AP Calculus AB Syllabus 2013-2014
Instructor: Mr. Connor
Location: Room 323
Email: jconnor@bradfordareaschools.org
Office hours: Before and after school, period 5A
Text Book: Larson, Hostetler, & Edwards, 2006, Calculus of a Single Variable, 8th edition,
Course Overview:
Calculus is the gate through which students wanting advanced training in most scientific,
mathematical and technical fields must pass. This full year scholar course provides the
academically talented high school senior with the equivalent of a semester of college calculus.
Since a full year is devoted to the course, more emphasis can be placed on multiple methods of
solving problems. Students will explore the traditional, algebraic approach to calculus as well as
use graphing calculators to represent functions numerically, graphically, and symbolically.
Major topics include the theory and application of limits, continuity, derivatives, and integration.
Calculator: Texas Instruments TI-84 Plus. Calculators are a very important part of this course.
They will be used to interpret results and support conclusions by examining graphs and tables of
values. The calculators will also be used to find zeros of a function, compute the derivative of a
function numerically, and compute definite integrals numerically. Calculators are provided by
the school and may be signed out for at home use.
Grading: Grades will be assigned according to the Bradford Area School District Grading scale
and policy. 6-6 week grades are computed using the following weighted scale.
Tests – 45% - There will be one test a marking period which will include released AP
questions. As we progress through the year the tests will be comprised entirely of released AP
questions.
Quizzes – 30% - Expect 3 to 4 quizzes a marking period
Released AP Questions – 20% - At least once a marking period, students will be given a set of
released AP questions to complete and turn in for a grade. This is essentially a take home quiz.
Practice Problems – 5% - At various points during each marking period, the class will complete
problems sets or projects in class.
Review for the AP exam
This schedule leaves about 3 weeks for review of topics before the Advanced Placement test.
Throughout the course, I will be giving the students practice problems to work on. They will be
given multiple choice and free-response questions relating to the chapter that we are working on.
Each free response question will need to have written explanations with them. The explanations
must be submitted in a paragraph like format. We will compare different questions already
written out to see what different scores look like given the criteria. Each student is required to
complete these questions and hand them in for a grade. I will hold study sessions after school to
get help on the question. A few Saturdays before the exam, I will hold practice exams for them
to try, and grade them to see where they stand. After each exam I will go over all the questions
in class, and have them fix their mistakes. These make for good study guides for the test.
Course Timeline:
Chapter 1: Limits and Their Properties (2-3 weeks)
A Preview of Calculus
Finding Limits Graphically and Numerically
Definition
Properties
Evaluating Limits Analytically
Trig Limits
Limits with radicals
Limits of composition functions
Limits of functions that agree at all but one point
Continuity and One-Sided Limits
One and two sided limits
Removable discontinuity
Nonremovable discontinuity – Jump, asymptote, or oscillating
Intermediate Value Theorem for continuous functions
Infinite Limits
Asymptotic behavior
End behavior
Visualizing limits
Chapter 2: Differentiation (5-6 weeks)
2.1 The Derivative and the Tangent Line Problem
Tangent to a curve
Slope of a curve
Normal to a curve
Definition
2.2 Basic Differentiation Rules and Rates of Change
Constant, Power, Sum and Difference, and Constant Multiple Rules
Sine and Cosine
Rates of Change
2.3 Product and Quotient Rules and Higher-Order Derivatives
Product and Quotient Rules
Trigonometric functions
Second and higher order derivatives
Acceleration due to gravity
2.4 The Chain Rule
Composition of a function
Power Rule
Trig functions with the Chain Rule
2.5 Implicit Differentiation
Implicit and Explicit functions
Differential method
Second derivative implicitly
Slope, tangent, and normal
2.6 Related Rates
Applications to derivatives
Guidelines for related rate problems
Chapter 3: Applications of Differentiation (4-5 weeks)
3.1 Extrema on an Interval
Relative extrema
Critical numbers
Finding extrema on a closed interval
Absolute extrema
3.2 Rolle’s Theorem and the Mean Value Theorem
Illustrating Rolle’s Theorem
Tangent line problems and instantaneous rate of change problems with the Mean Value Theorem
3.3 Increasing and Decreasing Functions and the First Derivative Test
Testing for increasing and decreasing
First Derivative Test for extrema
Applications
3.4 Concavity and the Second Derivative Test
Testing for concavity
Points of inflection
Second Derivative Test for extrema
3.5 Limits at Infinity
Horizontal Asymptotes
Limits at infinity
Trig functions
Infinite limits at infinity
3.6 A summary of Curve Sketching
Rational functions
Radical functions
Polynomial function
Trig function
3.8 Newton’s Method
Approximate zeros
3.9 Differentials
Tangent line approximation
Error propagation
Chapter 4: Integration (4-5 weeks)
4.1 Antiderivatives and Indefinite Integration
Definition
Integration Rules
Vertical Motion
4.2 Area
Sigma notation
Upper and lower sums
4.3 Riemann Sums and Definite Integrals
Subintervals with equal and unequal widths
Definition
Continuity
Area of a region
Properties of definite integrals
4.4 The Fundamental Theorem of Calculus
Guidelines for using FTC
Mean Value Theorem for integrals
Average Value of a function
Second fundamental theorem
4.5 Integration by Substitution
Composition function
Change of variables
Power rule for integration
4.6 Numerical Integration
Trapezoidal Rule
Simpson’s Rule
Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions, Chapter 6:
Differential Equations (5 weeks)
5.1 The Natural Logarithmic Function: Differentiation
Definition
Properties of the Natural Logarithmic Function
Definition of e
Derivative of ln
5.2 The Natural Logarithmic Function: Integration
Log rule for integration
Trig functions
5.3 Inverse Function
5.4 Exponential Functions: Differentiation and Integration
Definition of
Operations and properties with exponential functions
6.1 Slope Fields and Euler’s Method
General and particular solutions
Slope fields – Visualizing and sketching
Approximating solutions with Euler’s method
6.2 Differential Equations: Growth and Decay
Growth and decay model
Chapter 7: Applications of Integration (3-4 weeks)
7.1 Area of a Region Between Two Curves
Area between two curves
Intersecting curves
7.2 Volume: The Disk Method
Disk and washer method
7.3 Volume: The Shell Method
Teaching Strategies:
I try to make my teaching as differentiated as possible. Students are taught through
lecture, explorations, group work, graphing calculators, and class discussions. Students are
evaluated based on quizzes and tests. Homework is not graded, unless it is practice questions for
the AP exam. I feel homework is for their benefit, and if they want to do well on tests and
quizzes, they will need to keep up with the homework. Tests include a variety of questions, from
explanation, to plain old plug and chug. Most questions will require students to write out
explanations in a paragraph format. This strategy gets them used to using well written sentences
on the AP free response questions. AP style questions are used on tests and quizzes throughout
the year. The students keep an index of terminology related to Calculus in the back of their
notebooks. This proves as a useful tool when trying to figure out problems, where they get stuck
on the language. Students are encouraged to form study groups outside of class, and/or attend
the after school tutoring program offered through the school. My goal is for them to become self
learners, and to better prepare them for the college setting.
6-6 week grades are computed on a point system using quizzes, test, practice AP problems, and
activities and/or labs.
Homework: Given, but not graded, unless they are the practice AP problems. 5 AP questions
will be given and graded each six weeks. They will consist of 3 multiple choice and 2 free
response. The free response questions will need to have written explanations or they will not be
accepted. If they are not well written, the questions will be handed back for them to resubmit.
(25 points)
Quizzes: Given usually after each section, some sections are combined. (Points vary)
Tests: Given after each chapter. (100 points each)
Tests are used as a 7th marking period grade. They are all totaled and averaged at the end of the
year. These tests are considered their finals.
Some questions allow calculators, while others will not.
Student Activities:
Most activities will be used in conjunction with the graphing calculator. All three approaches to
problem solving will be utilized: numerical, graphical, and/or analytical. I will have them work
collaboratively in groups to decide what method would be best for the given problem. With each
problem the students will be expected to write down explanations on what they did and why they
did it.
Possible Calculator Topics:
Domain and range
Points of intersection
Roots of a function
1. Graphing functions
2. Limits: Graphical and Numerical
3. Tangent Lines
4. Derivatives: Approximate at a specific point
5. Integrals
6. Optimization
7. Related Rates
8. Slope Fields
Other activities and labs will be used throughout the year. An example of one of the activities
would be used during Chapter P – Preparation for Calculus.
Students will all be given cards with one of three graphs on it. The graphs will either be the
original function or the function with translations. There will be two other people on the room to
match up with. They will have to decide amongst themselves whether they are the parent graph,
or the translation. Once they have decided who is who, they will also need to write the equation
for their graphs. The other groups will decide if their equations are right or wrong.
Another activity comes from Chapter 2 – Derivatives.
Students will all be given cards with one of three graphs on it. The graphs will either be the
original function, the first derivative of the function, or the second derivative of the function.
The students will need to match up with the two other people in the room whose functions and
derivatives match. They will have to decide amongst themselves if they are the function, the first
derivative, or the second derivative.