Syllabus – AP Calculus AB
Course overview:
Calculus requires students to expand on many of the concepts that they have learned from previous
math courses. The relevance of these concepts is discovered through real world application problems
where science and math come together to explain the wonders of our physical world. I want students
to have a deeper understanding of how these concepts are applied. That means students will need to
stretch beyond number crunching and symbol manipulation. Topics addressed in class include Limits,
Continuity, Derivative Mechanics, Derivative Applications, Integration Mechanics, Integration
Applications and other related topics. Students are required to use precise language to describe these
concepts and the relationships between ideas. [C1]
Expectations:
Students are required to be active participants in the learning process. In order for students to be
successful in AP Calculus they should expect to work and study hard each day.
 Students can expect to take notes on a daily basis.
 A homework assignment will be given every class period.
 Students can expect a daily quiz to check for understanding of homework.
 Each unit will be tested with both multiple choice and short answer response questions.
 It is the students’ responsibility to seek extra help when they do not understand a concept or
skill. I suggest doing so immediately; do not wait until after the test to seek help. I am
available before school from 8:15 to 8:50 and after school from 3:50 to 4:15.
 I also suggest that students form study groups so as questions arise after school hours they
have a support network.
Functions from Multiple Representations
My goal is to show students the concepts of calculus are expressed in multiple ways. Many real life
situations use functions that can be expressed analytically, verbally, graphically or numerically. We
will work problems that represent all four of these representations throughout the year. Students will
be able to move with ease from one representation to another. [C2]
Justification of answers
Students are required to justify their answers on homework, quizzes and tests. Justifications should be
in the form of complete sentences. We will discuss the amount of work that it is necessary to show
and the correct way to justify your answer in class. [C3]
Technology
Students will be using a graphing calculator regularly during class. In addition, students can bring
their own device to school. Students are also encouraged to find apps for the iPad (or other device)
that are useful for explaining the concepts of Calculus. Although being in class for the lesson is
preferred, sometimes absences are unavoidable. The iPad apps can be very useful to explain lessons
that were missed or provide extra instruction as needed.
Graphing Calculator
It is highly recommended that students have their own graphing calculator. Students will be required
to bring your own calculator to the AP Exam. We have a class set of TI–84 plus calculators that
students can use during class, but homework assignments often require the use of a graphing
calculator. If you wish to purchase a calculator, I recommend the TI-84 or a TI-83. Do not buy a
calculator with a full QUARTY keyboard as they are not allowed on the AP Exam.
Students are expected to know basic calculator skills and be able to graph a function using an
appropriate window. During the review of elementary functions, we will explore how to use the
calculator to produce an equation using the regression equations from the STAT menu. The TABLE
feature will initiate our classroom discussions of the limit of a function. Many calculator dependent
solutions are based on manipulating graphs or understanding how several graphs are related to each
other. We will practice using the calculator to interpret results that are solved analytically. When a
function is expressed graphically, we can either describe its behavior in broad terms or provide details
of the function at specific points. When we use technology to graph and describe an analytical
function, we need to be sure that some of the behaviors are not being masked. [C4]
Assessments:
Students’ grades are based on the traditional methods of assessment such as tests, homework and
quizzes. Homework, quizzes and other daily classroom assignments will count as 30% of their
average, exams 70%. Exams not only address the concepts of the given unit, but they also are
designed to prepare students to know how to express their thinking in preparation for the AP exam. I
will include both AP style multiple choice and short answer questions on all exams throughout the
year. Students are required to answer some questions with a calculator and some without. All
questions will not be given full credit unless all the work is shown and answers are written in a
complete sentence. Students will also be assessed on their level of participation during class. We
will take turns presenting answers and being class leaders for the day. Also, due to time constraints,
and the necessity to keep all of the material fresh in our minds for the AP Exam, there will be
cumulative take home tests (in addition to the regular tests taken during class). Students are
encouraged to talk with each other, but expected to produce their own work; again credit is not
awarded to answers that have not been properly justified.
Review for AP Exam:
My goal is to leave some time before the exam to spend reviewing for the AP exam. We will go
through AP free response questions together in class to get an understanding of how the AP exam is
scored. Students will take mini tests in class with questions from released tests. Some questions allow
the use of a calculator and some do not. These mini tests will have the same time constraints as the AP
exam. We will then use the scoring guide to score the test. Also, I will hold after school review
sessions once a week during the month of April for any student that wishes to participate. I also
recommend students purchase an AP test prep book of some sort (new or used) to help in preparation
for the AP Exam.
Primary Textbook:

Anton, Howard, Irl Bivens, and Stephen Davis. Calculus: Early Transcendentals. 8th Edition.
John Wiley and Sons, 2005.
Supplemental Textbooks:


Larson, Ron, Robert P. Hostetler, and Bruce H. Edwards. Calculus with Analytic Geometry. 8th
Edition. Boston: Houghton Mifflin, 2006
Stewart, James. Single Variable Calculus: Concepts and Contexts. 4th edition. Brooks/Cole,
Belmont: Cengage Learning, 2010, 2005
Web/Other Resources:


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Published AP Tests
AP Central (apcentral.collegeboard.com)
Teacher created materials
AP Calculus Electronic Discussion Group
Contents of the Course
The following course contents are approximate; the number of days per unit may have to be
adjusted due to school wide testing days, weather conditions and other unforeseen events. [C1]
Unit 1 – Review, Limits & Continuity (appr. 9 days) – 1 Test
1.1 – 1.7 Selected Topics
2.1 Limits (An Intuitive Approach)
2.2 Computing Limits
2.3 Limits at Infinity; End Behavior of a Function
2.5 Continuity
Unit 2 – Derivative Mechanics (appr. 14 days) – 2 Tests
3.1 Tangent Lines, Velocity, and General Rates of Change
3.2 The Derivative Function
3.3 Techniques of Differentiation
3.4 The Product Rule and Quotient Rules
3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
4.1 Implicit Differentiation
4.2 Derivatives of Logarithmic Functions
4.3 Derivatives of Exponential and Inverse Trigonometric Functions
Unit 3 – Derivative Applications (appr. 15 days) – 2 Tests
5.1 Analysis of Functions I: Increase, Decrease, and Concavity
5.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials
5.3 More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical
Tangent Lines
5.4 Absolute Maxima and Minima
5.5 Applied Maximum and Minimum Problems
4.7 Related Rates
4.8 Local Linear Approximation; Differentials
5.7 Rolle’s Theorem; Mean-Value Theorem
5.8 Rectilinear Motion
Semester Test: Limits, Continuity & Derivatives Final
Unit 4 – Integration Mechanics (appr. 15 days) – 2 Tests
6.1 An Overview of the Area Problem
6.4 The Definition of Area as a Limit; Sigma Notation
6.5 The Definite Integral
6.2 The Indefinite Integral
6.6 The Fundamental Theorem of Calculus
6.3 Integration by Substitution
6.7 Rectilinear Motion Revisited Using Integration
6.8 Evaluating Definite Integrals by Substitution
6.9 Logarithmic Functions from the Integral Point of view
Unit 5 – Integration Applications (appr. 10 days) – 1 Test
7.1 Area Between Two Curves
7.2 Volumes by Slicing; Disks and Washers
7.3 Volumes by Cylindrical Shells
7.4 Length of a Plane Curve
7.6 Average Value of a Function and its Applications
Unit 6 – Integration Techniques & Topics (appr. 8 days) – 1 Test
8.1 An Overview of Integration Methods
8.5 Numerical Integration; Simpson’s Rule
9.1 First-Order Differential Equations and Applications
9.2 Slope Fields; Euler’s Method
9.3 Modeling with First-Order Differential Equations
AP Exam review is incorporated throughout the year in course work and activities,
as well as any time left after Unit 6.
[C1] – The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives;
Integrals as delineated in the Calculus AB Topic Outline in the AP Calculus Course Description.
[C2] – The course provides students with the opportunity to work with functions represented in a
variety of ways – graphically, numerically, analytically, and verbally – and emphasizes the
connections among these representations.
[C3] – The course teaches students how to communicate mathematics and explain solutions to
problems both verbally and in written sentences.
[C4] – The course teaches students how to use graphing calculators to help solve problems,
experiment, interpret results, and support conclusions.