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:

The United States has many different types of families. While most American families are traditional, (31) __________ a father, a mother and one or more children, 22 percent of all American families in 1998 were headed by one parent, usually a woman. In a few families in the United States, there are no children. These (32) ___________ couples may believe that they would not make good parents; they may want freedom from responsibilities of childbearing; or, perhaps they (33) ___________ physically able to have children. Other families in the United States have one adult who is a stepparent. A stepmother or stepfather is a person who joins a family by marrying a father or a mother. Americans (34) ___________ and accept these different types of families. In the United States people have right to privacy and Americans do not believe in telling other Americans what type of family group they must belong to. They respect each other’s choices regarding family groups. Families are very important (35) ___________ Americans.  

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:

The United States has many different types of families. While most American families are traditional, (31) __________ a father, a mother and one or more children, 22 percent of all American families in 1998 were headed by one parent, usually a woman. In a few families in the United States, there are no children. These (32) ___________ couples may believe that they would not make good parents; they may want freedom from responsibilities of childbearing; or, perhaps they (33) ___________ physically able to have children. Other families in the United States have one adult who is a stepparent. A stepmother or stepfather is a person who joins a family by marrying a father or a mother. Americans (34) ___________ and accept these different types of families. In the United States people have right to privacy and Americans do not believe in telling other Americans what type of family group they must belong to. They respect each other’s choices regarding family groups. Families are very important (35) ___________ Americans.  

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:

Last year, thieves broke into a Scottish stately home and stole only one thing: a rhino horn trophy, which at 1.5 meters was the longest in the world. Meanwhile, in China, pharmaceutical factories have been building up (31)______of antiques made from rhino horn, for the sole purpose of smashing them to powder to make the (32)_______ingredient of many of their medicines. And in Zimbabwe, 34 poachers died in 1990 in the search for the black rhino. Recently, conservationists met to (33)_______a campaign to persuade countries where rhino horn is still part of the traditional medicine to switch to substitutes. The biggest threat to the survival of the rhinoceros is the refusal of certain countries to enforce a ban on domestic trading in rhino horn. The rhino horn is included in many doses for disorders raging from fevers to nosebleeds. Horn, like fingernails, is made of keratin and has no proven medicinal (34)_______. Traditional substitutes, such as horn from buffalo or antelope, are regarded as second best. The battle is thought to be winnable. But it may be harder than the battle against the trade in ivory, for there is a (35)_______between the two commodities. Ivory is a luxury; rhino horn, people believe, could save the life of their child.  

Question 35:

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

GLOBAL WARMING

Few people now question the reality of global warming and its effects on the world’s climate. Many scientists (31) ________ 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 risk from the forces of the wind, rain and sun. (32) ________ to them, global warming is making extreme weather events, such as hurricanes and droughts, even more (33) ________ 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 (34) ________ by factories and power plants, thus attacking the problem at its source. They are in favor of more money being spent on research into solar, wind and wave energy devices, which could then replace existing power station. Some scientists, (35) ________, 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 31:        

Choose the word or phrase (A, B, C or D) that best fits the blank space in the following passage:

                                                               LOOK ON THE BRIGHT SIDE       

Do you ever wish you were more optimistic, some one who always (21)_____ to be successful? Having some one around who always fears the worst isn’t really a lot of (22)_____we all know someone who sees a single cloud on a sunny day and says: “It looks like rain.”. But if you catch yourself thinking such things, it’s important to do something (23)_____ it. You can change your view of life, (24)_____ to psychologists, it only takes a little effort, and you’ll find life more rewarding as a (25)______. Optimism, they say, is partly about self-respect and confidence, but it’s also a more positive way of looking at life and all it has to offer. Optimists are more (26)_______to start new projects and generally more prepared to take risks. Upbringing is obviously very important in forming your (27)_______ to the world. Some people are brought up to (28)______too much on others and grow up forever blaming other people when anything goes wrong. Most optimists, on the (29) _____hand, have been brought up not to regard failure as the end of the world - they just (30)_____with their lives.

Question 21:

Read the following passage and choose 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:

Why is it that many teenagers have the energy to play computer games until late at night but can’t find the energy to get out of bed (26) __________ for school? According to a new report, today’s generation of children are in danger of getting so (27)________ sleep that they are putting their mental and physical health at (28)_________. Adults can easily survive on seven to eight hours sleep a night, (29)____________teenagers require nine or ten hours. According to medical experts, one in five youngsters (30)___________ anything between two and five hours sleep a night less than their parents did at their age.

Question 26:

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.

A trend that has emerged recently is the sharing of childcare (1) __________ between husband and wife. Young couples will try to arrange their work schedules so that they work opposite hours or shifts in order that one parent is always home with the children. Since childcare is expensive, this saves money for the young couple trying to establish themselves and provide a secure environment for the family. Husband and wife may also share household chores. Some fathers are just as capable as mothers at cooking dinner, changing and bathing the baby, and doing the laundry. In some cases, the woman’s salary is for family (2) __________ and the father becomes the “househusband." These cases are still fairly rare. One positive trend, however, is that fathers seem to be spending more time with their children. In a recent survey, 41% of the children sampled said they spend equal time with their mothers and fathers. “This is one of our most significant cultural changes,” says Dr. Leon Hoffman, who co-directs the Parent Child Center at the New York Psychoanalytic Society. In practice, for over 30 years, Hoffman has found "a very dramatic difference in the involvement of the father in everything from care-taking to general decision (3) __________ around kids' lives.” Another factor has recently been added to the childcare formula. The number of people who work from home nearly full-time rose 23% from the last decade. The (4) _________ of technology - computers, faxes, teleconferencing - has made it easier for at-home workers to be constantly in touch. Will this new flexibility in the workforce bring a positive change for the (5) __________ of children? Only time will tell.  

Question 2:

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:   

There are several changes in the procedure for employees ___5___ wish to apply for vacant positions within the company. These changes make it much easier for in-house employees to fill vacancies that occur. First, __6__ most important difference is that employees will now be notified of all available positions before the positions are advertised for the general public. Accordingly, all in-house candidates will be interviewed before we see any out-side candidates, and we will offer the job to outside candidates only if no current employees are able to fill the position. Second, under the new procedure, in-house employees can be hired even if they don’t __7__ all job requirements. Under our old policy, in-house employees had to meet all job qualifications in order to obtain the vacant position. Now, however, employees who have proven themselves dedicated __8__ the company will be hired for a vacant position even if they are lacking some minor qualifications; training will be provided. A third change involves recommendations. Form now on, employees do not need to be recommended for an in-house position before they __9__. Instead, employees may apply as soon as they are aware of the vacancy. The remaining procedures and policies (those regarding increase in pay, interview procedure, and hiring approval) remain the same.

Question 9:

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

                                                                SCHOOL LUNCH

Research has shown that over half the children in Britain who take their own lunches to school do not eat (31) _______ in the middle of the day. In Britain, schools have to provide meals at lunchtime. Children can choose to bring their own food or have lunch at the school canteen. One shocking (32) _______ of this research is that school meals are much healthier than lunches prepared by parents. There are strict standards for the preparation of school meals, which have to include one portion of fruit and one of vegetables, as well as meat, a dairy item and starchy food like bread or pasta. Lunchboxes (33) _______ by researchers contained sweet drinks, crisps and chocolate bars. Children (34) _______ twice as much sugar as they should at lunchtime. The reseat will provide a better understanding of why the percentage of overweight students in Britain has increased in the last decade. Unfortunately, the government cannot instruct parents, but it can remind them of the (35) _______ value of milk, fruit and vegetables. Children can easily develop bad eating habits at this age, and parents are the only ones who can prevent it.

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 31 to 35:

Nearly all the discoveries that have been made through the ages can (31)……in books. The invention of the book is one of humankind’s(32)………achievements, the importance of which can not be overestimated. Books are very adaptable, providing us with both entertainment and information. The production of books began in Ancient(33)………though not in the form that is accessible to us today. The books read by the Romans, however, have some similarities to the ones we read now. Until the middle of the 15th century, in Europe, all books were written by hand. They were often(34) …………illustrated and always rare and expensive. With printing came the possibility of cheap, large-scale publication and distribution of books making (35)………more widespread and recognizable.  

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:

 In Germany, it's important to be serious in a work situation. They don't mix work and play so you shouldn't make jokes (31) _______ you do in the UK and USA when you first meet people. They work in a very organized way and prefer to do one thing at a time. They don't like interruptions or (32)_______ changes of schedule. Punctuality is very important so you should arrive on time for appointments. At meeting, it's important to follow the agenda and not interrupt (33) _______ speaker. If you give a presentation, you should focus (34) _______ facts and technical information and the quality of your company's products. You should also prepare well, as they may ask a lot of questions. Colleagues normally use the family names, and title - for example "Doctor" or "Professor", so you shouldn't use first names (35) _______ a person asks you to.

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 36 to 40:

Sugar tastes sweet because of thousands of receptors on the tongue which connect the substance with the brain. The taste of sweetness is universally accepted as the most pleasurable known, although it is a fructose. Abundant is the most common occurring sugar, (36)______ of which include fruit and honey. Sucrose, which supplies glucose to the body, is (37)______ from the sugar cane plant, and white sugar (pure sucrose) is used by food technologists to (38)______ sweetness in other substances. Approximately a dozen artificial sweeteners have been discovered; one of the earliest was Sorbitol from France. Manufacturers add large amounts of sugar to foodstuffs but never more than the (39)______ required to produce the optimum pleasurable taste. Surprisingly, this amount is similar for different people and in different cultures. No one has (40)______ discovered a way to predict whether a substance will taste sweet, and it was by chance alone that all the man-made chemical sweeteners were found to be sweet.

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 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 26:

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 30 to 34:

As a small-business owner, you can avoid many problems simply by improving communication in your office. By clarifying everyone’s expectations and roles, you'll help to (30) ________ greater trust and increased productivity among employees. Here are a few tips for doing so. Practice active listening. The art of active listening includes (31) ________ close attention to what another person is saying, then paraphrasing what you've heard and repeating it back. Concentrate (32)___the conversation at hand and avoid unwanted interruptions (cellphone calls, others walking into your office, etc.). Take note of how your own experience and values may color your perception. Pay attention to non-verbal cues. We don't communicate with words alone. Every conversation comes with a host of non-verbal cues-facial expressions, body language, etc. - that may (33) ________ contradict what we’re saying. Before addressing a staff member or (34) ________ a project conference, think carefully about your tone of voice, how you make eye contact, and what your body is "saying." Be consistent throughout. Be clear and to the point. Don't cloud instructions or requests with irrelevant details, such as problems with past projects or issues with long-departed personnel. State what you need and what you expect. Ask, "Does anyone have any questions?". Demonstrate that you prefer questions up-front as opposed to misinterpretation later on.

Question 34:

Question 33: 

A tiny village school is soon to celebrate its 110 birthday - against all expectations. Five years ago it seemed certain to close but parents and other villagers fought the local education authority and raised funds to keep it (31)_______. It is now ending its first term as a school (32)_____by the village community and the villagers are just proud of their achievement. They were furious when education chiefs tried to make them send the village children to other schools further away because the number of pupils at the village school was too (33)_____. The villagers started a huge campaign to (34) _____money. They collected enough to hire a teacher and begin to help with school cleaning, lunch supervision and lessons. Now the school is doing well and it seems (35)____ it will continue to run in the future. 

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:

A typical person needs about 1,800 calories per day to stay running. They keep your organs operating (31) ________ and your brain running. They also keep your body warm. A person gains weight because he or she consumes more calories per day than necessary. The only way to lose fat is to reduce the number of calories that you consume per day. This is the basic principle (32) ________ going on a diet. Unfortunately, diets don't work for most people. They do lose weight but then go off the diet and put it back. Building a sensible diet and exercise plan is the key to maintaining a consistent weight. You need to figure out how many calories you need in a day and how many you actually (33) ________. The next step is to add exercise so that you can raise the number of calories you can consume per day. Burning 250 or 500 calories per day can make a big (34) ________. You can ride an exercise bike while you are watching television or you can take the stairs instead of the elevator. Find an exercise partner. Exercises can be a lot easier if there is someone to talk to. It’s a good idea to wear firm fitting clothes if you are (35) ________. Tight clothing acts as a reminder of what you are trying to accomplish.

Question 34:

Choose the word or phrase (A, B, C or D) that best fits the blank space in the following passage:

                                                               LOOK ON THE BRIGHT SIDE       

Do you ever wish you were more optimistic, some one who always (21)_____ to be successful? Having some one around who always fears the worst isn’t really a lot of (22)_____we all know someone who sees a single cloud on a sunny day and says: “It looks like rain.”. But if you catch yourself thinking such things, it’s important to do something (23)_____ it. You can change your view of life, (24)_____ to psychologists, it only takes a little effort, and you’ll find life more rewarding as a (25)______. Optimism, they say, is partly about self-respect and confidence, but it’s also a more positive way of looking at life and all it has to offer . Optimists are more (26)_______to start new projects and generally more prepared to take risks. Upbringing is obviously very important in forming your (27)_______ to the world. Some people are brought up to (28)______too much on others and grow up forever blaming other people when anything goes wrong. Most optimists, on the (29) _____hand, have been brought up not to regard failure as the end of the world - they just (30)_____with their lives.

Question 28:

Read the following passage and mark the letter A, B, C, or D to indicate the correct word or phrase that best fits each of the numbered blanks from 24 to 28:

 Personal space is a term that refers (24)_____the distance we like to keep between ourselves and other people. When (25) ______we do not know well gets too close we usually begin to feel uncomfortable. If a business colleague comes closer than 1.2 meters, the most common response is to move (26)______. Some interesting (27)______have been done in libraries. If strangers come too close, many people get up and leave the building; others use different methods such as turning their back on the intruder. Living in cities has made people develop new skills for dealing with situations where they are very close to strangers. Most people on crowded trains try not to look at strangers; they avoid skin contact, and apologize if hands touch by mistake. People use newspapers (28) ______a barrier between themselves and other people, and if they do not have one, they stare into the distance, making sure they are not looking into anyone’s eyes.

Question 25:

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:

The 15th Asian Games took place from December 1 through December 15, 2006, in Doha, Capital of Qatar. More than 10,000 athletes, who (31)___________ 45 countries and regions, took part in 39 sports and 424 events of the Games, the most important event in Asia. Some new events such as chess and triathlon were also included in the Games.The 15th Asian Games was organized at 34 sporting (32)___________, including Khalifa Stadium, which hosted the opening and closing ceremonies. The Opening Ceremony of the 15th Asian Games, Doha 2006, at Khalifa Stadium, was the most (33)___________ opening of any Games with 50,000 people to get into Khalifa Stadium and more than one billion television viewers. The Doha Asian Games Organizing Committee (DAGOC) wanted to ensure that everybody who saw the ceremony would have a memory for life as suggested in the (34)___________"The Games of Your Life." The 15th Asian Games was a successful sporting event that all (35)___________ would never forget.  

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:

The Internet has truly transformed how students do their homework. (31) ____homework today still means spending time in the library, it’s for a different reason. Rather than using books for research, students today are (32) ______to the Internet to download enormous amounts of data available online. In the past, students were limited to their school’s (33) _________ of books. In many cases, they got to the school library and found out that someone had already taken the books they needed. Nowadays, such inconvenience can be avoided since the Internet never runs out of information. Students, however, do have to (34)_____sure that the information they find online is true. Teachers have also benefited from the homework which is done on the Internet. They do not need to carry student's papers around with them any more. This is because online (35)______allow students to electronically upload their homework for their teachers to read and mark. Of course, this also means that students can no longer use the excuse that the dog ate their homework!

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 24 to 28:

 Personal space is a term that refers (24)______the distance we like to keep between ourselves  and other people. When (25)______we do not know well gets too close we usually begin to feel uncomfortable. If a business colleague comes closer than 1.2 meters, the most common response is to move (26_______ . Some interesting (27)______ have been done in libraries. If strangers come too close, many people get up and leave the building; others use different methods such as turning their back on the intruder. Living in cities has made people develop new skills for dealing with situations where they are very close to strangers. Most people on crowded trains try not to look at strangers; they avoid skin contact, and apologize if hands touch by mistake. People use newspapers (28)______ a barrier between themselves and other people, and if they do not have one, they stare into the distance, making sure they are not looking into anyone’s eyes.  

Question 24:

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

THE FIRST WOMAN SCIENTIST Hypatia was born in Alexandria, in Egypt, in 370 A.D. For many centuries, she was the only woman scientist to have a place in the history books. Hypatia’s father was director of Alexandria University, and he (31) ________ sure his daughter had the best education available. This was unusual, as most women then had few (32) ________ to study. After studying in Athens and Rome, Hypatia returned to Alexandria where she began teaching mathematics. She soon became famous (33) ________ her knowledge of new ideas. We have no copies of her book, but we know that she wrote several important mathematical works. Hypatia was also interested in technology and invented several scientific tools to help with her work. At the (34) ________, many rulers were afraid of science, and anyone connected with it was in danger. One day in March 415, Hypatia (35) ________ attacked in the street and killed.  

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 17 to 21:

During the last 400 years, most scientists have (17) ________on mathematics in their development of their inventions or discoveries. However, one great British scientist, Michael Faraday, did not make (18)__________of mathematics. Faraday, the son of a poor blacksmith, was born in London in 1791 and had no (19) ______beyond reading and writing. In 1812 Faraday was hired as a bottle washer by the great chemist Humphry Davy. Later, Faraday became a greater scientist than Davy, making the last years of Davy's life embittered (20) __________ jealousy. Faraday made the first (21)__________motor in 1821, a device that used electricity to produce movement. 

Question 20:

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:

All relationships go through difficult times. In the past, when married couples had problems they usually didn’t (31) _________. They had to either (32) _________ with each other or continue to live together in an unhappy relationship. Getting divorced wasn’t an option for most people due to economic and social reasons. Some people believe that this wasn’t such a bad thing. They say that relationships require hard work and (33) _________. “If a relationship is going to last a lifetime, you have to keep working at it,” says Doreen, who is celebrating her fiftieth wedding anniversary this year. “It isn’t all roses and romance. No one perfect all of the time. These days young people give up when there’s the (34) _________ argument.” Experts agree that communication is key. The most important thing is to keep talking. How many times have you heard yourself say to somebody, “If only you’d listen!” or “I wish you wouldn’t do that!” The truth is, the (35) ______ couples talk, the better their relationship can be.  

Question 34:

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

Here are tips that help succeed in your job interview: Always arrive early. If you do not know (46) _________ the organization is located, call for exact directions (47) ____________ advance. Leave some extra time for any traffic, parking, or unexpected events. If you are running late, call right away and let someone know. The best time to arrive is approximately 5 - 10 minutes early. Give yourself the time to read your resume one more time, to catch your breath, and to be ready for the interview. Once you are at the office, treat everyone you encounter with respect. Be (48) _________ to everyone as soon as you walk in the door. Wear a professional business suit. This point should be emphasized enough. First (49) ____________ are extremely important in the interview process. Women should (50)_________ wearing too much jewelry or make up. Men should avoid flashy suits or wearing too much perfume. It is also important that you feel comfortable. While a suit is the standard interview attire in a business environment, if you think it is an informal environment, call before and ask. Regardless, you can never be overdressed if you are wearing a tailored suit.

Question 49:

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:

The Internet has truly transformed how students do their homework. (31) ____homework today still means spending time in the library, it’s for a different reason. Rather than using books for research, students today are (32) ______to the Internet to download enormous amounts of data available online. In the past, students were limited to their school’s (33) _________ of books. In many cases, they got to the school library and found out that someone had already taken the books they needed. Nowadays, such inconvenience can be avoided since the Internet never runs out of information. Students, however, do have to (34)_____sure that the information they find online is true. Teachers have also benefited from the homework which is done on the Internet. They do not need to carry student's papers around with them any more. This is because online (35)______allow students to electronically upload their homework for their teachers to read and mark. Of course, this also means that students can no longer use the excuse that the dog ate their homework!

Question 31:  

Cho tập gồm phần tử. Có bao nhiêu tập con của khác rỗng và số phần tử là số chẵn?  

Một tổ công nhân có người. Cần chọn người, một người làm tổ trưởng, một tổ phó và một thành viên. Hỏi có bao nhiêu cách chọn?  

Cho các số nguyên dương ,  . Mệnh đề nào sau đây sai?

Một lớp học có bạn học sinh trong đó có cán sự lớp. Hỏi có bao nhiêu cách cử bạn học sinh đi dự đại hội đoàn trường sao cho trong học sinh đó có ít nhất một cán sự lớp.  

Cho đa giác đều nội tiếp trong đường tròn tâm . Biết rằng số tam giác có đỉnh là trong điểm gấp lần so với số hình chữ nhật có đỉnh là trong điểm . Vậy giá trị của là:

Trong một tổ học sinh có em gái và em trai. Thùy là một trong em gái và Thiện là một trong em trai đó. Thầy chủ nhiệm chọn một nhóm bạn tham gia buổi văn nghệ sắp tới. Hỏi thầy chủ nhiệm có bao nhiêu cách chọn mà trong đó có ít nhất một trong hai em Thùy hoặc Thiện không được chọn?

Có câu hỏi khác nhau gồm câu khó, câu trung bình, câu dễ. Từ câu đó có thể lập được bao nhiêu đề kiểm tra, mỗi đề gồm câu khác nhau, sao cho mỗi đề phải có loại câu hỏi (khó, trung bình, dễ) và số câu dễ không ít hơn ?

Giả sử ta dùng màu để tô màu cho nước khác nhau trên bản đồ và không có màu nào được dùng hai lần. Số các cách để chọn những màu cần dùng là:

Một bộ ghép hình gồm các miếng gỗ. Mỗi miếng gỗ được đặc trưng bởi tiêu chuẩn: chất liệu, màu sắc, hình dạng và kích cỡ. Biết rằng có chất liệu (gỗ, nhựa); có màu (xanh, đỏ, lam, vàng); có hình dạng (hình tròn, vuông, tam giác, lục giác) và có kích cỡ (nhỏ, vừa, lớn). Xét miếng gỗ “nhựa, đỏ, hình tròn, vừa”. Hỏi có bao nhiêu miếng gỗ khác miếng gỗ trên ở đúng hai tiêu chuẩn?

Trong mặt phẳng cho điểm, trong đó không có điểm nào thẳng hàng và trong tất cả các đường thẳng nối hai điểm bất kì không có hai đường thẳng nào song song, trùng nhau hoặc vuông góc. Qua mỗi điểm vẽ các đường thẳng vuông góc với các đường thẳng được xác định bởi trong điểm còn lại. Số giao điểm của các đường thẳng vuông góc giao nhau nhiều nhất là bao nhiêu?