Search Online Courses And Queries About Online Schooling
AP Calculus BC Course Outline
1.0 Credit
This is a fullyear course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics. Both courses represent collegelevel 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 singlevariable 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
 OneSided Limits
 Handout: OneSided Limits Worksheet
 Assignment: OneSided 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
 PostTest
 Assignment: Calculus Posttest
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
Forest Trail Academy Accreditation and Memberships

Demi Arthur
“Forest Trail Academy is the BEST school ever, the staff is amazing!! I recently graduated from Forest Trail Academy after going there for 2 years. I went to public school…”Sarah Kosar
“FTA was a great alternative option for me so far as high school went. i transferred out during my junior year after having a rough time in public high school…” 
Audrey Barnett
“Forest Trail Academy has been a blessing to me. I compete in the sport of rodeo across many states, and it takes time and dedication to train and condition both …”Joshua Lawrence
“FTA gave me HOPE. I don’t have the pressures of exams and trying to keep up with the rest of the class. I get to go over the work as…” 
Brittany Wooten
“Hello my name is Brittany Wooten. I graduated from forest trail academy in 2009. I decided to choose fta because I wanted to accelerate my high school education. Fta was …”Yasmen Wass
“FTA has been a blessing to me!! I didn’t fit in at my old school, i had trouble learning in such a disruptive classroom which meant my grades falling, coming…” 
Allison H.
“Thank you Forest Trail Academy for helping my student excel! Placing my high school freshman in your program was the best choice! He works through the program at his pace…”Katie Bowcutt
“Katie Bowcutt wins title exaequo, PKRA Jr World Champion, 2013Freestyle Kiteboarding.Thanks for your support, Forest Trail Academy…”