Tuyển chọn và hướng dẫn giải 39 đề thử sức học kì môn Toán 12 nâng cao: Phần 1

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Tài liệu Tuyển chọn 39 đề thử sức học kì môn Toán 12 nâng cao được biên soạn nhằm giúp người đọc làm quen với các dạng đề thi học kỳ ở mức độ cao. Phần 1 giới thiệu các đề thi, mời các bạn cùng tham khảo nội dung chi tiết.

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'TTV ^ PHAM TRONG THU ^ G V T H P T Chuyen Nguyen Quang Dieu - Dong Thap) uyen chon ^ thit site hoc ky MON TOAN m NANG CAO i 9 Danh cho hoc sink tdp 12 chuang truth nangcap ,
\ NHi^ XUA'T B A N Dni H O C Q U O C Gin Hii N O I 16 Hdng Chuoi - Hai Bd TrUng - Hd Ngi M^i nj&i itdn Dien thoai : Bien t a p - Che ban: (04) 39714896; Hanh chinh: (04) 39714899; Tona bien tap: (04) 39714897 B6 sach JU\EN CHON 39 DE THLf SLfC HOC KI MOM TOAN \dp 10, Fax: (04) 39714899 11 va 12 nang cao diTdc bien soan va luyen chon diTa tren noi dung chtfcfng trinh THPT hien hanh; bp sach toan nay giup cac em c6 dieu kien lam quen \di cac dang de thi hoc ki d miJc dp cao. Rieng cuon 12 c6 them phan phu luc giup cac em l\X kiem tra, danh gid, bo sung kien thtfc ve todn THPT cho minh nhkm Chiu trdch nhi^m xuat ban tao nen toan can ban viJng chac cho cac em triTdc khi chinh thuTc bxidc vao ki thi Gidm ddc - Tong biin tap : IS. PHAM THj TRAM Dai hoc, Cao dang. Hi vpng bp sach se gop phan giiip cac em dat ket qua cao trong cdc ki thi, dong thdi la mot cong cu ho trd cho cac bac phu huynh giup cho con em hoc tap Bi^n tap BUI T H E tot hPn. CM ban C O N G TY KHANG V l f T Trong qua trinh bien soan, dij tac gia da c6' g^ng nhiftig cuon s^ch van c6 the Trinh bay bia C O N G TY KHANG Vlf T con nhffng khie'm khuyet ngoai y muon. Chung toi rat mong nhan di^Pc s\i gop y chan thanh ciia cac thay, c6 giao, cac em hoc sinh de trong Ian tai ban sau sach difdc hoan chinh hPn. Tong phdt hanh vd doi tdc lien ket xuat ban: Tac gia ra't cam Pn Nha xuat ban Dai hpc Quoc gia Ha Npi, Cong ty TNHH MTV DVVH Khang Viet da dpng vien, khuyen khich va tao mpi dieu kien de C O N G T Y TNHH MTV DJCH V g V A N H O A K H A N G V I | T cuon sach nay sdm den tay ban doc. Website: phamtrongthu.com.vn Dia Chi: 71 Dinh Ti§n Hoang - P.Da Kao - Q:1 - J P H C M DJen thoai: 08 39115694 - 39105797 - 39111969 . 39111968 Tac gia Fax: 08. 3911 0880 PHAM TRQNG THLf Email: khangvietbookstore®yahoo.com.vn Website: www.nhasachkhangvlet.vn SACH LifiN KET K i HigU DUNG T R O N G B Q S A C H TUYEN CHQN 39 THI THLf SL/C HQC KJ MON TOAN 12 NANG C A P Vectd phdp tuyen VTPT Vectd chi phi/dng VTCP M a so: 1 L - 1 1 5 D H 2 0 1 3 Dieu phai chiJng minh dpcm In 2 . 0 0 0 c u o n , k h d 1 6 x 2 4 c m Yeu cau biii todn YCBT Tail Cty T N H H M T V IN A N MAI T H j N H D L / C Mat phdng mp Dja c h l : 7 1 , Kha Van Can, P. H i e p Binh Chanh, Q . Thu Dure, TP. Ho Chi M i n h Ba't ddng thuTc BDT S6' xuat b 5 n : 4 2 0 - 201 3/CXB/05 - 5 8 / D H Q G H N ngay 0 3 / 0 4 / 2 0 1 3. Phifcfng trinh PT H$ phifdng trinh HPT Quyet d j n h xuat hkn so: 3 3 9 L K - T N / Q D - N X B D H Q G H N , c a p ngay 31/07/2013 Ba't phifdng trinh BPT In xong va n o p liAi c h i e u q u y IV n a m 2 0 1 3 Ve trdi VT Ve'phai VP
Ph^n I. B p BE THUr Sljrc HQC K I MON TOAN L6P 12 7 loi khuy§n cho thi sink vi phicang phdp gidi mOt bdi thi A. BQ DE THUf SlJC HQC K I I M d N TOAN LCJP 1 2 NhU chiing ta da bie't mon Toan la mon hoc chiem mot vi tri ra't quan trpng va then cho't, ra't can thic't do hoc cac mon khac tiT tieu hoc cho de'n cac Idp tren. Mon Toan DE THLT SLTC HOC K i I M O N TOAN L 6 P 1 2 giiip cac em nhan bie't cac moi quan he ve so' lUdng va hinh khong gian cua the gidi D E SO 1 hipn thifc. Nhd do ma cac em c6 phiTdng phap nhan thiJc mpt so mat ciia the' gidi xung Thdi gian lam bai: 120 pliut quanh va bie't each hoat dong c6 hieu qua trong ddi song. Mon Toan gop phan ra't quan trong trong vice rcn luycn phifdng phap suy nghl, phUdng phap suy luan, phUdng phap Cau I. (3,0 diem) Cho ham .so y = -x + 1 gidi quyet van de. No gop phan phat