## 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 & Review**

1- Welcome to AP Calculus BC

2- Course Syllabus

3- MLA Formatting Word 2007

4- MLA Documentation Updates

5- Completing Math Assessments

6- MLA Citation

7- MLA Incorporating Sources

8- Calculus On The Web

9- Review — Stuff You Should Already Know

**2- Limits & Continuity**

1- An Introduction to Limits & Continuity

Quiz: Introduction to Limits & Continuity

2- Tangent Lines & Rates of Change

Handout: Tangent Lines & Rates of Change Worksheet

Assignment: Tangent Lines & Rates of Change

3- The Limit

Handout: The Limit Worksheet

Assignment: The Limit

4- One-Sided Limits

Handout: One-Sided Limits Worksheet

Assignment: One-Sided Limits

5- Computing Limits

Handout: Computing Limits Worksheet

Assignment: Computing Limits

6- Infinite Limits

Handout: Infinite Limits Worksheet

Assignment: Infinite Limits

7- Limits at Infinity

Handout: Limits at Infinity Worksheet

Assignment: Limits at Infinity

8- Continuity

Handout: Continuity Worksheet

Assignment: Continuity

9- Additional Resources

Handout: Limits & Continuity Exam

Assignment: Limits & Continuity Exam

**3- Derivatives**

1- Introduction to Derivatives

2- Definition & Interpretation of the Derivative

Handout: Definition & Interpretation of the Derivative Worksheet

Assignment: Definition & Interpretation of the Derivative

3- Differentiation Formulas

Handout: Differentiation Formulas Worksheet

Handout: Derivatives Exam 1

Assignment: Differentiation Formulas

Assignment: Derivatives Exam 1

4- Product & Quotient Rule

Handout: Product & Quotient Rule Worksheet

Assignment: Product & Quotient Rule

5- Derivatives of Trig Functions

Handout: Derivatives of Trig Functions Worksheet

Assignment: Derivatives of Trig Functions

6- Derivatives of Exponential & Logarithm Functions

Handout: Derivatives of Exponential & Logarithm Functions Worksheet

Assignment: Derivatives of Exponential & Logarithm Functions

7- Derivatives of Inverse Trig Functions

8- Derivatives of Hyperbolic Functions

Handout: Derivatives of Inverse & Hyperbolic Trig Functions Worksheet

Assignment: Derivatives of Inverse & Hyperbolic Trig Functions

9- The Chain Rule

Handout: The Chain Rule Worksheet

Handout: Derivatives Exam 2

Assignment: The Chain Rule

Assignment: Derivatives Exam 2

10- Implicit Differentiation

Handout: Implicit Differentiation Worksheet

Assignment: Implicit Differentiation

11- Related Rates

Handout: Related Rates Worksheet

Assignment: Related Rates

12- Higher Order Derivatives

Handout: Higher Order Derivatives Worksheet

Assignment: Higher Order Derivatives

13- Additional Resources

Handout: Derivatives Exam 3

Assignment: Derivatives Exam 3

**4- Applications of Derivatives**

1- What’s the Big Deal About Derivatives, Anyway?

2- Rates of Change

3- Critical Points & Extrema

Handout: Critical Points & Extrema Worksheet

Assignment: Critical Points & Extrema

4- The Shape of a Graph

Handout: The Shape of a Graph Worksheet

Assignment: The Shape of a Graph

5- The Mean Value Theorem

Handout: The Mean Value Theorem Worksheet

Assignment: The Mean Value Theorem

6- Optimization

Handout: Optimization Worksheet

Assignment: Optimization

7- L’Hopital’s Rule

Handout: L’Hosptial’s Rule Worksheet

Assignment: L’Hospital’s Rule

8- Linear Approximations

Handout: Linear Approximations Worksheet

Assignment: Linear Approximations

9- Differentials

Handout: Differentials Worksheet

Assignment: Differentials

10- Newton’s Method

Handout: Newton’s Method Worksheet

Assignment: Newton’s Method

11- 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

**4- Integrals**

1- Working Backwards

2- Additional Resources

3- Indefinite Integrals

Handout: Indefinite Integrals Worksheet

Assignment: Indefinite Integrals

4- Computing Indefinite Integrals

Handout: Computing Indefinite Integrals Worksheet

Assignment: Computing Indefinite Integrals

5- Substitution Rule for Indefinite Integrals

Handout: Substitution Rule Worksheet

Handout: Integrals Exam 1

Assignment: Substitution Rule

Assignment: Integrals Exam 1

6- Area Problem

Handout: Area Problem Worksheet

Assignment: Area Problem

7- Definite Integrals

Handout: Definite Integrals Worksheet

Assignment: Definite Integrals

8- Computing Definite Integrals

Handout: Computing Definite Integrals Worksheet

Assignment: Computing Definite Integrals

9- Substitution Rule for Definite Integrals

Handout: Substitution Rule for Definite Integrals Worksheet

Assignment: Substitution Rule for Definite Integrals

10- Integration by Parts

Handout: Integration by Parts Worksheet

Assignment: Integration by Parts

11- Partial Fractions

Handout: Partial Fractions Worksheet

Assignment: Partial Fractions

12- 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

**5- Applications of Integrals**

1- What’s the Big Deal About Integrals, Anyway?

2- Area Between Curves

Handout: Area Between Curves Worksheet

Assignment: Area Between Curves

3- Volumes of Solids of Revolution (Part 1)

Handout: Method of Rings Worksheet

Assignment: Method of Rings

4- Volumes of Solids of Revolution (Part 2)

Handout: Method of Cylinders Worksheet

Assignment: Method of Cylinders

5- Volume

6- Work

Handout: Work Worksheet

Assignment: Work

Handout: Applications of Integrals Exam

Assignment: Applications of Integrals Exam

**6- Sequences & Series**

1- Sequences & Series

2- Additional Resources

3- Sequences

Handout: Sequences Worksheet

Assignment: Exploration: The Limit of a Sequence

Assignment: Sequences

4- Series: The Basics

Handout: Series Worksheet

Assignment: Series

5- Series: Convergence & Divergence

6- Special Series

7- Integral Test

Essay: Integral Test

8- Comparison Test

Handout: Comparison Test Worksheet

Assignment: Comparison Test

9- Alternating Series Test

Handout: Alternating Series Test Worksheet

Assignment: Alternating Series Test

10- Absolute Convergence

Handout: Absolute Convergence Worksheet

Assignment: Absolute Convergence

11- Ratio & Root Tests

Handout: Ratio & Root Test Worksheet

Assignment: Ratio & Root Test

12- Strategy for Series

13- Estimating the Value of a Series

14- Power Series

Handout: Power Series Worksheet

15- Taylor Series

Handout: Taylor Series Worksheet

Assignment: Power Series

Assignment: Taylor Series

16- Post-Test

Assignment: Calculus Post-test

**7- Review & Test Preparation**

1- Exam Format & Scoring

2- Exam Strategies & Tips

3- Practice, Practice, Practice!

Handout: AP Calculus BC – Section 1 Part A

Handout: AP Calculus BC — Section 1 Part B

Handout: AP Calculus BC — Section II Part A

Handout: AP Calculus BC — Section II Part B

Assignment: AP Calculus BC Review — Section I: Part A

Assignment: AP Calculus BC Review — Section I: Part B

Assignment: AP Calculus BC Review — Section II: Part A

Assignment: AP Calculus BC Review — Section II: Part B

**8- Course Survey**

Handout: Course Survey

Assignment: Course Survey

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