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# AP Calculus BC Course Outline

## 1.0 Credit

This is a full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both courses represent college-level mathematics for which most colleges grant advanced placement and credit. The content of Calculus BC is designed to qualify the student for placement and credit in a course that is one course beyond that granted for Calculus AB.

AP Calculus BC is the study of limits, derivatives, definite and indefinite integrals, polynomial approximations and (infinite) series. Though this is considered a study of single-variable calculus, parametric, polar, and vector functions will be studied. Consistent with AP philosophy, concepts will be expressed and analyzed geometrically, numerically, analytically, and verbally. Calculus BC covers topics that are usually included in the first 3 semesters of college calculus.

- 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 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 and explain solutions to problems both verbally and in written sentences.
- 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 support 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.

1- Introduction

- Welcome to AP Calculus BC
- Course Syllabus
- MLA Formatting Word 2007
- MLA Documentation Updates
- Completing Math Assessments
- MLA Citation
- MLA Incorporating Sources
- Calculus On The Web
- Review — Stuff You Should Already Know

2- Limits & Continuity

- An Introduction to Limits & Continuity
- Quiz: Introduction to Limits & Continuity
- Tangent Lines & Rates of Change
- Handout: Tangent Lines & Rates of Change Worksheet
- Assignment: Tangent Lines & Rates of Change
- The Limit
- Handout: The Limit Worksheet
- Assignment: The Limit
- One-Sided Limits
- Handout: One-Sided Limits Worksheet
- Assignment: One-Sided Limits
- Computing Limits
- Handout: Computing Limits Worksheet
- Assignment: Computing Limits
- Infinite Limits
- Handout: Infinite Limits Worksheet
- Assignment: Infinite Limits
- Limits at Infinity
- Handout: Limits at Infinity Worksheet
- Assignment: Limits at Infinity
- Continuity
- Handout: Continuity Worksheet
- Assignment: Continuity
- Additional Resources
- Handout: Limits & Continuity Exam
- Assignment: Limits & Continuity Exam

3- Derivatives

- Introduction to Derivatives
- Definition & Interpretation of the Derivative
- Handout: Definition & Interpretation of the Derivative Worksheet
- Assignment: Definition & Interpretation of the Derivative
- Differentiation Formulas
- Handout: Differentiation Formulas Worksheet
- Handout: Derivatives Exam 1
- Assignment: Differentiation Formulas
- Assignment: Derivatives Exam 1
- Product & Quotient Rule
- Handout: Product & Quotient Rule Worksheet
- Assignment: Product & Quotient Rule
- Derivatives of Trig Functions
- Handout: Derivatives of Trig Functions Worksheet
- Assignment: Derivatives of Trig Functions
- Derivatives of Exponential & Logarithm Functions
- Handout: Derivatives of Exponential & Logarithm Functions Worksheet
- Assignment: Derivatives of Exponential & Logarithm Functions
- Derivatives of Inverse Trig Functions
- Derivatives of Hyperbolic Functions
- Handout: Derivatives of Inverse & Hyperbolic Trig Functions Worksheet
- Assignment: Derivatives of Inverse & Hyperbolic Trig Functions
- The Chain Rule
- Handout: The Chain Rule Worksheet
- Handout: Derivatives Exam 2
- Assignment: The Chain Rule
- Assignment: Derivatives Exam 2
- Implicit Differentiation
- Handout: Implicit Differentiation Worksheet
- Assignment: Implicit Differentiation
- Related Rates
- Handout: Related Rates Worksheet
- Assignment: Related Rates
- Higher Order Derivatives
- Handout: Higher Order Derivatives Worksheet
- Assignment: Higher Order Derivatives
- Additional Resources
- Handout: Derivatives Exam 3
- Assignment: Derivatives Exam 3

4- Applications of Derivatives

- What’s the Big Deal About Derivatives, Anyway?
- Rates of Change
- Critical Points & Extrema
- Handout: Critical Points & Extrema Worksheet
- Assignment: Critical Points & Extrema
- The Shape of a Graph
- Handout: The Shape of a Graph Worksheet
- Assignment: The Shape of a Graph
- The Mean Value Theorem
- Handout: The Mean Value Theorem Worksheet
- Assignment: The Mean Value Theorem
- Optimization
- Handout: Optimization Worksheet
- Assignment: Optimization
- L’Hopital’s Rule
- Handout: L’Hosptial’s Rule Worksheet
- Assignment: L’Hospital’s Rule
- Linear Approximations
- Handout: Linear Approximations Worksheet
- Assignment: Linear Approximations
- Differentials
- Handout: Differentials Worksheet
- Assignment: Differentials
- Newton’s Method
- Handout: Newton’s Method Worksheet
- Assignment: Newton’s Method
- Midtest
- Assignment: Calculus Midtest
- Handout: Motion Part 1 Worksheet
- Handout: Motion Part 2 Worksheet
- Handout: Motion Part 3 Worksheet
- Assignment: Motion Part 1
- Assignment: Motion Part 2
- Assignment: Motion Part 3

5- Integrals

- Working Backwards
- Indefinite Integrals
- Handout: Indefinite Integrals Worksheet
- Assignment: Indefinite Integrals
- Computing Indefinite Integrals
- Handout: Computing Indefinite Integrals Worksheet
- Assignment: Computing Indefinite Integrals
- Substitution Rule for Indefinite Integrals
- Handout: Substitution Rule Worksheet
- Handout: Integrals Exam 1
- Assignment: Substitution Rule
- Assignment: Integrals Exam 1
- Area Problem
- Handout: Area Problem Worksheet
- Assignment: Area Problem
- Definite Integrals
- Handout: Definite Integrals Worksheet
- Assignment: Definite Integrals
- Computing Definite Integrals
- Handout: Computing Definite Integrals Worksheet
- Assignment: Computing Definite Integrals
- Substitution Rule for Definite Integrals
- Handout: Substitution Rule for Definite Integrals Worksheet
- Assignment: Substitution Rule for Definite Integrals
- Integration by Parts
- Handout: Integration by Parts Worksheet
- Assignment: Integration by Parts
- Partial Fractions
- Handout: Partial Fractions Worksheet
- Assignment: Partial Fractions
- Improper Integrals
- Handout: Improper Integrals Worksheet
- Assignment: Improper Integrals
- Handout: Motion Part 4 Worksheet
- Handout: Motion Part 5 Worksheet
- Assignment: Motion Part 4
- Assignment: Motion Part 5

6- Applications of Integrals

- What’s the Big Deal About Integrals, Anyway?
- Area Between Curves
- Handout: Area Between Curves Worksheet
- Assignment: Area Between Curves
- Volumes of Solids of Revolution (Part 1)
- Handout: Method of Rings Worksheet
- Assignment: Method of Rings
- Volumes of Solids of Revolution (Part 2)
- Handout: Method of Cylinders Worksheet
- Assignment: Method of Cylinders
- Volume
- Work
- Handout: Work Worksheet
- Assignment: Work
- Handout: Applications of Integrals Exam
- Assignment: Applications of Integrals Exam

7- Sequences & Series

- Sequences & Series
- Additional Resources
- Sequences
- Handout: Sequences Worksheet
- Assignment: Exploration: The Limit of a Sequence
- Assignment: Sequences
- Series: The Basics
- Handout: Series Worksheet
- Assignment: Series
- Series: Convergence & Divergence
- Special Series
- Integral Test
- Essay: Integral Test
- Comparison Test
- Handout: Comparison Test Worksheet
- Assignment: Comparison Test
- Alternating Series Test
- Handout: Alternating Series Test Worksheet
- Assignment: Alternating Series Test
- Absolute Convergence
- Handout: Absolute Convergence Worksheet
- Assignment: Absolute Convergence
- Ratio & Root Tests
- Handout: Ratio & Root Test Worksheet
- Assignment: Ratio & Root Test
- Strategy for Series
- Estimating the Value of a Series
- Power Series
- Handout: Power Series Worksheet
- Taylor Series
- Handout: Taylor Series Worksheet
- Assignment: Power Series
- Assignment: Taylor Series
- Post-Test
- Assignment: Calculus Post-test

8- Review & Test Preparation

- Exam Format & Scoring
- Exam Strategies & Tips
- Practice, Practice, Practice
- Handout: Calculus BC Section I Part A
- Handout: Calculus BC Section 1 Part B
- Handout: Calculus BC Section II Part A
- Handout: Calculus BC Section II Part B
- Assignment: AP Calculus BC Practice – Section I Part A
- Assignment: AP Calculus BC Practice – Section I Part B
- Assignment: AP Calculus BC Practice – Section II Part A
- Assignment: AP Calculus BC Practice – Section II Part B

9- Course Survey

- Handout: Course Survey
- Assignment: Course Survey

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