tricn tri thong minh, each suy nghl doc lap, linh 2x-l hoat, sang tao va vipc hinh thanh cac pham cha't can thie't cho ngifdi lao dpng nhiTcan 1. Khao sat siT bie'n thien va ve do thi (C) cija ham .so da cho. cii, can than, c6 y chi vu'pt kho khan, lam viec cd ke' hoach, cd ne nep va tac phong 2. ChtJ-ng minh rSng vdi moi m diTdng lhang y = x + m luon ciCt do thi (C) tai khoa hoc. Xua't phat tij' vi tri quan trong cua mon Toan, qua thifc le' giang day nhieu nam d hai diem phan biet A va B. Goi k ^ k j hin liTdt la he so goc cua cac tiep tuyen ca'p THPT. Toi nhan tha'y rang dc hoc sinh hoc to't mon Toan thi ngoai vice cac em n^m vdi (C) tai hai diem A va B. Tim m de tdng k, + k2 dat gia trj Idn nha't. vilng kie'n thilc trong sach giao khoa, ky nang tinh toan that tot ma con phai bie't phUdng C&u 11.(2,0 diem) phap giai mot bai thi nhif the nao trong luc dang thi dc cd diem cao. Muo'n lam dU'dc dieu nay thi sinh can phai tuan thii theo cac b\idc sau day: 1. Tim gia Irj idn nha't, gia tri nho nha't cua y = -2sin-'x + 3cos2x -6sinx. 1) That binh tinh trong luc lam bai thi. 2. Tinh gia tri bieu iMc T = ^' ' 2) Can doc that cham rai toan bp dc, danh gia sP bp dp de, khd cua cua cac cau, xem nhifng cau nao quen thupc, la vdi minh. 3) Giai ngay lap ti'fc cac cau ma ban tha'y de. 3. Giai phu-dng trinh 6.9" -13.6^ +6.4" =0. 4) Mot vai cau can thie't de'n sif suy nghl sau hdn, thi sinh can phai dpc ky cau hoi, Cau III, (2,0 diem) Cho hinh chop ti? giac deu S.ABCD c6 canh day la a, canh gach dirdi cac gia thie't vii ycu cau cua bai todn. Dinh hiTdng each giai, hinh dung dp ben la aS. Tinh the tich khoi chop S.ABCD. phiJc tap cua each giai de cd si/ li/a chpn diing din. 5) Trinh bay biii giai thi sinh khong nen lam tat, moi bifdc nen vie't mot dong de de Cau l\. (2,0 diem) kiem tra, vi giam khao cha'm bai thi theo ba rem nen cd mot bifdc nao dd sai thi van con 1. Cho ham so' y = In vdi X > -— . Chiang minh rang xy' +1 = e^ diem d nhu'ng biTdc bie'n ddi dung trUde dd. Cach hay nha't la lam xong btfdc nao kiem 2 + 3x 3 tra birdc ay de phat hicn ngay cho sai. 6) Trong qua trinh giai mot bai toan ne'u thi sinh gap khd khan giiJa chiifng, cd the 2. Giai ba't phu-dng trinh log4(2x^ +3x +1) > logT(2x + 1). chiifa khodng trong tren gia'y thi de bo sung sau va nhanh ehdng chuyen sang lam cau khac. CSu V. (1,0 diem) Cho ham so y - X- - 2 x + 2 m - l cd do thi (Cni).Tim m de 7) Khi da hoan tat bai thi, ne'u con thdi gian thi sinh nen dpc lai bai giai va ra soat x-1 lai cac chi tic't da trinh bay (thong thiTdng cdc loi thi sinh hay bd sdt biTdc lam la tap xac hiim so cd ciTc dai, ciTc tieu va khoang each giffa hai diem ciTc dai, ciTc lieu dinh, dieu kipn cd nghla ciia can bac chan, ham .so' logarit, doi can khi dCing phiTdng bang 6. ; phap doi bie'n dc tinh tich phan, loai bo nghicm ngoai lai trong phifdng trinh...) nham hoan thien bai thi td't hcJn cho de'n he't gid. DAP A N THAM KHAO -4 Cau Dap an Diem Nhieu hpc ird tdi day dp dung 7 Idi khuyen tren da trd thanh thii khoa dai hpc cua I nhieu triTdng, nhi/ng thanh cong nha't la toi cd hpc tro thu khoa "kep" khoi A va B cua 1. (2,0 diem) Khao .sat siT bie'n thien va ve dd thi (C) ciia ham... trirdng Dai hpc Khoa hpc TiT nhicn TP. HCM va Dai hpc Y DiTdc TP. HCM nam 2011. (10 Chuc cac thi sinh dat ke't qua cao trong cac ki thi diem) a) lap xac dinh D = R \ - 0,25 PHAMTRpNG THa [2
TuySn chon 39 th& sijfc hpc kl mOn Toan I6p 12 NSng cao - Phgm Trgng Thu Cty TNHH IVITV DWH Khang Vigt b) Su-bien thien: V i A' = (m +1)^ +1 > 0, Vm e K. Suy ra d luon luon cii (C) tai 0,25 1 hai diem phan biet vdi moi m. - Chieu bie'n thien: y' = - - •-i» 2 2 © hm y =-00, iim y =+oo => tiem can diJng: x =— Theo dinh li Vi-et Xj + X2 = -m, XjX2 = - — ^ — , suy ra 0,25 v2. kj + k 2 = - 4 m - - 8 m - 6 = -4(m + l)^ - 2 < - 2 . Bang bien thien: Suy ra gia trj Idn nhaft kj + k2 la - 2 khi m = - 1 . x II 1. (1,0 diem) Tim gia trj \6n nhS't, gia trj nho nhS't... —00 +00 2 (2,0 Ta C O y = -2sin' x + 3 ( l - 2 s i n x)-6sinx — diem) 0,25 y' = - 2 s i n ' ' x - 6 s i n ^ x - 6 s i n x + 3 (1) y 1 +00 Dat u = sinx, - 1 < u < 1 2 1 -00 2 Ta CO (1) vie't lai y = -2u'' - 6 u ^ - 6 u + 3. 0,5 c) Do th\) qua diem A ( l ; 0 ) , B(0; - 1 ) . y' = _6u^ - 1 2 u - 6 = -6(u2 +2u + l ) = -6(u + I)2
Tuyin ch(?n 39 dg tht> sijfc hpc kl mOn Toan I6p 12 Nang cao - Phgm Trpng Thu Cty TNHH MTV DWH Khang Vijt 3. (0,5 diem) G i a i phifcTng trinh... e (2) v2x 2 + 3x 0,25 Ta c6: 6.9" - 1 3 . 6 " + 6.4" = 0 6. -13. + 6 = 0(*) Ttr (1) v a (2) suy ra dpcm. v2. v2. 2. (1,0 diem) G i a i ba't phrf(/ng trinh... Datt = , t > 0. PhiTcfng trinh (*) trd thanh "x 0 ^ _ Dieu kien • « x > - i (*) 0,25 _3 2x + l > 0 1 " 2 v2y X> — 6t^ - 1 3 t + 6 = 0 » C^X=±1. 2 _2 _ ~ 3 " Taco log4(2x^+3x + l)>log2(2x + l ) v2y v2y V a y nghicm cua phifdng trinh da cho la x = ±1. o log4(2x^ + 3x + l ) > l o g 4 (2x + l ) ^ 0,5 Ill T i n h the tich khoi chop S . A B C D 2x^ + 3x + l > 4 x ^ + 4x + l (2,0 G o i O la tarn c u a hinh vuong A B C D . V i S . A B C D la hinh chop diem) tiJ g i a c d c u n c n S O 1 ( A B C D ) => S O 1 O A . 2x'^ + X < 0 -—< X < 0. 2 A S A O v u o n g tai O c6 K e t hdp (*) ta du'rtc tap nghicm cua bat phu'cfng trinh la so^ = S A 2 - O A 2 0,25 T = 5a^ a [ 2 . = (aV3)2 2 V T i m m de ham S(Y c6 ciic dai, ci/c t i e a . . (1,0 Tap xacdinh D = 1R\{1). aVlO diem) •SO = x^ - 2 x + 3 - 2 m g(x) D a o ham y' (x-l)2 (x-1)^ Dod6V,^3C^=-.SO.S^3C^ 0,5 H a m .so c6 ciTc dai va ciTc t i c u k h i va chi k h i g ( x ) = 0 c6 2 n g h i c m phan bict khac 1 1 a^/io 2 a-'Vio (dvtt). a =• A ' = - 2 + 2m > 0 3 2 o - m > 1. IV 1. (1,0 diem) ChuTng minh... g(l) = l - 2 + 3 - 2 m ^ O (2,0 Goi A ( x ^ ; y ^ ) , BCxjj; y n ) la hai diem cifc t r i diem) ' 2 ^ 2 + 3x AB = 6 o A B ^ = 36 ( X y - x ^ ) ' + ( y B - y A ) ' = 3 6 Dao h a m y ' = c : > ( X p - x ^ r + ( 2 x , 5 - 2 - 2 x ^ + 2 ) 2 =36 2 + 3x 0,5 6 2 + 3x 5(x,j - x ^ r = 36 o (Xjj + x ^ )^ - 4xyX^ = y (2 + 3x)^ 2 + 3x - 4(3 - 2m) = — o m = — ( t h o a man). 5 10 Ta CO x y ' + 1 = x + 1= (1) 2 + 3x 2 + 3x 6 7
Cty TNHH MTV DWH Khang Vi$t Tuyin chpn 39 6i IM sOc hoc ki mOn ToAn Iflp 12 Nang cao - Pham Trpng Thu THlIr SOC Kl -1 +00 D± S6 2 D E H O C I M O N Thdi gian lam bai: 120 phut T O A N L6P 12 0 0 - 0 Dodo Cau I. (3,0 diem) Cho ham so y = x"^ - 2x^ + 4 (I). - Ham so dong bien Ircn moi khoang ( - 1 ; 0) va (1; + oo). 1. Khiio sal siT bicn Ihicn va ve do Ihj (C) cua ham s6' (1). - Ham so nghich bien tren moi khoang ( - oo; -1) va (0; 1). 2. Tim cac giii Irj cua m de phUtlng trinhx'* - 2 x " - l o g 2 m = 0 c6 4 nghiem • Cyc trj: phan bicl. - Ham so dat cifc lieu x = ±1 va y^.^ = y( ± 1) = 3. C&u U. (2,0 diem) - Ham so dat ciTc dai x = 0 va y^^ = y(0) = 4. 1. Tim gia iri Idn nhiil ciia ham so' f(x) = x - ' + 3 x ^ - 7 2 x + 90 t r e n [ - 5 ; 5]. • Gioi han: lim y = + o o ; lim y =+CXD. Bang bien thien 2. Tinh gia trj bieu ihufc A = 49 X - 0 0 -1 0 +00 0 + 0 - 0 + +00 3. Giai bal phi/dng irinh 2-""" -21.2"^-"^^'+ 2 >(). +00 Cfiu HI. (2,0 diem) Cho hinh chop S.ABC c6 day ABC la lam giac vuong tai B, SA 1 (ABC). SA = iiyfl, BAC = 30", BC = a, M la trung diem ciia SB. Tinh the ' 1 31^ tich cua khoi tiJ dien MABC. c) Do thi (C): Qua cac diem ,(±2; 12). Cau IV. (2,0 diem) 1. Cho ham so y = c''' sin5x.ChiJng minh ring: y''-4y' + 29y = 0 (*). 3 \ 2 y =972 2. Giai he phi/dng Innh l o g ^ ( x - y ) = 3 Cau V. (1,0 diem) Cho ham so y = - ^ ^ c 6 do thi (C). Viel phiTdng Irinh x-1 tie'p tuyen ciia (C) c6 he so' goc la -1 . D A P A N T H A M K H A O Cau Dap dn Diem 2. (1,0 diem) Tim cac gia trj cua m de phtf(yng trinh... I 1. (2,0 diem) Khao sat si/ bien thien va ve do thj (C) cua ham... Ta CO x"* - 2x- - log2 m = 0 x** - 2x- + 4 = logj m + 4 = k. (3,0 a) Tap xdc diiih D = R. 0,25 De phmJng trinh da cho c6 4 nghiem phan biel diTdng thing diem) b) Sir bien thien: y = k cat do thj (C) tai 4 diem phan biet . DiTa vao do thj (C) • Sir bien thien: 0,5 cua ham so , la c6 3 < k < 4 •? X ~ 0 3 < log, m + 4
