Preface to how the Other Half Thinks Reading Answers

Jan 2, 2023

Preface to how the Other Half Thinks Reading Answers has been referenced from the IELTS book; Cambridge 11 Test 3, Reading Passage 3. The IELTS reading passage topic; Preface to how the Other Half Thinks Reading Answers comprises a total of 14 questions. The questions in this IELTS Reading topic are to be solved within a timeframe of 20 minutes. This IELTS Reading topic; Preface to how the Other Half Thinks Reading Answers is the inclusion of question types such as; choose the correct letter. The candidates are required to read this IELTS Reading passage carefully and answer the questions. Candidates can practice more of these IELTS reading topics from several IELTS reading practice papers that are available throughout the internet.

Check: Get 10 Free Sample Papers
Check: Register for IELTS Coaching - Join for Free Trial Class Now

Section 1

Read the Passage to Answer the Following Questions

Preface to how the Other Half Thinks Reading Answers

Occasionally, in some difficult musical compositions, there are beautiful, but easy parts – parts so simple a beginner could play them. So it is with mathematics as well. There are some discoveries in advanced mathematics that do not depend on specialized knowledge, not even on algebra, geometry, or trigonometry. Instead, they may involve, at most, a little arithmetic, such as ‘the sum of two odd numbers is even’, and common sense. Each of the eight chapters in this book illustrates this phenomenon. Anyone can understand every step in the reasoning. The thinking in each chapter uses at most only elementary arithmetic, and sometimes not even that. Thus all readers will have the chance to participate in a mathematical experience, to appreciate the beauty of mathematics, and to become familiar with its logical, yet intuitive, style of thinking.
One of my purposes in writing this book is to give readers who haven’t had the opportunity to see and enjoy real mathematics the chance to appreciate the mathematical way of thinking. I want to reveal not only some of the fascinating discoveries, but, more importantly, the reasoning behind them. In that respect, this book differs from most books on mathematics written for the general public. Some present the lives of colorful mathematicians. Others describe important applications of mathematics. Yet others go into mathematical procedures, but assume that the reader is adept in using algebra.
I hope this book will help bridge that notorious gap that separates the two cultures: the humanities and the sciences, or should I say the right brain (intuitive) and the left brain (analytical, numerical). As the chapters will illustrate, mathematics is not restricted to the analytical and numerical; intuition plays a significant role. The alleged gap can be narrowed or completely overcome by anyone, in part because each of us is far from using the full capacity of either side of the brain. To illustrate our human potential, I cite a structural engineer who is an artist, an electrical engineer who is an opera singer, an opera singer who published mathematical research, and a mathematician who publishes short stories.
Other scientists have written books to explain their fields to non-scientists, but have necessarily had to omit the mathematics, although it provides the foundation of their theories. The reader must remain a tantalized spectator rather than an involved participant, since the appropriate language for describing the details in much of science is mathematics, whether the subject is expanding universe, subatomic particles, or chromosomes. Though the broad.outline of a scientific theory can be sketched intuitively, when a part of the physical universe is finally understood, its description often looks like a page in a mathematics text.
Still, the non-mathematical reader can go far in understanding mathematical reasoning. This book presents the details that illustrate the mathematical style of thinking, which involves sustained, step-by-step analysis, experiments, and insights. You will turn these pages much more slowly than when reading a novel or a newspaper. It may help to have a pencil and paper ready to check claims and carry out experiments.
As I wrote, I kept in mind two types of readers: those who enjoyed mathematics until they were turned off by an unpleasant episode, usually around fifth grade, and mathematics aficionados, who will find much that is new throughout the book. This book also serves readers who simply want to sharpen their analytical skills. Many careers, such as law and medicine, require extended, precise analysis. Each chapter offers practice in following a sustained and closely argued line of thought. That mathematics can develop this skill is shown by these two testimonials.
A physician wrote, The discipline of analytical thought processes [in mathematics] prepared me extremely well for medical school. In medicine one is faced with a problem which must be thoroughly analyzed before a solution can be found. The process is similar to doing mathematics.’ A lawyer made the same point, “Although I had no background in law – not even one political science course — I did well at one of the best law schools. I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles. Lawyers who have studied mathematics can master the legal principles in a way that most others cannot.’

Questions 27-34

The Reading Passage has seven sections, A-G.
Which section contains the following information?

Write the correct letter, A— G, in boxes 27 — 34 on your answer sheet.
NB: You may use any letter more than once.

A reference to books that assume a lack of mathematical knowledge.

Answer: D
Supporting sentence: Other scientists have written books to explain their fields to non-scientists, but have necessarily had to omit the mathematics, although it provides the foundation of their theories.
Keyword: non-scientists, omit, assume, mathematical knowledge
Key Location: Section D, 1st line
Explanation: This is an accurate answer since, when other scientists create a book with non-scientists in mind, they leave out the math because they believe, sensibly, that non-scientist readers wouldn't be able to understand the books without it. In Section D, this is made quite plain.

The way in which this is not a typical book about mathematics.

Answer: B
Supporting sentence: I want to reveal not only some of the fascinating discoveries, but, more importantly, the reasoning behind them.
Keyword: differ, general public, reasoning, typical book
Key Location: Section B, 3rd line
Explanation: The author's book aims to convey a taste of mathematics to individuals who haven't had the opportunity to appreciate it, whereas a traditional math-related book would either discuss discoveries or mathematical techniques in depth. He does this by outlining the justification for many such ideas. The novel acquires its own distinctiveness in this way. Section B goes into great depth about all of this.

