#### Module 1
Introduction and Review

### Section 1.2
Fundamentals of Algebra

## (see Text
Sections 1.2 and 1.3)

#### Introduction

This section reminds you of
various ways of
rearranging algebraic expressions.

Your objectives
for this include both understanding and speed.

Understanding of these
operations will be
important for you to successfully follow the remainder of the course,
and speed
will also be important if you later need to be able to follow classroom
presentations in subsequent courses.

#### Study Notes and Discussion

This material should all be
familiar to you
so you should be able to proceed quickly and feel comfortable with
doing so.
But don’t skip it. Be sure to read all of the text sections carefully,
and work
the examples as you go.

One point worth emphasizing
with regard to
the material in Section 1.2 is that the radical sign is used just for
the __positive__
square root of a positive number. So
only, __not__
.
Sometimes
is called the *principal* square
root, but it is often just called “the square
root” - without a modifier.

The latter is the most common
usage in
current North American calculus courses and it is what we shall do in
this
course. It is true that some places people do talk of a positive number
*a* as having “two square roots”. But even
then the root sign is almost always taken as referring only to the
positive one
as we have indicated above. So, again, if you say
,
it will be considered **wrong**.

You should get help at once if
you have
trouble either understanding or applying any of the techniques
introduced in
Section 1.3. Notice that in Example 6 on
p.43 it is the numerator rather than the denominator that is being
‘rationalized’. You may have spent lots of time rationalizing
denominators in
high school, but there was never any really good reason for doing that
rather
than rationalizing numerators instead. (Actually what turns out to be
useful
most often in calculus is rationalizing **differences**
- either in the denominator or in the numerator.)

#### Practice Exercises

Check your
understanding and practice for speed by working through some of the
Exercises
on pp29-31 and 45-47

Do enough of the
odd numbered questions of each type to convince yourself that you can
get the
right answers quickly. (Note that, as usual, the answers are in the
back of the
text and complete worked solutions are in the student study guide - but
try to
avoid looking at answers or solutions until you have made your own best
effort).

As a bare minimum you should do
##5,15,25,55,65,85 and 97 from Section 1.2

and ##5,15,25,35,53,63,75 and
85 from
Section 1.3.