AP Calculus AB Syllabus
Course Overview:
This course covers all topics included in the Calculus AB topic outline as it appears in the AP Calculus
Course Description. The main objective of the course is to provide a strong foundation that will give
students the tools to succeed in future mathematics courses. The course will give students the
understanding of calculus concepts, related mathematical skills, and the appropriate technology to
enhance the process. Within a multi-representational approach, a balance between abstract concepts
and real applications is sought.
Textbook and Other Resources:
The textbook used for this course is Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel
Kennedy. Calculus- Graphical, Numerical, Algebraic. 1st ed. Menlo Park: Scott-Foresman AddisonWesley, 1999. Other resources include AP Calculus Course Description, AP Released Exams, and
Preparing for the AB AP Calculus Exam by George Best, Venture Publishing.
My website with links for this class:
Also get there by
http://msbigs.tripod.com/
www.schoolnotes.com
Course Planner:
UNIT 1 Families of Functions
5 days
Review summer packet that primarily
consists of Chapter One in our textbook.
Review and Test
UNIT 2 Limits and Continuity
12 days
2.1 Rates of Change and Limits
2.2 Limits Involving Infinity
2.3 Continuity
2.4 Rates of Change and Tangent Lines
Review and Test
UNIT 6 Differential Equations and
Mathematical Modeling
22 days
6.1 Antiderivatives and Slope Fields
6.2 Integration by Substitution
6.3 Integration by Parts
6.4 Exponential Growth and Decay
6.5 Population Growth
6.6 Numerical Methods
Review and Test
UNIT 3 Derivatives
30 days
3.1 Derivative of a Function
3.2 Differentiability
3.3 Rules for Differentiation
3.4 Velocity and Other Rates of Change
Review and Test
3.5 Derivatives of Trig Functions
3.6 Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Inverse Trig Functions
3.9 Derivatives of Exponential and
Logarithmic Functions
Review and Test
UNIT 4 Applications of Derivatives
25
days
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
4.6 Related Rates
Review and Test
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UNIT 5 The Definite Integral
22
days
5.1 Estimating with Finite Sums
5.2 Definite Integrals
5.3 Definite Integrals and Antiderivatives
5.4 Fundamental Theorem of Calculus
5.5 Trapezoid Rule
Review and Test
UNIT 7 Applications of Definite Integrals
20 days
7.1 Integral as Net Change
7.2 Areas in the Plane
7.3 Volumes
7.4 Lengths of Curves
8.1 L'Hopital’s Rule
Review and Test
UNIT 8 Review and Test
days
1
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AP Calculus AB Syllabus
Teaching Strategy:
Classes are a combination of lecture and group work. Students are encouraged to interrupt the
presentation at any time for clarification, if necessary. When graphing calculator techniques are
presented, students are given step-by-step instructions and work simultaneously on their own calculators.
Homework is required and checked. The Quick Review as well as most of the Section Exercises in each
section is assigned.
Students often present their solutions on the board. They are required to verbally explain their work to the
group. This sharpens their ability to communicate about mathematics. Other students are encouraged to
offer alternate methods of solution. Students are required to justify their answers in full sentences on
quizzes and tests.
Students are encouraged to develop more than one way to solve a problem. Frequent reference is made
to the Rule of Four in class. Topics involving functions, their limits, derivatives, and integrals are
represented graphically, numerically, analytically, and verbally, as often as possible.
Students often work together in groups. Concepts Worksheets that accompany out text are assigned as
labs. Students are able to interact with one another and share their insights.
Technology
The TI 84+ is used on the SMART Board in class. Each student uses an 84+SE and the TI Navigator. A
class set of TI 84+SE are available. However, most students have purchased their own calculator. All
students are expected to know how to use their calculators to find the zeros of a function, plot a function
in a specified window, numerically calculate the derivative of a function, and numerically calculate the
value of a definite integral. Students are expected to use their calculator to support the reasonableness
of an answer obtained by analytical methods.
Programs such as Riemann sums and slope fields are used as teaching aids. The calculator is used for
many useful demonstrations. When learning slope fields we project the screen with the grid turned on
and allow each student to plot several points. When conjecturing what the derivative of the sine curve will
be, we plot the slope at corresponding points. At the end of a demonstration like these, each student
must write about what they saw and correctly explain the mathematics involved. The class is often shown
a calculus demonstration or applet from the Internet projected onto a large screen using the SMART
Board, and asked to write about the mathematical principles that were demonstrated.
Student Evaluations
Quarter grades represent 40 percent of each semester grade. A midterm and final exam represent each
of the remaining 20 percent. Quarter grades are determined by frequent quizzes and chapter tests. Long
chapters are split in two. Cumulative formula quizzes are given quarterly. Take home problem sets are
also given as quizzes. Calculators are not always allowed during assessment. One quiz per quarter is
earned when a student is the section expert of the day and presents solutions and verbal explanations at
the board. Notebooks are required. A reworked problem section is eligible for extra credit. Homework is
assigned regularly and is checked frequently. Students keep a folder of previous AP questions that are
assigned throughout the year, to aid in their end-of-year review.
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Tests and major projects
Quizzes, Learn Checks, Quick Polls, and minor projects
Class/homework, Participation, Notebook, Attendance
60%
30%
10%
*** Please return the attached blue information card as acknowledgement of this syllabus. ***
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