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vyvy1177

5 năm trước

Tính nhanh

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Toán lớp 4

\(\sqrt{2x-1}\) = \(x\) + 1

Chứng minh bất đẳng thức:
\(a^{^{ }2}+b^2+c^2+\dfrac{3}{4}\ge a+b+c\)

Đề kiểm tra - Đề 2 - Câu 2 (SBT trang 200)

Cho điểm \(M\left(1;-2\right)\) và đường thẳng \(\Delta\) có phương trình :

\(3x-4y-1=0\)

a) Tìm tọa độ điểm M' đối xứng với M qua đường thẳng \(\Delta\)

b) Viết phương trình đường thẳng \(\Delta'\) đối xứng với \(\Delta\) qua điểm M

c) Viết phương trình đường tròn tâm M và tiếp xúc với đường thẳng \(\Delta\)

Bài 10 (SBT trang 189)

Biết \(\sin\alpha=\dfrac{3}{4}\) và \(\dfrac{\pi}{2}< \alpha< \pi\). Tính :

a) \(A=\dfrac{2\tan\alpha-3\cot\alpha}{\cos\alpha+\tan\alpha}\)

b) \(B=\dfrac{\cos^2\alpha+\cot^2\alpha}{\tan\alpha-\cot\alpha}\)

Bài 9 (SBT trang 189)

Tính các giá trị lượng giác của góc \(\alpha\), nếu :

a) \(\cos\alpha=-\dfrac{1}{4},\pi< \alpha< \dfrac{3\pi}{2}\)

b) \(\sin\alpha=\dfrac{2}{3},\dfrac{\pi}{2}< \alpha< \pi\)

c) \(\tan\alpha=\dfrac{7}{3},0< \alpha< \dfrac{\pi}{2}\)

d) \(\cot\alpha=-\dfrac{14}{9},\dfrac{3\pi}{2}< \alpha< 2\pi\)

Bài 8 (SBT trang 189)

Chứng minh rằng với mọi \(\alpha\), ta luôn có :

a) \(\sin\left(\alpha+\dfrac{\pi}{2}\right)=\cos\alpha\)

b) \(\cos\left(\alpha+\dfrac{\pi}{2}\right)=-\sin\alpha\)

c) \(\tan\left(\alpha+\dfrac{\pi}{2}\right)=-\cot\alpha\)

d) \(\cot\left(\alpha+\dfrac{\pi}{2}\right)=-\tan\alpha\)

Đề kiểm tra - Đề 2 - Câu 1 (SBT trang 200)

Cho elip (E0 có phương trình : \(9x^2+25y^2=225\)

a) Tìm tọa độ các tiêu điểm và các đỉnh của (E)

b) Tìm tọa độ các điểm M thuộc (E) sao cho M nhìn hai tiêu điểm \(F_1\) và \(F_2\) của (E) dưới một góc vuông

Bài 7 (SBT trang 189)

Cho \(\pi< \alpha< \dfrac{3\pi}{2}\). Xác định dấu của các giá trị lượng giác sau :

a) \(\cos\left(\alpha-\dfrac{\pi}{2}\right)\)

b) \(\sin\left(\dfrac{\pi}{2}+\alpha\right)\)

c) \(\tan\left(\dfrac{3\pi}{2}-\alpha\right)\)

d) \(\cot\left(\alpha+\pi\right)\)

Bài 6 (SBT trang 182)

Tìm số \(x\left(0\le x< 2\pi\right)\) và số nguyên k sao cho \(a=x+k2\pi\) trong các trường hợp

a) \(a=12,4\pi\)

b) \(a=-\dfrac{9}{5}\pi\)

c) \(a=\dfrac{13}{4}\pi\)

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