Một chất điểm chuyển động có phương trình chuyển động là \(s=-{{t}^{3}}+6{{t}^{2}}+17t\), với t(s) là khoảng thời gian tính từ lúc vật bắt đầu chuyển động và \(s(\text{m})\) là quãng đường vật đi được trong khoảng thời gian đó. Trong khoảng thời gian 8 giây đầu tiên, vận tốc \(v(\text{m}/\text{s})\) của chất điểm đạt giá trị lớn nhất bằng bao nhiêu?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Có: \(v={{s}^{\prime }}=-3{{t}^{2}}+12t+17\)
Ta đi tìm giá trị lớn nhất của \(v=-3{{t}^{2}}+12t+17\) trên khoảng \((0;8)\)
\(\begin{array}{*{35}{l}} {{v}^{\prime }}=-6t+12 \\ {{v}^{\prime }}=0\Rightarrow t=2 \\ \end{array}\)
Bảng biến thiên
Vậy vận tốc lớn nhất trong khoảng 8 giây đầu tiên là: 29 m/s.
Bộ Đề Kiểm Tra Giữa Học Kì I - Toán 12 - Cánh Diều là tài liệu học tập hữu ích giúp học sinh ôn tập và hệ thống lại kiến thức đã học. Với các dạng bài trắc nghiệm và tự luận phong phú, đề thi giúp học sinh rèn luyện khả năng tính toán, tư duy logic, đồng thời nâng cao kỹ năng giải quyết vấn đề một cách hiệu quả. Đây là công cụ hỗ trợ đắc lực để chuẩn bị cho các kỳ thi quan trọng.
Câu hỏi liên quan
Read the following announcement and choose the correct option that best fits each of the numbered blanks.
Career Orientation Workshop Announcement
Dear Students,
We are excited to announce that our school will be holding a Career Orientation Workshop on November 15th. This workshop aims (13) __________ you explore different career paths and gain valuable insights into the job market. Industry experts will be present to guide you through career opportunities, answer your questions, and provide advice on how to prepare (14) __________ your future career.
Don't miss this chance to discover your potential and (15) __________ clear goals for your future career!
Date: November 15th
Time: 9:00 AM - 11:00 AM
Location: School Auditorium
We look forward to seeing you there!
Read the following passage and choose the correct option that best fits each of the numbered blanks.
Smart cities are designed to make life easier and more efficient for people. In a smart city, technology plays a big role in managing important services. (24) __________, there are systems that control traffic lights to reduce traffic jams and help people get to their destinations faster. Public transportation, like buses and trains, runs on time because it uses data to plan the best routes. Energy is also saved by using smart streetlights that turn on and off automatically. (25) __________ important feature of smart cities is their focus on the environment. Many smart cities use renewable energy sources, like solar and wind power, to reduce pollution. Additionally, smart homes allow people to control devices like lights and heaters through apps on their phones. All of these features work together to create a city (26) __________ is safer, cleaner, and more comfortable to live in. By integrating these technologies, smart cities aim to create safer, greener, and more comfortable living environments. More cities are adopting these solutions to (27) __________ the growing needs of their populations and improve living standards. (28) __________ cities are moving toward this model to improve the quality of life for their citizens.
Choose the correct answer to fill in the blank in each of the following questions.
She changed her career path __________ she was offered a scholarship to study architecture abroad.
Read the following passage and choose the correct answer to each of the questions.
1. In recent years, the idea of a six-hour workday has gained attention as a potential solution to modern work-life balance challenges. Sweden is one of the countries where this concept was tested, and the results have been eye-opening.
2. In 2015, a Swedish retirement home introduced a six-hour workday for its nurses. After the experiment, not only were the nurses happier and more energetic, but productivity also increased. The reduced working hours allowed employees to focus better during their shifts, leading to fewer mistakes and better care for patients. Moreover, absenteeism decreased, and employee satisfaction skyrocketed.
3. But how does a shorter workday improve productivity? Research suggests that the traditional eight-hour workday may lead to exhaustion, which causes workers to lose focus and make errors. By working fewer hours, they can maintain higher energy levels and complete tasks more efficiently. Studies from organizations like the OECD (Organisation for Economic Co-operation and Development) also show that countries with shorter average working hours, such as Germany and the Netherlands, have higher productivity rates compared to those with longer working hours.
4. Critics argue that a six-hour workday may not be suitable for all industries, and some businesses worry about potential cost increases. However, many proponents believe the long-term benefits, such as improved employee well-being and reduced burnout, outweigh these concerns.
5. As work-life balance becomes a priority in today's society, the six-hour workday could be a glimpse into the future of work, where employees are happier, healthier, and more productive.
(30) The word eye-opening in paragraph 1 is closest in meaning to __________.
Read the following advertisement and choose the correct option that best fits each of the numbered blanks.
Discover the Charm of Hanoi's Old Quarter!
Step back in time and explore the vibrant, (10) __________ streets of Hanoi's Old Quarter. Our exclusive guided tour will take you through hidden alleys, bustling markets, and centuries-old architecture so you can (11) __________ the true heart of Vietnam's capital.
