Advanced Placement Calculus

 

 

Well, my first year teaching this at my new school wasn't a disaster, so they are letting me teach BC again!

I'll continue revising this page for the new school year, updating and cleaning up as the need arises!

AB Syllabus
BC Syllabus
Homework
AP Central
Textbook
Labs
Return to Main

The two Syllabi at the left are different from the one-page document given to the students on the first day of class.  These are the "official" course syllabi required by the College Board's AP Audit.  Each contains information on the course philosophy, prerequisites, resources, assessments, and a topics outline.  The AB version is an older version since I haven't taught that course in a while, but the BC version is current.  Click one of the buttons to open and/or print the appropriate file.

 

My specific RHS faculty page can be found by clicking the Homework button.  It is updated daily with assignments and any upcoming quizzes or tests.

 

The College Board has a website dedicated to AP courses, and you can click the AP Central button at the left to check it out.  The site includes general information about all Advanced Placement courses, including philosophies, prerequisites, topic outlines, and practice questions.  You do have to register to be a member of AP Central (it's free), but there is a ton of information.

 

Students can click the Textbook  button to visit the Pearson/Prentice Hall (our textbook's publisher) website for practice quizzes for each chapter.  There are also several web links specific to most sections in the textbook, most of which appear to be helpful.

 

I'm trying to keep all of our major labs and activities posted on a separate page in an effort to reduce clutter here and copying at school.  Click the Labs button at the left to locate them.

 

 

Other Information and Activities:

 

Summer Packet Information. 

 

For those of you who are incoming calculus students, here are a few pieces of information that you might need or find useful.

 

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Summer Packet - Here is the "summer packet" for all incoming AP Calculus BC students.  Students should complete it at their convenience over the summer break.  Unlike some AP courses, completion is not a requirement and there will be no grade associated with this.  Students are, however, expected to understand the material contained in the packet when they enter class on the first day back.  Please note that this is a different packet than the one used for the AB course.  UPDATE, 6/17:  There was a typo in #33 that has been corrected.

 

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Summer Packet Answers - Here are the answers to the summer packet.  You should check your answers with this document and rework any that are incorrect.  If you continue to get the wrong answer, email me for help.

 

 

Classroom Information. 

 

The files in this section are more-or-less of an administrative nature, but I thought having them here in one place might help the semester go smoother for everyone.  Feel free to print out whichever ones you like

 
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BC Class Syllabus - Here is the syllabus for the fall semester course given out in class on the first day of school.  It contains a brief overview of the course, grading and classroom policies, and contact information.  For the record, this is not the same document as the "official" course syllabus required by College Board (that can be found by clicking the BC Syllabus button above at the left).

 
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BC Quarter Plans - This is a copy of what what some might call a pacing guide for the year.  I adjust it several times throughout the semester, but it should give you an idea of what needs to be done and the pace at which we have to do it!

 
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Textbook Problems - I used to post all of the textbook assignments here, but have found it better for students to have those unit-by-unit since we bounce around so much in the textbook.  I'm now including each instructional unit's assignments along with the learning targets in the Unit Review Information section below.  For the record, the daily homework assignments - including worksheets and other activities - can be found on the RHS homework site (just click the "Homework" button above).

 

 

Classroom Resources. 

 

Here is a little collection of files that should help supplement what we do in class.  I'll try to add more things as they pop up in class.

 
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Parent Functions Review - I have mentioned several times in class that knowing the general behavior of a few basic functions is key to being successful in calculus.  This document illustrates the most common parent functions, and many students like to print this off and keep it in their notebooks for quick reference.

 
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Limit Introduction - Here is a worksheet that summarizes the numerical and graphical approaches to evaluating limits.  I think the extra practice makes for a good review on the topic.  Here are my solutions.

 
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Continuity Introduction - This version of the worksheet given in class provides some answers and a few other details (including some terminology).  Here's a blank copy of the handout.

 
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Numerical Derivative Introduction - This document introduces how to find numerical derivatives analytically, graphically, numerically, and using the calculator.  There is one example worked out using each of the four methods.

 
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Derivative Review - This is just a summary of the common derivative rules and patterns used in this course.

 
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Curve Sketching Summary - I put this together rather hurriedly (that's code for let me know if you see something wrong), but it should help with all of those graph behavior problems.

 
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Integral Review - Big surprise... this is a summary of the common integral rules and patterns used in this course.

 
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Integration by Parts - Here's a little document demonstrating the "table technique" for evaluating certain integrals that require integration by parts.

 
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Euler's Method - This document was written to demonstrate how to use Excel for Euler's method of approximating solutions to differential equations.  For the record, it is assumed the reader knows a little about Excel and a lot about Euler's method.

 
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Convergence Test Summary - Here is the "Convergence Test for Dummies" handout for Chapter 8.

 
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Convergence Test Strategy - This is a little flowchart that might help you decide when to use what convergence test.

 
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Convergence Test Conclusions - Some students have asked for a sample of how one should answer problems that require the use of the many convergence tests used in class.  This document should help answer those questions.

 
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Euler's Identity - I just thought this was a neat way of using power series to prove one of the cooler equations out there.

 

 

Unit Review Information. 

 

This section was cleared out over the summer, but here is where I will post each instructional unit's review information throughout the year.  Once any quizzes or tests are completed, I'll also post those along with their solutions.

 

1st Quarter 2nd Quarter

3rd Quarter

4th Quarter

Limits and Continuity

Learning Targets and Assignments

Analytical Limits Review

Limits Quiz

 

Graph Behavior

 

 

Integration

Power Series

 

Derivatives

Learning Targets and Assignments

 

Derivative Applications

 

Integral Applications

Convergence Tests

Differentiation

Antiderivatives and Integrals

Differential Equations

Parametric, Vector, and Polar Functions

 

 

 

Major Exam Resources.

 

The following links are a few files that you might find useful in preparation for both my major exams in class and the actual AP exam in May.  I hope to add to this list as the semester goes one, so check back from time to time.  If you have any suggestions, please let me know!

 

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1st Semester Exam.  When the time comes, I will post the study guide for the midterm exam here.

 
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2nd Semester Exam.  For those that have to take the final exam, I will post the study guide for it here.

 
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AP Exam Review - This document presents a quick overview of the topics covered on the AP exam.  The first couple of pages list a few patterns and techniques for differentiation and integration - think of it as a refresher for some of those obscure calculations.  The last couple of pages lists out the topics that are common on the AP exam - I encourage you to look over those and study the topics that are more-or-less vague to you.

 
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2010 BC Exam's Solutions - Here are my solutions to this year's FRQ's (the questions themselves can be found on the College Board's site).  I did these kinda quick, but I think everything is accurate... if you find an error, please let me know and I'll make the correction.

 

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Textbook Review - This is actually a student-created document using a different textbook, but I thought I'd leave it here until I can get it updated.  It basically goes through the textbook in a linear fashion highlighting topics that should be reviewed prior to the exam.  Some topics refer back to notes within a section of the textbook - these topics were presented in that lesson, but are not explicitly in the textbook.

 

 

TI-89 Mini-Tutorials. 

 

I had to create a few tutorial presentations for one of my online courses about the uses of the TI-89 calculator in a calculus course.  I thought others might find them helpful for certain topics.  The presentations below cover most of the important uses in AB, and I hope to add more (including BC stuff) soon.

 

NOTE:  These presentations assume the older OS... I'm hoping to eventually edit these to include some of the newer features (such as the impDif() command).

 

Basics Functions Limits Tables
Derivatives Implicit Differentiation Piecewise Functions Tangent Lines
Differential Equations Integrals    

 

 

Advanced Placement Averages.

 

For those interested, the table below shows the test averages for students taking the AP exam at my school.

  -  The data for 1999 and 2000 is for South Cobb High School, GA.

  -  The data for 2001 through 2008 is for Kennesaw Mountain High School, GA.

  -  The data for 2009 and 2010 (once available) is for Ravenwood High School, TN.

 

For the record, this data is not just for my students (that can be found here), but rather all AP Calculus students at my school.  As programs have grown and I've changed schools, I have had the opportunity to share these wonderful classes with others!

 

 

Exam Year

 

AB Exam

Number of Students

 

BC Exam

AB Subscore

Number of Students

 

 

1999

-

3.077

13

-

N/A

N/A

N/A

 

 

2000

-

4.000

3

-

N/A

N/A

N/A

 

 

2001

-

4.000

2

-

N/A

N/A

N/A

 

 

2002

-

4.417

12

-

4.800

4.800

5

 

 

2003

-

4.857

7

-

4.743

4.846

13

 

 

2004

-

4.500

12

-

4.550

4.800

20

 

 

2005

-

4.286

7

-

4.700

4.800

50

 

 

2006

-

4.000

12

-

4.213

4.681

47

 

 

2007

-

3.429

28

-

4.543

4.804

46

 

 

2008

-

3.696

23

-

4.644

4.889

45

 

  2009 - - - - - - -  
  2010 - - - - 3.813 - 16  

 

 

 

Software Downloads.

 

The links below take you to various places where you can download various software applications you might find useful in class.  Some are freeware, others are free trials and require purchase after a period of time.

 

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Advanced Grapher is a graphing software application that allows students to graph relations of different types in one window, then copy and paste them into other applications.  This versatile program has proven useful for students in their lab reports and other graphing activities.  A product key is required after 30 days.

 

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GCalc is a free online graphing program that has several capabilities useful in class.

 

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MathGV is another graphing software application that allows students to create certain three-dimensional graphs.  This one is especially helpful when working with solids of revolutions.

 

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JOde is an applet for creating slope fields for differential equations.  You can also approximate solutions using Euler's method.

 

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TI InterActive! is a software application from Texas Instruments that is basically a word processor and graphing calculator in one.  The language is practically identical to the TI-89.  Follow the link for more information and a downloadable demo version.

 

 

 

Just For Fun.

 

Here are a few quotes from class, as recorded by the 2003 group...

"That test was so easy!"

"Factorial SCREAMS ratio test."

"How do you not know that?"

"Partial fraction decomposition is easy for the 'calculurs' master."

"How do you do this integral thing again... just derive four times?"

"Well... if you can't plug numbers into a calculator by this time, you shouldn't be taking the AP test."

"Did you know that e ip + 1 = 0?"

"It's all about the recreational math!"

"The Chain Rule... how can I forget the Chain Rule!"

"Remember the trig..."

"Ah, trig... my old nemesis."

"Yeah... that's why the laptop says 'I suck' on it."