Pre-calculus Review Material
- Instructors for calculus courses expect students to know a
variety of mathematical topics and techniques that you will use
regularly in calculus. In our experience, many setbacks for
students in calculus courses stem from the need to review some of
these topics, most often from algebra and trigonometry.
- On this page, we provide a few pointers to resources that can
help you review relevant techniques. We provide links to Khan
Academy (KA) videos and problems sets for two reasons. First,
we use the KA problem set platform as our basic homework tool for
Math 3. Second, the videos provide an alternative to a
textbook to help students access the material in a different mode.
- We encourage every student planning to take calculus (at any
level) to look through these materials to brush up on topics that
might be rusty or that your previous curriculum might not have
covered. Putting in a little time up front can alleviate many
problems later in the term.
Algebraic manipulations of polynomials and rational functions
provide the foundation for a lot of the work we do in
calculus. In taking limits, for example, we often encounter
rational functions — quotients of polynomials — that need to be
analyzed and simplified before we can evaluate a limit.
For a broad overview, the sections
on Polynomial expressions, equations, and
and Rational expressions, equations, and
functions are a great place to start.
More specifically, here are some basic skills that come up over and
over again in calculus:
In addition to polynomials and rational functions, trigonometric
functions — sine, cosine, tangent, cotangent, etc. — appear both
theoretically and in application.
Again, for a broad overview, KA has a whole section
on Trigonometry, all of which appears regularly in
calculus. Specific relevant skills include: