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ĐỀ ĐỀ THI HỌC SINH GIỎI CẤP TRƯỜNG MÔN: TOÁN LỚP Thời gian: 150 phút Câu : (2 điểm) Cho P= a − 4a − a + a − a + 14a − a) Rút gọn P b) Tìm giá trị nguyên a để P nhận giá trị nguyên Câu 2: ( điểm) Chứng minh rằng: (n5 – 5n3 + 4n) M120 với m, n ∈ Z Câu : (2 điểm) a) Giải phương trình : 1 1 + + = x + x + 20 x + 11x + 30 x + 13x + 42 18 Câu 4: ( điểm) Trong hai số sau số lớn hơn: a = 1969 + 1971 ; b = 1970 Câu 5: (4 điểm): Cho tam giác ABC nhọn, đường cao AA’, BB’, CC’, H trực tâm a) Tính tổng HA' HB' HC' + + AA' BB' CC' b) Gọi AI phân giác tam giác ABC; IM, IN thứ tự phân giác góc AIC góc AIB Chứng minh rằng: AN.BI.CM = BN IC.AM (AB + BC + CA ) c) Tam giác ABC biểu thức đạt giá trị nhỏ nhất? AA' + BB' + CC'