Giải phương trình sau: \(cos3x+cos2x+sin^2x=2\)

1,Tìm GTLN và GTNN của hàm số:

a, \(y=\left(\frac{2x}{1+x^2}\right)^2-\frac{2x}{1+x^2}+2\)

b, \(y=\sqrt{1+x}+\sqrt{1-x}+\sqrt{1-x^2}\)

c, \(y=x\left(x+1\right)\left(x+2\right)\left(x+3\right)\) khi \(\left|x\right|\le1\)

2, Giá trị của tham số m bằng bao nhiêu để phương trình:

\(x+\sqrt{2-x^2}+x\sqrt{2-x^2}=m\)

3, Tìm m để bất phương trình sau có nghiệm:

\(x^2+\sqrt{4-x^2}< m\)

4, Tìm m để phương trình có nghiệm:

a, \(\left|x+2\right|-\left|x-2\right|=m\)

b, \(\sqrt{x+4}=m\left(1+\sqrt{4-x}\right)\)

c, \(\sqrt{x}=m\left(1+\sqrt{1-x}\right)+\sqrt{1-x}\)

5, Tìm m để \(\sqrt{\left(4+x\right)\left(6-x\right)}\le x^2-2x+m\) với \(\forall x\in\left[-4;6\right]\)

Giải phương trình sau:

\(3cos^22x-4=0\)

EX1 :Read the text below and choose the correct word for each space. For each question 1 -10, mark the correct letter A, B, C or D on your answer sheet.

Robots can work in places humans can't easily get to. These include deep oceans on distant planets or on sites with bad pollution. Robots are also used in factories (1) ________ they can work more quickly and accurately than a human, and without needing to rest. Improvements in technology over the past 50 years have (2) _______ that scientists are now able to create very clever robots. The most complicated of these can make (3) _______ for themselves, learn new things, and deal with problems. However, while robots that look like people are very common in science fiction films, they are very (4) _______ in real life. Making a machine that can balance and move on two legs is a real challenge and is unnecessary for most of the jobs we need robots to do for us. However, a Japanese robot (5)_____ as Asimo does walk on two legs and can even climb up and down stairs.

1. A. unless B. because C. although D. despite

2. A. intended B. supposed C. said D. meant

3. A. results B. decisions C. thoughts D. options

4. A. rare B. thin C. little D. narrow

5.A. called B. known C. named D. said

EX2: Mark the letter A,B,C or D on your answer sheet to indicate the word(s) CLOSET in meaning to the underline word(s) in each of the following question.

Her father died after he had brought up all of his children.

A. was in the dust

B. was out of this world

C. was the apple of her eyes

D. called it a day

1. Operation Stargate was the name of a secret spying operation that was run by the Pentagon in the United States for over 20 years. The aim of the operation was to (1) ............... the possibility of using mind readers, clairvoyants and astrologers to help with spying operations. The pentagon employed six of these psychic people, and the experiments were held at a secret military base in Maryland. Put in special rooms, the psychics were asked to concentrate on particular spting operations. By using a technique called 'remote viewing', they were asked to (2) ............... solutions to specific problems. The team had a limited number of successes. They were able to give (3) ............... of the layout of the building where American diplomats were held hostages in 1979, and on another occasion they assisted Customs officials by describing exactly where a drug dealer could be found. When a US diplomat was kidnapped in Italy, they described the town he was in and in addition said exactly what the building looked like. (4) ..............., they had many more failures than successes. In the end, the government ordered the CIA to take over the mission. The team was then examined by a group of experts, who were not (5) ............... by the results. They decided that (6) ............... the psychics had been right a few times, this had probably just happened by (7) ............... At other times, they were probably repeating information that they had (8) ............... in newspapers orr magazines. The military authorities now have the (9) ............ task of explaining to (10) ......... they wasted $ 20 million on the project.

