TRAN TIEN Tl/ - PHAN VAN HU&N - HUYNH VAN UT DE THI DAI HOC - CAO DANG Khoi A TOAN - LI - HOA THJ VlfN Tii^HbiNM THUAN NHA XUAT BAN DAI HQC QUOC GIA HA NQI F AH r.nhasachkhangvje )T THANH VIENDWH I - p. Dakao - Quan 1 - Tp.Ho Chi / - 39105797 - 39111969 - 391119d !yahoo.com.vn nsviet.vn 16 HANG CHUOl - HAI BA TRUNG - HA NOI Dien thoai: Bien tap - Che ban: (04) 39714896 Hanh chi'nh: (04) 39714899. Tonq bien tap: (04) 39714897 Fax: (04) 39714899 Chju tract! nhi$m xuat ban: Giam doc - Jong bien tap: TS. PHAM TH! TRAM Bien tap: BUI THE Che ban & trinh bay bia: TUONG VY Doi tac lien ket xuat ban: Nha sach SAO MAI 3Q SACH LIEN KET GSdl THIEU & HD GIAI CHI TIET OE THI OH - CO KHOI A: TOAN - LI - HdA Ma so: 1L-306 DH2012. ; In 2000 cuon, kho If x 24cm. Tai CTY TNHH MTV in Dudng sat Sai Gon. DC: 136/1A Tran Phu - Q.5 - TP. Hp Chi Minh. So xuat ban: 1264-2012/CXB/07-204/DHQGHN. Quyet dinh xuat ban so: 306LK-XH/XB-NXBDHQGHN In xong va nop luu chieu quy I nam 2013. BE THI TUYEN SINH DAI HQG,CAO DANG NAM 2004 - 2005 M6n: TOAN; Khoi A I Thdi glan lam bat: 1§C phut jcc +j(- Cau I (2,0 diem) (i-x)l (f- (J Cho ham so y = -x'+3x-3 2(x-l) '[i)^ = CI :rinib DRX q&T * 1) Khao sat ham so (1). ' n. _/)c 2) Tim m de diromg thang y;= m cat do thi ham so (1) tai hai diem A, B sao cho AB = 1. Cau II (2 diem) - (O .JUntsb nga auni hi I - x gnlrii gn6lj(3 1) Giai b^t phucjrirft-iil? 4(^^)x^^^n^nM log, (y-x)-log^ = l a- 2)tJiaihe phtfcfng trihh 1 X Cau III (3 diem)^ 14 trong mat phang ydi hi\a do Oj^dio-fiai diem A(0; 2) va Tim toa do trifc tarn va toa do taiii di/dng tron ngoai tiep cua tam giac OAB. II 2) Trong khong gian vdri he toa dp Oxyz cho hinh chop S.ABCD c6 day ABCD la hinh'thoi, AC cat iki goc toa do^9i''Biet A(2; 0; 0), B(0; 1; 0), S(0; 0; 2^2). Goi M la t^ung diem q^anh SC. a) Tinh goc va khoang each giifa'^^'dtfdng thang SA, BM. b) Gia suf mat phSng (ABJ^)^ ^tJ yCcfqg th&ng SD tai diem N. Tinh the tich khoi chop SrABM!st:^^^^4 ' ' ' ' Cau IV (2 diem) 1) Tinh tiqfer^an I = 1 + - VHiT 2) Tim he so cQa trong khai Cau V (1 diem) trivia" thanh da thufc cQa: I - • r ijb diiBod rifirij gaXi^jrfl (S Chq tam giac APC khong tuvthoa^man dieu kieh^ yj, +. - <- cos2A + cosB + 2 V2 cosC = 3. Tinh ba goc cusai tan>:giac ABC. 3 Cftu I. DAP AN 1 -x'+3x-3 1 , * Tap x^c dinh: D = R\{l}. xf2-x) * Str bien thien: y' = -^^ f; y' = 0<»x = 0, x = 2. 