DAI HOC TAN TAO TRU'ONG THPT NANG KIIIEU -* IDE CHiNH THirC Kil THI TUYEN SINH LOP 10 NAM HOC 2015-2016 MON THI: TOAN HOC (CHUYEN) Ngay thi: 05/06/2015 ThZri gian lam bai: 150 phut Cau (1,25 diem) Cho cac bieu thirc: a3 +1 A = a2 -1 a2-1 a+1' B= 2a2+7a+3 2a2-a-1 a) Rut gon cac bieu thirc A va B b) Tim tat ca cac gia tri nguyen cila a bieu thirc C = A + B la so nguyen Cau (1,5 diem) Trong N true toa vuong g6c Oxy, cho throng thing d: y = (m + 2)x + (m # —2) Goi A, B lin luol giao diem dm d viii true hoanh va true tung a a) Tim m dien tich tam gide OAB bang b) Xac dinh gia tri dm m de khoang each ter gOc tea de den clueing thing d bang Cau (1,75 diem) Giai phtrung trinh va N phucmg trinh sau: a) (x + 1)(2x + 3)(4x + 5)2 = ! b) (x2 + y2 = 13 txy — x — y = Can (2,5 diem) Cho tam gide ABC c6 ba goc nhon not tip duZyng tron (0; R) Ba duemg cao AD, BE, CF cat tai H Goi K la trung diem cila BC, AM la dual-1g kinh cila dtrong ton (0) a) b) c) d) Chimg minh ba diem H, K, M thing hang ChUng minh ABC = AEF Chimg minh OA vuong goc voi EF Goi p la nira chu vi dm tam giac DEF ChUng minh: SABc = Rp Cau (1,0 diem) Tim cac so tv nhien x, y thOa man: x2 + y =x+y+8 Cau (1,0 diem) Cho hai s6 thvc &rang a va b thoa: ab = Tim gia tri nho nhAt dm bieu thuc: P= a3 1+ b + b3 1+ a Cau (1,0 diem) Cho tam gide ABC co tam G MOt dtrong thing d di qua G cat cac doan thing AB, AC lin luert tai M va N Chung minh: SABC