What are the Topics Covered in Precalculus?
Precalculus is a course offered in high school designed to prepare students for studying calculus, which is the study of how things change over time. It may be required or elective and can help students in their future careers, especially those in science, technology, engineering and math.
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There are a lot of different topics covered in this class, and it can be daunting to some students. Fortunately, there are plenty of resources available to help students with this subject and get them on their way to success in calculus or elsewhere.
The main goal of this course is to prepare students for calculus, so the course is typically rigorous. Rigorous programs may include more challenging problems, explore theory and concepts in more depth, use a quicker pace or even introduce more advanced calculus topics and concepts earlier than other programs do.
In addition to helping students understand the basics of calculus, it also teaches them the basic concepts of algebra and trigonometry, which are two important foundational skills that can be invaluable for those who choose to continue studying the field.
Functions
Almost all of the concepts that are taught in precalculus relate to functions, which are mathematical expressions that can be graphed and are often used to solve math equations. There are many types of functions, including linear, quadratic, exponential, logarithmic, rational, trigonometric, and inverse trigonometric.
Understanding these functions is crucial to success in calculus and other higher-level math courses. Those who fail to grasp these concepts can find themselves lost and struggling to understand the more complicated and difficult material.
Finding the Right Curriculum for Precalculus
Since every student learns differently, a good curriculum can be a huge help when it comes to tackling precalculus. It should be able to explain these concepts simply and comprehensively, as well as fit the way a student learns best.
CTCMath
Using video lessons, CTCMath’s precalculus program explains a variety of topics, including linear, quadratic, polynomial and exponential functions, as well as trigonometric, logarithmic and rational functions. The lessons are short and to the point, with clear explanations and helpful demonstrations. They can be a great help to students who need extra assistance with math, but don’t necessarily have access to a teacher or someone else that can help them out.
AoPS
Another program that’s a little more rigorous than others, Art of Problem Solving’s precalculus textbook teaches through explanations that are concise and to the point, with thought-provoking demonstrations and examples that can really make these complex concepts a bit easier for students to understand. The textbook also has a lot of exercises and problem sets to practice these concepts in a way that can truly challenge students and reward them for their hard work.
Inverse Trigonometry
Inverse trigonometry, or trigonometric inversion, is a technique that allows students to calculate the angle of a triangle using a different variable than the one they’re trying to find the answer to. It’s a key part of preparing for more complicated topics in calculus and other higher level math classes, such as vector calculus.