a, với n thuộc Z
Để A là một số nguyên thì 3n + 1 chia hết cho n+1
mà n + 1 chia hết n +1
=> (3n+1) - 3. (n+1) chia hết cho n+1
<=> (3n+1)-( 3n +3) chia hết cho n+1
<=> 4 chia hết cho n+1
=> n+1 thuộc Ư(4)= {+-1; +-4; +-2}
nếu ............
cho biểu thức A=n+1/n-2(n thuộc Z)
a)tìm n để A là phân số
b)tìm n thuộc Z để A thuộc Z
c)tìm n thuộc Z để A có giá trị lớn nhất
Cho biểu thức A = n+2/n-5
a, Tìm điều kiện của n để A là phân số
b,Tìm n để A có giá trị nguyên
mik làm được phần a rồi chỉ còn phần b thôi
giúp mik nhé các bn !!
Bài 1: Cho A = n-2/n+3 
.Tìm giá trị của n để:
a) A là một phân số.
b) A là một số nguyên.
Bài 2
a) Tìm số tự nhiên n để phân số B= 10n-3/4n-10
đạt giá trị lớn nhất. Tìm giá trị lớn nhất đó.
b) Tìm các số tự nhiên x, y sao cho: 
x/9 - 3/y = 1/18
Bài 3: Một người bán năm giỏ xoài và cam. Mỗi giỏ chỉ đựng một loại quả với số lượng là: 65 kg; 71 kg; 58 kg; 72 kg; 93 kg. Sau khi bán một giỏ cam thì số xoài còn lại gấp ba lần số cam còn lại. Hãy cho biết giỏ nào đựng cam, giỏ nào đựng xoài?
Cho biểu thức \(\frac{15}{\left(n-3\right)\left(5-n\right)}\) ( n thuộc Z)
số nguyên n phải thỏa mãn điều kiện jgif để biểu thức trên là phan số?
Bài 1: Cho M = 48+20+a với a là số tự nhiên
Tìm a để M chia hết cho 4, không chia hết cho 4
Bài 2: Tích A =1.2.3.4.5....20 có chia hết cho 400 không
Bài 3:
a, Tìm số tự nhiên n để n+10 chia hết cho n+1
b, Tìm số tự nhiên n để3n +40 chia hết cho n+2
Chứng minh với mọi STN n thì :
n ( n + 2021 ) là số chẵn
Sông là j ? Nêu giá trị của sông ?
Lưu vực sông là j ?
Thuỷ chế sông phụ thuộc vào yếu tố nào ?
Hệ thống sông là j ?
Hãy tìm từ giống với các từ sau :
1. This - these
1. kind (a) – (a)
2. That -
2. Favour (n) – (a)
3. Grill (v) – (a)
3. Fame (n) – (a)
4. Fry (v) – (a)
4. Vietnam (n) – (a)
5. Help (v) – (a)
5. France (n) – (a)
6. Friend (n) – (a)
6. Japan (n) – (a)
7. Friend (n) – (a)
7. Interest (v) – (a)
ai giải giúp
Ex2: Stress
Với N , adj ( 2 âm tiết ) à 1st , V ( 2 âm tiết) à 2nd
1.A. yoga B. music C. relax D. hobby 2 – 1
2. A. dirty B. around C. noisy D. peaceful
3. A. future B. locate C. solar D. wireless
4. A. surround B. cottage C. robot D. planet
5.A. reuse B. reduce C. prepare D. mention
6.A. bottle B. paper C. symbol D. reuse
7. A. picnic B. reduce C. plastic D. water
8. A. channel B. programme C. distance D. control
9. A. garden B. summer C. support D. planet
10.A. replace B. supply C. provide D. sorrow
11. A. control B. giant C. solar D. software
12.A. picnic B. reduce C. plastic D. water
Ex3. MUTIPLE CHOICE
A. Thì quá khứ đơn – từ để hỏi – giới từ
0."Do you think that our houses will be___space?"
A.in B.on C.at D.to
1. We also watch films ______smart phones.
A.in B.at C.on D.to
2. "Do you think we will________holiday to the Moon?"
A.go B.go on C.go on the D.go for
3." ___do you do judo?" - "Twice a week.".
A. When B. Where C. How often D. Why
4. ___sports do you like watching on TV? .
A. How B. What C. Do D. How often
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 I am not very good____ playing football.
A. at B. in C. on D. for
7.My friend Mark is very good ________ volleyball. He plays volleyball very well.
A. in B. on C. at D. with
8. We often go swimming ________ Sunday morning.
A. in B. on C. at D. for
9.________ are the Olympic Games held? - Every four years.
A. When B. Where C. How long D. How often
10. I _______ born on the first of May.
A. were B. was C. are D. is
11.There .________ any eggs in the packet when I______ the kitchen.
A. was/ come B. were/ come C. was/ came D. were/ came
12.__________. you attend yoga class when I___________ at home?
A. Did/ stayed B. Didn’t/ didn’t stayed
C. Did/ didn’t stayed D. Did/ stayed
13.The meeting .___________5 minutes ago.
A. finished B. finish C. did not finish D. did finish
14. When _______ she _____________ the report?
A. do/ finish B. did/ finished C. did/finish D. didn’t/ finished
15. I ___________. my close friend a cushion for her chair yesterday.
A. gave B. give C. gived D. given
16.Yesterday, I ___________ to a souvenir shop near the exit of the aquarium.
A. go B. gone C. went D. goes
B. Thì hiện tại hoàn thành
17.I_____the money from him yet.
A. haven’t received B. don’t receive
C.will receive D. am receiving
18. They_____ for nearly 50 years.
A. marry B. have been married
C. married D.will marry
19. How many times ______there so far? A few times.
A. have you been B. would you be
C. were you D. had you been
20.We_____ almost every lesson in this book so far.
A. study B. studies C. has studied D. have studied
21. We_____that television program.
A. never watch B. not never watch
C. have never watched D. has never watched
22. Up to then, I_____such a big fire.
A. have never seen B. had never seen
C. never seen D. never see
23. I____her since I _____a student.
A. know/ am B. knew/ was
C. have known/ am D. have known/ was
24. _____get tired of answering the same questions every day?
A. Have you ever B. Had you ever
C. Do you ever D. Are you ever
C. Thì tương lai đơn
25.We _____ have time to help you tomorrow.
A. may B. will C. must D. could
26.In the future, machines ______all the work for us.
A. are doing B. will do C.were doing D. do
27.I hope I _____ find it.
A. will B. could C. shall D. must
28. ______________________ (people/ live) on the Moon someday?
29. What ______________________ (the cars/ look) like in 20 years?
30. ______________________ (robots/ replace) humans?
31. Where ______________________ (you/ be) in 2040?
32. When ______________________ (humans/ five) on other planets?
33. _________________ (houses/ be) more environmentally friendly in the future?
34. ______________________ (computers/ take) over the world?
35. How ______________________ (fashion/ change)?
D. Câu điều kiện loại I
36. If we_______ waste paper, we will save a lot of trees.
A. repeat B. recycle C. rewrite D. remake
37. If it _____ fine tomorrow, we will go to the coast.
A. will be B. was C. is D. being
38. You_____ yourself ill if you don’t eat properly.
A. were to make B. make C. would make D. will make
39. If people_______-public transport, there will be less pollution.
A. used B. use C. could use D. will use
40. I______ you if you need my help.
A. am helping B. could help C. will help D. helped
41. Come on! _____ we hurry, we’ll miss the plane!
A. if B. unless C. in case D. supposed
42. If I see him, I _____ him a gift.
A. give B. would give C. will give D. gave
43. If you don’t keep silent, you ________wake the baby up.
A. will B. would C. had D. can
44. 1. If the train is late, we ………………….. to the office.
A. walk B. will walk C. would walk D. walks
45. She …………………….. if she has time.
A. calls B. would call C. will call D. calling
46. If it ……………………… too much, I will buy the smaller one.
A. costs B. will cost C. would cost D. cost
47. If the class. ………………………. full, we will find another one.
A. are B. will be C. were D. is
48. What will we do if the taxi ………………………..?
A. don’t come B. didn’t come C. doesn’t come D. had not come
E. Câu so sánh hơn nhất
49. Do you know__________ drink in Viet Nam?
A. popular B. more popular C. the most popular D. popularest
50. She is ______ singer I’ve ever met.
A. worse B. bad C. the worst D. badly
51. She sings _______ among the singers I have known.
A. the most beautiful B. the more beautiful
C. the most beautifully D. the more beautifully
52. She is_________ student in my class.
A. most hard-working B. more hard-working
C. the most hard-working D. as hard-working
53. She runs ___________ in my class.
A. the slowest B. the most slow C. the slowly D. the most slowly
54. She is the most ___________ girl in our class.
A. intelligent B. intelligentest C. tall D. tallest
55.Lan is the most_____________ student in my class.
A. hardwork B. hardworking C. good D. best
56. This book is the ___________________of all
A. bored B.boring C. more boring D. most boring
57. He finished the test _____________of all.
A. rapidly B. the most rapidly C. most rapidly D. more rapidly
58. That flight ticket is _________ of all.
A. expensive B. the most expensive C. more expensive D. the expensive
Ex 4: Closest in meaning
59. I'm sorry. I didn't mean to interrupt you. Please, go on and finish what you were saying.
A. talk B. quit C. continue D. stop
60. They decided to postpone their journey till the end of the month because of the epidemic.
A. take up B. turn round C. put off D. do with
61. At weekends the city centre is always packed with people.
A. busy B. crowded C. full D. quite
62. It’s a good idea to swap books with our friends.
A. change B. send C. exchange D. pull
63. Jack, come and give me a hand with cooking.
A. prepare B. help C. do D. make
64. My mother : “You have to look after your younger sister when I go out”
A. take after B. take care of C. take over D. look up
65. Who is going to look after your children when you’re at work?
A. search B. regard C. take care of D. help
66. I want to take part in the trip to the countryside.
A. participate in B. look after C. take over D. take off
67. We had a fantastic time in Ha Noi.
A. wonderful B. interesting C. good D. exciting
Ex5: Communication:
68. A: “ Thank you for helping me yesterday” B: …
A. Not at all. B. It’s my pleasure. C. It’s my fault. D. Congrats!
69. Havy: “Thanks for your help, Judy.” Judy: “……..”
A. With all my heart B. Never remind me
C. It’s my pleasure D. Wish you
70. Alice is talking to Mary about their plan of the weekend.
Alice: "How about visiting the church this weekend?" Mary: "......"
A. Well done B. Not at all C. That's a good idea D. No, thanks
71- Peter: “What a lovely house have!” - Tom: “__________”
A. No problem B. Of course not, it’s not costly.
C. Thank you. Hope you will drop in. D. I think so.
72. Mary: “How did you get here? ” David: “___________”
A. I came here yesterday B. The train was late
C. I was tired. D. I came here by train
73. “Congratulations to you on winning the first prize”- “……………”
A. You’re welcome. | C. It’s my pleasure |
B. Thanks a lot | D. It doesn’t matter |
74. “What a wonderful picture!” – “……………”
A. I’m glad to hear that | C. It’s nice of you to say so |
B. You don’t need to say so | D. Of course, I think so |
75. Daughter: “Dad! I have just won the first prize in the Olympic English Contest.”
Father: “__________________”
A. Congratulations! B. That’s a good idea.
C. Thank you. D. I’d love to.
76. Peter: “Don’t fail to send your parents my regards.”
Susan: “_____.”
A. You’re welcome. B. Thanks, I will.
C. Good ideas, thanks D. It’s my pleasure.
77. “I’ve passed my driving test”- John:
A. Congratulation. B. That’s good idea.
C. It’s nice for you to say so D. Do you?
78. A: “ Would you like to go swimming with me tonight?” B: “__________”
A. Yes, I will B. No, I won’t C. Yes, I’d love to D. Never
Ex 6: Writing:
Dang 1: HTHT va QKD
79. I started collecting stamps last winter.
A. I have collected stamps since last summer.
B. I have started collecting stamps since last summer.
C. I have collected stamps for last winter
D. I have not collected stamps before
80. They began playing tennis in the spring of 2012.
A. They have playing tennis since the spring of 2012.
B. They haven’t played tennis since the spring of 2012.
C. They have played tennis since the spring of 2012.
D. They have played tennis for the spring of 2012.
81. My father stopped smoking in 2014.
A.My father hasn’t smoked since 2014.
B. My father has smoked since 2014.
C. My father hasn’t smoked for 2014.
D. My father hasn’t smoked in 2014.
82. I began working as an activist when I was 20 years old.
A. I have working as an activist since I was 20 years old.
B. I have been working as an activist since I was 20 years old.
C. I have worked as an activist for I was 20 years old.
D. A. I have worked as an activist since I was 20 years old.
83. We started learning English 10 years ago.
A. We have learned English for 10 years.
B. We has learned English for 10 years.
C. We have learned English since 10 years.
D. We have learn English for 10 years.
Dang 2: So sanh hon nhat
84. English is more popular than any other languages in the world.
A. English is more popular language in the world.
B. English is the popular language in the world
C. English is the most popular language in the world
D. English is the least popular language in the world
85.Lan is more intelligent than any girls in the class.
A. Lan is the intelligentest girl in the class
B. Lan is the most intelligent girl in the class
C. Lan is intelligent in the class
D. Lan is the least intelligent girl in the class
86. Noone in the class is more patient than Kien.
A. Kien is the more patient in the class
B. Kien is the least patient in the class.
C. Kien is the patient in the class.
D. Kien is the most patient in the class.
Dang 3: Đặt câu hỏi cho từ gạch chân:
87. My mother watches TV three hours a day.
A. How many hours does your mother watch TV a day?
B. When does your mother watch TV a day?
C. How often does your mother watch TV a day?
D. How many hours do your mother watch TV a day?
88. My uncle often goes fishing on weekends.
A. When does your uncle often goes fishing ?
B. When does your uncle often go fishing ?
C. Where does your uncle often goes fishing ?
D. What does your uncle often goes fishing ?
89. Tom put the remote control on the bookshelf.
A. Where did Tom put the remote control?
B. Where do Tom put the remote control?
C. Why did Tom put the remote control?
D. When did Tom put the remote control?
90. They go to the English club twice a week.
A. When do they go to the English club?
B. What do they go to the English club?
C. How often do they go to the English club?
D. How often do they goes to the English club?
Dạng 4: Dùng từ gợi ý viết thành câu hoàn chỉnh:
91. If/ we/ cycle/ school/ every day/ we/ keep/ air/ clean and fresh
A. If we cycled to school every day, we will keep the air clean and fresh.
B. If we cycle to school every day, we keep the air clean and fresh.
C. If we cycle to school every day, we will keep the air clean and fresh.
D. If we cycle to school every day, we will keep the air clean and fresh.
92. If/ we/ use/ buses/ we/ reduce/ pollution.
A. If we use buses, we will reduce pollution.
B. If we will use buses, we reduce pollution.
C. If we uses buses, we will reduce pollution.
D. If we use buses, we reduces pollution.
93. Although/ I/ like/ cartoons/ I/ not/ watch/ them/ much.
A. Although I likes cartoons, I do not watch them much.
B. Although I like cartoons, I not watch them much.
C. Although I like cartoons, I do not watch them much.
D. Although I likes cartoons, I not watches them much.
94. Australians/ enjoy/ Christmas/ although/ Christmas season/ summer.
A. The Australians enjoy Christmas although Christmas season is in summer.
B. The Australians enjoys Christmas although Christmas season is in summer.
C. Australians enjoy Christmas although Christmas season is in summer.
D. The Australians enjoy Christmas although Christmas season in summer.
95. Although/ my mother/ tired/ she/ have to/ finish/ housework.
A. Although my mother tired, she has to finish her housework.
B. Although my mother is tired, she have to finish her housework.
C. Although my mother is tired, she had to finish her housework.
D. Although my mother is tired, she has to finish her housework.
