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Kv THr SO GIAO DUC VA DAO TAO A. 1*5;+"o). Ciu 2: Cho hinh l{p rr[I TRUNG HQC PHO THoNG QU6C GIA NAM 2017 Bii thi: M6n Toin Thdi gian ldm bdi: 90 philt, kh1itg kO thrli gian giao THANH PHO DA NANG B. Rr{-5}. C. (-"o;5), ABCD.A'B'C'D' canh a. Tinh phucrng D. de R. diQn tich S ciia mdt cAu r:goai tirip hinh lAp phuong ,1BCD.A'B'C'D'. Cflu 3: 'l'irh C,s=2r*7. B.s=4ra2. 4.. i=ita-- lr + -;1l6irg S c5c gi6 tri nghiQm cta phucnig' trinh ; , l-ltrg:r 5-log,r - = 1. C",s=4. B.s=s. A.,s=r. f).s=zau:'1. D.,s=12. tliang (rti:3-r--),+4=A. Phuongtrinh nAo dudidAy la CAu 4: Cho dLrirrg cong tC) 1y=x3 +2-r2 +3r+4 phuo:rg trinh c0a cluong thlng ti6p xirc vivi iC) vi'rong song r'6i (a'.)? ,ra Ctirmg A. 81.'r -27 1; + J2 = 0. B. .Y C. = 3-x i-4 81-r -2i y -1140 = 0. 268 3, D. l,= '11 C6u 5: Trong khdng gian vdi hC toa d$ Ox1,z, cho ba di6m ,1(1;2;3't, B(*2;-3'.-l) vd Cl(0:1;2). Tint toa dd di6m D 'birr"\ iriirir. sao c!-rc ,,1R{.-i; lii inil hiltl-i D. D(3:6:51. C. D(-t:t;;o). E" i-r1112;+) ,\, Di-:: 1 2:. (.- iiU n: 1- f.;,; ;;. i l" r.: i l,,- .-1.i,--:t,: ;i1 i"i ,, v I vi 1i i,, -;jItlg, 3i ;. nrinn Lli nac :arr dil .,i ; , t"g., -', !9x'il-lol''l i I ,iLirrSl | 1,-n' ,4." ,t; = lirs, I lrI * - 13. ,\t = iit l* 1.,e,1 "At l. f iu 7: liti: i-;j'i.l'0ri hi,:;: cria 1:fm s6 {(.x) =tan2 -r. i\. i i..,; i .., - ir: irc,:,rl + (-1 Fl' i'{.r) ,= -x + ian.r i C. C. ^a(r) = -,r + t:rn,r + C. D. Flri- lnlcc,srl+ C. :,r: + J 8: fdp.-.:i.iitriilu:il;',.lnsr.: s:-11i'- - li: .r'+ l * C. (*z;-^{i} u (J) + "o1. l}. lR. It. li{',{ 2}. A. (-2;+"r). Ciu 9: Cho harrr s5 y .- .r3 - 3r2. Mqnh dA nho sau diy ld sai? B. I{Am s6 AOng bi6n tr0n khoing (3;+co)' A. F{im 16 ding bi6n ff0rr !:hoing (-r;-2). Caal {--. I [i\irr s6 ngl:!cit l',i6rr trcn ki,oang t -?:0). CSu ltl: filrr A. l\r = a ',. i1'g, -1,5. finh 1/ = Ic-rg15135 theo g. -11-. .r -2 ,^i : 11]. a--1 Cffu 11: Trorrg kh6ng gian v6i hQ tqa sao cho tvlA2 + MBz datgi6 tri Cho him s6 y = Ciu C. ,v = o a. * 3" g D. C. uto;o;at). iliOnr lul trtn trqc Oz ,'i1(0;0;3). s6 ducmg tiQm c4n cila d0 thi hdm sd ld: - c. B.lrl=T' rr 2 D.4. t. - 3i' C. l,l= Jm" Trong khdng gian vdi h0 tqa dQ Oxyz, cho ba di6m phang (lBC). a a +1 13: Tinh m6dun c[a sO phuc z th6a mdn di0u kiQn 3z + (2 + i)V = 5 Cflu 14: -r I "'-. I 8.2. J3i. a. lrl rr = 2 D. A-= nhr5 nhAt. r/4..