AP Calculus AB - Quia



AP Calculus

Huron High School

2008-2009

Amy Marie Trotter Weerts

amy.weerts@k12.sd.us

Room: A124

Class Webpage:

Good times to see me with questions or concerns:

• Between 7:45 and 8:00 or 3:15 and 3:30

• Fifth period or eighth period

• By appointment

Course Overview

This is a rigorous course intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, geometry, and pre-calculus. Elementary functions, differential calculus and integral calculus will be the three major areas that will be studied through a thorough approach. The goal is for all students to have the background and knowledge base to take the AP Calculus exam in May.

Course Planner

Below is the sequence of our AP Calculus AB course. This course is taught on an A/B block schedule so class only meets every other day for 90 minutes.

|Section Numbers |Topics |Timeline |

|P.1 |Graphs and Models |1 day |

|P.2 |Linear Models and Rates of Change |1 day |

|P.3 |Functions and Their Graphs |1 day |

|P.4 |Fitting Models to Data |1 day |

|1.1 |A Preview of Calculus |½ day |

|1.2 |Finding Limits Graphically and Numerically |1 ½ days |

|1.3 |Evaluating Limits Analytically |1 day |

|1.4 |Continuity and One-Sided Limits |1 day |

|1.5 |Infinite Limits |1 day |

|2.1 |The Derivative and the Tangent Line Problem |2 days |

|2.2 |Basic Differentiation Rules and Rates of Change |2 days |

|2.3 |The Product and Quotient Rules and Higher-Order Derivatives |1 day |

|2.4 |The Chain Rule |1 day |

|2.5 |Implicit Differentiation |1 day |

|2.6 |Related Rates |2 days |

|3.1 |Extrema on an Interval |1 day |

|3.2 |Rolle’s Theorem and the Mean Value Theorem |1 day |

|3.3 |Increasing and Decreasing Functions and the First Derivative Test |1 ½ days |

|3.4 |Concavity and the Second Derivative Test |1 ½ days |

|3.5 |Limits at Infinity |1 day |

|3.6 |A Summary of Curve Sketching |1 day |

|3.7 |Optimization Problems |2 days |

|3.8 |Newton’s Method |1 day |

|3.9 |Differentials |1 day |

|4.1 |Antiderivatives and Indefinite Integration |1 day |

|4.2 |Area |2 days |

|4.3 |Riemann Sums and Definite Integrals |1 day |

|4.4 |The Fundamental Theorem of Calculus |1 day |

|4.5 |Integration by Substitution |2 days |

|4.6 |Numerical Integration |1 day |

| |Review of Logarithms |1 day |

|5.1 |The Natural Logarithm Function: Differentiation |1 day |

|5.2 |The Natural Logarithm Function: Integration |1 day |

|5.3 |Inverse Functions |1 day |

|5.4 |Exponential Functions: Differentiation and Integration |1 day |

|5.5 |Bases other than e and Applications |1 day |

| |SEMESTER ONE EXAM |1 day |

|5.6 |Differential Equations: Growth and Decay |1 day |

|5.7 |Differential Equations: Separation of Variables |1 day |

|5.8 |Inverse Trigonometric Functions: Differentiation |1 day |

|5.9 |Inverse Trigonometric Functions: Integration |1 day |

|6.1 |Area of a Region Between Two Curves |1 day |

|6.2 |Volume: The Disk Method |2 days |

|6.3 |Volume: The Shell Method |2 days |

|6.4 |Arc Length and Surface of Revolution |1 day |

|7.1 |Basic Integration Rules |1 day |

|7.2 |Integration by Parts |1 day |

|7.3 |Trigonometric Integrals |1 day |

|7.4 |Trigonometric Substitution |1 day |

|7.5 |Partial Fractions |½ day |

|7.7 |Indeterminate Forms and L’Hopitals Rule |1 day |

| |Slope Fields |1 day |

AP Exam Review

|Review Item |Timeline |

|2001 Free Response Exam |1 day |

|2002 Free Response Exam |1 day |

|2004 Free Response Exam |1 day |

|2005 Free Response Exam |1 day |

|2006 Free Response Exam |1 day |

|2007 Free Response Exam |Optional |

|Multiple Choice Exam #1 |2 days |

|Multiple Choice Exam #2 |2 days |

|Multiple Choice Exam #3 |2 days |

|Multiple Choice Exam #4 |2 days |

|Multiple Choice Exam #5 |2 days |

|Multiple Choice Exam #6 |Optional |

|Practice Exam: 2003 Released Free Response Exam |45 minutes + 45 minutes |

|Practice Exam: 2003 Released Multiple Choice Exam |50 minutes + 55 minutes |

After the AP Exam

|Journal Article: Read and Reflect |1 day |

|Journal Article: Read and Reflect |1 day |

|Course Reflection Paper |1 day |

Teaching Strategies

It is clearly stated by the teacher from the beginning of this course that the goal is to prepare each student with the skills and knowledge necessary to pass the AP Exam. This goal requires rigorous instruction by the teacher and sincere dedication from each student.

The course is designed to present the students with instruction on each of the topics listed above. Students are required to practice these skills and demonstrate competency on assessment devices. Students will integrate technology into topics through the use of the TI-83/84 calculator, Calculator Based Ranger (CBR), and Calculator Based Laboratory (CBL) and probes. Lab reports are prepared periodically using TI-Interactive in order to combine collected data with a written analysis of the results.

After all of the topics are presented, time is reserved for an intensive review of the procedures and format of the AP Exam. Students will use prior years’ exams and other resources to practice problems and see how their work would be scored by a national reviewer. Students are required to prepare a portfolio of all of their work from this review unit.

