AP Calculus AB
Syllabus
Wyalusing Valley Jr/Sr High School
Course Overview
My main objective in teaching AP Calculus is to enable students to appreciate the beauty
of calculus and receive a strong foundation that will give them the tools to succeed in
future mathematics courses. Students know they will work harder than ever, and our
expectation is that this hard work will enable them to succeed in the course. We work
together to help students discover the joys of calculus.
Course Planner
AP Calculus Syllabus
Chapter 1 Prerequisites for Calculus
Days
11
1.1 Lines
1.2 Functions and Graphs
1.3 Exponential Functions
1.4 Parametric Equations
1.5 Functions and Logarithms
1.6 Trigonometric Functions
Review Exercises/Test
1
2
1
2
1
2
2
Chapter 2 Limits and Continuity
2.1 Rates of Change and Limits
2.2 Limits Involving Infinity
2.3 Continuity
2.4 Rates of Change and Tangent Lines
Review Exercises/Test
Chapter 3 Derivatives
3.1 Derivative of a Function
3.2 Differentiability
3.3 Rules of Differentiation
3.4 Velocity and Other Rates of Change
3.5 Derivatives of Trigonometric Functions
3.6 Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Inverse Trigonometric Functions
3.9 Derivatives of Exponential and Logarithmic Functions
Review Exercises/Test
11 days
2
2
2
2
2
31 days
3
3
4
4
3
3
2
2
4
3
Chapter 4 Applications of Derivatives
4.1 Extreme Values of Functions
4.2 Mean Value Theorem
4.3 Connecting f’ and f’ with the Graph of f
4.4 Modeling and Optimization
4.5 Linearization (and Newton’s Method optional)
4.6 Related Rates
Review Exercises/Test
Chapter 5 The Definite Integral
5.1 Estimating with Finite Sums
5.2 Definite Integrals
5.3 Definite Integrals and Antiderivatives
5.4 Fundamental Theorem of Calculus
5.5 Trapezoidal Rule
Review Exercises/Test
Chapter 6 Differential Equations and Mathematical Modeling
25 days
5
2
4
5
3
3
3
26 days
3
4
8
5
3
3
20 days
6.1 Slope Fields Euler’s Rule
6.2 Antidifferentiation by Substitution
6.3 Antidifferentiation by Parts
6.4 Exponential Growth and Decay
6.5 Logistic Growth
Review Exercises/Test
5
4
4
4
3
Chapter 7 Applications of Definite Integrals
days
21
7.1 Integral as Net Change
7.2 Areas in the Plane
7.3 Volumes
7.4 Lengths and Curves
7.5 Applications from Science and Statistics
Review Exercises/Test
5
3
5
5
3
Technology
Teachers and students use TI-83 graphics calculators for all class work, evaluations, and
home work and practice problems for the AP exam. We use the calculator to investigate
concepts before using basic theoretical algebraic techniques. Several required uses of
functions are stressed such as: finding the zeros of a function; graphing functions in
different specified windows; finding the derivative using tables; finding the definite
integral using tables. In finding the derivative of functions, we begin with a basic
trigonometric function such as y = sin x. Students then estimate the slopes at various
points so they can then predict what the derivative would be.
Student Evaluation
Six week grades are computed using homework, writing, quizzes, and tests as individual
categories. Each six week grade represents 40 percent of the semester grade. The
midterm and final represent the remaining 20 percent of the grade. Students are
permitted to use a calculator on almost all assignments. As early as possible, practice AP
multiple choice problems are incorporated into evaluations. Midterms and Finals include
mock AP problems that follow the format of the AP exam. Questions from previous AP
exams influence assessment during the year. Homework assignments will sometimes be
based on collaborative efforts by students working together to solve complex problems.
These collaborative assignments require the use of graphics calculators to help students
solve problems. All assignments must be presented to the class so that all students can
interpret the results.
Oral Presentations and Research
All students are required to prepare a power point presentation where they describe in
detail on of the following topics: exponential/logarithmic equations, including
derivatives, integrals and the graphical behavior of the function; limits; derivatives and
integrals of functions, including the interpretation of the graphs; applications of
derivatives, including rectangular motion and rates of change; definite integrals involving
Riemann Sums; slope fields and differential equations; area and volume. All student
presentations must also include evidence of the history behind each concept as well as the
use of graphics calculators in describing the concept. A research paper must also be
written and turned in along with the presentation.
Students are also assigned specific group projects. For example the will be given
exponential growth and decay problems, such as determining when someone could have
been murdered using Newton’s Law of Cooling. After solving their problem each group
must present their conclusions to the group and justify their results. The results are
presented both graphically and numerically. Other students not presenting are able to
interact by asking questions as to how the results were obtained, and better yet if the
results “make mathematical sense.”
Teaching Strategies
During the first few weeks, we spend extra time familiarizing students with graphing
calculators. Students are taught the rule of three: Ideas can be investigated analytically,
graphically, and numerically. Students are expected to relate the various representations
to each other.
It is important for them to understand that graphs and tables are not sufficient to prove an
idea. Verification always requires an analytic argument. Each chapter test includes one
or two questions that involve only graphs or numerical data.
Communication is also stressed as a major goal of the course. Students are expected to
explain problems using proper vocabulary and terms. Like many teachers, I have
students explain solutions on the board to their classmates. This allows me to know
which students need extra help and which topics need additional reinforcement. Students
are also assigned projects in which they need to work with groups to solve more complex
math and then relate their findings to the class via a power point presentation.
Calculator Activities
The graphics calculator is used to help students develop an intuitive feel for concepts
before they are approached through typical algebraic techniques.
I use the calculator as a tool to illustrate ideas and topics. I stress the four required
functionalities of graphing technology:
1. Finding zeros of a function.
2. Sketching a function in a specified window.
3. Approximating the derivative at a point using numerical methods.
4. Approximating the value of a definite integral using numerical methods.
Primary Textbook
Finney, Demana, Waits, Kennedy. Calculus-Graphical, Numerical, Algebraic. AP
Edition. 3rd Edition. Pearson, 2007.