Calculus Notebook Project

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					                              Pre-Calculus Portfolio Project

                     In preparation for your future endeavors in mathematics, at Century
                       and beyond, you may find it helpful to have an organized resource
                       available that contains concepts you learned previously. Your final
                      project for Pre-Calculus is to create such a resource, the Pre-
                      Calculus Portfolio.

Your portfolio should include…
      Binding of some form (folder, small binder, report cover, ect.)
      Title Page
      Table of contents
      Page numbers on each page (even unused pages should have numbers)
      Topic cover pages (should be on the right hand side of the layout)
           o Each cover page should include some connection to the material to follow
                    For Example: Pictures of or quotes from mathematicians that developed
                       the concepts in the section, artistic rendition of applications of the
                       concepts or important symbols or formulas.
                    When assembled the pages should look as follows:
          Cover           Port.     Port.          Port.     Port.         Port.     Next
          Page            Page      Page           Page      Page          Page      Cover
                           1         2              3         4             5        Page

      Include all topics from each unit outlined below (5 Units)
           o Vocabulary that is underlined, must be defined
      Examples and diagrams to support the information (as necessary)
      All problems and supporting work for the Required Examples
           o The answer page for all Required Examples (if this page is not included, no
               example problems will be scored, and this section of the project will earn a zero)
      Final page containing the following statement written in your own handwriting, signed
       and dated
           o “I pledge on my honor that I have not given or received any unauthorized
               assistance on this assignment.”

      Be Neat!!!! This project should be final draft quality.
      Be creative!!!!! Use color and add your own style.
      Consider your audience when choosing a layout.

      The portfolio will be due on Friday, June 8th @ 1:15 pm.

Extra Credit Possibilities…
      Include the P-Unit
      Include the Extras section
      Turn in your portfolio early on Friday June 1st.
                               Pre-Calculus Portfolio

P-Unit: How to solve…
                                                     Point Breakdown:
    Linear Equations (P1)
    Linear Inequalities (P2)
                                                     ___________ Title Pages
    Interval Notation
    Quadratic Equations
          o Factoring (P3)                           ___________ Table of Contents
          o Quadratic Formula (P4)
          o Completing the Square (P5)               ___________ Page Numbers
    Quadratic Inequalities (P6)
    Absolute Value Equations/Inequalities (P7)      ___________ Topic Coverage
    Radical Equations (P8)
    Rational Equations (P9)                         ___________ Examples
          o Simplifying rational expressions (P10)
          o Simplifying complex fractions (P11)      ___________ Honor Code

                                                     ___________ Organization
Unit I: Functions                                     Organizational Scheme
    Function                                         Appropriate Page/Line Breaks
           o Domain                                   Correct Notation
           o Range (1)                                Neat & Final Draft Quality
           o How can you tell if a relation is a
               function?                             ___________ Creativity
                   Graphically                       Meaningful Use of Color
                   Algebraically (2)                 Personal Style in Design
           o How is domain determined? (3)           Consistent Cover Pages/Theme
    Function Composition (4)                         Original Diagrams/Examples
    Inverse Functions (5)
    One-to-One Functions                            (+) ________ Extra Topics
           o Graphically
           o Algebraically (6)                       (+) ________ Early Date
    Function Traits
           o Intervals of Increase & Decrease
           o Critical Points
                                                     ___________ Total Points
                   Rel-min & Rel-max (7)
    Function Transformations (8)                    ___________ Grade
    Piecewise Functions
           o Greatest Integer Function (9)
Unit II: Polynomial & Rational                           o  Range
         Functions                                       o  Vertical Asymptote (20)
    Standard Form of a Quadratic                        o  Properties
        Function (10)                                    o  What is the natural
    Characteristics of a Polynomial                        logarithmic function?
        Function                                    Properties of Logarithms
            o Domain                                    o Change of Base Formula
            o Continuous                                o 3 Properties (21, 22)
            o Smooth Curves                         Solving Exponential and
            o Parent Functions                       Logarithmic Equations
            o Leading Coefficient Test                  o Strategies for each
            o Number of Real zeros                      o When do extraneous
            o Number of Relative                            solutions occur? (23)
               Extrema                              Exponential and Logarithmic
            o IVT (11)                               Modeling
    Two Types of Division (12, 13)                     o 4 Types of models
            o Remainder Theorem                                  Graphs
            o Factor Theorem                                     Formulas (24)
    Polynomial Zeros
            o Finding a polynomial’s
               zeros (list strategies) (14)   Unit IV: Systems & Matrices
                     Sum/Difference              Solving Systems of Equations
                       of Cube Formulas                  o Definition of a Solution of
                       (15)                                 a System of Equations
            o Finding a polynomial                       o 3 Methods (25)
               given its zeros (16)               Multivariable Linear Systems
    Complex Numbers                                     o Steps for Partial Fraction
            o What is i? (17)                               Decomposition (26)
    Graphing Rational Functions
            o What is an asymptote?
                (3 types)                     Unit V: Conic Sections
            o When does a hole occur?             Circles
            o Guidelines for Graphing                    o Definition of a Circle
               (18)                                      o Characteristics of Circle
                                                         o Definition of a tangent
Unit III: Exponential & Logarithmic               Parabolas
          Functions                                      o Definition and Diagram
    Exponential Functions                                   of a Parabola
            o Definition                                 o Characteristics of
            o Graph                                          Parabolas
            o Domain                              How to Classify a Conic Section
            o Range                                  (27)
            o Intercept
            o Horizontal Asymptote
            o What is e?                      Extras: Skills Useful for Calculus
    Logarithmic Functions                        Factoring with Rational
            o Definition                             Exponents (E1)
            o Graph                               Difference Quotient (E2)
            o Domain

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