-' A.3. s5 nghicn bi6n tren khodng (0;2). Or1:, cho hai diem -a(2;-3;2) r'd 8{3;5;4). Tim tga d0 B. M(0;0;0). A. Mla;t); g). C6u 12: dQ D. Him l(0;0;5), 8(0;3;0) D.lzl=ze. vd C(l;0;0). Vii5t phuong trinh mat -lr-qn o 1 l4 l\Aa d6 thi 224 A. 5x + 15y + 3z -15 = 0. B. 3x + 5y + z - 5 = C' C. x+ y+52-5=0. D. t5.r+5y+32-15=0. c.1=i.2 D. 1 c. lzl= r:' D' lzl= l Cffu 15: Tinh 1 = Jx(l+ xz)ck. 0 B. I =1, A.1=1' 4 2 Cfru 16: Tinh m6dun A. l,l= Jl CAu 17: eua cria s6 phirc z = lzl=.6. B. mQt diiSm *2+3i. n[m ngodi mpt A. D' 1. a=1. vz4 CAu 19: Trong khdng gian v6i tf cAtr ngoai ti6p r B. lL =1. vz3 hQ tQa t' xirc cAu cti th6 dung duqc nhi6u nhAt bao nhi6u mdt phang ticp C' v6 s6' B. 4. CAu 18: Cho hinh l6p phuong ABCD.A'B'C'D'. Ggi Mlit di€mtrOn dulng gifta th6 Iich v, cta khoi chop M .ABCD vd th6 tich v, cira kh6i l{p phucrng. A. =l'4 d0 Oxyz, cho ba di6m t, Yl I ['z 9 chdo vtii m4t cAu d6? 2' CA'sao cho luIC = -3MA'' Tinh ti D. s6 =!. v24 YL Al2;0;0), B(0;a;0) vd C(0;0;6). Vi6t phuong trinlr nrqt diQn OABC. A. (.r * 1)2 + (Y +2)z + iz +312 = 56. C. (x-1)2 +(y -2)'n(z_342 =14. Ciu 20: C6 bao nhi6u lo4i t<ll6; Oa di€n d6u mi A. s. Ciu 2l : Tim nguyOn him B. B. (x+1)2 +(-v +2)2 +(z+312 =29' D. (x-1)2 +(y '2)2 +(z-3)2 =29' m5i mat cria n6 ld mQt tam gi6c d0u? C. 3. t. D. cira hdm s6 -/ ( x) = cot x. A. I(x)=lnlsinrl+C. B. F(x)=-ffi+c' 1 :x3-l:4t---lnI . b d voi a, b, c D. f(r) C' r(x)=-tan'r+C' .L Ciu 22: Cho 1=l:^ o"-l ^1 Q= o- + lb+c-. 2. li c6c s6 nguy6n ducrng h vir a li c = -lnlcosxl+ C' phdn sd tOi gian Tinh C D' 71' c.74. 8.70. A.7s. lYlitrungdi6m BC' T'inhth6 Cflu 23: Cho hinh l6p phucrng ABC'D.,1'B'C'D' canh a. Gqi ,4,1ldtrungdi6m.4'B', tich tr'cirakh6ifii diqn ,4DlvtN. A. t'- l l .t7 B. -.J V C.'y' =L., 12 Ciru24z Tr€n mpt phing toa d6, tflp hsp di6m bi6u di6n A. Ducrng trdn c6 phu<lrg trinh 12 -F y2 '=2' D. r'= -,. 2 cric s6 phuc z thoa cliAu C. Dudng th[ng c5 phucmg tr]nh r * y =2. Cflu 25: 56 nghiQm cua phuong trinh 2l-''o = 4 ,,] -i =i-. 6 kign izi = 2 la: B. Duong trdn c6 phuong trinh 'r2 + y2 = 4' D. Doan thang n6i hai di6m A(*2;0). B(2;0)' ld: C, Z, 8.0. 4.4. cau26; cho hdm s6 y = /(x) lien tpc tr6n R vd c6 d6 thi le duong cong nhu hinh v6 b€n. Xdt 4 mQnh d€ sau: (1):"Hdms6 y= f(x) datcucd4it4i xo=g" (2): "Hdm s6 y = f (x) c6 ba cgc tri" (3): "Phuong trinh /('x) = 0 c6 dring ba nghiQm thr'rc phdn biQt" (4): "Hdm sO dat gia tr! nh6 nh6t ta -2 tr6n .Io4n [-Z;Z]" Hoi trong 4 mQnh dd tr6n c6 bao nhiOu m€nh A. 1. Cia27z A. B. 3, cl6 dnngf c. 4. D. 1 thuAn io? Cho s6 phri'c z c6 phAn thr,rc vd phdn 6o khhc 0. 56 ndo trong c5c s6 sau la s6 + B. 2.7. C' z-7' D. z +-7. D. r. Z CAu 28: So duong iiQm cfln cita d6 thihdm s6 y' = -t11* A.z. B. o. -x+2 16' c.3. 'I'rang2ll rua dc thi224 Ciu 29: Cho hinh hQp cht nh$t ci, ba kich ihucic i6n luoJ li a. b, c. Tinh b6n kinh R cria m4t cAu ngopi tiiip hinh h6p d6. B. R= r7;rb'z A.R=Jo2*h2*c2. +r; D. R='l 222 az +b2 +c CAu 30: Trong khOng gian v6'i he toa d6 Oxyz, cho liai dir5m A(1;2;3) vd B(-5;2;-l). Vi6t phucrng trinh rnflt cAu (S; nhi)n AB ldm ducrng kfnh. A. C. _ 1x + 2)2 + (1, 2)2 1x+ 2)2 ciu3t: +(y-2)2 * (: - l;2 = 13. B.