Anne Arundel Community College

MAT 151: Pre-Calculus



CATALOG DESCRIPTION:

Open to all qualified students planning to take calculus. Topics include complex numbers; inequalities; linear, quadratic, polynomial, exponential, logarithmic and trigonometric functions; systems of equations and plane analytic geometry. Each section will require a graphing calculator and/or the use of a computer as determined by the instructor.

Prerequisite: Achieving an appropriate score on the mathematics part of the ACT or SAT, or completion of MAT 012 with a grade of at least B or scoring at an appropriate level on the Mathematics Placement Test.

Note: Credit is not given for both MAT 151 and MAT 121 or MAT 151 and MAT 131 or MAT 151 and MAT 142.

LEARNING OBJECTIVES:

Upon completion of this course, the student will be able to:
  1. Perform algebraic operations and solve a variety of algebraic and transcendental equations and inequalities.
  2. Perform algebraic operations on functions and use the language and symbolism of functions appropriately.
  3. Use linear, quadratic, polynomial, logarithmic and trigonometric functions to interpret and analyze relationships among variables.
  4. Graph relationships among variables, and interpret and analyze a graph.
  5. Solve applied problems at the Pre-calculus level.
  6. Use technology to assist in visualizing and solving problems.

COURSE OUTLINE:

Fundamentals:
  • Real Numbers (interval notation and absolute value only)
  • Rational Expressions
  • Equations
  • Modeling with Equations
  • Inequalities
  • Coordinate Geometry
  • Solving Equations and Inequalities Graphically
  • Lines
  • Modeling Variation

Functions:
  • What is a Function
  • Graphs of Functions
  • Average Rate of Change: Increasing and Decreasing Functions
  • Transformations of Functions
  • Quadratic Functions; Maxima and Minima
  • Modeling with Functions
  • Combining Functions
  • One-to-One Functions and Their Inverses

Polynomials and Rational Functions:
  • Polynomial Functions and Their Graphs
  • Dividing Polynomials
  • Real Zeros of Polynomials
  • Complex Numbers
  • Complex Zeros and the Fundamental Theorem of Algebra
  • Rational Functions

Exponential and Logarithmic Functions:
  • Exponential Functions
  • Logarithmic Functions
  • Laws of Logarithms
  • Exponential and Logarithmic Equations
  • Modeling with Exponential and Logarithmic Functions

Trigonometric Functions & Applications:
  • Angle Measure
  • Trigonometry of Right Triangles
  • Trigonometric Functions of Angles
  • The Law of Sines
  • The Law of Cosines
  • Trigonometric Graphs
  • More Trigonometric Graphs

Analytic Trigonometry:
  • Trigonometric Identities
  • Addition and Subtraction Formulas (Writing A sin x + B cos x as a single Sine or Cosine may be omitted.)
  • Double Angle, Half Angle Formulas (Sum-to-Product Formulas may be omitted.)
  • Inverse Trigonometric Functions
  • Trigonometric Equations

Conic Sections and Mathematical Induction:
  • Parabolas
  • Ellipses
  • Hyperbolas
  • Mathematical Induction
  • The Binomial Theorem

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