AP CALCULUS AB
Syllabus
Course Overview
In teaching AP Calculus, we cover all of the items in the Calculus AB
topic outline in the course description. We also wish to instill in students
an appreciation for Calculus and its applications by giving them a strong
foundation to prepare them to be successful on the AP Exam and in future
mathematics classes. Hard work and commitment is expected from
students in order for them to gain the most from time and effort to
understand, improve skills, and use technology.
Course Planner [C2]
We are on a Flex-Schedule which includes 45 and 90 minute classes. The
AP Calculus class meets everyday for 90 minutes for three terms or 27
weeks.
Below is the sequence of our AP Calculus Course. [C2]
First Term AP Calculus AB
Section
Numbers
1.1
1.2
1.3
1.4
1.5
1.6
2.1
2.2
2.3
2.4
3.1
3.2
3.3
3.4
3.5
Topics
Lines
Functions and Graphs
Exponential Functions
Parametric Equations
Functions and Logarithms
Trigonometric Functions
Review and Testing
Rates of Change and Limits
Limits Involving Infinity
Continuity
Rate of Change
Review and Testing
Derivatives of a Function
Differentiability
Rules for Differentiation
Velocity and Other Rates of Change
Derivatives of Trigonometric
Functions
Timeline
1 day
2 days
1 day
1.5 days
1 day
2 days
2 days
2 days
2 days
2 days
2 days
1.5 days
2 days
1 day
2 days
2 days
2 days
C2 – The course teaches
all topics associated with
Functions, Graphs, and
Limits; Derivatives;
Integrals; and Polynomial
Approximations and
Series as delineated in the
Calculus BC topic
Outline in the AP
Calculus Course
Description
3.6
3.7
3.8
3.9
Chain Rule
Implicit Differentiation
Derivatives of Inverse
Trigonometric Func.
Derivatives of Exponential and Log
Func.
Review and Testing
2 days
1 day
2 days
2 days
2 days
Second Term AP Calculus AB
Section
Numbers
4.1
4.2
4.3
4.4
4.5
4.6
5.1
5.2
5.3
5.4
5.5
6.1
6.2
6.3
6.4
6.5
6.6
Topics
Timeline
Extreme Values and Functions
The Mean Value Theorem
Connection f ‘ and f ― with Graph
of Func.
Modeling and Optimization
Linearization and Newton’s
Method
Related Rates
Review and Testing
Estimating with Finite Sums
Definite Integral
Definite Integrals and AntiDerivatives
Fundamental Theorem of Calculus
Trapezoid Rule
Review and Testing
Anti-Derivative and Slope Fields
Integration by Substitution
Integration by Parts
Exponential Growth and Decay
Population Growth
Numerical Methods
Review and Testing
2 days
2 days
1.5 days
3.5 days
3 days
2 days
3 days
2 days
2 days
1 day
2 days
2 days
2 days
2 days
2.5 days
2.5 days
2 days
2 days
2 days
2 days
Third Term AP Calculus AB
Sections
Numbers
7.1
7.2
7.3
7.5
8.1
Review
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Topics
Integrals as Net Change
Areas in the Plane
Volume
Applications from Science and
Statistics
Review and Testing
L’Hopital’s Rule
Practice Test
Precalculus and Limits
Graphing, Continuity, Inc/Dec,
Concavity
Differentiation, Max/Min, Chain
Rule
Essential Theorems
The Calculus of Motion
Mock AP Exam
Approx. of Areas, Def. of
Integration
Related Rats
Growth and Decay, Volume w/
Cross Sec.
Volumes of Revolution
Methods of Integration
Mock AP Exam
Timeline
1 day
2 days
2 days
2 days
2 days
1 day
2 days
1 day
1 day
1 day
1 day
1 day
2 days
1 day
1 day
1 day
1 day
1 day
2 days
Teaching Strategies [C4]
The expectations of students are much higher than most of
them have been exposed to in previous math classes. A
small part of our students have progressed through our
Integrated Math Program while the majority have gone
through the traditional track. From the beginning, students
are given a schedule culminating with the AP Exam.