(*-2)2 -(y+2'12 *12+l)2 =26. +(r-l)2: Jt3. D. (x- chohams6 /(x) A. s = l2lo1. a +(y*2)2 +(z+112 =52. . rinht6ng s = f( :=]*' r[3). =':' /fj=) . f( :=)" ""'. f(yJ\. 25^+5'[zotzi''[2oti)''\zon)''[:ori) \zon)' c. B. s=12107. 6 6 Cflu 32: Cho 2)2 ld s5 thuc du'crng lcrn hun 2. tinh t =i ,s = 6053. D. s = loo8. 6 *i, -tl{r. 2 .1) 1a B. i= !*a' -'t- *o' 32 A. I =--o' c. aa^ JJI 1= -?*at 332 -a2 Cf,u 33: Cho /'(x), g(x) ld hai hdm s6 lidn tuc tr6n dopn [-1;l] vd 1l I f (x)dx : 5, I g!)dx= 7. Ivl€nh d€ ndo sau dAy li /(r) D. ,l = !-o- *q332 . ld hdrn s5 chin, s(r) . ld ham s6 16. Bitlt sai? 0 I -l Ciu 34: Trong kh6n-e ..t8. Bi6t ring kinh R cua iriit tip 1I jg("r)rft=14. C. J Ufrl + g(x)]dr = 10. D. J [/(r) - g(x))dx =10, -i -l -l eian r,oi h0 toa d$ Ox.,-2, cho ba di€tn Al2;3;*4). B(1;l;2), C('3;2;-7). Gqi // ld trung di6m B. A" J/'(.r1dx=to hqp t6t cA c6c di6m ,{/ thoa didu kiQ, + UE +-vrc +UiXl= cdu do. A. t!;+;-c) vd R=12. B. I(Z;Z;-Z) Cflu 35: Cho him s6 y = ax4 + bx2 va 1,1,11 + c va R=12. C. tlc;c;-q) vd D lirmQt mflt cAu, tim tdm R=2. D. / vir brin t(Z;Z; c6 d6 thi nhu hinh b€n. Xric dinh c6c hQ sd a, l, c. B, 4., a=l;b=-2;c=A. C.. t1 a=j:A=-a:r=-1. 33 l1 D.a=''-fi=- 1'-g-i). a=7:b=-2',c=-1. JJ vdi ldi suAt 0,5%/thdng (lai tinh theo tirng th6ng t'a cQng ddn vdo gdc). K€ tir lirc gOi cu sau i fiAnE anh ta rrit ra l0 trigu d6ng d€ chi ti€u(th6ng cu6i cung :..rldj \!"41] khOng dri 10 trieu thi nit tr€|- Hai sau thcri gian bao lAu kC rri ngiry gOi ti0n, tdi kho6n ti6n gdi cua ngucri d6 v0 0 d6ng': (GiA st ldi suAt kh6ng thay d6i trortg sudt quri trinh nguoi d6 go'i ti6t ki€m) D. 102 th6ng. C. loo th6ng. B" t 03 th6ng. A. 101 ih6ng" Cfu 36: lr.lQt nguoi gcri ti6t kiqm 800 tri6u d6ng vdo mQt ng6n hdng C0u 37: Cho him s6 1, = ,3 + n,*2 + (m2 -3m\x + 4 voi m ld tham s5. tim rz d6 ham sao clro xr.x2 <0, A. ree B. [0;3]. ru E(0;3). s6 dat cuc tri tai hai di€m x,, x, C. me(-.o;0)u(3;+co)' D. me(-*;0lu[3;+co). Cffu38:Chohinhphdng(rI)gi6ihanbdic6cdulngcong/=12-2x+1 vd !=-x2 +5x+1. DatdiQntichcriahinh - r - 'd (l4li S=f[ll" u\c) A. Q=IS. Ciu 39: L:ho kh6i BD voi a,h,c.tt litc6cs6nguy6nduongua - B,g=:. c taphansdtoigian.Tinh p =a.b-c.c]- C.Q=9. di6n co chria d6y .4BL'D. Tinh D.Q=zt. phing (P) Alt[ vit song song vtii cIIr I,r ia th6 tich kh6i da diqn c6 chfra dinh S vit V. ld th6 tich kh6i da ch6p tir giric d€u S.ABL:D. Gqi ,L/ ld trung cli6m cira ,SC, mit chiat<tr6i t6p phuong thdnh 2 t<trOi Aa diQn, \=1. A. y. I chrlra ?. V" B. L=!, vz2 c. y.v, D. V, I v2 3 rl? i4rl-:aa, kin phdng kinh doanh cua nhd nghi thdy rdng: cir tlng Ciu 40: Trong mia cao di6m du lich, mQt tO hqp nhi nghi d Ed Ning gdm 100 phong tl6ng gi6 lu6n.lu6n khi gi6 thud ld 560 nghin ddng/pht)ng. Qua kh6o s6t c6c ndm tru6c gi6 phdng ldn xo./o(x > 0) so v6i lric kin phong (gi6 bQ phQn thuO 560 nghin d6ng/phdng) thi s6 phong cho thu6 giam di !'h. 5 Hoi nhi nghi phii ni6m ytit gi6 phdng ld bao nhi€u dil dat doanh thti cao nh6t? ,4.