Đề thi học sinh giỏi tỉnh Bà Rịa Vũng Tàu lớp 12 năm 2008 - 2009

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Đề thi học sinh giỏi tỉnh Bà Rịa Vũng Tàu lớp 12 năm 2008 - 2009 dành cho các bạn học sinh lớp 12 giúp các em ôn tập lại kiến thức đã học và đồng thời giáo viên cũng có thêm tư liệu tham khảo trong việc ra đề thi.

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Nội dung Text: Đề thi học sinh giỏi tỉnh Bà Rịa Vũng Tàu lớp 12 năm 2008 - 2009

SỞ GIÁO DỤC –ĐÀO TẠO KỲ THI CHỌN HỌC SINH GIỎI CẤP TỈNH TỈNH BÀ RỊA –VŨNG TÀU LỚP 12 THPT , NĂM HỌC 2008-2009 ĐỀ CHÍNH THỨC MÔN THI : TOÁN Thời gian làm bài :180 phút Bài 1 ( 4 điểm)
Cho hàm số: y  x 3  3x  2 có đồ thị là ( C) và một điểm M thay đổi trên đường thẳng (D) có phương trình: y = -3x + 2. Biện luận số tiếp tuyến kẻ được từ M tới ( C). Bài 2 ( 4 điểm) Tính các góc của tam giác ABC biết: 5 cos 2A  3  cos 2B  cos 2C    0 2 Bài 3 ( 4 điểm) Cho tứ diện ABCD nội tiếp mặt cầu tâm O bán kính bằng a. O nhìn các cạnh AB, BC, CD, DA một góc 60o . Tìm tứ diện có thể tích lớn nhất. Bài 4 ( 4 điểm) Xác định số hạng tổng quát của dãy số (u n ) biết rằng:  u1  2  3  u n 1  9u n  3u n ; (n  1, 2,3...) Bài 5 ( 4 điểm)
Hãy tìm hàm số f (x) xác định trên tập hợp các số thực không âm, nhận giá trị cũng trong tập đó và thỏa 3 điều kiện sau: 1) f  x.f (y)  .f (y)  f (x  y), x, y  0 2) f (2)  0 3) f (x)  0 , x  0;2  . ------------------------------------------------------ HẾT ---------- ----------------------------------------------- Họ và tên thí sinh: Số báo danh: Chữ ký giám thị 1:
SỞ GIÁO DỤC – ĐÀO TẠO KỲ THI CHỌN HỌC SINH GIỎI CẤP TỈNH TỈNH BÀ RỊA – VŨNG TÀU LỚP 12 THPT, NĂM 2008 – 2009 MÔN THI: TIN HỌC ĐỀ CHÍNH THỨC Thời gian làm bài thi: 180 phút Ngày thi: 11 – 11 – 2008 (Đề thi có 1 trang) Bài 1: Tính gần đúng với độ chính xác tùy ý (4 điểm) Cho f(x) là hàm đa thức có đạo hàm (khác không) lân cận nghiệm. Gọi xn là nghiệm gần đúng của f(x) thì: f(x ) xn+1 = xn - f '(xn ) là nghiệm gần đúng tốt hơn. n k Dựa vào công thức trên hãy viết chương trình tính a Với a, k, sai số tuyệt đối  (  10 -6) và nghiệm phỏng đoán ban đầu  nhập từ bàn phím. Bài 2: Ma phương bậc n (10 điểm) Cho một mảng 2 chiều cấp n x n với các phần tử là các số tự nhiên từ 1 đến n2, (mỗi số chỉ xuất hiện 1 lần) thỏa mãn tính chất: “Tổng các phần tử trên mỗi dòng, mỗi cột, mỗi một trong hai đường chéo đều có cùng một giá trị” Hãy viết chương trình liệt kê tất cả các ma phương bậc 5. Lưu ý sự khác nhau giữa các ma phương do phép biến hình đơn giản (quay, đối xứng) không được xem là một cách mới. Ví dụ về Ma phương bậc 3: 8 1 6 3 5 7 4 9 2 Tổng các phần tử trên các dòng, các cột, các đường chéo đều bằng 15. Các ma phương sau đây là một biến hình của Ma phương trên và không được xem là một cách mới: 4 3 8 4 9 2 6 1 8 9 5 1 3 5 7 7 5 3 2 7 6 8 1 6 2 9 4 Bài 3: Lập kế hoạch cho thuê máy (6 điểm) Công ty A có một cái máy cắt lúa để cho thuê. Đầu tháng công ty A nhận được đơn đăng ký thuê máy của m khách hàng. Mỗi khách hàng i sẽ cho biết tập Ni các ngày trong tháng cần sử dụng máy (i= 1, 2, …, m; tháng có 30 ngày). Công ty A chỉ có quyền hoặc là từ chối yêu cầu của khách hàng i hoặc là nếu chấp nhận thì phải bố trí máy phục vụ khách hàng i đúng những ngày mà khách hàng này yêu cầu. Hỏi công ty A phải tiếp nhận các yêu cầu của khách hàng như thế nào để tổng số ngày sử dụng máy là lớn nhất. Dữ liệu vào: File “Request.inp” - Dòng đầu tiên: Là một số nguyên K (1 ≤ K ≤ 30), mô tả số lượng khách hàng đăng ký thuê máy. - m dòng tiếp theo: mỗi dòng mô tả tập Ni các ngày trong tháng cần sử dụng máy của khách hàng thứ i. Dữ liệu xuất: File “Respond.out” - Dòng đầu tiên: Là một số nguyên, mô tả tổng số ngày cho thuê máy. - Dòng thứ 2: Mô tả các khách hàng được thuê máy. - Dòng thứ 3: Mô tả các ngày mà máy được cho thuê. Ví dụ: Request.inp Respond.out 4 10 3 5 7 9 1 4 2 4 6 8 1 2 3 4 5 6 7 9 10 15 1 2 7 1 2 4 6 10 15 -----Hết----- Họ tên thí sinh:…………………………………… Chữ ký GT 1:………………….. Số báo danh:………………………………………
