What is Pre-Calculus?

John, the founder of TabletClass Math and a middle and high school math teacher, introduces the topic of pre-calculus as a challenging course that is foundational for calculus. He emphasizes its importance for students considering college, regardless of their major, as calculus is a common requirement. John also discusses the necessity of understanding pre-calculus topics before moving on to calculus and shares his experience in creating an online math program with over a hundred courses, including pre-calculus.

The video script outlines a typical sequence of math courses in high school for students on a college prep track. Starting with algebra one in ninth grade, students progress through geometry and algebra two, with some schools combining algebra and geometry. It's noted that by the junior year, most students are in algebra two. The senior year offers a choice between statistics and pre-calculus, with a strong recommendation for the latter for those considering college, as it keeps the option to take calculus open.

The speaker delves into the topics covered in a pre-calculus course, emphasizing the importance of a strong foundation in algebra two. The course typically begins with a review of algebra one and two, covering equations, graphing, and functions. It then moves on to more advanced topics such as polynomial and rational functions, logarithms, exponential functions, and an in-depth exploration of trigonometry, including identities, equations, and applications.

The script continues with a discussion on the more advanced chapters in pre-calculus, including analytic geometry (conic sections), systems of equations, matrices and determinants, and sequences and series. It mentions the importance of understanding these topics for success in calculus. The need for reviewing algebra two material before taking pre-calculus is stressed, especially for those who struggled with it, to ensure a solid foundation for the more complex concepts that follow.

The final paragraph addresses the importance of preparation for pre-calculus. It suggests that students who struggled with algebra two should review the material, possibly through a course like the one offered by the speaker. The emphasis is on taking initiative and improving math skills step by step. The necessity of good note-taking for success in pre-calculus and advanced math courses is highlighted. The speaker encourages students to seek help when needed and not to underestimate the challenge of pre-calculus.