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