Calculus Syllabus



AP Calculus Syllabus – Mr. Tactay

COURSE OVERVIEW and PREREQUISITES

This course is designed for those students who have demonstrated mastery in algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise defined. In particular, before studying calculus, students must be familiar with the properties, graphs, and the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so on). Students must also be familiar with the various techniques and formulas for simplifying, factoring, and solving functions. In addition, it is expected for students to know the values of the trigonometric functions of the numbers 0, [pic], [pic], [pic], [pic], and their multiples.

The major topics of study will include functions, limits, differential calculus, and integral calculus.

COURSE OBJECTIVE

The primary objective of this course will be to understand the underlying mathematics of calculus. That is, to understand the geometrical and numerical meanings of each concept in conjunction with the algebraic processes involved in the study of calculus. Throughout the year you will be asked to interpret, understand, and apply the concepts and relationships of all major topics in four ways: geometrically (graphs), numerically (tables of data), algebraically (formulas, functions, etc.), and verbally. The textbook and supplementary material will reinforce this approach by encouraging the communication of solutions to problems both verbally and in written sentences. The ability to do so will greatly determine your success on the AP Calculus Exam.

CONTACT INFORMATION (541)386– 4500 ext.4651 or troy.tactay@hoodriver.k12.or.us

HOW TO GET HELP

You may receive help from Mr. Tactay before school starting from approximately 7:45 am, or during his Prep Periods, 3 and 7, during lunch (arrange with Mr. Tactay first), or after school. The school website currently contains my syllabus and assignment sheets. I will also try to include all handouts and grades on the website.

REQUIRED MATERIALS

It is your responsibility to come to class prepared. I expect you to bring your textbook (with a book cover on it), pencils or pens, and loose-leaf paper. A graphing calculator is required. You will also need to bring your tissues. MR. TACTAY WILL NOT PROVIDE CALCULATORS!!!

TEXTBOOK and RESOURCE MATERIALS

Calculus. Deborah Hughes-Hallett, Andrew M. Gleason, et al. John Wiley & Sons, Inc. 2005. Fourth Edition.

Amsco’s AP* Calculus AB/BC: Preparing for the Advanced Placement Examinations. Maxine Lifshitz. Amsco School Publications. 2004.

Master the AP* Calculus AB & BC Tests. W. Michael Kelly and Contributing Author, Mark Wilding. Peterson’s, a division of Thomson Learning, Inc. 2002.

* AP is a registered trademark of the College Entrance Examination Board, which does not endorse these books.

GRADING

Your grade is determined entirely by Chapter Tests and Final Exams.

Tests - Tests are worth 100 points each. They are curved according to your potential to pass the AP Exam. That is, a 90 average on tests would correlate to a potential of passing the AP Exam with a 3 score. An average in the upper 90’s would correlate to a 4. An average of over a 100 would correlate to a 5. They will be taken on scheduled dates. If you miss a test, you must make it up the day you return to class. NO EXCEPTIONS. You must make prior arrangements (before the test, not on test day) with Mr. Tactay in order to take the test on a later date.

Final Exam – This makes up 50% of your overall Semester Grade.

Academic Honesty – Any cheating in any form, despite how small, will result in an automatic zero points.

Grades in this course are based on specific measurable progress on the Common Core State Standards (CCSS) and from the AP College Board.

LETTER GRADES

A 90% and above C 70% - 79.94% F less than 60%

B 80% - 89.94% D 60% - 69.94%

TEST TAKING & QUIZ BEHAVIOR

Nothing is allowed on the desks during tests or quizzes except for a calculator (when allowed) and a writing utensil. Notes are not allowed. There will be absolutely NO FORM OF INTERACTION OR COMMUNICATION – VERBAL OR NONVERBAL - UNTIL EVERYONE HAS COMPLETED THE TEST. This includes talking, eye contact, passing notes, asking for pencil, paper, etc. If you need anything, raise your hand and ask Mr. Tactay. Leave your seats only to sharpen you pencil or to hand in your tests.

CONSEQUENCES: Inappropriate behavior during tests will result in lunch time detention or an automatic ZERO on the test.

TEST TIME LIMIT: You are to complete your tests or quizzes in the allotted time. You will be given the entire class period to complete your tests. YOU WILL NOT BE ALLOWED TO TURN IN AN UNFINISHED TEST AND COME BACK LATER TO FINISH IT.

CHAPTER TESTS & FINAL EXAM

Every question on the chapter tests will be an AP style question. The first semester is devoted to mastering the multiple choice portion of the AP Exam, while the second semester will be devoted to mastering the free response portion. Each chapter test will include material from previous tests. By the end of the first semester, the Final Exam will be equivalent to the entire multiple choice portion of the AP Exam. Similarly, the last chapter test in the second semester before the actual AP Exam will be comparable to the free response portion.

There will be about a month remaining after the AP Exam. An additional chapter will be covered at that time. That chapter test will only have material from that chapter and will take the place of the final exam.

THE AP CALCULUS EXAM

The AP Calculus Exam is on Wednesday, May 7, 2014. This is an A-Day. All topics, problems, and examples will represent the type of knowledge, skill, and understanding you will need to be successful on the AP Calculus Exam. This exam, as well as all other AP Exams, will give you a score ranging from 1 to 5. A score of at least a 3 is considered passing by most colleges.

AP Exam 2014

 

Regular Registration: $89 per exam, ($10-$18? for free/reduced lunch): Deadline is March 7, 2014

Late Registration: $139 per exam, (last year $25 for free/reduced lunch): Deadline is March 14, 2014

 

AP Pre-Administration Sessions: April 21 @3:15pm or April 22 @ 7:30am.

 

Students who have school related conflicts may choose to test late (sports contests) or if a student registers for two exams on the same day and time.

 

No exams will be ordered after March 14th.

 

If you have any questions, then contact Ms. Bentley, guidance counselor.

TARDY POLICY

This policy is for the entire semester and will start over for the second semester.

First three tardies: no consequence.

Fourth tardy: lunch detention in my classroom for 15 minutes. Failure to come to lunch detention will be an immediate referral.

Fifth and every tardy thereafter: a discipline referral will be given for each tardy.

LEAVING CLASS

You have a FIVE MINUTE LIMIT when leaving class. Leaving for more than that time will result in lunch time detention or a discipline referral. IT IS SCHOOL POLICY THAT YOU STAY IN THE CLASSROOM THROUGHOUT THE ENTIRE PERIOD. LEAVE FOR EMERGENCIES ONLY. You may not leave during the first 20 minutes of class. Doing so, even with the pass, will count as being tardy.

CELL PHONES, IPODS, and OTHER TECHNOLOGY IN CLASS

Cell Phones are not to be used in class, even if you are using it for its calculator capabilities. iPods, Kindles, and other technology are also not allowed. They all must be put away, OUT OF SIGHT and TURNED OFF completely. Using them in class will result in CONFISCATION, and an IMMEDIATE REFERRAL. A parent must come to the front office after school in order to get it back. To avoid potential use of unwanted technology, it is recommended to keep both hands above your desk at all times.

CALCULATOR USE IN CLASS

Graphing calculators are recommended to help understand and verify mathematical concepts. However, they should be used for mathematical purposes only. Any non-mathematical purposes (such as games, writing notes, drawing, or just typing in numbers or words so they run down your screen) the confiscation of the calculator. It will be returned at the end of the period.

Below are things that you need to know for your graphing calculator that will help you to become more successful.

1. Inputting functions into y=.

2. All keys involved in graphing a function. ie all the information under the keys "window", "zoom", "trace", and "graph."

Especially:

- Know how to change the window.

- Know how to solve an equation looking at the graph. ie use "zero" or “intersect” under the key "Calc."

- Know how to solve a system of equations of two graphs. ie use the "intersect" under the key "Calc."

- Know how to "Zoom In" and "Zoom Out" on a graph

3. All keys involved in creating a table of values of a function. ie the keys "table set" and "table."

Especially:

- Know how to create a table using a constant change in x.

- Know how to create a table by "asking" what x is.

4. Understand the information in "Mode," especially the fact that most trigonometric problems require the calculator to be in radian mode.

5. Basic knowledge of typing in functions correctly.

Especially:

- functions with automatic parenthesis like sin(, cos(, and ln(.

- inputting exponents

- inputting fractions

6. Use the key "Sto" to store a value for X then evaluate the value of a function at that point.

ACTIVITIES and WRITING ASSIGNMENTS

The use of calculators to solve problems and verify answers will be ongoing throughout the course. However, separate activities will be given to help conceptualize major ideas. Each activity below can be found in the course outline, denoted by *.

Group/Calculator Activity 1: Domain, Range, and Asymptotes

You will work in groups to predict the domain, range, and asymptotes of various functions, then verify using the calculator.

Group/Calculator Activity 2: Limits

You will work in groups to graphically and numerically evaluate limits using the calculator.

Calculator Activity 3: Zooming in to find the Derivative

You will zoom in at a point to find the derivative using a Difference Quotient. You will then verify using Math 8.

Writing Assignment 1: The Derivative

You will explain the meaning of the derivative, relating the graphical meaning of slope to the formal definition of the derivative.

Group Activity 4: Tangent Line Approximations

You will work in groups to find equations of tangent lines numerically (from a table of values) and algebraically (using the short-cuts) and use them to predict values.

Group/Calculator Activity 5: Optimization - Maximizing and Minimizing

You will work in groups to solve classic optimization problems. You will solve the problem first without the use of calculus by creating a table, then verify using the graph. You will then solve the problem using calculus.

Group Activity 6: The Definite Integral and Distance Traveled

You will work in groups to find the distance between two locations in town. You will record data of your velocities for three different cases – every two minutes, every minute, and then every 10 seconds. The definite integral using the trapezoid rule for the three different cases will estimate the distance traveled.

Writing Assignment 2: The Definite Integral

You will explain the meaning of the definite integral, relating the graphical meaning of area to the notation of the definite integral.

AP CALCULUS LEARNING GOALS and COURSE OUTLINE

* denotes Group/Calculator activity

Chapter 1: Review - Functions and Graphs (2 to 3 weeks)

A. Simplify, Graph, and Analyze Basic Functions and their Graphs

1. Slope and Equation of lines

2. Exponential, Logarithmic Functions, and Polynomials

B. Understand the Properties and Language of Functions and Inverses

* 1. Domain, Range, and Asymptotes - Group/Calculator Activity 1

2. Graphs of Inverse Functions

C. Graph a Function from a Family of Functions - Translations, Reflections, and Amplitudes

D. Graph, Solve, and Apply Trigonometric Functions

1. Unit Circle and Graphing

2. Solving and Applications

E. Understand Properties of Limits and Evaluating Limits

1. The Concept of Limits for Finding Horizontal or Vertical Asymptotes

2. Left and Right Hand Limits

3. The Limit Definition for Continuity/Discontinuity

* 4. Analyzing Limits Approaching a Finite Number and Infinity Graphically and Numerically

- Group/Calculator Activity 2

F. Evaluate Limits using Algebraic Techniques

1. Limits Approaching a Finite Number

2. Limits Approaching Infinity

3. Limits of Piecewise Functions

G. Evaluate Limits using L’Hôpital’s Rule

H. Understand Removable and Jump (Essential) Discontinuity

1. Graphical Analysis of Discontinuity – show on the calculator how to recognize

2. The Algebraic Relationship of the Function and the Discontinuity

Chapter 2: Introduction to The Derivative (3 weeks)

A. Understand the Graphical Definition of The Derivative - Slope of the Tangent Line

1. Relationship between the Derivative and its Function

2. The Derivative as the Average Rate of Change

3. Difference Quotient

B. Using the Formal Definition of the Derivative

1. Recognize the Definition

* 2. Find the Derivative at a Point Using the Definition - Calculator Activity 3

C. Understand, Interpret, and Apply the Derivative

1. Instantaneous and Average Velocity

2. The Meaning Behind the Units and Notations of the Derivative

3. Estimate the Derivative from a Tables of x, y Values

D. Graph the Derivative of a Function

E. Find the Equation of a Tangent Line

1. Use the Calculator to Find Slope at a Point

2. Estimate the Equation of a Tangent Line from a Tables of x, y Values

E. Analyze the Graph of a Function to Determine Values of the First and Second Derivatives

1. Find Critical Points from the Graph of the Function

2. Understand the Relationship between the Intervals of Increase or Decrease of

the Function and the Values of the First Derivative

3. Understand the Relationship between the Intervals of Concave Up or Down of

the Function and the Values of the Second Derivative

4. Sketch the First Derivative from the Behavior of the Function

F. Estimate the Second Derivative from Tables of Values

* G. Writing Assignment 1: The Derivative

Chapter 3: Rules and Shortcuts of The Derivative (3 weeks)

A. Find the Derivative of Powers, Polynomials, and Exponents

B. Find the Derivative of Trigonometric Functions

C. Find the Derivative of Natural Logs

D. Find the Derivative of the Chain Rule

D. Find the Derivative using the Product and Quotient Rules

*E. Find the Equation of a Tangent Line Using the Rules and Shortcuts for Derivatives

- Group/Calculator Activity 4

F. Find the Derivative of an Implicit Function

Chapter 4: Using Derivatives to Understand the Behavior of the Parent Function (2 to 3 weeks)

A. Find the Critical Points of a Function Using the Short-Cuts of the Derivative

1. Use the First Derivative Test to find Local (relative) extrema

2. Classify Critical Points and Endpoints as Global (absolute) extrema

B. Analyze the Graphs and Values of the First and Second Derivatives

1. Finding Intervals of Increase or Decrease of the Parent Function

2. Finding Intervals of Concave Up or Down of the Parent Function

3. Use the Second Derivative Test to Find Extrema

4. Sketch the First Derivative from the Behavior of the Function

*C. Optimization - Use the Derivative and Critical Points to Solve Problems that Maximize or Minimize Physical Measurements - Group/Calculator Activity 5

D. Related Rates - Use Implicit Differentiation to Solve Problems Involving Rates of Change Over Time

E. Use the Derivative to Solve Problems Involving Position, Velocity, and Acceleration of a Particle in Motion or Projectiles

F. Understand Basic Derivative Theorems

1. The Extreme Value Theorem

2. Rolle’s Theorem

3. The Mean Value Theorem

Unit 5: The Definite Integral (3 weeks)

A. Understand the Graphical Definition of the Definite Integral

1. Approximate the Area Under a Curve Using Riemann Sums

a. Left- and Right-Hand Sums

b. Midpoint Rule

2. Approximate the Area Under Using the Trapezoid Rule

*B. Group Activity 6

C. Use the Short-Cuts to Find the Antiderivatives or Indefinite Integrals of Power Functions

D. Apply The Fundamental Theorem of Calculus

1. Calculate the Definite Integral

2. Interpret the Meaning of the Definite Integral of Rates

(eg. Velocity, Gallons per minute, Population per year, etc.)

3. Find the Area Under the Curve of a Function

a. Interpret that Area as the Total Change of its Antiderivative

b. Use that Area to Graph the Antiderivative

E. Use the Definite Integral to Find the Average Value of a Function

*F. Writing Assignment 2: The Definite Integral

Chapter 6: More on The Definite Integral (3 weeks)

A. Integrate Exponential, Natural Logarithmic, and Trigonometric Functions

B. Integrate by u-Substitution

C. Solve Differential Equations by Separation of Variables

D. Find the Area Between Two Functions

E. Find the Volumes of Solids of Revolution

1. Disk Method

2. Washer Method

F. Find the Volumes of Solids with Known Cross Sections Perpendicular to the x or y axes

Additional AP Topics of The Definite Integral and AP Exam Review (3 weeks)

A. Analyze Two Rate Functions Over a Given Interval

B. Sketch the Slope Fields of the Solutions of Differential Equations

C. Solve Problems Involving The Fundamental Theorem of Calculus: Part Two

1. Derivatives of Definite Integrals

2. The Accumulation Function

D. AP Exam Review

The AP Exam

Wednesday, May 7, 2014, B-Day

Unit after the AP Exam : Miscellaneous Topics (3 weeks)

A. Limits of Trigonometric Functions

B. Derivatives of Inverse Trigonometric Functions

C. Graphing Functions Using First and Second Derivatives

D. Integration by Parts

E. More Definite Integral Applications

1. Income Stream

2. Density

3. Work

4. Pumping Water Problems

CLASSROOM EXPECTATIONS

1. NO TALKING!!!!

Do not be disruptive at any time during the entire class period. Being disruptive includes but is not limited to the following behaviors: - talking while Mr. Tactay is talking

- swearing or using inappropriate words

- making rude comments

- making noises with your pencil, chair, desk, etc.

- making noises with yourself (burping, whistling, talking to yourself, foot tapping, etc.)

- non-verbal communication with other students at inappropriate times

In other words, if Mr. Tactay corrects your behavior by telling you to “quiet down” or “stop doing that” or “get back to work,” then you are being disruptive.

2. No Cell Phones or other technology are allowed. Breaking this rule results in an IMMEDIATE REFERRAL and CONFISCATION. A parent must come to the front office after school in order to get it back.

3. Absolutely no eating of all food - especially gum, candy, and sunflower seeds – is allowed.

Breaking this rule results in an IMMEDIATE REFERRAL.

4. No soda, energy drinks, or even bottled water are allowed. Only water from non-disposable containers is acceptable. Breaking this rule results in an IMMEDIATE REFERRAL.

5. Pick up any pieces of trash – despite how small – which are on the floor and inside or on top of your desks. This will be easier if rules #3 and #4 are followed.

6. Come to class, be on time, and be in your seats when the bell rings for the start and the end of class. Leave your seats only when necessary such as sharpening your pencil, getting materials, and throwing away trash.

If the bells are not working, you will leave when Mr. Tactay releases you.

7. Work throughout the entire class period. Work only on MATH during class. No reading books, magazines, or assignments form other classes unless you are completely caught up.

8. No one is allowed to go to the library during class for any reason - not even to just get a book, catch up on HW in other classes, print stuff, etc.

9. Bring necessary materials – book, pencil, paper, tissues, calculator, etc. – to class everyday.

10. Leave everything on my desk alone. No one is allowed to touch or take anything in or on my desk without my permission.

11. Do not put your feet up on tables or chairs.

12. No sitting on desks or on the back supports of chairs.

13. No sleeping in class.

14. No one from outside of class is allowed to speak to you during class, except for teachers or parents.

15. No card playing – not even solitaire.

16. No switching seats. Stay in your assigned seats.

17. No eye contact with anyone else in class.

18. No socializing in class.

19. No passing notes in class.

20. No complaining, whining and making excuses.

21. No asking for free time or to go outside of class for a nature walk, exercise, etc.

22. No standing by the doors at the end of class. Stay seated in your chairs.

23. No childish behaviors such as spit wads, paper airplanes, throwing pencils at the ceiling, etc.

24. No painting, clipping, or chewing fingernails during class time.

25. Don’t ask dumb questions. In this class, a dumb question is a question that has nothing to do with math or does not have anything to do with the topic we’re discussing. If you don’t know if you have a dumb question, then it probably is . . . so don’t ask it.

Failure to follow ANY of the classroom expectations above may result in one or more of the following:

1) Lunch time detention

2) Removal from the classroom

3) Phone call to parents

4) Referral to the office

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