Calculus‎ > ‎Previous Units‎ > ‎

00-Algebra and Trig Review

Suggested Algebra and Trig Review

  • Study the following sections of Chapter 1 of the textbook. 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.

    • 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.

    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
          The Yellow Book (review of algebra, geometry, and pre-calculus) download and print if necessary 
          Khan Academy Trig 
          Patrick JMT Algebra Tutorials 
          Khan Academy Algebra 
          Patrick JMT Trig 
          Showing 5 items
          Nikhil Joshi,
          Sep 12, 2017, 2:28 PM
          Nikhil Joshi,
          Sep 18, 2017, 9:14 AM
          Nikhil Joshi,
          Sep 18, 2017, 9:15 AM
          Nikhil Joshi,
          Sep 18, 2017, 9:15 AM
          Nikhil Joshi,
          Sep 19, 2017, 9:36 AM