Đề thi học sinh giỏi cấp huyện môn Toán Lớp 7 - Năm học 2015-2016 - Phòng GD & ĐT Cẩm Thủy

ĐỀ THI CHÍNH THỨC
PHÒNG GD&ĐT CẨM THỦY
ĐỀ THI CHỌN HỌC SINH GIỎI LỚP 7
CẤP HUYỆN NĂM HỌC 2015 - 2016
Môn: Toán 7
Thời gian làm bài: 150 phút
Ngày thi: 05/4/2016
Câu 1: (4đ). Tính giá trị các biểu thức sau: 
a) A = b) B = 
c) C = (Với x là hợp số nhỏ nhất, y là số nguyên âm lớn nhất.)
d) D = ( 1,2 + 2,3 + 3,4 + ...+ 48,49 + 49,50) + 774,3.
Câu 2:(4đ). 
	a) Tìm x biết: = x + 2.
	b) Tìm GTNN của A = khi x thay đổi.
Câu 3 (4đ): 
a) Chưng minh rằng: là một số tự nhiên.
b) Tìm phân số có tử là 7 biết phân số đó lớn hơn - và nhỏ hơn - .
Câu 4: (6đ). Cho tam giác ABC có A < 900. Vẽ ra phía ngoài tam giác đó hai đoạn thẳng AD và AE sao cho AD AB và AD = AB; AE AC và AE = AC.
	a) Chứng minh: DC = BE và DC BE.
b) Gọi N là trung điểm của DE. Trên tia đối của tia NA lấy điểm M sao cho NA = NM. Chứng minh: ABC = EMA.
	c) Gọi P là chân đường vuông góc kẻ từ E đến AM. Chứng minh: EP // BC.
Câu 5:(2đ). 
	a) Tìm mọi số nguyên tố x, y thỏa mãn x2 - 2y2 = 1.
	b) Tìm các cặp số nguyên x, y sao cho x - 2xy + y = 0
BÀI LÀM
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