luyện giải đề trước kì thi vào lớp 10 ba miền bắc trung nam môn tóan

NGUYEN DlICT/iN(Chubien) NGUYEN ANHHOANG-NGUYEN DOANVU NGUYEN DlIC HOA - DO QUANG THANH - NGUYEN TH| TRINH UlYMGUIflilllllliCKiTHI VAO LdP 10 BA MliN B^c - Trung - Nam 1 NHA XUAT BAN TONG HOP THANH PHO HO CHI MINH , LUYEN GIAI DE TRl/dC KY THI VAO L6P 10 BA MIEN BAC - TRUNG - NAM MON TOAN NGUYIN DCTCTAN Chiu trach nhi^m xua't ban NGUYEN THI THANH Hl/ONG Bicn tap Sura ban in Trinh bay Bia QUOC NHAN HOANG NHLTT Cong ty KHANG VIET Cong ty KHANG VI^T NHA XUAT BAN TONG HOP TP. HO CHf MINH NHA SACH TONG H0P 62 Nguyen Thj Minh Khai, Q.l DT: 38225340 - 38296764 - 38247225 Fax: 84.8.38222726 Email: tonghop@nxbhcm.com.vn Website: www.nxbhcm.com.vn/ www.fidltour.com Tong phat hdnh CONG TY TNHH MTV D|CH Vy VAN HOA KHANG VI|T Oja Chi: 71 Dinh Tien Hoang - P.Oa Kao - Q.1 - TP.HCM Dien thoai: 08. 39115694 - 39105797 - 391 11969 - 39111968 Fax: 08. 3911 0880 Email: l<hangvietbookstore@yahoo.com.vn Website: www.nhasachkhangviet.vn In Ian thiJ I, so liiging 2.000 cuon, kho 1 6x24cm. Tai: CONG TY CO PHAN THL/ONG MAI NHAT NAM Dja chl: 006 L6 F, KCN Tan Binh, P. Tay Thanh, Q. Tan Phu, Tp. Ho C*iJ So DKKHXB: 1 55-1 3/CXB/44-24/THTPHCM ngay 31/01/2013. * Quyet dinh xuat Wn so: 152/QD-THTPHCM-2013 do NXB Tor Thanh Pho' Ho Chi Minh cap ngay 07/03/201 3 In xong va npp ILAJ chieu Ouv II nAm 201 3 tdi N6I DAU Quyen sach Luyen giai de trUdc ky thi vdo Idp 10 ba mien Bac, Trung, Nam mon Todn nham gop vao tu sach cua ban doc mot tai Heu toan thie't thiTc va bo ich giup cac em hoc sinh Idp 9 on luyen va nang cao kien thtfc todn, chuan hi tot trong cac ki thi tuyen sinh vao Idp 10. Quyen sach gom 2 phan : Phin 1 : Cac de thi toan. • A. De thi tuyen sinh vao Idp 10 THPT. \ • B. De thi tuyen sinh vao idp 10 chuyen. Bao gom de thi va hiTdng dan giai diTdc tuyen chon tif cac de thi tuyen sinh vao Iclip 10 cf mot so dia phu^dng (tCf nam 2010 den 2013). Ph^n 2 : Cac de toan on luyen. • A. De toan on luyen thi vao Idp 10 THPT. • B.De toan on luyen thi vao Idp 10 chuyen. Bao gom 20 de toan va hiTdng dan giai do chiing toi bien soan vdi nhieu dang toan khac nhau nh^m trd giup cac em hoc sinh ciing co, boi di/dng nang cao kien thufc toan. Chung toi da co gang tim Idi giai mdi, hay va ngan gon cho cac bai loan va sau Idi giai cijfa moi bai toan dcu co nhan xet va binh luan, vdi mong muon giup cdc em hoc sinh nam dUdc phUdng phap giai dang toan do, tim kiem bai toan tU'dng tif, b^i toan mdi, bai toan tong quat nhSm khdi day tiem nang tim toi sang tao trong hoc toan 5 hoc sinh. Mac dil chung toi da co gang rat nhieu trong bien soan, song chac han quyen sdch van con thicu sot. Raft mong nhan diTdc cac y kien dong gop tijf ban doc de cdc Ian in sau sach dU'dc hoan thien hdn. ; Xin tran trong cam dn CAC TAC GIA Nha sach Khang Viet xin tran trong giai thieu tai Quy doc gid vd xin Idng nghe moi y kim dong gop, de cuon sach ngdy cdng hay han, ho ich han. Thu xin gui ve: Cty TNHH Mpt Thanh Vien - Dich Vu Van Hoa Khang Vi?t. 71, Dinh Tien Hoang, P. Dakao. Quan 1, TP. HCM Tel: (08) 39115694 - 39111969 - 39111968 - 39105797 - Fax: (08) 39110880 Hoac Email: khangvietbookstore@yahoo.com.vn PHAN I. CAC DE THI TOAN A. Dfe THI TUYEN SINH vAO L6F 10 THPT m so 1: De thi tuyen sinh vao Idp 10 THPT, Tp. Ho Chi Minh nSm 2012 - 2013 3 D6 so 2: De thi tuyen sinh vao Idp 10 THPT, Tp. Ha Npi nam 2012 - 2013 8 De s6'3: De thi tuyen sinh vao Idp 10 THPT, Tinh Dong Nai nam 2012 - 2013 13 De so 4: De thi tuyen sinh vao Idp 10 THPT, Tp. Da Nang nam 2012 - 2013 16 so 5: De thi tuyen sinh vao Idp 10 THPT, Tinh Thi^a Thien Hue nam hoc 2012- 2013 19 B6 SO 6: De thi tuyen sinh vao Idp 10 THPT, Tp. Can Thd nSm 2012 - 2013 24 De so 7: De thi tuyen sinh vao Idp 10 THPT, Tinh Hai Phong nam 2012 - 2013 28 D6 so 8: De thi tuyen sinh vao Idp 10 THPT, Tinh Nghe An nam 2012 - 2013 32 De so 9: De thi tuyen .sinh vao Idp 10 THPT, Tinh Quang Ninh nam 2012- 2013 37 D6 so 10: De thi tuyen sinh vao Idp 10 THPT, Tinh Thanh Hda nSm 2012 - 2013 40 De s6'll: De thi tuyen sinh vao idp 10 THPT, Tinh Yen Bai nam 2012- 2013 44 D6 so 12: De thi tuyen sinh vao Idp 10 THPT, Tinh Ha Nam nam 2012- 2013 48 D6 so' 13: De thi tuyen sinh vao Idp 10 THPT, Tinh VTnh Phuc nam 2012 - 2013 51 De .so 14: De thi tuyen sinh vao Idp 10 THPT, Tinh Dak Lak nam 2012 - 2013 54 De so 15: De thi tuyen sinh vao Idp 10 THPT, Tinh Tuyen Quang nam 2012 - 2013 58 D6 so 16: De thi tuyen sinh vao Idp 10 THPT, Tp. Ho Chi Minh nam 2011 - 2012 61 De so 17: De thi tuyen sinh Idp 10 THPT, tinh Quang Nam nam 2011 - 2012 66 De so 18: De thi tuyen sinh vao Idp 10 THPT. tinh Daklak nam 2011 - 2012 69 De so 19: De thi tuyen sinh vao Idp 10 THPT, tinh Ninh Thuan nam 2011 - 2012 72 D6 so 20: Dc thi tuyen .sinh vao Idp 10 THPT, tinh Ha Tinh nam 2011 - 2012 75 De so 21: De thi tuyen sinh idp 10 THPT, tinh Thanh Hda nam 2011 - 2012 79 De so 22: Dc thi tuyen sinh vao Idp 10 THPT, tinh Kicn Giang nam 2011 - 2012 82 De so 23: De thi tuyen sinh vao Idp 10 THPT, tinh Khanh Hoa nam 2011 - 2012 85 D6 so 24: De thi tuyen sinh Idp 10 THPT, tinh Binh Dmh nam 2011 - 2012 88 D^ so 25: De thi tuyen sinh Idp 10 THPT, tinh Quang Ngai nam 2011 - 2012 92 D^' s6'26: De thi tuyen sinh vao Idp 10 THPT, Tp. Da Nang nam 2011 - 2012 96 f)c .so 27: Dc thi tuyen sinh vao idp 10 THPT, Tp. Ha Noi nam 2011 - 2012 99 D^ so 28: De thi tuyen .sinh vao Idp 10 THPT, tinh Quang Tri nam 2011 - 2012 103 De so 29: Dc thi tuyen sinh vao Idp 10 THPT. tinh Nghp An nam 2011 - 2012 106 De s6'30: De thi tuyen sinh Idp 10 THPT, tinh Ninh Binh nam 2011 - 2012 110 D6 SO 31: De thi tuyen sinh Idp 10 THPT, tinh Hai DiTdng nam 2011 - 2012 114 D6 .so 32: Dc thi tuyen sinh Idp 10 THPT, tinh Lang Sdn nam 2011 - 2012 118 Dd so'33: D^ thi tuycn sinh Idp 10 THPT, Tp.HCM, nam 2010 - 2011 121 Dc so 34: De thi tuycn sinh vao Idp 10 THPT, tinh Bac Lieu nam 2010 - 2011 127 De so 35: De thi tuycn sinh vao Idp 10 THPT, tinh Ba Ria - Vung Tau nam hoc 2010- 2011 129 B. Dfe THI TUY^N SINH VAO L6P lO CHUYftN De so' 36: De thi tuyen sinh vao Idp 10 chuyen Toan, Tp. Ho Chi Minh nSm hoc 2012- 2013 132 D^ s6' 37: De thi tuyen sinh vao Idp 10 chuyen TriTdng Dai Hoc SuT Pham, Tp. Ho Chi Minh nam hoc 2012 - 2013 135 D^ so' 38: De thi tuyen sinh vao Idp 10 chuyen Toan Trifdng Dai Hoc Sif Pham, Tp. Ho Chi Minh nam hoc 2012 - 2013 141 D^' so'39: De thi tuyen sinh vao Idp 10 chuyen TriTdng phd thong Nang khie'u, DHQG Tp.Ho Chi Minh nam hoc 2012 - 2013 146 so'40: De thi tuyen sinh vao Idp 10 chuyen TriTdng phd thong Nang khie'u, DHQG Tp.Ho Chi Minh nam hoc 2012 - 2013 151 B6 S6'41: DC thi tuyen sinh vao Idp 10 Chuyen TriTdng THPT Dai Hoc Sir Pham Ha Noi nam hoc 2012 - 2013 156 De s(")'42: Dc thi tuyen sinh vao Idp 10 Chuyen TriTdng THPT Dai Hoc SuT Pham Ha Noi nam hoc 2012-2013 161 Bi so 43: De thi tuyen sinh vao Idp 10 Chuyen TriTcfng THPT Chuyen Khoa Hoc TiT Nhien, Dai Hoc Qudc Gia Ha Npi nam hoc 2012 - 2013 165 D^ so' 44: De thi tuycn sinh vao Idp 10 Chuyen Trrfdng THPT Chuyen Khoa Hoc TiT Nhien, Dai Hoc Qudc Gia Ha Npi nam hoc 2012 - 2013 170 so'45: De thi tuyen sinh vao Idp 10 chuyen, Tinh Dong Nai nam hoc 2012- 2013 173 so'46: De thi tuyen sinh vao Idp 10 chuyen, Tinh Dong Nai nam hoc 2012- 2013 177 s6' 47: De thi tuyen sinh vao Idp 10 THPT Chuyen Toan, Tp.Can Thd nam hoc 2012- 2013 181 Bi so'48: De thi tuyen sinh vao Idp 10 THPT Chuyen Toan, Tinh Quang Ngai n3m hoc 2012- 2013 186 De so'49: De thi tuyen sinh vao Idp 10 THPT Chuyen Todn, Tinh Hu^g Yen nam hoc 2012-2013 190 D6 SO' 50: De thi tuyen sinh vao Idp 10 THPT Chuyen Toan, Trifdng THPT, Tinh Hai Du'dng nam hoc 2012 - 2013 196 Dl .so' 51: Dc thi tuyen sinh vao Idp 10 THPT Chuyen, Tinh Hoa Binh nam hoc 2012- 2013 200 DC ,s6' 52: De thi tuyen sinh vao Idp 10 THPT Chuyen Todn THPT, Chuyen Phan Bpi Chau, Tinh Nghe An nam hoc 2012 - 2013 204 t)6 s6'53: De thi tuyen sinh vao Idp 10 THPT Chuyen Lam Sdn, Tinh Thanh Hda nam hoc 2012- 2013 209 D^ .s6' 54: De thi tuye'n sinh vao Idp 10 THPT Chuyen Toan, Tinh Ba Ria - Vung Tau nam hoc 2012- 2013 213 Dd s6' 55: Dc thi tuyen sinh vao Idp 10 THPT Chuyen Toan, TriTdng THPT Chuyen Phan Boi Chau, Tinh Ba Rja - Vung Tau nam hoc 2012 - 2013 218 s6' 56: De thi tuyen sinh vao Idp 10 chuyen, tru'dng Dai hoc Su pham Tp. Ho Chi Minh nam hoc 2011 - 2012 223 De so' 57: De thi tuyen sinh vao Idp 10 chuyen toan, trifdng Dai hoc Sir pham Tp. Ho Chi Minh nam hoc 2011 - 2012 227 De so'58: De thi tuyen sinh vao Idp 10 chuyen toan, THPT chuyen, Tp. Ho Chi Minh nam hoc 2011 - 2012 232 D6 so'59: De thi tuyen sinh vao Idp 10 chuyen, tru-dng THPT chuyen, Dai hoc Sir pham Ha Noi nam hoc 2011 - 2012 237 D6 so' 60: De thi tuyen sinh vao Idp 10 chuyen toan, triTdng THPT chuyen Dai hoc Sir pham Ha Noi nam hoc 2011 - 2012 242 Dc s6' 61: De thi tuyen sinh vao Idp 10 chuyen toan, THPT tinh Binh Dinh nam hoc 2011 - 2012 245 De so'62: De thi tuyen sinh vao Idp 10 chuyen, trirdng pho thong nang khie'u, Dai hoc Quoc gia, Tp.HCM nam hoc 2011 - 2012 250 so'63: De thi tuyen sinh vao Idp 10 chuyen toan, trU'dng pho thong nang khie'u, Dai hoc Quoc gia, Tp.HCM ndm hoc 2011 - 2012 255 D(1 so'64: De thi tuyen sinh vao Idp 10 chuyen, triTdng THPT chuyen KHTN, DHKHTN, HiQG Ha Noi nam hoc 2011 - 2012 260 l.e .d' 65: De thi tuyen sinh vao Idp 10 chuyen toan, triTdng THPT chuyen KHTN, DHKHTN, DHQG Ha Npi nam hoc 2011 - 2012 264 D6 so 66: De thi tuyen sinh vao Idp 10 chuyen toan, THPT chuyen, Tp. Ho Chi Minh nam hoc 2010- 2011 269 D6 so' 67: De thi tuyen sinh vao Idp 10 chuyen, trifdng THPT Quoc hoc Hue nam hoc 2010- 2011 273 so' 68: De thi tuyen sinh vao Idp 10 chuyen toan, thanh pho Ha Noi, nam hoc 2010- 2011 279 s6'69: De thi tuyen sinh vao Idp 10 chuyen, trirdng pho thong nang khie'u, Dai hoc Quoc gia, Tp.HCM nam hoc 2010 - 2011 284 D^' s6' 70: De thi tuyen sinh vao Idp 10 chuyen, triTdng pho thong nang khie'u, Dai hoc Quoc gia, Tp.HCM nam hoc 2010 - 2011 289 PHAN II. CAC DE TOAN ON LUY|N A. De toan on luyen thi vao Idp 10 THPT 295 B. De toan on luyen thi vao Idp 10 chuyen 315 i';;" -it'// Cty TNHH MTV DWH Khang Viet Plian I. CAC DE THI TOAlV A. Di Tfli rmifi swfl yko i6? lo run D]fe so 1 DE THI TUYEN SINH VAO L(3P 10 THPT, TP.Hd CHf MINH ^- ' NAM HQC 2012 - 2013 Bai 1: (2 diem) Giai cac phiTctng trinh va he phiTdng trinh sau : '2x-3y = 7 a) 2x^-x-3 = 0 ,j , , b) 3x + 2y = 4 c)xVx'-12 = 0 y ^ d) x^-2V2X-7 = 0 Bai 2: (1,5 diem) , , a) Ve do thj (P) cija ham so y = ^x^ va di/dng thang (D): y = ~ + 2 tren cting mot he triic toa do. b) Tim toa do cac giao diem cua (P) va (D) d cau tren b^ng phep tinh. Bai 3: (1,5 diem) Thu gon cac bieu thiJc sau : 1 2V^ 1 ' a) A = ^ + — vdi X > 0; X ^ 1 , x + Vx x-1 x-V^ lot-, b) B = (2 - V3)726TT5^ - (2 + ^/3)^/26 - 15^3 Bai 4: (1,5 diem) Cho phiTcJng trinh: x^ - 2mx +m - 2 = 0 (x la an so) a) ChtJng minh rhng phtTdng trinh luon c6 nghiem phan biet vdi moi m. b) Goi X,, X2 la cac nghiem ciia phiTdng trinh. . , Tim m de bieu thiJc M = — dat gia tri nho nha't. X| + X2 - 6X|X2 Bai 5: (3,5 diem) Cho du-dng Iron (O) c6 tam O va diem M n^m ngoai diTdng tron (O). Dirdng thang MO c^t (O) tai E va F (ME < MF). Ve cat tuyen MAB va tiep tuyen MC cija (O) (C la tiep diem, A nam giffa hai diem M va B. A va C nKm khac phia doi vdi dirdng thing MO). a) ChiJng minh r5ng: MA.MB = ME . MF ' b) Goi H la binh chieu vuong goc ciia diem C len difdng thing MO. ChiJng minh tiJ giac AHOB noi tiep. c) Tren nijfa mat phing bd OM c6 chi^a diem A, ve nuTa du-dng tron diTcJng kinh MF; nufa diTdng tr6n nay cat tiep tuyen tai E cua (O) d K. Goi S la giao diem cua hai dudng thang CO va KF. Chtfng minh r^ng diTdng thing MS vuong goc vdi dufcfng thing KC. Chi?ng minh r^ng diTcfng thing MS vuong g6c vdi di/c(ng thing KC. Luygn giai 66 truOc kl thi v^o Idp 10 ba mign BSc. Trung, Nam mOn ToAn _ Nguyin DiJfc Ta'n d) Goi P va Q Ian Itfdt la tam diTdng tron ngoai tiep cac tam giac EFS va ABS va T la trung diem cua KS. ChiJug minh ba diem P, Q, T thang hang. Hl/dNG DAN GIAI Bai 1. a) a-b-c = 2-(-l) + (-3) = 0 Phu'dng trinh c6 hai nghiem phan biet Xi = -1, = -c 3 2 b) 2x - 3y = 4 <=> i 3x + 2y = 4 X = 2 9.2+ 6y = 12 4x -6y = 14 13x = 26 9x + 6y = 12 9x + 6y - 12 X = 2 fx = 2 i'K' "' [9.2 + 6y = 12 [6y =-6 [y =-1 He phiTdng trinh c6 nghiem (x; y) la (2; -1) c) Dat y = x^(y > 0). PhiTdng trinh trd thanh: y^ + y - 12 = 0 A = 1 + 48 = 49; N/A = 7 y, = ^ii^ = 3 (thich hdp); yj = ^^y^ = -4 (khong thich hdp) y, = 3. Ta CO x^ = 3 o X = ±73 Phifdng trinh c6 hai nghiem phan biet: x, d) A' = 2 + 7 = 9; yfA' =3 PhiTdng trinh c6 hai nghiem phan biet ' 1 1 Nhan xet: 1) Neu phi/dng trinh ax^ + bx + c = 0 c6 a - b + c = 0 thi phiTdng trinh c6 hai —c nghiem Xi = -1; X2 = — a 2) Ban doc hay giai he phi/dng trinh bKng phiTdng phdp the. 3) PhiTdng trinh dang ax" + bx^ + c = 0, dat y = x^ ta diTdc phiTdng trinh bac hai ay^ + by + c = 0. Giai tim y roi tim x. Bai 2. a)Ve (P), (D) Bang gia tri X -4 -2 0 2 4 4 1 0 1 4 X 0 4 X y 2 2 0 Cty TNHH MTV DWH Khang V b) PhiTdng trinh hoanh do giao diem cua (P) va (D) 1 X 11 -x^ = — + 2 o -x^ +-X- 2 = 00 x^+2x- 8 = 0 4 2 4 2 A'=1+8 = 9, >/A'=3 -1 + 3 ^ -1-3 x, = = 2 ; X2 = = -4 1 1 1 2 1 .2 x, = 2thi y, =-x( = 2^ =1 x, = -4 thi y, = -X? = -(-4)^ =4 ^ Vay (P) va (D) c^t nhau tai hai diem phan biet A(2; 1) va B(-4; 4) Nhan xet: De tim tpa do giao diem ciia (D) va (P) bang phep tinh ta lap 1 ~x phiTdng trinh hoanh do giao diem cua (D) va (P): -x^ = — + 2 4 2 Nghiem cua phu^dng trinh la hoanh dp cua cac giao diem. *' Bai 3. A = _L^.2V^ 1 X + >/x X - 1 X - N/X 1 2V^ Vx(Vx + i) (Vx+i)(V^-i) V^(V^-i) V^-l + 2x-V^-l 2x-2 2(V^ + l)(V^-l, v^(v^ + i)(v^ -1) v^(v^ + i)(v^ -1) vr(V5r + i)(vi -1) Luygn giSi dg truflc ki thi vao I6p 10 ba mign BSc, Trung, Nam man ToAn _ Nguygn Pile Tgn B = (2 - V3)V26 + I5V3 - (2 + S)yj26 - 1572 = ^2(2 - V3) (26 + 15N/3) - y(2 + ^/3) (26 - I5V2) = ^(7 - 4V3)(26 + I5V3) - ^(7 + 4V3)(26 - 15V2~ = Vl82 + 105>/3 - IO4V3 - 180 - Vl82 - 10573 + 104^3 - 180 72 72 ^ ^ 73 + 1) -J(>/3-l) + + i 2 72 72 72 Nhan xet jt 1) Nhan ra rang x + 7x=7x(7x + ij, x-i = ^7x + i)(Vx - ij, X - 7x = 7x|7x - ij. Tijf do de CO difdc Idi giai cua bai toan. 2) Ta CO (2 - 73)V26 + 1573 - (2 + 73)(26 - 1572) ' = ^(2 - 73) (26 + 1572) - ^(2 + 73) (26 - 1572) = = V2 + 73 - V2 - 73 , giup den B = 72 Bai 4. a) A' = - m + 2 = - m — + — = 4 4 m + — > 0, vdi moi m. 4 Vay phU"dng trinh c6 hai nghiem phan biet vdi mpi m. b) Theo he thiJc Vi-et ta c6: x, + XT = 2m, X|X2 = m - 2 -24 -24 Do do M = X|+X2-6x,X2 (X1+X2) -2X,X2-6X|X2 -24 -24 -6 (X| + Xj)^-8x,X2 (2m)^-8(m-2) m^ - 2m + 4 -6 -6 (m^ -2m + l) + 3 (m - 1)^ + 3 > -2 , vdi moi m Vi(m- I)^ + 3>3o < 2 o -6 > -2 (m - 1)' + 3 (m - 1)" + 3 M > -2. Dau "=" xay ra o (m - 1 )^ = 0 o m = 1 Vay M dat gia tri nho nhat bang-2, khi m = 1. '»' ^ X, Nhan xet: Day la bai toan van dung he thuTc Vi-et va can lUu y them la: (m- 1)^ + 3 >3 o < -(= 2) (m - + 3 de CO du-dc M >-2 Bai 5. a) Xet AMEA va AMBF cd EMA (chung). 3 (m - 1)^ + 3 > -2 MEA = MBF (Ttf giac AEFB noi tiep). Do do AMEA ^ AMBF => — = (g.g) MB Vay MAMB = ME.MF b) Xet AMCA va AMBC cd CMA (chung) MCA = MBC (He qua gdc tao bdi tia tiep tuyen va day cung) Do do AMCAAMBC (g.g) MC MA ^_2 x.AA^o => = => MC = MA.MB . MB MC MC 1 OC (Vi MC la tiep tuyen cua (O)) AMCO vuong tai C; CH la diTdng cao => MC^ = MH.MO Ta cd MA.MB = MH.MO (= MC^) •i Pi- xel AMHA va AMBO cd HMA (chung), — = MA (VI MA.MB = MH.MO). Do do AMHA MB MO AMBO (c.g.c) o MHA = MBO Vay tu" giac AHOB noi tiep. c) Ta cd MKF = 90" (Gdc noi tiep ch^n nuTa difdng tron, AMKF vuong tai K, KE la dirdng cao => MK^ = ME.MF