1- A. look through B. look down on C. look up D. look into

2- A. come into B. come up with C. come across D. come up agianst

3- A. description B. definition C. plan D. details

4- A. But B. Yet C. Although D. However

5- A. impressive B. impressing C. impressed D. impression

6- A. despite B. although C. in spite of D. besides

7- A. chance B. possibility C. occasion D. opportunity

8- A. come into B. come round C.come across D. come up against

9- A. embarrassed B. embarrassing C. embarrassment D. embarrass

10- A. critical B. criticize C. criticism D. critics

2, Điền từ vào chỗ trống:

curious, fold, illness, misbehaved, gestures, touched, opportunity, refused, manners, lonely

When Helen Keller was a baby, she had a fever. After her (1) ...... she became blind, deaf and dumb. It was the beginning of a (2) ...... life. No one could understand Helen and she couldn't see, hear or talk to people. As she grew older, she was (3) ....... to know what was going on around her. She (4)....... the lips of others when they spoke but she could not understand them. No one could understand Helen's (5)........ This made her very angry and she often kicked and screamed until she was very tired. Doctors couldn't help Helen. Her parents became exasperated when they couldn't find a teacher for her. It looked as though Helen would never have an (6)...... to learn. Things changed when Annie Sullivan decided to take up the challenge to teach Helen. During Annie's first breakfast with the Kellers, Helen (7)........ She grabbed other people's food off their plates and (8)....... to use a spoon. Annie took almost 2 hours to teach Helen how to (9).......... her napkin and eat properly. During that time, Helen lost her temper, but Annie was determined to teach naughty Helen table (10)...... Amazingly, Helen soon learned many things through the careful guidance of Annie Sullivan, her mentor.

3. Viết lại câu:

In Whales we saw Edward II'S birthplace.

In Whales we saw the castle ....................

1. Operation Stargate was the name of a secret spying operation that was run by the Pentagon in the United States for over 20 years. The aim of the operation was to (1) ............... the possibility of using mind readers, clairvoyants and astrologers to help with spying operations. The pentagon employed six of these psychic people, and the experiments were held at a secret military base in Maryland. Put in special rooms, the psychics were asked to concentrate on particular spting operations. By using a technique called 'remote viewing', they were asked to (2) ............... solutions to specific problems. The team had a limited number of successes. They were able to give (3) ............... of the layout of the building where American diplomats were held hostages in 1979, and on another occasion they assisted Customs officials by describing exactly where a drug dealer could be found. When a US diplomat was kidnapped in Italy, they described the town he was in and in addition said exactly what the building looked like. (4) ..............., they had many more failures than successes. In the end, the government ordered the CIA to take over the mission. The team was then examined by a group of experts, who were not (5) ............... by the results. They decided that (6) ............... the psychics had been right a few times, this had probably just happened by (7) ............... At other times, they were probably repeating information that they had (8) ............... in newspapers orr magazines. The military authorities now have the (9) ............ task of explaining to (10) ......... they wasted $ 20 million on the project.

1- A. look through B. look down on C. look up D. look into

2- A. come into B. come up with C. come across D. come up agianst

3- A. description B. definition C. plan D. details

4- A. But B. Yet C. Although D. However

5- A. impressive B. impressing C. impressed D. impression

6- A. despite B. although C. in spite of D. besides

7- A. chance B. possibility C. occasion D. opportunity

8- A. come into B. come round C.come across D. come up against

9- A. embarrassed B. embarrassing C. embarrassment D. embarrass

10- A. critical B. criticize C. criticism D. critics

2, Điền từ vào chỗ trống:

curious, fold, illness, misbehaved, gestures, touched, opportunity, refused, manners, lonely

When Helen Keller was a baby, she had a fever. After her (1) ...... she became blind, deaf and dumb. It was the beginning of a (2) ...... life. No one could understand Helen and she couldn't see, hear or talk to people. As she grew older, she was (3) ....... to know what was going on around her. She (4)....... the lips of others when they spoke but she could not understand them. No one could understand Helen's (5)........ This made her very angry and she often kicked and screamed until she was very tired. Doctors couldn't help Helen. Her parents became exasperated when they couldn't find a teacher for her. It looked as though Helen would never have an (6)...... to learn. Things changed when Annie Sullivan decided to take up the challenge to teach Helen. During Annie's first breakfast with the Kellers, Helen (7)........ She grabbed other people's food off their plates and (8)....... to use a spoon. Annie took almost 2 hours to teach Helen how to (9).......... her napkin and eat properly. During that time, Helen lost her temper, but Annie was determined to teach naughty Helen table (10)...... Amazingly, Helen soon learned many things through the careful guidance of Annie Sullivan, her mentor.

3. Viết lại câu:

In Whales we saw Edward II'S birthplace.

In Whales we saw the castle ....................

1. Operation Stargate was the name of a secret spying operation that was run by the Pentagon in the United States for over 20 years. The aim of the operation was to (1) ............... the possibility of using mind readers, clairvoyants and astrologers to help with spying operations. The pentagon employed six of these psychic people, and the experiments were held at a secret military base in Maryland. Put in special rooms, the psychics were asked to concentrate on particular spting operations. By using a technique called 'remote viewing', they were asked to (2) ............... solutions to specific problems. The team had a limited number of successes. They were able to give (3) ............... of the layout of the building where American diplomats were held hostages in 1979, and on another occasion they assisted Customs officials by describing exactly where a drug dealer could be found. When a US diplomat was kidnapped in Italy, they described the town he was in and in addition said exactly what the building looked like. (4) ..............., they had many more failures than successes. In the end, the government ordered the CIA to take over the mission. The team was then examined by a group of experts, who were not (5) ............... by the results. They decided that (6) ............... the psychics had been right a few times, this had probably just happened by (7) ............... At other times, they were probably repeating information that they had (8) ............... in newspapers orr magazines. The military authorities now have the (9) ............ task of explaining to (10) ......... they wasted $ 20 million on the project.

1- A. look through B. look down on C. look up D. look into

2- A. come into B. come up with C. come across D. come up agianst

3- A. description B. definition C. plan D. details

4- A. But B. Yet C. Although D. However

5- A. impressive B. impressing C. impressed D. impression

6- A. despite B. although C. in spite of D. besides

7- A. chance B. possibility C. occasion D. opportunity

8- A. come into B. come round C.come across D. come up against

9- A. embarrassed B. embarrassing C. embarrassment D. embarrass

10- A. critical B. criticize C. criticism D. critics

2, Điền từ vào chỗ trống:

curious, fold, illness, misbehaved, gestures, touched, opportunity, refused, manners, lonely

When Helen Keller was a baby, she had a fever. After her (1) ...... she became blind, deaf and dumb. It was the beginning of a (2) ...... life. No one could understand Helen and she couldn't see, hear or talk to people. As she grew older, she was (3) ....... to know what was going on around her. She (4)....... the lips of others when they spoke but she could not understand them. No one could understand Helen's (5)........ This made her very angry and she often kicked and screamed until she was very tired. Doctors couldn't help Helen. Her parents became exasperated when they couldn't find a teacher for her. It looked as though Helen would never have an (6)...... to learn. Things changed when Annie Sullivan decided to take up the challenge to teach Helen. During Annie's first breakfast with the Kellers, Helen (7)........ She grabbed other people's food off their plates and (8)....... to use a spoon. Annie took almost 2 hours to teach Helen how to (9).......... her napkin and eat properly. During that time, Helen lost her temper, but Annie was determined to teach naughty Helen table (10)...... Amazingly, Helen soon learned many things through the careful guidance of Annie Sullivan, her mentor.

3. Viết lại câu:

In Whales we saw Edward II'S birthplace.

In Whales we saw the castle ....................

1. Tìm m để:

\(x^2-\left|x+m\right|+3\ge0\forall x\in R\)

2. Trong mặt phẳng tọa độ Oxy cho 3 điểm A(-2;1), B(1;0), M(2;4) và đường thẳng \(\Delta:x-2y+3=0\)

Viết phương trình đường thẳng \(d\) đi qua B và khoảng cách từ A đến đường thẳng \(\Delta\) là lớn nhất

3.Trong hệ tọa độ Oxy, cho A(-1;3) và đường thẳng \(\Delta:4x-5y+3=0\). Biết H(a;b) là hình chiếu của A trên \(\Delta\). Tính S = a +9b

1. Tìm m để:

\(x^2-\left|x+m\right|+3\ge0\forall x\in R\)

2. Trong mặt phẳng tọa độ Oxy cho 3 điểm A(-2;1), B(1;0), M(2;4) và đường thẳng \(\Delta:x-2y+3=0\)

Viết phương trình đường thẳng \(d\) đi qua B và khoảng cách từ A đến đường thẳng \(\Delta\) là lớn nhất

3.Trong hệ tọa độ Oxy, cho A(-1;3) và đường thẳng \(\Delta:4x-5y+3=0\). Biết H(a;b) là hình chiếu của A trên \(\Delta\). Tính S = a +9b