SỞ GIÁO DỤC & ĐÀO TẠO KỲ THI CHỌN HỌC SINH GIỎI CẤP TỈNH TỈNH BÀ RỊA – VŨNG TÀU LỚP 12 THPT, NĂM HỌC 2008 – 2009 MÔN THI: TIẾNG ANH Thời gian làm bài: 180 phút ĐỀ CHÍNH THỨC Ngày thi: 11 – 11 – 2008 *Lưu ý: Đề thi gồm 06 trang; Thí sinh làm bài vào đề thi. SỐ ĐIỂM GIÁM KHẢO GIÁM KHẢO SỐ PHÁCH 1 2 I. Listen to two people, Sophie and Sally, arranging a party TWICE and choose the best answers to the questions. Circle your choices. (1 pt) 1. Who is going to book the restaurant? A. Sally B. Sophie C. Susie
2. How many people will be at the dinner? A. 50 B. 15 C. 55 3. What time will the booking be for? A. 7.00 B. 7.15 C. 7.30 4. What extra thing should the restaurant provide? A. A cake B. A special dish C. A plate with his name on 5. What are they thinking of doing after dinner? A. going home B. going to the movies C. dancing II. You are to hear one traveller talking about a recent holiday that he had with his wife in India. Listen TWICE and complete the notes that the man made during his holiday. (2 pts) Holiday in India. With: (1) ………………………………..company. Hotel name: The Shelton (Hyderabad) Number of days: (2) ……………………………………………………………… Total cost: (3) ……………………………………………………………… Problems
Room: (4) ………………………………… Bathroom not cleaned everyday. Food: (5) ……………………..…and spicy (6) ……………………………………. Service: (7) …………………………………………. Waiters: (8) …………………………………………. Excursions: (9) ……………………………………….(10) ………………………………. Action to take: Get some of our money back! III. Complete the passage by writing the correct form of the words/verbs given in brackets (2 pts): Going home after midnight – It was a cold December morning, two days before Christmas. When I looked at my wristwatch, it was almost 1 a.m. I had to hurry home because my aunt didn’t know I had (1.sneak) ……………....… out of the house to meet my friends. We were out singing carols. We would walk from house to house singing Christmas songs. In exchange for our good tidings, each (2.house) ……..………… would give us a little present. One night, we were requested to sing at the Christmas party hosted by a rich man. Upon receiving the invitation, we were (3.joy) ……….….…….–really excited. So my friends and I thoroughly rehearsed the Christmas songs that our host wanted to hear. At the
party, we sang Joy to the World, Carol of the Bells, Silent Night, and The Christmas Song. After each song, the audience broke into (4.applaud) ……….…….. Everybody, especially the host, enjoyed our performance. Afterwards, he offered us fine food and a (5.substance) …………....…… amount of money. We were having so much fun at the party that we lost track of time. Suddenly I realized that I had to go home. I felt nervous upon reaching our doorstep. I was dreading my aunt’s reaction. She was very strict, and my late (6.arrive) ……………….……. would surely make her angry. I was already imagining the (7.pain) ………………… words she would throw in my direction. Even so, I knocked on the door, leaving my situation to fate. When the door opened, I saw my (8.smile) ………..……… aunt. She let me in without a word. Surprising? I couldn’t explain her reaction. Perhaps her unusual cheer was due to the spirit of Christmas. My aunt’s positive mood didn’t last long – it was Christmas cheer, indeed. However, I have learned a couple of lessons from that experience. First, life is funny and (9.predict) ………..…………. Just when you’re expecting something bad, the opposite happens. You simply have to roll with the punches. Second, I would no longer sneak out of the house late at night and put my own safety at risk. If I have to go anywhere, I’d ask
