Melrose High School Syllabus
Department: Math
Course Number & Title: 205 Advanced Placement Calculus BC
Course Description:
Curriculum for this course includes the syllabus for the Advanced Placement Calculus BC
Examination of the College Board. All of the topics from AP Calculus AB are covered with the
following additional topics: advanced techniques of integration, calculus of parametric
functions, velocity and acceleration vectors representing two-dimensional motion, sequences and
series, and the epsilon/delta definition of limits. Students are expected to complete 4 open
responses and 4 core assignments. Curriculum for this course requires 5-8 hours a week of
independent practice such as homework, reading and projects. Graphing calculators are
required. Students enrolled in this course are required to take the AP Calculus BC exam.
MHS Learning Expectations:
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Students will develop the ability to communicate effectively.
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Students will be able to read effectively.
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Students will develop the ability to use technology responsibly and effectively.
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Students will develop the ability to problem solve effectively.
Essential Questions:
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How do limits guarantee the continuity of a function?
What is the connection between differentiability and continuity?
How is the antiderivative related to the accumulation function?
How can one apply numerical techniques to compute an integral without knowing the
associated antiderivative?
How are transcendental functions described using infinite series?
Students will know:
• The limit of a function can be found by
getting sufficiently close to a value not
actually reaching the value.
• Continuity is an essential condition for
theorems such as the Intermediate Value
Theorem, the Extreme Value Theorem, and
the Mean Value Theorem.
• First and second derivatives of a function
can provide information about the function
and its graph including intervals of increase
or decrease, local and global extrema,
intervals of upward or downward concavity,
and points of inflection.
• Differentiation rules provide the foundation
for finding antiderivatives.
• The definite integral of a continuous
function over a closed interval is the limit
of Riemann sums as the widths of the
subintervals approach zero.
• The coefficient of the nth degree term in a
Taylor polynomial.
Students will be able to:
• Determine limits of functions.
• Analyze functions for intervals of
continuity or points of discontinuity.
• Solve problems involving rates of change in
applied contexts
• Recognize antiderivatives of basic
functions
• Interpret the meaning of a definite integral
within a problem.
• Apply the Mean Value Theorem to describe
the behavior of a function over an interval.
• Construct and use Taylor polynomials.
Course Outline:
Semester One
Semester Two
Quarter 1:
Limits and their Properties
Differentiation
Applications of Differentiation
Integration
Quarter 2:
Log, Exponential and Transcendental
Differential Equations
Applications of Integration
Integration Techniques, L’Hopital
Quarter 3:
Infinite Series
Conics, Parametric and Polar
AP Review
Quarter 4:
AP Review and Practice
Primary Course Materials:
Primary Text: Calculus of a Single Variable, 10e (Larson, Edwards) AP Edition
Textbook Replacement Cost: $135
TI-84 Graphing Calculator
Grade Determination:
The total points will be broken down by category:
Summative
Tests, Quizzes, Problem Sets
65%
-There will be two tests (100 points each) per quarter (except for the 4th quarter).
-There will be a minimum of 5 quick quizzes (25 points each) per quarter. The
lowest
quick quiz will be dropped at the end of the quarter.
-AP Problem sets will be assigned for the end of each chapter. The number of
problem
sets per quarter and points will vary based on the length of the
chapter.
-Students can make test/quiz corrections for up to half of the lost points. All
test/quiz
corrections must be done before or after school with the teacher. All
corrections must be
done within six school days from when the assessment was
returned.
Exploratory/Formative
Homework
25%
-Homework will be assessed in a variety of ways. The most common ways will be:
-spot checking for completeness (all or nothing)
-collecting and grading
-homework quizzes
Performance Based Assessments
Core Assignments and Open Response
10%
-There will be one group core assignment per quarter.
-There will be at least one individual open response question per quarter.
Major Assignments: The major assignments for this course include: 4 Open Responses, 4 Core
Assignments, Midyear and Final exam.
Midyear & Final Exams: Midyear and Final Exams will be given. These exams count as 10%
of the respective semester grade. The average of the first and second quarter grades will count
90% in determining the first semester average. Similarly, the second semester average will
include the average of third and fourth quarter grades at 90% and final exam at 10%. The
average for the entire year will be the average of both semesters.
Q1 = 22.5%
Q2 = 22.5%
Midterm = 5%
Q3 = 22.5%
Q4 = 22.5%
Final = 5%