Course Name: Calculus AP

Instructor: Mr. Allison

 

Course Overview:

CALCULUS (AP) - Year – 1 Unit

The objective of this course is to provide students with an understanding of the role of calculus in the study of higher mathematics.  Topics covered include Analytic Geometry, functions, limits, and derivatives of algebraic functions with applications to maxima and minima problems, integration and application of the definite integral. Technology will also be utilized to help students identify graphs of functions and describe their properties, behavior, and tendencies.  Students will be instructed through classroom lecture and modeling.  Opportunities for individual practice and cooperative learning will also be given.  Activities designed to promote discovery of concepts and higher-order thinking skills will be provided through individual and group activities.  Students will be expected to participate in class activities and complete assigned work.

Course Objectives:

Upon successful completion of Skills Development, the student should be able to:

• Understand the meaning of the derivative in terms of rate of change and linear approximations.
• Be able to work with functions represented graphically, numerically, analytically, or verbally, and should understand the connections among these representations.
• Understand the meaning of the definite integral both as a limit of Reimann Sums and as a net accumulation of the rate of change.
• Bea able to model problem situations with functions, differential equations, or integrals.
• Be able to represent differential equations with slope fields, solve separable differential equations analytically, and solve differential equations using numerical methods such as Euler’s Method.

 

Classroom Rules:

• Attendance

It is absolutely necessary that you attend class on a regular basis.  In the case of an absence, you must get an excusal slip from your academy secretary before you return to class.  Do not enter the classroom without an excusal slip.

 

• Behavior

Class will begin promptly every day.  I expect you to come to class prepared and ready to work.  Off-task behavior is unacceptable.  Responsible and respectful behavior is expected at all times.  The following rules are to be followed at all times:  Be Respectful, Be Honorable, Be There, and Be Prepared.  A more detailed explanation of classroom rules and expectations follows in the Code of Conduct Contract.

 

• Tardies

You MUST arrive to class on time!  Class will begin promptly each day.  I expect you to be prompt as well.  Coming to class late is a disruption in the educational process of others; therefore, it will be handled in a very strict, consistent fashion.  I expect you to be in your seat when the bell rings; otherwise, that, too, will be considered a late.  Accurate records will be kept.  If you are late to class 2 times, a phone call home will be made.  If you are late an additional 2 times (total of 4 lates), another phone call home will be made and a log will be written.  Bottom line, BE ON TIME!!!!!!!

Course Materials:

1.)  Loose leaf notebook paper (provided)

2.)  Pencils

3.)  Calculator

4.)  Folder

Course Text & Readings:

                Calculus:  Scott Foresman – Addison Wesley

Assessments:

There will be a variety of formative and summative assessments used throughout the year including tests, quizzes, and classroom observation.

Grading Policy & Procedures:

• Grading Scale

Grades can be determined at any time throughout the term using the following grading scale:

                                                                100 – 93 %                A

                                                                92 – 82 %                  B

                                                                81 – 70 %                  C

                                                                69 – 60 %                  D

                                                                59 – 0 %                     F

 

• Academic Dishonesty

Any act of academic dishonesty (cheating on exams, plagiarism of homework, etc.) WILL NOT

BE TOLERATED and will result in the following:

 

1.)  a zero on the work involved

2.)  a phone call home to parent/guardian

3.)  a discipline log being sent to the office.

 

 

• Quizzes / Tests

Quizzes will be given throughout the units of study and may be announced or unannounced.  We quiz frequently throughout each unit of study.   

Tests will occur at the end of each unit of study.  They will always be announced at least two days in advance.  Please try to be in attendance on test days!  In some cases, we will review the day before a test.  If you are absent on a review day, you are still responsible for taking the test the day you return!  No exceptions! 

 

• Homework

Most of your learning experiences will take place inside the classroom; however, there are times when homework will be assigned.  You are expected to have your homework completed by the due date.  No late homework will be accepted.  No exceptions, no excuses.

   

 

 

 

 

 

 

Course Outline:

 

Prerequisites for Calculus

• Lines
• Functions and Graphs
• Exponential Functions
• Parametric Equations
• Functions and Logarithms
• Trigonometric Functions

Limits and Continuity

• Rates of Change and Limits
• Limits Involving Infinity
• Continuity
• Rates of Change and Tangent Lines

Derivatives

• Derivative of a Function
• Differentiability
• Rules for Differentiation
• Velocity and Other Rates of Change
• Derivatives of Trigonometric Functions
• Chain Rule
• Implicit Differentiation
• Derivatives of Inverse Trigonometric Functions
• Derivatives of Exponential and Logarithmic Functions

Applications of Derivatives

• Extreme Values of Functions
• Mean Value Theorem
• Connecting f’ and f” with the Graph of f
• Modeling and Optimization
• Linearization and Newton’s Method
• Related Rates

The Definite Integral

• Estimating with Finite Sums
• Definite Integrals
• Definite Integrals and Antiderivatives
• Fundamental Theorem of Calculus
• Trapezoidal Rule

Differential Equations and Mathematical Modeling

• Antiderivatives and Slope Fields
• Integration by Substitution
• Integration by Parts
• Exponential Growth and Decay
• Population Growth
• Numerical Methods

Applications of Definite Integrals

• Integral as a Net Change
• Areas in the Plane
• Volumes
• Lengths of Curves
• Applications from Science and Statistics

 

 

 

Code of Conduct Contract

2009 – 2010

v All Greater Johnstown regulations, responsibilities, and disciplinary options stated in the Code of Student Discipline book will be expected and followed for every student in this classroom.

 

v Point values will be assigned to each infraction.

 

1.)       Respect yourself, classmates, administration, faculty, staff, and

property of JHS.  Treat others as you wish to be treated.   

2.)       Students will be ON TIME FOR CLASS!  Sleeping or inactivity will

not be tolerated.

3.)       Students will remain seated at all times.

 

4.)       Students will raise their hands to talk.

 

5.)       Students need to be prepared for EVERY class.  No one will be

permitted to leave the classroom after the bell rings for the start of class.

6.)       Students are expected to do their own work.  Plagiarism and

cheating will result in disciplinary actions as stated in the Greater Johnstown School Handbook and could result in a failing grade for the year.

7.)       Students are expected in class EVERY DAY!  When absent, YOU are responsible for any make-up work.

 

8.)       Please leave food, candy, and drinks at home.

 

9.)       All electronic devices are prohibited in the classroom.  Specifically, cell phone possession is severely restricted.  Students caught with cell phones in their possession will have them confiscated and they must be picked up by a parent/guardian in the main office.

 

 

 

 

Please return this paper to Mr. Allison no later than Thursday, September 2nd.

 

I have read and understand the overall course structure as well as the student requirements and responsibilities.   I have also read the rules in the Code of Conduct Contract and understand them and the consequences that result if not followed. 

 

Student Name:
Student Signature :		Date:
Parent/ Guardian Name:		Relation:
Parent / Guardian Signature		Date: