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Where in paragraph 1 does the following sentence best fit? For many, the elegance of mathematical concepts often goes unnoticed amidst the complexity.

• [I]

• [II]

• [III]

• [IV]

The word “restricted” in paragraph 2 is OPPOSITE in meaning to ________.

• contained

• expanded

• confined

• enclosed

The phrase “secret sauce” in paragraph 3 could be best replaced by ________.

• unexpected benefit

• mysterious feature

• unnatural ability

• special element

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

• It allows users to create diagrams from mathematical expressions.

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

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

• It can automatically generate solutions to complex mathematical problems.

The word “they” in paragraph 4 refers to ________.

• users

• diagrams

• possibilities

• ideas

Which of the following best summarizes paragraph 3?

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

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

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

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

Which of the following is NOT TRUE according to the passage?

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

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

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

• Penrose’s developers want to make math easier to understand by using illustrations.

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

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

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

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

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

Which of the following can be inferred from the passage?

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

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

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

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

Which of the following best summaries the passage?

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

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

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

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