Đề thi học sinh giỏi 12

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Đề thi học sinh giỏi 12

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Hãy tham khảo đề thi học sinh giỏi lớp 12 để giúp các em biết thêm cấu trúc đề thi như thế nào, rèn luyện kỹ năng giải bài tập và có thêm tư liệu tham khảo chuẩn bị cho kì thi sắp tới đạt điểm tốt hơn.

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Nội dung Text: Đề thi học sinh giỏi 12

  1. 1)Có 2 cặp phương trình hóa học dưới đây, hãy xác định phương trình nào được viết đúng theo tỉ lệ số mol của chất oxi hóa và chất khử tham gia phản ứng? Giải thích 2MnO 4 + 3H2O2 + 6H 2Mn 2 + 4O2 + 6H2O (a) 2MnO 4 + 5H2O2 + 6H 2Mn 2 + 5O2 + 8H2O (a') FeSO4 + 4HNO3 Fe(NO3)3 + H2SO4 + NO2 + H2O (b) FeSO4 + 6HNO3 Fe(NO3)3 + Fe2(SO4)3 + 3NO2 + 3H2O (b) 2/ Đun nóng dung dịch sắt (II) axetat với axit pecloric đặc thu được dung dịch sắt (III) peclorat, khí clo và khí X. Lập phương trình hóa học (dạng phân tử) của phản ứng oxi hóa – khử trên. 3/ Lưu huỳnh có thể tạo ra nhiều axit chứa oxi có công thức chung là H xSyO z. Một trong số muối natri của những axit trên là Na xSyO z phản ứng với dung dịch KMnO4 có mặt HNO3 theo sơ đồ sau: NaxSyO z + KMnO 4 + HNO3 MnSO4 + Na2 SO4 + KNO3 + H2 O Biết rằng 0,01 mol Na xSyO z phản ứng vừa đủ với 200 ml dung dịch KMnO4 0,2M tạo thành dung dịch chứa 4,8 gam ion SO 2 , nếu tách riêng Na2SO4 tạo ra thì khối lượng 4 riêng của nó là 1,42 gam. a) Xác định số oxi hóa củ lưu huỳnh trong muốn Na xSy Oz trên. b) Hoàn thiện phương trình hóa học trên. 4/ Có 200 ml dung dịch A chứa hỗn hợp bari nitrat và sắt (III) nitrat. Cho từ từ dung dịch nitrat cacbonat vào dung dịch Aminoaxit cho đến khi kết tủa không tạo thêm nữa. Kết tủa thu được có khối lượng là 3,04 gam, đem tác dụng với dung dịch HCl dư thấy thoát ra 0,244 lít khí (1 atm, 25 oC). Viết các phương trình hóa học và xác định nồng độ mol các chất trong dung dịch A. Câu II. 1/ Dẫn 1 lít hỗn hợp khí gồm NH3 và O2 vào bình phản ứng rồi thực hiện phản ứng cháy. Kết thúc phản ứng, dẫn hỗn hợp tạo thành đi qua nước thấy chỉ còn 0,2 lít khí không tan trong nước. Các thể tích khí đo cùng điều kiện về nhiệt độ và áp suất. Biết rằng không xảy ra tương tác giữa sản phẩm cháy với các khí ban đầu để tạo ra chất mới. Tìm thành phần phần trăm thể tích NH3 trong hỗn hợp đầu. 2/ Khi trộn dung dịch hai muối có cùng số mol tạo thành 1,25 gam chất X (kết tủa) và dung dịch Y, X là muối của kim loại M (M có hóa trị 2 trong hợp chất). Tách riêng X rồi đem nung đến 1100 oC, muối X bị phân hủy thành 0,7 gam oxit MO và oxit Z (khí). Cô cạn dung dịch Y thu được 2 gam chất rắn là một muối khan, muối này bị phân hủy ở 215oC tạo ra 0,024 mol oxit T (khí) và 0,9 gam hơi nước. Xác định công thức phân tử hai muối ban đầu và viết các phương trình hóa học, biết số mol MO thu được bằng số mol Z. Câu III/ 1/ Công thức chung của Ankan là C nH2n+2. a) Tìm số electron có mặt và số electron tham gia tạo thành liên kết trong phân tử ankan. b) Trong phân tử ankan Aminoaxit chứa x nguyên tử cacbon bậc 1, y nguyên tử cacbon bậc 2, z nguyên tử cacbon bậc 3 và t nguyên tử cacbon bậc 4. Tìm biểu thức tính z theo các giá trị đã cho. c) Trong phân tử ankan X số liên kết giữa nguyên tử cacbon và hiđro gấp 2,8 lần số liên kết giữa hai nguyên tử cacbon. Khi clo hóa X chỉ tạo ra 3 dẫn xuất monoclo, còn nếu clo hóa trong điều kiện khó khăn hơn sẽ tạo ra 7 dẫn xuất điclo. Tìm công thức cấu tạo X. 2/ Cho khí clo đi qua CHCl3 (nhiệt độ sôi là 62oC) kèm theo chiếu sáng tạo ra hai hợp chất của cacbon là X1, X2 và chất khí Y. Y hòa tan tốt trong nước. Thành phần X1 và X2 trong hỗn hợp tạo thành phụ thuộc vào cường độ chiếu sáng, khi cường độ chiếu sáng yếu tạo ra chủ yếu là X1 (nhiệt độ sôi là 77oC); khi cường độ chiếu sáng mạnh tạo ra chủ yếu
  2. là chất rắn X2 có khối lượng mol lớn hơn X1 (bốc cháy ở 187oC). Giải thích (bằng cơ chế phản ứng ) và cho biết công thức phân tử các chất Y, X1 , X2. Câu IV. 1/ Hòa tan 2,07 gam axit cacboxylic đơn chức HA và 50 gam nước thu được dung dịch có khối lượng riêng là 1,03g/ml trong đó tổng số mol in H + và A- là 1,267.10-3. Biết độ điện li của axit HA bằng 1,42%. a) Tìm công thức phân tử của axit trên b) Tính hằng số phân li cua axit trên. 2/ Để tổng hợp CH3OH có thể thực hiện phản ứng CO + 2H 2 CH 3OH. Người ta trộn 4 mol khí CO với 1 mol khí H2 rồi cho vào bình phản ứng tổng hợp CH3OH ở nhiệt độ 450oC. Hiệu suất phản ứng này là 20%. a) Hỏi áp suất trong bình phản ứng thay đổi bao nhiêu lần? b) Tính hằng số cân bằng Kc của phản ứng ở nhiệt độ 450 oC c) Tìm số mol CO cần đem trộn với 1 mol H 2 ở cùng nhiệt độ trên để hiệu suất phản ứng là 25%. Câu V 1/ Viết phương trình hóa học (dưới dạng công thức cấu tạo) biểu diễn các biến hóa sau (ghi rõ điều kiện phản ứng, nếu có): C6H5CH3 p O2NC6H4Cl p O2NC6H4 CH2OH p O2NC6H4CHO p O2NC6H4COOH p H 2NC6H4COOH p HOC6H4COOH p Cl N 2 C6H4COOH 2/ Từ etilen và các chất vô cơ cần thiết khác, hãy viết các phương trình hóa học để tạo ra 5 ancol khác nhau, mà phân tử có không quá 4 nguyên tử cacbon. Câu VI 1/ Có sơ đồ chuyển hóa sau: [O] [O] +Br2/P xúc tác B D E G A +NaOH +HCl +HNO2 +C2H5OH/HCl X Y Z Biết A có công thức C6H12O3; Y có công thức C3 H6O3 và có trong sữa chua; từ 4,45 gam Z đem phản ứng với HNO2 thu được 4,5 gam Y (coi hiệu suất phản ứng là 100%). Xác định công thức cấu tạo các chất A,B,D,E,G,Y,Z,T. 2/ Khi thủy phân hoàn toàn 1mol pentapetit X thì thu được 3 mol glyxin, 1mol alamin, 1mol valin. Khi thủy phân không hoàn toàn X thu được hỗn hợp sản phẩm gồm 3 tripetit và 3 đipeptit. Khi xác định đầu N của animo axit trong tripetit trên thấy rằng 2 trong só đó có đầu N của amino axit thuộc về glyxin, còn lại thuộc về alamin. Cho X tác dụng với HNO2 thấy giải phóng N2. Xác định trình tự các amino axit trong phân tử X. Cho H=1; C=12; N=14; O=16; Na=23; Mg=4; S=32; Ca=40; Fe=56; Ba=137 (Hết) Nhờ các thầy giải giúp nghe
