MAC1147 - Precalculus Algebra and Trigonometry

Topical Outline with Specific Course Objectives

  1. Introduction of Functions, the Properties, Graphs, and Inverses
    1. Analyze and interpret functions using graphs, tables, and equations.
    2. Determine domain and range both algebraically and graphically.
    3. Construct the inverse of a function, including trigonometric functions, both graphically and algebraically when feasible.
    4. Demonstrate an intuitive understanding of functions including limits, continuity, increasing, decreasing, maximum and minimum values, and concavity.
  2. Polynomial, Rational, Exponential, Logarithmic, Piecewise-Defined, and Trigonometric Functions
    1. Model real-world applications using these functions.
    2. Explain the relationship between logarithmic and exponential functions.
    3. Demonstrate an understanding of the trigonometric functions as functions of real numbers.
    4. Analyze and interpret trigonometric functions using graphs, tables and equations.
    5. Discuss the scientific basis for radian measure.
    6. Apply radian measure to arc length and area.
  3. Conic Sections
    1. Identify and graph a conic section from its equation.
    2. Find the equation of a conic section from its description.
    3. Identify the attributes of a conic section.
  4. Coordinate Transformation
    1. Relate the algebra of functions to graphical representations.
    2. Use function notation to describe graphical transformations.
  5. Required Special Topics
    1. Use matrices and determinants to solve linear systems of equations.
    2. Demonstrate an understanding of Proof by Induction.
    3. Apply the Binomial Theorem.
    4. Recognize arithmetic and geometric sequences and series in summation or iterative notation.
    5. Solve non-linear inequalities numerically and graphically, as well as algebraically.
    6. Demonstrate the ability to find unknown angles and side lengths of right and nonright triangles using trigonometry.
    7. Solve applications using solutions of triangles.
  6. Trigonometric identities and conditional trigonometric equations
    1. Verify and apply trigonometric identities.
    2. Solve trigonometric equations numerically, graphically, and algebraically.
  7. Vector algebra and polar coordinates
    1. Demonstrate an understanding of vectors, their graphical representation and vector algebra.
    2. Sketch and identify graphs in polar coordinates.
    3. Convert rectangular equations to polar form and vice versa.
  8. Parametric equations
    1. Sketch and identify graphs using parametric equations.
    2. Convert rectangular equations to parametric form and vice versa.

Department Policies

  • Graphing Calculator not allowed on proctored tests or final exam
  • Comprehensive Final
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