\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{5}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{5}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2}{5}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2}{5}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{10}\)

=> x+1=10

=>x=9

cacs bạn 

1/2x3+1/3x4+...+1/x(x+1)=2/5

=> 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/x - 1/x + 1 = 2/5

=> 1/2 - 1/x + 1 = 2/5

=> 1/x + 1 = 1/10

=> x + 1 = 10

=> x = 9

1.Chứng minh rằng: \(\frac{12n+1}{30n+2}\)là phân số tối giản.

2.Chứng minh rằng: \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+.....+\frac{1}{100^2}< 1\)

3.Chứng minh rằng nếu ab + cd + eg \(⋮\)11 thì abcdeg \(⋮\)11

4.Chứng minh rằng: 10²⁸ + 8 \(⋮\)72

5.Chứng minh rằng: Cho S = 3⁰ + 3² + 3⁴ + 3⁶ +....+ 3²⁰⁰²

a) Tính S

b) Chứng minh S \(⋮\)7

6.Chứng minh rằng: A = 3 + 3² + 3³ + 3⁴ +.....+ 3¹⁰⁰ \(⋮\)120

Cảm ơn Mai Phương nhiều nha

Bài 4:

a: Thay x=-1 và y=0,5 vào y=ax+1, ta được:

\(a\cdot\left(-1\right)+1=0,5\)

=>\(a\cdot\left(-1\right)=0,5-1=-0,5\)

=>a=0,5

b: Khi a=0,5 thì \(y=0,5\cdot x+1\)

Lập bảng giá trị:

Vẽ đồ thị: 

Bài 3:

a: 

b: Tọa độ A là:

\(\left\{{}\begin{matrix}x=0\\y=-x+4\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=0\\y=-0+4=4\end{matrix}\right.\)

Vậy: A(0;4)

Tọa độ B là:

\(\left\{{}\begin{matrix}x=0\\y=x-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=0-4=-4\end{matrix}\right.\)

vậy: B(0;-4)

Tọa độ C là:

\(\left\{{}\begin{matrix}-x+4=x-4\\y=x-4\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-2x=-8\\y=x-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=4-4=0\end{matrix}\right.\)

Vậy: C(4;0)

c: A(0;4); B(0;-4); C(4;0)

\(AB=\sqrt{\left(0-0\right)^2+\left(-4-4\right)^2}=\sqrt{0^2+\left(-8\right)^2}=8\)

\(AC=\sqrt{\left(4-0\right)^2+\left(0-4\right)^2}=\sqrt{4^2+4^2}=4\sqrt{2}\)

\(BC=\sqrt{\left(4-0\right)^2+\left(0+4\right)^2}=\sqrt{4^2+4^2}=4\sqrt{2}\)

Vì \(CA^2+CB^2=AB^2\)

nên ΔABC vuông tại C

=>\(S_{CAB}=\dfrac{1}{2}\cdot CA\cdot CB=\dfrac{1}{2}\cdot4\sqrt{2}\cdot4\sqrt{2}=2\sqrt{2}\cdot4\sqrt{2}=16\)

Bài 2:

a: Thay x=2 và y=0 vào y=(m-2)x+m-1, ta được:

\(2\left(m-2\right)+m-1=0\)

=>\(2m-4+m-1=0\)

=>3m-5=0

=>3m=5

=>\(m=\dfrac{5}{3}\)

b: Thay x=0 và y=2 vào y=(m-2)x+m-1, ta được:

\(0\cdot\left(m-2\right)+m-1=2\)

=>m-1=2

=>m=3

Bài 1:

a: 

b: 

c: 

60 độ. Mình tính theo công thức:

Mà chỉ là công thức nhanh thôi.

* Địa hình châu Mĩ thay đổi từ tây sang đông:

– Dọc bờ biển phía tây là hai dãy núi cao và đồ sộ Coóc-đi-e và An-đét.

– Ở giữa là những đồng bắng lớn: đồng bằng Trung tâm và đồng bằng A-ma-dôn.

– Phía đông là các núi thấp và cao nguyên: A-pa-lát và Bra-xin.

Địa hình châu Mĩ thay đổi từ tây sang đông:

- Dọc bờ biển phía tây là các dãy núi cao và đồ sộ: Cooc-đi-e và An-đet.

- Giữa là những đồng bằng lớn: đồng bằng Trung tâm và đồng bằng A-ma-dôn.

- Phía đông là các dãy núi thấp và cao nguyên: dãy A-pa-lát, cao nguyên Guy-an, cao nguyên Bra-xin.

Địa hình châu Mĩ thay đổi từ tây sang đông:

- Dọc bờ biển phía tây là các dãy núi cao và đồ sộ: Cooc-đi-e và An-đet.

- Giữa là những đồng bằng lớn: đồng bằng Trung tâm và đồng bằng A-ma-dôn.

- Phía đông là các dãy núi thấp và cao nguyên: dãy A-pa-lát, cao nguyên Guy-an, cao nguyên Bra-xin.

REVISION FOR MID-TERM TEST

Part A. Pronunciation

Choose the word whose underlined part is pronounced differently

1. A.high                B.rough           C.tough           D.laugh

2. A.bag                B.frog              C.original     D.flag

3. A.hurricane       B.scarf            C.city              D.cracker

4. A.labour             B.flour           C.favour          D.honour

5. A.fear                B.earn             C.hear             D.clear

6. A.photo              B.favour       C.volleyball     D.laugh

7. A.cinema          B.comic           C.cake             D.cool

8. A.guess              B.big                C.sign            D.again

9. A.picture            B.sure              C.nurture        D.nature

10. A.rehearse      B.return           C.first            D.collector

11. A. half                B. fan               C. ferry           D. of

12. A. laugh              B. although     C. cough           D. paragraph

13. A. worker          B. teacher        C. sunburn      D. better

14. A. nurse             B. girl               C. pottery      D. return

15. A. melody        B. refer            C. surf             D. bird

Part B. Multiple choice

Exercise 1. Choose the best answer to complete the sentences

1. Phuong ____ drinking soft drinks because It’s not good for her health.

A. enjoys          B. hates         C. likes              D. loves

2. If you want to live long, you ____ eat much red meat.

A. have to                 B. shouldn’t              C. should           D. needn’t

3. Don’t read in bed, ____ you’ll harm your eyes.        

A. so         B. but               C. and                D. or

4. ________ judo is my brother’s hobby.          

A. Taking  B.  Doing          C. Going     D. Having

5. My father enjoys ________ wood.                       

A. carve     B. to carve        C. carving       D. in carving

6. I find making pottery ________                  

A. boring  B. is boring       C. bored     D. bores

7. Lan thinks ice-skating ________  

A. very dangerous      B. dangerous     C. is dangerous         D. danger

8. He looks so tired. He can’t keep his eyes open! He’s very hot too. I think he has

A. stomachache    B. a temperature          C. a cough                D. the flu

9. They like playing  football because it helps them ________

        A. relax            B. relaxing                C. to relaxing             D. relaxes

10. ________ glass bottles is my sister’s hobby.

        A. Finding         B.  Doing           C.  Talking                  D. Collecting

11. My mother dislikes________ to POP music.

A. listening                B. listens           C. listen           D. listened

12. You'll become healthier if you consume ________ soft drinks.

A.more                      B.less                        C.much                      D.fewer

13. My friend has decided to use ___________ electricity by using more solar energy instead.

A.more                      B.less                               C.much              D.fewer

14. It’s a pity that I ________ “Green Summer” programme last year.

A. don’t join              B. didn’t join           C. won’t join              D. haven’t joined

15. The examination is coming. Watch ________ TV

A. fewer           B. much             C. less                      D. more

16.  A: - This weekend I’m going to the SOS village to teach children there. // B: I ________ you.

A. have joined            B. will join                C. am joining             D. join

17. I find ________ football very useful.

A. play                            B. playing            C. to play         D. plays

18. You should spend your free time ________ books

        A. read                      B. to read        C. reading             D. to reading

19. I find this hobby is relaxing. I feel much better when I raise my voice to make musical sounds.

My hobby is ________

A. collecting                       B. cooking                 C. playing          D. singing

20. My father shares this hobby with me. We usually spend hours in the evening reading the instructions and creating small planes or cars. Our hobby is ________.

A. carving eggshells            B. making models      C. collecting things    D. carving wood)

21. You have a cough. Drink ________ warm water.

A. fewer                    B. much             C. less                       D. more

22. Don’t worry. I ________  you lose weight.

A. will help                        B. help                     C. helping         D. helped

23. Some people have a very bad habit of ________ in public. They spit anywhere.

A. smoking                 B. littering                        C. spitting                D. eating fast

24. It’s harmful for your body if you eat a lot of ________.

A. fruit and vegetables.      B. fruit                    C. vegetables              D. fast food

25. Nam wants to lose weight, ______ he began jogging last Sunday.

A.or          B.and                C.but        D.so

26. I ______ playing board games interesting because I can play them with my friends.

A.think             B.find               C.say         D.tell

27. This summer Lan _______ three volunteer activities.

A.has participated in         B.participated in        C.participates in        D.participating in

28. Before moving to Ha Noi, my parents _______ in Hai Phong.

A.have lived               B.have been living              C.lived                       D.live

29. The children _____ painting the mural over graffiti yet.

A. didn’t finish                B. haven’t finished               C. are finishing  D. hasn’t finished

30. ____ the elderly people in the nursing home so far, Julia?

A. have you visited             B. Did you visit          C. Do you visit           D. Are you visiting

31. People ______ between 1,600 and 2,500 calories a day to stay healthy

A. are needing               B. needed              C. have needed          D. need    

32. The room smells bad. Somebody ______ in here  

A. smoke                       B. has smoked               C. smoked          D. will smoke    

33. In that area, it _______ difficult to find enough food in winter.

A. has been                   B. was                   C. is                  D. will be

34. He ate a lot of junk food, so he ______ fat quickly

A. got                           B. gets                  C. has gotten             D. is getting                                         

35. I’ve ______ seen this film. Let’s watch something else. 

A. never                B. ever              C. already          d. yet

36. Be a Buddy was founded _______ to help the street children

A. since 2010                B. in 2011                      C. every year             D. until 2011

37. We often organize concerts to _______ funds for poor children.

A. donate          B. raise             C. volunteer               D. grow

38. Vietnamese people have had the ____ of helping one another since the early days of the country.              

A. custom         B. legend          C. tradition               D. religion

39. Community service is the work we do for the _______ of the community.

                            A. benefits            B. forces   C. problems               D. events

40. We’ve decided to clean up the lake ______ it is full of rubbish.

A. so         B. therefore              C. but                       D. because

Exercise 2. Mark the letter A, B, C or D to indicate the word(s) CLOSEST in meaning to the underlined word(s) in each of the following questions.

1. I don’t know why girls collect things. It’s a piece of cake.

A. unusual         B. easy                      C. boring           D. strange

2. Will you take up making pottery in the future?

A. continue                B. stop                      C. intend           D. start

3. You sound down Phong, are you OK?

A. feel sad                B. look happy             C. are ill                    D. seem tired

4. People should have between 1,600 and 2,500 calories a day to stay in shape.

A. be on a diet                   B. be fit and healthy          C. be full           D. finish your work

5. Why do people listen to Dr.Law’s advice?

A. view                      B. idea                      C. tip        D. experience

Exercise 3. Mark the letter A, B, C or D to indicate the word(s) OPPOSITE in meaning to the underlined word(s) in each of the following questions.

1.  I eat junk food all the time, so I am putting on weight.

A. increasing             B. gaining          C. losing            D. getting

2.More and more children are becoming obese.

A. underweight          B. fat                       C. chubby          D. overweight

3. Mi has the same hobby as Elena.

A. similar                  B. different              C. interesting            D. like

4. Collecting glass bottle is a useful hobby because it can help save the environment.

A. dangerous                     B. benificial                       C. good                      D. harmful

5. What can we do to reduce traffic jams?

A. increase                        B. get out of                     C. prevent                 D. avoid       

Exercise 4. Mark the letter A, B, C or D on your answer sheet to indicate the most suitable response to complete each of the following exchanges.

