Một chiếc cổng hình parabol dạng y=−12x2 có chiều rộng d=8m . Hãy tính chiều cao h của cổng. (Xem hình minh họa bên cạnh)

Khi quả bóng được đá lên, nó sẽ đạt độ cao nào đó rồi rơi xuống đất. Biết rằng quỹ đạo của quả là một cung parabol trong mặt phẳng với hệ tọa độ ,trong đó là thời gian (tính bằng giây ), kể từ khi quả bóng được đá lên; là độ cao( tính bằng mét ) của quả bóng. Giả thiết rằng quả bóng được đá lên từ độ cao . Sau đó giây, nó đạt độ cao và giây sau khi đá lên, nó ở độ cao . Hãy tìm hàm số bậc hai biểu thị độ cao theo thời gian và có phần đồ thị trùng với quỹ đạo của quả bóng trong tình huống trên.

Một của hàng buôn giày nhập một đôi với giá là đôla. Cửa hàng ước tính rằng nếu đôi giày được bán với giá đôla thì mỗi tháng khách hàng sẽ mua đôi. Hỏi của hàng bán một đôi giày giá bao nhiêu thì thu được nhiều lãi nhất?

Một vật chuyển động trong giờ với vận tốc () phụ thuộc vào thời gian có đồ thị của hàm số vận tốc như hình dưới. Trong khoảng thời gian giờ kể từ khi bắt đầu chuyển động, đồ thị đó là một phần của đường parabol có đỉnh và trục đối xứng song song với trục tung, khoảng thời gian còn lại đồ thị là một đoạn thẳng song song với trục hoành. Tính vận tốc của vật tại thời điểm .    

Một doanh nghiệp tư nhân A chuyên kinh doanh xe gắn máy các loại. Hiện nay doanh nghiệp đang tập trung chiến lược vào kinh doanh xe hon đa Future Fi với chi phí mua vào một chiếc là (triệu đồng) và bán ra với giá là triệu đồng. Với giá bán này thì số lượng xe mà khách hàng sẽ mua trong một năm là chiếc. Nhằm mục tiêu đẩy mạnh hơn nữa lượng tiêu thụ dòng xe đang ăn khách này, doanh nghiệp dự định giảm giá bán và ước tính rằng nếu giảm triệu đồng mỗi chiếc xe thì số lượng xe bán ra trong một năm là sẽ tăng thêm chiếc Vậy doanh nghiệp phải định giá bán mới là bao nhiêu để sau khi đã thực hiện giảm giá, lợi nhuận thu được sẽ là cao nhất.

Cho hình chữ nhật , . Trên các cạnh lần lượt lấy các điểm sao cho . Độ dài của trong khoảng nào sau đây thì diện tích tam giác đạt nhỏ nhất.

Một chiếc cổng như hình vẽ, trong đó , phía trên cổng có dạng hình parabol   Người ta cần thiết kế cổng sao cho những chiến xe container chở hàng với bề ngang thùng xe là , chiều cao là có thể đi qua được (chiều cao được tính từ mặt đường đến nóc thùng xe và thùng xe có dạng hình hộp chữ nhật). Hỏi đỉnh của parabol (theo mép dưới của cổng) cách mặt đất tối thiểu là bao nhiêu ?

Khi một quả bóng được đá lên nó sẽ đạt được độ cao nào đó rồi rơi xuống. Biết rằng quỹ đạo của quả bóng là một cung parabol. Giả thiết rằng bóng được đá từ độ cao 1m. Sau đó 1 giây nó đạt độ cao 8, 5m và 2 giây sau khi đá nó đạt độ cao 6m. Hỏi sau bao lâu quả bóng chạm đất (Tính chính xác đến hàng phần trăm).

