9t b6n ham s6 duqc li~t ke b6n phuang an A, B, C, D du6i day Hoi ham s6 d6 la ham s6 nao? A f ( x) = x - 3x2 • B f ( x) = - x + 3x = C f(x)=x -2x D f ( x) = x - 3x Cau 5: BiSt F (X) la m()t nguyen ham cua f duqc tinh theo cong thuc nao sau day? A C I: I: (X) va f (X) xac dinh tren [a; b] Khi d6 tich phan f(x)dx = F( a )-F(b ) B I: f ( x) dx = F (a)+ F (b) D J: f ( x) dx = F (b)- F(a) f ( x) dx = f I: f (X) dx (b)- f (a) y- Z- d' ' xyz, duang ' X = A ' dUO'l d"ay.? " 6: Trong 1r1 " C au u1ong g1an th~ang d : - = - - qua d'1em nao -1 A Q(2;-1;2) B M( -1;-2;-3) C P(1;2;3) D N( -2;1;-2) r' Cau 7: v6i gia tri nao cua A XE ( -2; 2) X thi ham s6 y = 1n ( - x ) xac dinh? B XE [ -2; 2] C Cau 8: Cho cfip s6 c()ng ( U11 ) v6i u1 = va u2 = XE Jll \ [-2; 2] D XElll\(-2;2) Cong sai cua cftp s6 c()ng da cho b~ng A -6 B C 12 D Cau 9: s6 each chQn hQC sinh tir hQC sinh la c c; A 27 • B 2! D Ai Cau 10: Khi tang ban kinh cua m~t c~u len hai l~n thi thS tich cua kh6i c~u gi6i h~n bai m~t c~u d6 tang len mfty l~n? A 2l~n B 4l~n " 11 : T'1m t~p " xac ' d'nh D cua " h'am so: y C au l C 6l~n = 1og2 -x · X D 8l~n A D = (1;+oo ) C.D=(0;1) D = ( -oo; 0) U ( 1; +oo) D D = JR \ {0} Cau 12: Trong khong gian Oxyz to~ d9 cua vecta ~ = ' A (2;-3;4) B (-3;2;4) Cau 13: Kh~ng dinh nao sau day la kh~ng dinh sai? 27 -3] +4k la c (2;3;4) ex+l e+l A Jxedx=~+C e+1 C D (2;4;-3) B f exdx = +C x+1 Jdx = 1n lxl + C D X Jcos2x =~sin2x+C Cau 14: ThS tich cua kh6i l~p phuang c~nh 2a b&ng A 8a B 2a C a D 6a Cau 15: Cho ham s6 y = x + co d6 thi (C) Bi~t diSm I la giao diSm hai duemg ti~m c~n cua x-3 T oa do" cua I 1'a (C) ? A (3;2) C ( -~;0} (2;3) B D ( 0;-~} Cau 16: Trong khong gian Oxyz, khoang each giua hai m~t ph~ng (P):x+2y+2z-10=0 va m~t ph~ng (Q) : x + y + 2z- = b&ng c D.- A.- B.- 3 Cau 17: Tim cac s6 thvc a va b th6a man 2a + (b + i)i = + 2i v6i i la dan vi ao D a= 1, b = A a =0, b = B a=-, b=1 C a= 0, b = Cau 18: Cho kh6i chop ru giac dSu co tftt ca cac c~nh b&ng 2a ThS tich cua kh6i chop da cho b&ng A J2a3 A A • , : Cau 19: Do thl ham so y = A B 8a3 x-1 -J C s.fia3 D 2.fia3 co bao nhieu duemg ti~m c~n? 25-x2 B D.4 C * Cau 20: Cho s6 thvc a > 0; a Gia tri cua logaz ( ifd) b&ng A - B - C - 14 Cau 21: Trong khong gian Oxyz, m~t cfiu co tam I(1;1;1) va di~n tich b&ng 4Jr co phuang trinh 1a A (x-1f +(y-1) +(z-1f =4 2 C (x+1) +(y+1) +(z+1) =4 Cau 22: Cho ham s6 y = f(x) co y= x ) la bao nhieu? f( 2 2 (x+1) +(y+1) +(z+1) =1 d~o D (x-1) +(y-1) +(z-1f =1 ham f'(x) = x( x -1 r( x+ 2f Khi s6 diSm Cl,l'C tri cua ham s6 A C Cau 23: Ki hi~u z1 , z la hai nghi~m phuc cua phuang trinh z - 3z + = Gia tri cua lz1i + lz2l b&ng A Co D 10 2JS J5 Cau24: Chohinh1~pphuong ABCD.A'B'C'D' G6cgifrahaim~tph~ng (A'B'CD) va (ABC'D') b~ng A 30° B 60° C 45° D 90° Cau 25: Duemg cong hinh ben 1a d6 thi cua ham s6 nao du&i day? x-1 A y= -x-1 B _ x+1 _ x+1 Y C y x-1 -x+1 x-1 D y=- x+1 ax-b ' C au 26 : Cho h'am soA y = - cor dAo th'l nhu h'nhb" en _~_T/t ~ _uang d'nh l nao du&i day 1a dung? x- A A < a ( 1; +oo) m, M l~n luqt la gia tri nh6 nh~t, gia tri l&n nh~t cua ham s6 f(x) tren do~n [0;6] Gia tri cua M 18 12 -m la b~ng 16 Cau 46: Cho ham s6 y = f (x) lien U)c tren R va co db thi nhu hinh ve du6i day T~p hqp tfit ca cac gia tri thvc cua tham s6 m dS phuang trinh f (sin x) = m co nghi~m thu()c khoang ( 0; tr) la y A ( -1;3) c (0;1) B ( -1; 0) D (-1;1) Cau 47: Cho kh6i chop S.ABCD, ABCD la hinh thang v6i hai day la AB va CD, AB = 2CD GQi E la m()t diSm tren c(;lnh SC M~t ph~ng (ABE) chia kh6i chop S.ABCD hai kh6i da di~n co thS tich b~ng T? ; SE b~ so SC ang A M -2 B -vr;6 - C -vr;:; -1 D J26 -4 2 Cau48: Chohams6 y=f(x)=x3 -6x +9x+l Phuangtrinh ![!(f(x)-1)-2]=1 cotfitcabaonhieu nghi~m thvc? A B 14 C 12 D 27 Cau 49: Cho hai s6 phuc z va w thoa man z + 2w = + 6i va jz- wj = Gia tri 16n nhfit cua biSu thuc jzj + jwj b~ng A.4J6 B.2~ C.~ D.3J6 Cau50:Chohams6 f(x)=mx +nx3 +px2 +qx+r(m, n, p, q, rEJR) Hams6 y=f'(x) codbthinhuhinh ve du6i day T~p nghi~m cua phuong trinh f (X) = r co s6 phfin tlr la y -1 A.4 B C.l D 8 (fJJ thi c6 06 trang) (fJJ c6 lm giai) Mon: Toan Thai gianlam bai: 90 phut, khong kS thai gian phat d~ Cau 1: Cho ham s6 y = f (X) lien t\IC tren dO:;l11 [ -1; 3] va c6 d6 thi nhu hinh ve du6'i day GQi M va m l~n luqt la gia tri 16'11 nhftt va nho nhftt cua ham s6 da cho tren do:;ln (-1; 3] Gia tri cua M- m b~ng y -1 :r -2 -A C.4 D.5 B.l Cau 2: DiSm M hinh ve ben du&i la diSm biSu diSn cua s6 phuc nao du6'i day? 1/ p I' z1 = -2 + 2i z = + 2i z = -2 - 2i z = - 2i Cau Trong khong gian Oxyz , cho m~t ph~ng ( P) : 3x- z + = Vecta nao du6'i day la m()t vecta phap tuy€n cua (P)? 114 Cau ~ = ( 3; -1; 2) = (-1; 0; -1) D:;lo ham cua ham s6 f' ( x) = In ( x + 1) f( x) =In( x 113 = ( 3; -1; 0) 112 = (3; 0; -1) + 1) b~ng f' ( x) = In 2x f'(x)=-/- X +1 f'(x) = ;x X +1 Cau 5: Tu ph6 A dSn ph6 B co duemg, m ph6 B dSn ph6 c co duemg Hoi co bao nhieu each dS di mthanh ph6 A qua B dSn C D 16 each A each B 12 each C 15 each Cau 6: Cho ham s6 y = f (x) co bang biSn thien nhu sau +oo -00 X ~5 ~+oo f(x) T6ng s6 ti~m c~n ngang va ti~m c~n dling cua d6 thi ham s6 da cho la A B C D.2 Cau 7: Cho cftp s6 c()ng ( U 11 ) co s6 h~ng dftu u1 = va cong sai d = Gia tri cua u4 b~ng A 22 B 17 C 12 D 250 Cau 8: Trong khong gian Oxyz, m~t cftu (S): x + y + z - 4x + 2y- 6z + = co tam la A ( -4;2;-6) B (2;-1;3) C ( -2;1;-3) D ( 4;-2;6) Cau 9: HQ nguyen ham cua ham s6 f (X) =ex +X la Cau 10: ThS tich cua kh6i non co thiSt di~n qua t11).c la tam giac dSu c~nh a b~ng B J31Ca3 C J31Ca3 48 24 Cau 11: Gia tri cua a dS ham s6 y = log2a+3 X d6ng biSn tren ( 0; +oo) la D B a > -1 C < a < Cau 12: Cho kh6i chop co thS tich b~ng 6a va di~n tich day b~ng a • ChiSu cao ctla kh6i chop b~ng A 6a B 3a C 2a D 18a A .J31Ca3 Cau 13: Cho 2 I f(x)dx = va I g(x)dx = 1, tich phan I(f(x) + 2g(x) )dx b~ng A.6 B c D.3 Cau 14: Trong khong gian Oxyz, vecta nao du6i day co gia vuong goc v6i m~t ph~ng (a): 2x- 3y + = 0? A ;(2;-3;1) B b(2;1;-3) Cau 15: Ham s6 y = -x4 + 2x3 - C ~(2;-3;0) D d(3;2;0) 2x -1 nghich biSn tren khoang D (1; +oo) Cau 16: Trong khong gian Oxyz, cho diSm A ( 2; -4; 6) M~t cftu duemg kinh OA co phuang trinh la 2 A x +y +z2 =56 Cau 17: Ki hi~u A B (x-1) +(y+2f+(z-3)2 =14 z1, z2 la hai nghi~m phire cua phuang trinh z = -3 Gia tri cua lz1+ lz2 b~ng B 2.J3 C D .J3 1 Cau 18: Kh6i h9p c6 di~n tich day b&ng S, d9 d:H c~nh ben b&ng d va c~nh ben t~o v&i m~t day g6c 60° c6 thS tich b&ng A SdF3 Sd SdF3 SdF3 2 Cau Trong khong gian Oxyz , cho hai diStn A ( 1; 3; -4), B ( -1; 2; 2) Phuong trinh m~t ph~ng trung t[\!c cua do~n th~ng AB 1a 4x-2y+12z+17=0 A 4x+2y+12z+7=0 4x-2y-12z-7 = C 4x+2y-12z-17=0 Cau 20: GQi ZI, z2 1a hai nghi~m phuc cua phuong trinh 3z - 2z + 27 = Gia tri cua zllz21 + z21zll b&ng A Cau 21: Gia tri eve tiSu Ycr cua ham s6 y = x + C 3J6 J6 ±- 1a X A Ycr = -3 Ycr = -1 C Ycr =3 D Ycr = Cau 22: Nguai ta t~o m9t 6ng thong gi6 b&ng each khoet m9t 16 c6 d~ng hinh tf\1 giua m9t 1d16i tf\1 b&ng kim 1o~i (ca kh6i trlJ.nay c6 cling tf\lc va chiSu cao), sau d6 c~t kh6i wa t~o ph§n b&ng Bi~t ban kinh day cua kh6i kim 1o~i ban d~u 1a 5m va chisu cao 1a 3m, hoi duang 1dnh day cua ph~n 16 duqc khoet phai 1a bao nhieu ds thS tich cua 6ng thong gi6 d~t gia tri 15, 751r m3 ? A 2m B 4m 79 C.-m 79 D.