2(x-l)^ ycD = y(2) = ycT = y(0) = |. Difdng th^ng x = 1 1^ tiem can dufng. Difdng th^ng y = —^x + 1 la ti^m can xien. * Bang bien thien: -00 0 0 + 0 +00 +00 3 2 2 * D6 thi: +00 -oc 2) Phufdng trinh hoanh dp giao diem cua do thi h^m so v<Ji difcfng th^ng y = m la: -x'+3x-3 2(x-l) - = m<»x'+(2m-3)x + 3-2m = 0 (*) Gidi thi$u & huang din gi^i chi tiSt thi BH khtfi A PhiTcrng trinh (*) c6 hai nghiem phan bi$t khi va chi khi: 3 1 A>0<=>4m^-4m-3>0<»m>— hoac m<— (**) 2 • 2 Vdi dieu kidn (**), during thing y = m c^t do thi ham so tai hai diem A, B c6 ho^nh do Xi, X2 la nghiem cua phiTcfng trinh (*). AB = 1 « = lC:> X,-X2 = lo(x,+X2)^-4x,X2 =1 1±V5 (2m-3) -4(3 -2m) = 1 m = -~- (thoa man (**)). Cfiu II. 1) Dieu kien: x > 4. 0 ^2(x^-16) Ta c6: ^ \-3>-7=^ Vx^ Vx-3 o^2(x'-16) + x-3>7-x o^2(x^-16)>10-2x * Neu x > 5 thi bat phiTcfng trinh dutfc thoa man, vi v6' trdi dtfcfng, ve phai am. * Neu 4 < x < 5 thi hai ve cua bat phUcfng trinh khong am. Binh phifcfng hai ve ta dUcfc: 2(x^ - 16) > (10 - 2x)^ o x^ - 20x + 66 < 0 « 10-^/34 < x < 10 +V34. Ket hcfp vdri dieu ki^n 4 < x < 5 ta c6: 10-V34 < x < 5. Vayx>10-V34. 2) Dilu ki§n: y > x v& y > 0. log,(y-x)-log4- = l o-log4(y-x)-log4^ = l «>-log4 y-x_ = 1<::>X = 3y y 4 Thg' v^o phifomg trinh x^ + y^ = 25, ta c6: [ 3y 1 l4 J + y'=25<=>y = ±4. So sdnh vdi dieu ki#n, ta dUdc y = 4, suy ra x = 3 (thoa man y > x). V4y nghi|m ciia h# phifcnig trinh \k (3; 4). GMi thi^u & hudng din giii chi ti^t 06 thi QH khdi A 5 UA-131ASUPL|; UA-LU03-OOq9A@3 L6e-696LU6e-Z6^50L6e-t^( OHdi- L ugnD - 09>teQ d - Sui AQNJIAHNVHliOt O o z I GdH IVQ XVHN )dLj pQ ma uo usAni !L 6L| IBQ OBA qujs usAna !U 3 '!>|sdgoe!quna '[lAI3-|/v Jf p :iBq pj Luaip UOLJO ai H 'qoja 'os JBQ Buojq CMUllAIJMO OH-cd Cau III. -ifb! irfv ?.v kfcrf ifkf nfirfq m^M§n- ififi (*) rinhi •gnXilufi*! 1), Ducfng thing qua jO^ vuSng .ggc y^i rBA^j/I;:^^^^^^^ trinh , ^ Dod^ ^hlng #a%, vii6ft^-g6c vidri 0A((); if^^'^ p^xik^ tMiih Difcfng thing qua A, vtiSiig goc ydfi B0|V3;il) c0 phucf^g trinh >/3x + y-2 = 0. jTi^^y Giai he hai (trong ba) phucfng trinh tren ta Auac tri^ctam H'^s/5;-lj Difdng trung trtfc canh OA c6phif9rng,trinh jr=r^^ Difcfng trung trUc canh OB c6 phtftfng trinh >?3x'+'^j- 2_= 0. Dirdrng trung triic canh AB c6 phtfcfng trinh Giai he hai (trong ba) phirang trinh treii ta; jdir^Cft Jtanv f^Ucfng. tron ,gg©aj)ti^tam gi^c OA^.!^ l^utj^uh^j yui-uAq jBd ifii 3 < x UBVL * .^,d2a)Tac6:,Q(-^;P; 0),.0(0; -1;,0), M(-1; Q; 4). SA = ^2; 0; -2\/2J ' ' '''' " ^^-^ =^'9^^ Jsi 9v isri ^nturiq BM = (H;-l;V2l , - ; ,SOl-(x-v) .sol .i.x < V nsm Borfi/S = 36 i §nt)ljriq Ofiv "srfT i omib fiKiieijl U9ifj iov rinBS o8 ;8) rinhi ^nialurfq eri sua rn$iri§n ^BV Goi a la goc giffa SA va BM. Ta, ^6.j, ^ + = '[^x ~ r)^x + f cosa = cos (SA, BM) SA.BM SA .BM a = 30". SA, BM" =(-2V2; 0; -2), AB = (-2; 1; O). SA,JBM]^AB ^:>2^: .8 n&fi nV)t :6u-> Vay d(SA, BM) = SA, BM 2b) Ta c6: MN // AB // CD, suy ra N la trung diem cua SD. Suy ra N SA=(2; 0; -2y^-mA^^Qr^- ()/_iKJ|r_!