^ B.lltt ('30 nghin ddng. D. 560 nghin nghin d6ng. d6ng, Cflu41:Tr€nrrr4tphingtgadQ Oxy,chodunngthtngdcriphuongtrinh x-,r'+10=0 vihai di6nr.l,Bldn lurolldc6c di6mbi6udi6ns6 phuc z1=1+3i, za=_.4+2i. Tims6phrlrczsaochodi6mbi6udi6n,llcianothudcduongthangr/ vd tu14+ lvtB bd nhitt" A. z=9-i. Ciu 42: cho sii phtrc zthba lz -l + 2il= D.:=-11-,. C. z=-9+i. B. z=-_5+5i. 3 ' N{6dun lon nh6t ciia s5 phirc z ld t--: u.@116 ,/t5tt4+615) ' .- ('. vrJ-6Vs. lj. -"- 5 Cku132Chos6us0th;rc p=(ru r')2 + i fft,tr,p,q,r.s thoa2m+nt-2paJ=0. lr,+-1,-t-4s+i--ii, Ciiitri l,hcnhAtciiabi€uthirc |nr"'fi .r.h=l'i vi-ll ,i p:ta*si1t6lg,:,t,.'I'f:;ir S =1,2 - i'. D. -i = i5 Cl. S = 1295. B. .S = 80. (rr-q)2 +(p-'s)2 codarg A. .\'= 671. Ciu 44: Cho hi.m s6 .), =,y4 ,n*2 + rit4 , vti rn id thanr so. l-im rr C0 di thi trirn s0 co 3 iliOm cyc tri tao thanh nrc\t ianl giao vudng. A. nt B. = -2. m l' L. =']. i'i,r: 45: firn tfp nghigrn S crie b:lt ;'riru,-ng lrrr.tit !,,rr, i ^ i.' l- '.,-r, A. D. m . -llil r,l'ilt j-\1 7lr) ::. (1. c. .l =(-1:0),',[8;26i. I]. S = (_1;81. y=,ar'- .\'. CSu 4tr: Ciro harrr sf; ''JcA-l' r'i.-:i ;i, jli iirairr sO. nlat ring. iilii rit-='! ','tii.t, giriirthid0thihdmc6hai ,Ji6mcuctriEvd('saochotamgi6clBCdi:uvtlri A. 5 = -39. t.&u 47: Cho l[ng trii luc giic nrqit gric tj0"" Tinh diQn C. Cdu ^i:'-[8;:5i. i'i pilliii:i ]' tdi phing (.{'3'1,\) i?o viii cli;, ri ttgu,v6r: du';rrE .:li2:-ir.'ii;rh,:r' -i,i-::il S = -.11. ,ltia'i)Eli .4'B'('I)'E'i"' c6 canlr tich xriiig qualll, -! tu , irlni; trit ngoiii ti6p iAng O6r' l-'ing: a. N1(', fi.t ARCDEF.;i' ]]'C '.D'r{'F'" B. s = 3.rr,''. 1., r r,'i j:1-L--:11= I ta: Cffu 48: Tap hqp c6c ditm nirn trong m6t phing tqa ciQ Or7 bi6u diSn s6 phirc z 16.13 A. B. s i,: ir.-i.- S = 2na1 l s-i1 | 7t -1ti ='t. C.MQiducnrgtrdnc6phucrngtrinlr rt*.,,2*::-i.y-15=0. D.Drio'ngtltingctlphuongtrinil .':-ii-10=(-) A" ivt6rducmgtrdnc,ophucnrglrinh xl r-1,2 r'.r*+31,-15-0. B.Durn-,gthingcopirutrngtrinh .r- Ciu 49: Cho kli6i l6p phucnrg ABCD.A'B'C'D'. Goit.L.V lAn lugt ldtrung cli6rn ct-it ti7 ra 'ii ). rnat nh,lng rC'-\l\ chiakhSii4pphuongthdnh2khSiAadiqn,<lat tr, lith6tichkh6idadiencoth6tichnhdra "v co thd tich lon. Tinh t. iarhitrchkhoi r tJadi€n il. f," /1 A.YL=!. -l,'2 3 B.A=lf. vz 23 Ciu 50: Cho 21, z, lit citc s6 phuc th6a mdn lrrl=lrrl= I vi lr, - ,rl= Jf. tinh .li