Ta cd MC^ = MA.MB = ME.MF = MK^ ^ MC = MK Xet AKMS (MKS = 90") va ACMS (MCS = 90") cd: • MK = MC, MS (canh chung) Do dd AKMS = ACMS (canh huycn - canh gdc vuong) ^j^,,, => MS la dudng trung trifc cua KC. Vay MSI KC. d) • Goi I la giao diem cua MS va KC fij? /((.ff ; ;; Tacd SIK = 90" i -f>^-'- • ^ • ' ' ' Luyjn giai 66 truflc k1 thi vAo I6p 10 ba mign BJc, Trung, Nam mOn ToAn _ NguySn Pile TSn AISK vuong tai I, IT la diTdng trung tuyen => TS = TI AMSC vuong tai C, CI la diTdng cao => MC^ = MI.MS Ta CO MI.MS = MC^ = MA.MB. Xet AMAI va AMSB c6 AMI (chung), — = ^ (vi MI.MS = MA.MB) MB MS Do do AMAI ^ AMSB (c.g.c) MIA = MBS => Tu" giac ABSI noi tiep. Ta c6n CO MI.MS = ME.MF (= MA.MB) /! A ME MI Xet AMEI va AMSF c6 EMI (chung), = (MI.MS = ME.MF) MS MF Do do AMEI AMSF (c.g.c) => MEI = MSF => TuT giac EFSI noi tiep. Hai dirdng tron (ABSI) va (EFSI) cat nhau tai S va I c6 tarn Ian lifdt la Q, P => PQ la du-dng trung triTc cua doan thang SI. Ma T thuoc diTdng trung tri/c cua doan thang SI (Vi TS = TI) nen T e PQ Vay P, Q, T th^ng hang. Nhan xet Cau a), b) quen thupc, cau c) ne'u nhan ra MC^ = MA.MB = ME.MF = MK' => MC = MF giijp den vdi Idi giai. Cau d) kho, chi ve cac tam P, Q khong nen ve cac du'dng tron (P), (Q) se rac roi tren hinh ve. De dang thay PQ la du'dng trung triTc cua doan thang SI, tim each chiJng minh TS = TI. KY THI TUYEN SINH VAO LdP 10 THPT, TP.HA NOI NAM HQC 2012 - 2013 Bai 1. (2,5 diem) 1) Cho bieu thiJc A = ^ ^ . Tinh gia tri cua A khi x = 36 Vx + 2 2) Rut gpn bieu thufc B ' ^ ^ :4il^(vdix>0;x^I6) Vx + 2 \Ix + 4 N/X - 4^ 3) Vdi cdc cua bieu thiJc A v^ B n6i tren, hay tim cdc gia tri cua x nguyen de gia tri cua bieu thuTc B(A - I) la so nguyen. Bai 2. (2,0 diem). Giai b^i toan sau bang each lap phiTcJng tnnh hoSc he phiTcfng tiinh: 12 Hai ngifdi cilng lam chung mot cong viec trong — gid thi xong. Neu moi ngirdi lam mot minh thi ngiTdi thuf nhat hoan thanh cong viec trong it hcfn ngirdi thu" hai la 2 gict. Hoi neu lam mot minh thi moi ngiTdi phai lam trong bao nhieu thcfi gian de xong cong vi^c? Cty TNHH MTV DWH Khang Vigt Bai 3. (1,5 diem) 1) Giai he phu'Png trinh X y X y 2) Cho phi/Png trinh: x^ - (4m - l)x + 3m^ - 2m = 0 (an x). Tim m de phiTdng trinh c6 hai ngiem phan biet Xi, X2 thoa man dieu kien: + xj =1 Bai 4. (3,5 diem) Cho dircfng tron (O; R) c6 du-cfng kinh AB. Ban kinh CO vuong g6c vdi AB, M la mot diem bat ki tren cung nho AC (M khac A, C): BM cat AC tai H. Gpi K la hinh chie'u cua H tren AB. 1) Chu-ng minh CBKH la tuT giac noi tiep 2) Chu-ng minh ACM = ACK 3) Tren doan thang BM lay diem E sao cho BE = AM. Chitng minh tam gidc ECM la tam giac vuong can tai C. 4) Gpi d la tiep tuyen cua (O) tai diem A; cho P la diem nam tren d sao cho hai diem P, C nam trong cdng mot nu-a mat phang bd AB va "^^'^^ = R . MA ChiJng minh du-dng thang PB di qua trung diem cua doan thang HK. Bai 5. (0,5 diem). Vdi x, y la cac so du-dng thoa man dieu kien x > 2y, tim gia tri „2 2 nho nha't cua bieu ihuTc: M = i- . xy Hl/dfNG DAN GIAI ' Bail, ' /36+4 6 + 4 10 5 r : 8 ' 4 1 1) Gia tri cua A khi x = 36 la: 5 4 2) B = N/36 +2 6 + 2 X + 16 _ >/x - 4) + (N/^ + 4) ,Vx+4 Vx-4j"Vx+2 (7x+4)(Vx+4) _ X-4V2+4Vx+16 Vx+2 x + 16Vx + 2 Vx+2 X + 16 V5^ + 2 3) B(A- 1) = X - 16 V^ + 2' X + 16 X -16 Vx+4 R + 2 -1 x - 16 X + 16 X - 16 Vx+2 2 _ 2 x-16 Vx+2 x-16 De B(A - 1) la so' nguyen thi x - 16 la iTdc cua 2. Tacdx- 16 = l;-l;2;-2ox = 17; 15; 18; 14 Vi x>0, x,t 16. Luygn dS trudc ki thi vao I6p 10 ba mjgn B&c. Trung. Mam mSn Toan , Mguygn Difc Tan Do vay x = 14; 15; 17; 18 la cac gia tri nguyen cua x can tim. Nhan xet: Day la cac bai toan de, quen thuoc Bai 2. Goi thdi gian ngiTdi thuT nhat lam mot minh xong cong viec la x (gicJ) 12 (Dieu kien x > — ) Thdi gian ngiTcfi thiJ hai lam mot minh xong cong viec la x + 2 (gid) 1 " Trong 1 gid, ngiTdi thiJ nhat lam diTdc: 1 : x = - (cong viec) Trong 1 gid, ngiTdi