Please enable JavaScript to view this page.

College Algebra

MTH 122W

College Algebra

MTH 122W

Course Description

Prerequisite: MATH LEVEL 6. Reviews the mechanics of basic Algebra and solidifies understanding by using algebraic techniques, constructing mathematical models, solving problems and interpreting results. Includes: algebraic expressions; equations and inequalities; functions, inverse functions, and graphs; polynomial and rational functions; radical functions; exponential and logarithmic functions; matrices and determinants; systems of equations and inequalities; complex numbers; sequences and series. A GRAPHING CALCULATOR IS REQUIRED. (60-0)

Outcomes and Objectives

Students will recognize and understand notation describing sets of real numbers.

Objectives:

  • Understand set and interval notation .
  • Apply the operations of intersection and union.

Students can work with complex numbers.

Objectives:

  • Define numbers in the form a + bi.
  • Add, subtract, multiply, and divide complex numbers.
  • Solve quadratic equations with complex solutions.

Students can work with sequences and series.

Objectives:

  • Find the terms of an arithmetic and geometric sequence.
  • Find the sum of an arithmetic and geometric series.
  • Apply the Binomial Theorem.

Students can communicate effectively about mathematics in writing.

Objectives:

  • Provide complete written solutions to problems using appropriate terminology.
  • Articulate important ideas and conclusions in writing.

Students will develop their problem-solving and mathematical modeling skills.

Objectives:

  • Solve real world problems involving linear equations, quadratic equations, exponential equations, logarithmic equations, rational equations, and systems of equations.
  • Use mathematical modeling to solve real world problems.
  • Clarify and analyze the meanings of words, phrases and statements.
  • Learn the meanings of relevant symbols used in the discipline and ways to use them.
  • Transfer problem solving strategies for use in new contexts.
  • Organize and present information or data in tables, charts, and graphs.
  • Use symbol systems to raise questions about models and proposed answers to problems.
  • identify, state and clarify arguments or reasoning, including those codified by systems of symbols.
  • Generate and assess solutions to problems.

Students will use graphing calculator technology to evaluate and analyze solutions to various functions.

Objectives:

  • Graph linear, quadratic, radical, polynomial, exponential, or logarithmic function.
  • Create a table of input/out pairs for any given function.
  • Determine an appropriate window to obtain a complete graph of a linear, quadratic, square root, exponential, or logarithmic function.
  • Find the intersection of any two functions
  • Evaluate any numerical expression involving linear, quadratic, rational, square root, exponential, or logarithmic functions.

Students can perform operations on polynomial functions.

Objectives:

  • Apply properties of positive integral exponents.
  • Perform addition, subtraction, multiplication and division of polynomial functions.
  • Perform synthetic division.
  • Factor polynomials.
  • Reduce rational expression to simplest form.
  • Add, subtract, multiply and divide rational expressions (including complex fractions).

Students can perform operations on radical functions.

Objectives:

  • Apply the properties of rational exponents.
  • Add, subtract, multiply and divide radicals, expressing solutions in simplest form.

Students can recognize, graph and solve problems relating to linear functions.

Objectives:

  • Graph ordered pairs of any relation and identify whether or not it is a function.
  • Graph any linear function.
  • Find the distance between any two points in the plane.
  • Find the slope of a line.
  • Find the equation of a line, given information.
  • Solve and graph a linear inequality.
  • Solve absolute value equations and inequalities.

Students will be able to graph any polynomial function

Objectives:

  • Determine intercepts, axis of symmetry and maximum or minimum of a quadratic.
  • Graph any quadratic function.
  • Use synthetic division to identify zeros and graph any polynomial function.

Students can solve nonlinear equations and inequalities involving a function of one variable.

Objectives:

  • Solve quadratic equations by factoring, the quadratic formula, and graphing.
  • Solve equations involving radicals.
  • Solve polynomial equations symbolically (using synthetic division).
  • Solve polynomial equations of degree greater than 2 using tables and graphs.
  • Solve quadratic inequalities.
  • Set up and solve application problems .

Students can recognize and understand concepts related to logarithmic and exponential functions.

Objectives:

  • Recognize an exponential or logarithmic function and its graph.
  • Solve exponential or logarithmic equations.

Students can solve systems of equations and inequalities.

Objectives:

  • Solve systems of 2 and 3 linear equations.
  • Solve linear programming problems.
  • Solve systems of inequalities graphically.
  • Set up and solve application problems.

Students can work with matrices and determinants.

Objectives:

  • Apply basic operations to matrices.
  • Evaluate determinants.
  • Solve systems of equations by matrix methods.