**AP Calculus BC – Course Syllabus**

Mr. Aaron Timmons – Room 134

859.381.3308 (x.2134)

Course Expectations & Philosophy:

AP Calculus BC is a rigorous course for motivated students that follows the AP Curriculum as outlined by the College Board. The main objective of the course is to prepare students to pass the AP Exam as well as future college-level mathematics courses in calculus. Advanced Placement Calculus BC is a year-long course that meets Tuesday, Friday, and every other Wednesday for approximately 90 minutes. The course proceeds AP Calculus AB which students take the previous year.

Successful completion of this course will be indicated by a proficient ability to:

· Work with and understand connections between functions represented in multiple ways

· Understand the meaning of the derivative both in terms of a rate of change and local linear approximation as well as use derivatives to solve a variety of problems

· Understand the relationship between the derivative and the definite integral

· Communicate mathematics both orally and in well-written sentences to explain solutions to problems

· Model a written description of a physical situation with a function, a differential equation, or an integral

· Use technology to help solve problems, experiment, interpret results, and verify conclusions

· Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement

· Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment

We will achieve these objectives by GNAWing on concepts during the entire course.

· G – graphical analysis without knowledge of an equation

· N – numerical analysis without knowledge of an equation

· A – analytic/algebraic analysis

· W – written/verbal methods of representing problems

Students will also be required to complete a written component for the class. Through this requirement, students will demonstrate their ability to answer the “how” and “why” of the various concepts covered throughout the year. The written component will be satisfied by completion of released AP free-response questions throughout the year, process papers on integration and applications, and journal entries at the end of each unit.

Technology & Resources:

Use of the TI-84, TI-89, or TI-Nspire is required for this course. Calculators will be used to:

· Conduct explorations

· Graph functions within arbitrary windows

· Solve equations numerically

· Analyze and interpret results

· Justify and explain results of graphs and equations

Other technology will include:

· www.mathdemos.gcsu.edu/mathdemos

· www.apcentral.collegeboard.com

· www.calculusapplets.com

· www.math.hmc.edu/calculus/tutorials/

Textbook:

Stewart, James. *Calculus: Early Transcendentals; AP Edition*. Seventh edition. Brooks/Cole, 2012.

This is a college textbook that integrates numerical, graphical, and analytic approaches in each section. Graphing calculator exercises are integrated throughout the text. Calculator and non-calculator explorations are presented to introduce important concepts. It is a traditional text that emphasizes students must be able to "do" calculus before it can be applied. AP free response and multiple choice items provide additional practice with skills and applications.

Tentative Topic Timeline:

**Although not specifically listed below, AP Calculus AB topics are incorporated into the AP Calculus BC lessons. All of the AP Calculus AB topics are listed in the table only at the end during the review/overview session prior to the AP exam.*

Unit 0: AP Calculus AB Review; Part I (4 days)

· Differentiation

· Integration

· Released AP Calculus AB Multiple Choice and Free-Response Questions

Unit 1: Techniques of Integration (12 days)

· 7.1 – Integration by Parts

· 7.2 – Trigonometric Integrals

· 7.3 – Trigonometric Substitution

· Supplement – Partial Fractions packet

· 7.4 – Integration of Rational Functions by Partial Fractions

· 4.4 – Indeterminate Forms and L’Hopital’s Rule

· 7.8 – Improper Integrals

* Students complete explorations and problems from textbooks with and without the graphing calculator to determine integrals both numerically and graphically. Later results are verified analytically. Problems from the textbook include practice with integration numerically, graphically, and analytically.

Unit 2: Conics, Parametric Equations and Polar Coordinates (10 days)

· 10.6 – Conic Sections

· 10.1 – Curves Defined by Parametric Equations

· 10.2 – Tangents and Areas (Parametric Form of the Derivative)

· 10.3 – Arc Length and Surface Area

· 10.4 – Polar Coordinates

· 10.5 – Areas and Lengths in Polar Coordinates

* Textbook problems in addition to released AP problems are practiced in class and are given as quiz and exam questions. Students must demonstrate competency to the AP grading scale. Students will work several graphing calculator-based experiments and investigations utilizing the polar and parametric features of the calculator. Based on the results seen on the calculator, students will be asked to provide specific, written and verbal arguments and support for different problems.

Unit 3: Vectors (Supplemented from Larson and Edwards; 7 days)

· Supplement – Vector Packet

· 11.1 – Vectors in the Plane

· 12.1 – Vector-Valued Functions

· 12.2 – Differentiation and Integration of Vector-Valued Functions

· 12.3 – Velocity and Acceleration

· 12.4 – Tangent Vectors and Normal Vectors

* Textbook problems in addition to released AP problems are practiced in class and are given as quiz and exam questions. Students must demonstrate competency to the AP grading scale.

Unit 4: Differential Equations (9 days)

· 9.1 – Modeling with Differential Equations

· 9.2 – Slope Fields and Euler’s Method

· 9.3 – Separable Equations

· 9.4 – Exponential Growth and Decay

· 9.5 – Logistic Growth

* AP released items and slope field exercises from AP Central and AP professional workshops are used throughout unit. Professional Focus series materials will also be used during this unit. Slope field programs from the Texas Instruments website (www.education.ti.com) will also be used to demonstrate the idea of slope fields to students.

(SEMESTER BREAK)

Unit 5: Infinite Sequences and Series (25 days)

· 11.1 – Sequences

· 11.2 – Series

· 11.3 – The Integral Test and Estimates of Sums

· 11.4 – The Comparison Tests

· 11.5 – Alternating Series

· 11.6 – Absolute Convergence and the Ratio and Roots Tests

· Supplement (9.7 from Larson and Edwards) – Taylor Polynomials and Approximations

· 11.8 – Power Series

· 11.9 – Representations of Functions as Power Series

· 11.10 – Taylor and Maclaurin Series

* AP released items and materials from AP Central and AP professional workshops are used throughout unit. Homework assignments from this unit will be components of actual AP exams that students will have to present orally to the class.

Unit 6: AP Calculus AB Review; Part II (10 days)

· Limits and Derivatives

· Differentiation

· Applications of Differentiation

· Integration

· Logarithmic, Exponential, and Other Transcendental Functions

· Applications of Integration

* Practice released AP Exams from AP College Board and utilize online resources from the National Math & Science Initiative (NMSI). Mock exam will be given and scored according to AP scoring guide so students may have numerical score of 1-5. Students will also team up to present selected multiple choice and free-response questions to the class. Students will be evaluated on effectiveness of verbal communication to the rest of the class.

Unit 7: Review for AP Calculus BC Exam (6 days)

· Supplement – Practice/Released AP Exams, review of all topics in AP Calculus BC Course Description

* Practice released AP Exams from AP College Board and utilize online resources from the National Math & Science Initiative (NMSI). Mock exam will be given and scored according to AP scoring guide so students may have numerical score of 1-5.

Unit 8: After the AP Exam (5 days)

· End-of-course projects

Grades:

Grades will be calculated based on a combination homework, quizzes, tests, and AP Exam prep. All tests will be divided into multiple-choice and free-response sections, each with a calculator and non-calculator section. AP scoring guidelines will be utilized in determining grades. Final grades will follow the Fayette County (Bryan Station High School) grading scale.

Study Sessions:

Two study sessions and a mock exam will be held during the second semester of school to help students prepare for the AP Exam. Presenters from across the nation will conduct lessons and give workshops for students to help them feel better prepared for the exam. **Attendance at 1 of the 2 sessions and completion of the mock exam is mandatory and will count as a grade.** Dates will be determined in the next couple months and will be communicated once they are set.

AP Exam:

Tuesday, May 6, 2015 (morning) – Details regarding registration will be announced soon.