thiJ hai lam diTdc: 1 : (x + 2) = (cong viec) X ~i~ ^ (4 H Trong 1 gid, hai ngiTdi lam chung diTdc: - + —i— (cong vice) hay 1 : — = — (cong viec) X X + 2 5 12 Ta CO phiTdng trinh — + —^-— X X + 2 _5_ 12 « 12(x + 2)+ 12x = 5x (x + 2) o 12x + 24 + 12x = 5x^ + lOx o 5x^ - 14x - 24 = 0 A' =49+ 120= 169, VA' = 13 X, = = 4 (thich hdp), Xj = ^—^ = ^ (khong thich hdp) 5 5 5 h Vay thdi gian ngiTdi thiJ nhat lam mot minh xong cong viec la 4 gid Thdi gian ngiTdi thi? hai lam mot minh xong cong viec la: 4 + 2 = 6 (gid) Nhan xet: Day la dang bai: Giai bai toan bang each lap phtfdng trinh, bai tocin ve cong vice, rat qucn thuoc vdi moi hoc sinh. Bai 3. flO 1) <=> < X y X y 'x = 2 6 _ 2 ^ J o 2 v — + — = 4 X y X y X = 2 y = 5 X y X = 2 y = 1 Vay he phiTdng trinh c6 nghiem (x; y) la (2; 1) 2) A = (4m -1)^-4 (3m^ - 2m) = 16m^ - 8m + 1 - 12m^ + 8m = 4m^ + 1 > 0, vdi moi m Vay phiTdng trinh c6 hai nghiem phan biet, vdi moi m. Theo he thiJc Vi-et, ta c6 • X, + X2 = 4m - 1 Xj.Xj = 3m^ - 2m Do do xf + X2 = 7 <=> (X| + Xj)^ - 2X|X2 = 7 « (4m - 1)' - 2(3m2 - 2m) = 7 o 16m^ - 8m + 1 <=> lOm^ - 4m - 6 = 0 o 5m^ - 2m - 3 = 0 Ta CO a + b + c = 5 + (-2) + (-3) = 0 c 3 mi = 1, m-, = — = — Cty TIMHH MTV \liang Vi$t 6m + 4m = 7 . (I:s;' 'A,- Vay m = 1, m = thi x^ + X2 = 7 Nhan xet: 1) Bai toan nay de, quen thuoc ' Is 2) Tufhethu'cVi-etc6xi+X2 = 4m-l,x,X2 = 3m^-2m Ta c6:xf + xj = (4m - 1)^ - 2(3m^ - 2m) = lOm^ - 4m + 1, giup den difdc m = 1; m = -— Bai 4. 1) ACB = 90" (goc noi tiep chan nuTa du-cJng Iron) Ti? giacCBKH c6 HCB + HKB = 90" + 90" = 180". Do do ti? giac CBKH noi tiep 2) Ta CO ACM = ABM (Hai gdc noi tiep ciing chan cung AM) ABM = ACK (Tu" giac CBKH noi tiep) Do do ACM = ACK 3) Ta CO CO 1 AB (gt) => AC = BC =^ AC = BC Xet ACM A va ACEB ta c6: AM = BE (gt); CAM = CBE (hai goc noi tiep cilng ch^n cung MC), AC = BC. Do do ACMA = ACEB (c.g.c) =>CM = CE, MCA = ECB Ta CO MCE = MCA + ACE = ECB + ACE = 90" AECM vuong tai C (MCE = 90") c6 CM = CE Do vay tarn giac ECM vuong can tai C . • 4) Goi N la giao diem cua PB va HK •{X Xet ABKH va ABMA c6 KBH (chung), BKH = BMA (= 90") /g^ Dod6ABKH-ABMA(g.g)=^-l^ = lJi=>:^ = — (1) MA MB MA KH Luyjn giai 6i frUSc ki thi vSo lOp 10 ba mi6n Ba. Nam mfln ToAn _ Nguyjn DCfc Ta'n Ta CO PA ± AB, NK ± AB => PA // NK APAB CO NK // PA => (2) AP BA BABK R _ BK ^ AP " NK ^ AP ~ 2NK " ^ " ' AP.MB „ ^ , MB R Ma = R (gt) => = — (3) MA MA AP • ' • Tir (1), (2), va (3) CO KH = 2NK. Do do N la trung diem cua HK . , Vay du'cing lhang PB di qua Irung diem ciia doan thang HK Nhan xet: Day la bai loan rat quen ihuoc doi vdi moi hoc sinh Idp 9. Bai 5. VI X, y > 0 v^ X > 2y Ta CO — > 2 va ap dung bai dang ihiJc Co-si cho hai so du'dng, ta c6 y x^ + 4y^ > lyjx^Ay^ <=> x^ + 4y^ > 4xy x^+y^ 4x^+4y^ 3x^ x^ + 4y^ Do vay M = — = — = + — ; xy 4xy 4xy 4xy 4 y 4xy 4 2 2 Dau "=" xay ra o x = 2y Vay gia tri nho nhaft cua bieu thiifc M la ^. Nhan xet: Tijr dieu kien rang buoc x > 2y, cho ta dif doan rang M dat gia tri nho nhat khi x = 2y. Tir do, giup dieu chinh he so thich hdp "x^" va "4y^" roi van dung ba't dang thiJc Co-si cho hai so du'dng de giai nhiT tren. x^ + y^ 4x^ + 4y^ Thao tac "bien" — thanh — giup c6 Idi giai dep. xy 4xy Tir Idi giai nay cung cho ta Idi giai khdng van dung ba't d^ng thuTc Co-si cho hai so du'dng nhu" sau: x^ + y^ 4x^ + 4y^ 3x^ + (x^ - 4xy + 4y^) + 4xy M = xy 4xy 4xy 4 y 4xy 4 2 NhU'vay M > ^ . Cty TNHH MTV DVVH Khang Vi^t at SO 3 KY THI TUYEN SINH VAO L(3P 10 THPT, TINH D5NG NAI NAM HOC 2012 - 2013 CSu 1.(1,5 diem) ^ h- 1) Giai phu'dng trinh: 7x^ - 8x - 9 = 0 ;(,:;;!• , •3x + 2y = l _4x + 5y-6 . " ,1 2) Giai he phu'cfng trinh: Cfiu 2. (2,0 diem) 1) Rut gon cac bieu thUc: M = ;=— ; N = —1= ' V3 ^-l 2) Cho Xi; X2 la hai nghiem ciia phUcfng trinh: x^ - x - 1 = 0 Tinh: — + — X, X2 Cfiu 3. (1,5 diem) Trong mat phang vdi he true toa do Oxy cho cac ham so: y = 3x2 ^j^. (p). y = 2x - 3 c6 do thi la (d); y = kx -1- n c6 do thi la (d,) vdi k va n la nhiJng so thifc 1) Vedo thi (P). 