To the Student
Contents
: Members of the PEA
Mathematics Department have written the material
in this book. As you
work through it, you will discover that algebra, geometry, and
trigonometry have
been integrated into a mathematical whole. There is no Chapter 5, nor
is there a section on
tangents to circles. The curriculum is problem-centered, rather than
topic-centered.
Techniques and theorems will become apparent as you work through the
problems, and you
will need to keep appropriate notes for your records — there are no
boxes containing
important theorems. There is no index as such, but the reference section
that starts on page
201 should help you recall the meanings of key words that are defined
in the problems
(where they usually appear italicized).
Comments on
problem-solving
: You should approach
each problem as an exploration.
Reading each question
carefully is essential, especially since definitions, highlighted in
italics, are
routinely inserted into the problem texts. It is important to make accurate
diagrams whenever
appropriate. Useful strategies to keep in mind are: create an easier
problem, guess and
check, work backwards, and recall a similar problem. It is important
that you work on each
problem when assigned, since the questions you may have about a
problem will likely
motivate class discussion the next day.
Problem-solving
requires persistence as much as it requires ingenuity. When you get stuck,
or solve a problem
incorrectly, back up and start over. Keep in mind that you’re probably
not the only one who
is stuck, and that may even include your teacher. If you have taken
the time to think
about a problem, you should bring to class a written record of your
efforts, not just a
blank space in your notebook. The methods that you use to solve a
problem, the
corrections that you make in your approach, the means by which you test
the validity of your
solutions, and your ability to communicate ideas are just as important
as getting the
correct answer.
About technology
: Many of the
problems in this book require the use of technology
(graphing calculators
or computer software) in order to solve them. Moreover, you are
encouraged to use
technology to explore, and to formulate and test conjectures. Keep
the following
guidelines in mind: write before you calculate, so that you will have a clear
record of what you
have done; store intermediate answers in your calculator for later use in
your solution; pay
attention to the degree of accuracy requested; refer to your calculator’s
manual when needed;
and be prepared to explain your method to your classmates. Also,
if you are asked to
“graph
y
= (2
x
−
3)
=
(
x
the expectation is that,
although you might
use your calculator to generate a picture of the curve, you should
sketch that picture in your notebook or
on the board, with correctly scaled axes.
