Trong mỗi ý a), b), c), d) ở mỗi câu, thi sinh chọn đúng hoặc sai
Trong mặt phẳng tọa độ Oxy, xét parabol \(({\rm{P}}):{\rm{y}} = {{\rm{x}}^2} - 4.\)
Trong mặt phẳng tọa độ Oxy, xét parabol \(({\rm{P}}):{\rm{y}} = {{\rm{x}}^2} - 4.\)
a) Hoành độ giao điểm của \(({\rm{P}})\) và Ox là -2 và 2.
b) \(\int {\left( {{x^2} - 4} \right)} dx = \frac{{{x^3}}}{3} + 4x + C.\)
c) \(\left| {{x^2} - 4} \right| = {x^2} - 4\forall x \in [ - 2;2]\)
d) Diện tích hình phẳng giới hạn bởi \(({\rm{P}})\) và Ox bằng \(\frac{{32}}{3}.\)
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
b) $\int (x^2 - 4)dx = \frac{x^3}{3} - 4x + C$. Vậy khẳng định sai.
c) Với $x \in [-2; 2]$, ta có $x^2 - 4 \le 0$. Do đó $|x^2 - 4| = -(x^2 - 4) = 4 - x^2$. Vậy khẳng định sai.
d) Diện tích hình phẳng giới hạn bởi $(P)$ và $Ox$ là $S = \int_{-2}^{2} |x^2 - 4|dx = \int_{-2}^{2} (4 - x^2)dx = (4x - \frac{x^3}{3})|_{-2}^{2} = (8 - \frac{8}{3}) - (-8 + \frac{8}{3}) = 16 - \frac{16}{3} = \frac{32}{3}$. Vậy khẳng định đúng.
Câu hỏi liên quan
Read the following passage about the impact of social media on mental health and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
[I] In recent years, social media platforms have become a central part of daily life, offering users countless ways to connect, share, and communicate. [II] While these platforms offer many advantages, experts have noted rising concerns about their effects on mental health, particularly among young people (Smith & Anderson, 2018). [III] Studies reveal that excessive social media use can contribute to feelings of anxiety, depression, and loneliness, despite its intention to promote connection and social interaction (Twenge & Campbell, 2019). [IV]
A primary reason for these mental health concerns is the tendency for social media users to compare themselves to others. Platforms like Instagram and Facebook often highlight idealized lifestyles, leading users to feel inadequate about their own lives. Additionally, the constant notifications and messages contribute to a "fear of missing out," or FOMO, which keeps individuals in a cycle of checking their phones, often reducing the quality of sleep and overall well-being.
There is also a growing body of research suggesting a link between social media use and decreased attention spans. When users frequently switch between apps and notifications, their ability to focus for extended periods may diminish (Rosen, 2019). This shift in attention can interfere with productivity, especially in academic and professional settings, where sustained focus is essential.
Addressing these challenges requires a multi-faceted approach. Some mental health professionals suggest limiting screen time and setting boundaries, such as "device-free" hours before bedtime. Others recommend engaging in offline activities, like reading or exercising, to reduce dependence on social media and build healthier habits. According to psychologists, such strategies can enhance mental resilience and allow for more meaningful, balanced relationships (Robinson & Smith, 2020).
Which of the following can be inferred from the passage?
Complete the sentence with the correct form of 'will' or 'be going to'.
A: Why is she wearing her best dress?
Một máy tạo rung được sử dụng để tạo ra sóng trên dây.
Tần số của máy tạo rung là 60Hz. Khi đó, vận tốc sóng truyền truyên dây là:
Trong tình huống dưới đây, chính sách giảm giá điện của Nhà nước tác động tích cực như thế nào đến đời sống người dân?
"Do ảnh hưởng bởi việc các tỉnh, thành phố thực hiện giãn cách nên hoạt động sản xuất kinh doanh đặc biệt là hoạt động của các doanh nghiệp chế biến, bảo quản thủy sản bị đình trệ. Bộ Công Thương và EVN đã đề xuất với Thủ tướng Chính phủ và được Chính phủ đồng ý cho thực hiện hỗ trợ giảm 10% tiền điện trên hoá đơn tiền điện cho các khách hàng".
Một vật khối lượng 10 kg được kéo đều trên sàn nằm ngang bằng một lực 20 N hợp với phương ngang một góc 300. Khi vật di chuyển 2 m trên sàn thì lực thực hiện một công
Nguồn lực tài chính là:
Đâu là nguyên nhân gây bệnh bên trong?
Biết A=B.C. Sai số tỉ đối của A có thể tính thông qua biểu thức
Have you heard about John? He has broken _____with his girlfriend.
- Một vật chuyển động thẳng nhanh dần đều với vận tốc đầu = 18 km/h. Sau 10 s, vật đạt vận tốc 15 m/s. Gia tốc của vật là
Một trong những cuộc thi nổi tiếng trong khuôn khổ dự án của Uỷ ban Văn hóa thông tin ASEAN (COCI) là gì?
Tại sao Hiến pháp năm 2013 lại xác định giáo dục là quốc sách hàng đầu của quốc gia?
Tất cả những gì đã diễn ra trong quá khứ, tồn tại một cách khách quan, không phụ thuộc vào ý muốn chủ quan của con người được gọi là:
Choose a suitable word or phrase (marked A, B, C or D) to fill in each blank.
Tam Chuc Pagoda is _________ tourist attraction in Ha Nam; hundreds of thousands of tourists flock to this area every year.