2) Tim k va n biet (d,) di qua diem T(l; 2) va (d,) // (d). Cfiu 4. (1,5 diem) Mot thuTa dat hinh chff nhat c6 chu vi bang 198m, dien tich bang 2430m^. Tinh chieu dai va chieu rong cua thuTa da't hinh chff nhat da cho. Cfiu 5. (3,5 diem) Cho hinh vuong ABCD. Lay diem E thuoc canh BC, vdi E khong trung B va E khong trung C. Ve EF vuong goc vdi AE, vdi F thuoc CD. Dirdng thdng AF c^t diTdng thing BC tai G. Ve diTdng thing a di qua diem A va vuong gdc vdi AE, di/dng thing a cit diTdng thing DE tai diem H. i\ • u AE CD 1) Chffngminh = . AF DE 2) Chffng minh rang tff giac AEGH la ti? giac noi tiep diTdng tron. 3) Goi b la tiep tuye'n cua du'dng tron ngoai tie'p tam giac AHE tai E, bie't b cat du'dng trung trffc cua doan thang EG tai diem K. Chffng minh rang KG la tiep tuye'n cua du'dng tron ngoai tiep tam giac AHE. Hl/OfNG DAN GIAI Cfiul. l)7x^-8x-9 = 0 A' = 16 + 63 = 79; VA^ = V79 PhiTdng trinh c6 hai nghiem phan biet x, = ^ , Xj = -—z-^ |3x.2y = l ^ 4x + 5y = 6 X = -1 2) 15x + lOy = 5 <=> <=> 8.(-l) + lOy = 12 o <=> < 7x = -7 8x + lOy = 12 X = -1 y = 2 8x + lOy = 12 fx = -l ^lOy = 20 He phiTdng trinh c6 nghiem (x; y) la (-1; 2) Nhan xet: Bai toan bay de va quen thupc doi vdi mpi hpc sinh Idp 9. C&u2. ^ Vl2j^ ^ _ 2^^ V3 73 V3 V3 N = ^-^^ = 2 - 2V2 + 1 ^ (^-Q = V2 - 1 72-1 72-1 72-1 2) a=: 1 >0, c = -l <0. PhiTPng trinh c6 hai nghiem phan biet Xi, X2 (xi, X2 khac 0). Theo he thuTc Vi-et ta c6 xi + X2 = 1, X|X2 = -1 1) M Do do — + — X2 + X, X,X2 -1 = -1 Nhan xet: Day cQng la bai toan de, thi sinh co the sijf dung A=l+4 = 5>0 de chiirng to phu'dng trinh co hai nghiem phan biet. X 1 -1 0 1 1 2 2 y = 3x^ 3 3 0 1 3 4 4 2) (d,)//(d)o k = 2 n ^ -3 . Ta CO k = 2 CtyTNHH MTV DVVH Khang Vi$t T (1; 2) e (d,) ^ 2 = 2.1 + n => n = 0 (ihich hdp) Vay k = 2; n = 0 Nhan xet: Day la bai toan do thj ham so ciing raft quen thupc. Cau 4. NiJfa chu vi ciia ihiira difl la: 198 : 2 = 99 (m) 99 Gpi chieu rpng ciia thijfa dal la: x(m) (Dicu kien x < —) si OX • t Chieu dai cua thiJa dat la 99 - x (m) Dien tich ciia thiira dat la x(99 - x) (m') hay 2430nr. Ta co phu^dng trinh x(99 - X) = 2430 X' - 99x + 2430 = 0 A = 99^ - 4.1.2430 = 9801 - 9720 = 81 7A = 9 99 + 9 99-9 X| = —:— = 54 (loai); Xj = —z— = 45 (nhan) 2 - • . 2 Vay chieu rpng ciia thufa dal la 45m ' ' Chieu dai cua thij-a dat la: 99 - 45 = 54 (m) Nhan xet: Day la bai toan giai bai loan bang each lap phu^Png trinh, loai toan hinh hpc ra't de va quen thupc. cau 5. 1) Tu" giiic AEFD co AEF + ADF = 90" + 90" = I8O" => Tu" giac AEFD npi liep => EAF = EDF Xet AEAF vii ACDE co AEF = DCE (= 90") DodoAEAF'^ ACDE (gt) ' AE AF AE CD • Vay CD DE AF DE 2) Taco EAF + HAG = 90", ' CDE + HEG - 90" (ACDE vuong tai C). EAF = CDE (chu-ng minh trcn). , ji Suy ra HAG = FIEG . Vay tiiTgiac AEGH npi tiep 3) Gpi O la trung diem ciia HE. Ta CO O la tarn du'dng Iron ngoai tiep tu" giac AEGH cQng la dU'cJng tron ngoai tiep tarn giac AHE. XetAOEKva AOGK c6 OE = OG (= R), OK (canh chung), ^ KE = KG (K thupc dirdng trung trifc cua EG. . i;* Do do AOEK = AOGK (c.c.c) ^ OEK - OGK 1 s 'i^' [...]... xay ra o x = y = 1, do vay chinh he so thich hdp trong vice van dung bat d^ng ihuTc Co-si cho hai so X dtfdng, giup cd difdc Idi giai b^i toan Luy5n giai dg truOc kl thi vao I6p 10 ba mign Bjc, Trung, Nam mOn Jo&n _ NguySn D(lc Ta'n Cty TNHH MTV DWH Khang Vigt ^ Thdi gian ca no xuoi dong tif A den B la: B 6 SO 15 KY THI TUYEN SINH VAO LdP 10 THPT, TINH TUYEN QUANG NAM HOC 2012 - 2013 CSu 1 (3,0 diem)... 