Calculus AP Syllabus

COURSE TITLE: Calculus AP
TEXT: Calculus-Graphical, Numerical, Algebraic; Finney
CODE: MAC612
GRADE LEVEL: 11-12 

Course Description:  Calculus AP provides an understanding of the fundamental concepts and methods of differential and integral calculus with an emphasis on their application, and the use of multiple representations incorporating graphic, numeric, analytic, algebraic, and verbal and written responses. Topics of study include: functions, limits, derivatives, and the interpretation and application of integrals. An in-depth study of functions occurs in the course. Technology is an integral part of the course and includes the use of graphing calculators, computers, and data analysis software. On a regular basis, graphing calculators are used to explore, discover, and reinforce concepts of calculus.

Meeting Times:  Calculus AP meets for 36 weeks. The class is offered during period 2, which meets for 90 minutes on the “odd” days.

Textbook:  Finney, R. L., Demana, F.D., Waits, B.K., and Kennedy, D. (2003). Calculus: Graphical, Numerical, Algebraic. Upper Saddle River, NJ: Pearson Education-Prentice Hall.

The Standards:  The Standards support the unifying themes of derivatives, integrals, limits, approximation, as well as applications and modeling in the course. Instruction is designed and sequenced to provide students with learning opportunities in appropriate settings. Teaching strategies include collaborative small-group work, pairs engaged in problem solving, whole-group presentations, peer-to-peer discussions, and an integration of technology when appropriate. In this course, students are often engaged in mathematical investigations that enable them to collaborate with peers in designing mathematical models to solve problems and interpret solutions. They are encouraged to talk about the mathematics of change in calculus, to use the language and symbols of calculus to communicate, and to discuss problems and methods of solution.

Prerequisites:  Our system has an open enrollment policy on all courses, but students should understand that this course is designed to be a fourth-year mathematics course, and the equivalent of a year-long, college-level course in single variable calculus. calculus sequence.  Students are expected to take the AP Calculus Exam at the end of this course.

Philosophy:  Understanding change is the basis of this course. The study of the concept of the derivative in calculus is the formal study of mathematical change. A key component of the course is fluency in the use of multiple representations that include graphic, numeric, analytic, algebraic, and verbal and written responses. Students build an understanding of calculus concepts as they construct relationships and make connections among the various representations. The course is more than a collection of topics; it is a coherent focused curriculum that develops a broad range of calculus concepts and a variety of methods and real-world applications. These include practical applications of integrals to model biological, physical, and economic situations. Although the The course requires a solid foundation of advanced topics in algebra, geometry, trigonometry, analytic geometry, and elementary functions. The breadth, pace, and depth of material covered exceeds the standard high school mathematics course, as does the college-level textbook, and time and effort required of students. AP Calculus AB provides the equivalent of the first course in a college development of techniques and fluency with algebraic symbolism to represent problems is important, it is not a primary focus of the course. Rather, the course emphasizes differential and integral calculus for functions of a single variable through the Fundamental Theorem of Calculus.

Roll of Technology:  Technology is used to enhance students’ understanding of calculus concepts and techniques. The College Board requires the use of graphing calculators for this course. Mathematical problem solving, investigations, and projects require adequate and timely access to technology including graphing calculators, databases, spreadsheets, Internet and on-line resources, and data analysis software. In this course, technology is introduced in the context of real-world problems, incorporates multiple representations, and facilitates connections among mathematics topics. Students use estimation, mental math, calculators, and paper-and-pencil techniques of calculus to conduct investigations and solve problems.

Internet Access and Online Resources :

■   Math Tools Website:

http://www.mathforum.org/mathtools/cell.html?&new_co=c

■   Math Archives: Calculus Resources On-Line Website:

http://archives.math.utk.edu/calculus/crol

Graphing Calculators: Students will utilize the TI-84 Graphing Calculator extensively throughout the course.

Major Evaluation Techniques: Students will be evaluated using assessments which document students’ growth and improvement in understanding the abstract concepts of Calculus. Evaluation processes may include written and oral work including presentations, journals, homework, reports, investigations, long term projects, and a variety of test formats.

Course Depth: The content and level of depth of the material for this course is equivalent to a college-level course. The course content is organized to emphasize major topics in the course to include the following: (1) functions, graphs, and limits; (2) derivatives, and (3) integrals. Building on most students’ prior knowledge, the course begins with a review of a variety of functions using multiple representations: graphic, numeric, algebraic, analytic, and verbal and written responses. Technology enhances students’ constructing an understanding of mathematical relationships among the different representations used in solving problems. This supports and leads to students’ development and visualization of properties of limits and continuity, and rates of change of functions.

The Derivative: The concept of a derivative is interpreted as a rate of change and local linearity. Using graphing calculators, numeric derivatives are examined. This is followed with a focus on derivatives of functions, algebraic, trigonometric, logarithmic, and exponential. Applications of the derivative are investigated through velocity, acceleration, and optimization problems. The definite integral is studied as a limit of Riemann sums and the rate of change of a quantity over a specific interval. This sequence of topics naturally leads to students’ introduction to the Fundamental Theorem of Calculus. Applications of definite integrals are also investigated which include summing rates of change, particle motion, areas in a plane, and volumes of solids.

Order of Topics: This order of topics within the course, not only provides a logical and systemic study to calculus, but also accommodates the frequent transfer of students within the schools of the system, so that transfer students can maintain a consistent flow of learning.

  • Essential Expectations: Upon successful completion of AP Calculus, the student should be able to:
  • Determine the rate of change for a function.
  • Understand the rule for continuity of a function.
  • Examine the importance of limits.
  • Determine the derivative of various types of functions.
  • Prove theorems involving the limit and derivative.
  • Solve problems involving absolute extrema.
  • Examine the behavior of functions using the various derivative tests.
  • Examine applications involving related rates.
  • Develop the Riemann Sum.
  • Analyze the antiderivative and the integral.
  • Verify the Fundamental Theorem of Calculus.
  • Examine calculus in relation to trigonometric functions.
  • Determine the area under and between curves.
  • Examine the calculus of exponential and logarithmic functions.
  • Solve problems involving exponential growth and decay.
  • Determine the volume of solids of revolution.
  • Implement the rules for integration.
  • Evaluate limits using L’Hopital’s Rule.

Grading Policy: Weighted grades are calculated for students completing and taking the requisite exam for Calculus AB.

Unweighted Scale                     Weighted Scale

A=4                                                        A=5

B=3                                                        B=4

C=2                                                        C=3

D=1                                                        D=2

F=0                                                         F=0

Being Successful : There will be at least one quiz given each week in addition to approximately two tests per quarter. If students do poorly on a quiz, they can request a second attempt to obtain a passing grade. The primary goal is to do whatever can be done to enable the student to achieve success.

Summer Review Packet:  Students are required to complete the Summer Review Packet prior to the first day of class.  The purpose of this is to review and reinforce the algebraic skills necessary to be successful in Calculus.  The packet will count as the first quiz grade.

Homework Policy: Late homework will only be accepted with a valid and substantial excuse from home.

Tardy Policy:  This is a very rigorous course in mathematics, and students are required to be in class on time and prepared to learn.  Students will be marked tardy if they arrive to class without their textbook, notebook, or pencil.

Support Survices / Tutoring / Extra Help: All students are encouraged to schedule time for extra help during their seminar period.

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