Tuy^n chpn 39 dg thif silc h(?c kl m6n Join I6p 12 Nang cao - Phgm Trpng Thu Cty TNHH MTV DWH Khang Vi$t II 1.(1,0 diem) Tim gia tri l
luyen cliyii M de l l i i j ;.ut ligc ki iiion l u a i i lup U' f^jiig ['hjni liuiig llii/ Cty TNHH MTV DWH Khang Vl^t 3X 2y =972 3 \2 [ 3 y + - \2 2. C h o l o g o S = a, log3 5 = b. Ta CO < ^
Cty TNHH MTV DWH Khang Vi^t Tuyln chgn 39 66 this sufc hpc kl mOn Toan Idp 12 Nang cao - Phgm Trgng ThU 2. (0,5 diem) Tinh... • Bang hien t h i c n : . 120 = logs 2^-53 = 31og5 2 + l o g , 5 + l o g j 3 X -00 0 2 +00 y' + 0 - 0 + 0,25 " = ^ +1+ ' 0,25 A — ^ ^ ^ ^ ^ _ ^ ^ + y la bj ill ab^ i 3. (0,5 diem) G i i i i phifc/ng trinh... Ta CO l o g ^ ( 9 ' ' + 8 ) = x + 29''+8 = 3"""- (*) 0,25 4 Dat t = 3^^, t > 0. PhiTdng Irinh (*) t r d thanh - 9t + 8 = 0 => \\l 0,5 [t = 8 [3^=8 [x = log3 8 0,25 /^ rx=o V a y n g h i c m ciia phifring Irinh da cho la [x = log3 8 -u o 1 2 3 X III 1. (1,0 diem) Chrfng minh rang S . A B C D la hinh chop deu. (2,0 Tur giac A B C D la hinh Ihoi v i c6 cac canh deu b ^ n g a. G p i 0 diem) la giao d i e m cua A C va B D . T a m giac SAC can ( v i c6 0,25 SA = SC = a ) va 0 la trung d i e m A C nen SO 1 A C . S 2. (1,0 diem) Tmv m de dififng thang d cat do thj ( C ) tai... Phu'dng trinh hoanh do giao d i e m cua d va (C) la 0,5 x-^ - 3 x ^ + 4 = m ( x - 3 ) + 4 o ( x - 3 ) ( x ^ - m ) = 0. T h c o de bai ta c6 m > 0, m ?t 9 va y'cVm ).y'( - V m ) = - 1 0,25 => '3m -6N/m)(3m + 6Vm) - - 1 9m^ - 3 6 m + 1 = 0 6 + >y35 m = 0,25 ^ 6-V35 (thoa man). ———Y m = T a m giac SBD can ( v i c6 SB = SD = a ) va O la trung d i e m 0,25 3 II 1. (1,0 diem) T i m gia trj \(in nha't, gia tri nho nhat... BDnen S O I AC. (2,0 .Tapxacdinh:D = [-l;3] Suy ra SO .L m p ( A B C D ) . 0,25 diem) 0,5 • y ' = 6x^ + 6x - 1 2 , y ' = 0 o X 1 hoac x = - 2 g D. V i SA = SB - SC = SD nen O A = OB = OC = O D va do do A B C D la hinh vuong. 0,25 • Ta CO y(3) = 46, y ( l ) = - 6 , y ( - 1 ) = H . 0,25 •Vay max y = 4 6 k h i x = 3 , min y = - 6 k h i x = l . V a y S . A B C D la hinh chop deu v d i difcfng cao la SO. 0,25 xe[-l;3i X6[-1;3] 15 14
'uy6'n chpn 39 dg \hCl SLfc hpc ki man To^n I6p 12 Mang cao - Phgm Trqng ThJ Cty TNHH MTV DWH Khang Vi^t 2. (0,5 diem) Tinh th^ tich hmh chop do. V Tim m de ham so'co c\ic dai va c\ic tieu... (1,0 Tapxacdinh: D = K \ { - I } V i ABCD la hinh vuong canh a nen OA= ^ • Trong tarn diem) x^ +2x + 2m + l g(x) 0,5 Dao ham: y' = - giac vuong SAO ta c6 SO = VsA^ - O A ^ = Ja^ - — = — (x + i r (x + 1)^ Ham so da cho c6 cifc dai, cifc tieu o g(x) = 0 c6 hai nghiem a^f2 Dod6V3^3C^=-.SO.S^3CO a2=^ (dvtt). 'A' = - 2 m > 0 0,5 3 2 phan biet khac - 1 o « m 0 va x ?t - y . CSu I I I . (2,0 diem) Cho hinh chop S.ABC c6 day la tam giac vuong can tai A c6 2x + y = 4 Ta CO AB = AC = 2a. Mat ben qua canh huyen vuong goc vdi mat day, hai mSt con lai log(x + y)^ - logx = 21og3 tao vdi day mot goc 30". Tinh the tich khoi chop. y = 4-2x Chuiy. (2,0 diem) < 1. Cho ham so y = x'^e^"'-^". Chu-ng minh rang: xy' - y(12 + 2013x) = 0. log(4 - x)^ = logx + log9 = log9x log^x + log^y = 2 x =I 2. Giai he phqdng trinh y = 4-2x y = 4-2x ly-2 x^y-2y + 9 = 0 X =1 o (nhan). x^ -17x + 16 = 0 'x = 16 x +2 X=:16 Cau V. (1,0 diem) Cho ham so y = CO do thi (C). Tim cac diem P, Q y = -28 x+1 thupc hai nhanh cua (C) sao cho do dai PQ nho nhat. Vay he phu'dng trinh da cho c6 nghiem (x; y) la: ^' ? - - r ; ^ :(1;2);/(1,6; - 2 8 ) . 6
Tuye'n cligii 39 de tl)U LUC lioc ki 111611 loan iup '. Nang cao - Phgm Trgng ThU Cty TNHH MTV DWH Khang Vi$t D A P A N THAM KHAO 3. (1,0 diem) Giai ha't phif(/ng trinh... Cdu Dap an Diem Ba't phU'dng trinh da cho tu'dng du'dng I 1. (2,0 diem) Khao sat sir bicn thien va ve do thi (C) cua ham... 4 ( x 2 - 2 x - 3 ) > 2 ' ' ^ x 2 - 2 x - 3 ) _ 2 x -3)(2''^ - 4 ) < 0 (3,0 Doc gia tiT giai_cach giai tiTdng tiT cau I . l de so' 3. diem) 2. (1,0 diem) Tim phrfcfng trinh cac dtft/ng thang qua diem... Ta CO hai tracing hdp Dirdng thing d qua A vdi he so goc k c6 phuTdng trinh -2x-3 0 x2>2 y =k x +4. Trui'fnf' hop 2: d la tiep xuc vcfi (C) khi va chi he phu'rtng trinh sau c6 nghiem: f ^ 7 r 19^ x^-2x-3>0 x < - l hoacx>3 -72 k = . Tiep tuyen d^ : y = x+ Do do ((ABC), (SAC)) = SKO = 30° 8 32 • 32 128 II 1. (0,5diem) Tim gia trj Icjfn nhat, gia trj nho nhat... Tu-dng tiT ta c6 SHO = 30°. (2,0 Taco r(x) = 3x2+20^"+' diem) Ma OK = va OH = 2?:^ = ^ 0 la trung diem BC. V i r ( x ) > 0 , V x e [-1;11. 