1. ‘I think model making is an expensive hobby.’ ‘____ it’s incredibly cheap.’

    A. You’re right      B. Certainly    C. No matter        D. Not at all

2. A: But it's ten o'clock already. Let's go out. 

    B: _______ . I think I'll stay at home and play Zooniverse on my computer. 

A. Yes, count me out          B. No, count me out          C. No, count me on     D. Yes. Wait for me.

3. A: I’ve got flu.                        // B: _____

A. Spend less time in front of screens                        B. Stay at home and have a rest

C. Apply an aloe vera lotion and drink lots of water      D. Eat less junk food and do more exercise.

4. Thanh: “Would you like to have some more ice cream, Binh?”//                Binh: “ ______”

A. Thanks. I’d love to.                B. Here you are.                C. I’m looking forward.        D. I do, too.

Question 20. Jim: "What a beautiful carved eggshell!"  //   Nam:" ________."

        A. You’re welcome              B. It’s very nice of you to say so

        C. I’m glad to tell you so     D. I don’t mind if you say that

Exercise 5. Mark the letter A, B, C or D to indicate the underlined part that needs correction in each of the following questions.

1. Eating carrots regularlyhelp you see better.

      A                             B           C             D

2. I collectedtoy cars since I was ten years old.

              A                  B                  C                D

3. We like playing karate because it isuseful for my health.

                     A                            B            C        D

4. Does  he  stillmake models next year?

        A              B         C                          D  

5. Tom washes his hand a lot, or he doesn’t have flu.

                  A                           B       C                                D 

6. Stay outdoors and do less  physical activities. You will be healthier.

       A                                     B                        C                                            D

7. She feelsitchy all over. I think she has a allergy.

              A         B                        C                     D

8. She didn’t done any vollunteer worklately.

              A                    B                           C          D

9. My daughter has donatedblood five monthsago.

                                       A               B                  C          D

10. Nga haseverfinished all the housework.

                 A      B           C             D  

Part C. Reading

Exercise 1: Read the passage and choose the correct answer A, B, or C

What you choose makes what you are. Here are four things you can do to make you happy.

Enjoy adventures

Visit a new place, do a new thing, or talk to a new person. This brings you new knowledge and experience.

Laugh louder

Laughter makes you happy, and it has a magic power of making the hearer happy, too. Laughter is like medicine. It makes people live longer.

Love others fully

Express your love more often. Don't keep it to yourself. You might not know how much you can make yourself and others happy by doing so.

Live positively

Remember that everybody has some valuable skills and abilities to contribute to life. Nobody is NOBODY. Learn to love and respect yourself and others. You'll feel happy.

1. What can you do to get more knowledge?

A.Visit a new place.            B.Use your skills to contribute to life.        C.Love people around you.

2. What can you do to live longer?

A.Take adventures.            B.Laugh louder.                          C.Live positively.

3. How good is it if you have a positive attitude?

A.You can laugh more.                B.You can do more things.          C.You can feel happy.

4. What is the purpose of this passage?    

A.To change people's ideas about life.

B.To give some advice on how to live happily.

C.To advise people to love others fully.

Exercise 2:Fill in each blank with a suitable word to complete the text

WHY DO JAPANESE PEOPLE LIVE LONGER?

The average lifespan of the Japanese is 78 for males and 85 for females, the (1) ......................................... in the world. The main secret lies in their food. The Japanese eat a lot of tofu, which is (2) ......................................... from soybeans. Tofu contains a lot of vegetable protein, calcium and Vitamin B. It doesn’t contain much fat, and it doesn’t provide (3) ......................................... calories. Seafood like fish and vegetables play an (4) ......................................... role in their diet, too. They cook the seafood with less  cooking oil and less time. For each meal, they have more  dishes on the table than us but they eat only a (5) .........................................  everything, never stuffing themselves. Japanese people also work very hard and do more  exercise. This helps them burn the calories off easily.

Exercise 3:Choose the corect word marked A, B, or C to fill in the folowing passage.

There are many reasons (1)________ it is important to have a hobby. First of all, a hobby can be a remedy for your (2)________. Because it is the activity you choose for yourself, it will always give you pleasure and (3)________ you relax. Even if you just spend a little time enjoying your hobby, you can see the difference (4)________ your spirit. Second, some hobbies can also (5)________ you financially. Many old people enjoy gardening. They grow a lot of trees and vegetables, so they can sell them for some money. In (6)________, a hobby can help you connect with other people. If you like collecting stamps, you can (7)________ a stamp club to share your albums with other collectors. If your hobby is carving eggshells, you can give your products to your friends (8)________ gifts.

1. A.for                     B.why                        C.because

2. A.happiness           B.pain                       C.tiredness

3. A.help                   B.have                       C.do

4. A.for                    B.in                            C.on

5. A.harm                  B.give                        C.benefit

6. A.addition             B.general                    C.conclusion

7. A.take part           B.go                           C.join

8. A.like                    B.as                          C.for

Exercise 4:Readthe flyer and tick T (true) of F (false)

START YOUR VOLUNTEER WORK TODAY!

Step 1: Think about why you want to volunteer. Is it because you want to help other people and the community? Do you want to meet new people? Do you want to get work experience? Do you want to make a difference to the world? Do you want to share things with people who are in need?

Step 2: Consider the volunteer work you find meaningful, and how much time you can spend on it. Think about what you love to do. Do you want to tutor younger children once a week? Do you want to work in a charity shop? Or do you want to take part in a community clean-up programme?

Step 3: Look for an organisation or activity in your community. Sign up for it. Stay committed. Ask for help if needed. Have fun as well as you will achieve more if you love what you do.

1.It's important that you know why you want to volunteer.

2.You should do work that is meaningful to you.

3.You shouldn't ask for help when volunteering because you are the one who is expected to give help.

4.You shouldn't have fun because volunteering is a serious job.

Part D. Writing

Exercise 1. Mark the letter A, B, C or D on your answer sheet to indicate the sentence that is closest in meaning to the original sentence in each of the following questions.

1. Mrs. Nga started doing volunteer work in 2019.

A. Mrs Nga did  volunteer work since 2019.

B. Mrs Nga has done  volunteer work in 2019.

C. Mrs Nga has did volunteer work for 2019.

D. Mrs Nga has done volunteer work since 2019.

2. Nam has donated books to street children  since he was 11 years old. 

A. Nam began to donate books to street children  when he was 11 years old. 

b. Nam began donating books to street children  since he was 11 years old. 

C. Nam began to donate books to street children  from he was 11 years old. 

D. Nam has begun to donate books to street children  since he was 11 years old. 

3. We have painted this mural for ten days.

A. We started to paint this mural for ten days.

B. We have painted this mural ten days ago.

C. We started painting this mural ten days ago.

D. We have painted  this mural since ten days ago.

4. This is the first time we have raised a fund for people in need.

A. We have ever raised a fund for people in need before.

B.  We have never raised a fund for people in need before.

C. We raised a fund for people in need before.

D. We  are going to raise a fund for people in need for the first time.

5. The last time I visited this nursing home was six months ago.

A. I have visited this nursing home for six months.

B. I haven’t visited this nursing home for six months.

C. I last visited this nursing home for six months.

D. I haven’t visited this nursing home six months ago.

6.  People in the countryside have less stress. They usually live longer.

A. People in the countryside have less stress because  they usually live longer.

B. Although people in the countryside have less stress, they usually live longer.

C. People in the countryside have less stress, so they usually live longer.

D. People in the countryside have less stress so they usually live longer.

7. Mrs. Lien wants to drink some cold water. She has a sore throat.

Mrs. Lien wants to drink some cold water, or he has a sore throat.

Although Mrs. Lien wants to drink some cold water, he has a sore throat.