Personal examples of being helped by mathematics

Answer: G
Supporting sentence: Many careers, such as law and medicine, require extended, precise analysis.
Keyword: testimonials, analyze, many careers, physician, lawyers
Key Location: Section G, (1st & 2nd examples)
Explanation: This is the right response because Section G has two testimonials, one from a doctor and the other from a lawyer, both of whom highlight how mathematics has aided them in their respective disciplines.

Examples of people who each had abilities that seemed incompatible

Answer: C
Supporting sentence: To illustrate our human potential, I cite a structural engineer who is an artist, an electrical engineer who is an opera singer, an opera singer who published mathematical research, and a mathematician
who publishes short stories.
Keyword: gap, not restricted, incompatible
Key Location: Section C, last line
Explanation: This is the appropriate response. It has been mentioned in section C, the author provides several examples of individuals who have succeeded in both the humanities and sciences to demonstrate that there isn't truly a gap and that anyone can close it.

Mention of different focuses of books about mathematics.

Answer: B
Supporting sentence: Some present the lives of colorful mathematicians. Others describe important applications of mathematics. Yet others go into mathematical procedures, but assume that the reader is adept in using algebra.
Keyword: different focuses, books, readers, general public
Key Location: Section B, last line
Explanation: The author discusses the numerous usual foci of books on mathematics written by other scientists in section B, thus this is the right response.

A contrast between reading this book and reading other kinds of publication.

Answer: E
Supporting sentence: You will turn these pages much more slowly than when reading a novel or a newspaper.
Keyword: non-mathematical readers, contrast, other publications
Key Location: Section E, 3rd line
Explanation: This is the right response since the author discusses in Section E how he presented his book to readers of all categories differently, making a comparison between his work and other authors' works.

A claim that the whole of the book is accessible to everybody

Answer: A
Supporting sentence: Each of the eight chapters in this book illustrates this phenomenon. Anyone can understand every step in the reasoning.
Keyword: all readers, accessible, chance to participate
Key Location: Section A, 4th line
Explanation: This is the right answer since the author states in Section A that he wants to offer everyone an opportunity to participate in the mathematical experience, therefore making the entire book accessible to everyone.

A reference to different categories of intended readers of this book

Answer: F
Supporting sentence: As I wrote, I kept in mind two types of readers: those who enjoyed mathematics until they were turned off by an unpleasant episode…This book also serves readers who simply want to sharpen their
analytical skills.
Keyword: types of readers, precise analysis, aficionados
Key Location: Section F, 1st & 2nd line
Explanation: This is the right answer since the author discusses in section F how he wrote the book with two categories of readers in mind.

Questions 35-40

Complete the sentences below. Choose ONE WORD ONLY from the passage for each answer.
Write your answers in boxes 35- 40 on your answer sheet.

Some areas of both music and mathematics are suitable for someone who is a Beginner

Answer: : Beginner
Supporting sentence: Occasionally, in some difficult musical compositions, there are beautiful, but easy parts - parts so simple a beginner could play them. So it is with mathematics as well.
Keyword: easy parts, simple, suitable, beginner, music, mathematics
Key Location: Section A, 1st line
Explanation: This is the right response since the author discusses how, although both math and music can be quite hard, there will still be elements that even a novice can understand and play, proving that both fields are appropriate for individuals who are just starting out. Therefore, "beginning" properly fills in the blank.

It is sometimes possible to understand advanced mathematics using no more than a limited knowledge of Arithmetic

Answer: Arithmetic
Supporting sentence: There are some discoveries in advanced mathematics that do not depend on specialized knowledge, not even on algebra, geometry, or trigonometry. Instead, they may involve, at most, a little
arithmetic, such as ‘the sum of two odd numbers is even’, and common sense.
Keyword: do not depend, little arithmetic, advanced mathematics
Key Location: Section A, 3rd and 4th line
Explanation: This is the appropriate response since the author cites examples of how understanding big mathematical discoveries frequently just requires a basic understanding of arithmetic and some common sense.

The writer intends to show that mathematics requires intuitive thinking, as well as analytical skills.

Answer: Intuitive
Supporting sentence: As the chapters will illustrate, mathematics is not restricted to the analytical and numerical; intuition plays a significant role.
Keyword: humanities, science, intuition, analytical, numerical
Key Location: Section C, 2nd line
Explanation: The author is attempting to show that there is no difference between how individuals in the arts and sciences think, and that arithmetic too involves both analytical and intuitive thinking, thus this is the acceptable response.

Some books written by scientists have had to leave out the mathematics that is central to their theories.

Answer: Scientists
Supporting sentence: Other scientists have written books to explain their fields to non-scientists, but have necessarily had to omit the mathematics, although it provides the foundation of their theories.
Keyword: omit, foundation, other scientists
Key Location: Section D, 1st line
Explanation: The author also highlights how other scientists remove mathematics when attempting to explain their topic to non-scientists despite though it is the basis of their theories, making this the acceptable response.

The writer advises non-mathematical readers to perform experiments while reading

Answer: Experiments
Supporting sentence: It may help to have a pencil and paper ready to check claims and carry out experiments.
Keyword: carry out experiments, check claims
Key Location: Section E, last line
Explanation: This is the right response since, while emphasising how uniquely written the book is, the author elaborates the step-by-step procedure, which can motivate the readers to try it out on their own to confirm. Therefore, experiment is the appropriate noun.

A lawyer found that studying theorems helped even more than other

areas of mathematics in the study of law.
Answer: Theorems
Supporting sentence: I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles.
Keyword: success, in particular, theorems, analyze
Key Location: Section G, 2nd para, 2nd line
Explanation: This is the appropriate response since the lawyer notes in his testimony how mathematics helped him succeed in law, but he specifically specifies "theorems," which were more important to his success than
any other subject. Therefore, "theorems" is a suitable term to use.