Technically a student coming into a Calculus class is
supposed to know both Algebra and Trigonometry.
The reality is often much different however. Most students enter a Calculus class woefully
unprepared for both the algebra and the trig that is in a Calculus class. This is very unfortunate since good algebra
skills are absolutely vital to successfully completing any Calculus course and
if your Calculus course includes trig (as this one does) good trig skills are
also important in many sections.
The intent of this chapter is to do a very cursory review of
some algebra and trig skills that are absolutely vital to a calculus
course. This chapter is not inclusive in
the algebra and trig skills that are needed to be successful in a Calculus course. It only includes those topics that most
students are particularly deficient in.
For instance factoring is also vital to completing a standard calculus
class but is not included here. For a
more in depth review you should visit my Algebra/Trig review or my full set of
Algebra notes at http://tutorial.math.lamar.edu.
Note that even though these topics are very important to a
Calculus class I rarely cover all of these in the actual class itself. We simply don’t have the time to do
that. I do cover certain portions of
this chapter in class, but for the most part I leave it to the students to read
this chapter on their own.
Here is a list of topics that are in this chapter. I’ve also denoted the sections that I
typically cover during the first couple of days of a Calculus class.
Review
: Functions Here is a quick review of functions, function
notation and a couple of fairly important ideas about functions.
Review : Inverse Functions A quick review of inverse functions and the
notation for inverse functions.
Review
: Trig Functions A review of trig functions, evaluation of trig
functions and the unit circle. This
section usually gets a quick review in my class.
Review : Solving Trig Equations A reminder on how to solve trig
equations. This section is always
covered in my class.
Review : Solving Trig Equations with Calculators, Part I The previous section worked problems whose
answers were always the “standard” angles.
In this section we work some problems whose answers are not “standard”
and so a calculator is needed. This
section is always covered in my class as most trig equations in the remainder
will need a calculator.
Review : Solving Trig Equations with Calculators, Part II Even more trig equations requiring a
calculator to solve.
Review : Exponential Functions A review of exponential functions. This section usually gets a quick review in
my class.
Review
: Logarithm Functions A review of logarithm functions and logarithm
properties. This section usually gets a
quick review in my class.
Review : Exponential and Logarithm Equations How to solve exponential and logarithm
equations. This section is always
covered in my class.
Review : Common Graphs This section isn’t much. It’s mostly a collection of graphs of many of
the common functions that are liable to be seen in a Calculus class.