What Topics Are in Precalculus?
The highest school math courses combine the concepts of algebra and trigonometry into one course, called precalculus. Although it can feel like a hodgepodge of different topics, there are some key things that are common to many precalculus curricula.
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The scope of a precalculus course will vary, depending on the curriculum and the needs of students. For some, a more rigorous precalculus curriculum is necessary to help them prepare for calculus and other advanced math courses. On the other hand, others may be able to learn precalculus more effectively by taking a less rigorous approach.
Often, a precalculus course will incorporate some of the material from both algebra and trigonometry, and this can be a good thing for students who have not had a lot of exposure to either subject in the past. It will also ensure that they have a solid foundation for the more challenging math courses that they will encounter later on in their education.
A good precalculus curriculum will include a range of topics, from the more fundamental and straightforward to the more advanced and complex. It should also provide a range of exercises and activities that will allow students to get a feel for how the subject works in real life and make sure they have a firm grasp on the basics.
Some of the more commonly encountered topics in precalculus include graph transformations, logarithms and polynomials, conic sections, sequences and series and limits. They will also learn about various function types and explore how to represent these in a variety of ways, including visually, numerically, verbally and analytically.
Art of Problem Solving offers a precalculus curriculum that does a great job of preparing students for more challenging courses and exams, and also for prestigious math competitions. It teaches through short, clear and to the point explanations that are followed by plenty of exercises to put these ideas into practice.
Another great precalculus program is Saxon Mathematics, which focuses on developing student skills and understanding in a back to basics approach. They do a good job of explaining concepts in a clear and concise manner, with lots of visuals and graphs to help students understand what they are looking at.
In addition to the traditional textbook-based curriculum, Saxon Math also offers a variety of online and interactive resources to help students better connect with the subject and develop their understanding. These resources can be especially useful if your student is interested in science, engineering or computer science and would benefit from a deeper exploration of math in the real world.
The course will also cover a variety of mathematical functions and techniques, such as product to sum, law of sines and cosines, the law of tangents and other related concepts. It will also introduce students to more advanced concepts, such as exponential and logarithmic functions, as well as limits.
The AP Precalculus curriculum is designed to prepare students for the advanced math and analysis required in AP Calculus AB and BC. It will also cover a wide range of concepts, such as Euclidean vectors, matrices and power functions. In addition to these core concepts, it will also offer a few topics that are unique to AP level courses, such as conic sections and sequences and series.