A.t,=ji. 2 t B.P=I. 2 s. Lt=?7 c.L=L. vi 2 ^^J, C.P= 4 P Ir v2 i 11 I =l-2, )'l 17' +*2"1. t; D. P=9' ) --- n6t --- Trang 4 4 - MdaO tni ZZa so_g]l4.o DrJc vA.oa o r4.o THANH PHO DA NANG KV rHI THt'TRrrNG Hec pHo rHoNG eroc Bii thi: NI6n Toin Thdi gian lctm GrA NAlr 2017 _bai; 90 phut. khdllg ke rhdi gian giao cdu, gdm 04 ffang) (Dd thi c10 c4:l Ho, tOn thi sinh: Me dd thi: S6 bao danh: ...........................Phong thi s6: Ciu f (r) =sint3r + f). L: Tim nguy€n hdm crla hdm s6 A. lf(x)ctr=-1cos(3, *[t*c. B. If(x)dx=-fcos(3x)+C. *[l*C. C. !f(x)cir=1cos(3x D. !f(x)dx=lcos(3x)+C. Ciu2: Cho haihdm s6 l-(x), g(r) li6n tuc tr€n IR, I A. Itf(r) + g(x)ldx C. Ik.f (x)dx = kl f = J f(x)dx + e [4. Mgnh d6 ndo sau d6y sai? B. If(r) + g(x)ldx = [ f (x)dx + I gQ)dx + C. D. itl(r) - g(x)ldx = I fQ)dx - i g})dx. I g!)dx. Q)dx. Ciu 3: Cho hdm s6 y = f (x) c6 d4o hdm li6n tpc tr6n doan [e;e2] .'1,'.1,io'1d*= 5 vd / (e) =l . Tinh . = .f(e2). I L. m=6. B. m=5e-1. Cf,u 4: Cho hdm sd 1, = --v3 + 3.t - l. N{6nh A. cid td cu'c dai cua hdm s6 la t. C. Gi6 tri cuc ti6u crla hdm s5 la -1. m=5+e. C. 116 D. nt=4. ndo sau d6y rlirng? B. gam s6 rh6ng co clrc rri. D. Eitlm cuc ,Jai cua him s,_r Ia Ciu 5: MQt hinh ch6p tam gidc ddu c6 cqnh d6y bdng 3a. cqnh b6n bang 2a.,,5. .-lr - l:-j; Tinh dien rich rnar c6u ngoai i,:n hrnh ch6p d6. A.S=l2aa2. B. S =gna2 C.s=l6ra2. . D. S =l3na2 Cf,u 6: Trong c6c s6 sau d0y, s6 nao c6 thC ld sO cpnh cria mQt hinh l6ng try? A. 36s 1. B. r+rs. C.3626. Ciu 7: Tim tflp xdc rlinh D ctahdm s6 .y = log;(.r2 - 3x + 2). D. 31 r5. D=(l;2). B. D=R. C. D=(-.c;l)w(2;+x). D. D=,<,,,{i;2}. Cflu 8: Goi zi"z2 IAn lLLort ld hai nghi€m cua phuong trinh z2 +22+8 = 0. Tinh gid rri cua bieu thfrc A. tri-l-Ll-I - lzliT l-.1- Ll.ta . A.p=g. 8.p,.."/l_:. C6u 9: Cho s6 phuc z=2-3i-(1+i). Goi di0m C.tr=4vl1_S. ,t/ D.p=S:.,: ln tli6m bii5u di6n cta s6 phac z trOn mrt phing toa d0. Tinr roa cri ,{.4. A. tufQ;$. B. ae:-zj. C. tuI(3;-Z). D. [1(t;--l) * phucrng Ciu l0: Cho trinh 4' - 2x+t 3 = 0 c6 mQt nghiOm duy nh6t ld a. Tinh P =alogt4+1. A..p=2, B.p=4. C.p=3. D. p=5. CAu 11: Trong kh6ng gian vdi hQ tqa dQ Oryz, tim toa dQ t6rn .r vd b6n kinh R cria m[t cAu (^S) c6 phucmg trinh *2 + y' + r? -zx - 4y +22 -3 =0. 4,, I{1;2;-t).R=3. B. I(1;2;-t),R=e. C. t1-t;-z;l).R=3. D. I1-t;-z;1),R=9 C0u 12: Durmg A. tiQm cQn tlimg cia d6 thi hdm s6 y = B. x=-1. Ciu 13: Cho hdm sO y = 2x3 *3mx2 + m+l v1i -y=1. ti6ut4i x=1. A. m=A. Ciu 14: Tim si5 A. z=-3. Ciu ,U, C. x=1. m ld tham s6. tim B. m=-1 . -i)z+2+i=0. C. nt=|. B, z =l+2i. C. D. x=2. tdt cit c6rc gi6 tri cria tham s6 D, m rr d6 hdm s5 dat cu'c =2 phric z Ul6t 1t 15: Trong khOng gian vdi duong thdng d? # hO z=!*1,. 