THIẾT KẾ BÀI GIẢNG HÌNH HỌC 10 NÂNG CAO

§3 Khoang each va goc (tiet 5, 6) MUC TIEU Kie'n thuc • Hge sinh nhd dugc cdng thiic tfnh khoang cich tii mdt diem din mdt dudng thing va cdng thiic tinh cosin ciia gdc giiia hai dudng thing KT nang t Viet dugc phuong trinh hai dudng phan giac ciia gdc tao bdi hai dudng thing cit Bie't each kiim tra xem hai diem d vl mdt phia hay khic phfa cua dudng thing Thai • Lien he dugc vdi nhiiu van dl cd thyc t l lien quan din dudng phan giac • Cd nhiiu sang tao bai toan mdi • Cd tinh thin ham hge ban II CHUAN BI CUA GV VA HS Chuan bi cua GV: GV: Chuin bi mdt sd cau hdi vl gdc giiia hai dudng thing, gdc giiia hai vecto de hdi hge sinh Chuin bi mdt sd hinh sin d nha vao giay hoac vao ban meca de chiiu niu cd may chiiu: Tu:hinh72, 73, 74 Ngoai cdn phai ve sin mdt sd hinh dl hudng din hge sinh thuc hien cic HD Chuin bi phin mau Chuan bi cua HS : • Dgc bii ki d nha, Chuin bi tdt mdt sd cdng cy de ve hinh: Thudc ke, 99 III PHAN PHOI THOI LUONG Bdi ndy chia ldm tiet: Tiei 1: Td ddu den hit phdn HD Tiet : Phdn cdn lgi vd hudng ddn bdi tap IV TIEN TDINH DAY HOC fl rsni cu GV: Kiem tra bdi cu 5' Cau hdi Em hay neu dinh nghia vl phuang trinh tham sd cua dudng thing Cau hdi Phuang trinh tham so cua dudng thang dugc xac dinh bdi nhiing ye'u td nao? Cau hdi Hay neu dinh nghia phuang trinh chfnh tic ciia dudng thing, mdi quan he cua nd vdi phuong trinh tham so B RM MOI HOAT DONG 1 Khoang each tu mdt diem den mdt dudng thang a) Muc dich Cho hge sinh ldm quen vdi mot cdng thifc tinh khodng cdch tif mgt dem din mgt dudng thdng bang phuong phdp tog b) Hudng thitc Men - Niu vd thifc hiin gidi bdi todn -Thifc hiii^^ 100 - Niu vi tri tuong dd'i cua diem vd dudng thdng -Thuc Men [?l] - Neu va giii bai toin -Thifc Men ^%2 - Niu vd hudng ddn HS thuc Men vi du trang 87 SGK c) Qud trinh thuc Men • Neu va thyc hien giai bai toan - Neu bai loan va cho HS thao luan GV ve hoac treo hinh 72 len bang A^y Hinh 72 Viec giai bai toan la khd ddi vdi hge sinh, vi vay GV cho bgc sinh xem xet ldi giai va giai thfch nhiing van dl hge sinh cdn nghi vin hoac thic mic Ddi vdi da so hge sinh, nen cdng nhan kit qui cua bai toan d(M ; A) k^M + by^ + cl v5 + b' • Thyc hien lt\, GV thifc hien thao tac 3' Hoat ddng cua giao vien Cau hdi Hoat ddng ciia hoc sinh Ggi y tra Idi cau hdi Hay tfnh khoang cich tii' diem M Ap dyng cdng thiic ta cd : din dudng thing A trudng | - + 151 hgp sau V25 a)M(13 ; 14) vi Zl : x - y + 15 = ; 101 Cau hdi • Hay tinh khoang each tit diim M Ggi y tra Idi cau hdi din dudng thang A trudng Trudc tien chuyin A vl dang phuong hgp sau trinh tdng quit b)M(5;-l)vaA: \"~'^~^\ [y = - + 3? 