0,25 BC BC Suy ra, f(x) dong bicn trcn [ - 1 ; 1 ]. AR a Taco 0 K = = a; SO = OK tan 3 0 ° = - p . Dodo max l"(x) = 1(1) = 1 + e^ xel-l;ll min f(x) = f ( - l ) = - 1 + - • xe|-l;l| Q 0,25 2 S The tich cua khoi chop S.ABC la: 2. (0,5 diem) Tinh... 1 ' ' 1 1 V. ARC = - SO.S, HP = - SO. AB. AC = - • • 2a.2a = — a ^ (dvtt) . log^/lO + l n ^ y i ^ - l ^ - = logl02 +lnc2 - l n e ~ ' = - + - + 1 = 2. 0,25 S.ABC 3 ABC ^ 9 ^ ' e 2 2 IV 1. (1,0 diem) Chitng minh... ^ 21og23_ 21og23 _ 2 1 o g 2 3 _ ^ (2,0 y' = 12x" .e^"'^" + x'^2013.e2'"-''' = x".e2"'3''(12 + 2013x) 0,25 diem) •xy'=x'^e^'"''''(12 + 2013x). Vay A = 4. Vay x y ' - y ( 1 2 + 2013x) = 0. 18
TuyS'n chpn 39 6i thi( sufc hpc ki mOn To&n I6p 12 MSIng cao - Ph^m Trpng Thu Cty TNHH MTV DWH Khang Vi?t 2. (1,0 diem) Giai h§ phtfcfng trinh... Dieu kien x >0, y >0. tren ''••2 Bien doi he phiTdng trinh da cho thanh log^(xy)::=2 2. Trnhgia iri bie'u ihtfc: A = 27'°''% Si""''+9"°'"'. xy=9 (1) x2y-2y + 9 =0 [ x - y - 2 y + 9 = 0(2) 3. Giai phu-dng trinh iogjyCx^ - 5 x + 6)^ = - l o g — — +Iog9(x-3)^. Tir(l) suy ra y = - (3). The (3) vao (2) ta diTdc x^ + x - 2 = 0. C&u III. (2,0 diem) Cho lang tru ABC.A'B'C'co A'.ABC la hinh ch6p tam giac X deu canh AB = a, canh ben A'A = b . Goi a la goc giiJa hai mat phang (ABC) Giai phi/dng trinh nay ta c6 x = 1 va x = - 2 (loai). va (A'BC). Tinh tan a va the tich khoi chop A.'BB'C'C . Vay he phifdng trinh da cho c6 nghiem (x; y) = (1; 9). CHulW. (2,0 diem) V Tim cac diem P, Q thuQc hai nhanh cua (C) sao cho do dai... l . C h o h a m s o y = e~'' sinx.GiaiphU'dngtrinh y''-i-4xy'-i-3y = 0. (1,0 T a c 6 y = ^ = l + ' diem) X + 1 X+ 1 x~-4x + y-t-2 = 0 2. Giai he phi/dng trinh 21og ( x - 2 ) - l o g y = 0 ( ^ ' y ^ Cho P -1 + a; 1 + - , Q - l - b la hai diem thuoc hai 2 V2 l a; CSu V. (1,0 diem) Cho ham so y = ^ ^ c6 do thi (C). Tim m de diTdng nhanh cua (C) vdi a, b la0cac so'di/dng. Ta c6: (I p 1 x-1 - + — = (a + br 1 + — - PQ^ = (a + b f + [ (ab)- J thang d c6 phifdng trinh y = - x + m c^t (C) tai hai diem phan biet. Ap dung BDT Co-si: DAP A NTHAM KHAO P Q 2 =(a + b)2 1+ - 1 > (27^)2.2.—= 8. ab Cdu Dap an Diem (ab)2 I 1. (2,0 diem) Khao sat siT bien thien va ve do thi (C) cua ham... Dodo minPQ = >/8 a = b = l. (3,0 Doc giii tif giai_cach giiii tu'dng tif cau 1.1 de so 3. Vay hai diem can tim la P(0; 2), Q(-2; 0). diem) 2. (1,0 diem) Tim m de difc/ng thang d cit (C)... Du'dng thang d co phi/dng trinh y = m(x - 3) + 20. 0,25 DE THCT SOC H O C Ki I M O N T O A N LdP 1 2 DE SO 5 PhiTdng trinh hoanh do giao diem cua d va (C) la Thdigian lam bai: 120 phut x^ - 3 x + 2 = m ( x - 3 ) + 20 c ^ ( x - 3 ) ( x ^ +3x + 6 - m ) = : 0 0,25 Cau I. (3,0 diem) Cho ham so y = x^ - 3x + 2 co do thj la (C). rx-3=o 1. Khao sat sir bien thien va ve do thj (C)cua ham so tren. X- + 3 x + 6 - m - 0 ( l ) 2. Goi d la du'cJng th^ng di qua diem A(3; 20) va c6 he so' goc m. Tim m de De d cat (C) tai ba diem phan biet co hoanh do Idn - 2 thi PT 0,25 di/cJng thang d cat (C) tai ba diem phan biet c6 hoanh do Idn - 2. (l)phai CO hai nghiem phan biet Idn hdn - 2 va khac 3. Cau 11. (2,0 diem) Dat t = x + 2thi(l)trc( thanh f(t) = t^ - 1 + 4 - m = 0 (2) 0,25 YCBT thi PT (2) CO hai nghiem duTdng phan bi^t khac 5 1. Tim gia tri Idn nha't, gia trj nho nhat cua y = f(x) = - ^ x ^ + x + ln(l - x) 21
