General Classroom Guidelines
Calculus I/Calculus II
AP Calculus BC
Mrs. Kelly Mahony - Rm 225
Email: Kelly.mahony@husd.org
Teacher Website: http://www.husd.org//Domain/1775
Teacher Phone #: 480-279-8173
This course may be taken for Dual Enrolment and/or AP.
MAT220/230 10 credits
Course Description
Calculus with Analytic Geometry I - Limits, continuity, differential and integral calculus of
functions of one variable. Prerequisites: Grade of "C" or better in [MAT182 and
(MAT150,MAT151 or MAT152)], or MAT187, or appropriate Math placement test score. Course
Notes: Students may receive credit for only one of the following: MAT220 or MAT221.
Calculus with Analytic Geometry II - Techniques of integration for both proper and improper
integrals with applications to the physical and social sciences, elements of analytic geometry,
and the analysis of sequences and series. Prerequisites: Grade of C or better in MAT220 or
MAT221 or equivalent
Text – Calculus a Single Variable 8th Edition, by Larson, Hostetler, Edwards
Barron’s AP Calculus, 12th Edition, by David Bock and Shiley Hockett (Must purchase on
your own)
Course Competencies – Upon completion of this course students will be able to: Students will
define and apply the properties of limits and continuous limits of functions. Students will
investigate derivatives graphically, numerically, and analytically. Students will explore the
relationship between continuity and differentiability. The derivative will be defined as the limit
of the difference quotient and interpreted as an instantaneous rate of change. Writing
equations of lines tangent to graphs of functions will be applied throughout the chapter.
Students will apply derivatives to analyze curves, model rates of change, and optimize functions.
Students will apply derivatives to analyze curves, model rates of change, and optimize functions.
Evaluate a definite integral using the Fundamental Theorem of Calculus. Understand the use of
the Mean Value Theorem for Integrals. Find the average value of a function over a closed
interval. Understand and use the Second Fundamental Theorem of Calculus. Students will
differentiate and integrate functions.
Course Content Introduction:
Our study of calculus, the mathematics of motion and change, is divided into two major
topics: differential and integral calculus. Differential calculus enables us to calculate rates of
change, to find the slope of a curve at any point, and to calculate velocities and accelerations of
moving objects. Integral calculus is used to find the area of an irregular region in a plane, to
measure lengths of curves, and to calculate centers of mass of arbitrary solids.
Most AP Calculus students enter this course with knowledge of the basic mechanics of
limits and derivatives. The task is to perfect each student’s mechanics and to develop his or her
understanding of the theory and the ability to use these ideas in applied calculus. Through
additional practice of the mechanics and through the development of the applications of
derivatives and anti-derivatives in problem solving, each student may accomplish this task.
This course provides students with the opportunity to work with functions through
multiple representations: graphically, numerically, analytically, and verbally, and emphasizes the
connections among these representations. In this course, students will use graphing calculators
such as Ti 83+, 84+, 84 color, and Ti-Inspire to solve problems, experiment, interpret results, and
support conclusions. If students are unable to purchase a calculator, we have a set of TI-84+
calculators which the students can use during class. If they need the calculator for homework
they can check one out or use online calculators. Students will become more proficient at
communicating mathematics, and explaining solutions verbally and in writing. In order to best
teach all students, I strive to present all topics in many different ways. Among these are
graphical, numerical, analytical and verbal approaches to almost all problems. I use virtual TI
programs for the TI-84+ projected onto the board regularly to give students an idea for the big
picture of a problem, often showing students how to use the table feature, or math menu
(zeros, derivative at a point, or numerical integral) in graphical mode, to get a more numerical
approach to problems. Early in the course students use their calculators to approximate and
arrive at a reasonable conclusion numerically of what the slope of a tangent line is to some
quadratic function at a particular point on that function. This activity then leads to further
investigation by the student doing the same thing graphically and analytically. I purposefully do
not teach nDeriv() or fnInt() commands until second semester; so that my students never
mistake calculator syntax for acceptable calculus notation. I instead teach the students to graph
the function, then use 2nd – TRACE and select either dy/dx or the command to find the area
under the curve. Finally, I use Geometer Sketchpad, and Calculus in Motion by Audrey Weeks to
help students visualize the different topics I am presenting, specifically for different theorems
and Solids by revolution.
Several examples of what students will be able to do with their graphing calculators are as
follows:
1. Plot the graph of a function with an arbitrary viewing window
2. Investigate limits of functions
3. Find the zeros of functions (solve equations numerically)
4. Confirm characteristics (e.g., concavity, POI) of graphs of functions
5. Compute partial sums
6. Numerically calculate the derivative of a function
7. Numerically calculate the value of a definite integral1
Calculators are not permitted on every assessment.
The first seven months of the class will be devoted to studying the topics covered in a
typical college Calculus 1 & II course. The next five weeks will be dedicated to review and
preparation for the AP exam. Throughout the year, information concerning the administration,
scoring, and content of the exam will be discussed. After taking the exam in May, students will
complete projects related to the topics they have studied in class during the year.
Students enrolled in AP® Calculus BC have successfully completed AP® Calculus AB as a
junior or are currently a junior and are learning AB and BC at the same time. We generally have
a handful of students who are seeking to further their mathematical knowledge and are looking
for a challenge for their senior year. Students enroll in second year calculus as an “Independent
Study.” Students are scheduled into my class during the same period as Calculus AB, and are
expected to participate in class regularly. Calculus BC students serve as tutors for the AB
students, working with students when they are stuck on a particular problem or concept. This
enables students to stay current on their skills from the year before, and provides new
explanations for students enrolled in AB. Calculus BC students are given separate assignments,
focusing on the different topics covered in the BC curriculum. Students in BC typically will
complete the chapter reviews for each unit in AB, as well as their own materials, further keeping
them up to speed on previous skills and allowing the juniors who have not taken AB before to
show proficiency of each AB topic.
Students are exposed to seven broad conceptual themes:
1. Working with functions represented graphically, numerically, analytically, or verbally.
Students should understand the connections among these representations.
2. The meaning of the derivative in terms of rate and local linear approximation.
3. The meaning of the definite integral both as a limit of the Riemann sums and as the net
accumulation of change.
4. The relationship between the derivative and the definite integral as expressed in both parts of
the Fundamental Theorem of Calculus.
5. Modeling of problem situations with functions, differential equations, or integrals.
6. Represent differential equations with slope fields, use technology to predict solutions with
slope field problems, solve separable differential equations analytically, and solve differential
equations using numerical techniques such as Euler’s method.
7. The meaning of polynomial approximation and series. Interpret convergence and divergence
using technology.
Course Outline:
Unit One: Limits and Their Properties (1 weeks)
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Find Limits Graphically and Numerically
Evaluating Limits Analytically
Continuity and One-Sided Limits
Infinite Limits
Intermediate Value Theorem
Unit Two: Differentiation (9 weeks)
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The Derivative and the Tangent Line Problem
Basic Differentiation Rules and Rates of Change
Product and Quotient Rules and Higher-Order Derivatives
The Chain Rule
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Unit Three:
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Implicit Differentiation
Related Rates
Extrema on an Interval
Rolle’s Theorem and the Mean Value Theorem
Increasing / Decreasing functions and the First Derivative Test
Concavity and the Second Derivative Test
Limits at Infinity (Horizontal Asymptotes)
A Summary of Curve Sketching
Optimization Problems
Differentials
Integration (2 weeks)
Antiderivatives and Indefinite Integration
Area
Reimann Sums and Definite Integrals
The Fundamental Theorem of Calculus
Integration by Substitution
Numerical Integration
Unit Four: Transcendental Functions: (3 weeks)
 The Natural Logarithmic Function – Differentiation
 The Natural Logarithmic Function – Integration
 Inverse Functions
 Exponential Functions – Differentiation and Integration
 Bases other than e and Applications
 Inverse Trigonometric Functions – Differentiation
 Inverse Trigonometric Functions – Integration
Unit Five: Differential Equations (3 weeks)
 Slope Fields and Euler’s Method
 Differential Equations: Growth and Decay
 Separation of Variables and the Logistic Equation
Midterm Exam: The midterm exam includes problems from the AP exams that test the
students’ abilities to connect concepts graphically, analytically, numerically, and verbally.
Unit Six: Applications of integration and Integration Techniques (4 weeks)
 Area of a Region Between Two Curves
 Volume – The Disk Method
 Basic Integration Rules
 Integration by Parts
 Indeterminate Forms and L’Hopital’s Rule
Unit Seven: Infinite Series (4 weeks)
 Sequences
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Series and Convergence
The Integral Test and p-Series
Comparisons of Series
Alternating Series
Ratio Root Tests
Taylor Polynomials and Approximations
Power Series
Taylor and Maclaurin Series
Unit Eight: Conic, Parametric Equations, and Polar Coordinates (4 weeks)
 Conics and Calculus
 Plane Curves and Parametric Equations
 Polar Coordinates and Polar Graphs
 Area and Arc Length in Polar Coordinates
Unit Nine:
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AP Review (5 weeks)
D & S Marketing Multiple Choice Practice
1997, 1998, and 2003 AP Exams
Free response questions: 2000 to present
Individual and group practice are used.
Test taking strategies are emphasized
Unit Ten: After the AP Exam: (3 to 4 weeks)
 Advanced Integration Techniques
 Project: Volume of a Known Cross Section Model
 Project: Vegetable and Fruit Lab
Activities/Projects:
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Free Response Practice: Students will be given four AP free response questions
from previous tests to solve in class either individually or in groups. The questions
will represent and require analytical, numerical, graphical, and verbal skills. There
will be both calculator and non-calculator questions. These practices will take place
2 or 3 times before the AP Review and then occur twice a week until the AP exam.
Special emphasis will be placed on helping students learn to justify answers in
complete sentence form.
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Volume of a known cross-section model Project: Students will build a 3-D model of
an assigned solid and will calculate the volume numerically using a spreadsheet and
cross-sections and also analytically using the cross-section formula.
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Vegetable and Fruit Lab: Students will work in pairs to determine the volume of a
banana, squash, potato, etc.’ using graph paper and their calculators and the disk or
washer method for determining volumes of solids of revolution. They will hand in a
written report that describes how they determined the volume and their findings.
Student Evaluation: Semester grades are calculated using homework, quizzes, and tests as
individual weighted categories. Grades are cumulative and represent 80% of the semester
grade; the final exam represents the remaining 20%. Homework is graded based on effort.
Notes are allowed on quizzes; however tests are to be taken without notes. Multiple choice AP
practice problems will be incorporated into quizzes and tests when appropriate. The midterm
exam and semester final use multiple choice questions in the format of the AP Exam.
Resources:
Bock, David, and Shirley O. Hockett. Barron's AP Calculus. Hauppauge, NY: Barron's, 2013.
Kamischke, Ellen. A Watched Cup Never Cools: Lab Activities for Calculus and Precalculus.
Berkeley, CA: Key Curriculum, 1999.
Larson, Ron, Robert P. Hostetler, and Bruce H. Edwards. Calculus of a Single Variable.
Boston: Houghton Mifflin, 2006.
Lederman, David. Multiple Choice & Free-response Questions in Preparation for the AP
Calculus (AB) Examination. Brooklyn, NY: D & S Marketing Systems, 1999.
I.
SUPPLIES
A. Classwork Notebook: The student is required to keep a large notebook or
binder to contain all notes and classwork.
B. Homework Notebook: You must work all homework and warm ups in a spiral
notebook or binder with your name on the front. Homework will be checked at
the end of each chapter for completion.
C. Calculator: TI-84, TI-84+, TI-84+C, TI-83, TI-Inspire can be used but be aware
that you might not have all of the programs. Can be rented from CGCC if taking
the course for dual enrollment
D. Barron’s AP Calculus, 12th Edition, by David Bock and Shiley Hockett (Must
purchase on your own). Needed throughout the year for practice.
II. BEHAVIOR
A. Rule: RESPECT is the key word towards proper behavior in any classroom.
 Respect others’ questions, answers, opinions, and property.
 Respect our space and keep it clean.
 Respect others’ think time; we work from bell to bell. When you enter
class, immediately start working the Warm Up in your notebook.
 Respect others’ feelings.
B. Respect my authority: Please speak only when appropriate.
C. Consequences:
 Tardiness: We will follow school policy, as outlined in the student
handbook, of After School Detention. Students assigned ASD will serve it
the following day to provide for parent notification.
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Misbehavior: You will first be asked to stop the behavior, if it continues
you will have a meeting with me after class. If you have not adjusted the
behavior after that I will be calling home to speak with your parents. If
the behavior continues still I will send a referral to the front office.
D. Leaving Class:
• All students leaving the classroom for any reason must sign out and take
the appropriate pass.
III. GRADES
A. The following grading scale is used to determine the letter grades of all
students.
A: 90-100
B: 80-89
C: 70-79
D: 60-69
F: 0-59
This instructor will not grant a request for a grade of "W" without a personal
conference with the student. Students should be cautious about a “W” grade, as
it may have serious consequences for financial aid, scholarships, and veteran’s
benefits, as well as auto or health insurance policies. Failure to officially
withdraw may result in a grade of F.
B. To earn College credit you must average a C for both semesters.
C. Your Final Grade will be based on the following:
70% Assessments
1) 40% Tests
2) 20% Quizzes
3) 10% Problem Sets: Students will work Problem Sets which contain test
questions from old AP tests.
10% Assignments
1) 10% Homework- Once or twice a week an open HW notebook quiz will be
given with problems from the homework.
20% Final Exam
D. You will be able to Re-Take one exam a semester if you fail and only if you have
come in for tutoring, get it signed by the tutor, and made test corrections. No
Re-Takes will be allowed on quizzes.
E. No late work will be accepted.
IV. CHEATING
A. Cheating includes having cheat notes, looking around the room during the test,
and talking before all papers are in as well as copying someone else’s
homework, project, quiz, or test.
B. CONSEQUENCES: Both students are guilty – the one who copied as well as the
one who let you copy. Therefore, both students will receive a zero for that work
as well as lose the privilege of dropping your lowest grade at the end of the
semester.
C. To maintain a secure testing environment, all students will be required to forfeit
their cell phone to a designated area in the classroom prior to all assessments.
This expectation mimics the regulations enforced by all state-and national
regulated standardized tests that students will take throughout their high school
career. In case of an emergency during the testing time, parents and/or
guardians may contact the front office to reach their student.
V. ABSENCES & MAKEUP WORK:
A. Any student that is absent is required to complete the work missed with in the
same amount of days that they were absent.
B. All major tests and quizzes can be made up at during lunches or after school at
the Tutor center.
C. You will also follow guidelines from the college about attendance to be able to
obtain credit for the class. If you miss more than 5 unexcused absences for the
class you may not be able to receive the college credit for the class.
VI. EXTRA HELP: I am available for extra help after school on Mon and Thur until 3:40 pm. If
you need other arrangements please speak with me. You may also go to CGCC for
free tutoring if you signed up for dual enrollment.
VII. VII. Communication In an effort to help your child be more successful in class and as a
part of our WFHS school community, I would like you to use the following parent
tools:
A. E-Alerts: Our school sends out automated email alerts for various school functions
like dances, athletics, testing dates, yearbook sales, etc., but you must be on the list
to receive them.
B. ParentVUE: Our schools use a software program called Synergy (Genesis), which
compiles student grades, attendance, transcripts, and contact information.
C. Teacher Websites: All teachers in our district have their own teacher website. These
pages will include digital versions of important documents for the class.
D. Standards for mathematics have changed over the last year please review the
standards that can be found by following this link.
http://www.husd.org/Page/13066
Dear Parent(s)/Guardian(s) and Student: Please read the attached Calculus BC syllabus. Sign and
date to acknowledge you have read, understand, and support of the classroom system. Please
return this page to Mrs. Mahony.
THANK YOU!
Student Name & Period:
______________________________________________________________________________
Mother/Guardian Name:
______________________________________________________________________________
During School Hours Phone Number:
_________________________________________________
E-mail Address:
______________________________________________________________________________
Father/Guardian Name:
______________________________________________________________________________
During School Hours Phone Number:
_________________________________________________
E-mail Address:
______________________________________________________________________________
Preferred Method of Contact:
______________________________________________________________________________
Does the student have DAILY access to a computer with internet?
YES
Does the student have DAILY access to a printer?
NO
YES
NO
I have read the class expectations for Mrs. Mahony’s Calculus BC class and understand that I
must take responsibility for my own academic success, as well as my classroom behavior.
Student Signature: _____________________________________________Date: ____________
I have read and discussed with my student the class expectations for Mrs. Mahony’s Calculus BC
Class.
Parent Signature: _______________________________________
Date:______________
DATE
TIME
REASON
RESULT