AP Calculus BC Syllabus

Teacher: Mr. Evans

Email: mark.evans@hcps.org (for large files email to, evans@scienceandmathacademy.com)

Text: Larson, R, Hostetler, R. P., & Edwards, B. H. (2006) Calculus with Analytic Geometry (8th ed.). Boston: Houghton Mifflin Company.

Course Description: This course is equivalent to a typical second semester college Calculus course. Topics covered will be a review of Calculus AB (limits, derivatives and their applications, and integrals and their applications), further integration techniques, infinite series, conics, parametric equations, polar coordinates, and vectors.

Course Objectives and Goals: My goal is to prepare students to be successful on the AP Calculus BC exam. To achieve this goal, students will gain a thorough understanding of the topics covered in the course outline.

Course Outline: The following is an outline of the topics we will cover and a rough estimate of the time we will spend on each chapter.

Review of Previous Calculus Topics
Time: 10 days

• Limits and Their Properties (Chapter 1)
  
• Differentiation (Chapter 2)
  
• Application of Differentiation (Chapter 3)
  
• Integration (Chapter 4)
  
• Logarithmic, Exponential, and other Transcendental Functions (Chapter 5)
  
• Application of Integration (Chapter 7)

Differential Equations (Chapter 6)
Time: 7 days

• Slope Fields and Euler's Method
  
• Differential Equations: Growth and Decay
  
• Separation of Variables and the Logistic Equation
  
• First-Order Linear Differential Equations
  

Integration Techniques, L'Hôpital's Rule, and Improper Integrals (Chapter 8)
Time: 10 days

• Basic Integration Rules
  
• Integration by Parts
  
• Trigonometric Integrals
  
• Trigonometric Substitution
  
• Partial Fractions
  
• Integration by Tables and Other Integration Techniques
  
• Indeterminate Forms and L'Hôpital's Rule
  
• Improper Integrals
  

Infinite Series (Chapter 9)
Time: 20 days

• Sequences
  
• Series and Convergence (Geometric Series included)
  
• The Integral Test and p-Series
  
• Comparisons of Series
  
• Alternating Series
  
• The Ratio and Root Tests
  
• Taylor Polynomials and Approximations (Lagrange error bound included)
  
• Power Series
  
• Representation of Functions by Power Series
  
• Taylor and Maclaurin Series
  

Conics, Parametric Equations, and Polar Coordinates (Chapter 10)
Time: 15 days

• Conics and Calculus
  
• Plane Curves and Parametric Equations
  
• Parametric Equations and Calculus
  
• Polar Coordinates and Polar Graphs
  
• Area and Arc Length in Polar Coordinates
  
• Polar Equations of Conics and Kepler's Laws
  

Vectors and the Geometry of Space (Chapter 11)
Time: 15 days

• Vectors in the Plane
  
• Space Coordinates and Vectors in Space
  
• The Dot Product of Two Vectors
  
• The Cross Product of Two Vectors in Space
  
• Lines and Planes in Space
  
• Surfaces in Space
  
• Cylindrical and Spherical Coordinates
  
• Vectors in the Plane (Finney)
  

AP Review
Time: 6 days

• We will try many free-response questions from previous AP Calculus tests
  
• We will review all previously covered topics
  

Post AP Calculus Exam

• Further explorations of Calculus using Mathematica®
  
• Surfaces in Space
  
• Cylindrical and Spherical Coordinates
  

Grading:

• Daily Quizzes: There will be a daily quiz most days. It will consist of 3 questions and will be completed independently at the beginning of the period. Each quiz will be worth 9 points and the top 10 quizzes in a quarter will be counted.
  
• Tests: There will be a test at the conclusion of each chapter. Each test will be worth 100 points. There will be a non-calculator section and calculator section to every test.
  
• Quizzes: There will not be many regular quizzes. When we do have a quiz it will be worth 25 points. Expect a quiz in the middle of Series, Polar Coordinates, and Vectors.
  
• Homework: Daily homework will be assigned every day. It will not be formally graded, unless students are not completing the homework. This is to prepare students for typical first and second year college math courses.
  
• Spirals: Spirals are take home quizzes that review material throughout the course. Each spiral is worth 20 points. Students will receive a spiral every 2-3 weeks. Spirals will be assigned on Monday’s or Tuesday’s and due on Friday (regardless of whether the class meets). If they are turned in on Wednesday you will receive 2 bonus points and on Thursday 1 bonus point. You may work with others students. You must show work.
  
• Mathematica Labs/Assignments: Approximately one Mathematica assignment per chapter. The assignments will enhance the current chapter or review previous calculus material. Each assignment will be worth 20-30 points
  
• Tutoring: AP Calculus BC students will tutor AP Calculus AB students 2 hours per quarter. Each quarter this is worth 25 points.
  
• Note: Mr. Evans reserves the right to change grading policies as seen fit.
  

Calculators:
“The use of a graphing calculator in AP Calculus is considered an integral part of the course. Students should be using this technology on a regular basis so that they become adept at using their graphing calculators. Students should also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when technological tools are unavailable or inappropriate.” (Excerpt taken from the CollegeBoard, Calculus Course Description.)
You must have a graphing calculator that fits the following requirements (preferably a TI-84 or TI-89.)
• Plot the graph of a function within an arbitrary viewing window
• Find the zeros of functions (solve equations numerically)
• Numerically calculate the derivative of a function, and
• Numerically calculate the value of a definite integral.

Classroom Expectations:

• Be on time. Sharpen you pencil if necessary and get in your seat before the bell rings. If you are not in your seat when the bell rings, you are late.
  
• Be prepared for class. Bring a pencil, notebook, textbook (covered) and calculator.
  
• You will not be permitted to go to your locker during class.
  
• Use of the bathroom is a privilege that is allowed at the discretion of Mr. Evans. You will be permitted to use the restrooms on the third floor only.
  
• Make up work will be given for excused absences only. You will be allowed to make-up missed work according to the HCPS policy. It is your responsibility to see the teacher for the assignment.
  
• All work must be on time to be accepted for credit. Field trips, rehearsals, or any other absences known in advance are not an excuse for late work. Submit it early or give it to a classmate to submit it for you.