NOTE:  This course is no longer used at University Park
 
                                  MATH 40
    
    COURSE DESCRIPTION: (GQ) Algebra, Trigonometry, and Analytic
    Geometry (5:5:0) Concepts of algebra; equations; inequalities;
    functions; graphs; polynomial and rational functions; exponential
    and logarithmic functions; trigonometry; analytic geometry; complex
    numbers.
    
    PREREQUISITES: Satisfactory performance on the mathematics
    proficiency examination.
    
                                  TOPICS
    
    BASIC ALGEBRAIC CONCEPTS
    The Real Number Systems
    Order Properties and Absolute Value
    The Arithmetic of Rational Numbers
    Exponents and Radicals
    The Arithmetic of Polynomials
    Factoring
    Rational Fractions and Fractional Expressions
    
    EQUATIONS AND INEQUALITIES OF THE FIRST AND SECOND DEGREE
    Linear Equations
    Quadratic Equations
    Completing the Square and the Quadratic Formula
    Complex Numbers
    Equations That Are Convertible to Linear or Quadratic Forms
    Linear Inequalities
    Inequalities and Absolute Value
    Quadratic and Other Nonlinear Inequalities
    Applications
    
    
    FUNCTIONS AND GRAPHS
    The Cartesian Coordinate System and Graphs of Equations
    The Function Concept
    Graphs of Functions
    Combinations of Functions
    One-to-One Functions and Inverses

    LINEAR AND QUADRATIC FUNCTIONS
    Equations of Lines
    Properties of Lines and Line Segments
    Linear Functions
    Quadratic Functions
    Parabolas with Horizontal Axes; Circles
    
    HIGHER-DEGREE POLYNOMIAL AND RATIONAL FUNCTIONS
    The Remainder Theorem and the Factor Theorem
    Synthetic Division
    The Fundamental Theorem of Algebra and Its Corollaries
    Rational and Irrational Roots
    Graphing Polynomial Functions
    Rational Functions
    



    EXPONENTIAL AND LOGARITHMIC FUNCTIONS
    The Exponential Function
    Inverses of Exponential Functions
    Properties of Logarithms
    Applications of Exponential and Logarithmic Functions
    
    THE TRIGONOMETRIC FUNCTIONS
    Measurement of Angles
    Special Angles
    Trigonometric Functions of Angles
    Trigonometric Functions of Real Numbers
    Trigonometric Identities
    The Addition of Formulas for Sine and Cosine
    Double-Angle, Half-Angle, and Reduction Formulas
    Trigonometric Equations
    Graphs of the Trigonometric Functions
    The Inverse Trigonometric Functions

    THE SOLUTION OF TRIANGLES
    Right Triangle Trigonometry
    The Law of Sines
    The Law of Cosines
    Areas of Triangles

    SYSTEMS OF EQUATIONS AND INEQUALITIES
    Linear Systems
    Nonlinear Systems
    
    THE CONIC SECTIONS
    The Parabola
    The Ellipse
    The Hyperbola
    
    8/13/92