Một công ty muốn thiết kế hộp dựng sữa với thể tích 1 đã giao cho hai nhóm thiết kế: * nhóm 1: Thiết kế vỏ hộp là hình hộp chữ nhật với đáy là hình vuông * nhóm 2: Thiết kế vỏ hộp là hình trụ. Biết rằng để tiết kiệm được nguyên vật liệu thì vỏ hộp phải có diện tích toàn phần nhỏ nhất, do đó các nhóm phải tìm cách thiết kế sao cho diện tích vỏ hộp nhỏ nhất. Kí hiệu  diện tích vỏ hộp nhỏ nhất theo phương án của nhóm 1 và là diện tích vỏ hộp nhỏ nhất theo phương án của nhóm 2. Tính tỉ số   ?         

Một công ty muốn thiết kế hộp dựng sữa với thể tích 1 đã giao cho hai nhóm thiết kế: * nhóm 1: Thiết kế vỏ hộp là hình hộp chữ nhật với đáy là hình vuông * nhóm 2: Thiết kế vỏ hộp là hình trụ. Biết rằng để tiết kiệm được nguyên vật liệu thì vỏ hộp phải có diện tích toàn phần nhỏ nhất, do đó các nhóm phải tìm cách thiết kế sao cho diện tích vỏ hộp nhỏ nhất. Kí hiệu  diện tích vỏ hộp nhỏ nhất theo phương án của nhóm 1 và là diện tích vỏ hộp nhỏ nhất theo phương án của nhóm 2. Tính tỉ số   ?         

Trong giai đoạn từ năm 1980 đến năm 1994, tỉ lệ phần trăm những hộ gia đình ở Mỹ có ít nhất một đầu máy video (VCR) đã được mô hình hóa bởi hàm số sau: trong đó là thời gian được tính bằng năm . Thời điểm mà con số VCR tăng nhanh nhất gần với giá trị nào nhất là :

Một người nông dân có 15 000 000 đồng để làm một cái hàng rào hình chữ E dọc theo một con sông (như hình vẽ) để làm một khu đất có hai phần chữ nhật để trồng rau. Đối với mặt hàng rào song song với bờ sông thì chi phí nguyên vật liệu là 60 000 đồng là một mét, còn đối với ba mặt hàng rào song song nhau thì chi phí nguyên vật liệu là 50 000 đồng một mét. Tìm diện tích lớn nhất của đất rào thu được.           

  Bạn TÀI muốn có USD để đi du lịch châu Âu. Để sau năm thực hiện được ý định thì hàng tháng bạn TÀI phải gửi tiết kiệm bao nhiêu (làm tròn đến hàng đơn vị)? Biết lãi suất một tháng.  

Cho một tấm nhôm hình vuông cạnh 6 cm. Người ta muốn cắt một hình thang như hình vẽ. Tìm tổng x + y để diện tích hình thang EFGH đạt giá trị nhỏ nhất.  

Công ty SỮA ÔNG THỌ chuyên sản xuất các hộp sữa hình trụ có thể tích bằng 314 cm3. Chi phí nguyên liệu làm 2 phần nắp hộp sữa là 200 đ /cm2 và chi phí nguyên liệu phần vỏ bao quanh hộp sữa là 400 đ/cm2. Hỏi bán kính đáy của hộp là bao nhiêu để chi phí làm hộp đựng sữa là ít nhất (Lấy )  

Một tấm đề can hình chữ nhật được cuộn tròn lại theo chiều dài được một khối trụ có đường kính 44,9 cm. trong thời gian vừa qua nhà trường đã sử dụng để in các băng rôn, khẩu hiệu tuyên truyền cho các em học sinh trường THPT Hậu Lộc 2 không sử dụng pháo trong dịp Tết Nguyên Đán do đó đường kính của cuộn đề can còn lại là 12,5cm. Biết độ dày của tấm đề can là 0,06cm, hãy tính chiều dài L của tấm đề can đã sử dụng ? (làm tròn đến hàng đơn vị).        

Một chi tiết máy có hình dạng như hình vẽ 1, các kích thước được thể hiện trên hình vẽ 2 (hình chiếu bằng và hình chiếu đứng).   Người ta mạ toàn phần chi tiết này bởi một hợp kim chống gỉ. Để mạ  bề mặt cần số tiền 150000đ. Số tiền nhỏ nhất có thể dùng để mạ 10000 chi tiết máy là bao nhiêu? (làm tròn đến đơn vị nghìn đồng). 

Một chiếc xô hình nón cụt đựng hóa chất ở phòng thí nghiệm có chiều cao 20 cm, đường kính hai đáy lần lượt là 10cm và 20 cm. Cô giáo giao cho bạn An sơn mặt ngoài của xô (trừ đáy). Tính diện tích bạn An phải sơn (làm tròn đến hai chữ số sau dấu phẩy).         

Một trang chữ của một tạp chí cần diện tích là . Lề trên, lề dưới là 3cm; lề phải, lề trái là 2cm. Khi đó chiều ngang và chiều dọc tối ưu của trang giấy lần lượt là:  

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 32 to 36:

School exams are, generally speaking, the first kind of tests we take. They find out (32) _____ much knowledge we have gained. But do they really show how intelligent we are? After all, isn’t it a fact that some people who are very successful academically don’t have any common sense? Intelligence is the speed at which we can understand and react to new situations and it is usually tested by logic puzzles. (33) _____ scientists are now preparing advanced computer technology that will be able to “read” our brains, for the present, tests are still the most popular ways of measuring intelligence. A person’s IQ is their intelligence (34) _____is measured by a special test. The most common IQ tests are run by Mensa, an organization that was founded in England in 1946. By 1976 it had 1,300 members in Britain. Today there are 44,000 Britain and 100,000 worldwide, (35) _____ in the US. People talking the tests are judged in relation to an average score of 100, and those (36) _____ score over 148 are entitled to join Mensa. This works out at 2% of the population. Anyone from the age of six can take the tests. All the questions are straightforward and most people can answer them if allowed enough time. But that’s the problem – the whole point of the tests is that they’re against the clock.