  3. ĐỀ THI HỌC SINH GIỎI 12 MÔN : TIẾNG ANH - LẦN II PART I : VOCABULARY ( 20pts ) A . Choose the word/ phrase which best completes each sentence : 1. Please sit down and ........................... yourself at home . A. do B. made C. help D. get 2. When her father was younger , he ....................... a fortune selling clothes . A. did B. made C. does D. makes 3. Did they ask you what examinations you’ve ...................... ? A. overcome B. passed C. succeeded D. obtained 4. Have you been for an ...................... yet ? A. overview B. inspection C. appointment D. interview 5. Jane ...................... to write back as soon as she got my letter but months can go by before I get a reply these days . A. has always used B. always use C. always used D. is always used 6. It was not until she arrived in class ...................... realized she had forgotten her book. A. and she B. when she C. she D. that she 7. We have been informed that ...................... animals at the 200 are starving to death. A. most of B. almost the C. most all D. most of the 8. The firm went bankrupt and their shares became ...................... A. priceless B. unworthy C. invaluable D. worthless 9. Two of the boys in the art class were doing self- portraits by looking at ...................... in the mirror . A. each other B. oneself C. themselves D. one another 10. The shop assistant ...................... me so much for the book . A. cost B . requested C. required D. charge B. Complete each sentence by giving the correct form of word in bracket : 1. The book describes the ...................... between a mother and her son . (RELATE) 2. There is a lovely description of the author’s early ...................... (CHILD) 3. The teacher warned the children that if they ...................... again, they’d be punished. ( BEHAVE) 4. Great works of art like the Mona Liza are ...................... ( PRICE ) 5. What a lovely painting ! Your daughter much be very ...................... (ART ) 6. Librarians spend a lot of their time ...................... books . ( CLASS ) 7. Some people claim to be able to ...................... the future . ( TELL ) 8. “ A Taste of Death ” is about two famous men who are found ...................... in a church . ( DIE ) 9. In the past few years this area has become heavily ...................... . ( INDUSTRY ) 10. Please don’t be so ...................... , I can’t do all the work by my self . ( REASON ) PART II : READING PRACTICE ( 30 pts) A. Cloze Test : Fill in each of the numbered blanks in the passage with one suitable word : ENDANGERED SPECIES The future of the African elephant depends on man . No (1)................. can human beings and (2) ................. animals live in harmony throughout vast areas of (3) ................. continent as was possible in days gone by, for man’s needs have increased as well -1-
  4. (4)................. his numbers. There are regions , (5) ................. as the Congo forests and the equatorial Sudan , (6) ................. the old relationship may remain for a (7) ................. more years or even generations but in general it has gone . Conservation , (8) ................. it is to be effective , must be a positive , constructive policy, (9) ................. it is wishful thinking to imagine otherwise, (10) .................in the case of the elephant. And if this is not yet true of the whole of (11) ................. , it soon will be for the increase (12) ................. the human population is almost universal .Where human (13) ................. and wild animals find themselves in competition (14) ................. each other, the animals will lose . Even if there appears to be (15) ................. room for both, man will not tolerate for long a situation in (16) ................. elephants and other creatures make even occasional raids (17) ............... his fields of food or economic crops. For many years this has been (18) ................. major cause of conflicting interests and (19) ................. of the reasons why so many elephants have been (20) ................. to control their numbers. 1. .............................................. 2. .............................................. 3. .............................................. 4. .............................................. 5. .............................................. 6. .............................................. 7. .............................................. 8. .............................................. 9. .............................................. 10. .............................................. 11. .............................................. 12. .............................................. 13. .............................................. 14. .............................................. 15. .............................................. 16. .............................................. 17. .............................................. 18. .............................................. 19. .............................................. 20. .............................................. B. READING COMPREHENSION : Read the following text and choose the best answer for each question : Over the past 600 years, English has grown from a language of few speakers to become the dominant language of international communication. English as we know it to day emerged around 1350, after having incorporated many elements of French that were introduced following the Normal invasion of 1066. Until the 1600s, English was, for the most part, spoken only in England and had not extended even as far as Wales, Scotland, or Ireland. During the course of the next two centuries, English began to spread around the globe as a result of exploration, trade ( including slave trade ), colonization , and missionary work. Thus , small enclaves of English speakers became established and grew in various parts of the world. As these communities proliferated, English gradually became the primary language of international business, banking, and diplomacy. Currently, about 80 percent of the information stored on computer systems world wide is in English. Two thirds of the world’s science writing is in English, and English is the main language of technology, advertising, media, international airports, and air traffic controllers . Today there are more than 700 million English users in the world, and over half of these are nonnative speakers, constituting the largest number of nonnative users than any other language in the world. 1. What is the main topic of this passage ? A. the number of nonnative users of English B. the French influence on the English language -2-
  5. C. the expansion of English as an international language D. the use of English for science and technology 2. As used in line 3 , the word “ elements ” is not similar to which of the following : A. declaration B. features C. curiousities D. customs 3. English was spoken in .......................... in the 1600s . A. England B. Wales C. Scotland or Ireland D. all are correct 4. According to the passage all of the following contributed to the spread of English around the world except A. the slave trade B. the Norman invasion C. missionaries D. colonization 5. Approximately when did English begin to be used beyond England ? A. in 1066 B. around 1350 C. before 1600 D. after 1600 6. The word “ enclaves ” in line 9 could best be replaced by which of the following ? A. communities B. organizations C. regions D. countries 7. The word “ proliferated ” in line 10 is closet in meaning to which of the following ? A. prospered B. organized C. disbanded D. expanded 8. Which of the following is closet in meaning to the word “ constituting ” in line 17 ? A. looking over B. sitting down C. doing in D. making up 9. According to the passage, approximately how many nonnative users of English are there in the world to day ? A. a quarter million B. half a million C. 350 millionD. 700 million 10. According to the passage what does the writer mean ? A. English is very important to master B. English is necessary for business, technology advertising , media , international airports and air traffic controllers C. English is used in many countries in the world . D. A, B , C are correct C. FILL IN EACH BLANK WITH THE BEST FIT : (A, B , C , D ) Mr John Brown lived his entire life in a small town in the North of England . He never left the house (1) ...................... he had been born, never married, never went on holiday and had no friends . He worked in a local factory for (2) ...................... forty years but even the people who had worked with him for years (3) ...................... very little about him . He wore the same clothes year in year out, and (4) ...................... he shopped regularly at the local store, he bought only the most basic foodstuffs, never changing his purchases from one week to the next . So (5) ...................... he died last month neighbors and local people were astonished to learn that Mr Brown was not just a rich man, he was in fact (6) ...................... millionaire . He had no bank account, no money invested anywhere but in the various drawers, cupboards and boxes in the house there were hundreds and thousands of bank (7) ...................... and coins . It took police over two weeks to clear the house and the bank clerks took just as long to (8) ...................... all the money. “We had absolutely no idae that he had been hiding his money over the years ” one of his neighbours (9) ...................... “ In fact We used to feel sorry for him, We thought he was a poor old man unable to (10 ) ...................... anything better for himself !” 1. A. which B. where C. who D. what 2. A. until B. above C. over D. across 3. A. reminded B. held C. had D. knew 4. A. although B. but C. because D. however 5.A. while B. when C. during D. that -3-
