Cho a,b là hai số thực.

CMR: (a²+b²)(a⁴+b⁴)≤(a+b)(a⁵+b⁵)

Với a<2b<0, rút gọn \(\dfrac{1}{a-2b}\)√b²(a²-4ab+4b²)

Giải hệ phương trình

x^2+y^2=1

x^3+y^3=1

II. FIXED EXPRESSIONS/ COLLOCATION/ IDIOMS

EXERCISE:  Complete each of the following sentences with a phrase from the box

1.     She was chosen for the job ……………………………….. her qualifications

2.     Discrimination ……………………….. sex, race in that country has been increasing dramatically.

3.     A wide range of postcards and other souvenirs are ……………………….. in the visitors’ centre.

4.     According to researchers, 400 people a year die of this disease ……………………………….. .

5.     ……………………………….. should you sign the contract unless you are sure you understand it.

6.     Mr Knight cannot be here, so his wife will accept the prize ………………………………...

7.     They agreed to tell the truth ……………………….. their names would not be used in the article.

8.     Nuclear power is relatively cheap. ………………………….., you could argue that it's not safe.

9.     She has been ……………………………….. for the past two months because she put on too much weight during the winter.

10.            Mike and I were pretty serious for about a year, but our relationship has been ………………………………..ever since we graduated.

11.            We are not ……………………………….. and don't speak to each other much.

12.            We delayed our departure ………………………………..the bad weather.

13.            All of these people operating behind the scenes work to put the newscast ………………………...

14.            I’m sorry. I didn’t break the vase ………………………………...

15.            I thought I'd go to the movies, but ………………………………..I'd rather stay home.

16.            I've been ……………………………….. all day, and I'm really tired.

17.            The show was ………………………………..being canceled due to low ratings.

18.            Rain or shine, he is at the office at 7:30 ………………………………...

19.            Change your life today. Don't gamble on the future, act now, ………………………………...

20.            The program is ………………………………..of closure due to lack of funding.

21.            When life gets hard and you want to give up, remember that life is full of ……………………………….. .

22.            Through an unfortunate ……………………………….. your letter was left unanswered.

23.            Many insurance companies are ………………………………..to increase premiums to avoid bankruptcy.

24.            ……………………………….., the new project will be starting in June.

25.            I try to do the job ………………………………...

26.            The Federal Reserve Bank raised interest rates to keep inflation ………………………………...

27.            Our daughter Rosie was really worried about her history exam, but in the end she passed it ………………………………... We're very proud of her.

28.            Sorry, but I don't think I'll be able to make it to work today. I'm feeling a bit ………………………………...

29.            The new transportation policy was made ………………………………..decreasing car traffic.

30.            -She left the country ……………………………….. arrest if she returned.

31.            It’s important to be aware of the need to participate in the training and dialogue program, ……………………………….. issues or problems to be addressed.

III. PHRASAL VERBS

EXERCISE:  Complete each of the following sentences with a phrasal verb from the box

1.     The government should ………………………………..taxes for poor people if they can't afford to pay them.

2.     -We've decided to ………………………………..our apartment. We'll paint it, redecorate it and buy some new furniture.

3.     We'll have to ……………………..the air-conditioning while they fix it. It's going to be really hot!

4.     When he was young, he ………………………………..being a famous football player.

5.     She ………………………………..her little girl as a fairy.

6.     Why don't you ……………………..on your way home from work and help me cook some food?

7.     The demand for mobile phones shows no signs of ………………………………...

8.     Several recent reports show the one reason why students ………………………………..college is due to financial reasons rather than academic.

9.     I don't feel like going out to a restaurant. Let's stay home and …………………………….. tonight.

10.            How can I get my son to ………………………………..all his vegetables? He says he hates them and leaves most of them on his plate. 

11.            His attempt to persuade the boy ……………………………….. failure.

12.            If you keep going outside in this weather without shoes, you'll ………………….. catching a cold.

13.            After a great concert and lots of dancing, the New Year's Eve celebrations ……………………………….. a fantastic display of fireworks.

14.            He jumps from one topic to another. I can't make out what he is ………………………………..

15.            Depletion of the ozone layer leaves the earth's surface increasingly ……………………………….. harmful radiation from the sun.

16.            Since her parents passed away in a car accident, she hasn’t had anyone to …………………….. .

17.            It was unbelievable -- it took two years to set the whole thing up and it …………………………….. at the last minute!

18.            I am so tired. I don't think I ……………………………….. going shopping today.

19.            She hired a detective to ……………………………….. if her husband was having an affair.

20.            Being addicted to computer games makes him ……………………………….. in his class.

21.            Maria ……………………………….. some of her colleagues and decided to look for a new job.

Exercise 27: Choose the best answer

1.     I shift/ modify the vase to a more suitable place.

2.     It took him a while to adapt/ alter himself to his new surroundings.

3.     Since 1946 Vietnam’s constitution has been amended/ changed 5 times

4.     We found it cheaper to modify/ adjust existing equipment rather than buy new.

5.     The council is expected to adopt/ adapt the new policy at its next meeting.

Exercise 28 : Choose the correct option

1.     The company is launching/ starting a new model next month.

2.     The company initiated/ launched a management training programme for small businesses.

3.     The company launched/ started a huge advertising campaign.

4.     This controversial plan is sure to initiate/ arouse strong opposition

Exercise 29 : Choose the correct option

1.     King Richard II was famous/ infamous for his cruelity.

2.     He is one of France's most celebrated/ notorious painters.

3.     The city is notorious/ famous for its traffic jams.

5.     Shilpa Shetty was infamous/well-known in India, but few people in the UK had heard of her.

6.     Dali is one of Spain’s most notorious/celebrated artists.

7.     The British are renowned/ infamous for their love of animals.

Exercise 30: Choose the correct option

1. The branch has separated/ classified from the trunk of the tree.

2. In the study families are classified/ seperated according to their incomes.

3. The present law discriminates/ distinguishes unfairly against women.

4. The computer program was unable to classify/ distinguish between letters and numbers.

Exercise 31: Choose the best option

1. All the people involved in the accident have now been released/ discharged from hospital.

2. Raw sewage was discharged/ ejected from the treatment plant directly into the river.

3. She was formally discharged/ expelled by the court.

4. He was expelled/ evicted from school for disruptive behaviour.

5. They were forced to leave as part of a government drive to eject/ expel illegal immigrants.

6. Firefighters took two hours to release/ discharge the driver from the wreckage.

7. A group of noisy protesters were ejected/ discharged from the meeting.

8. He was evicted/ expelled from the rent house for not paying the rent

Exercise : Choose the best answers

1.      Paris is _______ exciting ________ London.

A. as – than                  B. as – as                 C. more – as               D. most – than

2.      Peter is the ________ student in my class.
A. taller                         B. so tall as            C. the tallest               D. tallest

3.      He drives as _________ his father does.
A. careful                      B. more carefully C. the most careful     D. carefully as

4.      You can take _______ books as you want.
A. as many                    B. as much             C. so much                 D. too many

5.      He finished the test ________ of all.
A. rapidly                      B. the most rapidly                                   C. most rapidly      D. more rapidly

6.      He doesn’t go out _________.

A. as often as he would                                                                  B. more often as he did

C. as often as he once was                                                              D. as often as he used to

7.      Of the five students, Mary is ____­­­­­____ .

A. more intelligent      B. the more intelligent                               C. most intelligent D. the most intelligent

8.      The deep oceans contain some of the ________ of all living creatures.

A. strangest                 B. strange                C. as strange as          D. strange

9.      Computers are considered as        _______  tools today.

A. much modern than  B. modern as           C. the most modern   D.more modern

10.  One of the ____ diseases mankind has ever faced is cancer.
A. best                           B. better                 C. worst                      D. worse

11.  Although Mary studied very _______, she did not get good results last semester.

A. hardly                      B. harder                 C. hard                       D. hardiest

12.  There are ______ diseases being treated by laser beams.

a. more or less             B. more than           C. more and more      D. less than

13.  ________ the weather is, __________ I feel.

A. The warmer / the more good                  B. The warmer / the better             

C. The warmer  /  the more                                                             D. The warmest / the best

14.  The _____ they come, the ______ seats they can get.

a. early – better           B. earlier – gooder         C. early – the best         D. earlier – better  

15.  Of the two sister, Mary is _________ .

a. the taller                   B. the tallest           C. the more taller       D. taller

16.  The more you water this plant, the _______ it will grow.

A. faster                       B. tall                      C. wetter                    D. best

17.  It’s becoming _________ to find a job.
A. more difficult and more                          B. more and more difficult   

C. most and more difficult                          D. more difficult than

18.  The economic conditions today are ________ they were in the past.

A. much more good     B. much better than                                    C. much better            D. the best than

19.  The more you practise, ______ you can speak the language.

A. the more well          B. the better            C. more better            D. the more

20.   His house is _______ mine.

A. twice as big as        B. as twice big as    C. as two times big as         D. as big as twice

21.  Sarah speaks so _______ that I can’t understand her.

A. fast                          B. fastly                  C. faster                     D. fastest

22.  The harder you try, ________ you will get.

A. the results are better                                                                   B. the best result  

C. the better results                                     D. the more better results

23.  The more crowded the shop is, __________ to pay for the goods

A. the more longer you have to wait           B. the more long you have to wait

C. the longest you have to wait                   D. the longer you have to wait

24.  The more electricity  you use, ___________ .

A. the higher your bill will be                     B. the higher will be your  bill

C. the bill will be higher                                                                  D. the highest your bill will be

25.  Actually, today I feel ____________ than I did yesterday.

A. bad                         B. worse                   C. worst                      D. the worst

26.  The sun is ___________ when seen from mercury than when seen from the earth.

A. more much brilliant                                B. much more brilliant C. much brilliant more                            D. much brilliant

27.  I have               opinion about the new manager as you.

a. as                             b. as same                c. similar                    d. the same

28.  The new television tower is twice                 the old one.

a. higher than              b. as high as             c. highest                    d. higher as

29.  John’s grades are higher than _________ .

A. his sister is             B. his sister              C. that of his sister    D. those of his sister

30.  The bigger the supermarket is, __________.

A. the choice is wide                                   B. the wider the choice is.

C. the more the choice is                              D. the wider the choice it is.

31.  “The inflation rate in Greece is five times ______ my country,” he said.

A. as much as              B. more than            C. as many as that in D. as high as that in

32.  There were two small rooms in the beach house, ______ served as a kitchen.

A. the smaller of them                                 B. the smaller of which         C. the smallest of which            D. smallest of that

33.  Petrol is……. it used to.

a. twice as expensive as                               b. twice expensive more than

c. twice more than expensive                      d. more expensive than twice

34.  This is ____ the most difficult job I’ve ever had to do.

     A. by far              B. by heart                C. by chance               D. by myself

35.  As television programmes become more popular, they seem to get worse.

A.  The more popular be come television programmes, the worse they seem.

B.   The popular television programmes, the worse they seem.

C.   The more popular television programmes become, the worse they seem.

D.   The most popular television programmes  become, the worst they seem.

36.  The better you are at English, more chance you have to get a job with international organizations.

                A               B                         C                                   D

37.  The bigger of the three daily meals for most American families is dinner, served at about six

                A                                             B                                          C                D

o’clock.

38.  The early we leave, the sooner we will arrive.

               A            B            C                     D

39.  Many people believe that New York is the most great city in America.

         A                                                      B             C               D

40.  The older people are, the more weaker they are

      A    B              C                D

41.  We live far from our house. We miss it very much.

The farther ……………………………………………………………………………..

42.  This is the most intereating novel I have ever read.

I have never …………………………………………………………………………….

43.  I can’t cook as well as my mother can.

My mother ………………………………………………………………………………