MAC1105 - College Algebra

Topical Outline with Specific Course Objectives

  1. Number Work and Simplifying Skills
    1. Use the properties of radicals, complex numbers, and exponents within the context of solving equations and graphing.
    2. Decide when an exact answer is needed and when an estimate is acceptable. Estimate to a reasonable degree of accuracy.
    3. Define, use and recognize absolute value as distance on the coordinate line.
    4. Discuss the historical and scientific basis for the number “e”.
  2. Functions and Relations
    1. Recognize and model linear, quadratic, exponential, logarithmic, absolute value, radical, rational and polynomial functions in various settings including applications.
    2. Know the properties, graphs, and equations of linear, quadratic, exponential, logarithmic, absolute value, radical, rational and polynomial functions.
    3. Identify the domain, range, and inverse for functions or relations expressed graphically or symbolically.
    4. Analyze situations, functions and data from charts, tables and graphs for the purpose of describing behavior (e.g., increasing, decreasing), identifying specific information (e.g., maximum, minimum values), and making predictions (e.g., predicting future trends).
    5. Determine the major characteristics of graphs such as intercepts and asymptotes.
    6. Deduce the possible shape of the graph from a given equation and vice-versa.
    7. Use the algebra of functions and be able to relate it to the graphical representations.
    8. State and illustrate the fundamental properties of inverse functions.  Discuss the concept of inverses in a broad context and give examples.
    9. Recognize, use, and discuss the inter-relationships among roots of polynomial functions, factors of polynomials, and solutions of polynomial equations.
    10. Discuss the historical and scientific basis for the logarithm.
    11. Use the properties of exponential and logarithmic functions to solve equations, including equations which arise in applied settings.
  3. Equations and Systems of Equations and Inequalities
    1. Choose and apply appropriate methods for solving systems of equations and inequalities, and describe the situation graphically where possible. Justify choice of method.
    2. Describe the relationships among the discriminant, solutions of quadratic equations, and intercepts of parabolas.
    3. Apply appropriate methods for solving quadratic equations, and discuss the advantages and disadvantages of each method.

Department Policies

  • Graphing Calculator Required
  • Group Activities and Projects Required
  • Common Comprehensive Final
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