C4– The course teaches
students how to
communicate
mathematics and explain
solutions to problems
both verbally and in
written sentences.
The teacher tries to function as a coach allowing students and teacher to
work together to reach the goal of scoring well on the AP Exam. Students
are given many opportunities to share their knowledge and work together
as a team to reach their goals. This also improves their ability to
communicate mathematically.
After each test students are asked to work on sample free response and
multiple choice questions. This allows students to not only slowly begin
to prepare for the AP test, but it puts extra emphasis on communicating the
mathematics that they have learned.
Technology and Computer Software [C3, C5]
The teacher uses the TI-83 and TI-84 graphing calculators
to help in presentations. Students all have one of these two
calculators. The graphing calculator helps students develop
an intuitive idea about concepts even before they are
approached algebraically. An emphasis is made to students
that they need to know the limitations of the graphing
calculator. Next year we will also be implementing the use
of the TI84 Navigator system into our classrooms.
PowerPoint presentations are also used to aid in teaching and reviewing
many important concepts.
Many resources are also taken from the web to help improve
understanding.
http://apcentral.collegeboard.com/apc/members/exam/exam_questions/803
1.html
http://www.geocities.com/gkellymath/calculus.html
http://www.ies.co.jp/math/java/calc/index.html
http://archives.math.utk.edu/visual.calculus/
http://chs.mesa.k12.co.us/Departments/math/JohnSidanycz/Calculus1New
Page.htm
C3– Evidence of
Curricular Requirement:
The course provides
students with the
opportunity to works with
functions in a variety of
ways—graphically,
numerically, analytically,
and verbally—and
emphasizes the
connections between
these representations.
C5– The course teaches
student how to use
graphing calculators to
help solve problems both
verbally and in written
sentences
Student Evaluation
Term grades are computed on homework (20% of final grade) , quizzes
and tests (80% of final grade). Parts of the tests are constructed with
multiple choice and constructed response questions. Some of the tests and
practice AP Exams use multiple-choice questions follow the format of the
AP Exam. Questions from previous AP Exams strongly influence
assessments. Chapter tests are given similar to the AP test in that
calculators are allowed for parts of the test and not for other parts.
Teacher Resources
Primary Textbook
Finney, Ross; Demana, Franklin; Waits, Bert; and Kennedy, Daniel,
Calculus Graphical, Numerical, Algebraic, Scott Foresman Addison
Wesley, 1999.
Technology Resources [C5]
Tips for TI-83 Users, Texas Instruments,
education.ti.com/us/product/tech/89/downtips.html All students are
required to have a TI-83, TI-84, or TI-89 calculator.
Student Activities
Students frequently work and demonstrate solutions of problems on the
board to demonstrate their knowledge, share their expertise with others,
and communicate mathematically.
Students sometimes work together on difficult problems and report as a
group. They collaborate to produce one paper that is evaluated for
mathematical correctness and quality of presentations.
Activities include, but are not limited to, the following:
1. Curve Sketching Matching Game (Matching the
graph of f with its 1st and second derivative. [C3]
2. Slope Field Matching Game [C3]
3. Banana Split: Experimenting with area and volume
using the cross section of a banana. [C4]
4. The Bunt Cake: using a bunt cake to present the concept of
finding volume using Cylindrical shells. [C4]
C3– Evidence of
Curricular Requirement:
The course provides
students with the
opportunity to works with
functions in a variety of
ways—graphically,
numerically, analytically,
and verbally—and
emphasizes the
connections between
these representations.
C4– The course teaches
students how to
communicate
mathematics and explain
solutions to problems
both verbally and in
written sentences.
C5– The course teaches
student how to use
graphing calculators to
help solve problems both
verbally and in written
sentences