Tuy^n chqn 3 9 dg thil sutc hgc ki mfln Toan Idp 12 NSng cao - Phgm Trgng Thii Cty TNHH MTV D W H Khang Vigt A = 4m -15 > 0 N e u l < x < 2 thi 3 x ^ - 1 4 x + 15 = 0 c i > x = - - S = l >0 J5 o — < m < 4. P = 44 -- m p = m>() 4 V a y phiTdng trinh da cho co tap nghiem la ^ = -j - j r(5) - 24 - m ;t 0 III Tinh the tich khoi chop A . ' B B ' C ' C . II 1. (0,5 diem) Tim gia tri l B C l A'M 8 Suy ra goc giifa m p ( A B C ) va m p ( A ' B C ) la A ' M A = a. Dodo max l"(x) = f(0) = 0; min l"(x) = r ( - 2 ) = - 4 + ln3. 2.(0,5 diem) Tinh... 3 .27'"83^^=3-^'«g3f^ /3'°83f^ =6-^=216. -5^=625. 2 2 aVJ a\/3 AH = - A M = - - ^ - = - ^ 3 3 2 3 1 aN/^ \ HM = - A M = — ^ 3 6 Vay A = 2 1 6 + 6 2 5 + 16 = 857. 3. (1,0 diem) Giai phtfc/ng trinh., •A'H = V A ' A ' - A H ^ -^V9b2-3a^ l
Tuy§'n chpn 39 thif sifc hpc ki m6n Toan I6p 12 MSng cao - Pham Trpng Jhd Cty TIMHH MTV DVVH Khang Vi?t D E THCT S O C H O C K i I M O N T O A N L 6 P 1 2 oiSp 6 Thdi glan lam bar. 120 phut V a y the lich khoi chop A.'BB'C'C la Cflu I. (3,0 diem) Cho ham so y = (1) ' , a^Vsb^-a^ V = V2-V,= (dvtt) • 1. Khao sat s i f b i e n thicn va ve do thj (C) cua ham s 6 ' ( l ) . IV 1. (1,0 diem) G i a i phxidn^ trinh... 2. T i m M G (C),biet rSng tiep tuyen vc'Ji (C) tai M ciit Ox, Oy hin lUdt tai A, (2,0 diem) T a c o y ' = e ^ (cosx - 2xsinx). B tao thanh tarn giac O A B c6 dien tich bilng — (vdi O la go'c toa dp). 4 • , • • y" = e ^ ( - 4 x c o s x + 4x s i n x - 3 s i n x ) . Cfiu I I . (2,0 diem) Do do y " + 4 x y ' + 3y = 0 - 4 6 " " x^sinx = 0 ; ^ ., . , , ,, , , , 1 + sin^ X + cos^ X 1. T i m gia Iri kJn nhat, gia tri nho nhal cua y = T T — X = 0 h o a c sin X = 0 X = k ; : , k e Z . 1 + sin x + cos X 2. (1,0 diem) G i a i he phiTi/n^ trinh... ^ logy 16+2 log I 5 log25 4-log | 3 D i c u k i c n x > 2, y > 0. 2. T i n h gia t r i b i e u thiJc: M = 3 ^ +5 5 B i c n doi he phiTdng trinh da cho thanh 3. G i a i bat phU'cfng trinh log-,^ X + 31og2 X > ^ i o g ^ ^ 16. x - 4 x + y + 2 =0 x " - 4 x + y + 2 = 0 (1) Cflu I I I . (2,0 diem) Cho hinh chop tam giac deu S.ABC c6 canh ben bKng a va 2 1 o g ^ { x - 2 ) = 21og^y x - 2 =y (2) tao vdi milt day A B C g o c a . G o i O la tam cua tam giac deu A B C . 1. T i n h theo a the tich cua khoi chop S.ABC. The (2) vao (1) ta diTdc x " - 3 x = 0 . 2. G o i M, N Ian liTdt la trung d i e m cua A B va A C . Mat ph^ng (P) qua M N va G i a i phufc^ng trinh nay ta c6 x = 3 va x = 0 (loai). V a y he phiTcJng trinh dii cho co nghiem (x; y ) = (3; 1). song song \6\O cat SA tai d i e m E. ChiJng minh ^^"^^^ ^ — • Vs.ABC 16 V 11m m de 6\iHn^ t h a n j j d c6 phiTc/ng t r i n h y = - x + m c a t (C). (1,0 CSiuW. (2,0 diem) PhiTdng trinh hoanh do giao d i e m cua (C) v d i d la diem) 1. T i m diio h a m ciia cac ham .so: x~ + x - I = - x + m o 2 x " - mx + m - 1 = 0 {*•) (x 1) a) y = ( x ^ - 2 x + 2)e''. x-1 b) y = S"^" + 3''cos2x. d cat (C) tai hai d i e m phan biet log (3y-l) = x o (*) CO hai nghiem phan biet khac 1 2. G i a i he phi/dng trinh 2 (x; y e R). A = m=-8m + 8>0 2 - m +m-l?i0 (ihoa) C&u\. (1,0 diem) rii/2 T i m m de du'cJng t h i n g y = m ch dU'cJng cong y = ^ ^ "^^—- t a i hai d i e m x -1 m > 4 + 2V? phan biet A , B sao cho O A vuong goc OB (\6i O la goc tpa do). Vay m < 4 - ly/l hoac m > 4 + 2 V2 i h i d cat (C) tai hai d i e m phan hiC't. 94 25
Cty TNHH MTV DWH Khang Vigt TuyS'n chpn 39 thtJ sifc hpc ki mOn To^n \dp 12 Nang cao - Ph^m Trpng Jhu D A P A N THAM KHAO miny= min f(t) = - tai t = - 1 x = - + — , k e Z. Cdu Dap an Dieim 2. (0.5 diem) x e R - ' Tinh... l e | - l ; II 6 ' 4 2 1. (2,0 diem) Khao sat stf bien thien va ve do thj (C) cua ham... -U.!:ylfi+21og| 5 log25 4 - l o g | 3 (3,0 Doc gia tiT giai_cach giai ttfc^ng tiT cau I.l de so' 1. Tac6:M = 3 +5 ^ 0,25 diem) 2. (1,0 diem) Tim M e (C), biet rang tiep tuyen vtfi (C) tai M ... _ ^I()gy4-21()gy5 ^^I(>g25 4+I(>g,3 2x, . PhiTdng trinh tiep tuyen d cua (C) tai M , 4 Goi M la y-y„ = l " ( x , , ) ( x - x ^ , ) 0,25 0,25 V"^3^,^3,og5.^2^^^^32 2 , ^ 2x^, 2x 2x^ 5 5 o y= + l (x„+l)^ (x„ + l)2 3. (1,0 diem) Giai bat phUc/ng trinh... d cat Ox tai A => A(-x,^ • 0). Dicu kien x > ( ) (*). 0,25 Vdi dicu kien trcn ba't phUdng trinh da cho tifdng diTdng d cat Oy tai B => B 0,25 l o g ^ - x + 3 1 o g T X > - l o g , 2"^ c=> log^"x + 3 1 o g 2 X - 4 > 0 / 2 ^2 ~ 2 T2 S - ^ « ' x 2 K 1 [log T X < - 4 1 4 2 (X +1)2 4 X„+l 4 - o X < 16' — 0,25 [log2X>l . x>2 2=-\,-1 2x^ + Xy + 1 = 0 (v6 nghiem) 0 < X< — Kct h(Jp dicu kien (*) la diTdc 16- x>2 0,25 1 . Vay M,(1;1),M2 — ; - 2 2 Vay tijip nghiem ciia BPT da cllola T = fo; — u l 2 ; + o o ) . x„ = - - = > y ( , = - 2 II 1. (0,5 Tim gia trj l(?n nha't, gia tri nho nhat. (2,0 III 1. (1.0 diem) Tinh theo a the tich cua khoi chop S.ABC. diem) l + l-"^sin^2x 2 - ' ^ ( l - c o s 4 x ) . (2,0 Vi SO 1 (ABC) nen SAO = a => SO = asina, AO - acosa Ta CO y = 0,5 4 8 _ 13 + 3cos4x diem) => AB = a\/3cosa. l^l-Um'-lx 2 - ' ( l - c o s 4 x ) ~ ^ ^ + 2cos4x The tich khoi chop deu la 2 Dat t = c o s 4 x , - l < t < l . 4 0,5 V,S . A B C - 3' . 4 ^ .SO ''^ 4^ cos^asina (dvtt). Ham so r(t)=:i^^t^ c 6 V(i) = - 16 >0, V t e [ - 1 ; 1]. 14 + 2t (14 + 2tr 2. (1,0 diem) Chtfng minh... Suy ra ham so tang trcn [-1; 1] Goi I la giao diem ci'ia MN va AO. 0,5 Do do max y = m a x f(l) = 1 tai t = 1 o x = — , k € Z. AE AT xeK t e | - l ; l| ' 2 Suy ra I la trung diem cua MN vii EI // SO ^ — = — ( D 1/; 27
Tuyg'n chpn 39 dg thCf siJc hpc ki mOn Toan I6p 12 Nflng cap - Phgm Trpng Thu Cty TNHH MTV DVVH Khang ViSt AI=-AF Vay h0 phu'dng trinh dii cho c6 n g h i e m (x; y) = 0,25 \ 7 Goi F la trung diem ciia BC. Ta c6 < V Tmi m de diicVng thang y = m cat difcfng cong... AO=-AF I 3 (1,0 x" + mx - 1 diem) . Goi d: y = m va (C): y = S. . Phu'dng trinh hoanh do giao d i e m ciia d va (C) la 0,25 X +mx-l :=mx" = l - m (X 1) C'^) x-1 . d cat (C) tai hai diem phan biet A, B c6 hoanh d o x j , X2 khi jm -d-m) 0,5 T i r ( l ) va (2) => — = - . AS 4 0,5 m= (thoa dieu kien (**)). Do ^5 "^AMNE _ A M AN AE _ 3 V
Tuygn chpn 3 9 6i thtf sifc hgc kl m a n Toan I6p 12 NSng cao - Ptigm T r p n g T h a Cty TNHH M T V D W H Khang Vi$t CSu I I I . (2,0 diem) Cho hinh lang try drfng A ' B ' C ' . A B C c6 day la tarn gi^c vuong A B C tai B . Gia suf A B = a, A A ' = 2a, A C ' = 3a. G o i M la trung d i e m y ' = O o t = - U ( - l ; 1) hoac t = - - e ( - l ; ! ) • cua A ' C va I la giao d i e m cua A M vii A'C. T i n h the tich tiJ dien l A B C . ^ 23 , . 1 C a u I V . (2,0 diem) Dodo min y = — k h i s i n x = xe . — -; — 27 3 0,25 1. Cho ham so y = 0" ln(2 + sinx). ChuTng minh (2 + s i n x ) ( y ' - y ) = e'^cosx. 2 2 2. G i a i bat phiTdng Irinh 25''+^ + 9 " + ' > 3 4 . 1 5 \ 2. (0,5 diem) T i m gidi han.. ,. ln(2x + l ) - l n ( 3 x + l ) ^ ln(2x + l ) ^ ,. ln(3x + l ) C S u V . (1,0 diem) Cho h a m so y = x - l + — ! — c 6 do thi ( C ) . T i m tren (C) hai hm = 2hm 3 lim 0,25 x+1 x^o 2x 0 3x d i e m d o i xufng nhau qua dufcing thang d : y = x + !. = 2-3 = - l . 0,25 3. (1,0 diem) G i a i phtftfng trinh.. DAP AN THAM KHAO log^^3 f 3 - Vx2-2x + l l = i o l o g , ^ 3 (3 - |x - 1 | ) = 1 (1) Cdu Dap an Diem V J Z 2 0 0 -3 x ' ' - 9 x + 13 = 0 o (x, - X 2 ) [ ( x , + X 2 ) ^ - X j X j - 3 ( x , + X 2 ) + 3 m ] = y j - y 2 (3) 9 + yf29 X = (loai) Ma X, + X 2 =2; x,X2 =m. 0,25 TxiO) la CO V a y tap nghiem cua phu'dng trinh da cho la y , - y 2 = ( x , - X 2 ) ( 4 - m - 6 + 3m) = 2(x, - X j K x i X j - 1 ) 0,25 - 3 + ^/5 9-y[29 0,25 T = Suy ra dpcm. II 1. (0,5 diem) T i m gia tri gia trj nho nhS't... III T i n h the tich ti? di^n l A B C . (2,0 H a m SO y C O the vie't l a i y = sin-'x - (1 - 2 s i n ^ x ) + sinx + 2 (2,0 Trong tarn giac vuong A ' A C ta c6: diem) hay y = sin'^x + 2sin"x + sinx + 1 diim) 0,25 0,25 A C = \/9a2-4a2 =aV5. Dat t = sinx, t e ( - l ; 1). Tir do trong tam giac vuong A B C , t h i Ta c6: 1(1) = t'' + 2 l ^ + 1 + 1, r'(l) = 31" + 4t + 1 0,25 B C = V5a2 - a ^ - 2 a . 30 11
