AP Calculus BC Course Guide

This challenging course will provide you with the opportunity to greatly expand your mathematical knowledge and prepare you for further studies in mathematics, sciences, and engineering. AP Calculus BC covers the first two (typically out of three) semesters of college-level Calculus. Most US colleges and universities grant advanced placement and/or credit for one or two semesters of Calculus for high AP Calculus exam scores. To find out a specific institution’s policy, consult its catalog or web site. This rigorous course consists of four main components:

· Functions, Graphs, and Limits

· Derivatives

· Integrals

· Polynomial Approximations and Series

All students in this class are expected to take the AP Calculus BC exam which is scheduled for Wednesday, May 9, 2007 at 8:00 AM.

With whom will you be working in this course?

You will be working with Mr. Mazzoni whose primary goal is to guide you as you learn. I earned a bachelor of science degree in Mathematics with a minor in education and have taught calculus since 1998. You will also be working with your classmates, each of whom will be making a unique contribution to this class. In turn, you will contribute to the class by sharing your ideas, mistakes, discoveries, inventions, and solutions.

Our “classroom”

Your classroom at Bellaire High School is the place where ideas are brought together and formalized. Our classroom is a place for learning. However, a significant amount of learning must take place outside of the classroom during individual and group studies. Successful calculus students spend a significant amount of time outside of class internalizing important concepts.

Homework

Homework will be assigned daily and must be completed on-time (usually the next day) to keep up with new material. In order to succeed in this course, you must complete all homework. Homework will not be graded on a regular basis since it is part of the learning process and mistakes and questions are expected. At this level of study, I am providing you with more flexibility and freedom. Ideally, you would solve every assigned problem each night, however I know that this is not always possible. With this freedom comes the responsibility to keep up with your work. You should consult your notes, book, and classmates as you learn, but there is no benefit from copying the work of others. As you complete your homework, remember to pay close attention to details, justify your steps, and show all of your work. (You must do all of these on class tests and the free response section of the AP exam.) If you are under a time constraint, you will be better off skipping a few similar homework problems instead of rushing through all of them. Some words of caution: even if you have found it unnecessary to do all of your homework in previous math courses to be successful, it is extremely unlikely that this will be the case for Calculus.

Quizzes

Quizzes may be given occasionally and are designed to check your understanding of a recent homework assignment. Quizzes are typically worth about 10-30 points, last 10-15 minutes, and are usually not quite as difficult as a major test since they may be given before you have completely mastered a concept. Quizzes may or may not be announced.

Major tests

There are usually two 100 points tests each grading period. Tests will be held on Thursdays preceded by a review day in most cases. I will always provide a detailed list of topics to be covered on each test. To be fully prepared for a test, make sure you understand all class notes, activities, and discussions and complete all homework assignments. Do not limit your study time to the night before the test! Review notes, homework, and previous tests regularly. Practice additional textbook problems not assigned for homework. A few minutes before a test is not the time to ask questions or to “cram!” I will not be able to answer questions the day of a test after 7:30 a.m., between classes, or during lunch. Tests will start promptly when the bell rings and must be turned in when the class ends. No extra time will be given on tests. It is possible that some tests may be curved and the curve is based on the assumption that every student has had the same amount of time to complete the test.

Tests will typically include questions that review previous test topics. Test formats will vary, but can include free response questions of differing lengths and multiple choice questions. Although some questions will be similar in nature to questions from the text book, other questions may require you to use the knowledge that you have obtained to solve original and challenging problems. You will have to think, reason, and make decisions! In order to receive full-credit on test problems, you must show all of your work. Partial credit may be given on free response questions, but not on multiple choice questions. Tests will generally be returned by the following Monday. Dishonorable actions will not be tolerated under any circumstances in or out of our classroom.

Presenting solutions

This will become an important component of this course. This is not intended to be a high pressure exercise, rather it will provide you with the opportunity to occasionally present your work and for us to discuss techniques, procedures, notation, mistakes, etc.

Extra credit

There may be opportunities to earn extra credit points throughout the year. Extra credit is only available to those students who are in-class (or have an excused absence) on the day it is given. Additionally, you can earn 2 points for returning signed progress reports (up to 4 points per grading period). In fairness to all, no extra credit will be offered on an individual basis. No extra credit will be awarded to students who accumulate any unexcused absences during a six-week grading period.

Late work policy

All homework and make-up work should be completed on time. Extra credit will not be accepted late. On the rare occasions when I collect homework, the maximum percentage of points that can be earned depends on when the work is completed (an example of a 20 point assignment in which 18 of the original points were earned is shown):

on-time up to 100% of points 18 (max 20) points = 90%

1 day late up to 85% of points 15 (max 17) points = 75%

2 days late up to 70% of points 13 (max 14) points = 65%

³ 3 days late up to 50% of points 9 (max 10) points = 45%

Grade calculations

Each six-week grade will be calculated by dividing the points you have earned (including extra credit) by the total possible points you could have earned during that grading period. Your semester grade will be the average of three six-week grades and a final exam. If you maintain an average below 80, it will be suggested that you transfer to AP Calculus AB if immediate improvement is not shown. Averages below 75 will result in a strong recommendation to transfer. Please note that BHS policy states that you cannot transfer out of a class until the end of the first six-weeks grading period. It is sometimes better to move to AP Calculus AB and have a better chance at earning a semester of college credit than to struggle through AP Calculus BC. Transferring to “AB” does not mean you have failed! It is still a rigorous, Advanced Placement, college-level course!

Final exams

The Fall final exam is cumulative for the first semester and the Spring final exam is cumulative for the entire year. Review material will be provided for the Fall semester final exam. To prepare for the Spring final exam, use the same material and procedures recommended for preparing for the actual AP exam since the format will be similar and, of course, the topics will the same. It is my hope that all Seniors will be exempt from the Spring final exam. However, only Seniors meeting all of the requirements (85 or above average, 3 or fewer excused absences, no unexcused absences, and at least satisfactory conduct) will be exempt. All non-Seniors and non-exempt Seniors must take a cumulative final exam during the scheduled final exam time in May.

Progress reports

Detailed progress reports will be made available online at the midpoint and end of each six-week grading period. Progress reports must be signed by a parent and returned promptly. Two extra credit points will be given to those students who return signed progress reports on-time.

Where can I get help when I do not understand something?

Please do not hesitate to ask questions … there are no dumb questions in this class! Due to the amount of material we will be covering, there may not be enough time during a typical class period to answer all of your questions. You may not realize you have a question until days after we cover a particular topic. I will generally be available Tuesdays and Wednesdays 11:45 a.m. - 12:15 p.m. in room 214 and as needed to answer questions. If students are interested, I can conduct test review sessions. Since you will be working with other students in your class on a regular basis, help each other! Communicate online, call someone, or meet for study sessions. Also, consult family members with math backgrounds and other outside reference materials including the Internet. The pace of this course will be extremely rapid at times. This is to ensure that all of the required material is covered. Remember: Help does not mean copying work or having someone else do the work for you! Any time that you need help with academic or other matters, your teachers, counselors, and principals are available and willing to help you.

Materials

Bring the following with you to every class meeting (unless told otherwise):

· Loose leaf paper (or a spiral notebook) and a pencil

· Graphing calculator

· A three-ring binder might be helpful to keep notes, tests, handouts, etc. (1 - 1.5” binders seem to work well)

· All assignments completed

A textbook has been issued to you for this course. You are responsible for maintaining it and returning it in good condition at the end of the year (or if you drop the course). Please note that the textbook for this course has a replacement cost of approximately $100.

Calculator use in this class and on the AP exam

I recommend that you use a TI-83 or TI-84 Plus or Plus SE graphing calculator. TI-85 and TI-86 calculators will also work well, but I have had little experience with those and will not be able to answer many questions about how to use them. If enough students have their own calculators, I have TI-83 Plusses that students can check out for the year. Please bring your graphing calculator to class every day. Although you will not need your calculator every day, there are many times in which I will spontaneously use the calculator. In fairness to all, TI-89s or any calculator with a computer algebraic system (CAS) will not be allowed for class tests. The AP exam is written so that using a TI-89 does not provide an advantage and therefore it may be used for that exam. We will be using graphing calculators frequently during class and, although it is not necessary to have your own to complete homework, it can be very helpful.

In the past, I have had a few students who have decided to play calculator games during class. If you choose to play games during class, your calculator will be taken until the end of the day and the all programs will be deleted.

Classroom procedures

Attendance. It is very important that you are present every day. However, if extenuating circumstances arise and you must be absent, I will allow you to make-up any missed work if the absence is excused. It is your responsibility to obtain material from me or classmates and to arrange any needed make-up times. Typically, you will be allowed two nights to make-up work. Consult the Student Handbook for consequences of unexcused absences. Skipping will not be tolerated and will result in an unexcused absence and a call to your home.

