Preface to 'How the other half thinks: Adventures in mathematical reasoning': reading answers and analysis
In the preface to his book, a mathematician explains that some deep mathematical ideas need nothing more than simple arithmetic and common sense. He wants non-specialists to follow real mathematical reasoning, argues that maths uses intuition as well as analysis, and quotes a doctor and a lawyer whose maths training helped their careers.
The section matching (27-34) uses every section from A to G, with B used twice, in no particular order. The sentence completion (35-40) goes back to the start and follows the passage from A to G.
Answer key and self-check
Type what you wrote and hit mark. Hide the key first if you haven't done the passage yet. Every question number jumps to its explanation.
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Questions 27-34 · Matching information (sections A-G)
How to attack this block: Eight items for seven sections, so one letter repeats (B, which compares this book with other maths books). Several items talk about 'books', so be precise: maths books for the public are in B, books by scientists in D, and this book's readers in A, E and F.
Question 27
Answer: DSection D, first sentence
Which section mentions books written for readers who are assumed not to know maths?
Other scientists have written books to explain their fields to non-scientists, but have necessarily had to omit the mathematics
Question says → Passage says
books that assume a lack of mathematical knowledgebooks to explain their fields to non-scientists… had to omit the mathematics
Why: These books are aimed at non-scientists, so the authors leave the maths out. Writing without maths for that audience means assuming readers don't know it. D.
The trap: B also describes other books, and one type 'assume that the reader is adept in using algebra'. That's the opposite assumption: those books expect maths knowledge.
Question 28
Answer: BSection B, middle
Which section explains how this book is unlike usual maths books?
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.
Question says → Passage says
not a typical book about mathematicsthis book differs from most books on mathematics
the way in whichIn that respect
Why: 'In that respect' points back to the way it's different: it shows the reasoning, not just the discoveries. 'Differs from most' = 'not typical'. B.
The trap: A also describes what's special about the book (only simple arithmetic needed), but it never compares it with other maths books.
Question 29
Answer: GSection G
Which section has people describing how maths helped them personally?
A physician wrote, 'The discipline of analytical thought processes [in mathematics] prepared me extremely well for medical school.
Question says → Passage says
personal examplesA physician wrote / A lawyer made the same point
being helped by mathematicsprepared me extremely well / I attribute much of my success there to having learned, through the study of mathematics
Why: G quotes a doctor and a lawyer in their own words ('me', 'I'), each saying maths helped them succeed. Those are personal examples. G.
The trap: F introduces these 'testimonials' and mentions law and medicine, but the actual examples only arrive in G.
Question 30
Answer: CSection C, last sentence
Which section gives people with talents that seem not to go together?
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
Question says → Passage says
examples of peopleI cite
abilities that seemed incompatiblethe two cultures: the humanities and the sciences
Why: Each person combines a science skill with an arts skill, the two 'cultures' the section says are supposedly separated. That's abilities that seem incompatible. C.
The trap: G's doctor and lawyer used maths in their careers, but medicine and maths don't seem incompatible. Their point is that one helped the other.
Question 31
Answer: BSection B, last three sentences
Which section mentions the different things maths books focus on?
Some present the lives of colorful mathematicians. Others describe important applications of mathematics. Yet others go into mathematical procedures
Question says → Passage says
different focusesSome present… Others describe… Yet others go into
books about mathematicsmost books on mathematics written for the general public
Why: B lists three kinds of maths book: biographies, applications and procedures. 'Some… others… yet others' is the signal for different focuses. B again, which is allowed.
The trap: D is about books by scientists on their own fields, not books about maths. And people often avoid B because they've already used it for 28.
Question 32
Answer: ESection E, third sentence
Which section compares reading this book with reading other things?
You will turn these pages much more slowly than when reading a novel or a newspaper.
Question says → Passage says
a contrastmuch more slowly than
other kinds of publicationa novel or a newspaper
Why: Novels and newspapers are other kinds of publication, and 'more slowly than' is the contrast. E.
The trap: B contrasts this book with other maths books, but those are the same kind of publication. The question wants different types, like novels.
Question 33
Answer: ASection A, middle
Which section claims that anyone can follow all of the book?
Each of the eight chapters in this book illustrates this phenomenon. Anyone can understand every step in the reasoning.
Question says → Passage says
the whole of the bookEach of the eight chapters / every step
accessible to everybodyAnyone can understand / all readers will have the chance
Why: 'Each of the eight chapters' and 'every step' cover the whole book, and 'anyone can understand' means accessible to everybody. A.
The trap: E says the non-mathematical reader 'can go far', but going far isn't the same as understanding everything.
Question 34
Answer: FSection F, first two sentences
Which section describes the different types of reader the book is aimed at?