(10.permit)……………..…….. from an adult. Whether I’m allowed to go or not, at least I’d be free from fear. IV. Choose the words or phrases that best complete the sentences. Circle your choices (2 pts) 1. By 2 o’clock, he _____________ on the drum for three hours. I hope he stops soon! a. will have been practicing b.will be practicing c.has been practicing d.is practicing 2. I dread ___________ what would have happened if the lifeguard hadn’t seen you. a. thinking b. to think c. think d. thought 3. As ______ captain of __________ ship, I have complete __________ authority. a. the / the / Ø b. Ø / the / Ø c. a / a / the d. a and b 4. Neither Julie nor Sue ____________ to work today because they are both ill. a. goes b. go c. is going d. are going 5. Indigo is a vat color, _______called because it does not dissolve in water. a. which it b. it is c. but d. so
6. Helen’s parents were very pleased when they read her school _____________. a. report b. papers c. diploma d. account 7. Our teacher ___________ us some difficult exercises for homework. a. set b. put c. obliged d. made 8. Why don’t we go to the park _____________? a. in the car b. with a car c. with car d. by the car 9. Not only ___________ to assess students’ ability, but it is also used to arrange classes. a. to use the exam result b. is the exam result used c. the exam result is used d. using the exam result 10. The two cars for sale were in poor condition, so I didn’t buy ___________. a. both of them b. either of them c. neither of them d each of them 11. They had ________ ashtrays on the table. a. two square glass b. square two glass c. glass two square d. two glass square
12. The air inside a house or an office building often has higher concentrations of contaminants __________ heavily polluted outside air. a. than does b. more c. as some that are d. like of 13. Following the guidelines for speaking and voting established by the book Robert’s Rules of Order, _________ during meetings. a. and avoid large decision-making organizations' procedural confusion b. large decision-making organizations avoid procedural confusion c. is procedural confusion avoided by large decision making organizations d. are avoiding procedural confusion in large decision making organizations 14. I was told yesterday that the car had been fixed but it’s broken down ___________ again. a. even b. still c. yet d. right 15. Practically ___________ in the group passed up the opportunity to attend the computer skills seminar. a. each one b. anyone c. someone d. no one
16. For the new museum visitor ____________ for the veteran museum goer, the Museum Highlights Tour offers an excellent opportunity to see the most popular exhibits. a. too b. in addition c. as well as d. further 17. Bright colors _________ people with dark complexions. a. fit b. effect c. match d. suit 18. Please don’t _______________ the phone on me again! a. hang over b. hang out c. hang up d. hang on 19. None of the children would ____________ breaking the window. a. put in for b. own up to c. live up to d. come down to 20. You’re having problems now but I’m sure things will change __________ the better soon. a. on b. to c. by d. for V. IDENTIFY underlined words or phrases that are wrong and then CORRECT them (2 pts). Ex: 0. (A)No matter how (B)hardly she tried, she (C)failed the (D)entrance exam. => 0. B: hard
1. (A)The aircraft is traveling 50 times (B)faster than the (C)speed of (D)a pistol bullet. 2. Today (A)the number of people (B)who enjoy sports (C)is almost double (D)those of twenty years ago. 3. Natural predators, (A)disturbing from tourists, and pollution (B)have all (C)contributed to the (D)decline of the animal. 4. In some societies, (A)hiring people (B)cook, clean, (C)take care of children, and (D)do the yard work. 5.Some paper dolls, (A) which were once (B) relatively cheap, are (C) previously considered valuable collectors’(D)items. 6. Crickets rub (A)the legs (B)together to make (C)their chirping (D)sound. 7. Conservationists (A)hope that (B)someday captive wildlife (C)populations will be reestablished in (D)a wild. 8. The (A)scars of (B)the earthquake remain in the (C)naked rock, and stunted trees mark (D)their fault line. 9. Blowing out birthday candles is an (A)ancient test to see if a (B)growing child is (C)very strong to blow out a greater (D)number each year. 10. (A)Unlike a tractor (B)is, a mule (C)won’t turn over on a steep hillside (D)and crash the driver.
=> 1……………….. 2………………….. 3. ………………… 4. ………………….5. ………………… 6……………….. 7…………………. 8. ………………… 9. ……………..….10. ………………. VI. Comple the passage by writing in each blank with ONE suitable word. (2 pts) War Against Illiteracy Continues - In 1939 only 15 per cent of the school-age population attended school, while 80 per cent of the (1) ……………… population was illiterate. In 1945, President Hồ Chí Minh promised to provide all Vietnamese (2) …………… the chance to read and write. He wanted to eradicate illiteracy. The campaign was (3) ………..…huge success, and over 10 million people became literate between 1946 and 1954. From 1954 to 1975, illiteracy was eradicated in the 12-50 age group in (4) ………………northern provinces. Based on this success, the population of remote regions was targeted next. Finally, the third campaign came into (5) ………..……in the south, and from 1975 onwards 1.5 million people learned to read and write. Việt Nam now enjoys an excellent literacy rate of 94 per cent, and figures (6) ……………that more than 80 per cent of school-age children attend school. Now our challenge is (7) ……….……..… ensure that the remaining 20 per cent join them.- President Hồ Chí Minh insisted on (8)………..…..….…being learning opportunities
for everybody. The areas (9) …..……… the illiteracy rate remains highest, however, are often remote mountainous regions. Here the population is sparse, communication is often difficult, there is a lack of transportation, and there are (10) …………… opportunities for economic development than in highly populated urban areas. VII. Read the passage and choose the word that best completes each blank. Circle your choices (3 pts) A FUTURE IN THE DARK - For many of us, we are working, traveling and shopping in hours that used to be (1) ......... for relaxation and sleep. But, according (2) ......... the results of tests being (3) ......... by scientists, we are no longer getting enough darkness in our lives. In fact, (4) ......... shows that a growing number of health and environmental problems are (5) ......... a loss of darkness. Life has evolved with a day/night circle. People who go (6) ......... this day/night rhythm will notice an adverse impact on (7) ......... immune systems, and that’s not a good sign. We are (8) ......... a conflict between what our mind wants, and what our internal body clock prepares for us. Some experts (9) ......... that our biological clock is similar to the conductor of an orchestra, with the multiple rhythms of the body (10) ......... the various orchestra sections. The body clock is (11) .........on the light/dark cycle and it governs us for every (12) .........of activity and rest in our lives. It ensures that all
our various internal systems are working together – this is its sole (13) .......... By moving to 24-hour living, and not taking into (14) .........the dark side, we will effectively be throwing away the advantages of evolution, (15) ......... we care to admit it or not. 1. a. conserved b. reserved c. upheld d. defended 2. a. to b. at c. in d. with 3. a. carried out b. carried through c. worked up d. worked off 4. a. demonstration b. display c. research d. confirmation 5. a. prone to b. open to c. due to d. next to 6. a. down with b. without c. through d. behind 7. a. its b. his c. her d. their 8. a. creating b. contributing c. giving d. increasing 9. a. explain b. discuss c. enquire d. debate 10. a. describing b. corresponding c. expressing d. representing 11. a. done b. based c. decided d. established
12. a. prospect b. attitude c. position d. type 13. a. reason b. project c. purpose d. desire 14. a. interest b. importance c. detail d. account 15. a. so that b. whether c. unless d. in case VIII. Read the passage then choose the best answers. Circle your choices (1 pt) LIMITS OF THE HUMAN BODY - In the second millennium, one frequently asked question is: What are the limits of the human body? Is there a point at which it is physically impossible to do something? ‘One thing we’ve all learned in the last 30 years or so is that just about anything is humanly possible,’ says Dr. Jack Wilmore, from Texas A&M University and author of The Physiology of Sport and Exercise, part of which examines the limits of the human body. ‘As the new millennium progresses, I think you’ll see more records continue to fall in every sport. The talent pool is better than ever. Never before have so many good athletes competed, and not just in this country, but all over the world. With more people involved and competing, records will fall and new standards will be set.’
Many believed that it was physically impossible for a human to run a mile in under four minutes, but Roger Bannister proved that theory wrong with a three minute, 59 second mile (1.609 kilometers) in 1954. Today, sub four-minute miles are considered routine even in high school. And Bob Beamon stretched human performance in the 1968 Olympics with his historic long jump of 8.9027 meters. In an event in which a record is usually broken by mere inches, he shattered the previous jump by 0.6096 meters, but even his record was broken in 1991. ‘We’ve all seen reports of people doing superhuman feats of strength under duress, such as a man lifting a car off a child,’ Wilmore adds. ‘So we know that the human body can do things that go far beyond normal activity. That’s why it’s foolish to say any record can’t be broken. Who’s to say it won’t happen?’ One additional factor is just now becoming more understood and heavily emphasized: sports psychology. Getting inside the athlete’s head can be as effective as training and long workouts. According to Wilmore, the psychological aspect of sports should not be discounted because we now know that what makes the athlete tick mentally can be all-important. He points out that ‘most professional teams have hired sports psychologists for their players. It’s just another way of tapping into a human’s full potential.’
‘In addition, every aspect of athletics – training, nutrition, injury treatment – is far better than it’s ever been. Better coaching, training techniques, equipment and other factors all contribute to make today’s athletes more competitive than ever,’ he believes. ‘Children today tend to specialize in one or two sports instead of competing in several as was common twenty five years ago,’ Wilmore says. ‘That means they start concentrating on a sport much earlier and more intensely, and they become much better at it.’ Wilmore also says that the chances of women achieving new heights in athletics could be greater than men, as more women are now involved in sports than at any other time and they are starting at about the same age as boys, meaning that they are more skilled than the previous generation of girls. ‘Plus, women are taller and stronger than ever. It used to be rare to see a girl who towered above you. Now it seems like you see them every day.’ ‘There’s a lot we don’t know yet about the human body,’ he adds. ‘And one of those things is the full range of human potential. It can be foolish to try and put limits on what the human body can do.’ 1. What initial comment does Dr. Jack Wilmore make? a. There will always be limits to what the human body can achieve. b. It will become more and more difficult for athletes to break records.