Cho hàm số \(y = f(x)\) có bảng biến thiên như sau:
Số nghiệm thực của phương trình \(2f(x) − 11 = 0\) là
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta có: \(2 f(x)-11=0 \Leftrightarrow f(x)=\frac{11}{2}\)
Số nghiệm của phương trình là số giao điểm của đồ thị hàm số \(y=f(x)\) và đường thẳng \(y=\frac{11}{2}\).
Dựa vào bảng biến thiên, ta thấy đồ thị hàm số \(y=f(x)\) cắt đường thẳng \(y=\frac{11}{2}\) tại 2 điểm phân biệt.
Vậy phương trình \(2 f(x)-11=0\) có 2 nghiệm phân biệt.
Với cấu trúc mới lạ và đa dạng, Đề Thi Tham Khảo Đánh Giá Năng Lực Năm 2025 – ĐHQG Hà Nội – Đề Số 4 giúp thí sinh phát huy tối đa khả năng Giải Quyết Vấn Đề, Sáng Tạo và Tư Duy Định Lượng. Bài thi bao gồm ba phần chính: Toán Học Và Xử Lí Số Liệu, Văn Học - Ngôn Ngữ, Khoa Học/Tiếng Anh. Mỗi phần thi đều được thiết kế với các dạng câu hỏi phong phú, không chỉ đánh giá kiến thức lý thuyết mà còn kiểm tra khả năng phân tích dữ liệu, xử lý thông tin và vận dụng thực tế. Đây là lựa chọn hoàn hảo cho học sinh muốn tự tin chinh phục kỳ thi đánh giá năng lực.
Câu hỏi liên quan
Con hãy lựa chọn đáp án Đúng hoặc Sai
Đỗ Phủ cùng quê với nhà thơ Lý Bạch, Hạ Chi Trương, đúng hay sai?
Mỗi hoạt động kinh tế có vai trò khác nhau nhưng chúng có mối quan hệ mật thiết, tác động qua lại với nhau, đảm bảo cho nền kinh tế không ngừng:
Ý tưởng kinh doanh là bao gồm những suy nghĩ, và hành động như thế nào?
Mark the letter A, B, C or D on your answer sheet to indicate the correct option that best fits each of the numbered blanks from 18 to 23.
AI (Artificial Intelligence) is revolutionizing the medical field by providing more accurate diagnoses and personalized treatment plans. Since its development, AI has become increasingly integrated into healthcare, (18) ___________. One of the most prominent examples is its use in medical imaging, where AI-powered systems are capable of detecting diseases, like cancer, with remarkable precision.
AI systems are particularly valued for their ability to process vast amounts of data quickly, enabling doctors to focus on patient care rather than administrative tasks. These advancements have led to (19) ___________, allowing for better overall outcomes. Not only does AI reduce the potential for human error, but it also continuously improves through learning from new medical data.
Medical AI systems have also (20) ___________. By analyzing genetic information and patient histories, AI can suggest potential treatment options that may have been overlooked by human experts. Moreover, these systems often lack the information needed to recommend the best treatment, ensuring that treatments are more effective and better suited to individual needs.
Despite the many benefits, some critics argue that there are still ethical concerns about the widespread adoption of AI in healthcare. For example, (21) ___________ could lead to overreliance on machines, reducing the need for skilled medical professionals. However, proponents believe that as AI continues to evolve, the medical field will revert to traditional methods By working alongside human experts, AI has the potential to transform healthcare, making it more efficient and accessible for all.
In summary, the rise of AI in medicine is an exciting development that shows great promise. It is essential (22) ___________. As these technologies advance, doctors may struggle to trust AI in complex cases.
Read the following passage about fitness trends 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.
FITNESS TRENDS
[I] Reformer Pilates is an advanced and more intense variation of traditional Pilates. [II] Since this type of equipment isn’t something you would typically have at home, you’ll need to visit a specialized Pilates center to try it. [III] While it might look easy at first, don’t be fooled - by the end of the session, your thighs will be burning, and you might struggle to walk up or down stairs for a few days afterward. [IV] This workout pushes your body to its limits, providing a more challenging experience than standard Pilates, and many find it an effective way to build both strength and flexibility.
Trampolining is another popular fitness trend, and although it may seem like child's play, it’s actually a highly effective workout. Jumping up and down on a trampoline can leave you feeling exhausted after just a few minutes. Surprisingly, it’s even better for heart health than running, while also improving coordination and helping to reduce stress levels. Trampolining is gaining widespread popularity, with new centers popping up that feature as many as 150 trampolines. These facilities offer options for everyone: you can enjoy 'freejumping, where you bounce without an instructor, or pay for professional lessons to learn the best techniques and get the most out of your workout. Many people are discovering that trampolining combines fun and fitness in a way that makes staying active much more enjoyable.
If you're someone who is typically active but feeling down or emotionally drained, Dynamic Running Therapy might be just what the doctor ordered. This trend involves running with a therapist, combining the benefits of physical exercise with talk therapy. Though these sessions are often more expensive than typical therapy sessions because of the professional fees, they offer significant advantages. Running while talking helps distract you from any discomfort, allowing you to cover longer distances, and creates a relaxed, open environment that can make it easier to talk compared to the usual therapist’s office setting.
Which of the following best paraphrases the underlined sentence in paragraph 1?
Biểu thức của moment của một lực với một trụng quay là
Theo em, giá trị của hàng hóa được đo bằng gì?
Mệnh đề nào sau đây đúng?
Một trong những đặc điểm tiêu biểu trong văn hóa tiêu dùng của người Việt Nam là gì?
Để tìm kiếm thông tin về virus Corona, em sử dụng từ khoá nào để thu hẹp phạm vi tìm kiếm nhất?
Read the following passage about Singapore Science Centre 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.
The Singapore Science Centre, situated on a sprawling six-hectare site in Jurong, offers a captivating way to explore the wonders of science and technology. Here, visitors can engage with interactive exhibits that make learning both fun and memorable. Clap your hands, and colorful bulbs will light up; spin a wheel, and it will activate a fan. This engaging environment sparks curiosity and fuels the imagination of both children and adults.
The centre boasts more than four hundred exhibits across various fascinating topics, including solar radiation, communication, electronics, mathematics, nuclear energy, and evolution. These exhibits are designed to foster interest in science and technology among the public, making the centre a hub for educational exploration.
Notably, it is the first science centre to be established in Southeast Asia. Officially opened in 1977, the centre now welcomes an average of 1,200 visitors daily, highlighting its enduring popularity and educational value.
The exhibits are thoughtfully arranged across four main galleries: the Lobby, Physical Sciences, Life Sciences, and Aviation. To ensure a fresh and engaging experience, the exhibits are renewed annually, encouraging repeat visits. Visitors are encouraged to interact with the exhibits, as opposed to traditional “hands-off” policies in most museums. Here, pushing buttons, turning cranks, or pedaling mechanisms are all part of the fun and learning experience.
The Discovery Centre, added in 1985, is specially designed for children aged three to twelve, providing an exciting space for young minds to explore and experiment. Most recently, a stone-age exhibit was introduced, showcasing extinct animals and early human life, offering insights into prehistoric times.
With its interactive displays and immersive environment, the Singapore Science Centre continues to inspire a love for science and discovery, making it an unforgettable destination for learners of all ages.
The word hands-off in paragraph 3 could be best replaced by______.
Tính thẩm mĩ thể hiện ở chỗ:
Ngành tài chính - ngân hàng không có vai trò nào sau đây?
Đáp án nào không đúng khi nói về tiểu sử của nhà thơ Nguyễn Khuyến?
Vật có khối lượng 3kg chuyển động trên đường thẳng với vận tốc 4m/s đến va chạm vào vật 2 đứng yên có khối lượng 5kg. Sau va chạm vật 2 chuyển động với vận tốc 3m/s còn vật 1 chuyển động như thế nào? (Bỏ qua ma sát)
Phương án nào sau đây là một lợi ích của số hóa văn bản?
Với quy luật về sự thống nhất và hoàn chỉnh của vỏ địa lí, khi tiến hành các hoạt động khai thác tự nhiên trong vỏ địa lí cần hết sức chú ý điều gì?
Công nghệ nào sau đây được ứng dụng trong chế biến sản phẩm trồng trọt?
Read the following advertisement 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 1 to 6.
Biosphere 2025: Where Your Home Breathes With The Planet
The people (1)_________ in Biosphere homes report improved health and lower utility bills. Never (2)_________ off until tomorrow what you can do today for our planet!
Visit our showroom (3)_________ how Biosphere technology can transform your home. Our (4)_________ system removes 99.9% of pollutants while connecting to your smartphone.
We handed customers (5)_________ to our specialists for personalized consultations. (6)_________ design your space with eco-friendly materials that last for generations.
Biosphere 2025 - Your home's natural connection to Earth!
Limited time offer: 15% discount on all smart home installations before June 30th!
Website: www.biosphere2025.com
Call: (555) 987-6543
Email: connect@biosphere2025.com
Đâu không phải là thiết bị thông minh?