Tardy. Students are expected to be seated and have materials ready when the tardy (second) bell rings. This includes your book, notebook, binder, calculator, and sharpened pencil on your desk. If you will be arriving late, you must obtain a tardy permit. Please enter the room quietly and “tune-in” to the lesson quickly.

Written Excuses / Permits. I will designate an area in your classroom for you to leave permits. Notes to excuse absences must be given to the attendance office the day you return. If you must leave campus early or arrive late during my class, you must provide a note signed by a parent and the attendance office. Additionally, you must sign out/in at the attendance office when you leave/arrive. Please do not disrupt the class with notes or permits.

Conduct grades

I anticipate no conduct problems. Everyone in this class has the right to learn, free from any fears of being harmed, intimidated, or embarrassed. Any conduct issues that do arise will be dealt with swiftly. I have the right to help you and your classmates learn without disruption or interference. Thus, you are expected to adhere to the following rules of conduct:

· Respect everyone and everything - no exceptions

· Participate, concentrate, listen, and follow directions from “bell to bell”

· Follow the rules and policies of Bellaire High School as listed in the Student Handbook

E = 0-1 infractions, S = 2-3 infractions, P = 4 infractions, U = 5 or more infractions. Infractions include, but are not limited to, working on non-calculus work in class, excessive tardiness, writing on desks, playing games on calculators or PDAs, and showing disrespect. Arrive to class on-time, ready to work when the bell rings. I reserve the right to assign conduct grades according to overall conduct and attitude demonstrated during each grading period.

Topical Outline and Tentative Test Schedule

Although major changes to this test schedule are unlikely, you will be informed of any adjustments.

1^st 6-week grading period

08/24/06 Test #1: P1 – P6, 1.1 – 1.2 Prerequisites; Intro to Limits

09/14/06 Test #2: 1.3 – 1.5, 2.1 – 2.5 Limits; Definition of Derivative; Differentiation Techniques

2^nd 6-week grading period

10/05/06 Test #3: 2.6, 3.1 – 3.7, 3.9 Graphical and Other Applications of Differentiation

10/26/06 Test #4: 4.1 – 4.6 Antiderivatives; The Fundamental Theorem of Calculus; Basic

Integration Techniques

3^rd 6-week grading period

11/16/06 Test #5: 5.1 – 5.5, 5.7, 5.8 Differentiation, Integration, and Applications of

Transcendental Functions

12/07/06 Test #6: 6.1 – 6.4 Geometric Applications of Integration (Volume, Surface Area,

and Arc Length)

4^th 6-week grading period

01/18/07 Test #7: 7.1 – 7.4, 7.7, 7.8 Additional Integration Techniques; Indeterminates and

L’Hôpital’s Rule; Improper Integrals

02/08/07 Test #8: 8.1 – 8.6 Sequences; Tests for Convergence and

Divergence of Series

5^th 6-week grading period

03/01/07 Test #9: 8.7 – 8.10 Taylor Polynomials; Power Series; Taylor Series

03/29/07 Test #10: 10.1 – 10.4; 12.1 – 12.3 Parametric Equations and Calculus; Polar Graphs; Area in

Polar Coordinates

6^th 6-week grading period

04/26/07 Test #11: 5.6; 16.1 – 16.2, Differential Equations (Separation of Variables); Slope Fields;

Euler’s Method; Logistic Function

The AP Calculus BC Exam

Test date: Wednesday, May 9, 2007 in the morning

Test duration: 3 hours and 15 minutes

Section I 1 hour and 45 minutes

· Part A: 28 multiple-choice questions without a calculator (55 minutes)

· Part B: 17 multiple-choice questions with a graphing calculator (50 minutes)

Section II 1 hour and 30 minutes

· Part A: 3 free response questions with a graphing calculator (45 minutes)

· Part B: 3 free response questions without a calculator (45 minutes)

Further details about the exam will be provided during class throughout the year.

What happens after the AP Calculus exam?

Since the AP Calculus exam is quite early in May, there are seven class days remaining after the exam. Many of you will miss some class days while taking other AP and IB exams. Bring materials to class so that you can study for other exams. The free response questions are released a few days after the administration of the exam and we will go through those six questions together during class. This allows me the opportunity to obtain feedback from you about specific questions and problem areas and allows you to form a preliminary assessment of your exam performance.

Please note that modifications to the information contained in this document may be provided to you during class throughout the school year.

Last Revision: 06/13/2006

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