Read the following passage about the A Vision of a Harmonious Multicultural Society and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
By 2050, our world will have undergone remarkable transformations in how different cultures coexist. The walls that once divided nations are vanishing into thin air as global citizens embrace diversity like never before. Technology will serve as the great equalizer, with translation devices making language barriers a thing of the past. In urban centers worldwide, neighborhoods will showcase architectural influences from multiple cultures, creating spaces where everyone feels at home regardless of their background. Public spaces will feature gardens with plants from different continents, symbolic of how various cultures can thrive together in one environment.
[I] Education systems will prioritize cultural literacy alongside traditional subjects. [II] Schools will teach world history from multiple perspectives rather than through a single cultural lens. [III] Students will routinely participate in virtual exchange programs, allowing them to form friendships with peers around the world without leaving their classrooms. [IV] Government policies will recognize that a harmonious multicultural society requires institutional support, with resources allocated to community centers where cultural exchange happens organically through shared meals, festivals, and collaborative art projects.
Economic systems will evolve to value diverse approaches to business and innovation. Companies will actively seek employees from varied backgrounds, recognizing that diverse teams create more innovative solutions. Traditional knowledge from indigenous communities will be respected and incorporated into sustainable development practices. The entertainment industry will produce content that authentically represents multiple cultures, moving beyond stereotypes to show the complexity within each tradition. Digital platforms will help preserve endangered languages and cultural practices through accessible archives and learning tools.
The greatest achievement of this harmonious world will be a new understanding of human identity. People will identify with multiple cultural traditions simultaneously without feeling conflicted about their loyalties. Holidays from various traditions will be celebrated collectively, creating new hybrid celebrations that honor multiple heritages. The concept of "us versus them" will gradually fade as people recognize shared values across different traditions. While challenges will remain, the dominant attitude will be one of curiosity rather than fear when encountering differences.
Which of the following best summarises paragraph 3?
Thông tin của thị trường giúp người mua điều gì?
Trong một cuộc thi pha chế, hai đội A, B được sử dụng tối đa \(24\) g hương liệu, \(9\) lít nước và \(210\) g đường để pha chế nước cam và nước táo. Để pha chế \(1\) lít nước cam cần \(30\) g đường, \(1\) lít nước và \(1\) g hương liệu; pha chế \(1\) lít nước táo cần \(10\) g đường, \(1\) lít nước và \(4\) g hương liệu. Mỗi lít nước cam nhận được \(60\) điểm thưởng, mỗi lít nước táo nhận được \(80\) điểm thưởng. Đội A pha chế được \(a\) lít nước cam và \(b\) lít nước táo và dành được điểm thưởng cao nhất. Tính \(a-b\).
Read the following passage about lifelong learning and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from from 18 to 22.
In today’s rapidly changing world, lifelong learning has become more important than ever. Lifelong learning is essential for personal and professional growth. To stay relevant and competitive in the job market, (18) _________.
One of the key benefits of lifelong learning is personal growth. By learning new things, individuals can boost their self-esteem and confidence. By exploring new subjects and hobbies, individuals can expand their horizons and discover new passions.
(19) _________. By acquiring new skills, individuals can increase their employability. By staying up-to-date with the latest trends and technologies, individuals can increase their value to employers, (20)______. However, lifelong learning can be challenging. (21) _________. Balancing work, family, and personal commitments can make it difficult to find time for learning.
To make the most of lifelong learning, people, especially the young, (22) _________. By breaking down larger goals into smaller, achievable steps, individuals can stay motivated and make progress. By breaking down larger goals into smaller, achievable steps, individuals can stay motivated and make progress.
Mark the letter A, B, C, or D on your answer sheet to indicate the sentence that best combines each pair of sentences in the following sentences.
She tried very hard to pass the driving test. She could hardly pass it.
Read the following passage about Building Understanding Across Nations and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
In our interconnected world, cultural ambassadors play a vital role in bridging the gaps between different nations and peoples. These dedicated individuals and groups serve as links between cultures, fostering mutual understanding and respect through various activities and programs. Their mission is to showcase their own cultural heritage while learning about and appreciating others, creating pathways for meaningful dialogue and lasting connections across borders.
Cultural ambassadors employ numerous methods to achieve their goals. They organize traditional festivals and art exhibitions that display unique customs, allowing visitors to experience different cultures firsthand. Language exchange programs enable people to communicate more effectively, while cultural workshops teach traditional crafts, music, and dance. These ambassadors also utilize digital platforms to reach wider audiences, sharing stories and traditions through social media and online events that connect people from different corners of the world.
Despite their important work, cultural ambassadors face several challenges in their mission. Stereotypes and prejudices can create barriers to understanding, while language differences sometimes lead to misunderstandings. Limited resources and funding may restrict their activities, and political tensions between nations can complicate their efforts. However, these dedicated individuals persist in their work, believing that personal connections and shared experiences can overcome these obstacles and promote harmony among different communities.
Looking ahead, the role of cultural ambassadors becomes increasingly significant in our global society. Their efforts to build bridges between nations contribute to reducing conflicts and fostering peace. Through their continued dedication to promoting cross-cultural understanding, these ambassadors help create a more inclusive and connected world where differences are celebrated rather than feared. This ongoing process of cultural exchange remains essential for building a future based on mutual respect and cooperation.
Which of the following is NOT mentioned as a method used by cultural ambassadors?