[ Posted by Joe Brandell
Wed, 07 Jul 2010 21:17:15 GMT ]
Pre-AP
What a great week! I am so happy for the growth we made as a group, and I look forward to hearing from you if you have any questions.
Attached below is a file of the websites we found that addressed rates of change and other cool stuff we found on-line that week:
Pre-AP Websites - June 2011
The blog below this post is for my incoming AP Calculus students with the prerequisite knowledge outlined for them to examine over the summer. Please take the time to examine the material cited on the blog.
Thanks again for the great week. If I can be of any assistance to you in the future, please do not hesitate to contact me.
AP Calculus
This post is for both the Grandville and the Lapeer teachers who participated in my Summer Institutes. I hope you had a great experience, and I look forward to hearing how well your students performed on the AP Exam next May.
Below is a link to the most recent set of Calculus Websites collected by former students. In addition, the previous blog offers a different collection of websites to support derivatives and limits. Please download the file below, and read the blog posted earlier to examine that information as well.
AP Calculus Websites - June 2011.doc
As with the Pre-AP teachers, if I can be of any assistance to you in the future, please do not hesitate to contact me.
Posted in Teacher education
[ Posted by Joe Brandell
Wed, 07 Jul 2010 17:33:00 GMT ]
Hey!
I am looking forward to working with each of you next year! It is going to be a great year, and our goal is the successful completion of the BC Calculus AP Exam. This will earn you 8 credits, which is huge. Though I am sure most of you will want to continue with mathematics in college with Calc 3 and Differential Equations (LOL), these credits might complete the math requirements for your program. This is a very important class, and I know you will do very well.
This posting describes what you can expect the first weeks of the course, along with the prerequisite knowledge that is assumed to be mastered. Though this is not exactly “summer homework,” it does outline the content expectations entering the class, what the first assessments will look like, and how to prepare over the summer to get so you can optimize (no pun intended) your chances for excellent grades the first marking period.
Using This Site
This posting will remain on BrandellCentral until school starts in the fall. You will see many postings on this site, as it is where I put information for the graduate classes I teach at Oakland University, updates regarding the AP institutes I facilitate over the summer, and the blogs I post concerning education. Feel free to read and comment on my blogs.
For this particular posting, there are three attachments: Sample/Practice Quizzes, Solutions to Sample/Practice Quizzes, and Online Calculus Resources. I will reference them in this posting, and they are available for downloading.
Prerequisites: Content Expectations Entering The Class
Obviously, Honors Precalculus is the prerequisite course, though some people take summer classes at OCC in Precalculus to satisfy this requirement. Prerequisite content falls into one of three categories: functions and algebra, limits, and derivatives. I will go into more detail in the sections below.
Functions and Algebra
The “basics” for this class that need to have been mastered include (but are not limited to):
Σ Factoring trinomials (aka, quadratics) without a calculator
Σ General shape of linear, quadratic, cubic, exponential and logarithmic functions without a calculator
Σ The general shape of sine and cosine over the interval without a calculator
Σ The “classic” values of sine and cosine (e.g., 0, "pi"/6, "pi"/4, "pi"/3, "pi"/2 ) without a calculator
If you can handle these “basics” without wetting yourself, and you have solid (but not necessarily perfect) algebra skills, you will be off to a good start.
Limits
Knowledge and understanding of limits will be essential for this course for one main reason: I will not formally teach limits. Due to our time constraints, I will assume you have a working understanding of one and two-sided limits, limits to infinity, and infinite limits. Connected with this notion of limits is the concept of continuity and the three-prong test for continuity. Again, I will not be teaching these concepts, so please make sure you are familiar with them when you enter class in the fall.
Derivatives
The “difference quotient” that you learned in Algebra 1 (i.e., the change in "Y" over the change in "X" ) plays a very important role in AP Calculus. When we combine the notions of “rate of change” with limits, we can determine the instantaneous rate of change, which can be applied at specific points or generalized as an expression. There are several key concepts that you will need to have prepared for the fall, including:
Σ Finding the derivative of a polynomial using the 4-step process
Σ Working knowledge of derivative rules for polynomial functions
Σ Working knowledge of power rule
Σ Working knowledge of derivative rules for all six trig functions, e^x, a^x, ln x, and log(a)x
If you don’t have these objectives mastered when you start the school year, it is not the worst thing in the world. However, having these skills and concepts as working knowledge will give you an advantage when we start the class in September.
Sample/Practice Quizzes
I suspect the last thing you want to do is bring a calculus book home and study over the summer. I assume that you would like to use this summer to do anything and everything but school work. I don’t blame you. Still, here are samples of “retired” quizzes that have been used early in the first marking period that cover this material. You may examine them as needed . . . or not . . . I can tell you that you will be at an advantage if you have an understanding of these concepts when you begin the class in September. At the bottom of this posting, you can access the Sample/Practice Quizzes as a single attachment. The solutions to the quizzes are also available for downloading (use wisely . . . work the problems first, then look at the answers . . . LOL).
Resources
You did not think I would abandon you, did you? Additionally, listed at the end of the Sample/Practice Quizzes are the online resources that you can/should use if you get stuck. There are several types of sites provided to meet your individual needs. You could look these over before, during, or after you complete the quizzes provided. They are excellent resources and will help you make sense of these concepts if you are troubled (or if your alarm clock finally goes off on September 1 and you decide to do these problems). These are the online resources we will be using the entire 2010-2011 school year, so keep them handy if you get stuck on any concept next year.
Preparing Over The Summer
In all seriousness, you really do not have to do much of anything if you do not want to. Some of you might want to stay current with what you have learned this past semester regarding limits, derivatives, and trigonometry. The online resources offered are just a few of the sites available for support. If you did not learn the derivative rules for ex, ax, ln x, or log a x, they are pretty simple and can be found at several of the presented sites. The sample problems are fairly rote and will be easy to do. If you plan to really work on this stuff over the summer, then pace yourself. Examine not only the quizzes provided, but also look at the sample problems offered at the different sites. They provide excellent practice to keep your skills sharp.
If you really don’t want to do anything this summer, but want to start the school year ready to roll, return to BrandellCentral about three days before school starts and do the sample quizzes. If you don’t remember something, you still have time to figure it out before class starts.
If you don’t do any of this, that’s cool; just know that I will go through this material really fast the first week. I will proceed as if those topics have been previously mastered, only needing a “refresher” to bring them back to working knowledge.
The First Few Weeks Of Class In The Fall . . .
As I mentioned, I will proceed to discuss limits, trigonometric ratios, and functions the first days of class. I will then immediately go into derivatives, the four-step process, and derivative rules. At some point, soon thereafter, we will incorporate antiderivatives and the chain rule. This is really our first unit of study. It is a skill-based unit, with a few “interesting” twists added to the mix (at least I think they are interesting . . . ☺). Your first quizzes will be much like the Sample/Practice Quizzes.
Additional Support
I will be quite busy this summer. If I am not teaching at Oakland University or conducting an AP Institute, I will be on my kayak on some lake. If you need to contact me, I am available via email at jlbrandell@comcast.net or on Facebook or Twitter. If you are patient with my response time, I do promise to get back with you.
HAVE A GREAT SUMMER, AND I CAN’T WAIT TO WORK WITH YOU IN THE FALL!
BC Calculus - Summer Work - Practice Quizzes - June 2010.doc
Solutions to Sample-Practice Quizzes - June 2010.doc
Online Calculus Resources - June 2010 .doc
Posted in Calculus