3x + 2y-13 = 0; Tit dd ta cd : d(M, A) = |3.5 + ( - l ) - | ^— ~~ ^ = VI3 • • Vi trf ciia hai diem ddi vdi mdt dudng thing Dat vin d l : (SGK) Cho dudng thang ^ : ax + Z^y + c = va diim M(Xf^ ; y^) NIu M' la hinh chieu (vudng gdc) ciia M tren A thi theo ldi giai ciia bai toan tren, ta cd M'M axj^ + byj^ + e =kn, dd k a^+b^ Tuong ty niu cd diim N(Xfj ; y^) vdi V la hinh chie'u cua N tren A thi ta ciing cd N'N = k'n ,{Yong66k , _ tfxyy + by^ +c a^+b^ • Thuc hien ?1 GV thifc hien thao tac 3' Hoat dgng cua giao vien Cau hdi Hoat ddng cua hge sinh Ggi y tra Idi cau hdi Cd nhan xet gi vl vi trf cua hai k va k' ciing diu va chi M vaN diim M, N dd'i vdi A k va k' nim vl mdt niia mat phing bd A Cling da'u ? 102 ^ Ggi y tra Idi cau hdi Cau hdi Cd nhan xet gi vl vi trf ciia hai k va k' khac diu va chi M va N diim M, N dd'i vdi A k va k' nim ve hai niia mat phing bd A khic da'u ? • Neu kit luan GV neu kit luan sau Hai diim M, N nim ciing phia dd'i vdi A va chi (axf^ + byf^ + c)(axp^ + by^ + c) > ; Hai diim M, N nim khic phia dd'i vdi A va chi (ax;^ + byi^ + c)(ax^ + by^ + c) < • Thyc hien - ^ GV thifc hien tiiao tac 3' Hoat ddng ciia giao vien Cau hdi Hoat ddng ciia hge sinh Ggi y tra Idi cau hdi Thay cac gia tri ciia cac diim A, k^— 1; kg = 9; k(; = —9 B, C va A tim cic so k Cau hdi • Ggi y tra Idi cau hdi Cd nhan xet gi vl vi tri ciia A, B, A va B cung phfa dd'i vdi A =J> A khdng C dd'i vdi A cit canh AB; * A va C; B va C khac phfa dd'i vdi A=> A cit cac canh AC va BC 103 • Neu va giai bai toan - GV neu bai toan va cho HS thao luan bai tdin - GV Ve hmh 73 len bang Hinh 73 Cho HS tra ldi cac cau hdi sau HI Cho hai dudng thing cit Hay tim tap hgfp cac diem each diu hai dudng thing 66 • Thyc hien " ^ GV thifc hien thao tac 3' Hoat ddng cua giao vien Cau hdi Hoat ddng cua hge sinh Ggi y tra Idi cau hdi Ggi M (x; y) Tinh khoang each J _ \aix + biy + ci\ tii M de'n A ^ ^af + bf Cau hdi Tfnh khoang each tii M den A 2- Ggi y tra Idi cau hdi \a2X + ^2= Cau hdi Khi nao M thudc dudng phan giic 104 b2y+C2\ V«2 + b2 Ggi y tra Idi cau hdi ciia gdc tao bdi Aj va A2 Khidi=d2 \aix + biy + ci\ «2^ + ^2>'+ ^2 ^af + bf ^''l + bl Vay^ , —-= Ttr dd ta cd aix + biy + Cl ^ a2X + Z?2>' + ^2 _ ^ ^laf + bf ^jal -r bl * Thyc hien vf dy Diy la bai toan van dyng hai kT nang: - Vi tri cua hai diim dd'i vdi mdt dudng thing - Phuang trinh dudng phan giic ciia hai dudng thang GV cin dua cac cau hdi: HLHay viit phuang trinh hai dudng phan giac va ngoai cua gdc A H2: A la phan giac cua gdc A nao? Sau dd hudng din hge sinh giai bai toan Ket qud Dudng phan giac la mdt hai dudng 4x + 2y -13 = (dudng phan giic d^) 4x - 8y + 17 = (dudng phan giac ^2)Thu toa B va C vao phuang trinh cua dj va d2 va su dyng tinh chit * B va C nim ciing phfa vdi dudng thing thi dudng thing la phan giac ngoai * B va C nim khic phia vdi dudng thing thi dudng thing dd la phan giac i/2: x - y + = 105 HOAT DONG 2 Gdc giiia hai dudng thing a) Muc dich Cho hge sinh ldm quen vdi mgt cong thifc ve goc giica hai dudng thdng b) Hudng thuc Men - Niu vd dinh nghia ve goc giila hai dudng thdng -Thitc Men [?2] - Neu chii y -Thlfc hiin ^ - Neu vd gidi bdi todn - Th uc Men ^ ^ ^ -Thue hiiii^\^ - Neu vd hudng ddn HS thuc hiin vi dii trang 87 SGK c) Qud trinh thitc Men • Neu dinh nghia Dinh nghTa Hai dudng thing a va b cit tao bd'n gdc So nhd nhit cua cic gdc 66 dugc ggi la so ciia gdc giira hai dudng thing a va b, hay don gian la gdc giila a va b Khi a song song hodc triing vdi b, ta quy udc gdc giifa ehiing bdng • Thyc hien [?l| Hinh 74 106 GV ve hinh 74 va cho HS thao luan cau hoi GV thifc hien thao tac 2' Hoat ddng ciia hge sinh Hoat ddng cua giao vien Ggi y tra Idi cau hdi Cau hdi Gdc giii^ a va b bing bao nhieu 60" do? Cau hdi Ggi y tra Idi cau hdi So sanh gdc dd vdi gdc giua hai Hai gdc bii vecto M , V va gdc giiia hai vecto M', V • GV neu chii y Gdc giiia hai dudng thing cit a va b, kf hieu la (a, b), ludn nhd hon hoac bing 90 nen ta cd (a,b) = (u ,v) niu (u , v ) < 90 , (a, ^) = 180° - (/7, V ) niu (/7, v ) > 90°, dd u, v lin lugt la vecto chi phuong cua avab • Thyc hien^r GV thifc hien thao tac 3' Hoat ddng cua giao vien Cau hdi Tim toa vecto chi phuang cua hai dudng thing Cau hdi Tim gdc hgp bdi hai dudng thing dd Hoat ddng ciia hge sinh Ggi y tra Idi cau hdi ill =(2;1),"2 =(1^3) Ggi y tra Idi cau hdi 2.1 + 1.3 cos(A,A )= ' ^ 1— ' = ^ ; V5.V1O V2 Gdc giiia hai dudng thing bing 45" 107 • Neu va giai bai toan GV neu bai toan 3, cho HS thao luan cau hdi Giai bai bing • Thyc hien ^ r GV thifc hien thao tac 3' Hoat ddng ciia giao vien Hoat ddng ciia hge sinh Ggi y tra Idi cau hdi Cau hdi Tim cosin ciia gdc giiia hai dudng thing A, va Ai Iin lugt cho bdi cac phuang trinh msfA, A 2T J) ^ ' j la^on +b]b:>\ ' ' / 7 ^Ja(+b{.^ai+bi = cos(/7,, ii2)\ ajX + bjy + Cl = va Ggi y tra Idi cau hdi a2X + b2y + C2 = ^1^2 + bib2 = Cau hdi Tim diiu kien de hai dudng thing Al va A2 vudng gdc vdi • GV neu kit luan kl'^2 +'^1^2! a) cos(Ai,A2) cos(^l, ^2) dd hi, «2 a\' +bi- ^0-2' +b2^ Iin lugt la vecto phap tuyin cua Ay, A2 b) A] J_ A2 a\a2 + b\b2 = • Thyc hien^C GV thifc hien thao tac 3' Hoat ddng ciia giao vien Cau hdi Tim gdc giua hai dudng thing A^ 108 Hoat ddng ciia hoc sinh Ggi y tra Idi cau hdi coscp = => (p = 90° hay A, A2 Cau hdi Tfnh khoang cich tir mdi diem M(3 ; 5), V(-4 ; 0), F(2 ; 1) tdi A va xet xem dudng thing zl cit canh nao ciia tam giic MNP Ggi y tra Idi cau hdi Ggi a va p lin lugt la gdc giiia A vdi Ox va Oy Ta cd : cosa = cosp=- ^ =:> a * 36°52' ; p*53°8' Bai Hudng dan a) Thay lan lugt toa cua O va M vao ve trai phuang trinh ciia d, ta dugc : dg = - + = va df^ = X - y + Do dd diim M thudc niia mat phing bd d va chiia gdc toa O 2(x - y + 2) > hay x - y + > Thay toa A vao vl trii phuong trinh ciia d ta cd : d^ = - + = Viy A nim nua mat phang bd d va chiia O b) Diem 0'(x'; y') ddi xiing vdi O qua d o{ 'OO' ^I -d ,^^ [dQ.=-do (1) (2) (dg va do' dugc ki hieu tuong ty nhu d cau a) ( l ) o x ' + y' = (2) o x' - y' + = - hay x' - y' = -4 Vay x' = - 2, y' = Do dd O' (-2 ; 2) c) Vi OA = khdng ddi nen chu vi tam giac OMA nhd nhit MO + MA nhd nhi't Vdi mgi M tren d ta ludn cd MO = MO' nen MO + MA = = MO' + MA > O'A, diu bing xay M d giiia O' va A hay M la giao diim cua d va dudng thing O'A Viet phuang trinh dudng thing O'A rdi giai he phuong trinh de tim toa dd ciia M 191 Bai Hudng dan A' ddi xiing vdi A qua I va chi A' // A hoac A' = A, ddng thdi A' va A each deu I Tu dd suy phuang trinh A' cd dang : Ax + By + C = Do d(I ; A) = d(I; A') nen C = -2(Axo + Byo) - C Vay A' cd phuong trinh : Ax + By - 2(Axo + Byo) - C = hay Ax + By + C - 2(Axo + Byo + C) = Cd the giai each khac (xem ldi giai bai toan dudi day) nhu sau : Lay mdt diem M thugc A, tim diem M' ddi xung vdi M qua I rdi viet phuong trinh A' qua M' va song song vdi A Bai Hudng dan Tim toa dinh ching ban A, la giao diem ciia hai dudng thing da cho Tun diem C ddi xiing vdi A qua I rdi \ ilt phuong trinh hai canh cdn lai (mdi canh nim tren dudng thing song song vdi mgt hai dudng da cho) DS : X + 3y - 30 = va 2x - 5y + 39 = Bai Hudng dan m a) (1) la phuang trinh dudng trdn + (m + I) - > c^ m < — hoac m > b) Tam dudng trdn cd toa m [y = m + I X = Khu m td' he tren ta dugc 2x + y - = 8 m < — ==> -2x - 5 x 0 m>0 192 Vay tap hgp tam ciia cac dudng trdn la hai phan ciia dudng thing cd phuong trinh 2x + y - = iing vdi x < hoac x > — Bai Hudng din Do hai dudng trdn cit nen chung khdng ddng tam, suy Ai - A2 va Bj - B2 khdng the ciing bing khdng Giao diem ciia hai dudng trdn da cho cd toa la nghiem cua phuong trinh : x2 + y2 + 2A|X + 2B^y + Cj = x2 + y2 + 2A2X + 2B2y + C2 o ( A i - A ) x + ( B i - B ) y + C i - C = (*) ' Vay niu hai dudng trdn cit tai M va N thi toa cua M va N thoa man phuang trinh (*), hay (*) la phuang trinh dudng thing di qua M va N Dd cung la phuong trinh trye dang phuong ciia hai dudng trdn da cho Bai Hudng dan x2 +y2 +2Axo +2Byo + C = (Xo + A)2 +(yo + B)2 - ( A + B - C ) = = d - R =./M/(C) d d la khoang each tii' M tdi tam dudng trdn (C) va R la ban kfnh dudng trdn (C) Bai GV chira tai Idp Hogt ddng cua gido vien Hogt ddng ciia hoc sinh Cau hdi Ggi y tra Idi cau hdi Hay viet phuang trinh dudng thing di qua A Cau hdi Hay xac dinh tam va ban kfnh ciia Dudng thing A qua A cd phuang trinh a(x + 2) + b ( y - ) = Ggi y tra Idi cau hdi Dudng trdn (C) cd tam 0(0 ; 0), ban 193 dudng trdn kfnh R = Ggi y tra Idi cau hdi Cau hdi Tir dieu kien cua dudng thing tiep xiic vdi dudng trdn, hay viet phuang trinh tiep tuyen dd A la tilp tuyin cua (C) I 2a-3b • y^ + b^ =2 ^ \ a - b | = 2Va2^b2 AT = AT = TT' = T J - AT.OT ^/A T ^ + O T = 3.2 12 V9 + Bai 10 Hudng din a) Elip (E) cd hai tieu diim (-1 ; 0) va (1 ; 0) Hypebol (H) cd hai tieu diim (-3 ; 0) va (3 ; 0) b) HS ty ve c) (-V5 ; O) va (Vs ; o) 194 Bai 11 Hudng din a) A cit (E) he phuang trinh 2x - y - m = cd hai nghiem phan biet [4x^+5y^-20 = DS : -2V6 < m < 2V6 b) A va (E) cd mdt diim chung he phuang trinh chi cd nghiem m = ±2V6 Bai 12 Hudng din a) DS : Elip cd : Tieu diim (-4 ; 0), (4 ; 0) Dinh (-5 ; 0); (5 ; 0) va (0 ; - ) ; (0 ; 3) b) Hypebol (H) cd hai dinh (-4 ; 0); (4 ; 0) va hai tieu diim (-5 ; 0) va (5 ; 0) , , , Gia su phuang trinh chfnh tac cua hypebol la 'a = suy < ,a2+b2 = 25 x2 y2 a2=16 b2=9 X y a2 b2 — = Khi dd ta co : Phuang trinh chfnh tic cua hypebol la 16 2 ^ +^ = 25 d) Tii he phuang trinh X y 116 de dang tfnh dugc x = 2 Txx d d ta CO : X + y = J_ J_ =1 2.25.16 41 y^=9 2.16 41 41 25 16 881 —- 41 195 Bai 13 Hudng dan HS dn tap Iai phuang trinh ciia parabol, phuang trinh tiep tuyen ciia parabol Dap sd MI la tiep tuyen ciia parabol Bai 14 Hudng dan Dat M(xi ; y,), N(X2 ; y2)- Do M va N thudc (P) nen Xj = 2y2, X2 = 2y2 (vdi x,, Xi , yj, y2 khac 0) Diiu kien de OM ON la X1X2 + yiy2 = Tii' dd suy yjy2 = — (*) Phuang trinh dudng thing MN la : (y2 - yi)x - (X2 - Xi)y + yiX2 - Xiy2 = hay (y2 - yi)[x - l(yi + y2)y + 2yiy2] = yi ^ yi vi niu yj = y^ thi X] = X2, dd M = N, khdng thai man diu bai Vay phuang trinh cua MN la : x - 2(yi + y2)y + 2yiy2 = hay x-2(yi+y2)y =0 (do (*)) Dl tha'y ring dudng thing MN ludn di qua diem cd dinh HOAT DONG naC^NG DfiN Bfil TfiP TRfiC NGHIEM SGK GV: Chi cdn neu ddp dn trd ldi 196 ;0 Hudng din Chgn (C) Hudng din Chgn (B) Hudng din Chgn (A) Hudng din Chgn (D) Hudng din Chgn (A) Hudng din Chgn (D) Hudng din Chgn (D) Hudng din Chgn (A) Hudng din Chgn (B) 10 Hudng din Chgn (B) 11 Hudng din Chgn (A) 12 Hudng din Chgn (B) 13 Hudng din Chgn (A) 14 Hudng din Chgn (D) 15 Hudng din Chgn (A) 16 Hudng din Chgn (D) 17 Hudng din Chgn (D) 18 Hudng din Chgn (B) 19 Hudng din Chgn (A) 20 Hudng din Chgn (C) 21 Hudng din Chgn (A) 22 Hudng din Chgn (D) 23 Hudng din Chgn (D) 24 Hudng din Chgn (C) 197 G l l THIEU MOT SO DE KIEM T R A CHU'ONG III D E SO I Phan (Trie nghiem khach quan, bgc sinh lam 10', thu bai ngay) Cdu Dudng thing 2x + 3y -5 = cd vecto chi phuang la: (a) (2; 3); (b) (-2 ; 3); (c) (3 ; 2); (d) (-3; 2) Cdu Dudng thang 2x + 3y -5 = song song vdi dudng thang nao sau day: (a)y=|x+l (b)y = x - ; (c) y = X- 5; (d) y = x Cdu Dudng thing nao sau day tilp xiic vdi dudng trdn cd phuang trinh : , ^ X +y = ( a ) x - V y + = 0; (b) x - V3 y + = 0; (c)2x+V2y+1=0; (d) y = x Cdu Elip sau day cd mdt tieu diim la 2 :^+>^ =l (a)(0; V5); (b) (2V5;0); (c)(0;-V5); (b) (-V5;0); Phan (Tu luan, lam 35') Cho hai dudng thang cd phuang trinh: 198 A : 2x + y - = 0; d : x + 3y - = 0; a) Tim giao diim cua hai dudng thing b)Vie't phuong truth dudng thing di qua M(l; 1) va song song vdi A Tun giao diem ciia nd vdi d c) Vie't phuang trinh dudng thing di qua M, cit d va A tai A va B ma M la trung diem AB HUdNG DAN V A DAP A N Phdn Trac nghiem khdch quan d, moi cdu 0,5 d) Ciu DA d a a b Phan (Tu luan) 2x + y-2 a) ( 3d) Ta thiy giao diim ciia A va d la nghiem ciia he , [x + 5y - i = Giai ta dugc 1(1; 0) la giao diim cua A va d b) (3 d) Dudng thing di qua M va song song vdi A cd dang : 2x + y -(2.1 + 1) = hay 2x + y - = (A') Giao cua A' vdi d la nghiem ciia he {2x + y -3 = [x + 3y - = Giai ta duoc x = —, y = — 5 c) (2d) Ggi M'( —; —) la giao diim cua A' va d Ta tha'y M la trung diim cua AB va chi M' la trung diem ciia IA TiT dd ta suy A Viit phuang trinh dudng thang di qua AM la dudng thing cin tim 199 DES0 Phan (Trie nghiem khach quan, hge sinh lam 10', thu bai ngay) Cdu Dudng thing x + 3y -5 = cd vecto chi phuang la: (a) (2; 3); (b) (-2 ; 3); (c) (3; 2); (d) (-3; I) Cdu Dudng thing 2x + y -5 = song song vdi dudng thing nao sau diy: (a) y = - X + I (b) y = 2x - 5; (c)y = - x - ; (d) y = x Cdu Dudng thang nao sau day tiep xiic vdi dudng trdn cd phuong trinh : 2 X +y = ( a ) x - V y +2 = 0; (b) x - Vs y + = 0; ( c ) x + V y * =0; (d) y = x Cdu Elip sau day cd mdt tieu diem la 2 ^ +^ = 16 (a)(0; V5); (b) (2V5;0); (c)(0;-V5); (b) (-V7;0); Phan (Tu luan, lam 35') Cho dudng thing cd phuong trinh: A : 2x + y - m = 0; va mdt dudng trdn cd phuang trinh (x-2)2 + ( y - 1)2=1 200 a) Tfnh khoang each tii' tan dudng trdn de'n dudng thing m = b) Xac dinh m dl dudng thing tiep xiic vdi dudng tron c) Viet phuang trinh dudng thing di qua tam ciia dudng trdn va vudng gdc vdi A HUONG DAN VA DAP A N Phdn Trdc^ nghiem khdch quan d, moi cdu 0,5 d) Cau I DA d c a d Phin ( Tu luan) a) ( 3d) Khi m = I, dudng thing cd phuang trinh A : X - y - = 0; dudng trdn da cho cd tam la I ( ; I) Khoang each tit I den A l a : 7— — VP + 4- v^ b) (3 d) Dudng thing A tiep xiic \di dudng tron va chi khoang each tir din A bing R hay |2.2-I-w| Tir dd ta suy m = - V5 va m = + V5 c)(2d) Dudng thing vudng gdc vdi A di qua I cd dang : x + 2y-(l.l +2.I) = 0hayx -2y -3 = A : 2x + v - = 0; d : X + 3y - = 0; 201 MUC LUC • • Trang Ldi noi dau Chuang II - TICH VO HJCfNG CUA HAI VECTO VA Q N G DUNG (TIEP THEO) §3 He thdc lugng tam giac On tap chuong II Chuang III - PHUONG PHAP TOA DO TRONG MAT PHANG 202 40 56 §1 Phuong trinh tdng quat ciia dUdng thing 59 §2 Phuong trinh tham so cua dudng thing 79 §3 Khoang each va goc 99 §4 Oudng tron 117 §5 Duong elip 135 §6 Dudng hypebol 153 §7 Dudng parabol 169 §8 Ba dudng conic 178 On tap chuong III 186 THIET KE BAI GIANG HINH HOC 10 - NANG CAO, TAP HAI IRAN VINH NHAXUAT BAN HA NOI Chiu trdch nhiem xudt bdn : NGUYfiN KHAC Biin tap : OANH PHAM QUOC TUAN Vebia : T A O THANH HUYEN Trinh bdy : CHU MINH Sita ban in : PHAM QUOC TUAN In 1.000 cuon kho 17 x 24 cm, tai Cong ty CP in Phuc Yen SdOKKH xuat ban: 68 - 2009/CXB/67^ TK-06/HN In xong va nop luU chieu nSm 2009 Sach lien ket v6i Cong ty CO phan In va Phat hanh sach Viet Nam ktBGtoUpclOT2NC IK rtiti ^ " INPHAVI Phat hanh tai Cong ty co phan In va Phat hanh sach Viet >>*" 2015609 Dia chi : 78 - Dong Cac - Dong Da - Ha Noi 22.000 D OT: (04) 511 5921 - Fax: (04) 511 5921 S'' Gia: 22.000d