^-^ Koo ,0 < — nia oCI 2 j£ £ •^^"'^A ''s^''='('()^ ^\f^^6y^' ' s"^*^^ -^^^'3 "^^^ ^^^^ "^^^ - V,,3^=iFsA,SMl.SB=i^- o llr • V,^^,=-^||_SA,SMJ.SN 3 ny VS.ABMN = Vs.ABM + Vg.AMN ^4-^ 7 CauIV. .0 > M tsV 1) Bht t = => X = +1 =>dx = 2tdt. X = 1 => t = 0, X ^^r^ <f^'=^P Ta c6: J = = 2 0 1 + t J t It3_lt2+it''-2rn|t + li '1^ = 3 1 ^ = 41n2. 3 0 V -11 t+1 OP = 2 Jo + 2-21n2 3 2 • UA-UJOD-OOL|BA@3JOIS> •6LU6e-Z.6/lS0L6e-t'69SL I u^no - og>|PQ -d - SuBOH AHNVHllONH i|>|ij3esegu-MM/ 2 o mww.nhasachkhan H MOT THANH VI^NO Hoans - P- Dakao - Quan 1 - Tp h 15694-39105797-39111969-3 (store@yahoo,com.vn achkhangviet.vn f ir y -2) [l + x^(l-x)J=C°+C;x^(l-x) + C,V(l-x)'-h + C^x^ (1 - X / + C^x* (1 - X + C^x'° (1 - x)' + +Q^x'^ (1 - xf + C,^x'^ (1 - x) V C^x'^ (1 - x/. Bllc cua X trong 3 so hang dau nho hdn 8, bac cua x trong 4 so hang cuoi 16n hcfn 8. Vay x® chi c6 trong cac so hang thuT thiif nam, vdi he so' tifcfng iJng \k: Q\.(Z\, Suy ra: as = 168 + 70 = 238. Gfiu V. Goi M = cos2A + 2V2 cosB + 2V2 cosC - 3 = 2cos'A-l + 2V2.2cos^i^.cos^^^-3. 2 2 Do sin—>0, cos^—^<1 nen M<2cos^ A + 4V2sin—-4. 2 2 2 Mac khac tarn gidc ABC khong tu nen cos A > 0, cos^ A < cos A. /— A Suyra: M<2cosA + 4V2siny-4 = 2 = -4sin^- + 4V2sin 2 2 2 l-2sin^ — + 4V2siny-4 = -2 V|y M < 0. >/2sin^-l <0. TPfteo gid thid't: M = 0 o cos A = cos A B-C , cos = 1 . A 1 sm—= -7= 2 4i A = 90° B = 45° C = 45° 8 Gidi thifu & hadng din giii chi ti«ft id thi E>H kh5i A OE THI TUYEN SINH DAI HQC, CAO DANG NAM 2005 - 2006 Mon: TOAN; Khoi A Thdi gian lam bai: 180 phut C&u I (2,0 diem) Goi (Cm) la do thi cua hkm so y = mx + — (*) (m la tham s6'). X 1) Khao sat siT bien thien va ve do thi cua h^m so (*) khi m = —. 4 2) Tim m de ham so (*) c6 CLTC tri va khoang each tii diem cUc tieu cua (Cm) den tiem can xien cua (Cm) bling -1=. v2 Cau II (2,0 diem) 1) Giai bat phLfdng trinh VSx-l -Vx-1 > V2x-4. 2) Giai bat phUcfng trinh cos^3xcos2x - cos^x = 0. cau III (3,0 diem) 1) Trong mat ph^ng v(?i he toa do Oxy cho hai dudng th^ng di: X - y = 0 v^ d2: 2x + y - 1 = 0. Tim toa do cAc dinh hinh vuong ABCD biet rkng dinh A thuoc di, dinh C thuQC d2 v^ cac dinh B, D thupc true ho^nh. 2) Trong khong gian v6i he toa do Oxyz cho dtfdng th^ng d: ^ = -^ = ^ vk mat ph4ng(P): 2x+y-2z + 9 = 0. a) Tim toa do diem I thuQC d sao cho khoang ckch tii I dS'n mSt ph^ng (?) bang 2. b) Tim toa do giao diem A cua difcfng thing d va mat phing (P). Viet phiftftig trinh tham so cua di/cfng thing A nkm trong mat phing (P), biet A di qua A va vu6ng g6c vdti d. Cau IV (2,0 dilm) 1) Tinh tich phan I = sin2x + sinx dx. J vT+Scosx 2) Tim so nguyen dtfofng n sao cho: C^„ -2.2CL, +3.2^CL, -4.2^Cl„., + +(2n + l).2^''CJ::l = 2005 (C|; la s6' to hcfp chap k cua n phan tur). Gidi lhi§u & hu<Jn- Jjn gi&i chi ti«ft dS thi OH khtfi A 9 Y. Cho X, y, z la so dLfOng tho^ iriitri^-H^I^- = 4. Chufng minh r^ng: 1 1 - + - 1 2x + y + z X + 2y + z x + y + 2z DAPAN CauJ.;;; . Oh mBii BUO rrb ob ' . 1) Ta cq m,= => y = -x+ ^ * Tap xac dinh: D = MAJO}. , * Sif bien thien: , 1 1 x'-4 , ^ ^ ^ fmerb O.S) II JJAD . y = y• ^0X =-2, X = 2. 4 - x4^ < f - X - - f - xcv xinhi grrrrtjrif! ,C) (1 ycD = y(-2)rf -1^?^ =.?^^oSf^fjo3 riniii -sntyurfq isd ieiO (S Dirdng thang x = 0 la tiem can durng. ^ ^ J • • ;ra9ii>0,8) III UG3 |y^ng thing y,n,^;c,)a,tifPI^9$^^^^^ Jfim -noiT (I * Bang bien thien: = - ^ - t^ ,jb Douj^.! |\b gnfh GOQA §n6i(y riniri rinib 0E;2ob r.oj DEMS' ;b + .Si! 0>ri i>L«j odudj ( ,8 f?fixb a«o .s^^Jj oebrij 0 rii^ib gnfirii gfioljb-oJio s^xO 6b BO JD = G + s Bfn n'^)^, ^ jjf° :.>60 gaBorfjf orb aes'b louriJ m'sib ob^BoJ inxi {.« -00, m 8v * Do thi: .(1) gnBiiq jBm .GV b gn^rii snt>'ut4 -5 010 .2 gnBd ("5) gneriq A rnuib osig 6b Boi miT (d »"ub Buo 03 mfid) rinhi gmoliriq j^^eiV .^\t)v aog gnouv KV A m^ib A laid 0,Si) VI USD —-r , = I fiB^iq rioiJ ri(T?iT (I :qr ^'hm n gn^olib asYtrgn oa miT (2 .0x7 nlf [ n Buo JI qBrio q'ori oi 08 B1 P ) [...]... H 1 A ' D va B H 1 AA nen B H 1 (AOO 'A' ) Suy r a : VOOAB = ^.BH.SAOO Ta c6: A ' B = A / A B " - A ' A " = aj3 BD = VA'D' -A' B' = ^ A B O ' D deu 3VD OHO =a B H = ^ V i AOO' la tarn giac vuong can canh ben bSng a n e n : SAOQ' = - ^a^ Vay the t i c h k h o i t i l dien OO'AB l a : V = Gidi thiSu & hadng dSn gial chi tiet de thi DH khoi A 3 2 2 = 12 (dvtt) mi 19 N i l ONOHJ - y O H N Y A 0 8 Omi DE THI. .. (loai) hoac x = - (thoa man) 4 Nghiem cua phiTcfng t r i n h la: x = 2 va x = — 4 2 Goi H la trung diem cua BC S u y r a A ' H 1 (ABC) va A H = - B C = - N / a - + 3 a ' =a 2 2 Do do A ' H ' = A ' A ' - A H ' = Sa' => A' H = aV3 Vay V ^ ^ 3 , = i A ' H S , , 3 , = ^ y (dvtt) Trong tarn giac vuong A ' B ' H c6: H B ' = V A ' B ' " + A ' H - = 2a nen tam giac B ' B H can t a i B' Dat (p la goc giCfa hai... h a t t r o n g cac so ao, a i , + y+ 3 + ^ IS ONG TIN lA V I E T NAM = 4096 T i m so a C a u V.b Theo chtforng t r i n h p h a n ban (2 diem) 1 G i a i phiJcJng t r i n h log2x-i(2x^ + x - 1) + logx.^i(2x - 1)^ = 4 2 Cho l a n g t r u A B C A ' B ' C c6 do dai canh ben bang 2a, day ABC la t a m giac vuong t a i A, A B = a, AC = aVs cua dinh A va h i n h chieu vuong goc t r e n m a t p h a n g (ABC)... va A H = (2t - 1; t - 5; 2 t - 1) Vi A H ± d n e n A H u = 0 « SCfDUNG 2(2t - 1) + t - 5 + 2(2t - 1) = 0 t = 1 Suy r a H(3; 1; 4) Gi6i thigu & hudng dan gial chi tiet thi DH khoi A Di VA 29 HA NOI - 2007 2 Goi K la hinh chieu vuong goc cua A tren mSt phang (a) Ta CO d (A, (a) ) = AK < AH (tinh chat dtfofng vuong goc va di/dng xien) Do do khoang each tif A den (a) lorn nhat khi va chi khi AK = AH,... PHAN TL/CHQN Thf sinh chi dU(?c chgn lam can V .a hoac cau V.b C a u V a Theo chifong t r i n h T H P T k h o n g p h a n ban (2 diem) 1 T r o n g m a t p h a n g v d i he t o a do Oxy, cho t a m giac ABC c6 A( 0; 2), B ( - 2 ; - 2 ) v a C(4; - 2 ) Goi H l a chan difdng cao ke tCr B; M va N I a n luat l a t r u n g d i e m cua cac canh A B va B C V i e t phi/cfng trinh difdng t r o n d i qua cac... s ^ xdx 0 C a u I V (1,0 diem) Cho h i n h chop S.ABCD c6 day A B C D l a h i n h t h a n g vuong t a i A va D; A B lO A HOC TON A D = 2a, C D = a; goc giufa h a i m a t p h a n g (SBC) va (ABCD) bkng 60° G o i I l a t r u n g d i e m cua canh A D B i e t h a i m a t p h a n g (SBI) va (SCI) cung vuong goc vdri m a t p h i n g (ABCD), t i n h t h e t i c h k h o i chop S.ABCD theo a C a u V (1,0 diem)... dtf&ng t h i n g A A ' va B ' C t h i c = B ' B H p Vay cos c = p 4 2. 2a 1 a 32 Gi(3i thigij & hudng dlin giai chi tiet a6 thi DH khfii A DE THI TUYEN SINH DAI HOC NAM 2009 - 2010 Mon: TOAN; Khol A Thdi gian lam bai: 180 phut I PHAN CHUNG CHO TAT CA THI SINH (7,0 diem) C a u I (2,0 diem) x+2 Cho h a m so: y = 2x + 3 jNG TIN (1) IviET NAM 1 Khao sat sil b i e n t h i e n v a ve do t h i cua h a m so (1) 2... SINH DAI HQC NAM 2008 - 2009 M6n: TOAN; Khdi A Thdi gian lam bai: 180 phut I PHAN CHUNG CHO TAT CA THI SINH C a u l (2 d i e m ) Cho h a m so y = mx" + ( 3 m " - 2 ) x ^ '- -2 (1), v(5i m la t h a m so thiTc x + 3m 1 FQiao sat sii b i e n t h i e n va ve do t h i cua h a m so (1) k h i m = 1 2 T i m cac gia t r i ciia m de goc giCifa h a i difoTig t i e m can ciia do t h i h a m so (1) bang 45° C a u... c6: a + b = a^ + b^ - ab X y (1) A = a^ + b^ = (a + bXa" + b ' - ab) = (a + b ) ' TCr (1) suy r a : a + b = (a + b)^ - 3ab Vi ab< ^a + b ^ ' V n e n a + b > (a + b) - - ( a + b ) ' 2 y =^ (a + b ) ' - 4 ( a + b ) < 0 = > 0 < a + b < 4 Suy r a : (a + b ) ' . 1 AA nen BH 1 (AOO&apos ;A& apos;). Suy ra: VOOAB = ^.BH.SAOO Ta c6: A& apos;B = A/ AB" - A& apos ;A& quot; = aj3 BD = VA'D' -A& apos;B' =a =^ ABO'D deu BH=^. Vi AOO'. cac daj^^la hai hin^h ti^on tarn 0^ ya Q', b^h kinh day bang chieu cao va bkng a. Tren diiofng trpn,day tam O lay diem A, tren diidng tron day tam O' lay diem B sao cho AB. TRAN TIEN Tl/ - PHAN VAN HU&N - HUYNH VAN UT DE THI DAI HOC - CAO DANG Khoi A TOAN - LI - HOA THJ VlfN Tii^HbiNM THUAN NHA XUAT BAN DAI HQC QUOC GIA HA NQI F AH r.nhasachkhangvje