22 tqa d6 Oxyz, choduong thing d,', 1 D. = 2tr y+l I 3. 22 -z -l . Di6m ndo sau ttdy thuQc Tranc l/+ - Me dd thi 223 A. tuf{s;t;3). Ciu p(i;2;3'). B. p(-l;l;*t). C. D. .ry(5;0;3). '2 -* *o * x2 + t7 . Menh da ndo sau d6y dring? A. Hdm s6 c6 mQt cuc ti6u vi khdng c6 cr,rc dai. B. Ham s6 c6 mQt cuc dai vi khdng c6 cyc ti6u. C. Hdm s6 c6 mdt cuc ti6u vd hai cuc d4i. D. nam sd c6 m6t cuc dai vd hai cuc ti6u. Cdu 17: Hdm sti ! = -x3 + 2x2 - l0 d6ng bi6n trdn khoing: A. ( ,. [c. [n.[0,1] (, J: J:J \. J: ,/ ', ,,, 16: hdm s6 y = Cher .o;o) Ciu " 18: Cho hdm s6 y = tn, A, M = ln2-1. Ciu +,+\ 1,ol -lr2 z +1.Tim giritri 16n nn[t B. M =1-h2. 882 19: Tinh ilgo hdm cria hdm s5 y = 5loe: Cfiu 20: Tim t{p nghidnr S _ lltrl. cira hdm sd tren C. M l.z_) l. =1+u.2. l,t =!. x . 5lo-.2,1n5. B. ),,=5loer,-l.1ogz.x. A. ),,- U cua b5t phucrng trinh log, (+ C. y,=5 log:x. xln? ln-5, D. y,= ' 5"tt'.I:. xln2 -:x) -+. < a A.s=i-*.ll I j.! / Ciu 2l: s.s=11,:l [:'-.] !4 ' Cho hinh n6n C.,s-z \ D.s=( ,: j) (.V) c6 b6n kinh dutrng tron diiy R=2 vatlQ ddi duong sinh / = 4. Tinh di€n rich rung quan)r S,,, ciia krinh n6n (.\-). A. S*q =82. B. &q =16n. C" -\, =+r. D. .\n =g. I Ciu22:Chohais5thuc a"b th6a3a+2b=1 vir t=il(*+b)sinxdx=4.Tinhgiiitribi6uthuc p =a-.b. 0 A. P=ll. Cflu 23: Tim A. s6 phri'c ; th6a (3 + i)z = (3 +V)i r=t+1i. 2 CAu24: lvi0t hinh P=_7. B. c. P=4. . r=?+i. 3 B. D. P=_tg. C. r=1+1. 2' D. z=t*?r. '3" li; ch6p tam giSc diu S.ABC c6 canh d6v bing a vd th6 rich l' ='..*' 12 . Tinh d0 ddi canh b6n Sl cua hirrh ch6p. A,. sA = t la. 3j 13. .s.4 = ^G :-\2a. Cflu 25: Trong lih6ng gian vcri hC toa d6 phSng (a) ld: A. ;=Q;o;-l). C. s,t = o,1. OxVz, cho mdt phang (a) '.2x B.;=(l;0;-1). D. .s:^/ =, a. * z +-l = 0. Ir,lot vecto phap tui,en cua mat C.i=(z:-r;t). D.i=(-2:0;-l). Ciu 26: Cho hinh lang tru ABC.A'B'C' co dity ABC liltanr gi6c vu6ng tqi B, ,18 = u , .{C-E = 300 . Hinh chi6u vu6ng g6c cria dinh A ' l6n m4t phing UBC) ld trung di6m /1crla cqnh AB, G6c giira canh b0n vd mqt dily c0a lang tru bang 601 Tinh theo a th6 tich kh6i lang ffv ABC.A,B,i, . A. i;--) 'il24 3a- Cfru 27: Tinh dao hdm c0a hdrn s6 A. .y' = 2' .1n2. 4 ! : . .i r;3 p. vla'. C. y, = !=. D. 8 = Z' di 8 . B. y, = 2, . Cfiu 28: Trong kh6ng gian vdi h0 toa 3u' c. -r J e--3 B. Oxyz, cho ba di6m in2 y, = x.2,-t. l(a;0;0), B(0;&;0) vd C(0;0;c;. Vi6t phuong trinh mar cau ngo4r trep tu di€n OABC. ,*'-]:-'r+&:*c:. - z \ 2) ('r., r /.,]'=,,:+]r+c:. B. i.,*ij'.,.ir,*11' \ :,J -i'-r.i *(-\--r) ^.(r**j'*(r.1j'*['n: c. f ,-il'* (r-!]'*f =-i)'= g-t n,: D. tt-..: ,-i, "'["l',- {'}' \. 