AP Syllabus With Course Outline.website

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AP Calculus

Course Syllabus

Course Description: The main objective of the AP Calculus AB course is to provide the student with sufficient calculusknowledge and skills to give them the ability to score well on the AP Exam as well as to experience success in any subsequentmath courses they may undertake. Emphasis is placed on discovery through use of the graphing calculator and problem solvingapplications.

IMPORTANT NOTE: All Advanced Placement students are required to take the AP Exam at the school districts expense.The date of the AP Exam is determined by the College Board and will be announced to the students once the College Boardsets the date. The exam is traditionally administered sometime between May 1 and May 15 each year and will be administeredhere at United High School.

Instructional Philosophy: Students are encouraged through teacher example, assignments, and class discussions todemonstrate solutions analytically, graphically, and numerically. A comfortable classroom atmosphere in which students arenot afraid to make mistakes allows for frequent, rich discussions of problems and alternate approaches to solutions.Students almost daily put solutions to problems on the board and are expected to give explanations to the class. Clearcommunication skills are further developed on tests and quizzes. Students are required to present clear, mathematicallycorrect explanations for a portion of the exam questions.

Textbook Information:

Title: Calculus, June 2001Authors: Larson, Hostetler, EdwardsPublisher: Houghton Mifflin CompanyISBN: 0-618-14918-X

Description: This text offers an appropriate blend of applied and traditional calculus. An abundance of skill, application,exploration, writing, and critical thinking problems allow the teacher to address fundamental concepts of calculus thoroughly.Technology has been integrated throughout the text in order to allow opportunities for exploration and investigation.

Calculator Information:

The TI-83 and/or the TI-89 are used for all teacher explanations and presentations. Each student also uses either the TI-83 or TI-89.


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Grading Procedures (Homework, Quizzes, Tests)

1.

Homework will be assigned daily and will be checked occasionally. Your grade will be based on the amount of workcompleted.

2.

Homework will always be due at the next class period unless stated otherwise by the teacher. All assignments should bedone in PENCILand ALL WORK MUST BE SHOWN! You will not receive credit if your work is notshown.

3.

Quizzes can be given at any time that the teacher deems necessary and will vary in value. They may be announced orunannounced.

4. There will be a test at the middle and/or end of each chapter and will vary in point value.

5.

A cumulative final will be given at the end of the year. A midterm may be given in January.6. Grades will be based on the tests, quizzes, homework, and projects.7. Bonus work may be given occasionally. TAKE ADVANTAGE OF BONUS WORK EARLY! No last minute bonus work will be

assigned.8.

You are encouraged to keep track of your grade by checking Sapphire often.9.

Cheating or talking during a test, (whether you are finished or not) will result in a reduction of your grade (possibly to azero). Have RESPECT for others while they are finishing their exams!

10.

Quarter grades will be based on the following grading scale, as determined by district policy:A 93-100% Excellent ProgressB 85-92% Good ProgressC 77-84% Average ProgressD 70-76% Poor Progress

F Below 70% FailureI IncompleteW Withdrawal from classP Passing the course

11. The school-wide homework policy and grading scale for United Jr./Sr. High School is included in the Parent-StudentHandbook (this handbook is available on-line @http://www.unitedsd.net). Progress reports will be mailed each 4 weeksand grades will be updated weekly on EdLine, our on-line grade reporting system.

Course Assessment Plan:

Grades will be calculated as follows:

Quarter Homework 15% Year First Quarter 22.5%

All Other Grades 85% Second Quarter 22.5%

Third Quarter 22.5%Fourth Quarter 22.5%

Cumulative Final 10%

Attendance And Make-Up WorkIf it is necessary for you to miss class, it is your responsibility to make-up all work missed. This includes notes, homework,and handouts. You must make-up all work within a period of time equal to the number of days you missed, plus one day. Forexample, if you miss three days of school, work must be made-up within four days. If you were present when a test wasannounced, you must take the test when scheduled.

Supplies and Materials Needed:Bring to class daily:

1.

Textbook2.

Folder/Binder/Notebook3.

Sharpened pencil and eraser4.

Completed homework
http://www.unitedsd.net/http://www.unitedsd.net/http://www.unitedsd.net/http://www.unitedsd.net/


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Rules and Procedures:

1.

Be in your seat and prepared to work when the bell rings. I have hall duty between classes and expect you to beready to work when I enter the room.

2.

Bring all materials to class daily.3.

Be an attentive listener and learner. Do not read or do other homework during class. There may be a fewopportunities to work on other homework, but I will announce to the class when those opportunities arise.

4.

No talking during announcements.5. Students are not permitted to have food in the classroom. Gum is permitted if chewed quietly.

6.

