Cho nửa đường tròn tâm O đường kính AB. Vẽ tiếp tuyến d tiếp xúc với đường tròn tại C. Từ A và B kẻ AM và BN vuông góc với đường d. Gọi D là hình chiếu của C trên AB. Chứng minh CD^2 = AM.BN

cho tam giác ABC vuông tại A. Đường cao AH, trung tuyến AM. Gọi I,K lần lượt là hình chiếu của H trên AB,AC

a) CM: \(\dfrac{HB}{HC}=\dfrac{AB^2}{AC^2}\)

b) CM: AI.AB=AK.AC
c) Cm: AM⊥IK

d) tính diện tích tứ giác AIMK biết AB=30cm, AC=40cm

P= \(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}+\dfrac{x+4}{1-x}\right)\div\left(1-\dfrac{3}{x-1}\right)\)

a) rút gọn P

b) tìm x để P > 0

c) tìm giá trị của x để P đạt giá trị nguyên dương nhỏ nhất

cho P=\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\dfrac{\sqrt{x}+1}{x-1}\)

a) Rút gọn P

b) CMR: P<\(\dfrac{1}{3}\)

c) tìm GTLN của P

3 Complete each sentence with one of the words from the box.

a) I'll send someone to call for the parcel on Thursday.

b) You'll have to work hard to keep........... with the rest of the class.

c) Jean didn't expect to come up............ such difficulties.

d) It's not fair. You're always picking............ me.

e) Terry sang the first verse and then everyone joined...........

f) I came............. one of your novels in a second-hand bookshop.

g) I'm not interested in buying anything. I'm just looking..................

h) Don't you think the manager should deal........... this problem?

i) George came................ a lot of money when his uncle died.

j) You look very guilty! What have you been getting up................ ?

tính: \(\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{1+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+....+\sqrt{1+\dfrac{1}{\left(n-1\right)^2}+\dfrac{1}{n^2}}\)

6. People can get the latest ________and enjoy interesting programs on it.
A. computer B. website C. information D. the Internet

7. ________ from factories is one cause of water pollution
A. waste B. materials C. treasure D. dynamite

8. I don’t spend much time________ the Net. I’m too busy with my homework.
A. going B. making C. playing D. surfing

9. I can’t easily get access________ the Internet because of living in the country.
A. for B. to C. into D. about

10. We should put garbage bins around here to prevent lazy students________throwing trsh.
A. for B. against C. from D. away

11. They were riding________the forest.
A. over B. to C. for D. through

12. Let’s do it, ________?
A. shall we B. shall I C. don’t you D. shan’t we

13. I am a student, ________?
A. aren’t I B. am not I C. aren’t you D. am I

14. You should avoid________ in such a dangerous river.
A. swim B. to swim C. sitting D. swimming

15. I think most children are creative enough to write________ poems.
A. beauty B. beautiful C. beautifully D. beautify

16. If we go on littering, the environment will become________ polluted
A. seriously B. serious C. hardier D. hardly

17. They wanted their school________ more beautiful and attractive.
A. become B. to become C. becoming D. becomes

18. I’m worried________ our environment are getting worse.
A. which B. that C. what D. whose

19. He is going to the post office ________ he wants to send a letter.
A. as B. however C. and D. although

20. I won’t meet him ________ he doesn’t come.
A. because B. if C. although D. unless

In the UK we each use about two hundred steel food and drink cans every year. Steel cans are popular because they are convenient, easy to store and unbreakable. But when you have finished with a can what do you do with it? Do you throw it away and forget all about it? Probably! But behind the scenes there are people whose job is to make sure that the steel is never wasted. In fact, recycling or re – using steel cans is so successful that every day of the year more than five million cans start new lives in new steel products.

After you have thrown away your can, what happens? Well, first of all it is collected by the men who empty your dustbin each week and taken to a tip, together with all the other household rubbish. Then the rubbish is sorted and the steel cans are taken separately to a special factory which turns old cans into high quality steel. It’s this steel that may well find its way back into your home in the form of knives and folks, garden equipment and, of course, food and drink cans.

So next time you open your fizzy drink, just remember where your can may have been!.

21. What is the text mainly about?
A. The production of canned food and drink in the UK.
B. Collecting household rubbish.
C. Recycling food and drink cans.
D. How steel cans are made

22. Why do the use a lot of cans?

A. Because we can throw them away and forget all about them.
B. Because they are convenient, easy to store and unbreakable.
C. Because they can be collected by the men who empty your dustbin each week and taken to a tip.

D. Because they are taken separately to a special factory which turns old cans into high quality steel.

23. Why would somebody read the text?
A. to learn about the soft drink industry.
B. to understand how rubbish is collected.
C. to find out more about how steel is made.
D. to discover what happens to old cans.

24. How do we know that re – using steel is very successful?
A. Every person eses 5000 cans a year.
B. Over 5,000,000 cans are recycled daily.
C. All cans and tins are now made from steel.
D. It reduces the amount of waste to collect.

25. What does the writer suggest about our attitude to old cans?
A. We don’t care what happens to them.
B. We should be more careful where to throw them.
C. We could help by sending them to the factory.
D. We are making things difficult for the dustbin men.

Cho biểu thức:

C = \(\dfrac{\sqrt{a}\left(2\sqrt{a}+1\right)}{8+2\sqrt{a}-a}+\dfrac{\sqrt{a}+4}{\sqrt{a}+2}-\dfrac{\sqrt{a}+2}{4-\sqrt{a}}\)1) Tìm điều kiện của a để biểu thức C có nghĩa. Rút gọn C

2) CMR: 0 < C \(\le\dfrac{3}{2}\). Từ đó suy ra C chỉ nhận một giá trị nguyên duy nhất với \(a\ge0;a\ne4\)

3) Tính gtri của biểu thức C khi a là số nguyên thỏa mãn \(a^2+a-16=4.25^b\left(b\in N\right)\)

Tìm tất cả các giá trị nguyên của x để biểu thức : \(x-\sqrt{x}+3\in Z\) ( ĐKXĐ: \(x\ge0;x\ne4\)

Tìm lỗi sai va sửa lại
FIRST DAY AT WORK
Well, Trisha, that's my own first day at my new job out of the way. I wasn't sure what to expect, but it turned out okay. My manager was really nice, much nicer than yours boss sounds from your letter. No sooner had i arrived at work than did he made me a cup of tea! It was a really pleasant surprise. Not only did he do that, but he was also kind enough to explain to me how everything worked. The office is really modern and its comfortable. The other people all have their own desks, but mine desk still hasn't been delivered, so i'm sharing with someone else for now. Little did i not realise when i took the job that i was going to enjoy it so much. I have finally found a job that i am happy in, and so will you have, i'm sure. Hope tomorrow's as much fun!