Course Syllabus for AP Calculus, 2014 – ’15 school year

Mr. Patrick Kosal(704) 799-8555 x1610

twitter.com/mrkosal

I.Course Overview:

AP Calculus is a course designed to meet the College Board Advanced Placement AB standards. Students are expected to take the AP Test for Calculus AB at the end of the year. This is a very challenging mathematics course, being the equivalent of one semester of college calculus. Students entering the class should have performed strongly in Algebra 2 and Pre-Calculus to be at standard.

The main instructional technique will be large group lecture, with students writing down notes, examples, and working out practice problems throughout the lesson. However, students will also be expected to connect prior knowledge to new topics through discussion, both in large and small groups. Discussing how the topics are related to each other will provide a necessary connection that we can use to fuel further lessons. Use of a graphing calculator will also be necessary to interpret difficult functions and data sets and to test hypotheses about functions and their behavior.

Our class will focus on the big ideas of basic calculus with a focus on problem-solving, exploring problems from multiple angles, and how to use a graphing calculator to assist in visualize and understand a given scenario. By mastering the building blocks of calculus (limits, derivatives, and integrals), students will be able to view the world through the eyes of calculus to appreciate the beauty and application of higher-level mathematics.

II.Requirements:

  1. Textbook (Calculus.James Stewart. 5th Edition. Brooks/Cole Publishing.), 3 Ring Binder, Paper (notebook &graph), Graphing Calculator,and Pencils
  2. Completion of Daily Work and Constructive use of class time
  3. Active participation in class discussions and a Positive Attitude!!

** Each student in AP Calculus class must have a graphing calculator to use each day in class (calculators may be checked out from the LNHS media center, but most students prefer to purchase their own). Preferred calculators for this course are TI-83 or -84s, but TI-89 or -92 calculators may be used as well. We will be using calculators to visualize functions of varying types as we predict their behavior and notice trends in data. The instructor will be using the TI-Smartview program to model calculator use on the computer / projector, while the TI-Navigator system will also be used to collect and interpret data quickly for instant feedback.

III.Assignments & Make-Up Work:

1.For each lesson, students will be assigned practice problems from the textbook, practice AP tests, or other resources. Answers for said practice problems will always be posted on my school website. I would recommend “bookmarking” my webpage since you’ll be referencing it often. Please check my Twitter feed or my school website to see what work you’re responsible for prior to your return.

2.Students, it is your responsibility to obtain notes, handouts, and assignments when you are absent.

3. I am available for extra tutoring before and after school in my classroom (610). Please take advantage of these sessions, whether you were absent or simply need some extra help – you will not be alone!! I keep normal school hours of 7:30 a.m. until 4:00 p.m. Make it a point to stop by, but don’t wait until the last minute; my room is very, very crowded on mornings / afternoons right before a test.

4. Quizzes and Tests are my main way of assessing your progress and will be given regularly. Each Friday students can expect a quiz or test to be given so be prepared! As with the AP Test, some of the assessments will be non-calculator and some will be calculator-required. Occasionally I will use multiple choice questions in my assessments so students can apply problem-solving techniques. When free-response problemsare assigned, students will always be expected to supporttheir answers with mathematical evidence and written explanations.

5. I do not allow re-testing for AP & Honors-level courses, so be sure to adequately prepare for examinations. Taking good notes, attending tutoring sessions for extra practice, keeping up on assignments, and participation in class discussions / activities is the most effective way for an AP Calculus student to earn high marks on exams.

IV.Assessments:

First Three Nine WeeksFourth Nine Weeks

  1. Cumulative Exams (100 points each) 1. Calculus Manual (300 points)
  2. Quizzes (10 – 50 points each); one to two a week2. Cumulative Exams (100 points)
  3. Cumulative Nine-Week Exam (200 points)3. Quizzes (10 - 50 points)
  4. Random Homework Checks (10 points each)4. Random Homework Checks (10 points each)

V.Topics Covered:

  1. Limits, Functions, Graphs, and Continuity (3 weeks)

Objectives: The student will be able to:

  1. describe the idea of finding a limit
  2. evaluate limits algebraically
  3. evaluate limitsfrom a graph or table
  4. find equations of vertical and horizontal asymptotes
  5. determine the end behavior of a function
  6. determine whether a function is continuous at a point
  7. classify discontinuities as “removable”, “jump”, or “infinite”
  8. understand and apply the “Intermediate Value Theorem”
  9. understand and apply the “Extreme Value Theorem”
  1. The Derivative (12 weeks)

Objectives: The student will be able to:

  1. describe the meaning of a derivative
  2. find the derivative of a function using the limit definition of a derivative
  3. find whether a function is differential at a point
  4. find whether a function is locally linear at a point
  5. determine and explain how being continuous and differentiable are related
  6. use the theorems on differentiable on differentiation to find derivatives of polynomial and rational

functions (Power Rule, Product Rule, Quotient Rule, Chain Rule)

  1. find the equation of the tangent line to a curve at a point
  2. find the equation of the normal line to a curve at a point
  3. understand average and instantaneous rate of change
  4. apply implicit differentiation
  5. find higher order derivatives
  6. find the derivative & tangent line for an inverse function
  7. using the 2nd derivative and points of inflection to determine concavity of a function
  8. graphing the derivative from data, both by hand and with a graphing calculator
  9. apply derivatives to solve Related Rate and Optimization problems
  10. understand the definition of the derivative using the symmetric difference quotient
  11. understand and apply the Mean-Value-Theorem
  12. use the First and Second Derivative Test
  13. connect and with the graph
  14. find derivatives of Polynomial, Rational, Exponential, and Trigonometric Functions
  15. solve Rectilinear Motion problems
  16. determine an anti-derivative for a given function
  1. Applications of Integrals (6 weeks)

Objectives: The student will be able to:

  1. approximate areas under a cure with left-hand, right-hand, midpoint, and trapezoid methods
  2. use the Riemann Sum definition to calculate area under a curve
  3. calculate areas under and between curves
  4. understand and apply the Fundamental Theorems of Integral Calculus
  5. evaluate definite integrals with and without a calculator
  6. calculate the average value of a function
  7. find the net distance traveled by an object
  8. find the total distance traveled by an object
  9. use integration by “u-substitution”
  10. evaluate indefinite integrals using the Power Rule and the Chain Rule for integration
  11. find volumes of solids of revolution using the disk and washer method
  12. find volumes of solids with known cross sections
  1. Differential Equations (2 weeks)

Objectives: The student will be able to:

  1. solve differential equations by the method of “separation of variables”
  2. solve growth and decay problems, logistic problems, and other applications to differential equation
  3. understand slope fields
  4. sketch a slope field given a differential equation

VI. AP EXAM REVIEW (4 weeks) - AP Test: TuesdayMay 5, 2015, Morning Session, 8:00 AM

Major Project for 2nd Semester:CALCULUS MANUAL

** each student will be responsible for creating their own calculus manual that is typed, illustrated, and filled with examples from each lesson. Manuals must be bound and are due the week before the AP Calculus Test (due date: Tuesday, April 28th, 2015). Extra credit may be given for projects that are above and beyond the minimum requirements

** each topic highlighted above must have at least one full page explaining its use in the world of calculus, at least one illustration or graph that visually explains the topic, at least two example problems with written explanations and solutions shown, and three practice problems for the reader to attempt.

** one full week will be given in class in mid-April for students to work on their Calculus Manual, while occasional work days will also be provided throughout the school year. I also plan on assigning deadlines for smaller sections of the project throughout the school year to check students’ progress and give feedback

VII.Exam Calendar (Subject to Change on Teacher’s discretion)– Students may keep their most recent graded exam to review & use in studying. On the day of the next exam, students must hand in their previous exam.

Nine Week:1st2nd3rd September 5 November 14 January30

September 19November 25February 13

October3December12February 27

October 17December 19March 13

9week Exam:October 31January 9March 27

VIII.Additional Note from Teacher – AP Calculus is a very rigorous course designed to challenge each student. If a student fails to put forth a strong individual effort, the teacher reserves the right to request the student be removed from the course at the end of the first semester. I truly hope that I do not need to make such a request. Please understand that there will be bumps in the road, but if the student is willing to work, he or she will massively improve his or her critical thinking skills and their mathematical ability. Each student enrolled in the course is required to pay for and take the AP exam. If you have any further questions about the class, please feel free to contact me.