2) l'1) \ 2; 4 2,] 'r'' -gl' 2) n{l-,-!))1'=- a Trens 2i.1 - Nla d€ thi 223 lx=t Cfru 29: Trong kh6ng gian v6i hQ tga dd Oxyz, clio cluong thdng A,]y=t , mflt phing (P) c6 phucmg trinh l"---1- 2x+y-22+1=0. Gqi l/ lddi6rnthu6c A vdc6hodnhdQbing2.Tinhkhodng 11 A. rt=i. 33 )t circh c. d =4. B. a =L6-. d tir,V D. ddn (P). d =0. CAu 30: Cho hinh tru c6 b6n kinh duong tron day ld R = 3cm. Ggi S,r,S,, lAn luqt ld dien tioh xung quanh vd di6n tich todn phAn cira hinh tru. Tinh S = S,o - S,r. D. s=lLrcml. C. s= 6acm2. A" s=l|ncm2. B..s=9ncm2. Cf,u 31: Trong kh6ng gian v6'i hQ tga dQ Oxyz, cho mAt cAu (S):(x-3)2 +(y+2)z +(z-l)2 =9 vd mat phing (P):x+2y+22+11=0. Kho6ngc6chng6n nhl,t d tirmQt dilm Iv{ tr6nm?tcAu (S) cl6nm4tphing (P) ld: '7_'l_'7 D. d =-. B. d =t. C. d =1. A. d =:. q52 Chohinh thang ABCD AiCt ATA='iic=90', AB=Scm. BC=3cm, AC=7cm. Quayhinh thang ABCD trong c[ra n6 quanh duong thing AB t4o n6n mQt kh6i trdn xoay. eiet th0 fich V cira khdi trdn xoay c6 d4ng Ciu32: vd r,riA:n L'==!n roi ,r. le N, l hb A.,S=.11. laphAns6t6ieian.Tinh S =a-51s2. C..S=t09. B.S=-23. D.S=6i. C0u 33: Trong mta cao di6m du llch, mQt td hqp nhd nghi o Dd Ning g6m 100 phong rl6ng gi6luern-lu6n kfn phong khi gid thud ld 480 nghin d6ngiphong. Qua kh6o s6t c6c ndm tru6c bQ phAn kinh doanh c[ra nhd nghi thAy rdng: cir tdng voi ltc kin phdng (gi6 gia phong i€n xoh(." > 0) Hoi nhd nghi phai nienr ;''6t gi6 phong ld bao nhi€u dtl dat doanh thu cao nh6t? A. 540 nghin so d6ng. thuO 480 nghin dOng/phong) ddng. B. 660 nehin d6ng. ll La*C l:(r ., C. +go nghin Ciu3.1: Gqi l.i: B:Cl lamcitnghi0mciahiphuongtrinh p=(t-A)2 +(2-B)2+(3-C)2 cridqng ! yoi a.be N. bb I I :..q*S_;*,=,'.,. D. 600 nghin dong. Bi6tgi[trinh6 nhdt ru c0abi 6uthir.c ldphAnsotOigian. Tinh S =a2 -b3. C.5=-219. B.5=360. A.5=*463. thi s6 phong cho thu6 gidm Oi 11'o; ) D.S=0. Cdu35:Chohinhlangtrr,r ABC.A'B'C'v6'i AB--u, BC=2a, FEi:=60'. Flinhchitiuvuongg6cctia .4'l6nmEtt 'tinh thO tich phring (lEC) trung v6i trgng tirn G cua tam giin ABC. Ci6c gifr'a AA' vit mit phing (ABC) bing 60'. I,' cuattr6i ch6p .4'.ABC. A. i'= r.!' c'V3. 3 B. v 3 cflu36:chohdmso A. :,.:- B.s=i00!1 555 A. lirc6c s6 phric thoamdn R D. thuc a, P=-6. Ciu 39: Cho s6 phtSc z b c.s=s014. firn -rt lt,l=lrrl =2 vd lr, -rrl=..6. B.P=Jj. *'4 s6 --1 v' =+1 2 1 P=9' 4 CAu 38: Cho hai 1/: 6 r={lI4 s= l[]=l.r[-1=i.,./f r(\)=16*ro'-.rinht6ns i- l. - f(?:t:\ \ ]017 20ti ) " \zO0 ) [:Ol7 ,t i .l A.s=r008. Cfru 37: Cho =L. 3' C. c.P=!. 15 D.s=ryBq r'|ll P =l+2,, +--i't:. 4 .l 14 D.P=9. 16 thlarndn d6ng thcri ding thuc 3-o.2b =1152 vd loguq(a + b) B, P=-3. c6 phAn io im, C. P=8. th6a mdn d6ng thoi hai di6u -2. Tinh P = a * b. D. P=-9. kiQn lrl2 +22.V+lZl,2 =B vd z +V=2. Tinh m =11+ 2zl. A. m=^,|i. Csu 40: Tinh diQn tich .l thing x = 1. B. m=J10. C, rt=Jn. Y. *=JG' cua hinh phing gi6i h4n b<yi c6c dulng cong c6 phucrng trinh y = 1l -.r)s, Trqno | = e' vd, <tudng 11,1 Mi .tA thi 2?l A.S="-?. 