AP Calculus AB

Placement Test Available

Enroll in this Course

Open to: Grades 9 - 12

Prerequisites: Qualifying math score and completion of Precalculus with Trigonometry or the equivalent

Course Format: Individually Paced

Course Length: Typically 6 Months

Recommended School Credit: 1.0 credit

Course Code: CAB

Course Description

Description

This AP Calculus AB course covers topics typically found in a first-year college Calculus I course and explains topics in differential and integral calculus. This course prepares students to succeed in the Advanced Placement (AP) Calculus AB exam and the subsequent courses. Students will learn calculus by actively becoming engaged with the lectures, readings, animations, activities, and resources in the online textbook. In addition to the online textbook, students will be provided with written materials. Students can progress at their own rate with full comprehension of the course materials. Student knowledge will be assessed by completion of weekly exercises, online tutorials, supplementary readings, homework assignments, chapter tests, and other activities. This course has been reviewed and approved by the College Board to use the "AP" designation.

Topics include:

functions
graphs
limits and continuity
derivatives of basic functions
applications of the derivative
implicit differentiation
curve sketching
related rates
implicit differentiation to find the derivative of an inverse function
integration
applications of integration
geometric interpretation of differential equations via slope fields
L’Hopital’s rule

Timelines

Both 6-month and 3-month timelines are provided as possible guidelines for students to follow in order to finish within their desired time frame.

Students intending to take the AP exam should enroll by early January at the latest to allow enough time to complete the course before the May test date.

Materials Needed

Graphing calculator required, such as:

TI-83 PLUS
TI-84 PLUS
TI-85
TI-86
TI-89*

*Recommended

Although no textbooks are required for Calculus AB, students may find it helpful to use a single variable calculus textbook as a reference book, such as:

Calculus of a Single Variable (8th ed.) by Larson, Hostetler, and Edwards; Houghton Mifflin.

ISBN: 0618503048

Detailed Course Information

Course Details

To view detailed course information, please click here:

AP Calculus AB course details

System Requirements

CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course requires high-speed Internet access (such as Cable or DSL) for online lesson videos. Your browser will need to allow javascript, login cookies, and popup windows from ctyjhu.org, bluejay.cty.jhu.edu, and any other course web sites.

You may also need the Java Runtime Environment.

6 Month and 3 Month Timelines

Timelines

AP Calculus AB - 6 Month Timeline
AP Calculus AB - 3 Month Timeline

AP Calculus AB - 6 Month Timeline

Week	Topics Covered	Activities: Exercises, Discussion, Assigments, and Labs	Chapter test
1	Chapter 1: The Basics 1.1 Overview 1.2 Precalculus Review Chapter 2: Limits 2.1 Concepts of the Limit 2.2 Evaluating Limits Supplementary notes Intermediate Theorem Squeeze Theorem	Exercises 1.1.1 through 1.2.4 Exercises 2.1.1 through 2.2.4 Discussion 1: Calculus History Chapter 2 Homework	Chapter 2 test
2	Chapter 3: Introduction to Derivatives 3.1 Understanding the Derivative 3.2 Using Derivative 3.3 Some Special Derivatives Supplementary note Differentiability	Exercises 3.1.1 through 3.3.2 Calculus Lab 1: Average and Instantaneous Velocity Chapter 3 Homework	Chapter 3 & 4 test
3	Chapter 4: Computational Techniques 4.1 The Power Rule 4.2 The Product and Quotient Rules	Exercises 4.1.1 through 4.2.2
4	4.3 The Chain Rule	Exercises 4.3.1 through 4.3.3 Chapter 4 Homework
5	Chapter 5: Special Functions 5.1 Trigonometric Functions 5.2 Exponential Functions	Exercises 5.1.1 through 5.2.2	Chapter 5 test
6	5.3 Logarithmic Functions Supplementary note Differentiation Notation	Exercises 5.3.1 through 5.3.3 Discussion 2: Concept of Derivative Chapter 5 Homework	Chapter 5 test
7	Chapter 6: Implicit Differentiation and Calculus of Inverse Function 6.1 Implicit Differentiation Basics 6.2 Applying Implicit Differentiation	Exercises 6.1.1 through 6.2.2	Chapter 6 test
8	6.3 Inverse Functions 6.4 The Calculus of Inverse Functions 6.5 Inverse Trigonometric Functions Supplementary note Derivative of Function Inverses	Exercises 6.3.1 through 6.5.3
9	6.6 The Calculus of Inverse Trigonometric Function 6.7 The Hyperbolic Functions	Exercises 6.6.1 through 6.7.3 Whiteboard Lab 1: Calculator Techniques on Function Derivatives and Graphs Chapter 6 Homework
10	Chapter 7: Practical Application of the Derivative 7.1 Position and Velocity 7.2 Linear Approximation	Exercises 7.1.1 through 7.2.3	Chapter 7 test
11	7.3 Optimization 7.4 Related Rates	Exercises 7.3.1 through 7.4.5 Calculus Lab 2: Volume of a Cylinder Discussion 3: Applications of Derivative
12	Supplementary note Local and Absolution Extreme Values	Chapter 7 Homework
12	AP Calculus AB Midterm Exam
13	Chapter 8: Curve Sketching 8.1 Introduction 8.2 Critical Points 8.3 Concavity Supplementary note Mean Value Theorem	Exercises 8.1.1 through 8.3.3	Chapter 8 test
14	8.4 Graphing Using the Derivative 8.5 Asymptotes	Exercises 8.4.1 through 8.5.5 Calculus Lab 3: Curve Sketching Chapter 8 Homework	Chapter 8 test
15	Chapter 9: The Basics of Integration and Differential Equations 9.1 Antiderivatives 9.2 Integration by Substitution	Exercises 9.1.1 through 9.2.2	Chapter 9 test
16	9.3 Illustrating Integration by Substitution 9.4 The Fundamental Theorem of Calculus	Exercises 9.3.1 through 9.4.5 Discussion 4: Fundamental Theorem of Calculus
17	9.5 Separable Differential Equations	Exercises 9.5.1 through 9.5.4 Chapter 9 Homework
18	Chapter 10: Applications of Integration 10.1 Motion 10.2 Finding Area Between Two Curves 10.3 Integrating with Respect to y	Exercises 10.1.1 through 10.3.3	Chapter 10 test
19	10.4 The Average Value of a Function 10.5 Finding Volumes Using Cross-Sections	Exercises 10.4.1 through 10.5.2
20	10.6 Disk and Washers 10.7 Shells	Exercises 10.6.1 through 10.7.3
21	10.8 Work 10.9 Moments and Centers of Mass Supplementary Pumping Out a Tank	Exercises 10.7.1 through 10.9.2 Whiteboard Lab 2: Calculator Techniques on Area Under the Curve and Numerical Integration Chapter 10 Homework
22	Chapter 11: Differential Equations 11.1 Separable Differential Equations 11.2 Exponential Growth and Decay Supplementary notes Slope Field	Calculus Lab 4: Slope Field
23	Chapter 12: L’Hopital’s Rule and Improper Integrals 12.1 Indeterminate Quotients	Exercises 12.1.1 through 12.1.4	Chapter 12 test
24	12.2 Other Indeterminate Forms	Exercises 12.2.1 through 12.24
25	12.3 Improper Integrals Supplementary Extra Remarks on Improper Integrals	Exercises 12.3.1 through 12.3.3 Chapter 12 Homework
26	Chapter 13: Review 13.1 The Close of Calculus I Chapter 14: Math Fun 14.1 Paradoxes 14.2 Sequences	Exercises 13.1.1 through 13.1.2 Discussion 5: Calculus Story and the Future	none
26	AP Calculus AB Final Exam

AP Calculus AB - 3 Month Timeline

Week	Topics Covered	Activities: Exercises, Discussion, Assigments, and Labs	Chapter test
1	Chapter 1: The Basics 1.1 Overview 1.2 Precalculus Review Chapter 2: Limits 2.1 Concepts of the Limit 2.2 Evaluating Limits Supplementary notes Intermediate Theorem Squeeze Theorem	Exercises 1.1.1 through 1.2.4 Exercises 2.1.1 through 2.2.4 Discussion 1: Calculus History Chapter 2 Homework	Chapter 2 test
1	Chapter 3: Introduction to Derivatives 3.1 Understanding the Derivative 3.2 Using Derivative 3.3 Some Special Derivatives Supplementary note Differentiability	Exercises 3.1.1 through 3.3.2 Calculus Lab 1: Average and Instantaneous Velocity Chapter 3 Homework	Chapter 3 & 4 test
2	Chapter 4: Computational Techniques 4.1 The Power Rule 4.2 The Product and Quotient Rules	Exercises 4.1.1 through 4.2.2
2	4.3 The Chain Rule	Exercises 4.3.1 through 4.3.3 Chapter 4 Homework
3	Chapter 5: Special Functions 5.1 Trigonometric Functions 5.2 Exponential Functions	Exercises 5.1.1 through 5.2.2	Chapter 5 test
3	5.3 Logarithmic Functions Supplementary note Differentiation Notation	Exercises 5.3.1 through 5.3.3 Discussion 2: Concept of Derivative Chapter 5 Homework	Chapter 5 test
4	Chapter 6: Implicit Differentiation and Calculus of Inverse Function 6.1 Implicit Differentiation Basics 6.2 Applying Implicit Differentiation	Exercises 6.1.1 through 6.2.2	Chapter 6 test
4	6.3 Inverse Functions 6.4 The Calculus of Inverse Functions 6.5 Inverse Trigonometric Functions Supplementary note Derivative of Function Inverses	Exercises 6.3.1 through 6.5.3
5	6.6 The Calculus of Inverse Trigonometric Function 6.7 The Hyperbolic Functions	Exercises 6.6.1 through 6.7.3 Whiteboard Lab 1: Calculator Techniques on Function Derivatives and Graphs Chapter 6 Homework
5	Chapter 7: Practical Application of the Derivative 7.1 Position and Velocity 7.2 Linear Approximation	Exercises 7.1.1 through 7.2.3	Chapter 7 test
6	7.3 Optimization 7.4 Related Rates	Exercises 7.3.1 through 7.4.5 Calculus Lab 2: Volume of a Cylinder Discussion 3: Applications of Derivative
	Supplementary note Local and Absolution Extreme Values	Chapter 7 Homework
	AP Calculus AB Midterm Exam
7	Chapter 8: Curve Sketching 8.1 Introduction 8.2 Critical Points 8.3 Concavity Supplementary note Mean Value Theorem	Exercises 8.1.1 through 8.3.3	Chapter 8 test
7	8.4 Graphing Using the Derivative 8.5 Asymptotes	Exercises 8.4.1 through 8.5.5 Calculus Lab 3: Curve Sketching Chapter 8 Homework	Chapter 8 test
8	Chapter 9: The Basics of Integration and Differential Equations 9.1 Antiderivatives 9.2 Integration by Substitution	Exercises 9.1.1 through 9.2.2	Chapter 9 test
8	9.3 Illustrating Integration by Substitution 9.4 The Fundamental Theorem of Calculus	Exercises 9.3.1 through 9.4.5 Discussion 4: Fundamental Theorem of Calculus
9	9.5 Separable Differential Equations	Exercises 9.5.1 through 9.5.4 Chapter 9 Homework
9	Chapter 10: Applications of Integration 10.1 Motion 10.2 Finding Area Between Two Curves 10.3 Integrating with Respect to y	Exercises 10.1.1 through 10.3.3	Chapter 10 test
10	10.4 The Average Value of a Function 10.5 Finding Volumes Using Cross-Sections	Exercises 10.4.1 through 10.5.2
10	10.6 Disk and Washers 10.7 Shells	Exercises 10.6.1 through 10.7.3
11	10.8 Work 10.9 Moments and Centers of Mass Supplementary Pumping Out a Tank	Exercises 10.7.1 through 10.9.2 Whiteboard Lab 2: Calculator Techniques on Area Under the Curve and Numerical Integration Chapter 10 Homework
11	Chapter 11: Differential Equations 11.1 Separable Differential Equations 11.2 Exponential Growth and Decay Supplementary notes Slope Field	Calculus Lab 4: Slope Field
12	Chapter 12: L’Hopital’s Rule and Improper Integrals 12.1 Indeterminate Quotients	Exercises 12.1.1 through 12.1.4	Chapter 12 test
12	12.2 Other Indeterminate Forms	Exercises 12.2.1 through 12.24
13	12.3 Improper Integrals Supplementary Extra Remarks on Improper Integrals	Exercises 12.3.1 through 12.3.3 Chapter 12 Homework
	Chapter 13: Review 13.1 The Close of Calculus I Chapter 14: Math Fun 14.1 Paradoxes 14.2 Sequences	Exercises 13.1.1 through 13.1.2 Discussion 5: Calculus Story and the Future	none
	AP Calculus AB Final Exam