ruygn chpn 39 6i thiT site hpc kl mOn Toan Iflp 12 NSng cao - Ph^m Trpng Thi/ Cty TNHH MTV D W H Khang Vigt Do(AA'C'C)l(ABC)nen A' , M , C' X-1 + = - x + m2x - ( m - l ) x - m = 0 ( x ? t _ i ) . trong (AA'C'C) X +1 m-I ke I H J. AC (H e AC) =^ IH 1 (ABC). X = Vn3' Toa do trung diem I cua PQ la IH CI 2a / ^ 3m+ 1 / ' ^ Thco dinh li Ta-lct ta c6 = / / 1 ^ ^ 0,75 y =-X +m = • / ' ^ CA' AA' / 1 ^ V,CI^AC^2=. =2 ^d _ _ D \ C , , , 3m+ 1 m-1 , lA' A'M l A ' + CI 3 K H I e d ncn + 1.0iai ra ta co m = 1. 4 4 IH CI 2 ,u 2^^, 4a 0,5 => = = —=>IH = - A A = i Khi do hoanh do hai diem P, Q la nghiem cua phU"dng trinh AA' CA' 3 3 3 The tich cua ti? dien lABC la: 2x--I = 0c^x = ± ' 0,75 V , A R r = ' S . R p . I H - ' AB.BC.IH- ^ a.2a."^'^ - "^'^ (dvtt) 1 1 lABC 3 ABC 6 3 9 Vay hai diem can tim la P +1 , Q +1 IV 1. (1,0 diem) Chtfiig minh... (2,0 (ngU'rtc lai). diem) Taco y' = (^'') ln(2 + sinx) + c''(ln(2 + sinx))' 0,5 DE THCT S O C H O C Kl I M O N T O A N L 6 P 1 2 X . . , c"cosx DE S O 8 = ln(2 + sinx) + Thdi gian lam bai: 120 phut 2 + sinx e''cosx C&ul. (3,0 diem) 0,25 2 + sinx 11 Cho ham so y = - — + x ^ + 3 x - — . Vay (2 + s i n x ) ( y ' - y ) = c''cosx. 0,25 3 3 2. (1,0 diem) Giai ba't phU't/ng trinh... 1. Khao sat siTbicn thicn va ve do thi (C) cua ham so da cho. \ 2. Tim tren do thi (C) hai diem phan biet M , N doi xiJng nhau qua true tung. 2,;x+l^gx+l >34i5x - -34 - + 9>0 0,25 Cfiu 11.(2,0 diem) UJ l3 In^x 1. Tim gia trj Idn nha't va gia tri nho nhat cua ham so y = tren dean x 0,5 1; f e^y- [ X >0 - >1 cos-^-log,9-log,6 |^]yog^4 2. T i n h A = 2008. 49" 3 It Vay tap nghiem cua bat phifdng trinh da cho la 0,25 T = (_«,; - 2 ] u [ ( ) ; + « 3 ) . 2x-y 3. Giai he phu'cJng trinh 32''~y-26.3 2 =27. V Tim t r e n (C) hai diem do'i xitng nhaa.. (1,0 ^log^Cx-y)^^ Ne'u P, Q la hai diem tren (C) doi xiJng nhau qua difdng th^ng diem) d : y = x +1 thi phufcJng trinh diTdng PQ (vuong goc vdi d) c6 0,5 CSu I I I . (2,0 diem) Cho hinh chop S.ABCD c6 day ABCD la hinh vuong canh a. dang d':y = - x + m. Canh ben SA vuong g6c vdi day, M la diem di dong tren canh CD, H la hinh Phu'dng trinh hoanh do giao diem cua (C) va d'la 19 33
Cty TNHH MTV D W H Khang VH Tuygn chpn 39 gj thCf sOfc hpc k1 mOn To^n lap 12 NSng cao - Phgm TrpnQ Thu chie'u cua dinh S Icn BM. Tim vj tri cua diem M tren CD de the tich kho'i chop Dodo max y = y(e^) = — ; S.ABH la Idn nha't. Tinh the tich Idn nhat do, biet SA = h. Cfiu IV. (2,0 diem) xe|l;c'l e min y = y(l) = 0• 1. Cho ham so y = sin( In x) + cos(ln x). ChiJng minh y + xy' + x^y' = 0. 2. (0,5 diem) Tinh... xe|l;L•'| (I 2. Giai bat phiTdng trinh (^^fl + T^sJ + |V7^^V48
Tuygn chgn 39 66 M sijfc hgc kl mOn ToAn Idp 12 Nang cap - Phgm Trpng Tha Cty TNHH MTV DVVH Khang Vi$t III T i n h the tich \dn nhat... V Tim a de (P) tiep xiic (C). (2,0 Dat C M = x ( 0 < x < a ) - (1,0 X - X+ 1 2 diem) diem) x-1 = x +a Q 0 VxeR 0,5 « x - 0 (3) 0,5 2 2 The (3) vao (1) ta dUdc a = - 1 . L i luan V < — = > V ^ , , = — khi x - a, titc la M ^ D . 0,5 V a y a = - 1 thi (P) tiep xiic v d i (C). 12 '"^^ 12 IV 1. (1,0 diem) ChiJng minh... (2,0 , cos(lnx)-sin(inx) DE THlIr SQC HOC Kl I M O N T O A N L 6 P 1 2 diem) 0,25 DE S O S X Thdigian lam bai: 120 phut '1 r 1Y y'' = ( c o s ( i n x ) - s i n ( l n x ) ) — + — (cos(lnx)-sin(inx)) C&ul. (3,0 diem) X U ; 0,5 Cho h a m s o ' y = -^^^—^ (1) -sin(inx)-cos(lnx) cos(!nx)-sin(Inx) 2cos(lnx) x-1 1. K h i i o sat sif b i c n thien va vc do thi ( H ) cua ham so (1). x2 x^ x2 The" y , y ' , y " vao y + x y ' + x ^ y " , rut gon l a i ta diTdc dpcm. 0,25 2. G o i I la t a m d o i xtfng cua ( H ) . T i m d i e m M thuoc ( H ) sao cho tiep tuyen 2. (1,0 diem) G i a i M't phMng trinh... cua ( H ) tai M vuong goc v d i dU'dng thang I M . C&u 11.(2,0 diem) N h a n t h a y : |V7 + V48 J.JV? - N/48 ) = 1 1. T i m gia trj U'ltn nhii't va gia tri nho nhat ciia ham so f ( x ) = e"''''^^(4x^ - 5 x ) Datl= Vv + V48 , t>0. trendoan - ; - 0,5 • [2 2. PhiTcJng trinh da cho trd thanh t + - < 14 < » - 14t + 1 < 0 2. G i a i phirang t r i n h log^^ 8 - l o g 2 x 2 + logy243 = 0. * j i o 7 - V48 < t < 7 + V48 3. G i a i b a t p h i f d n g t r i n h 2 " ^ " ' - 2 ^ ^ ' " " ^ > 3 . " C S u I I I . (2,0 diem) Cho hinh chop S.ABC c6 hai mSt b e n S A B va S A C vuong o ( V 7 + V48 < yJl + ^f4^ < yll + yf4S o - 2 < X < 2. 0,25 g6c v d i mat day. D a y A B C la tam giac can dinh A , co diTdng cao A D = a,mat ben SBC la tam giac deu canh SB lao v d i mat day goc a . V a y tap n g h i e m cua bat phUdng trinh da cho la T = ( - 2 ; 2). 0,25 37