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks from 46 to 50:

When you read something in a foreign language, you frequently come across words you do not fully understand. Sometimes you (46) ______ the meaning in a dictionary and sometimes you guess. The strategy you adopt depends very much upon the degree of accuracy you require and the time at your disposal. If you are the sort of person who tends to turn to the dictionary frequently, it is (47) ______ remembering that every dictionary has its limitations. Each definition is only an approximation and one builds up an accurate picture of the meaning of a word only after meeting it in a (48) ______ of contexts. It is also important to recognize the special dangers of dictionaries that translate from English into your native language and vice versa. If you must use a dictionary, it is usually far safer to consult an English-English dictionary. In most exams you are not permitted to use a dictionary. (49) ______ you are allowed to use one, it is very time-consuming to look up words, and time in exams is usually limited. You are, therefore, forced to guess the meaning of unfamiliar words. When you come across unknown words in an exam text, it is very easy to panic. However, if you develop efficient techniques for guessing the meaning, you will overcome a number of possible problems and help yourself to understand far more of the text than you at first thought likely. Two strategies which may help you guess the meaning of a word are: using contextual clues, both within the sentence and outside, and making use of clues (50) ______ from the formation of the word.

Question 47:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase thet best fits each of the numbered blanks from 31 to 35:

 Victor Gruen, an American architect, revolutionized shopping in the 1950s by creating the type of shopping centre that we now call a shopping mall. Gruen's (31) _______ was to provide a pleasant, quiet and spacious shopping environment with large car parks, which usually meant building in the suburbs. He also wanted people to be able to shop in all kinds of weather. He (32) _______ on using building designs that he knew people would feel comfortable with, but placed them in landscaped ‘streets’ that were entirely enclosed and often covered with a curved glass roof. This was done to (33) _______ some of the older shopping arcades of city centres, but while these housed only small speciality shops, Gruen's shopping malls were on a much grander scale. Access to the whole shopping mall was gained by using the main doors, which (34) _______ the shopping ‘streets’ from the parking areas outside. As there was no need to keep out bad weather, shops no longer needed windows and doors, and people could wander (35) _______ from shop to shop. In many cities, shopping malls now contain much more than just shops; cinemas, restaurants and other forms of entertainment are also growing in popularity. 

Question 34:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase thet best fits each of the numbered blanks from 31 to 35:

 Victor Gruen, an American architect, revolutionized shopping in the 1950s by creating the type of shopping centre that we now call a shopping mall. Gruen's (31) _______ was to provide a pleasant, quiet and spacious shopping environment with large car parks, which usually meant building in the suburbs. He also wanted people to be able to shop in all kinds of weather. He (32) _______ on using building designs that he knew people would feel comfortable with, but placed them in landscaped ‘streets’ that were entirely enclosed and often covered with a curved glass roof. This was done to (33) _______ some of the older shopping arcades of city centres, but while these housed only small speciality shops, Gruen's shopping malls were on a much grander scale. Access to the whole shopping mall was gained by using the main doors, which (34) _______ the shopping ‘streets’ from the parking areas outside. As there was no need to keep out bad weather, shops no longer needed windows and doors, and people could wander (35) _______ from shop to shop. In many cities, shopping malls now contain much more than just shops; cinemas, restaurants and other forms of entertainment are also growing in popularity. 

Question 33:

Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct word or phrase thet best fits each of the numbered blanks from 31 to 35:

 Victor Gruen, an American architect, revolutionized shopping in the 1950s by creating the type of shopping centre that we now call a shopping mall. Gruen's (31) _______ was to provide a pleasant, quiet and spacious shopping environment with large car parks, which usually meant building in the suburbs. He also wanted people to be able to shop in all kinds of weather. He (32) _______ on using building designs that he knew people would feel comfortable with, but placed them in landscaped ‘streets’ that were entirely enclosed and often covered with a curved glass roof. This was done to (33) _______ some of the older shopping arcades of city centres, but while these housed only small speciality shops, Gruen's shopping malls were on a much grander scale. Access to the whole shopping mall was gained by using the main doors, which (34) _______ the shopping ‘streets’ from the parking areas outside. As there was no need to keep out bad weather, shops no longer needed windows and doors, and people could wander (35) _______ from shop to shop. In many cities, shopping malls now contain much more than just shops; cinemas, restaurants and other forms of entertainment are also growing in popularity. 

Question 32:

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase for each of the blanks:

In an age when technology is developing faster than ever before, many people are being attracted to the idea of looking back into the past. One way they can do this is by investigating their own family history. They can try to  (37)               out more about where their family came from and what they did. This is now a fast-growing hobby, especial in countries with a  (38)                short history, like Australia and the United States. It is one thing to spend some time going through a book on family history and to take the  (39)               to investigate your own family's past. It is quite another to carry out the research work successfully. It is easy to set about it in a disorganised way and  (40)          yourself many problems which could have been avoided with a little forward planning. If your own family stories tell you that you are connected with a famous character, whether hero or criminal, do not let this idea take over your research. Just treat  it as an interesting possibility. A simple system for collecting and storing your track. The most important thing, (41)      find?  

