Bài 1: Tìm số tự nhiên n để \(\left(3n+2\right)⋮\left(n^2+n+1\right)\)

Bài 1: Cho \(\Delta ABC\) có góc A = 90 độ, D là điểm thuộc AC, từ C vẽ đường thẳng d \(//\) với BD. Vẽ BE \(\perp\) d tại E. Chứng minh \(\Delta BAE\sim\Delta DBC\)

Bài 2: Cho \(\Delta ABC\) nhọn, tìm trên các cạnh BC, AC, AB là D, E, F sao cho chu vi \(\Delta DEF\) đạt giá trị nhỏ nhất

Bài 1: Cho hàm số y = (2m -1)x + m +1 (*)

a, Tìm m để đồ thị hàm số (*) đi qua A(-1;3)

b, Tìm m để đồ thị hàm số (*) cắt đường thẳng y = 2x -1 tại điểm có tung độ -3

c, Tìm m để đồ thị hàm số (*) và y = x+1, y = 2x -1 đồng quy

Bài 2: Cho hệ phương trình \(\left\{{}\begin{matrix}3x-2y=m+4\\5x+3y=8m-6\end{matrix}\right.\) với m là tham số

Tìm m để hệ có nghiệm (x;y) thỏa mãn \(A=x^2-2y^2\) đạt giá trị lớn nhất

Bài 3: Cho phương trình \(x^2-2mx+m^2-m+1=0\) với m là tham số

a, Tìm m để phương trình có 2 nghiệm phân biệt

b, Tìm m để \(A=x_1\cdot x_2-x_1-x_2\) đạt giá trị nhỏ nhất

Giải bất phương trình \(\dfrac{15-2x}{-5}\ge1\)

Bài 1: Tìm giá trị nhỏ nhất của P= \(\dfrac{x^2}{1+x^4}\)

Bài 2: Tìm x, y, z thỏa mãn phương trình \(9x^2+y^2+2z^2-18x+4z-6y+20=0\)

Bài 3: Chứng minh rằng với n là số tự nhiên và \(n\ge2\) thì

\(S=1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}\) không phải là một số tự nhiên

III. Read the text and look carefully at each line. Tick (Ö) the lines which are correct and pick out the unnecessary words. There are two examples at the beginning (0 and 00). Write your answers on the right lines provided.

CAMPING

SECTION B: READING COMPREHENSION

I. Read the text below and choose the best word or combination of words to fill in each blank. Write your answers (A, B, C or D) in the box provided.

AUDIOBOOKS - BOOKS ON CASSETTE

In the modern world, there is a wealth of leisure activities to choose from Entertainment industries (1) __________ for your leisure time. You can watch TV, listen to music, go to an art gallery or concert or, of course, read a book. Sometimes it seems that reading is (2) __________ because, (3) __________ you’re a fast reader, it can take a (4) __________ amount of time to finish a novel, for example. But in the modern world, time is something that can be in short supply.

Book publishers haven’t been (5) __________ to realize this and are now selling a product which needn’t (6) __________ as much of your time but still tells you an excellent story. The new products is the audiobook - cassette recordings of shortened novels, often read by well-known personalities or the authors themselves. Audiobooks are relatively new but people are becoming more aware of them and sales are increasing (7) __________.

One of the attractions of audiobooks is that they’re (8) __________ listening to the radio, only better. You can listen to what you want when you want, and you won’t ever miss anything. Much of their appeal (9) ________ in their flexibility. They allow you do to other things while you’re listening, such as driving or (10) __________ the housework. For some people, audio books can be a much more enjoyable way of gaining knowledge than reading

II. Fill in each of the numbered blanks with ONE suitable word. Write your answers (A, B, C or D) in the box provided.

About two hundred years ago man lived in greater harmony with his environment because industry was not much developed. Today the situation is quite (1) _________. People all over the world are worried about what is happening to the environment, because of modern industry and the need for more and more energy. Newspapers and magazines write (2) _________water pollution, air pollution and land pollution. Why is there so much (3) ________ about pollution. After all, people have been polluting the world around them for thousands and thousands of years. But in the past, there were not many people and (4) ________of room in the world so they could move to another place when their settlements became dirty.

Now, however, many parts of the world are (5)_________, people live in big cities and much of our waste, especially waste from factories, electric (6) _______ stations, the chemical industry and heavy industry is very dangerous. Fish die in the lakes, rivers and seas; forest trees die (7)_______. Much of this dangerous waste goes into the air and is carried by the wind for great distances. The earth is (8) ________home . We must take care of it for ourselves and for the next generations. This means (9) _________our environment clean.

The importance of this task is pointed out by ecologists, the scientists who study the (10)_______ between living things and the environment. However, each of us must do everything possible to keep the land, air and water clean.
III. Read the passage carefully and choose the best option for each sentence.

Most of us lead unhealthy lives: we spend far too much time sitting down. If, in addition, we are careless about our diets, our bodies soon become flabby and our systems sluggish. Then the guilt feelings start : “I must go on a diet”, “ I must try to lose weight” “ I must get more fresh air and exercise”, “I must stop smoking”, “I must try to keep fit” . There are some aspects of our unhealthy lives that we cannot avoid. I’m thinking of such features of modern urban life as pollution, noise, rushed meals and stress. But keeping fit is a way to minimize the effects of these evils.

The usual suggestion to a person who is looking for a way to keep fit is to take some sports. While it is true that every weekend you will find people playing football and hockey in the local park, they are outnumbered a hundred to one by the people who are simply watching them. It is an illusion to think that you will get fit by going to watch the football match every Saturday, unless you count the effort required to fight your way through the crowds to get to the best seats.

For those who do not particularly enjoy competitive sports – and it is especially difficult to do so if you are not good at them – there are such solitary activities as cycling, walking and swimming. What often happens, though, is that you do them in such a leisurely way, so slowly, that is doubtful if you are doing yourself much good, apart from the fact that you have at least managed to get up out of your armchair. Of course you can be very thorough about exercise, even fanatical. Many sports shops now sell frightening pieces of apparatus, chest-expanders and other mysterious gadgets of shiny spring steel, which, according to the advertisements, will bring you up to an Olympic standard of fitness, provided that you follow a rigorous and regular programme of exercises. Such programmes generally involve long periods of time bending these curious bits of metal into improbable shapes.

It all strikes me as utterly boring and also time-consuming. Somebody suggested recently that all such effort was pointless anyway because if you spend half an hour every day jogging round the local park, you will add to your life exactly the number of hours that you wasted doing the ‘jogging’ in the first place. The argument is false even if the facts are correct, but there is no doubt that exercise in itself can be boring.

Even after you have found a routine for keeping in shape, through sport or gymnastics or isometrics, you are still only half way to good health, because, according to the experts, you must also master the art of complete metal and physical relaxation. Now, this does not mean snoozing in the armchair or going dancing ( which is a good form of exercise in itself ) . It has to do with deep breathing , emptying your mind of all thoughts, meditation, and so on.

Yoga, as practiced in the West, is the most widely known and popular of the systems for achieving the necessary state of relaxation. Contrary to popular belief, you do not have to learn a lot of strange words or become a Buddhist in order to benefit from Yoga. It seems ironical, though, that as our lives have improved in a material sense, we have found it increasingly necessary to go back to forms of activity – physical effort on the one hand, and relaxation on the other – which were the natural way of life of our forefathers.

1. Unfitness is the result of ___________.

A. lack of fresh air and exercise B. overeating, smoking and living in town

C. not eating properly and not getting enough exercise D. not taking part in sports

2. Pollution, noise and stress are examples of ___________.

A. causes of unfitness B. bad features of living in towns C. the things we must avoid if we are to stay healthy D. industrial life and work

3. Our reaction to being out of condition is to ___________.

A. give up smoking and go on a diet B. start a programme of keep-fit exercises

C. make resolutions to lead a healthier life D.take up a sport

4. A lot of people who go to the park at the weekend are ___________.

A. football players B. football spectators C. keep-fit enthusiasts D. unfit or unhealthy

5. You cannot really enjoy competitive sports unless you are ___________.

A. young enough to play them B. very good at them C. fit enough to play them D. a solitary kind of person

6. The reason we don’t get much out of solitary sports such as walking is that we do not _________.

A. do them often enough B. have the encouragement of others

C. take them seriously enough D. do them vigorously enough

7. The writer does not like keep-fit programmes because he thinks ___________.

A. they take up too much time B. there are much easier ways of getting fit

C. they are a waste of time D. the apparatus is very silly

8. To be healthy we must ___________.

A. keep fit and active B. keep fit and learn to relax

C. be active and practise Yoga D. be very careful about what we eat and drink

9. Many people believe that in order to practise Yoga ___________.

A. you must learn a special vocabulary B. it is better to become a Buddhist

C. you must learn to relax completely D. you must wear special clothing

10. Our forefathers were healthy because ___________.

A. their way of life involved both exercise and relaxation B. they were careful to get plenty of fresh air and keep fit

C. they lived in the country and spent time out of doors D. they had simple work to do and very little to worry about

I. Finish each sentence in such a way that it means exactly the same as the one printed before it.

II. For each of the sentences, write a new sentence as similar as possible in meaning to the original sentence, using the word given in CAPITALS. This word must not be altered in any way.

1. I don’t think this record will ever be popular. (CATCH)

_________________________________________________________________________.

2. A police car has just stopped outside. (UP)

_________________________________________________________________________.

3. They didn’t punish Karen, only gave her a warning. (GOT)

_________________________________________________________________________.

4. What are you trying to say? (AT)

_________________________________________________________________________.

5. Graham stopped talking to deal with a customer. (OFF)

_________________________________________________________________________.

Bài 1: Tam giác ABC vuông tại A có góc B =50 độ,gọi M là điểm di chuyển trên AC,M không trùng với A và C,kẻ CH vuông góc với BM tại H,CH cắt BA tại O.
a, Chứng minh OA.OB=OC.OD
b, Tính góc OAH
Chứng minh rằng khi M di chuyển trên AC thì BM.BH + CM.CA không đổi

Bài 1: Cho x,y là các số thực khác 0 thỏa mãn \(x^2+y^2< x^2y^2\)

Chứng minh \(x^2+y^2>4\)

Vẽ hình chiếu đứng, bằng, cạnh của hình nón có chiều dài 50mm, đường kính 40mm trong trường hợp đáy hình nón song song với mặt phẳng chiếu đứng (vẽ theo tỉ lệ 1:1)

Giúp mk với, mai kiểm tra rồi

Bài 1: a, chứng minh rằng nếu P(x) chia hết cho (x - a) với a là hằng số thì P(x) có 1 nghiệm là x = a

b, chứng minh rằng nếu P(x) chia hết cho (x - a) với a là hằng số thì P(x) có 1 nghiệm là x = a

Bài 2: K thực hiện phép chia, hãy xác đinh xem đa thức dư ở trong mỗi phép chia là bao nhiêu

a, \(\left(x^3+2x^2-3x+9\right)⋮\left(x+3\right)\)

b, \(\left(9x^4-6x^3+15x^2+2x-1\right)⋮\left(3x^2-2x+5\right)\)