As I wrote, I kept in mind two types of readers
Question says → Passage says
different categories of intended readerstwo types of readers / This book also serves readers who simply want to sharpen their analytical skills
Why: 'Kept in mind two types of readers' = intended readers, and F then adds a third group who want sharper analytical skills. F.
The trap: B mentions 'readers who haven't had the opportunity' to enjoy maths, which is one group, not a set of categories.
Sentence completion (ONE WORD ONLY)
Questions 35-40
How to attack this block: The sentences follow the passage in order, one or two per section. Check the grammar of each gap: one needs an adjective ('___ thinking'), and three need plural nouns.
Question 35
Answer: beginnerSection A, first two sentences
Some parts of music and maths are easy enough for what kind of person?
parts so simple a beginner could play them. So it is with mathematics as well.
Question says → Passage says
Some areas of both music and mathematicssome difficult musical compositions… So it is with mathematics as well
suitable forso simple a… could play them
Why: The easy parts are 'so simple a beginner could play them', and 'so it is with mathematics' extends it to maths. 'A ___' needs one singular noun: 'beginner'.
The trap: 'Reader' and 'non-scientist' appear later in the passage, but this sentence's word for the easy-level person is 'beginner'.
Question 36
Answer: arithmeticSection A, fourth sentence
What limited knowledge can be enough to understand advanced maths?
Instead they may involve, at most, a little arithmetic, such as 'the sum of two odd numbers is even', and common sense.
Question says → Passage says
advanced mathematicssome discoveries in advanced mathematics
no more than a limited knowledge ofat most, a little
Why: 'No more than a limited' = 'at most, a little'. The subject named is arithmetic. Check the spelling.
The trap: Algebra, geometry and trigonometry are named in the sentence before, but as things you don't need.
Question 37
Answer: intuitiveSection C, second sentence
What kind of thinking does maths need besides analytical skill?
mathematics is not restricted to the analytical and numerical; intuition plays a significant role
Question says → Passage says
as well as analytical skillsnot restricted to the analytical and numerical
requires ___ thinkingintuition plays a significant role
Why: The gap sits before 'thinking', so it needs an adjective. The passage gives 'intuition' as a noun, but the adjective form 'intuitive' is in the text too ('the right brain (intuitive)', and 'logical, yet intuitive, style of thinking' in A).
The trap: Writing 'intuition' is the common slip: 'intuition thinking' isn't grammatical. Copy the adjective the passage already uses.
Question 38
Answer: scientistsSection D, first sentence
Who wrote books that had to leave the maths out?
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.
Question says → Passage says
have had to leave outhave necessarily had to omit
central to their theoriesprovides the foundation of their theories
Why: 'Leave out' = 'omit', 'central to' = 'provides the foundation of'. The writers are scientists, and 'books written by ___' needs a plural.
The trap: 'Non-scientists' is in the same sentence, but they're the readers, not the writers. Don't let the 'non-' slip past.
Question 39
Answer: experimentsSection E, last sentence
What does the writer suggest non-mathematical readers do as they read?
It may help to have a pencil and paper ready to check claims and carry out experiments.
Question says → Passage says
advisesIt may help
performcarry out
Why: 'Perform' = 'carry out', and what you carry out is experiments. Plural, one word.
The trap: 'Claims' is in the same sentence, but you check claims, you don't perform them.
Question 40
Answer: theoremsSection G, lawyer's quote
What area of maths did the lawyer find most helpful for studying law?
I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles.
Question says → Passage says
helped even more than other areas of mathematicsin particular
in the study of lawI did well at one of the best law schools
Why: 'In particular' singles out one part of maths above the rest: theorems. That's the 'even more than other areas' in the sentence. Plural noun.
The trap: 'Principles' ends the same sentence, but those are the legal principles the lawyer learned to analyse, not part of maths.
B again. The list of biographies, applications and procedures is the 'different focuses'. People avoid B because they already used it for 28.
Words from this passage worth keeping
elementary(A)
basic and simple
adept(B)
skilled
notorious(C)
famous for something bad
alleged(C)
said to exist, but not proven
tantalized(D)
teased by something you can see but not have
sustained(E)
continuing for a long time without stopping
aficionados(F)
keen fans who know a lot about something
unanticipated(G)
not expected
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The full Cambridge 11 Test 3 reading paper: all three passages, 60 minutes, marked the second you finish with a review of every answer. Already done it? Take it again and see if the same traps still get you.
Cambridge IELTS 11, Test 3, Reading Passage 3. The passage and questions belong to Cambridge University Press and are not reproduced here. We quote short extracts only as evidence for our own commentary, and the answers are published for self-marking. Get the book for the full text, or sit the test on Langujet.