Question 41:

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase for each of the blanks:

In an age when technology is developing faster than ever before, many people are being attracted to the idea of looking back into the past. One way they can do this is by investigating their own family history. They can try to  (37)               out more about where their family came from and what they did. This is now a fast-growing hobby, especial in countries with a  (38)                short history, like Australia and the United States. It is one thing to spend some time going through a book on family history and to take the  (39)               to investigate your own family's past. It is quite another to carry out the research work successfully. It is easy to set about it in a disorganised way and  (40)          yourself many problems which could have been avoided with a little forward planning. If your own family stories tell you that you are connected with a famous character, whether hero or criminal, do not let this idea take over your research. Just treat  it as an interesting possibility. A simple system for collecting and storing your track. The most important thing, (41)      find?  

Question 37:

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase for each of the blanks:

In an age when technology is developing faster than ever before, many people are being attracted to the idea of looking back into the past. One way they can do this is by investigating their own family history. They can try to  (37)               out more about where their family came from and what they did. This is now a fast-growing hobby, especial in countries with a  (38)                short history, like Australia and the United States. It is one thing to spend some time going through a book on family history and to take the  (39)               to investigate your own family's past. It is quite another to carry out the research work successfully. It is easy to set about it in a disorganised way and  (40)          yourself many problems which could have been avoided with a little forward planning. If your own family stories tell you that you are connected with a famous character, whether hero or criminal, do not let this idea take over your research. Just treat  it as an interesting possibility. A simple system for collecting and storing your track. The most important thing, (41)      find?  

Question 38:

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase for each of the blanks:

In an age when technology is developing faster than ever before, many people are being attracted to the idea of looking back into the past. One way they can do this is by investigating their own family history. They can try to  (37)               out more about where their family came from and what they did. This is now a fast-growing hobby, especial in countries with a  (38)                short history, like Australia and the United States. It is one thing to spend some time going through a book on family history and to take the  (39)               to investigate your own family's past. It is quite another to carry out the research work successfully. It is easy to set about it in a disorganised way and  (40)          yourself many problems which could have been avoided with a little forward planning. If your own family stories tell you that you are connected with a famous character, whether hero or criminal, do not let this idea take over your research. Just treat  it as an interesting possibility. A simple system for collecting and storing your track. The most important thing, (41)      find?  

Question 39:

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase for each of the blanks:

In an age when technology is developing faster than ever before, many people are being attracted to the idea of looking back into the past. One way they can do this is by investigating their own family history. They can try to  (37)               out more about where their family came from and what they did. This is now a fast-growing hobby, especial in countries with a  (38)                short history, like Australia and the United States. It is one thing to spend some time going through a book on family history and to take the  (39)               to investigate your own family's past. It is quite another to carry out the research work successfully. It is easy to set about it in a disorganised way and  (40)          yourself many problems which could have been avoided with a little forward planning. If your own family stories tell you that you are connected with a famous character, whether hero or criminal, do not let this idea take over your research. Just treat  it as an interesting possibility. A simple system for collecting and storing your track. The most important thing, (41)      find?  

Question 40:

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct word or phrase that best fits each of the numbered blanks:

Many animals in the wild are suspicious and fearful of human beings. Many animals would take flight instantly (31)______ a human approaches. Man, however, soon discovered that some animals can be tamed or domesticated. Unlike animals in the wild, these animals would (32) _______ man to come close to them. They would even allow their owners to stroke or pet them. In the early times, man would domesticate animals by setting traps to catch their young. A young animal is (33) _______ easily domesticated than an adult one. From young, the animal learns to trust and obey its owner. Many different kinds of animals have been domesticated. Some common examples are animals like horses, elephants, chickens and pigs. The dog, which is also (34) _______as “man’s best friend”, is one of the first animals to have been domesticated. One of the most unusual animals to have been domesticated is the pig. In England long ago, the pig was a wild animal. It was a ferocious and aggressive (35)_______ which was not easily captured. Yet nowadays, the domesticated pig is no longer the lean and tough creature it used to be.  

Question 34: