Mr. Murphy - Swartz Creek High School

AP® Calculus AB Course Syllabus

AP Calculus is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. The connections among these representations also are important. (The College Board – AP Calculus Teacher’s Guide)

Teaching Strategies

Lessons are typically introduced in lecture format using presentation software and the SmartBoard.  These lessons often include video clips of worked problems in addition to the live presentation by the instructor.  The lectures typically take one class period and then the following one to two days are used to work problems, either in groups or individually.  Classes may begin with a starter problem on the board or with students assigned to the whiteboards to present their work.

 

Throughout the course, emphasis will be placed on reading and writing mathematics for understanding.  Students will be challenged to write complete and thoughtful solutions that not only solve a problem, but also demonstrate understanding of the underlying concepts.  This expectation will hold for homework assignments, quizzes, and tests, as well as in-class presentation of solutions.  Students will be required in all of these areas, to write descriptive English sentences as well as mathematical sentences that communicate understanding of the concepts.  Emphasis will be placed on communicating to a varied audience, both with writing and speaking.

 

Students are encouraged to ask questions.  These concepts can be challenging and may take time and effort to master.  We will work as a group to meet these challenges together.

Graphing Calculator and Other Technology

When appropriate, we will make use of the TI-83/TI-84 graphing calculator. Chapter tests will have two components: one without the use of any calculator and the other half requiring the use of a graphing calculator. The graphing calculator allows the student to support their work graphically, make conjectures regarding the behavior of functions and limits among other topics thus allowing students to view problems in a variety of ways. The calculator helps students develop a visual understanding of the material. The most basic skills on the calculator: graphing a function with an appropriate window, finding roots and points of intersection, finding numerical derivatives and approximating definite integrals, should be mastered by all students. We will also utilize programs for the calculator such as Riemann sums, slope fields, and Newton’s method.

 

These graphing calculators are a great tool for experimenting with functions and graphical data.  They provide a platform for investigation of changes in conditions in a fast and efficient manner, allowing students to explore behavior without being bogged down in tedious calculation.  We will also rely on graphing calculators to interpret our results found by analytical means and support our conclusions to problems.  Students will be required to demonstrate that their solutions are backed up by the calculator and be able to communicate this effectively in writing.

 

Students will also be introduced to other computer resources, including many that are freely on the internet.  We’ll make use of Geogebra for graphical analysis and access videos and tutorials available online.

Tests

As with the AP Test, chapter tests are divided into two parts, “No Calculator”, “Graphing Calculator Required”. These tests may be held over a two-day period in some cases.

Grading

Semester grades are calculated as follows: 40% Marking Period 1, 40% Marking Period 2, 20% Final Exam.  Each marking period grade is a combination of homework, quizzes, tests, and student attendance, as specified in the student handbook.  Categories are weighted as follows: 20% assignments, 30% quizzes, 50% tests.  There will be approximately eighteen assignments, six quizzes, and three tests per marking period.  Grades are updated through PowerSchool on a regular basis.  You may view them at your convenience.

Text

Thomas' Calculus Early Transcendentals, Media Upgrade, 11th Edition. George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Giordano. ISBN-10: 0321495756 2008.

Other Resources

Class Website: http://dragonometry.net, AP Calculus Course Description, AP Released Exams

Chapter 1 Functions

Days

1.1 Functions and Their Graphs        

2

1.2 Identifying Functions; Mathematical Models

2

1.3 Combining Functions; Shifting a`nd Scaling Graphs

2

1.4 Graphing with Calculators and Computers

1

1.5 Exponential Functions

2

1.6 Inverse Functions

2

 

Chapter 2 Limits and Continuity

Days

2.1 Rates of Change and Limits        

2

2.2 Calculating Limits Using the Limit Laws

2

2.3 The Precise Definition of a Limit

2

2.4 One-Sided Limits and Limits at Infinity

2

2.5 Infinite Limits and Vertical Asymptotes

2

2.6 Continuity

2

2.7 Tangents and Derivatives

2

 

Chapter 3  Differentiation

Days

Part 1

3.1 The Derivative as a Function

2

3.2  Differentiation Rules for Polynomials, Exponentials,…

2

3.3 The Derivative as a Rate of Change

2

3.4 Derivatives of Trigonometric Functions

2

3.5 The Chain Rule

3

Part 2

3.6 Implicit Differentiation

3

3.7 Derivatives of Inverse Functions and Logarithms

2

3.8 Inverse Trigonometric Functions

2

3.9 Related Rates

3

3.10 Linearization and Differentials

2

Chapter 4 Applications of Differentiation

Days

4.1 Extreme Values of Functions

1

4.2 The Mean Value Theorem

2

4.3 Monotonic Functions and the First Derivative Test

2

4.4 Concavity and Curve Sketching

3

4.5  Applied Optimization Problems 

3

 

Chapter 5 Integration

Days

Part 1

4.8 Antiderivatives

2

5.1 Estimating with Finite Sums

1

5.2 Sigma Notation and Limits of Finite Sums

1

5.3 The Definite Integral

2

5.4 The Fundamental Theorem of Calculus

3

Part 2

5.5  Indefinite Integrals and the Substitution Rule

3

5.6 Substitution and Area Between Curves

3

Chapter 6 Applications of Definite Integrals        

Days

6.1 Volumes by Slicing and Rotation About an Axis

3

6.2  Volumes of Cylindrical Shells

3

6.3 Lengths of Plane Curves 

2

Chapter 7 Integrals and Transcendental Functions

Days

7.1. The Logarithm Defined as an Integral

2

7.2 Exponential Growth and Decay

3

Chapter 8 Techniques of Integration

Days

8.1 Basic Integration Formulas

3

8.7 Numerical Integration

2

Chapter 9 Further Applications of Integration

Days

9.1  Slope Fields and Separable Differential Equations

3

 

Review and Preparation for the AP Exam

Days

We’ll spend this time completing sample AP exam items in preparation for the AP exam.  Students will be assigned problems both in class and as homework and will work both individually  and in groups.

20

After the AP Test

Days

After the AP Test, we will still have roughly a month of school remaining.  In that time we will explore the following lessons, some in detail and some at an introductory level.

20

Part 1

4.6 Indeterminate Forms and L'Hopital's Rule
4.7 Newton's Method

Part 2

6.4 Moments and Centers of Mass
6.6  Work
6.7 Fluid Pressures and Forces

Part 3

8.2 Integration by Parts
8.3 Integration ... by Partial Fractions
8.4 Trigonometric Integrals
8.5 Trigonometric Substitutions
8.8  Improper Integrals