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