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Introduction
Cambridge International Examinations (CIE) Advanced Level Mathematics has been created
especially for the new CIE mathematics syllabus. There is one book corresponding to each
syllabus unit, exceptthat units P2 and P3 are contained in a single book. This book covers
the first Pure Mathematics unit,
Pl.
The syllabus content is arranged by chapters which are ordered so as to provide a viable
teaching course. The early chapters develop the foundations
of
the syllabus; students may
already be familiar with some
of
these topics. Later chapters, however,
are.
largely
independent .of each other, and teachers may wish to vary the order in
wh~ch
they are used.
Some chapters, particularly Chapters 2, 3 and the first four sections
of
Chapter 8, contain
material which is not in the examination syllabus for
Pl,
and which therefore cannot be the
direct focus
of
examination questions. Some
of
this is necessary background material, such
as indices and surds; some is useful knowledge, such as graphs
of
powers
of
x, the use and
meaning
of
modulus, and work on sequences.
A few sections include important results which are difficult to prove or outside the syllabus.
These sections are marked with an asterisk(*) in the section heading, and there is usually a
sentence early on explaining precisely what it is that the student needs to know.
Occasionally within the text paragraphs appear in
this type style. These paragraphs are
usually outside the main stream
of
the mathematical argument, but may help to give
insight, or suggest extra work or different approaches.
Graphic calculators are not permitted in the examination, but they are useful aids
in
learning
mathematics. In the book the authors have noted where access to a graphic calculator would
be especially helpful but have not assumed that they are available to all students.
Numerical work is presented in a form intended to discourage premature approximation.
In·
ongoing calculations inexact numbers appear in decimal form like 3.456
..
.,
signifying
that the number is held in a calculator to more places than are given. Numbers are not
rounded at this stage; the full display could be, for example, '1.456123 or 3 .456 789.
Final answers are then stated with some indication that they are approximate, for
example ' 1.23 correct to 3. significant figures' .
There are plenty
of
exercises, and each chapter ends with a Miscellaneous exercise which
includes some questions
of
examination standard. Three Revision exercises consoliate work
in preceeding chpaters. The book concludes with two Practice examination papers.
In some exercises a few
of
the later questions may go beyond the likely requirements
of
the
Pl
examination, either in difficulty or in length or both. Some questions are marked with an
<,tSterisf,
which indicates that they require knowledge ofresults outside the syllabus.
Cambridge
U_niversity
Press would like to thank OCR (Oxford, Cambridge and RSA
Examinations), part
of
the University
of
Cambridge Local Examinations Syndicate (UCLES)
group, for permission to use past examination questions set in the United Kingdom.
The authors thank UCLES and Cambridge University Press, in particular Diana
Gillooly, for their help in producing this book. However, the responsibility for the text,
and for any errors, remains with the authors.
Raymondsam2020-09-23书本也太老了吧，2020年已经新大纲了，旧版可以淘汰。