3 4l: Cf,u Cho hdm I C.,s=e-l. C.s= B.s=e-|. - 6 xsr5 v = -;i 3 c6 d6 thi (c). Bitit rdng tr6n B(0;*2)' Gqi 1 latrungdi'5mcriado4n to'{.Tinhkhoing A.d=+. 5' Ciu 42: Cho hdm sO 71-r; A, bb (c) cdch B.d=+ 5' ., D. ^g=e+.I. chi c6 hai di6m M,N f (a + b * x) = Ixf(x)dx=aif@+b-x)dx. l(2;0) va ti tir l il6nduongthing A :3x+41t-5=0. c.ct=3 .d=l li6n tuc tr6n [a;D] rh6a circhttOu hai di€m ,.r=+. f (x),yx u[o;b]. M€nh d6 ndo sau d6y d[ng? B.lxf@ax=(o+fl|,761ar. aaaa c.blxr(x\dr=oobl767a*. " D.1*fula*=*ira+b_x)dx. , 2.Ciu43:Timt6tc6cdcgiritri criathams6 z d6hdrns6 y= x+m-1*-l_ c6di6mcucdai vddiilmcucti6uthu6c x+m khoang (-a;o). 2 o ;" .7 A. 0. *. r. B. Cfru AlzCho hdm s5 y = I< {#:1 l"l- I n <3. C, _1<m <2. D. !.*.3. MOnh de ndo sau d6y cting? 5' A. IUdm rdtrr su s6 uu co hai Iral Glem di6m cuc oat dai vd mot mOt di€m cgc ti6u. titiu. B. Hdrn s6 c6 c' Hdm sd khang c6 di6m cgc dai vd c6 hai dii5m cqc ti6u. ;.;;rl s6 rn6t cti6m cgc <Iqi vd hai tliiim cuc ti6u. c6 m6t diiln cuc dai vd m6t di6m cuc ti6u tic, 9i: 1I Y!,-",elriSoi.ri6t kiem 700 tri6u d6ng vdo rn6t ngdn hdng v6i lai su6t o.s%'o/thdng (lSitinh theo timg thring vd ;fl::,'31l1",.?:i:1,.::,:1i:: :*,:::::.fi14;rr ffi'#',r;?{;ijL}i;i;:, ftffiif:lliJffi:r,*,liilil; gli::Fi;;, ffi:,;i;#*;#firJ,:ffi;iffljt 5ffili i8r:,,T,',1,:l'ilj::Hl'jl,T.:::::il'l::::j':: tii suai khong tlrar doi trons suot q;;ri;[;g;l;i;;1;1,?;e;; (Gia sii A. 87 tl-riing. B. as rhang. CAu 46: Cho hai s6 phric -2. 21, A,. zJi Cfru 47: Trong cric sti phric a. l',1=1 z2 th6a lr, B. z C. 86 thring. D. s4 thiing. - ql= I vd liz, -Zl= L Tim giii tri nho nh6t cria lr, _ ,rl. z"ti. C. 3. thoamdn di6u kign lzzi =l3z +v + i,,l='i c. 21, o. +_Ji. goi zo Id s5 phric c6 m6dun nho nh6t. Tim lal=i rr. lau f ?: ,li hdm s6 rrong hinh b6n td d6 thi cta m6t trong bdn hdm s6 dusc n6u trong b6n drip 5n A. B, : c, o. o5 ttii d6 rd cira hdm s6 ndo? A.y= -xa-B*2+1. !=.-xo-Bx,+l.B.-t,=_xa+8x2+l.]l,\il--\, B._r,=_xa+8x2+1. C. .r=r4-8.r1 +1. lr=ra-8r2+1. n -. r_-r3 ^ 2 D.),=_lrlr+3x2+!. lz6l. l,,i=j-i ,1, i , ,,,T\,' I' ,t i ,,.-,\ i :,i '' -# - f i l-rt -",r.lt -__]. r-+-l -'ttlll-"1* !' Jl*ra A. lJ @)dr = !r,r*, - ,[7) * c. C' t ft*lci*= 11'.[lJ*g' B. ! f(x)dr = |m{*, * Jr * ro ) * c. D. [f(x)ctx=f tnk -.,[t**ol*c. Cfiu 50: cho khdi tru c6 hai d6y ld hai duong trdn (o), (o') voi o, o' l[nluqr ld t6m cria hai r1iy, gpi s ld trung di6m cria oo'' Khdi ch6p ddu S.ABCD v6i <l6y ABCD nQi titip rluong trdn (o) .Gsi vt, v. btnlucyt tdth6 tich cua 4 kh6i rru vd thl!tich crta khtii ch6p d6u S.ABCD. Tinh A"k=6n. B.k=4n. t =L. v2 C.k=3n. *- H6t --- D. k =12n.