AP Calculus
Teacher: Mrs. Ang
sang@cojusd.org
Room 206
559-528-4731
Course Description:
Calculus is the mathematical study of change. It has two major branches, differential
calculus (concerning rates of change and slopes of curves), and integral calculus (concerning
accumulation of quantities and the areas under curves); these two branches are related to
each other by the fundamental theorem of calculus. Both branches make use of the
fundamental notions of convergence of infinite sequences and infinite series to a welldefined limit. Calculus has widespread uses in science, economics, and engineering and can
solve many problems that algebra alone cannot. (Wikipedia)
Prerequisites:
Algebra 1, Geometry, Algebra 2, and Advance Math (Pre-Calculus)
Textbook and Course Materials:

Textbook:
 Calculus Early Transcendental Functions by Larson, Hostetler, and Edwards

Reference:
 Calculus for Dummies
 Any Calculus by other authors
Materials:
 Graphing Calculator
 Lesson notebook
 Homework notebook
 Graph paper
 Line paper
 Color pencil
 Pencil/Pen
 Dry erase markers
 Binder
 Highlighter
Course Objectives:


Unit 1: Limits and Their Properties
Students will learn ….
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To estimate a limit using a numerical or graphical approach
Learn different ways that a limit can fall to exist
Study and use a formal definition of a limit.
Evaluate a limit using properties of limits
Develop and use a strategy for finding limits
Evaluate a limit using dividing out and rationalizing techniques
Evaluate a limit using the Squeeze Theorem
Determine continuity at a point and continuity on an open internal
Determine one-sided limits and continuity on a closed interval
Use properties of continuity
Understand and use the Intermediate Value Theorem
Determine infinite limits from the left and from the right
Find and sketch the vertical asymptotes of the graph of a function
Unit 2 : Differentiation
Students will learn…
 Find the slope of the tangent line to a curve at a point
 Use the limit definition to find the derivative of a function
 Understand the relationship between differentiability and continuity
 Find the derivative of a function using the Constant Rule, Power Rule,
Constant
Multiple
Rule,
Sum
and
Difference
Rules,
and
sine/cosine/exponential functions.
 Use derivatives to find rates of change
 Find the derivative of a function using the Product Rule, Quotient Rule, and
trigonometric function
 Find a higher-order derivative of a function
 Find the derivative of a composite function and transcendental function using
the Chain Rule
 Find the derivative of a function using the General Power Rule
 Distinguish between functions written in implicit form and explicit form
 Use implicit differentiation to find the derivative of a function
 Find derivative of functions using logarithmic differentiation
 Find the derivative of an inverse function
 Differentiate an inverse trigonometric function
 Find a related rate and use related rates to solve real-life problems
 Approximate a zero of a function using Newton’s Method

Unit 3: Applications of Differentiation
Students will learn…
 Understand the definition of extrema of a function on an interval
 Understand the definition of relative extrema of a function on an open
interval
 Find the extrema on a closed interval
 Understand and use Rolle’s Theorem
 Understand and use the Mean Value Theorem
 Determine intervals on which a function is increasing or decreasing
 Apply the First Derivative Test to find relative extrema of a function
 Determine intervals on which a function is concave upward or concave
downward
 Find any points of inflection of the graph of a function
 Apply the Second Derivative Test to find relative extrema of a function
 Determine (finite) limits at infinity
 Determine the horizontal asymptotes.
 Solve applied minimum and maximum problems
 Understand the concept of a tangent line approximation
 Compare the value of the differential, dy, with the actual change in y

Unit 4: Integration
Students will learn..
 Write the general solution of a differential equation
 Use Indefinite Integral notation for Antiderivatives
 Use basic integration rules to find Antiderivatives
 Find a particular solution of a differential equation
 Use sigma notation to write and evaluate a sum
 Understand the concept of area
 Approximate the area of plane region
 Find the area of a plane region using limits
 Understand the definition of a Riemann sum
 Evaluate a definite integral using limits
 Evaluate a definite integral using properties of definite integrals
Evaluation:
You will be graded on
 Participation/Citizenship
 Quizzes, Chapter Test, Unit Test, and Midterm and Final Benchmark
 Homework, Notes, Classwork, Projects
Grading Scale:
Letter
Percentage
Grade
A+
Grade
97-100
4.0 Scale
Scoring
4.0
A
93-96
4.0
A-
90-92
3.7
B+
87-89
3.3
B
83-86
3.0
B-
80-82
2.7
C+
77-79
2.3
C
73-76
2.0
C-
70-72
1.7
D+
67-69
1.3
D
63-66
1.0
D-
58-62
0.7
F
Below 58
0.0
Descriptor
Advanced – Thorough understanding of and
ability to apply the knowledge and skills
associated with the content.
Proficient – Adequate understanding of and
ability to apply the knowledge and skills
associated with the content.
Basic – Partial understanding of and ability to
apply the knowledge and skills associated
with the content.
Below Basic – Minimal understanding of and
ability to apply the knowledge and skills
associated with the content.
Far Below Basic - Not enough evidence or
effort to demonstrate understanding of the
content.
Citizenship
All students are expected to take an active part in the learning environment of the
classroom. This means coming to class on time and ready to learn. The following rubric will be
used to evaluate the citizenship component of college-career-citizenship readiness.
Unsatisfactory
Needs improvement
Satisfactory
Outstanding
Student makes no
effort to be on task.
Student has to be
reminded regularly to
stay on task.
Student is usually on
task
Student stays on
task and puts
forth effort
0----------5----------10
Student does not follow
directions and rules.
11---------13-------15
16------18-------20
Student listens and
follows directions
and rules most of
the time.
21-------2------25
Work Effort
Ability to
follow
instruction
0----------5---------10
Student is negative and
disrespectful towards
the teacher and/or
other students, and
makes no attempt to
change behavior
Respect/
0--------5--------10
Student constantly
needs reminders to
follow directions and
rules.
Student listens
and follows
directions and
rules the first
time.
21------ 24------25
11--------13--------15
Student continually
needs reminders to be
organized,
responsible, and
respectful to other
students and the
teacher.
11-------13--------15
16------18-------20
Student is usually
responsible,
organized, and
respectful to other
students and the
teacher
Student is
responsible,
organized, and
respectful to
other students
and the teacher
16-----18--------20
21-------24------25
Students frequently
interrupts class
through disruption.
Student participates
appropriately in
class and seldom
needs to be
corrected by the
teacher
16------18------20
Student
participates and
adds to the class
in a positive
manner
21------24------25
Responsibility
Behavior
Student consistently
disrupts class
interrupting other
student's right to learn
and the teacher's right
to teach.
0-------5-------10
Total Points
Missed Assignments/Exam Procedure:
11------13------15
It is expected that students will submit all assignments on time. It is the
student’s responsibility to inform the teacher that he/she will be absent and to
request any and all make-up work. Once the student has returned to class, all
make-up and alternative assignments must be completed within the number of
school days equal to or less than the number of school days the student has been
absent.
Please sign below to certify that you have reviewed the syllabus and understand the
course requirements.
Name of Student (print)
_________________________
Student Signature
__________________________________
Date
_________