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 that best fits each of the numbered blanks from 32 to 36:

School exams are, generally speaking, the first kind of tests we take. They find out (32) _____ much knowledge we have gained. But do they really show how intelligent we are? After all, isn’t it a fact that some people who are very successful academically don’t have any common sense? Intelligence is the speed at which we can understand and react to new situations and it is usually tested by logic puzzles. (33) _____ scientists are now preparing advanced computer technology that will be able to “read” our brains, for the present, tests are still the most popular ways of measuring intelligence. A person’s IQ is their intelligence (34) _____is measured by a special test. The most common IQ tests are run by Mensa, an organization that was founded in England in 1946. By 1976 it had 1,300 members in Britain. Today there are 44,000 Britain and 100,000 worldwide, (35) _____ in the US. People talking the tests are judged in relation to an average score of 100, and those (36) _____ score over 148 are entitled to join Mensa. This works out at 2% of the population. Anyone from the age of six can take the tests. All the questions are straightforward and most people can answer them if allowed enough time. But that’s the problem – the whole point of the tests is that they’re against the clock.

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 that best fits each of the numbered blanks from 31 to 35:

Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can help a person understand these changes and provide him (35)____the skills for adjusting to them.

Question 35: 

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 31 to 35:

Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can help a person understand these changes and provide him (35)____the skills for adjusting to them.

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 that best fits each of the numbered blanks from 32 to 36:

School exams are, generally speaking, the first kind of tests we take. They find out (32) _____ much knowledge we have gained. But do they really show how intelligent we are? After all, isn’t it a fact that some people who are very successful academically don’t have any common sense? Intelligence is the speed at which we can understand and react to new situations and it is usually tested by logic puzzles. (33) _____ scientists are now preparing advanced computer technology that will be able to “read” our brains, for the present, tests are still the most popular ways of measuring intelligence. A person’s IQ is their intelligence (34) _____is measured by a special test. The most common IQ tests are run by Mensa, an organization that was founded in England in 1946. By 1976 it had 1,300 members in Britain. Today there are 44,000 Britain and 100,000 worldwide, (35) _____ in the US. People talking the tests are judged in relation to an average score of 100, and those (36) _____ score over 148 are entitled to join Mensa. This works out at 2% of the population. Anyone from the age of six can take the tests. All the questions are straightforward and most people can answer them if allowed enough time. But that’s the problem – the whole point of the tests is that they’re against the clock.

Question 35:

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 31 to 35:

Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can help a person understand these changes and provide him (35)____the skills for adjusting to them.

Question 31: 

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 32 to 36:

School exams are, generally speaking, the first kind of tests we take. They find out (32) _____ much knowledge we have gained. But do they really show how intelligent we are? After all, isn’t it a fact that some people who are very successful academically don’t have any common sense? Intelligence is the speed at which we can understand and react to new situations and it is usually tested by logic puzzles. (33) _____ scientists are now preparing advanced computer technology that will be able to “read” our brains, for the present, tests are still the most popular ways of measuring intelligence. A person’s IQ is their intelligence (34) _____is measured by a special test. The most common IQ tests are run by Mensa, an organization that was founded in England in 1946. By 1976 it had 1,300 members in Britain. Today there are 44,000 Britain and 100,000 worldwide, (35) _____ in the US. People talking the tests are judged in relation to an average score of 100, and those (36) _____ score over 148 are entitled to join Mensa. This works out at 2% of the population. Anyone from the age of six can take the tests. All the questions are straightforward and most people can answer them if allowed enough time. But that’s the problem – the whole point of the tests is that they’re against the clock.

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 that best fits each of the numbered blanks from 31 to 35:

Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can help a person understand these changes and provide him (35)____the skills for adjusting to them.

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 that best fits each of the numbered blanks from 31 to 35:

Education is more important today than ever before. It gives them the specialized training they may need to (31)_______ for a job or career. For example, a person must meet certain educational requirements and obtain a license or certificate before he can practice law or medicine. Many fields, like computer operation or police work, (32)_______ satisfactory completion of special training courses. Education is also important (33)_______ it helps people get more out of life. It increases their knowledge and understanding of the world. It helps them acquire the skills that make life more interesting and enjoyable, such as the skills needed to participate in a sport, paint a picture, or play a musical instrument. Such education becomes (34)_______ important as people gain more and more leisure time. Education also helps people adjust to change. This habit has become necessary because social changes today take place with increasing speed and affect the lives of more and more people. Education can help a person understand these changes and provide him (35)____the skills for adjusting to them.

 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 that best fits each of the numbered blanks from 24 to 28:

Few people now realize the reality of global warming and its effects on the world’s climate. Many scientists (24) _______ the blame for recent natural disasters on the increase in the world’s temperatures and are convinced that, more than ever before, the Earth is at (25) _______ from the forces of the wind, rain and sun. According to them, global warming is making extreme weather events, such as hurricanes and droughts, even more severe and causing sea levels all around the world to rise. Environmental groups are putting pressure on governments to take action to reduce the amount of carbon dioxide which is given (26) _______ by factories and power plants, thus attacking the problem at its source. They are in (27) _______ of more money being spent on research into solar, wind, and wave energy devices, which could then replace existing power (28) _______. Some scientists, however, believe that even if we stopped releasing carbon dioxide and other gases into the atmosphere tomorrow, we would have to wait several hundred years to notice the results. Global warming, it seems, is to stay.

Question 25: