## Advanced Placement® Calculus AB

**Instructor: Valerie Nandor, Ph.D.**

Email: DrValerieN@gmail.com

"Calculus transformed and broadened the way I thought about math. During my own study of calculus years ago, I gained insight into *functions* as I learned to consider the individual points that comprise a function as a single, continuous entity. For example, I now view calculation of interest, whether at a high or a low interest rate, as a single problem which morphs gradually from simple interest to compound interest to continuously compounded interest, rather than as three discrete problems.

We will study the “big ideas” of Calculus – limits and continuity (which restrict and define the allowed values of a function); derivatives (generalizing the concept of slope to examine how functions change in response to a change in a variable); and integrals (adding up small intervals to find a total accumulation, such as the area enclosed within a curve or the distance traveled by an object with a changing acceleration). I am excited to share my appreciation for the beauty and richness of functions with my students."

-- Valerie Nandor, Ph.D.

AP® Course Audit Authorization for Calculus AB

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**Course Description**

This is a college-level calculus course designed to meet the Advanced Placement® curricular requirements for Calculus AB. The course is organized around the big ideas of limits, derivatives, and integrals. Within each topic, connections between equations, graphical representations, and verbal descriptions will be emphasized as students build a conceptual understanding of calculus and develop computational calculus skills.

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**The successful student will:**

- Recognize this is a college level calculus class
- Value that developing a thorough understanding of the material presented in this class will prepare them for the AP Calculus AB test
- Appreciate that calculus topics and skills build upon previous material and make a commitment to keep up with the class
- Respect process and clear communication equally with correct answers
- Engage with their classmates by working together on activities and sharing questions and insights
- Formulate and ask questions

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**Prerequisite Classes and Skills:**

- Successful completion of Geometry, Algebra II and Precalculus classes
- Mastery of the following skills
- Evaluating functions, following correct order of operations
- Solving linear equations
- Writing equations of lines and graphing linear functions
- Factoring, solving, and graphing quadratic functions
- Solving two simultaneous linear equations
- Graphing systems of inequalities
- Evaluating trigonometric functions at standard angles

- Working knowledge of the following skills
- Reducing and combining complex fractions
- Working with composite functions
- Identifying domains of functions
- Rearranging and evaluating logarithmic and exponential expressions
- Graphing and solving logarithmic and exponential functions
- Factoring and solving quadratic-like functions
- Factoring and solving quadratic trigonometric functions
- Using Pythagorean identities and other trigonometric identities to simplify trigonometric expressions
- Graphing trigonometric functions
- Evaluating inverse trigonometric functions

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**Required Materials:**

- The textbook for the class is Swokowski, Earl, Michael Olinick, Dennis D. Pence.
*Calculus*, 6th ed. Boston: Brooks Cole, 1996.- Students could instead purchase Swokowski’s
*Calculus of a Single Variable*, 2nd ed. which contains all of the chapters which will be studied in this course (but doesn’t include later chapters). - Used copies of both of these books are widely available.

- Students could instead purchase Swokowski’s

- Every student is required to own an AP-approved graphing calculator and use the graphing calculator for both in-class work and homework.
- The
**TI-84 graphing calculator**is suggested and will be used for demonstrations during class.

- The
- Students must have the ability to scan and email a document.

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**Classroom Expectations:**

- Students are expected to actively engage with their classmates by working together on activities and sharing insights and questions. Formulating questions and clearly communicating reasoning is valued during class discussions.
- Students are expected to complete homework assignments and take-home tests as assigned. Since Calculus topics build upon previous topics, it is extremely important to keep current with the class material.

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**At-home Expectations:**

- Students should expect to spend 3 - 4 hours between each class meeting to review notes, read the textbook, study for tests, complete any tests or quizzes, finish any at-home explorations, and do homework problems.
- A typical student should allocate up to 8 hours a week to work on this class outside of the webinar. However, there is no guarantee that an individual student won’t require more than 8 hours a week for this class.

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**Grading:**

- 80% tests and quizzes
- 20% participation

Final grades will be assigned using the following scale:

97.0 – 100% A+

93.0 – 96.9% A

90.0 – 92.9% A-

87.0 – 89.9% B+

83.0 – 86.9% B

80.0 – 82.9% B-

77.0 - 79.7% C+

73.0 - 76.9% C

70.0 – 72.9% C-

67.0 – 69.9% D+

63.0 – 66.9% D

60.0 – 62.9% D-

Below 60.0% F

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**Tests and Quizzes:**

There will be 1 – 2 quizzes during each chapter and 1 test at the end of each chapter.

Students will be on their honor to complete the quizzes and tests according to the directions

- Within the time allotted
- No resources allowed, other than a graphing calculator where indicated
- All work must be the students’ own work

Each problem will be graded on three components

- Correct notation and communication
- Calculus principles and algorithms applied
- Correctness of final solution

Tests and quizzes will be completed at home, scanned, and emailed to Dr. Valerie.

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**Participation:**

Student participation is integral to class discussions and activities. Asking questions, working with other students to create examples, and sharing insights and your own unique understanding of processes and theorems are all equally valuable.

Participation grades will include:

- Engagement in class discussions
- Participation in homework review
- Working with other students during in-class explorations
- Sharing results of at-home explorations
- Turning in corrected homework at end of each chapter

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**Homework:**

Homework is designed to assist students in learning the material and consists of a cycle of activities:

- Complete as many of the problems as you can, using class notes, examples, and the textbook as reference
- Discuss homework problems during class (on the assigned due date)
- Correct homework solutions and complete any remaining questions after class, consulting posted homework solutions as necessary
- Ask for additional help or resources as necessary
- Redo selected homework problems, without using any reference material, as one component of studying for a quiz or test

Homework will include both textbook problems and published AP exam questions.

Corrected and completed homework will be scanned and emailed to Dr. Valerie at the end of each chapter.

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**Explorations:**

Exploration activities allow students to build a conceptual understanding of calculus, complementing and connecting to the computational skills students are developing.

Some provide opportunities for students to reason with definitions and theorems, build notational fluency, and connect concepts and processes. Other activities present students with multiple representations of a function (graphical, numerical, analytical, and verbal) and build connections among them.

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**Course Outline:**

Limits and Continuity --

- Introduction to Limits (Section 1.1)
- Definition of Limit (Section 1.2)
- Techniques for Finding Limits (Section 1.3)
- Limits Involving Infinity (Section 1.4)
- Continuous Functions (Section 1.5)

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The Derivative --

- Tangent Lines and Rates of Change (Section 2.1)
- Definition of Derivative (Section 2.2)
- Techniques of Differentiation (Section 2.3)
- Derivatives of the Trigonometric Functions (Section 2.4)
- The Chain Rule (Section 2.5)
- Implicit Differentiation (Section 2.6)
- Related Rates (Section 2.7)

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Applications of the Derivative --

- Extrema of Functions (Section 3.1)
- The Mean Value Theorem (Section 3.2)
- The First Derivative Test (Section 3.3)
- Concavity and the Second Derivative Test (Section 3.4)
- Summary of Graphical Methods (Section 3.5)
- Optimization Problems (Section 3.6)
- Velocity and Acceleration (Section 3.7)
- Applications to Economics, Social Sciences, and Life Sciences (Section 3.8)

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Integrals --

- Antiderivatives, Indefinite Integrals, and Simple Differential Equations (Section 4.1)
- Change of Variables in Indefinite Integrals (Section 4.2)
- Summation Notation and Area (Section 4.3)
- The Definite Integral (Section 4.4)
- Properties of the Definite Integral (Section 4.5)
- The Fundamental Theorem of Calculus (Section 4.6)
- Numerical Integration (Section 4.7)

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Applications of the Definite Integral --

- Area (Section 5.1)
- Solids of Revolution (Section 5.2)
- Volumes by Cylindrical Shells (Section 5.3)
- Volumes by Cross Sections (Section 5.4)

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Transcendental Functions --

- The Derivative of the Inverse Function (Section 6.1)
- The Natural Logarithm Function (Section 6.2)
- The Exponential Function (Section 6.3)
- Integration Using Natural Logarithm and Exponential Functions (Section 6.4)
- General Exponential and Logarithmic Functions (Section 6.5)
- Separable Differential Equations and Laws of Growth and Decay (Section 6.6)
- Additional practice with Separable Differential Equations and Slope Fields (class notes)
- Indeterminate Forms and l’Hopital’s Rule (Section 6.9)

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For questions or more information about this course please contact:

**Instructor: Valerie Nandor, Ph.D.**

Email: DrValerieN@gmail.com

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