\(\frac{2}{x-1}+\frac{5}{x+2}=\frac{13}{x^2+x-2}.\)

\(\Leftrightarrow\frac{2\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}+\frac{5\left(x-1\right)}{\left(x+2\right)\left(x-1\right)}=\frac{13}{x^2+x-2}\)

\(\Leftrightarrow\frac{2x+4}{x^2+x-2}+\frac{5x-5}{x^2+x-2}=\frac{13}{x^2+x-2}\)

\(\Leftrightarrow\frac{7x-1}{x^2+x-2}=\frac{13}{x^2+x-2}\)

\(\Leftrightarrow7x-1=13\)

\(\Leftrightarrow7x=14\)

\(\Leftrightarrow x=2\)

\(\frac{2x-1}{x-3}=\frac{6x-1}{3x+2}\)

\(\Leftrightarrow\left(2x-1\right)\left(3x+2\right)=\left(x-3\right)\left(6x-1\right)\)

\(\Leftrightarrow6x^2+4x-3x-2=6x^2-x-18x+3\)

\(\Leftrightarrow4x-3x+x+18x=3+2\)

\(\Leftrightarrow20x=5\)

\(\Leftrightarrow x=\frac{1}{4}\)

People enjoy living in large cities. But cities have problems. One problem is that they frequently grow very rapidly. Transportation (23) _______ complicated. There are a lot of cars, buses and bicycles. As a result, people are trying to improve the big cities, and they are also planning for new cities. Plan A is a large city (24) _______ smaller cities around it. There is an open land with trees, fields, and lakes between the large city and smaller cities. Each small city is (25) _______. It has offices, schools, hospitals, and places of entertainment. In Plan B the cities are (26) _______by a road. In Plan c, the cities are in rings around the central city and all of them are connected to each other. The goal of all these plans is to limit the (27) _______of the large city.

23. A. becomes           B. returns             C. happens             D. develops

24. A. in                        B. for                    C. with                    D. at

25. A. entire                 B. finished            C. total                     D. complete

26. A. chain                 B. connected       C. attached              D. fastened

27. A. progress            B. growth              C. movement           D. improvement

            People enjoy living in large cities. But cities have problems. One problem is that they frequently grow very rapidly. Transportation (23) _______ complicated. There are a lot of cars, buses and bicycles. As a result, people are trying to improve the big cities, and they are also planning for new cities. Plan A is a large city (24) _______ smaller cities around it. There is an open land with trees, fields, and lakes between the large city and smaller cities. Each small city is (25) _______. It has offices, schools, hospitals, and places of entertainment. In Plan B the cities are (26) _______by a road. In Plan c, the cities are in rings around the central city and all of them are connected to each other. The goal of all these plans is to limit the (27) _______of the large city.

23. A. becomes           B. returns        C. happens      D. develops

24. A. in          B. for   C. with                     D. at

25. A. entire    B. finished      C. total                 D. complete

26. Ạ. chain     B. connected   C. attached      D. fastened

27. A. progress            B. growth        C. movement   D. improvement

IV. Rewrite the sentence so that the meaning doesn’t change: (3pts)

1. Do you mind if I open the windows?

=> Would you mind if I opened the windows?

2. “Is the Great Wall in China?” She asked me.

=> She asked me if the Great Wall was in China.

3. All of you must do this test carefully.

=> This test must be done carefully.

4. She asked him: “ Will you stay with your friends tomorrow?”

=> She asked him if he would stay with his friends the day after.

5. To go swimming is interesting.

=> It’s interesting to go swimming.

III. Put the correct form of the verb/ word in brakets: (2pts)

1.     The lights went out when we (watch) …were watching… television.

2.     Would you mind if I (carry) …carried… your luggage?

3.     The boy (sit) ……sitting…… next to me was very nervous.

4.     (you/ finish) ……Have you finished …… your homework yet, Ba?

5.     Nga asked Ba if he (go) ……went… to Sapa by train that day.

6.     Do you mind (help) ........helping..... me to do this exercise?

7.     Every week, there are two  (fly) ……flights......from Ha Noi to Nha Trang.   

8.     I spent my (child)........childhood.....  in the country.

          Graham Bell was born in Scotland in 1847, when he was a young man of twenty-three he moved with his parents to Canada. Before the year was over, young Graham had left his family and gone to Boston. Though Bell was a dreamer, he was also a pracal thinker and a man of action. In Boston, where he worked by day as a teacher of the deaf,  he worked far into the night experimenting with the electrical transmission of the sound. This led to the invention of the telephone.

…T….. 1.  Alexander Graham Bell was born in Scotland.           

…F….. 2.  He emigrated to Canada in 1860.  

…T….. 3.  He went to Boston when he was twenty-three.  

…T….. 4.  Graham Bell worked with the deaf in Boston.   

…T….. 5.  He experimented with the electrical transmission of the sound by day.

Choose the underlined words or phrases that are not correct in standard written English.(10 marks)

1. Tom looked at Ann and Ann looked at Tom. They looked at themselves.

A B C D

1. A man in dark glasses stood near the door.

A B C D

1. You must not let children to play in the kitchen because it’s a dangerous place.

A B C D

1. The man sitting opposite to me on the train kept staring at me.

A B C D

1. I don’t know why didn’t you answer the teacher’s question.

A B C D

1. The shopkeeper asked the boys don’t lean their bicycles against his window.

A B C D

1. I went out and took an umbrella with myself.

A B C D

1. Smoking cigarettes aren’t allowed in this hospital.

A B C D

1. The sweater that she ordered differs by the one that they sent.

A B C D

1. Please be careful for the dishes. It’s easy to break them.

A B C D

1. Tom looked at Ann and Ann looked at Tom. They looked at themselves.

A B C D

1. A man in dark glasses stood near the door.

A B C D

h) Ta có: \(\left\{{}\begin{matrix}\left|x-7\right|=\left|7-x\right|\ge7-x\\\left|x+5\right|\ge x+5\end{matrix}\right.\)

\(\Rightarrow\left|7-x\right|+\left|x+5\right|\ge\left(7-x\right)+\left(x+5\right)\)

\(\Rightarrow\left|x-7\right|+\left|x+5\right|\ge12\)

\(\Rightarrow H\ge12\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}7-x\ge0\\x+5\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\le7\\x\ge-5\end{matrix}\right.\)

\(\Leftrightarrow-5\le x\le7\)

Vậy, Min_H = 12 \(\Leftrightarrow-5\le x\le7\)

a) Ta có: \(A=2x^2-8x+10\)

\(=2\left(x^2-4x+5\right)\)

\(=2\left(x^2-4x+2^2+1\right)\)

\(2\left[\left(x-2\right)^2+1\right]\)

Ta lại có: \(\left(x-2\right)^2\ge0\)

\(\Rightarrow2\left[\left(x-2\right)^2+1\right]\ge2\)

\(\Rightarrow A\ge2\)

Dấu bằng xảy ra \(\Leftrightarrow\left(x-2\right)^2=0\)

\(\Leftrightarrow x-2=0\)

\(\Leftrightarrow x=2\)

Vậy Min_A = 2 \(\Leftrightarrow x=2\)

III. Complete the sentences with the verb + -ing.

do go play ski swim watch

1. Susan hates boxing but she loves playing football.

2. I don’t like swimming in the pool at the sports centre.

3. Does she like going shopping in the supermarket?

4. Peter loves doing judo.

5. They enjoy watching the Olympics on TV.

6. My brother and I really like skiing in the Alps in February.