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Dartmouth Mathematics Placement System

## 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.

Algebra

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 functions 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:

Trigonometry

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: