Tính:

\(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{2020}+\sqrt{2021}}\)

Cho x > 2019, y> 2019 thỏa mãn: \(\frac{1}{x}+\frac{1}{y}=\frac{1}{2019}\)

Tính gtrij biểu thức: P = \(\frac{\sqrt{x+y}}{\sqrt{x-2019}+\sqrt{y-2019}}\)

Tìm GTNN của biểu thức:

\(A=\sqrt{-x^2+2x+8}-\sqrt{-x^2+x+2}\)

Rewrite the following sentences without changing their original meanings.

1. " Should I tell this to her?" he asked himself ( whether )

→ He wondered...........................................

2. It's the first time Mary has gone to Viet Nam. ( before )

→ Mary has.................................................

Viết lại câu với những từ đã cho

1. She has studied Japanes for three years.

2. Hung last wrote to his pen pal five months ago.

→ Hung hasn't ..............................................

3. The last time we visited Kuala Lumpur was 3 years ago.

→ I haven't......................................................

4. When did you study English?

→ How long..........................................?

5. They began building this house 2 months ago.

→ They have.......................................

6. My father started to work in this factory last week.

→ My father has...................................

7. How long has he worked in the garden?

→ When ....................................?

8. How long ago did you learn music?

→ How long have.....................................

9. he started living in Ho Chi Minh City when he was 8.

→ He has ...........................................

10. He learnt English when he was 18.

→ He has ..........................................

11. They have worked in that factory for five years.

→ They began...................................

12. My father stopped smoking two years ago.

→ My father hasn't ...................................

13. We have learnt English for four years.

→ We started ..............................................

14. My father started to give up smoking last year.

→ My father has .........................................

15. They have worked in that factory since 2001.

→ They started................................................

16. Lan hasn't written to Maryam for a month.

→ Lan didn't.................................................

17. He has lived in Ha Noi since he was 12.

→ He started..................................................

18. I haven't met her for a long time.

→ I didn't....................................................

19. How long have you learnt French?

→ How long ago ..........................................?

20. How long have you bought this car ?

→ When did ..........................................?

21. When did you start to listen to classical music?

→ How long.....................................?

22. I saw her 10 years ago.

→ I haven't...........................................

23. The last time I saw him was in June

→ I.................................................

24. He started working in this company 5 years ago

→ He has..............................................

25. They began living here ten years ago.

→ They have................................................

26. Lan started to learn French since 2000.

→ Lan has been learning................................

27. The last time Lan went to the zoo was two years ago.

→ Lan..........................................................

28. I haven't eaten this kind of food before.

→ This is the first time..................................

Cho \(P=\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{x-2\sqrt{3}-3}{x-1}\right):\frac{\sqrt{x}+1}{\sqrt{x}-1}\)

a, Rút gọn P

b, Tính P khi x = \(4-2\sqrt{3}\)

c, Tìm x để P=2

d, C/m P ≤ 4 với mọi c thỏa mãn điều kiện

EX: Use the words and phrases to complete the passage.

1. The enermous 28-metre figure of Jesus gazing across/ East Sea with outstretched arms be located at the Southern end/ Small Moutain.

2. Built in 1971, this giant Jesus/ rest/ on a 10 metre-high platform.

3. The interior/ statue/ is bollow/ contains a spiral staircase/ 129 steps, ascending/ from the food/ of the statute/ to its neck.

4. There two shoulders of the figure be balconies, each able/ accommodate/ up to six people, which offer/ a splendid view/ the Surrounding landscape.

5. This is/ large sculpture/ Southern VN. Recent construction a pathway/ have made the 30-minute hike up the mountain/ more pleasant/ the panoramic view along the way/ be magnificent.

EX: Read the passage and choose each phrase to fill in the blanks

London has a pollution of about 7000000. It lies on the River Thames, (1)______ nearly 2000 years ago. From about 1800 until World War Two, London was the biggest city in the world, but now there are many citise (2)______

London is famous for many things. Tourists come from all over the world to visit its historic buildings, such as Buckingham Palace, (3)______, and the House of Parliament, (4)______ and hear the famous clock, Big Ben. They also come to visit its theatres, its museums, and its many shops, such as Harrods, (5)_____. And of course they want to ride on the big wheel next to the river.

Like many big cities, London has problems with traffic and pollution. Over 1000000 people a day use the London Underground, but there are still too many cars on the streets. The air isn't clean, but it is cleaner than it was 100 years ago.

For me, the best thing about London is the parks. There are five in the city centre. But my children's favorite place is Hamleys, (6)______ toy shop in the world.