Students are not permitted to have drinks in the classroom (see handbook, p. 5).7. Use the restroom before class. You will be given three emergency trips to the restroom each quarter. If restroom

privileges are abused, detention will be assigned.8. No electrical devices of any kind are permitted in the classroom (cell phones and cameras included). If I encounter

any electrical devices, they will be turned in to the office.9.

The dress code described in the student handbook will be enforced.10.

RESPECTyour classmates right to an education and my efforts to provide it.

Consequences

1.

Verbal warning.2.

Phone call to parents.3.

Detention.

4.

Referral to an administrator.5. **Appropriate behavior will result in positive consequences (class rewards, good notes/phone calls to your parents)

Extra Help: I am available Monday-Friday after school until 3:10 pm and during my planning period which will be period 1. Imay also be available during my duty period which is period 4. Check the schedule outside my room if you have questions.

Contact Information: Parents may contact me by phone, email or visiting the school.

Mrs. Jennifer [email protected] Number: (814)446-5615 ext. 2405Home Number: (814) 487-4506

Cell Number: (814) 341-8494

Available: 2:40-3:10 p.m. M-FPeriod 1Period 4

*Course Syllabus is Subject to Change at Teacher Discretion


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Course Outline

The indicated time spent is an estimate as classroom discussions and investigations often guide the depth of certain topics.

Prerequisite Chapter - Preparation for Calculus (5 days)

1. Graphs and Models

a. Sketch graph of an equation.b. Find the intercepts of a graph.c. Test a graph for symmetry with respect to an axis and the origin.d. Find the points of intersection of two graphs.e. Interpret mathematical models for real-life data.

2. Linear Models and Rates of Changea. Find the slope of a line passing through two points.b. Write the equation of a line with a given pint and slope.c. Interpret slope as a ratio or as a rate in real-life applications.d. Sketch the graph of a linear equation in slope-intercept form.e. Write equations of lines that are parallel or perpendicular to a given line.

3. Functions and Their Graphs

Activity: Students will use their graphing calculator to determine whether given functions are even, odd, or neither. Theyalso must describe a method for classifying a function as even, odd, or neither by inspecting the equation.

a. Use function notation to represent and evaluate a function.b. Find the domain and range of a function.c. Sketch the graph of a function.d. Identify different types of transformations of functions.e. Classify functions and recognize combinations of functions.

4. Fitting Models to Dataa. Fit a linear, quadratic, or a trigonometric model to a real-life data set.

Chapter 1 Limits and Their Properties. (20 days)

1. A Preview of Calculusa. Understand what calculus is and how it compares to precalculus.b. Understand that the tangent line problem is basic to calculus.c. Understand that the area problem is also basic to calculus.

2. Finding Limits Graphically and Numericallya. Estimate a limit using a numerical or graphical approach.b. Learn different ways that a limit can fail to exist.c. Study and use a formal definition of a limit.

3. Evaluating Limits Analyticallya. Evaluate a limit using properties of limits.b. Develop and use a strategy for finding limits.c. Evaluate a limit using dividing out and rationalizing techniques.

d. Evaluate a limit using the Squeeze Theorem.4. Continuity and One-Sided LimitsActivity: Students will use their graphing calculators to determine whether given functions are continuous over given

intervals.a. Determine continuity at a point and continuity on an open interval.b. Determine one-sided limits and continuity on a closed interval.c. Use properties of continuity.d. Understand and use the Intermediate Value Theorem.

5. Infinite Limits


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*Students will use their graphing calculators to find the limit of a function as it approaches some number c, once c has beenidentified analytically as not being in the domain of the function.

a. Determine infinite limits from the left and from the right.b. Find and sketch the vertical asymptotes of the graph of a function.

Chapter 2 Differentiation 25 days)

1. The Derivative and the Tangent Line ProblemActivity: Students will use their graphing calculator to graph a give polynomial function as well as several linear functions.

They must then determine which, if any, of the given lines appear to be tangent to the polynomial function at a predeterminedpoint and then explain their reasoning.

a. Find the slope of the tangent line to a curve at a point.b. Use the limit definition to find the derivative of a function.c. Understand the relationship between differentiability and continuity.

2. Basic Differentiation Rules and Rates of ChangeActivity: Students will collect poition data using a CBR. They will use the LIST feature of the TI-83 to reinforce the idea ofvelocity being the rate of change of position with respect to time at all points. They will then try to match a given velocitygraph and sketch the corresponding poistion graph.

a.Find the derivative of a function using the Constant Rule, Power Rule, Constant Multiple Rule, or Sum and Difference Rules

b. Find the derivative of the sine function and of the cosine function.d. Use derivatives to find rates of change.

3. The Product and Quotient Rules and Higher-Order Derivativesa. Find the derivative of a function using the Product Rule or Quotient Rule.b. Find the derivative of a trigonometric function.c. Find a higher-order derivative of a function.

