Course Description

Calculus is the mathematics of change. It describes the change in one variable related to the change of another variable. We will divide calculus into 3 sections. The first part of the year will cover limits and continuity. The second part will cover derivatives and their applications. The third part will cover integrals and their applications. This class is designed as a college level class. We will cover everything in the Calculus AB topic outline as it appears in the AP Calculus Course Description. This can be viewed at the website www.collegeboard.com. The primary book we will be using will be Calculus for the AP Course by BFW Publishers, Multiple Choice and Free Response Questions in Preparation for the AP Calculus (AB) Examination by David Lederman, AP Calculus Free Response Questions and Solutions 1989 – 1997, and by using collegeboard.com.

Instructional Philosophy

§ Instructional Approach

As the teacher, we, the math department, want to provide the very best education and learning experience for the students in my class. We, the math department, believe the teacher should work with the students in the classroom, not just be the lecturer.

§ A Typical Day in the Classroom

The class will begin each by reviewing homework completed the day before. The students should come into class and get out their homework and begin collaborating with their partner. If you get a different answer than your partner, work out the problem together and discuss the process with each other. I will go over any questions on the homework after that. The class will then learn the new material for the day. The approach for learning the new material varies from day to day. At the beginning of each new unit we will do an exploratory activity where you will be able to examine the topic and try and determine what is going on. The students will then discuss as a whole about the concepts. I will then explain the new details using as many examples as possible. The end of class will follow with a review of what was learned.

•  Teaching Strategies

We, the math department, will be using a variety of teaching strategies in the classroom. The following strategies will be used: lecture, group work, projects, presentations, games, computer labs, writing assignments and many more.

•  Classroom Design

The classroom design will change according to the strategy of teaching. Some designs include: u-shape, row, and cluster.

• Student Participation

You will be expected to be taking part in the class, by doing your work, paying attention, asking and answering questions. You can expect to have assignments every class period. Use your time wisely in class so that if you do have time to get started in class, you can acquire help.

Course Goals/Power Standards

1.  Limits and continuity

2. Derivatives and applications

3. Integrals and applications

*** The course goals and power standards above will be assessed by teacher observation, daily class work/homework, quizzes, tests and projects.

Materials

You will need a three-ring binder with loose-leaf paper. All work, graded work handed back, and notes should be kept there in an organized fashion. All work must be done in pencil. You also need a graphing calculator. If you are planning on purchasing one, I suggest the TI-84 Plus Silver Edition, TI-84, TI-89 or a TI-86. The TI-83 calculators will get you by in this class but you will have to do a little more work by hand.

Grading System

Your grade will come from tests, projects, homework, and classwork. Tests/projects will count 60% and homework/classwork will count 40%. You will generally have one to two tests per unit, some being cumulative and some not. Formats will vary, including multiple choice, short answer, and/or free response.

Homework/Classwork

You can expect to have assignments every class period. Use your time wisely in class so that if you do have time to get started in class, you can acquire help. Homework/classwork will be checked at random and will be graded on a completion/accuracy basis. Therefore, you should at least attempt each problem. If you have no idea how to do a problem, you should copy the problem and directions that go with it and then move on to the next problem. If you leave a problem blank, you will not receive credit for it.

Exams

Exams will be averaged as the school outlines.

Make-up Work

Make-up work is outlined in the student handbook. Tests and work should be made up within five school days and not during class time. Any work not made up will receive a 0. Make-up work is your responsibility. You should talk to me as soon as you return from an absence in order to stay up with the class. If you are absent from class the day before a test, you will be required to take the test with the rest of the class if no new material has been covered. Field trips do not count as absences; therefore, you are responsible for being up with the class when you return.

Help

Extra help is always available. Please ask for help! However, let me know when you plan to come in so I can be sure to be here. Do not wait until after you have done poorly on a test to get extra help. I don’t give retests. Get help from the beginning. Email me at ghunter@greenville.k12.sc.us with any questions you may have. I am available every morning at 8:00AM or after school by appointment.

Calculus Course Outline

Advanced Placement Calculus AB is designed as college-level Calculus I. Students are required to take the College Board AB Examination in May to determine college credit awarded. Extensive use of a graphing calculator will be a major requirement of this course. Technology is used regularly by students and teachers to reinforce the relationship among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results. Homework assignments will be enhanced by the use of the graphing calculator and many colleges require students to own a graphing calculator and be well trained in its use. Purchase of a graphing calculator is still a personal choice; be advised however that colleges have their own preferences and requirements. 

First semester we will cover units 1 - 5. We will break these units into smaller units throughout the semester.

Second Semester we will cover units 6 - 8 in addition to going deeper in all units with the use of AP Classroom.

Unit 1:  Limits and Continuity

Unit 2:  Differentiation: Defintion and Fundamental Properties

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Unit 4: Contextual Applications of Differentiation

Unit 5: Analytical Application of Differentiation

Unit 6: Integration and Accumulation of Change

Unit 7: Differential Equations

Unit 8: Applications of Integration

Goals:

•  Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.

• Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.

• Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change and should be able to use integrals to solve a variety of problems.

• Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

• Students should be able to communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.

• Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.

• Students should be able to use technology to help solve problems, experiment, interpret results, and verify conclusions.

• Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

• Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

Being Successful in this Class

Please remember, as this is an introduction to a college-level class, your behavior should mirror that of a college student. You should expect a good bit of work and studying. If, however, you put forth effort and follow the procedures outlined above, you will be successful in this class. You all have the potential; it’s up to you. We will work together to help you get the most out of this class. I look forward to this year with you!