De thi hsg
Chia sẻ bởi Thùy Dương |
Ngày 12/10/2018 |
74
Chia sẻ tài liệu: de thi hsg thuộc Đại số 8
Nội dung tài liệu:
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
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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