Advanced Placement Calculus

 

 

Well, I'm back to teaching calculus after a one-year hiatus (yeah!).  That means this page will become a bit more active now!

I've been revising for the new school year, but most of the material here is from previous AB and BC courses.

I'll update and clean up as the need arises!

AB Syllabus
BC Syllabus
Homework
AP Central
Textbook
Labs
Brooks/Cole
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 students taking AP Calculus BC next year.  Students are required to complete it at their convenience over the summer break and then bring it to class on the first day back.  Please note that this is a different packet than the one used for the AB course.

 

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Summer Packet Answers - Here are the answers to the packet mentioned above.

 

 

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 Pacing Guide (last updated on 12/30) - This is a copy of what I call my "quarter plans" 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 - This is a list of the exercises from the textbook that we will be attempting this year.  Since this is the first year I've used this particular textbook, I'm building the list as we go and hope to update it one unit at a time.  Regardless, this should give you some insight to the problems I suggest as the "bare minimum".  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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Limit Introduction - This is based on the handout given in class for the limit introduction and review.  Solutions and notes are provided (in red) to help you better understand the final answers.  If you would like another copy of it, here is a blank version of the handout.

 
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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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Parent Functions Review - Here is something that students can print out and use to review the more common parent functions used in this course.

 
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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. 

 

Needless to say, this part is "under construction" since little is posted.  My intent is to post solutions to unit reviews, quizzes, and tests for each quarter so that students can refer to them throughout the year.  The links that reference the textbook are labeled by chapters, hence the duplication in some places.

 

1st Quarter 2nd Quarter

3rd Quarter

4th Quarter

Limits and Continuity

Quiz 1

Chapter 2 Textbook Review

Test 1

Graph Behavior

Chapter 4 Textbook Review

Test 4

Integration

Quiz 7

Chapter 6 Textbook Review

Chapter 8 Textbook Review

Test 7

Infinite Series

Derivatives

Chapter 2 Textbook Review

Chapter 3 Textbook Review

Test 2

Derivative Applications

Chapter 4 Textbook Review

Test 5

 

Integral Applications

Chapter 7 Textbook Review

Test 8

Power Series

Differentiation

Quiz 3

Chapter 3 Textbook Review

Test 3

Antiderivatives and Integrals

Quiz 6

Chapter 5 Textbook Review

Test 6

Differential Equations

Chapter 6 Textbook Review

Test 9

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 Review  Here is the list of topics that students should review in preparation for the midterm exam.

 
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2nd Semester Exam.  For those that have to take the final exam, here is where I will post study guides and things of that nature.

 
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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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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 (once posted) 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 - - - - - - -  

 

 

 

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."