Technology and Computer Software

Teacher uses TI-84 graphing calculator combined with TI-Smartview and a Gateway Tablet PC for classroom presentations. Students are encouraged to use the features of Microsoft OneNote to organize notes taken from instructional presentations.

QUIA is also used as an instructional tool for this course. All handouts or worksheets needed for this course are available for download from our QUIA class page. Announcements, a calendar of study topics, assignments, quizzes, etc., and many other things can be found using this page.

Student Evaluation

Quarter grades are calculated from students’ performance on daily homework assignments, free-response and multiple-choice quizzes, writing assignments, discussion assignments, lab reports, and free-response and multiple-choice exams. Each quarter grade makes up 40 percent of the semester grade and the semester exam makes up the final 20 percent. It is the goal of the teacher to duplicate the format of the AP Exam by giving a multiple-choice and free-response form of every test and quiz. The text provides an excellent test bank of multiple-choice and open-ended problems that begin to prepare the students for the format of the AP Exam. However, the six weeks of intense review prior to the exam are reserved for students to be evaluated in an identical manner as they will be on the AP Exam.

Teacher Resources

Primary Textbook

Larson, Ron, Hostetler, Robert P., and Edwards, Bruce H. Calculus of a Single Variable. 7th ed. Boston: Houghton Mifflin Company, 2002.

Technology Resources

All students are required to have a TI-83/84 series graphing calculator. If students are financially unable to supply their own calculator, the school will provide them with one to use during the year.

The following hardware/software is used for the teaching and learning of problem solving, experimentation, data collection, and results interpretation.

Gateway Tablet PC

TI-83/84 Series Graphing Calculator

CBR

CBL with probes

TI-SmartView

TI-Interactive

Geometer’s Sketchpad

Applets that come with textbook

Data from Texas Instruments website.

Student Activities

Students will engage in multiple activities and lab experiments in order to integrate calculus into other disciplines. These activities include various methods of assisting students in visualizing their calculus, often including the use of a TI-83/84 series graphing calculator. Below is a list of the activities used and the calculus topic explored through the activity.

|Activity |Calculus AB Topic |

|“Is there a Limit?” |Exponential growth rates and limiting factors |

|Lukens, Jeff and Tower, Bob. Biology with the TI-83 Plus. Activity | |

|8. 2001 | |

|“The Bigger, the Better” |Surface area to volume ratios and limits |

|Lukens, Jeff and Tower, Bob. Biology with the TI-83 Plus. Activity | |

|2. 2001 | |

|Solids of Revolution with Playdough |Volume of revolutional solids. |

|“Walk This Walk” |Distance and velocity |

|Antinone, Linda., Gough, Sam., and Gough, Jill. Modeling Motion: | |

|High School Math Activities with CBR. Activity 3. 2000. | |

|“Good Vibrations” |Modeling sinusoidal curves |

|Antinone, Linda., Gough, Sam., and Gough, Jill. Modeling Motion: | |

|High School Math Activities with CBR. Activity 13. 2000. | |

|“Match This Note” |Sine curves and graph matching |

Grading:

Daily Work 30%

Quizzes 20%

Tests 40%

Accountability 10%

Grading Scale:

90-100% = A

80-89% = B

70-79% = C

60-69% = D

59% and below = F

*This grade distribution has been decided on by the Math Department here at Huron High School, it will be used by ALL Math teachers here at Huron High School

**Class participation, effort, work ethic, and classroom behavior can affect borderline grades.

Daily work will vary from day to day, but can consist of textbook practices, worksheets, project work, etc. Daily work will be given consistently to encourage constant study and review of the material which is necessary for mastering mathematic skills. Daily work will be graded on completion.

Quizzes will be given regularly to check comprehension of specific mathematical concepts.

Tests will be given throughout the year upon completion of each chapter of study. Only material covered thoroughly in class will be tested. There will be no surprises!

Projects will be assigned throughout the year to demonstrate deeper understanding of the material. Project topics and formats will vary greatly depending on the subject matter. Projects may be graded as daily work, quizzes, or tests.

Accountability is of paramount importance in a mathematics class. Each student will be awarded 100 accountability points at the beginning of each quarter. Points will be deducted for absences, tardies, improper use of computers or cell phones, etc.

Absences*: 50 points will be deducted after the 5th absence (of the semester) and 10 points will be deducted for every absence thereafter. It is school policy that the student loses credit for class after the 8th absence.

Tardies*: Each student will get one free tardy per semester. After the first tardy, 5 points will be taken off for each tardy. Coming to class without an ID is considered being tardy. If the student does not use his or her one free tardy, he/she will be awarded an additional 2% to his/her semester grade.

Computer games/ texting: Ten points will be deducted for each time a student is using his/her computer improperly, or text messaging on his or her cell phone.

*Time may be made up for absences and tardies to redeem points lost (by appointment with the teacher).

Classroom Rules and Policies:

• Respect for yourself, others, and all objects is expected

• When the teacher is talking, all other conversation STOPS!

• Food and drink are allowed, IF you can handle it - - you must clean up after yourself

• Tardiness is unacceptable.

• Academic Dishonesty: completely unacceptable, you will receive a zero on the assignment, or even an automatic failing grade in the class.

• Late work will not be accepted

• If you are absent due to a sport/music/church/etc. reason, the assignment must be completed and turned in before you leave.

• If you are absent due to a medical reason, family emergency, etc. you will have one to two days to make up the assignment depending on the situation.

• Retakes may be permitted in certain situations.

Submitting assignments to the “R” drive:

Period#_AssignmentName_LastFi

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