5 X, DE THI TUYEN SINH VAO L(3P 10 THPT, TJNH THL/A THIEN HUE = 4 + 12m^ nen « O 8 -A = _ 3 A , J IT -2 XI -! X2 — - x, = 2^1 + 3m^ NAM HOC 2012 - 2013 Bai 1 (2,0 diem) -.2 XT X,X2 ^ = 3 a) Cho bid'u thiJc: C = ^ ^ ^ ^ + (X, +X2)(x, - X j ) X ,1^2 X 8 -2.2Vr+W_ = - = 3 -3m^ Vl + 3m^ = 2 o 1 + 3m^ = 4 o m = ±1 = i Nhan xet: Day la bai loan ve phiTdng trinh bac hai va uTng diing cua he thiJc Vi-et,... + 5) = 300 5 69 60 X 3 X x+5 X x+5 3 207(x + 5) - 180x = x(x + 5) » 207x + 103 5 - 180x = x^ + 5x c:>x'- 2 2 x - 103 5 = 0 345 Cty TMHH MTV DVVH Khang Vigt Luy$n gi§i dg trutSc kl thi vio lOp 10 ba mjgn BSc Trung, Nam mOn ToAn _ Nguygn Difc Ta'n A ' = 121 + 103 5 = 1156, X| = F A O (Chung), A F O = A B D (= 90") ^/A' = 34 ^ 45 (thich hdp), x j = ^ ^ ^ "^"^ = - 2 3 (khong ihich hdp) Vay van toe xc luTa... X + y X - 20 100 x + y y 100 x + y 2(x + y) 5(x-y) X 70 = 7 X + y = 10 Do do A D K H ^ [x + y = 10 [y 7 3 (thich hdp) DH (vi DH.DO = DK.DC) DC c) Ta CO D B 1 BC, M O 1 BC (gl) =^ D B / M O / BDO = D O M ( T i n h chat cua hai tiep tuyen ca't nhau) Do do D O M = O D M => A M D O can tai M => D M = O M a) Giai bai toan bang each lap phiTcfng trinh loai toan chuyen dong, dang bai BD BD Idp 10 Nen b) M... x - 8 = 0 A ' = l + 8 = 9, VA^ = 3 1 ' x , = l 1^ = -2 X, = 4 thi y, = -1 4 ^ = 8 ; X2 = - 2 thi y-^ = -1 - 2 ) 2 = 2 2 „ ( X, = Vay M(4; 8) vaJ^(;:2L2)Jioac M(-2; 2) va M(4; 8) Luy$n giai dg trudc kl thi v^o Idp 10 ba mjgn BJc Trung, Nam mOn ToAn _ Nguygn 0(!c IJn Cty TNHH MTV D W H Khang Vi$t Nhan xet: Day la bai loan ve ham so va do thi, dang toan nay cung ra'l quen AOAD = C O OA ^ OD (= R) =>... du'cfng trung tuye'n (E la trung diem cua BD) => EM = EB = ED Xet AOME va AOBE c6: OM = OB (= R), EM = EB, OE (canh chung) 46 2 da cho thanh A ' + B ' + C ' = 0 tu-c la 'Vx - 34 - 1)^ + ( 7 y - 2 1 - if + ( 7 z - 4 - 3)^ = 0 tiif do tim diTdc x, y, z tinh diTdc gia tri cua bieu thuTc T i: X : •••• W Luyjn giJi dS trudc ki thi vAo Idp 10 ba mign BSc, Trung Nam mOn ToAn _ NguySn Dufc la'n D 6 S O 12 KY THI. .. (thich hdp), a = - 9 (thich hdp) a < — va a > - 1 a > — va a < - 1 2 V a y a = - 1 hoSc a = - 9 Nh§nxet: 1) Day la bai toan ve do thj h ^ m so' bac nhat rat quen thuoc va de v i i - - 1 < a < 2 2) Day la bai toan v e phifdng trinh bac hai mot an he thtfc V i - e t Lufu y rang K e t hdp v d i dieu k i e n ta c6 v d i 0 < a < thi A < phiTdng trinh hai nghiem phan bi$t N h a n x e t : Day la bai... phiTdng Irinh bac h a i : x ' - mx + m - 1 = 0 (1) X, 3x - y = 1 3x + 8y = 19 " < = 1) Giai he phiTcfng tnnh : =-yf2 Bai 2: 1) Bai 2: (2,5 diem) V5-2 Nh§n x e t : Bai loan nay raft de doi vdi mpi hpc sinh Idp 9 DE THI TUYEN SINH LdP 10 THPT, TJNH QUANG NAM NAM HOC 2011 - 2012 3-2 ^/5-2 2011 Bai 3: (1,5 diem) Cho ham so y = - x l 4 a) Ve do Ihj (P) cua ham so do 2) a) Khi m = 4, phiTdng tnnh (1) trd thanh... Luy^n giSi ai truOc k1 thi vao Idp 10 ba miSn Bjc, Trung, Nam mOn Join _ Nguyln Dufc Tin = (a + b) + a + = (a + b) + a + Dau 4a g y tai D , B M cMt A x tai C, E la trung d i e m c u a d o a n thang B D 2 1) Chtfng m i n h : A C , B D = AB\ 2) ChiJng m i n h : E M l a tiep t u y e n c u a nijTa diTdng tron t a m O b - 2 2 viyt la mot d i e m thupc nCfa diTdng iron (O), M khong trung v d i A v a B A... Xet AABC va ABDA c6 BAG = DBA (=90"), o o ' x-34=l;y-21=4;z-4 =9 ABC = BDA (cung phu vdi goc MDB) x = 3 5 ; y = 25;z= 13(thichhdp) Do do AABC ^ ABDA (g.g) AB => ', Do do T = x ' + y' + z' - 7 = 35' + 25' + 13' - 7 = 1225 + 625 + 1 6 9 - 7 •/ Nhan xet: Bai toan nay la bai toan kho nhat cua de thi nham giiip phan loai , AB V a y A C B D = AB^ ' = 2012 AC = BD hpc sinh Doi vdi cac ban hpc sinh gioi toan . UlYMGUIflilllllliCKiTHI VAO LdP 10 BA MliN B^c - Trung - Nam 1 NHA XUAT BAN TONG HOP THANH PHO HO CHI MINH , LUYEN GIAI DE TRl/dC KY THI VAO L6P 10 BA MIEN BAC - TRUNG - NAM MON. Ouv II nAm 201 3 tdi N6I DAU Quyen sach Luyen giai de trUdc ky thi vdo Idp 10 ba mien Bac, Trung, Nam mon Todn nham gop vao tu sach cua ban doc mot tai Heu toan thie't thiTc . Lang Sdn nam 2011 - 2012 118 Dd so'33: D^ thi tuycn sinh Idp 10 THPT, Tp.HCM, nam 2 010 - 2011 121 Dc so 34: De thi tuycn sinh vao Idp 10 THPT, tinh Bac Lieu nam 2 010 - 2011