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剑桥雅思11阅读Test3Passage3原文：
You should spend about 20 minutes on Questions 27-40, which are based on Reading Passage 3 below.
Preface to ‘How the other half thinks: Adventures in mathematical reasoning’
A 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.
B 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.
C 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.
D 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.
E 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.
F 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:
G 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.’
I hope you will share my delight in watching as simple, even nave, questions lead to remarkable solutions and purely theoretical discoveries find unanticipated applications.
Questions 27-34
Reading Passage 3 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.
27 a reference to books that assume a lack of mathematical knowledge
28 the way in which this is not a typical book about mathematics
29 personal examples of being helped by mathematics
30 examples of people who each had abilities that seemed incompatible
31 mention of different focuses of books about mathematics
32 a contrast between reading this book and reading other kinds of publication
33 a claim that the whole of the book is accessible to everybody
34 a reference to different categories of intended readers of this book
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.
35 Some areas of both music and mathematics are suitable for someone who is a __________.
36 It is sometimes possible to understand advanced mathematics using no more than a limited knowledge of __________.
37 The writer intends to show that mathematics requires __________ thinking, as well as analytical skills.
38 Some books written by __________ have had to leave out the mathematics that is central to their theories.
39 The writer advises non-mathematical readers to perform __________ while reading the book.
40 A lawyer found that studying __________ helped even more than other areas of mathematics in the study of law.
剑桥雅思11阅读Test3Passage3答案解析Question 27
答案：D
关键词：assume, lack of mathematical knowledge
定位原文：D段第1句“Other scientists have written books to…”
解题思路：题目：a reference to books that assume a lack of mathematical knowledge; 译文：提到了这样一些书，它们都设定其内容缺失数学专业知识。books所进行的assume是针对书的读者而言，也就是说，它们假设的是“读者并不具有(或者说缺乏)特别深厚的数学知识”，但在英语地道表达中此句并不需要出现readers这个单词，需要考生自行领会。回到原文中，have necessarily had to omit这个表达也清楚地表明这类书籍是“出于必要、不得不省略了”数学相关内容。也就是说，这些书并不是故意对数学专业知识避而不谈，而是考虑到了读者群的具体情况而刻意避免了深入艰涩的数学内容。
Question 28：
答案：B
关键词：not a typical book
定位原文： B部分第2段第1句“In that respect, this book differs from…”
解题思路：题目：the way in which this is not a typical book about mathematics;译文：本书在何种意义上并非一本典型的数学题材相关书籍。此题相対来说比较容易，只需考生看出not a typical book 与 differs from most books 的简单同义替换。
Question 29：
答案：G
关键词：personal examples, helped by
定位原文：G部分
解题思路：题目：personal examples of being helped by mathematics;译文：得到数学助益的个人案例。此题从理解题干或原文的角度来看都并不困难，文章中医生和律师的个人案例无论读懂哪一个都足以帮助解题。但如果考生仅仅只着眼于在文章中寻找某个关键词的同义替换，则无论 personal, example 还是help 都无法找到，反而会遭遇困难。
Question 30：
答案：C
关键词：examples of people, abilities, incompatible