Tour Highlights:
✔ Explore 36 Ancient Streets: Learn the stories behind each street and its traditional craft.
✔ Taste Authentic Street Food: Enjoy delicious pho, bun cha, and other local favorites at famous food stalls.
✔ Cycle Rickshaw Ride: Enjoy (12) __________ peaceful rickshaw ride through the Old Quarter's most iconic spots.
Contact us: +84 123 45 678
Book now and dive into the soul of Hanoi!
Read the following advertisement and choose the correct option that best fits each of the numbered blanks.
Discover the Charm of Hanoi's Old Quarter!
Step back in time and explore the vibrant, (10) __________ streets of Hanoi's Old Quarter. Our exclusive guided tour will take you through hidden alleys, bustling markets, and centuries-old architecture so you can (11) __________ the true heart of Vietnam's capital.
Tour Highlights:
✔ Explore 36 Ancient Streets: Learn the stories behind each street and its traditional craft.
✔ Taste Authentic Street Food: Enjoy delicious pho, bun cha, and other local favorites at famous food stalls.
✔ Cycle Rickshaw Ride: Enjoy (12) __________ peaceful rickshaw ride through the Old Quarter's most iconic spots.
Contact us: +84 123 45 678
Book now and dive into the soul of Hanoi!
Read the following passage and choose the correct answer to each of the questions.
1. In recent years, the idea of a six-hour workday has gained attention as a potential solution to modern work-life balance challenges. Sweden is one of the countries where this concept was tested, and the results have been eye-opening.
2. In 2015, a Swedish retirement home introduced a six-hour workday for its nurses. After the experiment, not only were the nurses happier and more energetic, but productivity also increased. The reduced working hours allowed employees to focus better during their shifts, leading to fewer mistakes and better care for patients. Moreover, absenteeism decreased, and employee satisfaction skyrocketed.
3. But how does a shorter workday improve productivity? Research suggests that the traditional eight-hour workday may lead to exhaustion, which causes workers to lose focus and make errors. By working fewer hours, they can maintain higher energy levels and complete tasks more efficiently. Studies from organizations like the OECD (Organisation for Economic Co-operation and Development) also show that countries with shorter average working hours, such as Germany and the Netherlands, have higher productivity rates compared to those with longer working hours.
4. Critics argue that a six-hour workday may not be suitable for all industries, and some businesses worry about potential cost increases. However, many proponents believe the long-term benefits, such as improved employee well-being and reduced burnout, outweigh these concerns.
5. As work-life balance becomes a priority in today's society, the six-hour workday could be a glimpse into the future of work, where employees are happier, healthier, and more productive.
(29) What does the passage mainly discuss?
Read the following passage and choose the correct option that best fits each of the numbered blanks.
One of the most exciting careers today is that of a wildlife photographer. Wildlife photographers travel to remote locations to capture (18) __________. The job requires not only advanced photography skills but also a deep understanding of animal behavior and nature. (19) __________, as it often takes hours, or even days, to get the perfect shot of a rare species or an incredible natural moment.
The thrill of encountering animals in the wild, from lions in the savannah to penguins in the Antarctic, (20) __________. Wildlife photographers also play a crucial role in raising awareness about conservation. Through (21) __________, they bring the beauty and fragility of wildlife to the world's attention and (22) __________ endangered species and ecosystems.
In conclusion, wildlife photography allows individuals to explore remote landscapes, capture breathtaking moments, and (23) __________. Despite the challenges, such as difficult weather conditions and potential dangers from wildlife, the reward of capturing a breathtaking moment in nature is priceless. It's a profession for those who are not afraid to take risks and who love being in the great outdoors.
Read the following passage and choose the correct option that best fits each of the numbered blanks.
One of the most exciting careers today is that of a wildlife photographer. Wildlife photographers travel to remote locations to capture (18) __________. The job requires not only advanced photography skills but also a deep understanding of animal behavior and nature. (19) __________, as it often takes hours, or even days, to get the perfect shot of a rare species or an incredible natural moment.
The thrill of encountering animals in the wild, from lions in the savannah to penguins in the Antarctic, (20) __________. Wildlife photographers also play a crucial role in raising awareness about conservation. Through (21) __________, they bring the beauty and fragility of wildlife to the world's attention and (22) __________ endangered species and ecosystems.
In conclusion, wildlife photography allows individuals to explore remote landscapes, capture breathtaking moments, and (23) __________. Despite the challenges, such as difficult weather conditions and potential dangers from wildlife, the reward of capturing a breathtaking moment in nature is priceless. It's a profession for those who are not afraid to take risks and who love being in the great outdoors.
Choose the correct answer to fill in the blank in each of the following questions.
__________ pedestrian zones and bike lanes should be expanded to encourage eco-friendly transportation in big cities.
Read the following announcement and choose the correct option that best fits each of the numbered blanks.
