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AP Calculus Syllabus
Teacher: Anthony Melton
Course Description: AP Calculus is a college-level course for students who have the
ability and desire to pursue college level study in high school. The content covered will
include a semester of differential calculus and a semester of integral calculus. College
credit can be obtained by passing the AP Exam. Due to deadlines, after-school and
Saturday classes may be required. Prerequisites: Algebra 1, Algebra 2, Geometry, and
Pre-Calculus (honors level courses preferred). Admittance to the class will be based on
previous mathematics course grades, teacher recommendations, and a student
application.
Textbook: Calculus of a Single Variable Ninth Edition
Brooks/Cole
Copyright 2010
Belmont, CA
ISBN 0-547-21290-9
Students will cover units on the following topics:
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Preparation for Calculus
Limits and Their Properties
Differentiation
Applications of Differentiation
Integration
Logarithmic, Exponential, and Other Transcendental Functions
Differential Equations
Applications of Integration
AP Calculus Examination Review
Grading Scale:
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90-100
80-89
70-79
60-69
0-59
A
B
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D
F
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Grades are determined as follows:
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Tests and quizzes
60%
Daily assignments, homework, open responses, notebooks, etc.
40%
Notebooks will include the title of each section, all notes and examples from the board
kept in order according to date, a section for AP Exam Questions, and an assignment
page.
Materials needed for class:
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Three ring binder—two-inch
Loose leaf paper
Tabs for notebook
Pencils
Graph paper
Graphing calculator TI-84 Preferred
Classroom rules:
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Be on time
Be prepared
Respect others
Follow student handbook
No food or drink in class
Late Work Policy:
All work must be turned in on time to receive full credit. Any late work, if accepted,
will lose 20 points per day.
Class Attendance:
It is very important to attend class every day. When class is missed for any reason, it is
your responsibility to get all notes and assignments for the day(s) missed and complete
the assignments as soon as possible.
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Basic Understanding:
We are here to do a job. Mine is to teach, yours is to learn. It will take teamwork for
us to be successful in accomplishing this task. Therefore, behaviors that prohibit me
from doing my job or you from doing yours will not be tolerated.
Maximum Time Usage:
It is very important for us to maximize our time usage in this class. When time is
wasted, the result is that you will spend more time at home doing homework.
Extra Class Time:
Homework discussions will be scheduled after school as needed. AP Calculus AB
study sessions will be held on 3 Saturdays prior to the AP Exam. Every student is
expected to attend these Saturday sessions. Also, when we miss school due to a snow
day, you will be expected to complete a snow packet assignment for each day missed.
These will be collected on the next day that school is in attendance. If the number of
snow days is excessive, more Saturday meetings may be required.
Unit 1 Preparation for Calculus (1-2 weeks)
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Sketch the graph of an equation
Find the intercepts of a graph
Test a graph for symmetry with respect to an axis and the origin
Find the points of intersection of two graphs
Interpret mathematical models for real-life data
Find the slope of the line passing through two points
Write the equation of the line with a given point and slope
Interpret slope as a ratio or as a rate in a real-life application
Sketch the graph of a linear equation in slope-intercept form
Write equations of lines that are parallel or perpendicular to a given line
Use function notation to represent and evaluate a function
Find the domain and range of a function
Sketch the graph of a function
Identify different types of transformations of functions
Classify functions and recognize combinations of functions
Fit a linear model to a real-life data set
Fit a quadratic model to a real-life data set
Fit a trigonometric model to a real-life data set
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Unit 2 Limits and Their Properties (2-2.5 weeks)
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Understand what Calculus is and how it compares to Pre Calculus
Understand that the tangent line problem is basic to Calculus
Understand that the area problem is basic to Calculus
Estimate a limit using a numerical and graphical approach
Learn different ways that a limit can fail to exist
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 a open interval
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 3 Differentiation (5-5.5 weeks)
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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
Find the derivative of a function using the Power Rule
Find the derivative of a function using the Constant Multiple Rule
Find the derivative of a function using the Sum and Difference Rules
Find the derivatives of the sine and cosine functions
Use derivatives to find rates of change
Find the derivative of a function using the Product Rule
Find the derivative of a function using the Quotient Rule
Find the derivative of a trigonometric function
Find a higher-order derivative of a function
Find the derivative of a composite function using the Chain Rule
Find the derivative of a function using the General Power Rule
Simplify the derivative of a function using algebra
Find the derivative of a trigonometric function using the Chain Rule
Distinguish between functions written in implicit form and explicit form
Use implicit differentiation to find the derivative of a function
Find a related rate
Use related rates to solve real-life problems
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Unit 4 Applications of Differentiation (5-5.5 weeks)
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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 apply Rolle’s Theorem
Understand and apply 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
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, if any, of the graph of a function
Determine infinite limits at infinity
Analyze and sketch the graph of a function
Solve applied minimum and maximum problems
Approximate a zero of a function using Newton’s Method
Understand the concept of a tangent line approximation
Compare the value of the differential, dy, with the actual change in y, ∆y
Estimate a propagated error using a differential
Find the differential of a function using differentiation formulas
Unit 5 Antiderivatives and Indefinite Integration (4-4.5 weeks)
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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 a 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
Evaluate a definite integral using the Fundamental Theorem of Calculus
Understand and use 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
Understand and use the Net Change Theorem
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Use pattern recognition to evaluate an indefinite integral
Use a change of variables to evaluate an indefinite integral
Use the General Power Rule for Integration to evaluate an indefinite integral
Use a change of variables to evaluate an definite integral
Evaluate a definite integral involving an even or odd function
Approximate a definite integral using the Trapezoidal Rule
Unit 6 Logarithmic, Exponential, and Other Transcendental Functions
(4-4.5 weeks)
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Develop and use the properties of the natural logarithmic function
Understand the definition of the number e
Find derivatives of functions involving the natural logarithmic function
Use the Log Rule for Integration to integrate a rational function
Integrate trigonometric functions
Verify that one function is the inverse of another function
Determine whether a function has an inverse function
Find the derivative of an inverse function
Develop properties of the natural exponential function
Differentiate natural exponential functions
Integrate natural exponential functions
Define exponential functions that have bases other than e
Differentiate and integrate exponential functions that have bases other than e
Use exponential functions to model compound interest and exponential growth
Develop properties of the six inverse trigonometric functions
Differentiate an inverse trigonometric function
Use the basic differentiation formulas for elementary functions
Integrate functions whose antiderivatives involve inverse trigonometric
functions
Use the method of completing the square to integrate a function
Review the basic integration rules involving elementary functions
Unit 7 Differential Equations (2-2.5 weeks)
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Use initial conditions to find particular solutions of differential equations
Use slope fields to approximate solutions of differential equations
Use separation of variables to solve a simple differential equation
Use exponential functions to model growth and decay in applied problems
Recognize and solve differential equations that can be solved by separation of
variables
Use differential equations to model and solve applied problems
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Unit 8 Applications of Integration (2-2.5 weeks)
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Find the area of a region between two curves using integration
Find the area of a region between intersecting curves using integration
Describe integration as an accumulation process
Find the volume of a solid of revolution using the disk method
Find the volume of a solid of revolution using the washer method
Fid the volume of a solid with known cross sections
Unit 9—AP Calculus Examination Review (5-6 weeks)
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Review the major topics on the AP Calculus AB Examination
Take two AP Calculus AB practice exams (On two separate Saturdays in the
month prior to the AP Calculus Exam—if needed)