Mrs. Lien has a sore throat, so she wants to drink some cold water.

Mrs. Lien wants to drink some cold water, but he has a sore throat.

8. She likes to collect books. It’s her favourite hobby.

She is interested on collecting books. It’s her favourite hobby.

She is interested in collecting books. It’s her favourite hobby.

She enjoys to collect books. It’s her favourite hobby.

She loves in collecting books. It’s her favourite hobby.

9. Nam loves to make pottery, so he goes to Bat Trang Village every Sunday.

Making pottery is Nam’s hobby because he go to Bat Trang Village every Sunday.

Making pottery is Nam’s hobby, so he goes to Bat Trang Village every Sunday.

Nam’s hobby is make pottery, so he goes to Bat Trang Village every Sunday.

Nam goes to Bat Trang Village every Sunday because he dislikes making pottery.

10. I find carving wood boring because it takes time.

I think carving wood boring because it takes time.

I think carving wood is boring because it takes time.

I think carving wood was boring because it takes time.

I think carve wood is boring because it takes time.

11. My sister/ not like/ ice-skating/ because/ think/ it/ dangerous.

My sister doesn’t like ice-skating  because she think (that)  it is dangerous.

My sister doesn’t like ice-skating  because she think it dangerous.

My sister don’t like ice-skating  because she think (that)  it is dangerous.

My sister doesn’t like ice-skating  because she thinks (that)  it is dangerous

12. It’s a good idea to do exercise regularly.

A. You should do exercise regularly.

B. You should do exercise regularly is good.

C. Do exercise regularly is  a good idea.

D. It’s a good idea you should doing exercise regularly.

13. I have oil skin, so I wash my face regularly.

A.  I wash my face regularly, because I have oil skin

B. Although I wash my face regularly, I have oil skin

C.  I wash my face regularly because I have oil skin

D. I wash my face regularly, but I have oil skin

Exercise 2. Mark the letter A, B, C or D on your answer sheet to indicate the most meaningful sentence written from the given words.

14. I / think / you / take up / jogging / because / it / suitable / health condition.

A.  I think you shouldn’tup  jogging because it is suitable for your health condition.

B. I think you should take up jogging because it is suitable for your health condition.
C. I think you should take up jogging because it is suitable with your health condition.

D. I think you should taking up jogging because it is suitable for your health condition.

15. She/ the / kind-hearted /woman / I/ ever/ met.

A. She is the most kind - hearted woman I have never met.

B. She is most kind - hearted woman I have ever met.

C. She is the most kind - hearted woman I have ever met.

D. She is most kind - hearted woman I have met.

16. How many / plays /  Shakespeare / write?
A. How many plays did Shakespeare write?

B. How many plays has Shakespeare written?

C. How many plays does Shakespeare write?

D. How many plays did Shakespeare wrote?

17. It / easy / get flu / so / we / should / try / keep / clean / more

A. It easy to get flu, so we should try to keep clean more.

B. It’s easy to get flu, so we should try to keeping clean more.

C. It’s easy to get flu, so we should trying to keep clean more.

D. It’s easy to get flu, so we should try to keep clean more.

18. You / need / patient / to make / beautiful / gifts / eggshells.

A.  You need to be patient to make beautiful gifts from eggshells.

B. You need to be patient to make beautiful gifts with eggshells.

C. You need to be patient to making beautiful gifts from eggshells.

D. You need  be patient to make  beautiful gifts of eggshells.

Exercise 3. Mark the letter A, B, C or D on your answer sheet to indicate the most meaningful sentence arranged from the given words.

19. apple / keeps / An / day / doctor / a / the / away.

A. An apple keeps the doctor away a day.

B. An day  a apple keeps the doctor away.

C. An apple keeps the doctor a day away.

D.  An apple a day keeps the doctor away.

20. sleep / are / the / cures / A / good / and / best / laugh / a / long.

A. A long laugh and a good sleep are the best cures.

B.  A good laugh and a long sleep are the best cures.

C. A good laugh are the best cures and a long sleep.

D. A good laugh and a long sleep cures are the best.

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