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00 Summer Assignment

AP Calc AB is a fast-paced, rigorous course designed to teach you calculus and to prepare you for the AP test in May. AP courses require dedication and focus on the part of the student - you are expected to take responsibility for your learning. I will provide guidance, instruction, resources, and support, but if you're going to learn the material and be ready for the test you must be prepared to study on your own time and work hard.

Although there is no summer homework per-se that you will turn in, you are expected to do the work suggested below to prepare yourself for next year. Your goal this summer is to maintain or develop the discipline to read the textbook, assess your understanding by doing homework even if it isn't turned in, and study on your own time. Just 30 minutes every day should be sufficient - it's a good habit to develop.

AP Calculus AB Suggested Summer Work

  • Download and study Chapter 1 of the textbook (see the bottom of this page). Do the following problems.

unit 1.1:  6, 8, 16, 18, 20, 24, 44, 46, 50

unit 1.2:  6, 8, 10, 12, 16

unit 1.3:  2, 4, 6, 18, 22, 36, 42, 44

It would serve you well to do more problems than just those listed above. Although you will not turn in these problems, similar problems will appear on the chapter 1 pre-test at the beginning of the year. You should know how to do these.

    • Memorize the values of sine, cosine, and tangent for the reference angles 0, pi/6, pi/4, pi/3, and pi/2. Know how to apply these reference angles to find sine, cosine, and tangent values in quadrants I-IV in the coordinate plane.
    • At the end of last year in pre-calc you should have received a copy of the "Yellow Book" which reviews basic algebra, geometry, and pre-calculus. You should be comfortable with the content in the yellow book and able to do most of the problems by the end of the summer. You don't have to turn in yellow book problems as homework but you are responsible for understanding the material. If you don't have a copy of the Yellow Book, I've included a link to a PDF below. 

    There will be a pre-test at the beginning of the year covering everything listed in the three bullet points above.

    The following table summarizes the content of chapter 1 and provides links to online tutorials that may be helpful to you.

     Important Concepts

     Video Tutorials

    Unit 1.1: Four Ways to Represent a Function

    • Understanding the interplay between the four ways of representing a function (verbally, numerically, visually, algebraically).
    • Finding the domain and range of a function, regardless of representation. 
    • Investigating even and odd functions. 
    • Working with piecewise defined functions.
      Function Introduction
      Function Expressions
      Domain and Range
      Recognizing Functions


      Unit 1.2: Mathematical Models - A Catalog of Essential Functions

      • The modeling process: developing, analyzing, and interpreting a mathematical model. 
      • Classes of functions: linear, power, rational, algebraic, trigonometric, exponential and transcendental functions. Include the special characteristics of each class of functions.
        Polynomial and Rational Functions
        Rational Expressions
        Exponential and Logarithmic Functions
        Basic Trigonometry
        Unit Circle Definition of Trig Functions
        Graphs of Trig Functions
        Trigonometric Identities


        Unit 1.3: New Functions from Old Functions

        • The mechanics and geometry of transforming functions. 
        • The mechanics and geometry of adding, subtracting, multiplying, and dividing functions. 
        • The mechanics and geometry of composing functions. 

          Composing Functions

          Function Inverses

          Piecewise Functions

          Shifting and Reflecting Functions

          Properties and Features of Functions

          Comparing and Interpreting Functions

          The links below  take you to algebra and trig review videos, which students have found helpful and provides a link to download a copy of the Yellow Book.

          Showing 5 items
          Khan Academy Algebra http://www.khanacademy.org/math/algebra 
          Patrick JMT Algebra Tutorials http://patrickjmt.com/#algebra 
          Khan Academy Trig http://www.khanacademy.org/math/trigonometry 
          Patrick JMT Trig http://patrickjmt.com/#trigonometry 
          The Yellow Book (review of algebra, geometry, and pre-calculus) download and print if necessary 
          Showing 5 items
          Nikhil Joshi,
          Jun 22, 2012, 2:35 PM
          Nikhil Joshi,
          Jun 22, 2012, 2:35 PM
          Nikhil Joshi,
          Sep 11, 2014, 8:20 AM