## AP Calculus BC

## AP Calculus BC

This course aligns with the learning outcomes for: AP Course (All regions)

Some question if online AP students can score high enough on their exams to receive college credit and placement. Students using StudyForge have done very well, even scoring on AP Calculus BC 12% above average, and our AP Calculus AB students scoring 41% higher than average on their AP test scores. However, if you narrow it down to the subset of students who had a certain minimum level of healthy interaction with the curriculum, the numbers skyrocket. Download our Whitepaper below to see how at one school, 100% of these engaged students passed the AP exam, with an 88% chance of becoming “very well qualified” (4) or “extremely well qualified” (5).

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FREE WHITEPAPER

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Note: AP Calculus BC only differs from AP Calculus AB in scope, not difficulty. For more information on the topics covered in AP Calculus AB, click here.

Some question if online AP students can score high enough on their exams to receive college credit and placement. Students using StudyForge have done very well, even scoring on AP Calculus BC 12% above average, and our AP Calculus AB students scoring 41% higher than average on their AP test scores. However, if you narrow it down to the subset of students who had a certain minimum level of healthy interaction with the curriculum, the numbers skyrocket. Download our Whitepaper below to see how at one school, 100% of these engaged students passed the AP exam, with an 88% chance of becoming “very well qualified” (4) or “extremely well qualified” (5).

AP Calculus BC covers the first two semesters of University Calculus (Calc 1 and Calc 2). It includes the topics covered in our AP Calculus AB course with the addition of parametric functions, polar functions, vector functions and analysis of series. Students will have the option to complete the AP Exam administered by the College Board and receive university credit.

Note: AP Calculus BC only differs from AP Calculus AB in scope, not difficulty. For more information on the topics covered in AP Calculus AB, click here.

**What is AP?**

Want to give your students a taste of college in the comfort of high school? By taking AP courses your students can develop their college skills, such as time management and critical thinking, all the while discovering their passions by studying subjects more in-depth.

**Why Should Your Students Take AP Courses?**

- Earn College Credit
- Save Money by Skipping Introductory Courses in College
- Graduate Early
- Stand out in College applications

**What Steps Does a School Need to Take?**

- Get approved to teach AP courses via College Board – Register your school with the College Board and complete the online AP Participation form. Click here to find out what this entails.
- You’ve been approved – Congratulations, now what? See this pdf on how to set up, enroll and order for your AP classroom.
- Start teaching! You will receive all materials, practice tests, and note packages your students need when they are enrolled in StudyForge class.
- Don’t Forget to Order your Exams by Nov 15th for all full-year and first-semester courses or Mar 15th for all courses that begin after Nov 15th.
- See all Teacher/Administrator resources at AP Central.

## Table of Contents

*Each lesson is designed to take 60 – 90 minutes to complete with the exception of major projects and assignments.

Lesson 1: Introduction to Calculus

Lesson 2: Review of Function Terminology And More

Lesson 3: Graphing Calculators

Lesson 4: Compositions and Transformations of Functions

Lesson 5: Some Common Functions

Lesson 6: Inverse Functions

Lesson 7: Exponential and Logarithmic Functions

Lesson 2: Review of Function Terminology And More

Lesson 3: Graphing Calculators

Lesson 4: Compositions and Transformations of Functions

Lesson 5: Some Common Functions

Lesson 6: Inverse Functions

Lesson 7: Exponential and Logarithmic Functions

Lesson 1: Introduction to Limits

Lesson 2: Properties of Limits

Lesson 3: Limits Involving Infinity

Lesson 4: Continuity and The Sandwich Theorem

Lesson 5: Applications of Limits

Lesson 2: Properties of Limits

Lesson 3: Limits Involving Infinity

Lesson 4: Continuity and The Sandwich Theorem

Lesson 5: Applications of Limits

Lesson 1: The Derivative

Lesson 2: Rules of Differentiation

Lesson 3: Trigonometric Derivatives and The Chain Rule

Lesson 4: Derivatives of Exponential, Logarithmic, and Inverse Trig Functions

Lesson 5: Implicit Differentiation

Lesson 2: Rules of Differentiation

Lesson 3: Trigonometric Derivatives and The Chain Rule

Lesson 4: Derivatives of Exponential, Logarithmic, and Inverse Trig Functions

Lesson 5: Implicit Differentiation

Lesson 1: Analyzing Functions Part I: Curve Sketching

Lesson 2: Analyzing Functions Part II: Maximums and Minimums

Lesson 3: Applied Maximum and Minimum Problems

Lesson 4: Distance, Velocity, Acceleration, and Rectilinear Motion

Lesson 5: Related Rates

Lesson 6: The Mean-Value Theorem and L’Hopital’s Rule

Lesson 7: Practice Test

Lesson 2: Analyzing Functions Part II: Maximums and Minimums

Lesson 3: Applied Maximum and Minimum Problems

Lesson 4: Distance, Velocity, Acceleration, and Rectilinear Motion

Lesson 5: Related Rates

Lesson 6: The Mean-Value Theorem and L’Hopital’s Rule

Lesson 7: Practice Test

Lesson 1: Area Approximation and Riemann Sums

Lesson 2: Introduction to the Definite Integral

Lesson 3: The Fundamental Theorem of Calculus

Lesson 4: Integrals and Antiderivatives

Lesson 5: Integration by Substitution

Lesson 6: Integration by Parts – Optional

Lesson 7: The Definite Integral

Lesson 2: Introduction to the Definite Integral

Lesson 3: The Fundamental Theorem of Calculus

Lesson 4: Integrals and Antiderivatives

Lesson 5: Integration by Substitution

Lesson 6: Integration by Parts – Optional

Lesson 7: The Definite Integral

Lesson 1: Finding The Area Under and Between Curves

Lesson 2: Volume by Discs (Slicing)

Lesson 3: Volume by Shells

Lesson 4: Work

Lesson 5: Average Value of a Function and Rectilinear Motion Revisited

Lesson 2: Volume by Discs (Slicing)

Lesson 3: Volume by Shells

Lesson 4: Work

Lesson 5: Average Value of a Function and Rectilinear Motion Revisited

Lesson 1: Differential Equations – An Introduction

Lesson 2: Initial Value Problems, Slope Fields, and Euler’s Method

Lesson 3: Linearization and Newton’s Method

Lesson 4: Numerical Approximation Methods with Integrals

Lesson 2: Initial Value Problems, Slope Fields, and Euler’s Method

Lesson 3: Linearization and Newton’s Method

Lesson 4: Numerical Approximation Methods with Integrals

Lesson 1: Exploring the Graphs of f, f’, and f” (Revisited)

Lesson 2: Relative Rates of Growth

Lesson 3: Using Calculus With Data in a Table

Lesson 4: Functions Defined By Integrals

Lesson 5: Integration by Parts (Review) – Optional

Lesson 6: Integrating Using Partial Fractions – Optional

Lesson 7: Improper Integrals – Optional

Lesson 2: Relative Rates of Growth

Lesson 3: Using Calculus With Data in a Table

Lesson 4: Functions Defined By Integrals

Lesson 5: Integration by Parts (Review) – Optional

Lesson 6: Integrating Using Partial Fractions – Optional

Lesson 7: Improper Integrals – Optional

Lesson 1: Parametric Curves

Lesson 2: Polar Curves

Lesson 3: Vector Curves

Lesson 4: Length of Planar Curves

Lesson 5: Area of Planar Curves (Polar Curves only)

Lesson 2: Polar Curves

Lesson 3: Vector Curves

Lesson 4: Length of Planar Curves

Lesson 5: Area of Planar Curves (Polar Curves only)

Lesson 1: Series

Lesson 2: Convergence

Lesson 3: Tests for Convergence Part I

Lesson 4: Tests for Convergence Part II

Lesson 5: Error Bound

Lesson 2: Convergence

Lesson 3: Tests for Convergence Part I

Lesson 4: Tests for Convergence Part II

Lesson 5: Error Bound

Lesson 1: Maclaurin Series

Lesson 2: Taylor Series and Error Bound

Lesson 3: Power Series

Lesson 4: Radius and Interval of Convergence

Lesson 5: Applications of Polynomial Series

Lesson 2: Taylor Series and Error Bound

Lesson 3: Power Series

Lesson 4: Radius and Interval of Convergence

Lesson 5: Applications of Polynomial Series

Lesson 1: Roller Coaster Project Part I

Lesson 2: Roller Coaster Project Part II

Lesson 3: Fish Stock Populations Project

Lesson 2: Roller Coaster Project Part II

Lesson 3: Fish Stock Populations Project

## Experience a lesson as your students would

## Don’t Take Our Word for It!

## See What Others Have to Say:

After my students had been using the StudyForge AP Calculus Curriculum I was thrilled as the number of students who scored a “5/5” on the AP exam almost doubled! – But I am even more thrilled now after discovering the reporting tools they have created to empower me as an online teacher!

## JOYCE

## Online AP Calculus Teacher at Sevenstar Academy

I think the videos are excellent. Unlike lectures, I can actually rewind back and forth as much as I want. In class, students kind of miss important information because they are busy writing notes.

## Alice

## AP Calc Student

This course prepared me well because I was able to get a 5/5 on the College Board Exam…

## Nick

## AP Calc Student

I love the course! I like how it’s really simple to understand and how everything is organized and it’s easy to access resources.

## Alina

## AP Calc Student

## Course Features

- Many lessons include fun, interactive applets and dynamic graphs which help foster a conceptual and even intuitive understanding of fundamental topics.
- Digital DESMOS Graphing Calculator within the course

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