Không chuyên Toán nhưng theo kinh nghiệm thì khi làm mấy cái chững minh kiểu này thì e cứ cho nó là đúng rồi làm ngược lại cho nó dễ hơn.

Đặt : \(\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+...+\frac{1}{80}\)=A

Ta thấy A< 7/12

Cái đặc biệt ở đây là phân số 7/12

\(\frac{7}{12}=\frac{1}{4}+\frac{1}{3}\)

< nhìn dễ ra thôi 3+4=7 ; 3x4=12 >

Tiếp thep e tách cái phần dãy A ra thành 2 phần đi

\(A=\left(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{60}\right)+\left(\frac{1}{61}+\frac{....1}{80}\right)\)

Lại tiếp tục phân tích:

\(\frac{1}{41}+\frac{1}{42}+\frac{1}{60}>\frac{1}{60}+\frac{1}{60}+.....+\frac{1}{60}\)< có 20 phân số 1/60>

Vì 1/41 > 1/60 ; 1/42>1/60.....

<=> \(\frac{1}{41}+\frac{1}{42}+...+\frac{1}{60}>\frac{20}{60}=\frac{1}{3}\left(1\right)\)

Tương tự:

\(\frac{1}{61}+\frac{1}{62}+...+\frac{1}{80}>\frac{20}{80}=\frac{1}{4}\left(2\right)\)

Từ (1) và(2) suy ra A> 1/3+1/4 =7/12

\(\frac{1}{41}+\frac{1}{42}+....+\frac{1}{80}>\frac{7}{12}\) (đpcm)

Tìm lỗi sai và sửa lại
The reason(A) what -> why (B) I didn't come(C) to the party was that I was ill(D)

1, you have to study hard, or you will fail the next exam.

If...you don't study hard, you will fail the next exam

2, please come before 8 am, otherwise, you can’t meet her.

If...you come before 8 a.m , you can't meet her

3, tell her the truth when you see her tomorrow. If.. you see her tomorrow, tell her the truth

4, you press this button to stop the machine.

-> If you want to stop the machine, you can press this button

5, i hope it is sunny tomorrow because i can go to the beach then.

-> If it is sunny tomorrow, i can go to the beach

6, make me some coffee and i will give you one of my biscuits

.-> If you make me some coffee , i'll give you one of my biscuits

7, in the snowy weather, we don’t go to school.

-> If it is in the snowy weather, we won't go to school

8, i only come if they invite me.

If... they don't invite me, i won't come

9, work hard or you can’t pass the exam.

If... you work hard, you can pass the exam

10, practise speaking every day or you can’t improve your English.

If....you don't practise speaking everyday, you can't improve your English

Can/ l/ am /that/ you/ come /pleased

-> I am pleased that you can come

ls/ class/ always /she/ talking /in

-> Iss she always talking in class?

change the sentence in negative and interrogative

there are some books on the tables

Phủ định: There aren't any books on the tables

Nghi vấn: Are there any books on the tables

Choose the correct answer:

1) I usually play football when i have____.

A.spare time/ leisure time B. good time C.no time D.times

2) In team sports, the two teams_____against each other in order to get the better score.

A.are B. do C.make D.compete

3)_____draw on the walls and tables, please.

A.Do B.Don't C.Should D.Shouldn't

4)Nam plays sports very often, so he looks very_____.

A.sport B.sports C. sporty D. sporting

5)Last summer, I_____fishing with my uncle in the afternoon.

A.go B.went C. goes D.going

6) I like watching football matches, but Im not very good_____playing football.

A.at B.in C.on D.for

7)Team sports are sometimes called_____sports.

A.compete B.competition C.competior D.competitive

8)"_____do you do judo?" - "Twice a week."

A.When B.Where C.How often D.Why

9)_____sports do you like watching on TV?

A.How B.What C.Do D.How often

10)Football is regarded_____the most popular sports in the world.

A.for B.as C.like D.of

11)Sports and games_____an important part in our lives?

A.play B.do C.go D.make

12)When you go to the zoo, don't_____the animals.

A.play B.do C.tease D.watch

1. Some body was recording our conversation.

-> Our conversation was being recorded

2. We have seen her since last week

-> She has been seen by us since last week

3. Bill is using the computer at the moment

-> The computer is being used by Bill at the moment

4. Doctors have treated many people for burn

-> Many people for burn have been treated by doctors

5. People were watching the match on TV

-> The match was being watched on TV

6. Nobody has stolen his watch

-> His watch hasn't been stolen

7. Mai does't do the test well

-> The test isn't done well by Mai

8. Our father hasn't repainted the gate gray

-> The gate hasn't been repainted pray by our father

9. Alex wasn't singing a song when the doorbell rang

-> A song wasn't being sung by Alex when the boorbell rang

10. My mother usually feeds the dog

-> The dog is usually fed by my mother

11. Alot of people can't use the train

-> The train can't be used by a lot of people

12. The little girl has eaten the eggs

-> The eggs has been eaten by the little girl

13. People play soccer all over the world

-> Soccer is played all over the world

14. The postman brought the mail early today

-> The mail was brought early by postman today

15. My sister will hold a party next Sunday

-> A party will be held by my sister next Sunday

1. What music is seriuos and TRADITIONAL Western European music? (antonym)
A. uncommon : không phổ biến
B. incorrect: không đúng , sai
C. impossible : không thể
D. irregular : không thường xuyên
2. We were woken early by the sound of the birds .........
A. song
B. sing
C. singer
D. singing < đây là sử dụng Hiện tại phân từ của V nhé>
3. Do you know what kind of music does Minh like? (need correcting)
A. Do
B. know
C. kind of
D. does Minh like < thực ra câu này là câu hỏi khi Do lên đầu câu rồi nên phía sau có trợ động từ "does" nữa là sai . Ta có thể sửa lại thành (that) Minh likes.
4. Our teacher lives in a small house on this town. (Wh_ques)
=> Where does your teacher live?

< bạn chú ý phần in đậm có giới từ in + a small house + on + this town -> chỉ địa điểm cụ thể => từ để hỏi ở đây là " where" nhé . Còn "which" là hỏi cho vật : cái nào, vật nào...>

Đặt câu hỏi cho từ in đậm
1/ Mary is coughing because she has a cold
-> Why is Mary coughing?
2/ I've had this car since the beginning of october
-> When have you had this car?
3/ Our break last 10 minutes

-> How long does your break last?

Sắp xếp:

run out/ non-renewable /comes / energy /from/ that/ sources /will/ some day.

=> Energy that comes from non-renewable sources wil run out some day.

Pick out a word which is stressed on different position from the others.

1. A. audience I. B. religion C. compose D. memorial

2. A. wilderness B. lyrical C. detective D. motion

3. A.shortage B. powerful C. character: D. disaster

viet lai cau

1 my dad often goes to work at seven fifteen

My dad often ...............................go to work at a quarter past seven..........................

2.there isn't any picture in my bebroom

My bedroom doesn't ............................have any picture..........................

3no girl in my group is more harl-working than me

I am...............................the most hard-working girl in my group..............................

4.I have never seen this film

This is the .............................first time i have ever seen this film..................................

5.this is the first time we have been Spain

I've .............................never been to Spain before ................................

6.my favourite tv program is cartoon

I like ...........................cartoon program.............................

7.this film isn't as interesting as that one

That film ......................is more interesting than this film.....................................

8.It's was raning, so we stayed indoor

We stayed ........................indoor because it was rainning............................

9.This film is boring but I enjoy it

Although .....................this film is boring, I enjoy it...............................

1. "Are you a plumber?", he asked me

-> He asked me.................if I was a plumber.......................

2. Nam said: "I will call Mai in 5 minutes"

-> Nam said..................that he would call Mai in 5 minutes...........................

USE ' IT WAS NOT UNTIL..'

We didn't meet her until we moved to HN

-> It was not until we moved to HN that we didn't meet her

Rewrite the sentences

1. " We are living in a small village in Hoa Binh", Minh said

➜ Minh said that____________they were living in a small village in Hoa Binh_______________

2. John told his mum that he would sweep the house before she came back

➜ " I _________will sweep the house before you come back_____________", John said to his mum

3. " I want to become a mathematician", John said.

➜ John said that___________he wanted to become a mathematician_________

4. " Daisy, I can't go fishing this week ", Linda told

➜ Linda told Daisy that ________she couldn't go finishing that week__________

5. " Mike , I don't have Science today ", Mark told

➜ Mark told Mike that_________he didn't have Science that day________

Make sentences from the cues given

1. Milions of email/send/ every minute /the day

-> Millions of email are sent every minute of the day.

2. It/ important/be/polite and respectful / when/you/online

->It's important to be polite and respectful when you are online

3. Since its creation/ the Internet/open up / lots of/ new ways/us /communicates

-> Since its creation, the Internet has opened up lots of new ways for us to communicate

4. Most teenagers/ would rather/chat/their friends/ online/see/ them/in person

-> Most teenagers would rather chat with their friends online than see them in person

5. How/you/ think/people/ communicate/in the future?

-> How do you think about people to communicate in the future

6. Don't phone/me/9.30 a.m/ because/I/have/a/video conference /then

-> Don't phone me at 9.30 a.m because I will be having a video conference then

7. If/you/have/good/non-verbal/ communicationskills/ you/be/more successful/ meetings

-> If you have good non-verbal communication skills, you'll be more successful in meetings

8. Last year/he/decided/ stop /use/Facebook/personal communication/family and friends

-> Last year he decided to stop using Facebook for personal communication woth family and friends

điền vào mỗi khoảng trống trong các câu sau đây với A,AN,THE, or 0

1: He disappeared without __X____ trace and suddenly turned up on __A___ cold winter evening.

2: I thought he was ___THE__ honest man at ___THE___ first, but I was wrong.

3: London, ____THE____ capital of Great Britain, is on _____THE____ Thames.

4: He earned _____A____ living as ______AN____ office boy.

5: They're going to build ____A___ university on _____THE_____ outskirts of the city.

6: She asked her mother for ___X_____ permission to go to _____THE______ movies last night.

7: I heard her sing ____A___ popular song on ___X____ air yesterday.

8: Have ___THE_____ police found ____X___ person who stole your motorbike ?

9: This morning he had ___A_____ boiled egg for ____X____ breakfast.

10: ____THE____ man is slowly destroying ____THE___ environment.

I. circle the wrords which has a different stress from the othes
1. A.natural B.recycle C.protect D.insread
2. A.explain B.compost C.sandal D.milkman

II. Choose the word that has the underlined part pronounced differently from the others
3. A.tight B.revive C.describe D.victim
4. A.would b.wound C.could D.should

vt lại câu vs từ trog ngoặc:

1, I live in Ha Noi. My friend lives in HCM city. ( same city)

-> I and ny friends live in tha same city

2, Would you please give me a hand? (mind)

-> Would you mind giving me a hand?

3, It is interesting for me to study English culture. (find)

-> I find it interesting to study english culture

4, We spent nearly a week making these toys. (took)

-> It took us nearly a week to make these toys

5, Peter isn't trying to solve his financial problems. (effort)

-> Peter doesn't make every effort to solve his financial problems

Giúp mình với ạ ! (tìm lỗi sai và sửa)
1. During an -> the earthquake, you should be away from heavy furnitures or appliances.
A B C D
2. They watched -> were watching TV last night when the earthquake began.
A B C D
3. We'd better hurry, or the train might leaves -> leave without us.
A B C D
4. Neil Amstrong, the first man to walk on the moon, who -> bỏ taught at Cincinati University in the 1970s.
A B C D
5. My uncle has lived -> lived / used to live in Hanoi for 10 years, but he is now living in HCM City.
A B C D

my sister went to market .she wanted to buy some fruits (to infinitive)

--> My sister went to the market to buy some fruits

choose the word or phrase in each sentence that needs correcting

i ask my brother about -> for < ask (s.b) for s.th : hỏi xin cái gì/ hỏi vì cái gì > some money, but i know he'll not lend me because he's very mean

Bạn có thể sử dụng một trong só các từ điển sau để tra từ nhé sẽ có kèm theo VD

Bạn để lại link những câu bạn còn cần mn giúp nhé!

choose the best answer

1. I have to save much money..... myself a small house

A. bought B. to buy C. buying D. buy

2. choose the word whose underline part is pronounced differretnly from the other

A.songs B. feelings C. news D delights

3.He has never felt so.....in his life

A.embarassed B.embarass C.embarassing D.embarassingly

1. Lam was lazy , so he did not finish his homework

Because of_____being lazy/ Lam's laziness/ the fact that Lam was lazy, he didn't finish his homework_________

2. She has not visited her grandparents for 3 months

She last__________visited her grandparents 3 months ago___________

3. That is maryam Lan and Nga met her last week

That is__________maryam Lan who Nga met last week___________

4.“ I am going to spend my summer vacation in the countryside ”, Perter said to me

Peter told _________me that he was going to spend his summer vacation in the countryside_________

II. For each question, complete the second sentence so that it means the same as the first. Use the word in brackets. You may need to change the word. Write NO MORE THAN THREE WORDS.

Here is an example.

0. The bookshop is opposite the library. ____________________ a bookshop opposite the library. (THERE)

Answer: 0. There is

1. Don’t go out in the rain because you’ll get wet. If _________you go out__________ in the rain, you’ll get wet. (GO)

2. When she invites me, it is possible that I will go. _________If she invites__________ me, I’ll go. (IF)

3. Children don’t have to go to school on stormy days. If it is stormy, children __________won't have to____________ go to school. (HAVE)

4. You should decrease your use of water, or you will have to pay a lot. If you ___________don't decrease your___________ use of water, you will have to pay a lot. (REDUCE)

5. These trees need water or they will die. If you __________don't water____________ these trees, they will die. (WATER)

Thảo nào ban nãy làm mà thấy nó kì kì

1)I find it impossible to believe what he said (unbelievable)

