Câu 1: Biểu thức \(\sqrt{x^2+2023}-2024\) có giá trị nhỏ nhất bằng:

A. \(\sqrt{2023}-2021\)
B. -2024

C. 0

D. \(\sqrt{2023}\)

Câu 2: Chọn khẳng định đúng trong các khẳng định sau:

A. Hai góc kề nhau có tổng số đo bằng 180⁰.

B. Hai góc so le trong bằng nhau.

C. Hai góc đồng vị bằng nhau.

D. Hai góc đối đỉnh bằng nhau.

Câu 3: Cho a, b, c là ba đường thẳng phân biệt. Biết a song song với b và b vuông góc với c thì kết luận nào sau đây đúng?

A. a song song với c.

B. a trùng với c.

C. a vuông góc với c.

D. a không vuông góc với c.

Câu 4: Trong các phát biểu sau, phát biểu nào diễn đạt đúng nội dung của tiền đề Euclid?

A. Qua điểm A nằm ngoài đường thẳng d có ít nhất một đường thẳng song song với d.

B. Nếu qua điểm A nằm ngoài đường thẳng d mà có hai đường thẳng cùng song song với d thì chúng trùng nhau.

C. Có duy nhất một đường thẳng song song với một đường thẳng cho trước.

D. Cho điểm A nằm ngoài đường thẳng d. Đường thẳng đi qua A và song song với d không phải là đường thẳng duy nhất.

     In an effort to fight pollution and help the environment, the Marina Hills Ecology Club offers free trees to institutions willing to plant them on their grounds. Among those that took advantage of the offer was Marina Hills High School. After consulting with his teachers on where to plant the trees, Principal Max Webb contacted the Ecology Club. But when the seedlings arrived, Webb had an idea. Instead of planting the young trees in front of the school, he thought it would be better to put them behind the school, where the sun gets very hot in the afternoon. “It gets so hot inside the building that the students start to sweat during their afternoon classes,” said Webb. “Now the shade from our trees will bring them some relief.”

     “There was no argument from the teachers,” he added. “When I proposed the idea, everyone said, “Why didn’t I think of that?”. “The relief won’t come until the trees grow taller, but the school will not have to wait long because it requested two species of trees that grow quickly. “Time is key, and we wanted our trees to get big fast,” said Webb. “We were given a wide choice, from shrubs to fruit trees. We requested eucalyptus and willow trees.” Webb said he is also looking forward to finally seeing some wildlife in the school yard at Marina Hills High School. “If all you have is a grass lawn with no trees, you can’t expect the local birds to come and visit,” said Webb. “They have no place to make their nests. Now that will change, and we’ll be able to see birds from our classroom windows.”

28. What would be the most appropriate headline for this article?

     A. Local School Gets Greener             B. student Wins Science Award

     C. Principal Discovers New Trees        D. Teacher Leads Ecological Club

29. What problem does Principal Webb talk about?

     A. Pollution in the city                         B. Classrooms that are too hot

     C. Tall trees that block the view           D. Wild animals that destroy trees

30. What did the Ecology Club do for Marina Hills High School?

     A. It helped design the school yard.                 B. It put flowers in the classrooms.

     C. It sold seeds to the school.                          D. It provided free trees.

31. What decision was changed?

     A. Which trees should be dug up.

     B. When the old trees should be cut down.

     C. Where the new trees should be planted.

     D. Which type of tree should be chosen.

32. What can be inferred from the article about eucalyptus and willow trees?

     A. They grow quickly.

     B. They become extremely tall.

     C. They are less expensive than fruit trees.

     D. They do not grow flowers in the springtime.

In an effort to fight pollution and help the environment, the Marina Hills Ecology Club offers free trees to institutions willing to plant them on their grounds. Among those that took advantage of the offer was Marina Hills High School. After consulting with his teachers on where to plant the trees, Principal Max Webb contacted the Ecology Club. But when the seedlings arrived, Webb had an idea. Instead of planting the young trees in front of the school, he thought it would be better to put them behind the school, where the sun gets very hot in the afternoon. “It gets so hot inside the building that the students start to sweat during their afternoon classes,” said Webb. “Now the shade from our trees will bring them some relief.”

     “There was no argument from the teachers,” he added. “When I proposed the idea, everyone said, “Why didn’t I think of that?”. “The relief won’t come until the trees grow taller, but the school will not have to wait long because it requested two species of trees that grow quickly. “Time is key, and we wanted our trees to get big fast,” said Webb. “We were given a wide choice, from shrubs to fruit trees. We requested eucalyptus and willow trees.” Webb said he is also looking forward to finally seeing some wildlife in the school yard at Marina Hills High School. “If all you have is a grass lawn with no trees, you can’t expect the local birds to come and visit,” said Webb. “They have no place to make their nests. Now that will change, and we’ll be able to see birds from our classroom windows.”

28. What would be the most appropriate headline for this article?

     A. Local School Gets Greener             B. student Wins Science Award

     C. Principal Discovers New Trees        D. Teacher Leads Ecological Club

29. What problem does Principal Webb talk about?

     A. Pollution in the city                         B. Classrooms that are too hot

     C. Tall trees that block the view           D. Wild animals that destroy trees

30. What did the Ecology Club do for Marina Hills High School?

     A. It helped design the school yard.                 B. It put flowers in the classrooms.

     C. It sold seeds to the school.                          D. It provided free trees.

31. What decision was changed?

     A. Which trees should be dug up.

     B. When the old trees should be cut down.

     C. Where the new trees should be planted.

     D. Which type of tree should be chosen.

32. What can be inferred from the article about eucalyptus and willow trees?

     A. They grow quickly.

     B. They become extremely tall.

     C. They are less expensive than fruit trees.

     D. They do not grow flowers in the springtime.

Chúc mừng năm mới 2023! Kính chúc mọi người có sức khỏe, niềm vui và gặt hái được nhiều thành công trong năm mới nhé, chúc cộng đồng chúng ta tiếp tục phát triển mạnh mẽ và giữ vững ngôi hệ thống web thịnh hành nhất Việt Nam!

Mình rất hóng bạn nào giải được bài toán đầu tiên của năm, và mình sẽ trao 2GP cho bạn giải được nhé:

Cho x,y,z > 0. Chứng minh rằng:

\(\left(x+y+z\right)^2\left[\dfrac{\dfrac{1}{\sqrt{xy}}}{\sqrt[5]{x^5+2023x^2y^2\sqrt{xy}+y^5}}+\dfrac{\dfrac{1}{\sqrt{yz}}}{\sqrt[5]{y^5+2023y^2z^2\sqrt{yz}+z^5}}+\dfrac{\dfrac{1}{\sqrt{xz}}}{\sqrt[5]{x^5+2023x^2z^2\sqrt{xz}+z^5}}\right]\)

\(\ge\dfrac{27}{\sqrt[5]{2023+2}}\)