Folsom Cordova Unified School District
Vista Del Lago Course Expectations
AP Calculus BC
Mr. Xiong
Room H110
vxiong@fcusd.org
Course Information: Welcome to 2nd term of Calculus - AP Calculus BC. This class is based on
the curriculum set by AP Central and the College Board. This class is a college or university
level course and the score you receive on the AP exam can count as credit at some institutions. The
pace and workload of this class will be the same as a college course. This course will require you to
work with functions represented in a variety of ways – graphically, numerically, analytically, and
verbally. We will also look at the connections among these representations. It is the expectation
that all students enrolled in this course will take the AP Calculus AB/BC exam.
Textbook and Resources:
Larson, Ron, and Bruce H. Edwards. Calculus of a Single Variable. 10th ed. Belmont, CA :
Brooks/Cole 2014.
It is your responsibility to take care of your assigned textbook. Students will be held financially
responsible for any lost or damaged textbook or if you turn in a book that is not your assigned book.
Supplemental materials include but are not limited to the following texts:
Supplemental materials include the following texts:
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Foerster, Paul A. Calculus Explorations. Emeryville: Key Curriculum Press, 1998.
Barron’s AP Calculus Study Guide
D&S Practice Exams for AP Calculus
Princeton Review AP Calculus Study Guide
Website:
URL: http://apcentral.collegeboard.com
The AP Central page provides several key articles (including those discussing the role of sign charts
and solving differential equations) as well as an archive of past free-response questions, which will
be used regularly throughout the course to familiarize students with the AP style of questioning.
Students may go online to http://www.larsoncalculus.com/ to access math tutors for additional help
and work out solutions to all odd-numbered exercise through Calc Chat.
Required Class Materials: Each student should bring the following items to class everyday:
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Textbook
Pencil/ Color Pens / highlighters / rulers
Line paper / Graph Paper
3-ring binder or notebook
Whiteboard marker
Graphing Calculator (mandatory). TI–83, TI–84 or TI–89 (preferred),
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
Grading: Your grade in this course will be composed of the following:
Homework/ Classwork/ Quizzes/projects: 10%
Tests: 55%
Semester Final: 35%
Letter grades will be based on the following scale:
90-100%= A
80-89%= B
70-79%= C
60-69%= D
Below 60%= F
Final Exam Clause: Due to the importance of the final exam, the students’ final grade in the class
cannot be more than one grade higher than the grade on the final exam. The following rules will
prevail regardless of the student’s overall percentage:
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In order to earn a semester grade of A(-), the final exam grade must be at least a B(-).
In order to earn a semester grade of B(-), the final exam grade must be at least a C(-).
In order to earn a semester grade of C(-), the final exam grade must be at least a D(-).
Parents and students may utilize the PowerSchool Portal to access grades online.
Warm-up and Notes: There will be a warm-up written on the board at the beginning of each class
period. Students are expected to be in their seat working on their warm-up when the bell rings. I
will be lecturing on the course material nearly every day and students are required to take notes.
Students will write all warm-up activities and notes in a notebook dedicated to this course.
Homework/Classwork: This class will be taught like a college course – lecture, notes, and applied
projects. It is imperative that you come to class, take good notes, and do your homework diligently.
Expect homework every night. Homework is to be done neatly so that I can read it. Chances are if
you can’t read it, then I can’t either. Work and diagrams must accompany every problem unless
otherwise instructed. Remember the AP Exam is the goal that we are working towards and all work
done in this class is a step towards this goal. Homework quizzes will be given frequently to provide
a formative assessment of student understanding.
ALL homework, quizzes, and test must show the aspects required on the AP exam –
graphically, numerically, analytically, and verbally. All student work must follow these
guidelines.
representation as to how you arrived
 Completed in pencil
 All work is shown.
to your answer.
 Work is complete, neat, and
 All graphs are completed on graph
organized with correct calculus
paper
words and notations.
 The final solution is clearly stated
 If you use a calculator to obtain an
 Answers must be exact or
answer you must show the Calculus
approximated to exactly 3 decimal
places.
Expect homework every night. Homework will be graded daily for completeness. Homework
checks will be given periodically where students will write down and completely solve a few chosen
questions from the homework. You may be required to present your solutions to the class
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
Assessments: Homework quizzes will be given throughout each unit, with or without notice. Tests
will be given at the end of a unit and always announced in advance. The students will take a
comprehensive final exam at the end of the semester (including materials from Calculus AB).