-m C au 23: Trong khong gian Oxyz , cho hai vecta ~ ( 2; 1; -3), y(l; 0; -1) TQa d9 cua vecta ; = ~ + y 1a A ;( 4;1;-1) ; (3;1;-4) ; (0;1;-1) ; ( 4;1;-5) Cau 24: Cho hinh ch6p S.ABC c6 day ABC 1a tatn giac vuong din t~i A, AB =a, c~nh ben SA vuong g6c v6'i m~t ph~ng day, g6c t~o b&i hai m~t ph~ng (ABC) va (SBC) b~ng 60° va chi SA b~ng r;; A 'Y3a J6a Gia tri 16n nh~t cua ham s6 y = -3x4 +4x3 1a Cau C J6a J6a -1 10 Cho a va b 1a hai s6 thvc duong thoa man a b = 16 Gia tri cua 41og a+ 1og b b~ng 20 Cho I (X)' I (-x) lien 1\!C tren IR va thoa man 21 (X)+ 31 (-x) = -2 K~t qua tich phan X +4 I= f~ 1( x )dx 1a Cau I= Jr I=!!_, I=!!_ 10 20 2 D6 thi ham s6 y = x - 3x + 2x -1 c~t d6 thi ham s6 y = x - 3x + t~i hai diSm phan bi~t A, B Khi d9 dai AB 1a AB = AB = 2/i AB = AB = Cau 29: NSu logs a+ log4 b2 = va log4 a +logs b = thi gia tri cua log2 ( ab) b~ng A.9 C.l B 18 D.3 y Cau 30: Cho hatn s6 y = f(x) lien tt;tc tren ~ va ham s6 y = g( x) = x.f( x ) co d6 thi tren do~n [0;2] nhu hinh ve ben BiSt dien tich s cua mi6n duac t6 dam b~ng ~' kSt qua • tich phan I = f (x) dx la f A I=- I B I=- C I= Sl I I D I= 10 X Cau 31: Buemg ti~m c~n dung va ti~m c~n ngang cua d6 thi ham s6 y = _!_- hl A Ti~m c~n dtrng x = va ti~m c~n ngang y = x B Ti~m c~n dtrng X = va ti~m c~n ngang y = -3 C Ti~m c~n dtrng x = , khong co ti~m c~n ngang X = va ti~m c~n ngang y = D Ti~m c~n dtrng C!lu 32: Cho ba s6 duong a, b, c thOa man dieu kien ' duo'l r d" "nh d.;\_e nao Mv ay 1'a d'ung.? Jb -Fc ,-Fc fa ,fa Jb b+ c c+ a a+ b 1ftp tbanh m(lt c~p s6 c(lng A Ba s6 a, b, c l~p m{)t c~p s6 c{)ng ; -b,1 1"~p t h'nh " cap ;; so;; c9ng " B B a so-, a m9t a c 2 C Ba s6 a , b , c2 l~p m{)t c~p s6 c{)ng Fa, D Ba s6 Jb, fc l~p m{)t c~p s6 c{)ng Cau 33: Co 10 vien bi co ban kinh khac nhau, vien bi xanh co ban kinh khac va vien bi vang co ban kinh khac Hoi co bao nhieu each ch9n vien bi co du ba mau? A 42913 B 42912 C 429000 D 42910 Cau 34: Trong kh6ng gian Oxyz, cho hai m~t c~u (S1 ), (S2) co phuong trinh l~n luqt la (S1 ): x + y + z = 25; (S2): x + y + (z -1)2 = M()t duemg th~ng d vuong goc v&i vecta ~ = ( 1; -1; 0), tiSp xuc v&i m~t c~u ( S2) va c~t m~t c~u ( S1 ) theo m{)t do~n th~ng co d{) dai b~ng Vecta chi phuong cua d la A u1 = (1; 1; F3) B u2 = ( 1; 1; J6) C u3 = (1; 1; 0) D ii; = ( 1; 1; -F3) Cau 35: Cho kh6i non ( N) dinh S, chi6u cao la aF3 va d9 dai duemg sinh la 3a M~t ph~ng ( P) di qua dinh S, c~t va t~o v&i m~t day cua kh6i non m{)t goc 60° Di~n tich thiSt di~n t~o bm m~t ph~ng ( P) va kh6i non ( N) b~ng A 2a JS B a F3 F3 .J5 C 2a D a 2 Cau 36: Cho ham s6 y = 2x + 3( m -1)x + 6( m- 2)x -1 G9i S la t~p hqp t~t ca cac gia tri thvc cua m dS ham s6 co hai diSm eve tri dSu thu{)c (-2; 1) I