Objectives:
Continue introducing concept of the derivative (Calculus topic)
Become fluent with the algebra that comes up often when working with derivatives
This Part 1 video deals with a function that does NOT include a radical.
Objectives:
Continue introducing concept of the derivative (Calculus topic)
Become fluent with the algebra that comes up often when working with derivatives
This Part 2 video deals with a function that does DOES include a radical.
Throughout the final quarter we get acquainted with the "Ugly Algebra" that has hindered so many students in my previous AP Calculus classes. The linked PDF includes numerous worked-out examples and numerous exercises for you to try on your own, with answers on the last pages.
The first Chapter in any conventional Calculus course covers limits... unless it's covered first in PreCalculus.
In this class we introduce Limits as our final topic of the year, and those going on to AP Calculus will be tasked with finishing the chapter over the summer (with the aid of my videos, other online resources, and my willingness to meet over the summer if needed).
Getting Limits out of the way before the first day of AP Calculus class should put us in great position to cover all the required material during the year and even have a few days leftover to feel extra-prepared for the AP exam.
I'll be the first to admit that the topic of limits alone is not the most exciting, but they provide the foundation for fascinating things to come.
Many a cynical student thinks of Limits as "that stuff we studied at the beginning of the course and then stopped using once we learned better tricks." To some degree it's true that Limits help us discover more efficient techniques for doing things in Calculus, and once we master those techniques, we tend to leave Limits behind for a while. However, whenever a new dilemma comes up that none of our snazzy tricks can help us solve, Limits come back to the rescue.
Here is the Introduction to Limits handout and assignment.
Here are all pages of the Calculus textbook that you'll need for the PreCalculus course in a single PDF. This PDF also includes all pages for the AP Calculus AB summer assignment. Be sure to take advantage of the bookmarks that help you navigate through the pages. The file is a bit large at 20 Mb.
If you prefer to download the chapter sections one at a time, including answers to odd-numbered questions, use the following:
Or, if you prefer all the above pages in a single PDF, be sure to take advantage of the bookmarks that help you navigate through the pages:
ALL pages required for AP Calc AB Summer Assignment, as listed above (a bit large at 20 Mb)
Limits
Here are some practice questions to help determine your readiness. Get solutions from Mr. W.
More exercises from another textbook (Rogawski, 2nd ed.)
Also use class handouts and assignments from Calculus text for practice
"Ugly Algebra"
Includes functions with radicals and binomials raised to powers greater than one. This "Ugly Algebra" PDF includes ten worked-out examples and seventeen exercises for you to try on your own, with answers on the last pages.
Here is the Q4 Exam study guide, including some sample multiple choice questions. The Q4 exam officially only covers all the content from fourth quarter, although many of the skills you learned earlier in the year supported your learning of the Q4 material.
The exam will consist of 16 multiple choice and 10 free response questions. You will have up to the full two hour exam time to complete it.
For further study guidance, review the lesson plan and assignments for all lessons in Q4.