We’re precalculus honors teachers. In this year of Covid and reduced instructional time, what topics can we cut (Demana textbook) that would not hurt our kids in either calc AB or BC?
I'm not sure of your details, like how much you have already covered, how often your classes meet, etc., but here is how I would adjust this textbook for specifically preparing students for AP Calculus. I happen to use this textbook for precalc and I use Larson for AP Calculus AB.
Comments on Table of Contents
- Functions and Graphs
- Polynomial, Power, and Rational Functions
- Exponential, Logistic, and Logarithmic Functions
- Trigonometric Functions
- Analytic Trigonometry
- Chapter 4 trig is necessary for AP Calc, but chapter 5 is not. I think it is important that students see some trig identities, but it is incredibly unlikely that any students will lose AP Calc exam points for not knowing a trig identity.
- Applications of Trigonometry
- Chapter 6 is useful for Calc BC but unnecessary for Calc AB. If your students will be going into Calc AB, and you are pressed for time, I would skip Chapter 6. They will still need to understand particle motion for Calc AB, but they do not need this chapter to develop that understanding.
- Systems and Matrices
- Linear algebra is an incredibly important topic, but one that just isn't necessary for AP Calc. I would drop this chapter if really pressed for time.
- Analytic Geometry in Two and Three Dimensions
- It is debatable how useful chapter 8 is for Calc BC, but I would say it is not useful for Calc AB.
- Discrete Mathematics
- I cover 9.1 through 9.5 but skip everything beyond that in chapter 9. Sequences and series are the most important for AP Calc from this chapter.
- An Introduction to Calculus: Limits, Derivatives, and Integrals
- I would leave as much time for this chapter as possible, and especially focus on the concept of limits. That way, students will be entering AP Calc next year ahead of the game in some respects.