  6. 6. A. the B. this C. a D. one 7. A. papers B. money C. letters D. notes 8.A. number B. count C. guess D. make 9. A. said B. spoke C. mentioned D. told 10. A. pay B. spend C. afford D. give PART III : GRAMMAR AND STRUCTURES (25 tps) : A. Fill in each blank one suitable preposition (5 tps ) : 1. The boss has been ill ......................... flu for the last week . 2. I am very impressed ......................... your work . 3. I wasn’t pleased ....................... my exam result . 4. I am disgusted ........................ Stephen .................... the way he treats Julia . 5. We all agree ....................... most things . 6. What does it mean if you dream .................... fire ? 7. She is not only indifferent ..................... other people, she is very rude .................... them as well. 8. The party went on ................................................... dawn . 9. I know he is slow ............................................................ understanding . B . Give the correct form of verb in bracket (5 tps ) : 1. What’s the matter ? You (hurt) your leg ? How you (do) it ? 2. I (consider) buying a house but I already (change ) my mind . 3. We (find) it difficult to convince the ticket inspector that we (lose) our tickets . 4. I can’t help (feel) sorry for the hungry children . If only there (be) peace in the world . 5. She’s always forgetting (give) back the money she borrowed from me . 6. I’ll never forget (meet) the King . B. Sentence – Transformation (10 tps ) : 1. They arranged for the police to arrest the man.  They had ..................................................................................................................................... 2. I’m planning to sell this car and buy another one .  I’m thinking ................................................................................................................................ 3. Card games are not my speciality, although I can play a bit .  I’m not ......................................................................................................................................... 4. Don’t pay any attention to what he says .  Don’t take ................................................................................................................................... 5. “ Let’s go for a walk in the park ” said Andrew .  Andrew suggested ..................................................................................................................... 6. His rude behaviour is too much for me (PUT)  His rude behaviour .................................................................................................................... 7. John didn’t celebrate until he received the offer of promotion in writing (NOT)  Not until ...................................................................................................................................... 8. We have no seats left for the concert on December 14 th (BOOKED )  All the seats ................................................................................................................................ 9. I don’t know which dress to buy . I can’t decide (MIND )  I don’t know which dress to buy. I can’t ................................................................................ 10. They accused me of causing the accident (BLAME )  They put ..................................................................................................................................... D . Find the mistakes in the following sentences and correct them . (One mistake in each sentence ) 1. Our Spanish professor would like us to spend more time in the laboratory to practise our pronunciation . 2. It was him who came running into the classroom with the news . 3. Even though she looks very young , she is twice older than my twenty- year-old sister . -4-
  7. 4. Mr Peter used to think of him as the only president of the company . 5. The price of crude oil used to be a great deal lower than now, wasn’t it ? 1. ......................................... 2. ................................................ 3. ......................................... 4. ................................................ 5. .......................................... IV . WRITING (25 pts ) Your close friend has just passed the exam of university of education. Write a letter about 100 to 150 words to share his feelings . THE END ! GOOD LUCK TO ALL OF YOU ! -5-
  8. Së Gi¸o dôc v ® o t¹o Kú thi chän HäC SINH GIáI TØNH thanh ho¸ Năm h c: 2008-2009 Môn thi: To¸n Đ CHÍNH TH C L P : 12 THPT S báo danh Ngày thi: 28/03/2009 ……………………. Th i gian: 180 phút (không k th i gian giao đ ) B i 1(5,0 ®iÓm) Cho h m sè y = x 3 − 3 x 2 + 2 cã ®å thÞ (C) 1. Kh¶o s¸t sù biÕn thiªn v vÏ ®å thÞ (C) cña h m sè. 2. BiÖn luËn theo m sè nghiÖm cña ph−¬ng tr×nh: x 3 − 3 x 2 + 2 = m 3 − 3m 2 + 2 3. Víi mçi ®iÓm M thuéc (C) kÎ ®−îc bao nhiªu tiÕp tuyÕn víi (C)? B i 2(4,0 ®iÓm) 1 e2 x2 1. TÝnh tÝch ph©n: I = ∫ 2 dx 0 x + 4x + 4 2. Cã bao nhiªu sè tù nhiªn cã 6 ch÷ sè ®«i mét kh¸c nhau m trong ®ã chØ cã mét ch÷ sè lÎ ? B i 3 (5,0 ®iÓm) π π 1. Gi¶i ph−¬ng tr×nh: sin(3x − ) = sin 2 x. sin( x + ) 4 4 2. T×m gi¸ trÞ cña m ®Ó bÊt ph−¬ng tr×nh sau nghiÖm ®óng víi mäi x m m m ( 2 − log 2 ) x 2 − 2(1 + log 2 ) x − 2(1 + log 2 ) < 0. m +1 m +1 m +1 x+log2 y x − log y 3. Víi gi¸ trÞ n o cña x, y th× 3 sè u1 = 8 , u2 = 2 2 , u = 5y theo thø 3 tù ®ã, ®ång thêi lËp th nh mét cÊp sè céng v mét cÊp sè nh©n. B i 4 (5,0 ®iÓm) 1.Trong mÆt ph¼ng to¹ ®é Oxy cho ®−êng trßn (C) cã ph−¬ng tr×nh: 2 x 2 + ( y − 1) = 1 Chøng minh r»ng víi mçi ®iÓm M(m; 3) trªn ®−êng th¼ng y = 3 ta lu«n t×m ®−îc hai ®iÓm T1 , T2 trªn trôc ho nh, sao cho c¸c ®−êng th¼ng MT1`, MT2 l tiÕp tuyÕn cña (C). Khi ®ã h y viÕt ph−¬ng tr×nh ®−êng trßn ngo¹i tiÕp tam gi¸c MT1T2. 2. Cho h×nh chãp S.ABC cã ®¸y ABC l tam gi¸c vu«ng c©n (AB = BC =1) v c¸c c¹nh bªn SA = SB = SC = 3. Gäi K, L lÇn l−ît l trung ®iÓm cña AC v BC. Trªn c¹nh SA, SB lÇn l−ît lÊy c¸c ®iÓm M, N sao cho SM = BN = 1. TÝnh thÓ tÝch cña tø diÖn LMNK. B i 5 (1,0 ®iÓm) Cho n l sè nguyªn lÎ v n >2. Chøng minh r»ng víi mäi a kh¸c 0 lu«n cã: a2 a3 an a2 a3 a n −1 an (1 + a + + + ... + )(1 − a + − + ... + − )
  9. Së Gi¸o dôc v ® o t¹o Kú thi chän HäC SINH GIáI TØNH thanh ho¸ Năm h c: 2008-2009 Môn thi: To¸n §¸p ¸n ®Ò chÝnh thøc L P : 12 THPT Ngày thi: 28/03/2009 §¸p ¸n n y gåm cã 5 trang B i §¸p ¸n v híng dÉn chÊm §iÓm B i1 1(3®) 5® 1. TËp x¸c ®Þnh: R y , = 3x 2 − 6 x ; y ,, = 6 x − 6 0,5 x = 0 2 Sù biÕn thiªn y, = 0 ⇔  x = 2 ,, y = 0 ⇔ x =1 0,5 B¶ng biÕn thiªn x −∞ 0 1 2 +∞ , + 0 - 0 + y y,, - 0 + 1,0 y 2 U (1;0) +∞ −∞ -2 3 §å thÞ : y 2 −1 2 1,0 1+ 3 O 1 1+ 3 3 x −2 2. (1®) §Æt f (m) = m 3 − 3m 2 + 2 3 2 3 2 Sè nghiÖm cña ph¬ng tr×nh x − 3 x + 2 = m − 3m + 2 l sè giao ®iÓm cña 3 2 ®êng th¼ng y = f (m) = m − 3m + 2 víi ®å thÞ (C) Tõ ®å thÞ (C) ta cã -1 < m < 0; 0 < m 2 0,5 m > 3 VËy *  m < −1 ph¬ng tr×nh cã 1 nghiÖm  * m =∈ {− 1; 0; 2; 3} ph¬ng tr×nh cã 2 nghiÖm
  10. * − 1 < m < 0; 0 < m < 3 ph¬ng tr×nh cã 3 nghiÖm 0,5 3.(1®) 3 2 M thuéc ®å thÞ (C) suy ra M (a; a − 3a + 2) .®êng th¼ng (d) tiÕp xóc víi (C) t¹i T(x0;y0) th× (d) cã ph¬ng tr×nh: 2 3 2 y = (3 x 0 − 6 x 0 )( x − x 0 ) + x 0 − 3 x 0 + 2 0,25 3 2 2 3 2 M ∈ (d ) ⇒ a − 3a + 2 = (3 x − 6 x0 )(a − x0 ) + x − 3x + 2 0 0 0 ⇔ (a 3 − x0 ) − 3(a 2 − x0 ) − (3x0 − 6 x0 )(a − x0 ) 3 2 2 [ ⇔ (a − x0 ) 2 x0 − (a + 3) x0 + 3a − a 2 = 0 2 ]  x0 = a a −3 ⇔ (a − x0 )( x0 − )=0⇔ 2  x0 = 3 − a 0,25  2 3−a TH1 a= ⇔ a = 1 ⇒ M ≡ I (1 ; 0) cã 1 tiÕp tuyÕn duy nhÊt 0,25 2 3−a 0,25 TH2 a ≠ ⇔ a ≠ 1 ⇒ M ≠ I (1 ; 0) cã 2 tiÕp tuyÕn 2 B i2 1 x2 4® 1.(2®) I= e2 ∫ 2 dx 0,25 0 x + 4x + 4 1 u = x 2 du = 2 xdx x2   TÝnh J= ∫ 2 dx §Æt  dx ⇒  1 0,5 0 x + 4x + 4 dv = ( x + 2) 2 v = − x + 2   1 1 1 1 x2 x 1 dx ⇒J =− + 2∫ dx = − + 2 ∫ dx − 4∫ 0,5 x+2 0 0 x+2 3 0 0 x+2 1 1 1 1 5 3 − + 2 x 0 − 4 ln x + 2 0 = − + 2 − 4(ln 3 − ln 2) = − 4 ln 0,5 3 3 3 2 5 3 0,25 ⇒ I = e 2 − 4e 2 ln 3 2 2.(2®) − − −− − − −− − − −− − − − Ta kÝ hiÖu sè A l a1a2 a3a4 a5 a6 • Cã 5 kh¶ n¨ng chän mét ch÷ sè lÎ • Mçi c¸ch chän 1 ch÷ sè lÎ v 5 ch÷ sè ch½n cã P6=6! C¸ch s¾p xÕp 6 ch÷ sè 0,5 ® cho v o 6 vÞ trÝ tõ a1®Õn a6 Nh vËy cã 5.P6 =5.6! c¸ch s¾p xÕp 10 ch÷ sè tõ 0 ®Õn 9 v o 6 vÞ trÝ tõ a1 ®Õn a6 m mçi c¸ch chØ cã mét ch÷ sè lÎ. *Trong tÊt c¶ c¸c c¸ch s¾p xÕp ®ã th× nh÷ng c¸ch xÕp cã ch÷ sè 0 ®øng ë vÞ trÝ a1 kh«ng ph¶i l mét sè cã 6 ch÷ sè 0,5 1 * Do tÝnh b×nh ®¼ng cña c¸c ch÷ sè ® chän cã sè c¸ch s¾p xÕp kh«ng ph¶i 6 5.6! 0,5 l sè cã 6 ch÷ sè v b»ng = 5.5! 6 VËy sè c¸c sè cã 6 ch÷ sè m trong nã chØ cã mét sè lÎ l 5.6! - 5.5! = 5!(30 - 5) = 25.5! = 3000 sè 0,5 B i3 π 5® 1.(2®) §Æt t = x + khi ®ã ph¬ng tr×nh ® cho trë th nh 4
  11. π 0,5 sin(3t − π ) = sin( 2t + ) sin t ⇔ − sin 3t = cos 2t sin t (*) 2 §Æt z = sin t §K z ≤ 1 ph¬ng tr×nh (*) trë th nh z = 0 3x − 4 z 3 + (1 − 2 z 2 ) z = 0 ⇔ 6 z 3 − 4 z = 0 ⇔  2 2 0,5 z =  3 π 0,25 * z = 0 ⇒ sin t = 0 ⇔ t = kπ ⇒ x = − + kπ ; k ∈ Z 4 2 2 1 − cos 2t 2 1 * z2 = ⇒ sin 2 t = ⇔ = ⇔ cos 2t = − = cosα 3 3 2 3 3  α  π α 2t = α + l 2π t = 2 + lπ  x = − 4 + 2 + lπ ⇔ ⇔ ⇒ ,l ∈ Z 2t = −α + l 2π t = − α + lπ  x = − π − α + lπ   0,5  2  4 2 π π α 0,25 VËy PT cã nghiÖm l x = − + kπ , x = − ± + lπ . k , l ∈ Z 4 4 2 m 2.(2®) §Æt a = 1 + log 2 , bÊt ph¬ng tr×nh ® cho trë th nh: m +1 (3 − a) x 2 − 2ax − 2a < 0 (1) 0,5 VÕ tr¸i cña (1) l mét tam thøc b©c hai Èn x cã hÖ sè cña x l 3 − a . 2 TH1: 3 - a = 0 ⇔ a = 3 0,5 Khi ®ã (1) l 6 x− 6 < 0 ⇔ x < 1 suy ra (1) kh«ng nghiÖm ®óng mäi x a > 3 3 − a < 0 a > 3  TH2  , ⇔ 2 ⇔  a < 3 ⇔ a > 6 ∆ < 0 a + 2a(3 − a) < 0  a > 6 0,5  m m Víi a > 6 ta cã 1 + log 2 >6⇔ > 32 m +1 m +1 31m + 32 31 ⇔
  12. 3.(1®) a + c = 2b NÕu c¸c sè a, b, c ®ång thêi l cÊp sè céng v cÊp sè nh©n th×  2 ac = b suy ra a, c l nghiÖm cña pt: x 2 − 2bx + b 2 = 0 ⇔ x = b tõ ®ã a = b = c. 0,25  x + log y x − log y 2 =2 2 (1) Theo b i ra ta cã hÖ: 8   0,25  x − log2 y 2  = 5y (2) Tõ (1) 3x + 3 log 2 y = x − log 2 y ⇔ x = −2 log 2 y , thay v o (2) ta ®−îc: 1 0,5 2 −3 log 2 y = 5 y ⇔ 5 y 4 = 1 ⇔ y = 4 5 ⇔ x = 2 log 2 4 5 = log 2 5 2 B i4 1.(3®) §−êng trßn (C) cã t©m I ( 0 ; 1 ) b¸n kÝnh R = 1 5® §iÓm T thuéc trôc ho nh th× T( t ; 0) §iÓm M( m; 3) thuéc ®−êng th¼ng y = 3 , ta cã: Ph−¬ng tr×nh ®−êng th¼ng MT: 0,5 x −m y −3 = ⇔ 3x + (t − m) y − 3t = 0 t −m −3 Do MT l tiÕp tuyÕn cña (C) nªn kho¶ng c¸ch tõ t©m I cña (C) ®Õn MT b»ng 1, hay 0,5 t − m − 3t 2 2 = 1 ⇔ (m + 2t ) 2 = 9 + (t − m) 2 3 + (t − m ) ⇔ t 2 + 2mt − 3 = 0 (*) Do ph−¬ng tr×nh (*) lu«n cã hai nghiÖm t1 , t2 víi mäi m nªn lu«n tån t¹i hai ®iÓm T1(t1;0) v T2(t2;0) ®Ó MT1v MT2 l tiÕp tuyÕn cña (C). * Theo ®Þnh lý Vi Ðt cã t1 + t2 = -2m. Ph−¬ng tr×nh ®−êng trßn (C1) ngo¹i tiÕp tam 0,5 gi¸c MT1T2 cã d¹ng: x 2 + y 2 + 2ax + 2by + c = 0 V× M, T1, T2 thuéc ®−êng trßn (C1) nªn cã hÖ m 2 + 9 + 2ma + 6b + c = 0 (1)  2  t1 + 2at1 + c = 0 (2)  2 t 2 + 2at 2 + c = 0 (3)  Tõ (2) v (3) suy ra 0,5 2 2 t1 − t 2 + 2a (t1 − t 2 ) = 0 (do t1 ≠ t 2 ) ⇔ t1 + t 2 + 2a = 0 ⇔ −2m + 2a = 0 ⇔ a = m. 2 Thay v o (2) ta cã t1 + 2mt1 + c = 0 2 0,5 Do t1 l nghiÖm cña(*) nªn t1 + 2mt1 − 3 = 0 ⇒ c = −3 Thay c = -3 v o (1) ta ®−îc: 2 2 m2 + 2 m + 9 + 2m + 6b − 3 = 0 ⇔ b = − 2 2 2 m2 + 2 VËy ph−¬ng tr×nh cña (C1) l : x + y + 2mx − y −3 = 0 2 0,5
  13. 2.(2®) LÊy ®iÓm E thuéc SA sao cho AN=1 suy ra NE// AB // KL 0,5 ⇒ S ∆NKL = S ∆EKL ⇒ VMNKL = VMEKL ; S ∆EKM = 1 S SKC 0,5 6 MÆt kh¸c kho¶ng c¸ch tõ L ®Ðn mÆt ph¼ng (MKE) b»ng BK 2 1 0,5 VËy VKLME = VSABC m 12 1 1 17 1 17 1 17 34 VSABC = SK .S ABC = . = ⇒ VKLMN = . = (®vtt) 0,5 3 3 2 2 6 2 12 6 2 144 S M E N K C A L B B i5 Coi a l Èn , ®iÒu kiÖn a kh¸c 0 1® a 2 a3 an a2 a n −1 §Æt u = 1 + a + + + ... + ⇒ u, = 1+ a + + ... + 2! 3! n! 2! (n − 1)! 2 3 n −1 n a a a a v = 1− a + − + ... + − 2! 3! (n − 1)! n! a2 a3 a4 a n−2 a n −1 0,25 ⇒ v , = −1 + a − + − + ... + − 2! 3! 4! (n − 2)! (n − 1)! an , , an Khi ®ã u = u + , v = −v − n! n! a2 a4 a n −1 u + v = 2(1 + + + ..... + ) > 0 víi mäi a v n lÎ n > 2 0,25 2! 4! (n − 1)! §Æt vÕ tr¸i cña bÊt ®¼ng thøc cÇn chøng minh l f(a) , , , an an an Ta cã f (a ) = uv + vu = u (−v − ) + v(u − ) = − (u + v) n! n! n!  ,  f (a ) > 0 khi a < 0 Do u + v > 0 , a ≠ 0 ⇒  , 0,25  f (a ) < 0 khi a > 0  Ta cã b¶ng biÕn thiªn a −∞ 0 +∞ , f (a) + - f (a ) 1 do a kh¸c 0 nªn f(a)
  14. SỞ GD- ĐT THỪA THIÊN HUẾ ĐỀ THI HỌC SINH GIỎI 12 TRƯỜNG THPT NGUYỄN CHÍ THANH Môn : TIẾNG ANH Thời gian: 150 phút I.VOCABULARY & GRAMMAR. Part 1: Choose the word or phrase which best completes each sentence. Circle the letter A, B, C or D next to the correct word or phrase. 1. He refused to give up work,................he ‘d won a million pounds. A. despite B. however C. even though D. as though 2. They were ..............for smuggling jewellery into the country. A. jugded B. arrested C. accused D. warned 3. At the end of the winter, the price of winter clothes in the shops usually .............. A. drops B. lowers C. sinks D. reduces 4. Have you got time to discuss your work now or are you ..............to leave? A. thinking B. planned C. around D. about 5. I don’t see any .............. in arriving early at the theatre if the show doesn’t start until 9 o’clock. A. cause B. aim C. point D. reason 6. Would you mind .......... these plates a wipe before putting them in the cupboard? A. making B. doing C. getting D. giving 7. She did all the work .......... her own. A. by B. on C. for D. with 8. ........................Tom , he can’t possibly go alone - he is far too young. A. As if B. As for C. As D. As far as 9. I have to leave before seven and so ............... A. leave you B. you have C. you do D. do you 10. By half past ten tomorrow morning I ..................along the motorway. A. will drive B. am driving C. drive D. will be driving Part 2: Read the text below. Use the words given in capitals at the end of each line to form a word that fits in the space in the same line People are fascinated by robots. Some of them look like FASCINATION (1)...........................dolls to play with . Most of them look like other machines MECHANIC of today's high technology. Serious research on(2)........................................... INTELLIGENCE robots began in the 1960s in several countries . Now we are on the fifth (3)......... .......................of robots. The first robots were very expensive. They GENERATE cost $ 500,000 when a (4) ..........................could do the same work for $ 15 WORK an hour .One of the(5) ................................of robots is that they can work in ADVANTAGEOUS situations that are(6) .......................................or harmful for human workers. DANGER Japan leads the world in the(7) ....................................of robots . They have DEVELOP 12,000 working and(8) ........................30,000 per year, most of them for PRODUCTION export. Nissan, a (9) ............................automobile company , spent $ 600 JAPAN million on robots for a new factory in the United States .It will be the most (10) ...................................advanced factory of its kind. TECHNOLGY
  15. Part 3: Read the text below and think of the word which best fits each space. Use only one word in each space. After each space you are given a clue to the kind of word that is missing. A POP STAR John Lennon was (0)born in Liverpool in 1940. He was always ( adjective)..........................................on music and played in pop group(2) ....................................................(preposition) school and Art college . John ( 3).........................................................(verb) married to Cynthia in 1962 and they had a son , (4) ................................( relative pronoun) name was Julian. At that time, John was a member of a group (5) ....................................(past participial) “ The Beatles” . Many beautiful songs (6) .................................... ( auxiliary verb) written by John and wherever the group went, crowds of fans gathered to see them . They (7) ...............................................(modal verb) scream and faint when “ The Beatles” played and lots of people have their hair cut in a Beatles style. Soon, everyone had heard (8)..................................... (preposition) “ The Beatles” and John was (9).......................................(adjective) richer than he had ever thought. Having achieved world - wide success, John started to make records (10) ...................................... (preposition) his own after 1968 , and it was in the same year when (11) .................................................. ( possessive adjective) marriage to Cynthia came to an end. He had met Yoko Ono,( 12) .......................... ( relative pronoun) he married the following year. John lost weight and grew his hair long , as can (13) ................................( auxiliary verb) seen on the covers of the records that he made with Yoko. He set up home in the United States and had a son called Sean. Many people considered John Lennon to be (14) ............................................(article) most talented of all “The Beatles”. He sang about peace and love and so when he was murdered by one of his fans, outside his New York department , the whole world (15)...........................................(auxiliary verb) shocked . More than 50,000 fans turned up to a ceremony in his memory. He was only forty when he died. II. READING Part 1: Fill in each numbered space with ONE suitable word An unforgettable birthday It was the day of my grandmother’s 80th birthday when the sitting room ceiling fell down .All the family were there , at my uncle Phillip’s house, ..................(1) was a large , old building situated in a small , peaceful village north- west (2) ..........................Oxford . We (3) .......................already finished lunch and , as (4) .............................was such a beautiful afternoon, we were all outside (5) ..................... the garden , drinking coffee and catching (6)............................on all the family news . Grandmother, (7) ....... .......................was rather deaf ,was (8)............................usual, telling stories about her childhood in Manchester, (9).............................in the sunshine , laughing children and barking dogs chased each (10) ...............................around. Suddenly, (11).................................was a tremendous crash . We all looked round in astonishment, wondering that what on earth had (12)...............................Uncle Phillip and my father ran into the house , and then my sister and I (13)........................... There , the most extraordinary sight met our eyes. The sitting - room was (14).............................ruins and the air was thick with dust, Uncle Phillip was standing in the (15) ...........................of the room, holding Tabatha , his cat , who looked terrified. “It was one of the problems of living in a house as old (16) ...............................this”, he
  16. explained calmly . Meanwhile, outside, Grandmother asked (17) ...............................more coffee and enquired when the cake (18)........................... be cut. III.WRITTING Part 1: Complete the second sentence so that it has a similar meaning to the first sentence. 1. That meal was excellent ! What............................................................................................................................................ 2. I don’t really want to visit the museum. I ‘d rather ............................................................................................................................... 3. Please don’t smoke in this area of the restaurant. Customers are requested ................................................................................................................. 4. “ I ‘m sorry, Angela” said Martin , “ I’m afraid I ‘ve damaged your car” Martin apologised ............................................................................................................................. 5. Although he took a taxi, Peter arrived late for the concert. In spite .............................................................................................................................................. 6. Daisy finds it easy to make friends. Daisy has no ...................................................................................................................... 7. Mary regretted buying the second- hand car. Mary wished ............................................................................................................................ 8. Tony finally managed to get a good job . Tony finally succeeded..................................................................................................................... 9. Charles lives near his aunt’s house . Charles doesn’t ............................................................................................................................ 10. It was such a dirty beach that we decided not to stay. The beach ............................................................................................................................ 11. I don’t really want to have lunch yet. I ‘d rather ............................................................................................................................ 12. It looks like rain to me. I.......................................................................................................................................................... 13. The people who were there didn’t notice anything unusual. No- one ............................................................................................................................ 14. She left university five years ago. It is ....................................................................................................................................... 15. The gate is closed to stop the children running into the road. The gate is closed so that ..............................................................................................................
  17. ĐÁP ÁN I.VOCABULARY & GRAMMAR. Part 1. (10 points) one point for each correct answer Q# 1 2 3 4 5 6 7 8 9 10 Key C B A D C D B A B D Part 2. (10 points) 1. mechanical 2. intelligent 3. generation 4. worker 5. advantages 6. dangerous 7. development 8. produce 9. Japanese 10. technologically Part 3. (15 points) one point for each correct answer 1. keen / hooked 2. at 3. got 4. whose 5. called 6. were 7. would 8. of 9. much /far 10. on 11. his 12. whom 13. be 14. the 15. was II. READING Part 1. (18 points) one point for each correct answer 1. which 2. of 3. had 4.it 5.in / admiring 6.up 7.who 8. as 9. while 10. other 11. there 12. happened / occurred 13. followed 14. in 15. corner / middle / centre 16. as 17. for 18. would /could / might III. WRITING Part 1. (15 points) one point for each correct answer 1. what an excellent meal ( that /it was) 2. I ‘d rather not visit / go to the museum 3. Customers are requested not to smoke in this area of the restaurant. 4. Martin apologized to Angela for damaging / having damaged her car. 5. In spite of taking/ having taken / the fact that Peter had taken a taxi, he/ Peter arrived late for the concert. 6. Daisy has no problem (s) difficulty (in) making friends trouble 7. Mary wished (that) she had not bought the second - hand car 8. Tony finally succeeded in getting a good job. 9. Charles doesn’t live far from his aunt’s house. 10. The beach was so dirty / such a dirty one/ place that we decided not to stay. 11. I ‘ d rather not eat/ have ( my) lunch yet. 12. I think (that) it will/ might/ may / is going / likely to rain 13. No- one there noticed anything strange. 14. It is five years since she left university/ was at university / was a university student 15. The gate is closed so that the children can not / are unable to / will not run into the road.
  18. ĐỀ THI HỌC SINH GIỎI 12 – VÒNG TRƯỜNG MÔN : TIẾNG ANH- Năm học 2010-2011 Thời gian: 180 phút I. PHONETICS: 10 pts A. Pick out the word whose underlined part is pronounced differently from those of the other words (chọn từ mà phần gạch dưới có cách phát âm khác với các từ kia) 1. A. naked B. sacred C. needed D. walked 2. A. pens B. dogs C. boots D. lies 3. A. moon B. mood C. blood D. soon 4. A. angry B. ask C. hat D. bad 5. A. easy B. please C. pleasure D. teacher B. Underline the stressed syllable of the following words (gạch dưới những âm tiết nhấn của các từ sau) influence – accuracy – elementary – humanity – employee II. VOCABULARY: 20 pts A. Give the right form of word given in brackets (cho dạng đúng của từ) 1. Her sudden ………………………………… gave us a big surprise (arrive). 2. Do you like this new ………………………………… of apples (vary). 3. I was late because I ………………………………… how much time I’ll need (estimate). 4. My son could never be a teacher. He’s far too ………………………………(patient). 5. ………………………………… covers the sky at night (dark). 6. Vietnam declared its ………………………………… in 1945 (depend). 7. I’m ………………………………… of spiders (terror). 8. I couldn’t sleep for a week. I suffered from constant ………………………………… (sleep). 9. Small children are very ………………………………… in their behaviour. They just copy what they see (imitate). 10. There was a sudden ………………………………… of clapping and cheering as he rose to receive the Nobel Peace Prize (burst). B. Choose the correct answer to fill in each bland (chọn đáp án đúng) 1. She ………………………………… her neighbour’s children for the broken window. A. complained B. blamed C. accused D. denied 2. He let the letter ………………………………… onto the floor. A. fall B. falls C. falling D. fell 3. The house is old and it’s in bad ………………………………… A. condition B. damage C. state D. situation 4. He couldn’t afford to ………………………………… his car repaired. A. pay B. make C. do D. get 5. Of course he can lift that ! He’s as ………………………………… as a horse. A. tough B. big C. heavy D. strong 6. Can you deliver this letter ………………………………… hand? A. with B. by C. in D. to 7. The firemen fought for three hours before they managed to ………………………………… A. give up B. put out C. break off D. cut back 8. We have agreed ………………………………… the need for firm action. A. for B. on C. in D. at 9. After Joe’s mother died, he was ………………………………… up by his grandmother. A. brought B. taken C. grown D. drawn -1-
  19. 10. I have lived near the railway for so long now that I’ve grown ………………………………… to the noise of the trains. A. accustomed B. familiar C. unconscious D. aware III. GRAMMAR AND STRUCTURES : 25pts A. Find the part that needs correcting (tìm lỗi sai cần sửa). 1. Mrs Taylor smokes usually 20 cigarettes a day and her health is A B C badly affected. D 2. Many habits such as smoking, staying up late, and overeating can be A B C harm to our health. D 3. There can’t be enough rice this year for the country because of bad A B C whether. D 4. Jimmy felt happily when he heard the interesting news. A B C D 5. We are talking about the old man and his dog which are living next A B C door to us. D B. Put the verbs in the correct tense: 1. When my father (1)………………………………… (retire) next month, he(2) ………………………………… (teach) for 30 years. 2. He heard the clock (3) ………………………………… (strike) six and knew that it was time for him (4) ………………………………… (get) up. 3. I wish I (5) ………………………………… (know) you needed the book. I (6) ………………………………… (buy) it for you in London. 4. Ask your friends (7) ………………………………… (sit) on the same bench (8) ………………………………… (exchange) the papers you and they (9) ………………………………… , (10) ………………………………… (correct) the grammatical mistakes you can find in your friends’ paper. C. Finish each of the following sentences in such a way that it means the same as the written one. 1. My shoes need to be cleaned before the interview.  I must have ……………………………………………………………………………… 2. Just when I arrived at the station, the train was starting to move.  No sooner ………………………………………………………………………………… 3. “Let’s take some flowers to Aunt Penelope”, Jane suggested.  Jane suggested ………………………………………………………………………… 4. they were unable to finish their tennis game because of a heavy shower.  A heavy shower ………………………………………………………………………… 5. Whoever did that must have been a very brave person.  Only ……………………………………………………………………………………………… … 6. Nancy is proud of being a good cook.  Nancy prides ……………………………………………………………………………… -2-
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