定位原文： C段最后一句 “To illustrate our human potential, I…”
解题思路：题目：examples of people who each had abilities that seemed incompatible; 译文：举例同时具有的各种能力看起来似乎并不协调的人物例子。需灵活理解题干中的incompatible一词，未必一定是“不可兼容的”，也可以泛指“似乎有矛盾、不一致”这样的状态。言下之意，一个人可以既具备这类能力，又同时具有另外一类不同的能力，而看似这两种能力好像不应该同时出现在一个人的身上。原文中列举了四人，每个人都在两个截然不同的领域中有所建树，正是为了表达这样的意思。
Question 31：
答案：B
关键词：different focuses
定位原文：B 部分第2段后3句 “Some present the lives …”
解题思路：题目：mention of different focuses of books about mathematics;译文：提到了不同的数学类书籍的不同关注点。此题从理解题干意思到理解原文意思都不困难。题干属于总结阐述型，而原文则给出细节，具体列举有哪几类着眼点各自不同的数学类书籍。
Question 32：
答案：E
关键词：contrast, other kinds of publication
定位原文：E段第3句“You will turn…”
解题思路：题目：a contrast between reading this book and reading other kinds of publication; 译文：比较阅读此书和阅读其他出版物的不同体验。此题最容易的入手点在于“其他出版物”这个信息，文中的novel和newspaper都能与此构成对应，只需按部就班读到此处信息即可。
Question 33：
答案：A
关键词：whole of the book, accessible to everybody
定位原文： A部分第1段最后一句和第2段第2句“Anyone can understand …”“Thus all readers…”
解题思路：题目：a claim that the whole of the book is accessible to everybody; 译文：声称这本书的所有部分都能让每个人看懂。此题相対比较简单，A部分中无论是看到第一段还是第二段的相关内容，都可比较顺利地得出答案。
Question 34：
答案：F
关键词：different categories, intended readers
定位原文：F部分第1段“As I wrote, I kept…”
解题思路：题目：a reference to different categories of intended readers of this book; 译文：提到这本书的目标读者群的不同类别。本题没有什么难度，定位后可以比较轻松地解题。
Question 35：
答案： beginner
关键词：both music and mathematics, suitable
定位原文：A部分第1段第1、2句“Occasionally, in some difficult musical…”
解题思路：题干说“音乐和数学中都有某些领域是适合于这样的人的”。根据语法可以推知此处应该寻找某种“人”，回到原文中可以迅速、轻松定位“音乐”这个信息，根据So it is...as well的信息也可认定此处确实是音乐与数学并列被提及的答案出处，再通过阅读定位句可得答案为beginner。
Question 36：
答案： arithmetic
关键词：understand advanced mathematics, limited knowledge
定位原文：A部分第1段第3、4句“There are some discoveries… ”
解题思路：题干说“有时候要理解高等数学也只不过需要使用关于_____的一点有限知识就足够了”。考生可以轻松用advanced mathematics回到原文中定位，也不必在看到可能不熟悉的algebra geometry, or trigonometry 担心，根据本句上下文看出它们都是“高等数学”的具体举例内容即可。下一句则以instead和a little 来表明此处列举的内容“并不高深”，对比题干要求可知答案为arithmetic。
Question 37：
答案： intuitive
关键词：as well as, analytical skills
定位原文：A部分第2段最后一句“Thus all readers will…” 或C段第一句 “I hope this book…”
解题思路：题干说“作者意在展示数学除了需要分析技巧外也需要_____思维”。其实在文中两处都可找到答案。第一次是在A部分，虽然没有analytical这个定位词，但有logical这个类似信息，按部就班通读全文完全可以通过此句中的yet对比关系确定答案为intuitive;但如果更倾向于利用关键词analytical skills和as well as这个并列关系来寻找答案的话，更容易的定位出现在C段中，可以直接找到analytical原词，再利用and并列关系可以确定答案为intuitive。
Question 38：
答案： scientists
关键词：leave out, central to their theories
定位原文：D段第1句“Other scientists have written…”
解题思路：题干说“一些由_____写出来的书不得不省略一些对于他们的理论来说至关重要的数学知识”。细读题干可以推知空格内必然是作者、人，此处考査考生是否认识原文中omit一词为leave out词组的同义替换，如果有此词汇基础则可比较轻松地得出答案为 scientists。
Question 39：
答案： experiments
关键词：perform, while reading
定位原文：E段最后两句“You will turn these pages…”
解题思路：题干说“作者建议非数学专业出身的读者们在阅读此书时进行_____”。考生应该不难看出原文中 turn these pages 与题干中 while reading 的同义替换，只是在确定具体答案的时候需要仔细辨別，因为句中给出了两个并列信息，分别是 check claims 和 carry out experiments。 经过对比可知，只有carry out才能与perform对应，因此答案为experiments。
Question 40：
答案： theorems
关键词：lawyer, helped, even more than, other areas
定位原文：G部分第2段第2句 “I attribute much of my success there…”
解题思路：题干说“一个律师发现在其学习法律的过程中学习_____甚至比其他数学领域知识更有帮助”。根据此信息可以得知空格内必定需要填写某个具体的数学领域。利用lawyer可以轻松定位，仔细阅读定位部分可以知道，只有in particular这个词组之后的内容才有可能是具体数学领域知识，由此得出答案为theorems。
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