Phân tích các đa thức sau thành nhân tử:
a)4x
4 + 4x3 − x2 − x
b)1− 2a + 2bc + a 2 − b2 − c2
c)(x − 7)(x − 5)(x − 4)(x − 2) − 72
Câu 2. Tìm x, biết(x+5)(4-3x)-(3x+2)2+(2x+1)3=(2x-1)(4x2+2x+1)
Câu 3.
a) Cho a, b, c là các số nguyên thỏa mãn a + b + c = 2020 . Chứng minh rằng:
P = (ab + c – 2019)(bc + a – 2019)(ca + b – 2019) là số chính phương.
b) Cho x, y, z là các số tự nhiên thỏa mãn (xy + yz + zx)(x + y + z) = xyz + 2.
Tính giá trị của P = x2019 + y2019 + z2019.
Câu 4.
a) Tìm giá trị nhỏ nhất của biểu thức + 2020
b) Cho ba số nguyên a, b, c có tổng chia hết cho 6. Chứng minh rằng
M = (a + b)(b + c)(c + a) – 2abc , chia hết cho 6.
c) Tìm tất cả các số nguyên dương và số nguyên tố thỏa mãn .

Cho a, b, c là các số nguyên thỏa mãn a + b + c = 2020 . Chứng minh rằng:
P = (ab + c – 2019)(bc + a – 2019)(ca + b – 2019) là số chính phương.

Cho hình bình hành ABCD, M là trung điểm của BC. Gọi H là chân đường vuông góc
kẻ từ A đến DM. Chứng minh BA = BH.
2. Cho tam giác ABC có góc A tù. Dựng ra bên ngoài tam giác hai tam giác: tam giác ABD
vuông cân tại D và tam giác ACE vuông cân tại E. Dựng hình bình hành ADKE. Chứng
minh tam giác BKC vuông cân.
3. Cho hình thang ABCD (AB || CD), AB < CD. Gọi E, F, M lần lượt là trung điểm của BD,
AC, CD. Qua E vẽ đường thẳng vuông góc với AD, qua F vẽ đường thẳng vuông góc
với BC, qua M vẽ đường thẳng vuông góc với CD. Chứng minh 3 đường thẳng này
đồng quy.
4. Cho hình bình hành ABCD, O là giao điểm hai đường chéo. Đặt OA = a, OB = b. Chứng
minh rằng
a. AB2 + AD2 = 2a
2 + 2b2

b. Tổng bình phương các cạnh của hình bình hành bằng tổng bình phương các
đường chéo.

5. Cho tam giác ABC, AM là trung tuyến, AB = 5cm, AC = 13cm, AM=6cm. Gọi a, b lần lượt
là các đường vuông góc với BC tại B và C. Gọi D là giao điểm của AM và a, gọi E là
giao điểm của AB và b, Chứng minh rằng CD ⊥ ME .

HELP ME!!!!!!!!

IV/ Find out and correct the mistakes if necessary: Correction

1. My mother is more busy on workdays than at weekends. ......................................

2. He works very hardly and never gets bad marks at Maths. ......................................

3. This is a most boring film. I don't like looking it again. ......................................

4. It's the writing English that cause difficulties to foreigners. .......................................

5. The football fans only stop to shout when the football match finish. .....................................

V/ Write a short passage , using the words provided

1. first / bicycle / make / Scotland // ® ..............................................................................................

2. It / build / man / Macmillan // ® ......................................................................................................

3. His / bicycle // two wheels / modern / bicycle // ®............................................................................

4. But / it / much / difficut / ride // ® .....................................................................................................

5. It / heavier / because / made / wood ®.............................................................................................

6. It / not have / rubber / tires // It / wooden / wheels // ® .......................................................................

7. This / make / uncomfortable / bumpy roads // ® ................................................................................

8. But / Macmillan / lucky / one thing / he / not get / flat / tire //®.......................................................

VI/ Cloze exercise :

A man was tired (1)________living in his old house in the country and wanted to sell it and buy a (2)_________ one . He attempted to sell it for a long time but he was not (3)___________ , so at last he decided to solve the problem (4)_____________ using an estate agent. The agent advertised the house a few days (5)_____________, the owner saw a very attractive photo of it , (6)___________

a wonderful description of its gardens , in an expensive ( 7)_____________.

After the house owner (8)___________ the magazine through, he at (9)___________ telephoned the estate agent and said to him " I'm sorry, Mr Jones, but I've decided (10)__________ to sell my house after all . (11)______________ reading your advertisement in that magazine, I can see that it's just the kind of house I want to live all my (12)_______________"

I/ Multiple choice :

Guesthouses with ( vacations / vacancies) are often hard to find. I looked for a sign which said Rooms

( to let / to rent) . I like a room with its own ( toilet / cabinet ) or at least with a ( washbasin / sink ) where I can shave and I prefer it to be on the ground ( stage / floor ).A room with a ( view / sight ) of

the surrounding( countryside / land ) is what I like best. A holiday hotel should have a friendly

( manager / director) who welcomes the ( guests / clients ) at all times. Unfortunately, the best hotels are always ( full / filled). I like hotels where the lifts aren't ( out of order/ broken) and which don't cost too (much / many) A big ( bill/ menu) at the end always (spoils / ruins) a good holiday and make you wish you had ( stayed / rested) at a cheaper ( place / space )

II/ Rewrite the sentences :

1. You should have an early night, so that you don't feel tired.

® So as ........................................................................................................................................

