What is PreCalculus?
A Quick Intro to What’s Covered
The following provides an outline of all the topics you would expect to see in a typical Precalculus class (i.e., Trigonometry and Math Analysis).
All of the topics are covered in detail in our Online Precalculus Course.
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An Overview of Precalculus Topics
An Overview of Precalculus Topics
The following sections provide links to our complete lessons on all Precalculus topics, starting with Trigonometry and progressing through Math Analysis.
Precalculus is a course that is designed to prepare students for Calculus, either in high school or college.
Now, calculus is the study of how things change over time; therefore, the goal of precalculus is to equip students to handle rigorous and dynamic concepts by helping them to connect their previous learning from Algebra and Geometry.
To do this, Pre-Calculus is divided into two major categories: Trigonometry and Math Analysis.
40 Videos 400+ Examples
Trigonometry, which is the study of triangles, typically begins with an understanding of basic functions, then branches into how triangles and their angles can be drawn and represented in rotations, degrees and radian measure.
With this foundation, students then introduced to the Unit Circle, which enables them to explore trigonometric graphs, trig identities, and trig equations, as well as how to solve both right and oblique triangles.
And lastly, students will explore new graphing planes called the Polar and Complex Coordinate systems.
37 Videos 500+ Examples
Whereas Math Analysis, which some instructors sometimes call Algebra 3, digs deeper into algebra concepts. Specifically, functions, domain and range, and end behavior.
The focus of math analysis is not to just review or solve more complicated equations, but to show students how to represent them in various formats (i.e., graphically, numerically, and verbally).
In particular, students will study polynomial functions, rational functions, exponential and logarithmic functions and limits and learn how to express their findings using various modalities.
Trigonometry vs Precalculus?
Precalculus encompasses both trig and math analysis; therefore a precalculus course will cover more topics than just a trigonometry course alone.
Why is precalculus hard?
Precalculus, which is a combination of trigonometry and math analysis, bridges the gap to calculus, but it can feel like a potpourri of concepts at times.
Students are suddenly required to memorize a lot of material as well as recall various concepts from their previous math courses. This can sometimes feel like they’re drinking from a firehose.
For example, students are thrown into the world of radians and angles, with very little preparation because they were only briefly exposed to trigonometry years earlier in their geometry course.
In fact, what was learned in geometry is either inadequate or a distant memory for most students, thus leaving many feeling like they are learning a foreign concept with little to no background.
Consequently, some students have a steep learning curve upon entering precal and will feel like they are swimming in unchartered waters for a while.
Now, most students agree that math analysis is “easier” than trigonometry, simply because it’s familiar (i.e., it’s very similar to algebra). But, it too can come with its own set of challenges, as concepts are more complex and students are expected to not only arrive at the correct answer but to show proper reasoning and logic.
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