Đề thi thử Tiếng Anh Tốt nghiệp THPTQG 2025 - THPT Nguyễn Trãi (Thường Tín, Hà Nội)

Read the following passage and mark the letter A, B, C, D on your answer sheet to indicate the best answer to each of the following questions from 1 to 10. 

Some people look at an equation and see a bunch of complicated numbers and symbols while others see beauty (I). Now, thanks to a new tool created at Carnegie Mellon University, anyone can now translate the abstractions of mathematics into beautiful and instructive illustrations (II). This exciting new tool is named Penrose after the mathematician Roger Penrose, who is famous for using diagrams and other drawings to communicate complicated mathematical ideas (III). Penrose enables users to create diagrams simply by typing mathematical expressions and letting the software do the drawing (IV). 

Unlike a graphing calculator, these aren't restricted to basic functions, but can be complex relationships from any area of mathematics. "Some mathematicians have a talent for drawing beautiful diagrams by hand, but they vanish as soon as the chalkboard is erased," said Keenan Crane, an assistant professor of computer science and robotics. "We want to make this expressive power available to anyone."

Diagrams are often underused in mathematical communication, since producing high-quality illustrations is beyond the skill of many researchers and requires a great deal of time and effort. Penrose addresses these challenges by letting diagram-drawing experts turn their knowledge about creating diagrams into computer codes so that other users can access this capability using familiar mathematical language and a computer. "We started off by asking: 'How do people translate mathematical ideas into pictures in their head?"" said Katherine Ye, a Ph.D. student in the Computer Science Department who is involved in the development of Penrose. "The secret sauce of our system is to empower people to easily 'explain' this translation process to the computer, so the computer can do all the hard work of actually making the picture." 

Once the computer learns how the user wants to see a mathematical object visualized - a vector represented by a little arrow, for instance, or a point represented as a dot it uses these rules to draw several candidate diagrams. Users can then select and edit the diagrams they want from a gallery of possibilities. A special, simple-to-learn programming language was also developed so that they can easily convey the ideas in their minds to the Penrose system, Crane said. "Mathematicians can get very picky about notations," he explained. "We let them define whatever notation they want, so they can express themselves naturally." 

The researchers will present Penrose at the SIGGRAPH 2020 Conference on Computer Graphics and Interactive Techniques, which will be held this July. "Our vision is to be able to dust off an old math textbook from the library, drop it into the computer and get a beautifully illustrated book -that way more people understand," Crane said, noting that Penrose is a first step toward this goal. 

(Adapted from sciencedaily.com)

Question 1. Where in paragraph 1 does the following sentence best fit? 

"For many, the elegance of mathematical concepts often goes unnoticed amidst the complexity". 

A. (III) 

B. (II) 

C. (IV) 

D. (I) 

Question 2. The word "restricted" in paragraph 2 is OPPOSITE in meaning to 

A. expanded 

B. enclosed 

C. contained 

D. confined 

Question 3. The phrase "secret sauce" in paragraph 3 could be best replaced by 

A. special element 

B. unnatural ability 

C. unexpected benefit

D. mysterious feature

Question 4. According to the passage, which of the following is NOT mentioned as a feature or benefit of the Penrose tool?

A. It allows users to create diagrams from mathematical expressions. 

B. It can produce high-quality illustrations without requiring advanced drawing skills. 

C. It enables users to communicate mathematical ideas using a programming language. 

D. It can automatically generate solutions to complex mathematical problems. 

Question 5. The word "they" in paragraph 4 refers to

A. possibilities 

B. users 

C. diagrams 

D. ideas

Question 6. Which of the following best summarizes paragraph 3?

A. Penrose enables users to translate mathematical ideas into diagrams using expert knowledge and computer codes.

B. Katherine Ye discusses the challenges mathematicians face when trying to visualize complex ideas.

C. Penrose allows users to create high-quality diagrams quickly without needing artistic skills.

D. Diagrams in mathematics are often underused due to the time required to create them.

Question 7. Which of the following is NOT TRUE according to the passage?

A. Penrose's developers want to make math easier to understand by using illustrations.

B. Mathematical diagrams that are drawn by hand on chalkboards are not long-lasting.

C. Diagrams are usually not widely used to illustrate or communicate mathematical ideas.

D. Penrose uses common mathematical rules to draw diagrams for a mathematical object.

Question 8. Which of the following best paraphrases the underlined sentence in paragraph 4?

A. Users can choose and modify the diagrams they prefer from a collection of options.

B. Users can view and customize the diagrams they wish to use from an assortment of images.

C. Users can browse and alter the diagrams they like from a variety of choices.

D. Users can create and adjust the diagrams they desire from a selection of examples.

Question 9. Which of the following can be inferred from the passage?

A. In general, mathematicians are not very good at remembering and defining notations.

B. How a mathematical object should be visualized varies from person to person.

C. Almost all people consider traditional math textbooks to be extremely boring.

D. Hand-drawn diagrams are not as beautiful and easy to understand as digital diagrams.

Question 10. Which of the following best summaries the passage?

A. The researchers at Carnegie Mellon University are focusing on the history of mathematical diagrams and their importance in education.

B. Penrose is a new tool that allows users to create complex mathematical diagrams easily, enhancing mathematical communication and understanding.

C. The development of Penrose by Carnegie Mellon University aims to replace traditional graphing calculators with a tool that can only produce basic mathematical functions.

D. Penrose enables mathematicians to draw by hand and provides them with a programming language to express their ideas naturally.

Read the following passage and mark the letter A, B, C or D on your answer shee to indicate the best answer to each of the following Questions from 11 to 18.

Vietnamese cultural identity is a rich and intricate tapestry that reflects the nation's long and storied history. Rooted in over a thousand years of civilization, Vietnam's cultural identity is a fusion of indigenous traditions and external influences, shaped by its geographical location and historical interactions.

First and foremost, at the heart of Vietnamese culture is a deep reverence for family and community. Confucian values emphasizing respect for elders, filial piety, and social harmony have played a pivotal role in shaping Vietnamese society. These values are reflected in the close-knit family structures, hierarchical relationships, and communal rituals that are integral to daily life.

Secondly, Vietnamese cuisine is celebrated worldwide for its exquisite flavors and diversity. With its emphasis on fresh ingredients, fragrant herbs, and balanced flavors, Vietnamese food tells a story of the country's agricultural heritage and regional variations. Iconic dishes like pho, banh mi, and spring rolls have become global favorites, representing the culinary artistry deeply ingrained in Vietnamese culture. Also, Vietnam's artistic expressions are equally captivating. Traditional art forms like water puppetry, silk painting, and folk music continue to thrive alongside contemporary artistic movements. Áo dài, a graceful traditional dress, exemplifies the fusion of elegance and modesty in Vietnamese fashion, symbolizing cultural pride and identity.

Today, in the face of modernization and globalization, Vietnamese cultural identity remains resilient. While adapting to the challenges of the 21st century, the Vietnamese people continue to honor their traditions, celebrate their unique cultural expressions, and pass on their heritage to future generations, ensuring that their cultural identity remains vibrant and enduring.

(Adapted from Saigoneer)

Question 11. The word "indigenous" in paragraph 1 is opposite in meaning to______.

A. local

B. foreign

C. traditional

D. native

Question 12. Which of the following is NOT mentioned as Confucian values emphasizing respect for?

A. social harmony

B. individualism

C. elders

D. filial piety

Question 13. The word "reverence" in paragraph 2 could be best replaced by_______

A. criticism

B. admiration

C. disrespect

D. indifference

Question 14. Which of the following best paraphrases the underlined sentence in paragraph 3?

A. As a traditional dress, the áo dài reflects the combination of sophistication and simplicity in Vietnamese fashion, representing the nation's cultural values.

B. The graceful áo dài, a traditional Vietnamese attire, signifies the blend of elegance and restraint, illustrating the pride and identity of Vietnamese culture.

C. Known as a traditional dress, the áo dài beautifully combines elegance with modesty, serving as a symbol of Vietnam's cultural identity and pride.

D. The áo dài, known for its elegance and modesty, represents a blend of Vietnamese fashion that embodies cultural identity and pride.

Question 15. The word "Their" in paragraph 4 refers to_______.

A. Agricultural heritage                B. Vietnamese cuisine

C. Vietnamese people                D. Traditional art forms

Question 16. Which of the following is TRUE according to the passage?

A. Water puppetry is no longer practiced in Vietnam.

B. Vietnamese cultural identity is static and unchanging.

C. Vietnamese cuisine has gained international recognition.

D. Modernization has completely erased Vietnamese traditions.

Question 17. In which paragraph does the writer mention a present concession relationship?

A. Paragraph 2        

B. Paragraph 1        

C. Paragraph 4        

D. Paragraph 3

Question 18. In which paragraph does the writer state that Vietnamese cultural identity is influenced by both internal and external factors?

A. Paragraph 1

B. Paragraph 3

C. Paragraph 4

D. Paragraph 2

Mark the letter A, B, C, or D on your answer sheet to indicate the correct arrangement of the sentences to make a meaningful exchange or text in each of the following Questions from 19 to 23.

Question 19.............................................

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Question 21.

a. Online education has grown in popularity due to its flexibility, allowing students to balance their studies with personal and professional responsibilities.

b. This means that students can attend classes from anywhere in the world, without being tied to a specific location.

c. In addition to convenience, online courses often provide a wide range of resources, such as recorded lectures, discussion forums, and interactive assignments.

d. In conclusion, online education offers students the flexibility and resources they need to succeed, especially in today's fast-paced world.

e. Furthermore, online platforms are accessible at any time, allowing learners to study at their own pace, which is particularly beneficial for those with busy schedules.

A. a-b-e-c-d        

B. b-c-e-d-a        

C. a-e-b-c-d        

D. d-a-c-e-b

Question 22.

a. Mark: "Yeah, I really needed to relax after such a stressful week at work."

b. Alice: "Did you do anything fun this weekend, Mark?"

c. Alice: "I'm glad to hear that! What did you do?"

d. Mark: "I went hiking in the mountains. The fresh air was amazing."

e. Alice: "That sounds like a perfect way to unwind!"

A. c-b-a-e-d        

B. d-b-a-e-c        

C. c-e-d-b-a        

D. b-a-c-d-e

Question 23.

a. I wanted to tell you that I've recently accepted a new job in New York, and I'll be moving there next month. It's a big change, but I'm really excited about this new chapter in my life.

b. Dear Emily,

c. I'm planning to visit my family before the big move, and I'd love to see you if you're free during that time.

d. Hope this message finds you well! I wanted to catch you up on some recent news.

e. Take care, and I hope to see you soon!

A. a-b-d-e-c        

B. d-a-b-c-e        

C. b-d-a-c-e        

D. b-a-d-c-e

Read the following passage 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 24 to 28.

The future of electric vehicles (EVs) is promising, as technological advancements and environmental concerns (24)_______. As governments worldwide implement stricter emissions regulations and offer incentives for EV adoption, manufacturers are investing heavily in research and development. (25)_______, resulting in longer ranges and faster charging times. For instance, new solid-state batteries have the potential to enhance energy density and safety, making EVs more practical for everyday use.

Additionally, the rise of autonomous driving technology is set to revolutionize the way we interact with vehicles. Many electric models are now equipped with advanced driver-assistance systems (26)_______. Furthermore, the integration of smart technology allows for seamless connectivity, enabling drivers to monitor their vehicle's performance and locate charging stations through mobile apps.

As charging infrastructure continues to expand, (27)_______, the convenience of owning an EV is increasing. This transition to electric vehicles not only promises a reduction in carbon emissions but also fosters a cleaner, healthier environment. Overall, (28)_______ and sustainable transportation.

Question 24.

A. from which drive the automotive industry toward a sustainable transformation

B. driving the automotive industry toward a sustainable transformation

C. drive the automotive industry toward a sustainable transformation

D. that drive the automotive industry toward a sustainable transformation

Question 25.

A. which not only enhance safety but also pave the way for fully autonomous driving

B. whose not only enhance safety but also pave the way for fully autonomous driving

C. who not only enhance safety but also pave the way for fully autonomous driving

D. whose not only enhance safety but also pave the way for fully autonomous driving

Question 26.............................................

............................................

............................................

Question 28.

A. electric vehicles for innovation hold immense potential for the future

B. the future of electric vehicles holds immense potential for innovation

C. immense potential for innovation holds the future of electric vehicles

D. the future for innovation holds immense potential of electric vehicles

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 29 to 34.

Solo Female Travelers Club- Global Greeter Network

Looking to enhance your travel experience with a local perspective? Join the Global Greeter Network, a service (29)______ to connect travelers with friendly locals eager to (30)________ you around. Whether you're (31)________ in a guided tour, a scenic walk, or simply being dropped (32)________ at a spot of interest, this program offering flexible options allows you to explore new destinations without the hassle of finding transportation. Perfect for solo female travelers wanting (33)_______ locals and like-minded explorers, the Global Greeter Network provides access to exclusive travel groups. Share experiences, make friends, and discover hidden gems. This service is designed for those eager to experience (34)_______ in a safe, comfortable way.

(Adapted from Solo Female Travelers)

Question 29.

A. was designed        

B. design        

C. that designed        

D. designed

Question 30.

A. see        

B. show        

C. go        

D. look

Question 31.

A. interesting        

B. interest        

C. interestingly        

D. interested

Question 32.

A. to

B. about        

C. on        

D. off

Question 33.

A. meeting        

B. meeting        

C. to meet        

D. meet

Question 34.

A. culture authentic local                                 B. authentic culture local

C. authentic local culture                                 D. local authentic culture

Read the following leaflet 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 35 to 40.

EXPLORE CULTURAL DIVERSITY

Culture is the heart of every society, reflecting traditions, values, and creativity. By understanding different cultures, we enrich our perspectives and build connections with (35)_______. Whether through art, language, or celebrations, culture (36)________ our identities and offers a window into the lives of others.

Why Embrace Cultural Diversity?

Celebrate Differences: Every culture has unique traditions, from festivals and dances to foods and clothing. (37)_______ experiencing these, we gain a deeper appreciation of our global community.

Language as a Key: Learning even a few words in another language can open (38)______ to new friendships and understanding.

Art & Music: Cultural (39)_______ in music, paintings, and performances are windows into a community's history and values.

Get Involved!

Attend local cultural festivals.

Try traditional cuisines from around the world.

(40)_______ art and films from different countries.

Celebrating culture brings us closer together.

Question 35.

A. other        

B. the other        

C. others        

D. another

Question 36.

A. forms        

B. shapes        

C. creates        

D. establishes

Question 37.............................................

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Question 40.

A. Contribute to        

B. Commit to        

C. Engage with        

D. Share with

_______ THE END _______