Career Orientation Workshop Announcement
Dear Students,
We are excited to announce that our school will be holding a Career Orientation Workshop on November 15th. This workshop aims (13) __________ you explore different career paths and gain valuable insights into the job market. Industry experts will be present to guide you through career opportunities, answer your questions, and provide advice on how to prepare (14) __________ your future career.
Don't miss this chance to discover your potential and (15) __________ clear goals for your future career!
Date: November 15th
Time: 9:00 AM - 11:00 AM
Location: School Auditorium
We look forward to seeing you there!
Choose the word that differs from the other three in the position of stress in each of the following questions.
Read the following passage and choose the correct option that best fits each of the numbered blanks.
Smart cities are designed to make life easier and more efficient for people. In a smart city, technology plays a big role in managing important services. (24) __________, there are systems that control traffic lights to reduce traffic jams and help people get to their destinations faster. Public transportation, like buses and trains, runs on time because it uses data to plan the best routes. Energy is also saved by using smart streetlights that turn on and off automatically. (25) __________ important feature of smart cities is their focus on the environment. Many smart cities use renewable energy sources, like solar and wind power, to reduce pollution. Additionally, smart homes allow people to control devices like lights and heaters through apps on their phones. All of these features work together to create a city (26) __________ is safer, cleaner, and more comfortable to live in. By integrating these technologies, smart cities aim to create safer, greener, and more comfortable living environments. More cities are adopting these solutions to (27) __________ the growing needs of their populations and improve living standards. (28) __________ cities are moving toward this model to improve the quality of life for their citizens.
Choose the correct answer to fill in the blank in each of the following questions.
The organization __________ financial aid to thousands of students since its establishment in 2010.
Choose the correct answer to fill in the blank in each of the following questions.
They quickly __________ the solar energy stored in the batteries during the cloudy week.
Read the following advertisement and choose the correct option that best fits each of the numbered blanks.
Discover the Charm of Hanoi's Old Quarter!
Step back in time and explore the vibrant, (10) __________ streets of Hanoi's Old Quarter. Our exclusive guided tour will take you through hidden alleys, bustling markets, and centuries-old architecture so you can (11) __________ the true heart of Vietnam's capital.
Tour Highlights:
✔ Explore 36 Ancient Streets: Learn the stories behind each street and its traditional craft.
✔ Taste Authentic Street Food: Enjoy delicious pho, bun cha, and other local favorites at famous food stalls.
✔ Cycle Rickshaw Ride: Enjoy (12) __________ peaceful rickshaw ride through the Old Quarter's most iconic spots.
Contact us: +84 123 45 678
Book now and dive into the soul of Hanoi!
Read the following passage and choose the correct option that best fits each of the numbered blanks.
One of the most exciting careers today is that of a wildlife photographer. Wildlife photographers travel to remote locations to capture (18) __________. The job requires not only advanced photography skills but also a deep understanding of animal behavior and nature. (19) __________, as it often takes hours, or even days, to get the perfect shot of a rare species or an incredible natural moment.
The thrill of encountering animals in the wild, from lions in the savannah to penguins in the Antarctic, (20) __________. Wildlife photographers also play a crucial role in raising awareness about conservation. Through (21) __________, they bring the beauty and fragility of wildlife to the world's attention and (22) __________ endangered species and ecosystems.
In conclusion, wildlife photography allows individuals to explore remote landscapes, capture breathtaking moments, and (23) __________. Despite the challenges, such as difficult weather conditions and potential dangers from wildlife, the reward of capturing a breathtaking moment in nature is priceless. It's a profession for those who are not afraid to take risks and who love being in the great outdoors.
Choose the word that differs from the other three in the position of stress in each of the following questions.
Read the following passage and choose the correct option that best fits each of the numbered blanks.
One of the most exciting careers today is that of a wildlife photographer. Wildlife photographers travel to remote locations to capture (18) __________. The job requires not only advanced photography skills but also a deep understanding of animal behavior and nature. (19) __________, as it often takes hours, or even days, to get the perfect shot of a rare species or an incredible natural moment.
The thrill of encountering animals in the wild, from lions in the savannah to penguins in the Antarctic, (20) __________. Wildlife photographers also play a crucial role in raising awareness about conservation. Through (21) __________, they bring the beauty and fragility of wildlife to the world's attention and (22) __________ endangered species and ecosystems.
In conclusion, wildlife photography allows individuals to explore remote landscapes, capture breathtaking moments, and (23) __________. Despite the challenges, such as difficult weather conditions and potential dangers from wildlife, the reward of capturing a breathtaking moment in nature is priceless. It's a profession for those who are not afraid to take risks and who love being in the great outdoors.
Choose the correct arrangement of the sentences to make a meaningful paragraph/letter in each of the following questions.
a. Additionally, organizing outdoor activities such as tree planting or clean-up days helps students connect with nature.
b. First, schools can organize recycling programs, where students actively participate in sorting and reducing waste.
c. Second, teachers can include environmental topics in lessons to raise awareness about issues like pollution and climate change.
d. Finally, rewarding environmentally-friendly behavior can motivate students to adopt sustainable habits.
e. There are several effective ways to encourage students to protect the environment.
