\(\widehat{ACB}=180^0-\left(\widehat{BAC}+\widehat{ABC}\right)=50^0\)

\(\Rightarrow\widehat{AOB}=2.\widehat{ACB}=100^0\) (góc ở tâm gấp đôi góc nội tiếp chắn cùng dây cung)

1D 2B 3C 4A 5A 6C 7A 8A 9B 10A 11C 12D 13D 14D 15A 16D 17A 18C 19C 20D 21D 22C 23C 24A 25B 26C 27D 28B 29C

1 D

2 B

3 C

4 A

5 A

1.

\(y'=\dfrac{3}{\left(x+2\right)^2}\Rightarrow\left\{{}\begin{matrix}y'\left(-1\right)=3\\y\left(-1\right)=-2\end{matrix}\right.\)

Phương trình tiếp tuyến:

\(y=3\left(x+1\right)-2\Leftrightarrow y=3x+1\)

2.

\(y'=2x+3\)

\(\Rightarrow\left\{{}\begin{matrix}y'\left(1\right)=5\\y\left(1\right)=2\end{matrix}\right.\)

Phương trình tiếp tuyến:

\(y=5\left(x-1\right)+2\Leftrightarrow y=5x-3\)

3.

\(y'=\dfrac{-4}{\left(x-1\right)^2}\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow\dfrac{x_0+3}{x_0-1}=2\Rightarrow x_0+3=2x_0-2\)

\(\Rightarrow x_0=5\)

\(\Rightarrow y'\left(5\right)=\dfrac{-4}{\left(5-1\right)^2}=-\dfrac{1}{4}\)

Phương trình tiếp tuyến:

\(y=-\dfrac{1}{4}\left(x-5\right)+2\Leftrightarrow y=-\dfrac{1}{4}x+\dfrac{13}{4}\)

4.

\(y'=2x+2\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow x_0^2+2x_0+4=3\)

\(\Rightarrow x_0^2+2x_0+1=0\Rightarrow x_0=-1\)

\(\Rightarrow y'\left(-1\right)=2.\left(-1\right)+2=0\)

Tiếp tuyến: 

\(y=0\left(x+1\right)+3\Leftrightarrow y=3\)

5.

\(y'=\dfrac{5}{\left(x+1\right)^2}\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow\dfrac{5}{\left(x_0+1\right)^2}=\dfrac{5}{9}\)

\(\Rightarrow\left(x_0+1\right)^2=9\Rightarrow\left[{}\begin{matrix}x_0=2\\x_0=-4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}y_0=-\dfrac{2}{3}\\y_0=\dfrac{8}{3}\end{matrix}\right.\)

Có 2 tiếp tuyến thỏa mãn:

\(\left[{}\begin{matrix}y=\dfrac{5}{9}\left(x-2\right)-\dfrac{2}{3}\\y=\dfrac{5}{9}\left(x+4\right)+\dfrac{8}{3}\end{matrix}\right.\) \(\Leftrightarrow...\)

6.

\(y'=2x-3\)

Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow2x_0-3=1\Rightarrow x_0=2\)

\(\Rightarrow y_0=2^2-2.3+1=-1\)

Phương trình tiếp tuyến:

\(y=1\left(x-2\right)-1\Leftrightarrow y=x-3\)

1 T

2 T

3 F

4 T

5 D

6 D

T T F T A D

1 My sister has learned English for 5 years

2 A supermarket was built near the airport last year

3 I spent three hours cleaning the house yesterday

6 The wall built three weeks ago fell down

7 Unless you leave me alone, I will call the police

8 The suspects are being followed by the police 

10 Nobody in this team is as good at playing football as Tom

\(10\times10-6+5:2\\ =100-6+2,5\\ =94+2,5\\ =96,5\)

`10xx10-6+5:2`

`=100-6+5/2`

`=94+5/2`

`=188/2+5/2`

`=193/2`