AP  Calculus AB and BC 

 

On-Line for 2012-2013 School Year

 

We have three sections. Two of them prepare for the “AB” exam, one taught by Jeff Lanctot and the other taught by Susan Gilleran. The other, taught by Susan Gilleran, prepares for the “BC” exam. The AB exam is equivalent to two-thirds of a year of college calculus and the BC exam is equivalent to a full year of college calculus. 

 


 

Section 1 – Calculus AB

Teacher: Jeff Lanctot

Email: jfrylan@inbox.com

Text: Calculus of a Single Variable - Early Transcendental Functions, 5th edition by Larson and Edwards. The specific ISBN# is 978-0-538-73552-0; the list price is approximate $140 for a new hardcopy version and less for an e-book or used version.

 

Technical Requirements:

·         High speed Internet access

·         e-mail

·         TI-83/84 or TI-89 scientific calculator

·         Scanner to submit multiple handwritten pages as a single PDF file

Class Tuition Fee: $650.

Who Should Apply: The course is open to students in 10th through 12 grades who have strong mathematical skills and interests.  Students should have completed High School mathematics though and including geometry, algebra II, trigonometry (particularly radian measure and periodic functions), and elementary functions and their notation.  These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions.

Equivalent to a 1st semester college level calculus course, Calculus AB is intended for students interested in majoring in mathematics, engineering, any of the sciences including earth or environmental sciences, pre-med, or architecture.  Successful completion of this course and the AP Exam in May provides credit at most major colleges and universities.  Perspective students in this course should review their targeted college or university websites for specific expectations.

Course Description:  Calculus has been one of the most influential ideas in human history.  Its impact on our daily lives is incalculable with most changes in the past 300 years coming from technological and scientific developments fundamentally based upon calculus.  Calculus pulls together many of topics studied in previous math courses and transforms them from mechanical, seemingly unrelated topics into powerful, interrelated tools for analyzing real-life situations – situations that involve motion and change.  This course provides the foundation on which we can truly understand and advance the world around us.

This course prepares students for the AP Calculus AB Exam.  It covers all of the topics specified by CollegeBoard, the administrators of the AP Exam in May, including the study of limits, derivatives, integration and their applications.

Like most PA Homeschoolers courses, this course has no specific meeting time, yet has a clear schedule with readings and assignments.  Each week I provide an overview of the topic being studied with a keen focus on the key points as well as the identifying areas beyond the scope of the course.  Our textbook is the primary source of information and was specifically selected for readability and coverage of material.  My teaching philosophy is to not waste the student’s precious time with unnecessary reading, videos, projects, assignments, or required scheduled “chats”, but to focus attention on the key topics of the course.  Videos correlated directly to the textbook problems will be available to students but are not required.  I will often reference additional resources which may provide another perspective on the topic being studied but these again will be optional.

Students are expected to spend 8-10 hours weekly on the class  This will include reading, completing practice problems, simulated AP multiple choice questions, and free response problems.  There is a secure web board for all members of the class (and parents) to post all kinds of comments, questions, interesting fun facts or links, or even non-calculus related communication between members of the class. I make myself available as much as humanly possible – via the web board, via email, and via online chat or telephone if necessary – and work very hard to respond to questions as quickly as possible.

Grading:  Grading will be based upon completed homework assignments (I post the answers before the student has to submit them so they can check and correct their answers a priori), short quizzes, and unit tests.  Grade points are also earned by completing Multiple Choice Questions with a student being able to continue answering questions until the required number of points are achieved.

Calculus BC:  Calculus BC extends Calculus AB with some additional topics requiring it to be a faster-paced, more intensive course than this course.  At this time, I am only offering the AB course.

How to register:  Simply click on the link below, download the MSWord document to fill out and submit via email.  I will review the application and get back to you within a few days.  If accepted, you may register and pay the course tuition through the PAHS Online Store.

http://www.mgutilan.com/info/CalculusABApp.doc

Instructor Qualifications: While this will be my first year teaching Calculus AB over the Internet, I have been a teacher of AP Calculus in a public school for the past few years.  I have also been teaching AP Physics through PA Homeschoolers for the last 2 years, so am not only well versed on the issues of on-line learning, but also bring a deeper understanding of the value of Calculus as a mathematical tool.  I have a B.S. and an M.S. in Engineering from the University of Massachusetts and Cornell University, respectively.  Prior to teaching, I worked as an electrical engineer and technology executive for 20+ years for companies including Bell Laboratories, Alcatel, Motorola, and Verizon.  I now teach high school mathematics on Cape Cod in Massachusetts.  My wife, Mary, and I homeschooled our three children through high school.


 

Section 2 – Calculus AB

 

Teacher: Susan Gilleran

 

E-mail: sgillera@mac.com

Texts Required: Calculus 8th Edition by Ron Larson, Robert Hostetler, Bruce Edwards (2006) ISBN 061850298X. (available at discount rates at locations such as www.campusbooks.com)

Be Prepared for the AP Calculus Exam Second Edition by Mark Howell and Martha Montgomery Copyright © 2011 by Skylight Publishing ISBN 978-0-9824775-5-7. (available through amazon.com)

Technical Requirements:

  • Computer, high-speed internet access, e-mail capability
  • Scanner to send multiple handwritten pages as a single PDF file via e-mail
  • Scanner to PDF file capability
  • Graphing calculator – TI-89 or TI-83/84 Plus (available at a discount on some sites).

 

Who Should Apply: All students should have completed the equivalent of four years of high-school level mathematics designed for college-bound students. These would typically be referred to as Algebra I, Geometry, Algebra II / Trigonometry and Pre-Calculus covering advanced topics in algebra, trigonometry, analytic geometry and elementary functions including linear, polynomial, rational, trigonometric, exponential, logarithmic, inverse trigonometric and piecewise-defined. In particular, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on). Prospective students should be ready to commit 11-12 hours per week to this class.

 

Course Fee: $705

 

Course Description: This course prepares students for the AP Calculus AB Exam. There are two AP Calculus Exams given each year - Calculus AB and Calculus BC. There are two courses designed to prepare for the exams, each to be taught over a full high school academic year. The Calculus BC course includes all of the material included in the Calculus AB course plus additional topics.

 

Most colleges and universities offer a sequence of courses in calculus. Because of this, it depends on the policies of the institution and the results of your AP Exam as to where you are placed in their sequence of courses. The content of Calculus BC is designed to qualify the student for placement and credit in a course that is one course beyond that given for Calculus AB. Typically, Calculus AB is the first semester of college calculus and BC is the first and second semester.

 

This study of calculus, the mathematics of motion and change, is divided into two major topics: differential and integral calculus. Differential calculus enables us to calculate rates of change, to find the slope of a curve, and to calculate velocities and accelerations of moving bodies. Integral calculus is used to find the area of an irregular region in a plane, to reconstruct distance from velocity, and to calculate volumes of arbitrary solids.

 

You will be accessing an Assignments Page on a daily basis, at any time you want to, where you will find a posting of one month of assignments with new Comments posted every week day discussing such things as that day’s topic, a problem from yesterday’s or today’s assignment, or a recent test. There will often be instructional videos, links to interesting sites or helpful documents to download. Periodically there will be a "tidbit" added to the daily Comments of such subjects as Fractals, the biography of a mathematician, an in-depth explanation of the irrational number e, a different slant on what integration is, etc.

 

You will be interacting with your classmates, teaching assistants and me through an online Discussion Board provided through Google Groups. You will post any questions you have about the reading material or the homework assignments, answer each other’s questions, as well as post solutions to problems. Questions can always be sent directly to me at any time also.

 

My daily Comments are meant to introduce the material you are about to read in a conversational manner. My philosophy is that students learn by not only listening and observing (which you will do through the videos) but most importantly through the homework assignments. I have selected a text particularly because of the wide variety of exercises that it offers. I have put a significant amount of time in selecting the exercises that I assign. I provide you with step by step solutions to every assigned problem along with examples of each problem you can review before beginning your homework.

 

Each assignment will build on previous assignments so success will depend on your daily response to the challenge. While this course is not for the faint-hearted because it’s rigorous and demanding, I’ll dare say it’ll also be one of the most challenging opportunities of your life as a student. And one of the most significant lessons you’ll learn is that along with the greatest challenges come the greatest rewards.

 

Instructor Qualifications: I earned a BS and secondary teaching certificate in Mathematics from Wayne State University, and an MBA from Lawrence Technological University. I taught high school mathematics before moving to the business world at Ford Motor Company where I was an Information Technology Manager.

 

This will be my seventh year teaching the AP Calculus courses for PA Homeschoolers. I have also completed two five day College Board summer institutes - one dedicated to teaching AP Calculus AB and the other addressed AP Calculus BC. I’m looking forward to an exciting year that’s sure to be an adventure for everyone involved.

 

Click here to read class reviews from past participants in Susan Gilleran’s classes

 


 

Section 3 - Calculus BC

 

Teacher: Susan Gilleran

 

E-mail: sgillera@mac.com

Texts Required: Calculus 8th Edition by Ron Larson, Robert Hostetler, Bruce Edwards (2006) ISBN 061850298X. (available at discount rates at locations such as www.campusbooks.com)

Be Prepared for the AP Calculus Exam Second Edition by Mark Howell and Martha Montgomery Copyright © 2011 by Skylight Publishing ISBN 978-0-9824775-5-7. (available through amazon.com)

Technical Requirements:

  • Computer, high-speed internet access, e-mail capability
  • Scanner to send multiple handwritten pages as a single PDF file via e-mail
  • Scanner to PDF file capability 
  • Graphing calculator – TI-89 or TI-83/84 Plus (available at a discount on some sites).

 

Who Should Apply: All students should have completed the equivalent of four years of high-school level mathematics designed for college-bound students. These would typically be referred to as Algebra I, Geometry, Algebra II and Pre-Calculus covering advanced topics in algebra, trigonometry, analytic geometry and elementary functions including linear, polynomial, rational, trigonometric, exponential, logarithmic, inverse trigonometric and piecewise-defined. In particular, students must be familiar with the properties of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on). All students must complete a comprehensive and thorough Pre-Calculus course prior to admission to this class. A list of topics that must have been covered in the Pre-Calculus course will be provided to any student applying for admission.

 

This class is intended for the most serious minded of students. It is equivalent to one year of college calculus so students must come to the class with a strong and successful background in the study of mathematics. The prospective student must be self-reliant, self-directed, and self-disciplined. Prospective students should be ready to commit 12-13 hours per week to this class.

 

Course Fee: $715

 

Course Description: This course prepares students for the AP Calculus BC Exam. There are two AP Calculus Exams given each year - Calculus AB and Calculus BC. There are two courses designed to prepare for the exams, each to be taught over a full high school academic year. The Calculus BC course includes all of the material included in the Calculus AB course plus additional topics.

 

Most colleges and universities offer a sequence of courses in calculus. Because of this, it depends on the policies of the institution and the results of your AP Exam as to where you are placed in their sequence of courses. The content of Calculus BC is designed to qualify the student for placement and credit in a course that is one course beyond that given for Calculus AB. Typically, AP Calculus AB is the first semester of college calculus and BC is the first and second semester.

 

This study of calculus, the mathematics of motion and change, is divided into two major topics: differential and integral calculus. Differential calculus enables us to calculate rates of change, to find the slope of a curve, and to calculate velocities and accelerations of moving bodies. Integral calculus is used to find the area of an irregular region in a plane, to reconstruct distance from velocity, and to calculate volumes of arbitrary solids.

This Calculus BC course goes beyond the AB course, covering additional techniques of integration, venturing into the world of parametric equations, polar coordinates and graphs, vectors in the plane, as well as delving deep into the wonderful and complex arena of infinite series.

You will be accessing an Assignments Page on a daily basis, at any time you want to, where you will find a posting of one month of assignments with new Comments posted every week day discussing such things as that day’s topic, a problem from yesterday’s or today’s assignment, or a recent test. There will often be instructional videos, links to interesting sites or helpful documents to download. Periodically there will be a "tidbit" added to the daily Comments of such subjects as Fractals, the biography of a mathematician, an in-depth explanation of the irrational number e, a different slant on what integration is, etc.

 

You will be interacting with your classmates, teaching assistants and me through an online Discussion Board provided through Google Groups. You will post any questions you have about the reading material or the homework assignments, answer each other’s questions, as well as post solutions to problems. Questions can always be sent directly to me at any time also.

 

My daily Comments are meant to introduce the material you are about to read in a conversational manner. My philosophy is that students learn by not only listening and observing (which you will do through the videos) but most importantly through the homework assignments. I have selected a text particularly because of the wide variety of exercises that it offers. I have put a significant amount of time in selecting the exercises that I assign. I provide you with step by step solutions to every assigned problem along with examples of each problem you can review before beginning your homework.

 

Each assignment will build on previous assignments, so success will depend on your daily response to the challenge. While this course is not for the faint-hearted because it’s rigorous and demanding, I’ll dare say it’ll also be one of the most challenging opportunities of your life as a student. And one of the most significant lessons you’ll learn is that along with the greatest challenges come the greatest rewards.

 

One Semester Course Option: If a student chooses to take AP Calculus AB one year and wants to take AP Calculus BC after it but wants to skip the first semester of AB topic material there is an option to join the BC class in mid-December. Registration is required at the beginning of the school year by August 15th. There will be a limited number of students accepted into this program so register early. For further information about this option please contact Mrs. Gilleran at sgillera@mac.com.

 

Instructor Qualifications: I earned a BS and secondary teaching certificate in Mathematics from Wayne State University, and an MBA from Lawrence Technological University. I taught high school mathematics before moving to the business world at Ford Motor Company where I was an Information Technology Manager.

 

This will be my seventh year teaching the AP Calculus courses for PA Homeschoolers. I have also completed two five day College Board summer institutes - one dedicated to teaching AP Calculus AB and the other addressed AP Calculus BC. I’m looking forward to an exciting year that’s sure to be an adventure for everyone involved.

 

Click here to read class reviews from past participants in Susan Gilleran’s classes


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