AP Calculus BC Course Syllabus 2017/2018

Course Overview

AP Calculus BC is a rigorous, college-level mathematics course designed to provide students with a deep conceptual understanding of differential and integral calculus. The course follows the curriculum established by the College Board and prepares students to take the AP Calculus BC examination in May. AP Calculus BC includes all topics covered in AP Calculus AB, plus additional advanced topics such as parametric equations, polar functions, vector functions, improper integrals, and sequences and series.

Course Description

AP Calculus BC explores the concepts and techniques of differential and integral calculus and their applications. Students will investigate the fundamental concepts of limits, continuity, differentiation, integration, and series. Emphasis is placed on multiple representations of functions, numerical approaches to problems, and verbal and written explanations of mathematical concepts. The course is designed to develop student understanding of calculus through exploratory activities, collaborative problem solving, and technology-enhanced investigations.

The course is intended for students with strong mathematical backgrounds (having completed Pre-Calculus with an A or B grade) and exceptional work habits. Due to the accelerated nature and increased depth of content, AP Calculus BC requires significant dedication and independent study beyond the classroom. Students are expected to invest approximately 1-2 hours per day outside of class on homework and independent study.

Course Objectives

Upon completion of the AP Calculus BC course, students will be able to:

• Understand and apply the concepts of limits, continuity, derivatives, and integrals
• Solve problems using techniques of differentiation and integration
• Apply calculus concepts to model and solve real-world problems
• Use graphical, numerical, and analytical methods to understand and solve calculus problems
• Communicate mathematical ideas effectively through written and verbal explanations
• Utilize technology to explore calculus concepts and solve problems
• Develop a deeper understanding of the relationship between derivatives and integrals
• Apply advanced techniques of integration
• Solve differential equations and model applications
• Analyze sequences and series, including power series and Taylor series
• Work with parametric equations, polar coordinates, and vectors
• Demonstrate proficiency on the AP Calculus BC examination

Course Materials

• Textbook: "Calculus: Graphical, Numerical, Algebraic" 5th Edition by Finney, Demana, Waits, and Kennedy
• Calculator: Graphing calculator (TI-84 Plus CE or TI-89 Titanium recommended)
• Notebook: Three-ring binder with dividers for notes, homework, and assessments
• Writing Utensils: Pencils, erasers, pens, and highlighters
• Graph Paper: For graphical representations of functions and mathematical models
• Ruler and Protractor: For precise graphing and geometric applications

Course Content

First Semester

Unit 1: Limits and Continuity

• Concept of limits and techniques for evaluating limits
• Intermediate Value Theorem and Squeeze Theorem
• One-sided and two-sided limits
• Infinite limits and limits at infinity
• Continuity and discontinuities
• Horizontal and vertical asymptotes

Unit 2: Differentiation

• Definition of the derivative as a limit
• Differentiability and continuity
• Tangent lines and rates of change
• Rules for differentiation (Power, Product, Quotient, Chain Rule)
• Implicit differentiation and related rates
• Derivatives of inverse functions, inverse trigonometric functions, and exponential and logarithmic functions

Unit 3: Applications of Differentiation

• Extrema on an interval using the First Derivative Test
• Rolle's Theorem and Mean Value Theorem
• Concavity and points of inflection using the Second Derivative Test
• Curve sketching using derivatives
• Optimization problems
• Linear approximations and differentials

Unit 4: Basic Integration

• Antiderivatives and indefinite integration
• Area under curves using Riemann Sums
• Definite integrals and the Fundamental Theorem of Calculus
• Numerical integration methods (Trapezoidal and Simpson's Rules)

Second Semester

Unit 5: Differential Equations

• Slope fields and differential equation modeling
• Solving separable differential equations initial-value problems
• Exponential growth and decay models and logistic models

Unit 6: Applications of Integration

• Area between curves
• Volumes by cross-sections, disks, and washers
• Volume by cylindrical shells
• Arc length and surface area of revolution
• Physical applications (work, fluid force, center of mass)

Unit 7: Advanced Integration Techniques

• Integration by parts
• Trigonometric integrals
• Trigonometric substitution
• Partial fractions
• Indeterminate forms and L'Hpital's Rule
• Improper integrals

Unit 8: Parametric, Polar, and Vector Functions

• Parametric equations and calculus with parametric curves
• Vector-valued functions and calculus with vector functions
• Polar coordinates and polar graphs
• Area and arc length in polar coordinates

Unit 9: Sequences and Series

• Sequences, limits of sequences, and convergence
• Series and convergence tests (comparison, ratio, root, integral)
• Alternating series and absolute convergence
• Power series and radius of convergence
• Taylor and Maclaurin series and polynomial approximations
• Applications of series

Unit 10: AP Exam Review

• Comprehensive review of all units
• Practice examinations and timed AP-style questions
• Multiple-choice and free-response practice
• Test-taking strategies for AP Calculus BC

Assessment Methods

Student progress will be regularly assessed through the following:

• Homework: Daily assignments to reinforce concepts and develop problem-solving skills
• Quizzes: Short, frequent assessments targeting specific skills and concepts
• Tests: Comprehensive evaluations covering multiple topics requiring application of concepts
• Projects: Real-world application problems and mathematical modeling tasks
• Free-Response Questions: Practice of AP-style free-response questions throughout the course
• Midterm and Final Exams: Comprehensive cumulative assessments at the end of each semester
• Class Participation: Active engagement in discussions, group work, and problem-solving activities

Grading Policy

Grading Scale:

• A: 90-100%
• B: 80-89%
• C: 70-79%
• D: 60-69%
• F: Below 60%

Academic Integrity

Academic honesty is fundamental to the learning process. All students are expected to submit their own work and to acknowledge any collaboration or assistance received. Cheating on assessments, copying homework, or plagiarizing will not be tolerated. Consequences for academic dishonesty may include receiving a zero on the assignment, disciplinary action, and notification of parents/guardians.

Additional Resources

• College Board AP Calculus BC Course Description
• Khan Academy AP Calculus BC modules and practice exercises
• Videos and practice problems on MIT OpenCourseWare
• AP Calculus BC Released Exams and Free-Response Questions
• Tutoring sessions: Tuesdays and Thursdays 3:00-4:00 pm in Room 203
• College Board's AP Classroom website

Contact Information

Instructor: Dr. Sarah Mitchell

Email: s.mitchell@schoolname.edu

Office Hours: Monday, Wednesday, Friday 2:30-3:30 pm

Room: 203 Mathematics Building