4. The Chain Rule*Students are asked to find the derivative of a function using both the Product/Quotient Rules and the Chain Rule. They

are then asked to compare their results and comment on which method is simpler.a. Find the derivative of a composite function using the Chain Rule.b. Find the derivative of a function using the General Power Rule.c. Simplify the derivative of a function using algebra.

d. Find the derivative of a trigonometric function using the Chain Rule.5. Implicit Differentiation

Activity: Students are asked to graph an implicit equation using two methods: 1. Switching the x and y roles and graphingthe two resulting equations and 2. Setting the graphing calculator to parametric mode and graphing the equations. Studentswill conclude the activity by deciding if the graph has a tangent line at a given point and then explaining their reasoning.

Activity: Students are given several graphs of optical illusions in which lines intersect families of curves. In each case, thelines appear to be curved. The students are also given the equations for the for the families of curves and asked to finddy/dx for indicated values of x and y.

a. Distinguish between functions written in implicit form and explicit form.b. Use implicit differentiation to find the derivative of a function.

6. Related Ratesa. Find a related rate.

b. Use related rates to solve real-life problems.

Chapter 3 Applications of Differentiation (35 days)

1. Extrema on an intervala. Understand the definition of extrema of a function on an interval.b. Understand the definition of relative extrema of a function on an open interval.c. Find extrema on a closed interval.

2. Rolle's Theorem and the Mean Value Theorema. Understand and use Rolle's Theorem.


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b. Understand and use the Mean Value Theorem.3. Increasing and Decreasing Functions and the First Derivative Test

Activity: Students will find the relative extrema of a given function over a given interval by applying the First DerivativeTest. After the students find the extrema using this analytic approach, they will then be required to use the TI-83 to graphthe given function. Once they are able to view the graph of the function, students will be required to use the zoom and tracefeatures to estimate the relative extrema in order to compare their analytic solutions to their graphical approximations.

a. Determine intervals on which a function is increasing or decreasing.b. Apply the First Derivative Test to find relative extrema of a function.

4. Concavity and the Second Derivative Testa. Determine intervals on which a function is concave upward or concave downward.b. Find any points of inflection of the graph of a function.c. Apply the Second Derivative Test to find relative extrema of a function.

5. Limits at Infinitya. Determine (finite) limits at infinity.b. Determine the horizontal asymptotes, if any, of the graph of a function.c. Determine infinite limits at infinity.

6. A Summary of Curve Sketchinga. Analyze and sketch the graph of a function.

7. Optimization Problemsa. Solve applied minimum and maximum problems.

8. Newton's Methoda. Approximate a zero of a function using Newton's Method.

9. Differentialsa. Understand the concept of a tangent line approximation.b. Compare the value of the differential, dy, with the actual change in y, "delta" y.c. Estimate a propagated error using a differential.d. Find the differential of a function using differentiation formulas.

Chapter 4 Integration (25 days)

1. Antiderivatives and Indefinite Integrationa. Write the general solution of a differential equation.

b. Use indefinite integral notation for antiderivatives.c. Use basic integration rules to find antiderivatives.d. Find a particular solution of a differential equation.

2. Areaa. Use sigma notation to write and evaluate a sum.b. Understand the concept of area.c. Approximate the area of a plane region.d. Find the area of a plane region using limits.

3. Riemann Sums and Definite IntegralsActivity: Students will investigate the converse of the following theorem: "If a function f is continuous on the closed

interval [a,b], then f is integrable on [a,b]. In small groups, they will determine if the converse is true. Once their group hascome to a decision they will be required to write an explanation of their reasoning, including examples. They will also be

required to describe the relationship among continuity, differentiability, and integrability.a. Understand the definition of a Riemann sum.b. Evaluate a definite integral using limits.c. Evaluate a definite integral using properties of definite integrals.

4. The Fundamental Theorem of Calculusa. Evaluate a definite integral using the Fundamental Theorem of Calculus.b. Understand and use the Mean Value Theorem for Integrals.c. Find the average value of a function over a closed interval.d. Understand and use the Second Fundamental Theorem of Calculus.

5. Integration by Substitution


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a. Use pattern recognition to evaluate an indefinite integral.b. Use a change of variables to evaluate an indefinite integral.c. Use the General Power Rule for Integration to evaluate an indefinite integral.d. Use a change of variables to evaluate a definite integral.e. Evaluate a definite integral involving an even or odd function.

6. Numerical Integrationa. Approximate a definite integral using the Trapezoidal Rule.b. Approximate a definite integral using Simpson's Rule.

c. Analyze the approximate error in the Trapezoidal Rule and in Simpson's Rule.

Chapter 5 Logarithmic, Exponential, and Other Transcendental Functions (35 days)

1. The Natural Logarithmic Function: Differentiationa. Develop and use properties of the natural logarithmic function.b. Understand the definition of the number e.c. Find derivatives of functions involving the natural logarithmic function.

2. The Natural Logarithmic Function: Integrationa. Use the Log Rule for Integration to integrate a rational function.b. Integrate trigonometric functions.

3. Inverse Functions

Activity: Students will be required to explain how to "undo" several given functions. They will then use their explanationsto write the inverse function of each given function. Next, students will use the TI-83 to graph each function and its inversein the same "square" viewing window. Students must turn in a paragraph or two on their observations of each pair of graphs.

a. Verify that one function is the inverse of another function.b. Determine whether a function has an inverse function.c. Find the derivative of an inverse function.

4. Exponential Functions: Differentiation and Integrationa. Develop properties of the natural exponential function.b. Differentiate natural exponential functions.c. Integrate natural exponential functions.

5. Bases Other than e and Applicationsa. Define exponential functions that have bases other than e.

b. Differentiate and integrate exponential functions that have bases other than e.c. Use exponential functions to model compound interest and exponential growth.

6. Differential Equations: Growth and Decaya. Use separation of variables to solve a simple differential equation.b. Use exponential functions to model growth and decay in applied problems.

7. Differential Equations: Separation of Variablesa. Use initial conditions to find particular solutions of differential equations.b. Recognize and solve differential equations that can be solved by separation of variables.c. Recognize and solve homogeneous differential equations.d. Use a differential equation to model and solve an applied problem.

8. Inverse Trigonometric Functions: Differentiationa. Develop properties of the six inverse trigonometric functions.

b. Differentiate an inverse trigonometric function.c. Review the basic differentiation formulas for elementary functions.9. Inverse Trigonometric Functions: Integration

a. Integrate functions whose antiderivatives involve trigonometric functions.b. Use the method of completing the square to integrate a function.c. Review the basic integration formulas involving elementary functions.

10. Hyperbolic Functionsa. Develop properties of hyperbolic functions.b. Differentiate and integrate hyperbolic functions.c. Develop properties of inverse hyperbolic functions.


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d. Differentiate and integrate functions involving inverse hyperbolic functions.

Chapter 6 Applications of Integration (25 days)

1. Area of a Region Between Two Curvesa. Find the area of a region between two curves using integration.b. Find the area of a region between intersecting curves using integration.c. Describe integration as an accumulation process.

2. Volume: The Disk Methoda. Find the volume of a solid of revolution using the disk method.b. Find the volume of a solid of revolution using the washer method.c. Find the volume of a solid with known cross sections.

3. Volume: The Shell Methoda. Find the volume of a solid of revolution using the shell method.b. Compare the uses of the disk method and the shell method.

4. Arc Length and Surfaces of Revolutiona. Find the arc length of a smooth curve.b. Find the area of a surface of revolution.

5. Worka. Find the work done by a constant force.

b. Find the work done by a variable force.6. Moments, Centers of Mass, and Centroids

Activity: Students will cut an irregular shape from a piece of cardboard. First, they will find the centroid by holding apencil point vertically and moving the object on the pencil point until the centroid is located. Next, they will divide the objectinto representative elements, making necessary measurements and numerically approximating the centroid. Finally, studentswill compare their results and present their findings to the class.

a. Understand the definition of mass.b. Find the center of mass in a one-dimensional system.c. Find the center of mass in a two-dimensional system.d. Find the center of mass in a planar lamina.e. Use the Theorem of Pappus to find the volume of a solid of revolution.

7. Fluid Pressure and Fluid Force

a. Find fluid pressure and fluid force.


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I, THE UNDERSIGNED STUDENT, ACKNOWLEDGE THAT I HAVE RECEIVED A COPY OF THE COURSE

SYLLABUS FOR MRS. BUCHKOVICHS CLASS. I HAVE READ THE DOCUMENT THOROUGHLY AND

UNDERSTAND ITS CONTENT.

PRINT YOUR NAME

SIGNATURE

DATE


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STUDENT INFORMATION SHEET

Name:________________________________________________________________________________________________

Home Phone________________________________________ Birth date_______________________________________

Address:______________________________________________________________________________________________

Parent Guardian First and Last Name(s)______________________________________________________________

Parent/Guardian Work Phone and/or Cell Phone______________________________________________________

What grade do you expect to get from this class?_______________________________________________________

Are you taking any other math classes this year? If yes, which class(es)?_______________________________

Do you have a computer available for your use at home? Yes - No Do you have access to the Internet at

home? Yes - No If you do have Internet access, what type is it? Dial-Up - High Speed

Name some of your interests/hobbies:_________________________________________________________________

What extracurricular activities do you participate in at United?________________________________________

Do you have a job? If so, where, and how many hours per week (on average) do you work?

What are your plans for the future (if you have any yet)?_______________________________________________

Name two things I should especially know about you._________________________________________________

AP Syllabus With Course Outline.website

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