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?

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    $\begingroup$ Is this the text you're referring to? rhinebeckcsd.org/teachers/cbaccaro/tinymce/js/tinymce/plugins/… $\endgroup$ – Brendan W. Sullivan Jan 16 at 16:32
  • $\begingroup$ I'd suggest you look at a copy of the calculus text, the one we use is by the same 3 of 4 authors. Your precalc book runs 1000 pages, it's not as if we use 100% of this text in pre-calc. But, you have to be careful not to skip too much. Last year, when Covid hit, we decided Vectors didn't need as much attention as usual. Complex numbers? Not so much for AB, but needed for BC. I respect the question, but tough to answer. $\endgroup$ – JTP - Apologise to Monica Jan 16 at 16:44
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    $\begingroup$ I use that text for Precalc and also teach AP Calc AB after. Do you usually cover every chapter and section? You don't need to spend much time on trig identities. Calc BC needs chap 6, but AB does not. If you are pressed, Drop chap 7. Linear algebra is important, but not for AP Calc. I would drop chap 8. Chapter 9 need not be covered beyond 9.5. $\endgroup$ – Carser Jan 16 at 17:35
  • $\begingroup$ -1 on the question. Needs more detail to be generally communicative or useful. $\endgroup$ – Daniel R. Collins Jan 20 at 0:38

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

  1. Functions and Graphs
  2. Polynomial, Power, and Rational Functions
  3. Exponential, Logistic, and Logarithmic Functions
  4. Trigonometric Functions
  5. 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.
  1. 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.
  1. 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.
  1. 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.
  1. 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.
  1. 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.
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    $\begingroup$ I was going to write almost exactly this answer. $\endgroup$ – mweiss Jan 18 at 16:58

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