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12099162 Kính chào các thầy, cô. Khi cài đặt phần mềm , trên PowerPoint và Word sẽ mặc định xuất hiện menu Bộ công cụ Violet để thầy, cô có thể sử dụng các tính năng đặc biệt của phần mềm ngay trên PowerPoint và Word. Tuy nhiên sau khi cài đặt phần mềm , với nhiều máy tính sẽ...
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Người gửi: Thùy Dương
Ngày gửi: 10h:18' 12-03-2017
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ĐỀ BÀI
Câu 1 (2 điểm): Phân tích đa thức thành nhân tử
 
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Câu 2 (3 điểm): Cho biểu thức A = 
a) Tìm giá trị của x để biểu thức A xác định.
b) Tìm giá trị của x để biểu thức A có giá trị bằng 0.
c) Tìm giá trị nguyên của x để biểu thức A có giá trị nguyên.
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Câu 3 (5 điểm): Giải phương trình:
a) 
b) 
c)  (phương trình có hệ số đối xứng bậc 4)
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Câu 4 (4 điểm):
a) Tìm GTNN:  b) Tìm GTLN: 
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Câu 5 (6 điểm) Cho tam giác ABC nhọn, các đường cao AA’, BB’, CC’, H là trực tâm.
a) Tính tổng 
b) Gọi AI là phân giác của tam giác ABC; IM, IN thứ tự là phân giác của góc AIC và góc AIB. Chứng minh rằng: AN.BI.CM = BN.IC.AM.
c) Chứng minh rằng đường thẳng DF luôn đi qua một điểm cố định khi điểm M di động trên đoạn thẳng AB.
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Đề 2
Câu 1 (2 điểm) : Cho biểu thức A = 
a) Rút gọn biểu thức A b) Chứng minh rằng giá trị của A luôn dương với mọi x ≠ - 1
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Câu 2 (3 điểm):
a) Chứng minh rằng: Với mọi x ( Q thì giá trị của đa thức :
M =  là bình phương của một số hữu tỉ.
b) Giải phương trình 
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Câu 3 (1,5 điểm): Đa thức P(x) bậc 4 có hệ số bậc cao nhất là 1. Biết P(1)=0 ; P(3)=0 ; P(5)= 0.
Hãy tính giá trị của biểu thức: Q= P(-2)+7P(6)
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Câu4 (2,5 điểm): Cho tam giác ABC vuông tại A, đường phân giác AD. Vẽ hình vuông MNPQ có M thuộc cạnh AB, N thuộc cạnh AC, P và Q thuộc cạnh BC. Gọi E và F lần lượt là giao điểm của BN và MQ; CM và NP. Chứng minh rằng: a) DE song song với AC b) DE =DF; AE =AF.
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Câu5 (1 điểm): Chứng minh bất đẳng thức:
 Với 
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Bài 1 (4,0 điểm). Cho biểu thức: 
a. Rút gọn P b. Tìm các giá trị của x để P = 6
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Bài 2 (4,0 điểm).
a. Cho các số a, b, c, d nguyên dương đôi một khác nhau và thoả mãn:
. Chứng minh A = abcd là số chính phương.
b. Tìm a nguyên để a3 – 2a2 + 7a – 7 chia hết cho a2 + 3.
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Bài 3 (3,0 điểm). a. Tìm giá trị nhỏ nhất của biểu thức: A = (x – 1)(2x – 1)(2x2 – 3x – 1) + 2017
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b. Giải phương trình: 
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Bài 4 (3,0 điểm).
a. Gọi a, b, c là độ dài ba cạnh của tam giác thỏa mãn: a3 + b3 + c3 = 3abc. Chứng minh tam giác đều.
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b. Cho x, y, z dương và x + y + z =1. Chứng minh rằng : 
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Bài 5 (5,0 điểm). Cho O là trung điểm của đoạn AB. Trên cùng một nửa mặt phẳng có bờ là cạnh AB vẽ tia Ax, By cùng vuông góc AB. Trên tia Ax lấy điểm C (khác A), qua O kẻ đường thẳng vuông góc với OC cắt tia By tại D.
a. Chứng minh AB2 = 4 AC.BD
b. Kẻ OM
 
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