TRUING THPT NANG KHIELT DAI HOC TAN TAO BE CHINH THfiC Id THI TUYEN SINH LOP 10 NAM HOC 2014 — 2015 Mon thi: TOAN (CHUYEN) Ngay thi: 13-06-2014 Thei gian: 150 phut (khong ke theri gian phat de) Can 1: (1,5 diem) Cho Neu thirc: p ( + AFc AFc + 3) x + 3A5 a) Rilt gon bieu thirc P b) Tim x de P = Cau 2: (2,0 diem) Cho Parabol (P): y = x2 ya duong thang d: y = mx + a) Chang minh vat moi gta tri cua m, duong thang d luon di qua mot diem M co dinh b) Chung minh duong thang d luon cat Parabol (P) tai hai diem A, B phan biet Tinh dien tich tam gide OAB theo m Cu a 3: (1,0 diem) Giai phtrung trinh: x2 — 8x + + 2-V2x + = Cau 4: (2,5 diem) Cho ba duong tam: (A, R); (B ,r); (C, x) Ba duong tron tiep xuc ngodi doi mot ya ding tiep )(fie voi throng thang xy ttro:ng frng tai cac diem M, N, P ,nhu hinh ye Duemg thang qua B song song Wei xy cat AM tai D GO E la trung diem ciia MN a) Chimg minh: MN = 2V7r b) Chirng minh: = + c) Chimg minh to giac ADEB not tiep d) Tinh dien tich tam gide ABC, biet R = yar=4 N a Cau 5: (1,0 diem) Tim cac gta tri dia a phtrung trinh sau co nghiem nguyen: x2 — (a2 + 2)x + a2 + = Cau 6: (1,0 diem) Cho x, y, z cac s6 thirc duong thee: x + y + z = Chimg minh: a) x + yz = (x + y)(x + z) b) yz + _ zx xy , -tz+xy x+yz y+zx < 3— Cau 7: (1,0 diem) Cho to giac ABCD va mot diem ben to giac Goi S la dien tich to giac ABCD Chung minh rang : 0A2 + OB2 + 0C + OD 2S