AP Calculus AB
Presenter – Larry Peterson
Course Description for AB Calculus. Larry Peterson
The calculus session will cover all topics on the Calculus AB syllabus which includes limits and continuity, definition of derivative, applications of the derivative, rate of change, Mean Value Theorem, Riemann sums, average value, integration, applications of integration, Fundamental Theorem of Calculus, slope fields, applications of antidifferentiation and separable differential equations. This institute is designed to focus on the content knowledge described in the AP syllabus as well as techniques and ideas for developing a successful AP program. We will cover topic content, strategies, and teaching techniques for presenting the material for student understanding will be shared. We will use multiple representations ‑ graphical, numerical, analytic, and verbal ‑ to foster a more complete understanding of calculus. Sample problems from previous AP exams will be given and solved together to develop an understanding of the material and the College Board philosophy including Understanding by Design. Participants will also receive a variety of classroom‑tested activities and calculator programs to enhance their own teaching. We will discuss ways to prepare students for the AP exam. Participants should bring a TI‑83/84 graphing calculator.
Tentative Outline
Pre-Calculus Review
Summer worksheet
Calculator activities
Limits
Graphically
Numerically
Visual representations
Algebraically
Applications
The Derivative
Introduction Activity – The 20 Minute Ride
Graphical representation
Difference quotients
Formal definition
Rules for differentiation
Implicit derivatives
Explicit derivatives
Applications of the Derivative
Curve analysis
Max and Min
Increasing and decreasing behavior
Inflection points
Concavity
Tangent and normal lines
Local linearization
Optimization problems
Particle motion
Calculator representation
Related rates
Applications
Student Activities
Card match
Calculus Reaction Course
Relay races
Anti-Derivatives
Substitution Roundtable
Differential equations
Slope fields
The Definite Integral
Riemann Sums
Trapezoidal Rule
Fundamental Theorem of Calculus
Applications
Area
Volumes of solids of revolution
Volumes of solids with known cross section
Model activity
The Integral as an Accumulator
Preparing for the AP Exam
Time lines
The AP Philosophy
Past Exams
Larry Peterson – Bio
Larry Peterson earned his B.S. in Mathematics Education from Utah State University and his M. Ed. from Weber State University. He has taught AP* Calculus since 1976, currently teaching AP* Calculus and AP* Statistics at Northridge High School in Layton, Utah.
Larry’s experience with Advanced Placement ranges from Calculus to Computer Science to Statistics. He has been a reader for the AP* Calculus exam for 14 years, serving as a Table Leader for the past 6 years. In 2003 and 2004 Larry was also a Question Leader. He is also a regular presenter at state, regional, national, and international conventions in mathematics and technology and has published materials for both AP* Calculus and AP* Statistics.
In addition to his work as a College Board consultant, Larry served a six-year term as a member of the Board of Directors of the National Board for Professional Teaching Standards. His awards include: Milken Educator, Tandy Scholar, Disney American Teacher Award winner, and Utah Teacher of the Year.