-> I find what he said is unbelieveable

2) collecting butterflies is Mary's great passion( crazy)

-> Mary is crazy about collecting butterflies

Hi các bạn Trâm không rõ có phải là người mà bạn đăng bài đề cập tới là người phàn đối hay không nhưng mk sẽ nói vài điều nữa ngắn gọn thôi

1. mk ko ngăn cấm nha chỉ là nhiệm vụ của mình thôi bạn đăng đi đăng lại trôi bài của người khác họ cũng tức mà mk xóa và chỉ để lại 1 cái ghim lên CHH nhưng có war nên mk lại phải gỡ nó vì CHH là gương mặt của web mà nếu nó ko đẹp thì ấn tượng đầu tiên về web sẽ khác

2. Có vài bạn bất mãn với cách xử lí của mk mà có thể coi đó là láo hay là vô lí hay là ác thì tùy các bạn nghĩ mk chả áp đặt lên các bạn được nhưng khi nào các bạn đăng bài cần giúp mà nó bị trôi mãi vì có ai đó đăng đi đăng lại các bạn có tức ko có tìm người giải quyết hộ ko ? Ở vị trí CTV đôi khi làm việc thì có bạn ưa bạn ghét chịu thôi biết sao được

3. Như mk đã nói cuộc thi về lịch sử + địa lý cũng hay mà chỉ là cuộc thi vui thôi thì ok....

Rewite the sentences

1) if you don't eat less and get more exercise , you won't lose weight (otherwise)

-> eat less and get more exercise; otherwise, you won't lose weight

2) the police thought John murdered the old lady(suspected)

-> the police suspected John murdered the old lady

3) good friends are wonderful to have (it)

it's wonderful to have good friends

XIII. Find the one mistake (A,B,C or D) in these sentences and then correct them:

1. Some movie fans can't (A)separate fantasy(B) from reality and (C)confused -> confuse an actor with the character he plays

giải thích: bạn để ý chữ "can't" nhé và ngay sau đó ta có V " seperate" ko chia -> hợp lí và nối với từ "and" thì V phía sau giống vơi V trước tức là nó sẽ là V<bare>

2. We're (A)always (B)amazing -> amazed (C)by John's (D)incredible travel stories

giải thích: cái này thì nó thuộc phần kiến thức khi nào sử dụng Adj_ed và khi nào sử dụng tính từ Adj_ing

+ Adj_ed -> dùng để diễn tả cảm xúc của người nó về một sự vật hiện tượng nào đó

+Adj_ing -> dùng để diễn tả cảm giác cái gì đó khiến bạn cảm thấy thế nào

4. (A)The comedian worked (B)hardly -> hard to (C)entertain the (D)children in the hospital.

giải thích: hard <Adj> đc chyển thành adv cũng là "hard" còn hardly cũng là Adv nhưng mà là Adv chỉ tần suất mang nghĩa làm hiếm khi

5. (A)The critic's (B)description of the film made it (C)sound very (D)applealed -> applealing < cái này gần giống với câu 2>

5. Part of (A) the entertainment of seeing a movie is understanding how the director (B)combination -> combine a (C)range of different styles to (D)attain an artistic goal

giải thích: how là từ để hỏi tiếp sau đó là S ... và a range of... là O vậy ở đây ta cần một V thay cho là N

6. They (A)find (B)photography (C)very (D)interseted -> interesting -> kiến thức như ở câu 2

Rewrite the sentences without changing the original meaning

1) you should study harder if you want to get success (better)

-> you had better study harder if you want to get success

2) she loved to play badminton (keen)

-> she keened on playing badminton

3) i find it impossible to believe what he said.(crazy)

-> I find what he said is crazy

4) collecting butterflies is Mary's great passion

-> Mary's great passion is collecting butterflies

Rewrite the sentences without changing the original meaning

1) you should study harder if you want to get success (better)

-> you had better study harder if you want to get success

2) she loved to play badminton (keen)

-> she keened on playing badminton

3) i find it impossible to believe what he said.(crazy)

-> I find what he said is crazy

4) collecting butterflies is Mary's great passion

-> Mary's great passion is collecting butterflies

1.My teacher said" I hope you will get good marks next examination

-> My teacher said that she hoped I would get good marks next examination

2. The boss said to the secretary,"Do you want me to help you?"

-> The boss asked the secretary if she wanted him to help her

3. mrs.Carol said,"My family was very poor When I was achild"

-> Mrs Carol said that her family had been very poor when she had been a child

4.My brother said to me,"Where did you go with your friends yesterday?"

-> My brother asked me where I had gone with my friends the previous day