MAC1140 - Precalculus Algebra

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. Demonstrate an understanding of both composition and decomposition of functions.
    4. Construct the inverse of a function, both graphically and algebraically when feasible.
    5. Demonstrate an intuitive understanding of functions including limits, continuity, increasing, decreasing, maximum and minimum values, symmetry and concavity.
    6. Demonstrate an understanding of transformations graphically, symbolically, and numerically.
    7. Graph and write equations for piecewise-defined functions.
  2. Polynomial and Rational Functions
    1. Identify multiplicities of zeros and their effect on the graph.
    2. Create graphs and write equations given sufficient information.
    3. Use formal limit definitions and limit notation to define the end behavior and vertical and horizontal asymptotes for functions given in numerical, graphical, and symbolic forms.
    4. Determine when a rational function has a hole and the point at which it occurs.
  3. Exponential and Logarithmic Functions
    1. Create graphs and write equations for exponential and logarithmic functions given sufficient information.
    2. Use formal limit definitions and limit notation to define the end behavior and vertical and horizontal asymptotes for functions given in numerical, graphical, and symbolic forms.
    3. Demonstrate mastery of the logarithmic properties by applying them in a variety of settings.
    4. Understand the inverse relationship and use it to solve exponential and logarithmic equations.
    5. Use exponential, logarithmic, and related functions in science based applications.
  4. Solving Equations and Inequalities
    1. Solve non-linear equations and inequalities numerically, graphically, and symbolically.
    2. Recognize when a solution is approximate and have a rough idea of its accuracy.
    3. State exact solutions in proper mathematical form.
  5. 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.
  6. Matrices
    1. Perform basic matrix algebra and demonstrate knowledge of the commutative properties.
    2. Use expansion by cofactors to compute the determinant of matrices up to dimension
    3. Construct the inverse of a matrix using row operations.
    4. Use matrices and determinants to solve linear systems of equations.
  7. Sequences and Series
    1. Recognize arithmetic and geometric sequences and series in summation or iterative notation.
    2. Demonstrate an understanding of sequences and series notation by expanding a given formula and by creating a formula for a given expansion.
    3. Find the sum of a finite series.
  8. Special Topics
    1. Apply the Binomial Theorem.
    2. Demonstrate an understanding of Proof by Induction.
  •  Department Policies
  • Graphing Calculator not allowed on proctored tests or final exam
  • Comprehensive Final
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