De thi tuyen sinh lop 10 chuyen mon Toan 20122013 Tinh Quang Binh

<span class='text_page_counter'>(1)</span>SỞ GIÁO DỤC VÀ ĐÀO TẠO QUÃNG BÌNH ĐỀ CHÍNH THỨC MÃ ĐỀ: 014. Câu 1:(2,0 điểm) Cho biểu thức B =. KỲ THI TUYỂN SINH LỚP 10 THPT NĂM HỌC 2012 – 2013 MÔN THI : TOÁN (Thời gian: 120 phút không kể thời gian giao đề) Ngày thi: 04/7/2012 1 2 1 + + x −x x−1 x 2. a) Rút gọn biểu thức B. b) Tìm tất cả các giá trị nguyên của x để biểu thức B có giá trị nguyên. Câu 2:( 1,5 điểm) Giải hệ phương trình sau:. ¿ 3 x + y=3 2 x − y =7 ¿{ ¿. Câu 3:( 2,0 điểm) a) Giải phương trình: x 2 −2 x − 3=0 b) Cho phương trình bậc hai: x 2 −2 x +n=0 ( n là tham số). Tìm n để phương trình có hai nghiệm x 1 , x 2 và thỏa mãn: x 1 + x 2 =8 Câu 4:( 1,0 điểm) Cho các số thực x , y thỏa mãn: x+ y=2 Tìm giá trị nhỏ nhất của biểu thức: Q=x 3 + y 3 + x 2+ y 2 . Câu 5: ( 3,5 điểm) Cho tam giác ABC đều có AH là đường cao, N là điểm bất kì trên cạnh BC ( N khác B,C). Từ N vẽ NE vuông góc AB, NF vuông góc AC ( E thuộc AB, F thuộc AC). a) Chứng minh: A, E, N, H, F cùng nằm trên một đường tròn. b) Gọi O là trung điểm của AN. Chứng minh các tam giác OEH và OFH là tam giác đều, từ đó suy ra OH EF. c) Tìm giá trị nhỏ nhất của đoạn EF khi N chạy trên cạnh BC, biết độ dài cạnh của tam giác ABC là a. Bài làm 2. 2. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................. ...................................................................................................................................................................................................................................

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