The first semester of our course covers chapters 1 through 3. This primarily means we discuss the analysis of various types of functions including linear, quadratic, cubic & other polynomials, rationals, logarithms and exponentials. In our study, we talk about the basic concepts related to these functions: domain, range, continuity, extrema, symmetry, intercepts, etc and then examine how these change (or don't change) when various transformations are applied. These chapters also include some great opportunities for applications of the functions including vertical free fall problems and finance problems.
Our study of trigonometry begins upon finishing chapter 3. This past year that fell about 2 weeks before Christmas break. Typically we cover the functions, their inverses and the associated identities most of the second semester. This means our year typically ends at the end of chapter 5.
Goal for this year...
Our algebra 2 teacher did an AMAZING job last year of digging more deeply into functions. I expect this will speed our study this year. My goal for the upcoming year is to finish at least chapters 1-4 in first semester and start with trig identities in second semester.
My questions...
Am I expecting too much to cover that much material in first semester?
Calculus teachers: Should I follow the order of the book - Vectors (Ch 6), Matrices (Ch 7), Conics (Ch 8), etc - or are there certain chapters that I should DEFINITELY cover to best prepare my students for calculus?
For Calculus, if you can cover chapter 6 through an introduction to polar coordinates, then Sequences and Series your students will be able to destroy the AP exam next year or will have many more examples in their heads if they take calculus in college.
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