There will be no Unit Test-Retakes
Most written assessments will consist of two parts – calculator and non-calculator. Each of these
will also consist of multiple choice and free response questions. This is to prepare you for the actual
AP exam format. Most tests will be graded 50% multiple choice and 50% free response. Multiple
choice questions will require justification for credit. All free response questions will be of the
format of 9 points per question. The free response questions will require you to justify and explain
your thought process, in Calculus terms, how your solution was found – even with the use of a
calculator. Each portion will be timed. I will make every effort to make every test and quiz with
the same difficulty level equivalent to an AP type exam problem.
AP Exam Final – Full AP Exam
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Free Response Calculator
Free Response Non-Calculator
Multiple Choice Calculator
Multiple Choice Non-Calculator
Extra Credit: Students are expected to do assigned work and study for tests to do well in the
course. Extra credit assignments should not be expected.
Academic Dishonesty: All Vista students are expected to adhere to the rules of responsible
scholarship, requiring all student grades to be earned honestly through hard work and good study
habits. More information about the consequences for students who violate Vista’s Academic
Honesty Agreement is available on the Academic Dishonesty Policy page of the school website
Citizenship: Citizenship is reported separately from the academic grades. Course citizenship
includes both work habits and attitude/behavior – excessive tardies and unexcused absences will
negatively impact a student’s citizenship. Good citizenship is vital to a positive productive school
environment. Please refer to the student handbook or Vista’s website for information on citizenship
marks.
Tutoring: Please come and see me if you need help. I will be sure to find a time that works for both
of us. Afterschool sessions may be required in reviewing for the AP Exam. A mock exam may be
given prior to the AP Exam.
AP Exam: Thursday, May 5
For more information on AP Exam fees and fee reductions visit:
http://professionals.collegeboard.com/testing/ap/about/fees
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
Tardy Policy: Vista tardy policy will be enforced in my classroom –refer to hand book for details
Make-ups: If you have an excused absence, it is the students’ responsibility to inquire about missed
work and to schedule a time to make up that work. Any work assigned before the student’s absence
and due on the day of the absence is due the first day the student returns to school unless other
arrangements have been made. One day will be given for each absence to allow students to complete
work they have missed due to absence. All work must be made up, including: notes, classwork,
homework, quizzes and tests. All make-up work will be administered during lunch or before school.
Any work not made up by the required date will receive no credit. Any work missed due to a school
activity must be completed and received on the due date. Students should request work several days
ahead of time if they are expecting to be absent.
Cell Phones: Cell phones should not be used in class as it interrupts the educational environment.
Students’ phones will be confiscated if they are using them for any reason during class time. The
first time the phone will be returned at the end of the school day. After that offense, the parent will
be contacted and will have to come to the office to pick up the student’s phone.
Classroom Rules: Students are expected to follow the guidelines/expectations outlined in the
student handbook. In order to create a safe and positive classroom environment, we expect you to
always:
 BE SAFE:
o Keep hands, feet, and objects to yourself
 BE RESPONSIBLE:
o Be on time in your seat when the bell rings
o Be prepared to learn by bringing materials, and participate,
o No gum or food, except water
o Sharpen your pencils before the bell rings
o Do not cheat
 BE RESPECTFUL:
o Be a good listener - Avoid interrupting when other people are talking
o Use appropriate language
o Do not distract other students from learning
o Follow directions
o Do not leave your desk without asking permission, even to throw away trash or
sharpen your pencil
o Working on other subjects is permitted only if you have finished your math
assignment
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
AP Calculus BC Syllabus
2015
I have read the “rules and expectation” sheet for Mr. Xiong’ Calculus course. I will help monitor
his/her progress in this course through the PowerSchool Portal at least every other week. I will
make sure that he/she has all the proper supplies needed for this class in order to succeed. If I have
any questions concerning my child’s progress in this course, I will e-mail Mr. Xiong
(vxiong@fcusd.org).
Keep a copy of the procedures in your math binder/notebook for reference but turn in the
signature portion below for my records. Thank you.
_______________________________________
Name of Parent/Guardian (Print)
____________________________
Parent Signature
______________
Date
I have read the “rules and expectation” sheet for Mr. Xiong’ Calculus course with my teacher. I
realize the things I must do to be successful in this course. I promise to work hard and do my best.
If I need help I will make it a point to go see Mr. Xiong, ask my parents for help, or go to tutoring.
_______________________________________
Name of Student (Print)
____________________________
Signature of Student
___________________
Date
Please fill in the following contact information:
Phone number:___________________________
Parent Email:___________________________
Student Email: ___________________________
Preferred school to home communication method: (circle one) phone / email
Do you have internet access at home? ____
Are you able to print documents at home? _____
Please use the back to comments (Is there anything you would like me to be aware of?).
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
Pedagogical Practices:
Graphical, Numerical, Analytical, and Verbal Understanding
It is my practice to provide continuous multiple representations for the conceptual
development of calculus. Students are expected to understand topics graphically, numerically, and
analytically and be able to explain their answers verbally using “Calculus” terms. Students are
presented with a great deal of material to assist their complex understanding of calculus. The
textbook delivers numerous problems which require an analytical understanding of concepts. These
problems are supplemented with additional problems that utilize graphs and data tables to emphasize
graphical and numerical understanding of key concepts.
Conceptual understanding is emphasized at least as much as the algorithms of integration and
differentiation. Justification, using the language of calculus, is a critical component of both
instruction and assessment. More and more frequently, a student is expected to respond to “AP-like”
questions within small group discussion, assignments, quizzes and exams. Students must justify
their answers to questions both verbally and in written sentences using proper “Calculus” language.
Understanding takes priority over computation. Advanced Placement questions are dealt with
weekly. From the time that a topic is taught, an appropriate test question is presented to them in
class. Often, they self-grade these questions to enhance their understanding of the approach the
readers take to scoring their exams and reinforce their understanding of proper written justifications
of answers. The extensive library of questions from the College Board as well as problems from
additional resources offers a plethora of options to present to the student. They work frequently in
small groups to encourage peer interaction and the language of calculus. Groups often present their
solutions to the class in an effort to practice the written and verbal understanding of topics.
Graphing Calculators
Graphing calculators are used extensively throughout the course. Students will use them to
solve an equation, collect data to model calculus concepts, and represent functions graphically.
Students must be able to use the calculator to find roots of equations, discuss domain and range, and
the graphical characteristics of an even and odd function. Within the topics of Limits and
Continuity, a graphing calculator is used to analyze limits both numerically, using tables, and
graphically, using the zoom feature. Piecewise and rational functions are graphed to discuss
continuity and discontinuity. Students are taught to use the integration and differentiation
capabilities to confirm analytical response. Some examples of graphing calculator activities include
the following:
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Using a graphic calculator, students must explore and explain partial sums and explore
convergence and divergence graphically. They compare series convergence or
divergence and the sequence that generated the series. This provides the student an
inductive way to discover the nth test for divergence. Students are required to show an
understanding of convergence both analytically and graphically through this exercise.
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
Students must justify their answers through written sentences and present their results to
the class verbally.
 Using a graphing calculator, the students will model the spread of a flu virus using their
knowledge of logistic growth functions, regression, differentiation, and integration. The
students collect numerical data on the spread of the flu using a random generator. The
graph of the total number infected is analyzed, as well as the graph of the derivative.
Students run a regression on data to find the proportional constant. Then they integrate
the differential equation, using partial fractions to create the logistical curve. They are
then given actual data from the Center for the Disease Control and perform the same
process using actual data. Results of the exercise must be justified in writing using
sentences.
Course Outline
Block Schedule – 90 minutes per day for 89 days = 1 year on traditional schedule
Unit 1 - Calculus AB Review: Limits and Differentiation - 10 Days
 Limits
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Rates of Change – Tangents, velocities, and other rates of change
Limits at a Point – One sided limits, two sided limits, limits that do not exist
Tangents and Velocity - two points to find tangent (secant line), instantaneous velocity and
average velocity.
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Limits at Infinity –Asymptotes, infinite limits at infinity, lim
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1
 0 , lim e x  0 , limits
x  x r
x 
algebraically and graphically
Calculating Limits using Limit Laws – Limit Laws to find algebraically, direct substitution,
greatest integer function, Squeeze Theorem, estimating limits from graphs or tables of data
Precise Definition of Limits -  -  proofs and definition of limits
Continuity – Definition of continuity, graphical representation of continuity, continuity in
terms of limits, jump discontinuity, removable discontinuity, infinite discontinuity,
The Intermediate Value Theorem.
Differentiation
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f a  h  f a
h 0
h
f  x  f c
Definition of Differentiable – If f '  x   lim
, then the function is
x c
xc
Definition of Derivative as a Limit lim
differentiable at point “c”, functions that are continuous but not differentiable,
dy
, f '  x  and derivatives with respect to different variables
dx
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Derivative Notation f ',
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Rules for Differentiation – Power rule, product rule, quotient rule, chain rule
Higher Derivatives – 1st, 2nd, 3rd, and nth derivatives of functions, correlation using position,
velocity, acceleration, and jerk
Derivative of Trig Functions – Derivatives of sine, cosine, tangent, cosecant, secant and
cotangent
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Folsom Cordova Unified School District
Vista Del Lago Course Expectations
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Implicit Differentiation – Differentiating with respect to x when y and x are present in the
function
Separable Differentiable Functions – solving equations using separable differentiable
functions, specifically, exponential growth and y’=ky
Related Rates – Differentiating functions with respect to time, applications of related rates
Slope Fields – Introduction to slope fields, analyze graph of derivative using slope fields,
translating graphs of f’(x) to f(x) and f(x) to f’(x) with initial conditions
Related rates project (see student activity 1)
Extreme Value Theorem
First Derivative Test – Absolute and Local Extrema
Second Derivative Test – Determine concavity and points of inflection
Mean Value Theorem – Rolle’s Theorem and Mean Value Theorem and applications
Curve Sketching – Sketching the graph of a f(x), f’(x), and f’’(x) using the first and second
derivative tests to determine intervals of increasing/decreasing, local/absolute max and min,
concavity, and points of inflection
Use of the calculator to find derivatives, zeros, extrema
Newton’s Method of Approximation - Using Newton’s iterative process to find an
approximation of a root both graphically and algebraically
Optimization Problems – Finding max and min to maximize or minimize
Unit 2 - Review of Integration Techniques (13 Days)
 Area between two curves
 Volume
 Volume of known cross sections
 The Integral as Net Change
 Fundamental Theorem of Calculus
 Arc length
 Surface Area
 Applications to particle motion
 Applications in Physics, including the integral as Work, Total Fluid Force, and Centroid
Unit 3– Advanced Integration (13 Days)
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Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration by Partial Fractions
L’Hopitals Rule and its application
Improper Integrals and their convergence or divergence, including the use of L’Hopital’s
Rule
Application of new techniques in context of finding area, centroid, volume, including
applications to motion on a line.
Unit 4 – Sequences and Series (23 Days)
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Sequences
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
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Convergence and Divergence of sequences.
Definition of series as a sequence of partial sums and convergence of series is defined as
the convergence of the sequence of partial sums
Exploration of Geometric Sequence and Proof of Summation Formula for finite and
infinite series
Applications of Geometric series
Harmonic series
Telescoping Series
Nth test for divergence
Integral Test is studied as the area of rectangles and the relationship to improper integrals
and the p-series
Direct comparison and limit comparison tests for convergence
Alternating Series test
Alternating Series Remainder and Error Bound
The Ratio and Root Test
Taylor polynomials and approximations, using the graphical representation as a
introduction
Maclaurin series and the general Taylor series centered at x = a.
Power Series and the radius and interval of convergence
Taylor and Maclaurin Series for sin x, cos x, and 1/(1-x)
Manipulation of series to form a new series from a known one
Techniques for this manipulation include multiplying constants and or variables,
integration and differentiation of series
Functions defined by power series
Taylor’s Theorem along with LaGrange Error Bound
Unit 5 - Plane Curves, Parametric Equations and Polar Curves (15 Days)
 Plane curves and parametric equations
 Derivatives of parametric equations including velocity and acceleration
 Vectors to represent motion along a curve
 Derivatives of vector valued functions and applications including velocity vector,
acceleration vector, speed, and distance traveled
 Polar coordinates and polar graphs
 Differentiation of polar curves
 Area and arc length of polar curves
Unit 6 - Differential Equations (15 Days)
 Solving separable differential equations for general and particular solutions
 Use slope fields to determine particular solutions to differential equations
 Understanding the calculus used to create the logistic curve and how to solve logistical
equations with applications in logistical growth functions
 Numerical solution to differential equations using Euler’s Method
Folsom Cordova Unified School District
Vista Del Lago Course Expectations
AP Exam Final – Full AP Exam
 2 Free Response Calculator
 4 Free Response Non-Calculator
 Multiple Choice Non-Calculator
 Multiple Choice Calculator