2. The passengers don't realize how lucky they have been.

® Little .............................................................................................................................................

3. He went to the zoo last year and that is where he saw a real lion for the first time.

®Before he ........................................................................................................................................

4. People say that he can speak three foreign languages fluently.

® He is...............................................................................................................................................

5. Who has got this house ? ® Whom ..............................................................................................

6. How wide do you think the longest river of Vietnam is ?

® What ...............................................................................................................................................

7. You won't make progress in English if you don't learn it carefully and industriously.

® Unless ...........................................................................................................................................

8. " Don't forget to come to my birthday party tomorrow ," he said

® He told ........................................................................................................................................

II. Choose from the options the correct form of the word in brackets by circling the corresponding letter A, B, C, or D:

11. In the supermarket, goods are (sell) at a fixed price.

A. sale B. selling C. sold D. seller.

12. What is the (high) mountain in Vietnam?

A. highest B. height C. heighten D. higher.

13. You should not leave (value) things in your car while you go shopping.

A. valuation B. valuables C. values D. valuable

14. I would like to try on this dress. Where is the (change) room?

A. changeable B. changing C. changed D. unchanged

15. (In the supermarket) Customer: Where can I find chocolates? Saleman: They are displayed at the (count).

A. counting B. countless C. countable D. counter

16. Thang Long is the (old) bridge in Hanoi.

A. oldest B. eldest C. older D. elder

17. In the (commerce) center, there is a wide range of commodities available.

A. commerciality B. commercialize C. commercializing D. commercial

18. In Ho Chi Minh City, it is (heat) almost all year round.

A. heated B. hottest C. hot D. heating

19. This hat is the __________ of all.

A. expensivest B. more expensive C. cheapest D. cheaper

20. Of all the stories I have, this is the most __________ one.

A. better B. best C. interesting D. interest

III. Indicate one mistake in each of the following sentences. Circle either A, B, C, or D.

21. I find that tomato soup tastes well than potato soup.

A B C D

22. Today is not hot as yesterday, as said in the weather forecast.

A B C D

23. This picture is most colourful than the one in the hall.

A B C D

24. Tom is said to be smart than Mary at doing maths.

A B C D

25. She moved to a comfortabler seat in the departure lounge.

A B C D

IV/ Rewrite the sentences :

26. We have a lot of work to do today. ® There is ............................................................................................

27. Let’s go for a walk after dinner. ® Why ..................................................................................................?

28. Peter is a good football player. ® Peter can .........................................................................................

29. Why isn’t this telephone working, Mum? ® What’s ................................................................................?

30. What date is your birthday ? ® when ...................................................................................?

III. Put each verb in brackets into a suitable tense - form (0.5 pt.)

IV. Underline ONE mistake in each sentence and correct it (1 pt.) Correction

V. Supply the correct prepositions to complete the sentences below (0.5 pt.)

1. I haven’t seen Linh ____________ my birthday party.

2. We’ve already waited ____________ a year.

3. To be a member of our organization, you can register ____________ today.

4. The birds started singing ____________ half past four this morning.

5. The farmer tied the tiger to a tree ____________ a rope because he didn’t want it to eat the buffalo.

I. Rewrite each sentence so that it has a similar meaning to the first one, using the given word (1 pt.)

1. The last time she visited me was five months ago. (FOR)

……………………………………………………………………………………………………………….

2. My uncle likes gardening more than fishing. (PREFERS)

……………………………………………………………………………………………………………….

3. “Don’t make such a mess in your room”, said Mrs. Hanh to her son. (TOLD)

……………………………………………………………………………………………………………….

4. My brother is too young to drive a car. (NOT)

……………………………………………………………………………………………………………….

5. Tam doesn’t type as fast as she used to. (USED)

……………………………………………………………………………………………………………….

II. Write full sentences, using the clues given (1 pt.)

1. Many residents / store owners / be / concerned / new mall / for / a few months//

……………………………………………………………………………………………………………….

2. There / be / different / ways / learn / same / number / new / words//

……………………………………………………………………………………………………………….

3. She / used / work / hard / when / she / be / student//

……………………………………………………………………………………………………………….

4. As / Little Pea / run / festival / she / drop / one / her shoes / and / lose / it//

……………………………………………………………………………………………………………….

5. Ho Chi Minh Communist Youth Union / organization / Vietnamese / youth / 15 / 30 / year / age//

……………………………………………………………………………………………………………….