Home Study Companion: Precalculus
If you are wondering whether to skip from Algebra 2 directly to Calculus or whether to take Precalculus first, the answer (almost always) is to take Precalculus first. Gaining depth is more important than racing ahead, and the depth offered through this course is tremendous. Recording this course has been a remarkable experience for me, personally. I have grown in my appreciation for Foerster’s work in the process. In my career I have taught out of several other Precalculus textbooks, but none of them is in the same league with Foerster when it comes to teaching problem solving and real-world applications.
I am using the 3rd edition of Foerster’s Precalculus with Trigonometry available from Kendall Hunt, which recently took over its publication from Key Curriculum Press. (Follow the Kendall Hunt link and use the order form on the right side of their web page.) The videos are usable (a little less conveniently but probably much more economically) with the 2nd edition as well using this cross-reference table for finding which videos correspond with which chapters. There are major chapter-level rearrangements, but except for a few modified sections and the addition of Chapter 16 in the 3rd edition, most of the content is the same.
Here is the list of problems whose solutions are worked out in the videos (listed in 3rd edition order). These would constitute reasonable assignments. For additional practice most of the odd numbered problems have (bare) answers in the back of the student edition of the book.
The course is now being distributed as a direct digital download. It makes heavy use of computational tools, primarily a scientific calculator, spreadsheet programming, GeoGebra, and Sage.
In this course I use GeoGebra in lieu of “graphing calculators.” Download the Classic Edition, Ver 5 and start getting to know it. Graphing calculators are severely limited by their clumsy user interfaces and small screen sizes. All students using this course are using computers, so graphing and computational software on a larger platform make sense.
One further step I am taking in this course is to introduce RPN calculators, the system developed for scientific calculators by Hewlett-Packard. Students are free to use any calculator they have in any mode they like, but in this course I will be doing the on-screen calculations in RPN. A pocket calculator should be optimized to be able to evaluate expressions fluently and reliably. RPN notation takes a little getting used to at first, but it is wonderful for its fluency and reliability. I describe my HP calculator as an “extension of my brain.” RPN is a parenthesis-free notation system. Even quite complicated expressions can be computed without having to keep track of nested parentheses.
There are several RPN options. The on-screen calculator Calc98, which Math Without Borders students have seen in my videos since Algebra 1, has the ability to switch into RPN mode. A better RPN calculator I became aware of recently is Free42, which emulates the top-of-the-line HP-42s calculator. This one is especially nice since it is available for Windows, Mac, and Linux, but also as an iPhone and Android app. If you have a cell phone, Free42 may well meet your hand-held calculator needs. A manual for Free42 is available here. If you want a stand-alone hand-held RPN calculator, the most practical option is the HP-35s, which sells in the $50 range.
(Make Your Calculator an Extension of your Brain)
Another even more powerful computational tool, introduced in the last quarter of the Precalculus course, is Sage, available to use online or download from http://www.sagemath.org. Sage is useful all the way from high school math through university and professional level mathematics. Many of the tutorials available online are aimed at university level mathematics and might overwhelm Precalculus mathematics students. I have therefore recorded a short introduction to Sage that covers most of the needs of this course and posted it to YouTube. You can watch it here.
For practice you can access the Sage file shown in the video and interact with it directly here: Zip file of the Sage file shown in the video. Download this file, then unzip it to your desktop. Start Sage, then upload the sws file into Sage.
Also check out the YouTube “channel” http://www.youtube.com/user/sagemath. Linda Fahlberg-Stojanovska has created a number of Sage video tutorials at a simple level that are relevant to a number of the topics in this course.