Thales là định lí lớp mấy ạ

cho hình vuông ABCD .Qua điểm A vẽ một đường thẳng cắt cạnh BC tại E và cắt đường thẳng CD tại F.CMR
\(\dfrac{1}{AB^2}=\dfrac{1}{AB^2}+\dfrac{1}{ÀF^2}\)

Cho Bt \(P\left(x\right)=\dfrac{x-2\sqrt{x}+1}{\sqrt{x}-1}\left(\dfrac{x+\sqrt{x}}{\sqrt{x}+1}+1\right)\)
với x > hoặc = 0 và x # 1
a) rút gọn
b) Tìm x để \(2x^2+P\left(x\right)\) _< 0

1. cho biểu thức :

\(P=\dfrac{x\sqrt{x}-8}{x+2\sqrt{x}+4}+3\left(1-\sqrt{x}\right)\)với x≥0

a) rút gọn biểu thức

b) Tìm các giá trị nguyên dương của x để biểu thức \(Q=\dfrac{2P}{1-P}\)nhận giá trị nguyên

Cho biểu thức \(P=\left(2+\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(2-\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)
Với giá trị nào của a thì P có giá trị \(\sqrt{\dfrac{\sqrt{2}-1}{1+\sqrt{2}}}\)

For question 46-55, read the text below and decide which word A, B, C or D best fits each space. Write your answer on YOUR ANSWER part.

Diaries

A diary is a daily record of events, thoughts and feelings (46)______ either for the writer's own personal satisfaction or for (47)______ use. Most diarists (48)______ expect nor necessarily want anyone else to read what they have written, so, on the (49)______ only they and perhaps their relatives and (50)______ friends ever see their writings. On the other hand, some people do write with the (51)______ of informing and entertaining the public, although often diaries are only (52)______ and published after the author's death.

One example of a diarist who never expected his diary to be (53)______ by the public was Samuel Pepys, who lived in the 17th century. His diary is the most impressive (54)______ the English language, recording some of the greatest (55)______ in English history, yet it is also the story of a most lovable man’s life.

46. A. possessed B. held C. kept D. stocked

47. A. later B. latter C. late D. then

48. A. not B. either C. none D. neither

49. A. all B. general C. whole D. everything

50. A. narrow B. close C. near D. tight

51. A. reason B. fact C. intention D. function

52. A. explored B. excavated C. discovered D. invented

53. A. seen B. revealed C. shown D. exhibited

54. A. to B. for C. of D. in

55. A. problems B. materials C. events D. numbers

For question 36-45, read the text. Use the words given in CAPITALS to form a word that fits in the numbered gaps. There is an example at the beginning (0). Write your answer on YOUR ANSWER part.

It is sometimes said that your schooldays are the (0. happy) days of your life, and people often feel that this should be a period of (36. ENJOY). However, exams often affect students’ happiness, and many students express a (37. PREFER) for alternative methods of assessment, where the work they do throughout the year counts towards their final mark. They say that exams test short-term memory and (38. KNOW) which is forgotten immediately after the exam. Also, assessing coursework as part of the final marks changes students' (39. BEHAVE); making them more (40. RESPONSIBILITY) about studying. There are some students, however, who prefer final examinations, saying that in (41. COMPARE) they only have to work hard for two months a year and so they have more time for their leisure (42. ACT). They say that some students receive (43. ASSIST) with their coursework from their parents, so it is not an accurate (44. MEASURE) of how hard they have worked or of their real (45. ABLE) in the subject they are studying.

Read the text and think of the word which best fits each gap (76-85). Use only ONE WORD in each gap. Write your answer on YOUR ANSWER part.

This summer, a group of 16-year-old students are taking (76)_________ in a three-week programme designed to teach them new skills and (77)_________ them used to working with people they have never met before. (78)_______ things go according to plans, in two years’ time, nearly one in six teenagers will be involved in the programme with (79)_________ eventually aim of offering it to (80)_________ young person in the country. So far, every group has (81)________ two weeks living (82)________ from home (many for the first time), initially on an outdoor course, with activities, (83)________ as rock climbing, rafting, and trekking, and then spending a week in self-catering accommodation where they are planning and setting (84)________ a volunteering project. At the moment, the students are putting their plans into action not (85)________by cooking for themselves but also by organizing a night outside sleeping rough in order to raise money for a local homeless shelter.

For question 36-45, read the text. Use the words given in CAPITALS to form a word that fits in the numbered gaps. There is an example at the beginning (0). Write your answer on YOUR ANSWER part.

It is sometimes said that your schooldays are the (0. happy) days of your life, and people often feel that this should be a period of (36. ENJOY). However, exams often affect students’ happiness, and many students express a (37. PREFER) for alternative methods of assessment, where the work they do throughout the year counts towards their final mark. They say that exams test short-term memory and (38. KNOW) which is forgotten immediately after the exam. Also, assessing coursework as part of the final marks changes students' (39. BEHAVE); making them more (40. RESPONSIBILITY) about studying. There are some students, however, who prefer final examinations, saying that in (41. COMPARE) they only have to work hard for two months a year and so they have more time for their leisure (42. ACT). They say that some students receive (43. ASSIST) with their coursework from their parents, so it is not an accurate (44. MEASURE) of how hard they have worked or of their real (45. ABLE) in the subject they are studying

Choose the letter A, B, C, or D to indicate the correct answer to each of the following questions. Write your answer on YOUR ANSWER part.

26. Peter: “This is your first trip abroad, isn’t it?” ~Van: “________.”

A. Yes, it sounds awful B. No, I haven’t been there before

C. Yes, so I’m looking forward to it D. No, it’s expensive

27. We have been looking for him everywhere but he was nowhere ________.

A. saw B. seen C. seeing D. to be seen

28. Teachers like students to be _____ and listen to what they are saying.

A. prudent B. attentive C. qualified D. viable

29. The girl and her pets ________ are playing in the garden look cheerful.

A. which B. who C. that D. whose

30. He need not stay here, _________?

A. does he B. doesn’t he C. need he D. needn’t he

31. You can’t let an opportunity like that ________ – it’s too good to miss.

A. go over B. go off C. go down D. go by

32. Many of these apps are written _________different languages.

A. by B. of C. in D. with

33. Look! This ______ of roses is so fresh.

A. pinch B. clove C. bunch D. shoal

34. Jenny __________ down the road on her new bike.

A. set up B. set on C. set in D. set off

35. The more paper we save, the _________ wood we use for making it.

A. little B. less C. fewer D. smaller