Course Outline for Mathematics 255
Noncredit Intermediate Algebra

Effective: Fall 2019
SLO Rev: 10/22/2018
Catalog Description:

MTH 255 - Noncredit Intermediate Algebra

90.00 Hours

May be repeated 99 time(s)
This noncredit course is part of a noncredit certificate of competency in Preparation for College Mathematics for the Business and STEM pathway. This course is free and is intended to prepare students for the rigor of college-level mathematics coursework required in STEM fields. Students may repeat this course until mastery of the skills is met. This course covers the same content as MTH 55 Intermediate Algebra. Students who are transitioning to college, who are unsure of their abilities, or who have been out of school for while may prefer to take the noncredit MTH 255 instead of MTH 55 since it is free and may be repeated. This course covers topics of Intermediate Algebra, such as quadratic equations, parabolas and circles, functions and their graphs, systems of equations, radical equations, as well as exponential and logarithmic functions and equations. This is a great class for students interested in the Business or STEM fields who want some more preparation before transitioning to college-level math.
1701.00 - Mathematics, General
Letter Grade Only
Type Hours
Lecture 90.00
Total 90.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. solve for a particular variable in a formula;
  2. state the domain and range of a given function or given the graph of a function;
  3. state domains and ranges of a function in set-builder and interval notation;
  4. solve compound inequalities;
  5. solve equations and inequalities involving absolute values;
  6. graph linear inequalities in two variables;
  7. graph linear inequalities in one variable;
  8. solve systems of linear equations in three unknowns using elimination and substitution;
  9. solve applications involving a system of linear equations;
  10. multiply polynomials;
  11. factor polynomials by greatest common factor, by grouping, and using special forms;
  12. solve polynomial equations;
  13. problem solve applications that involve polynomials;
  14. solve quadratic equations by factoring, completing the square, square root principle, and using the quadratic formula;
  15. solve equations in quadratic form;
  16. perform basic operations on complex numbers;
  17. find complex roots of a quadratic equation;
  18. sketch the graphs of linear, quadratic, rational, radical, exponential, and logarithmic functions;
  19. apply translations and reflections to obtain new graphs of quadratic, rational, radical, exponential, and logarithmic functions;
  20. identify the domains and ranges of linear, quadratic, rational, exponential, and logarithmic functions;
  21. sketch the graph of a circle and identify domain and range;
  22. multiply, divide, add, and subtract rational expressions;
  23. simplify complex rational expressions;
  24. solve rational equations;
  25. solve applications that involve rational equations;
  26. problem solve applications that involve direct and inverse variation;
  27. apply the properties of and perform operations with radicals;
  28. apply the properties of and perform operations with rational and integer exponents;
  29. solve radical equations;
  30. find inverse functions algebraically;
  31. given a graph of a function, sketch the graph of the inverse function;
  32. perform function composition;
  33. solve exponential and logarithmic equations;
  34. apply properties of logarithms;
  35. solve growth and decay applications;
  36. find the distance between two points;
  37. find the midpoint of a line segment.
Course Content:
  1. Functions
    1. Define functions and introduce function notation
    2. Find domain and range from a given function or when given a graph of a function
    3. Review set-builder and interval notation
    4. Algebra of functions, add, subtract, multiply and divide functions
    5. Function composition
  2. Systems of Equations
    1. Review solving system of linear equations in two variables by graphing, substitution
    2. Systems of equations by elimination
    3. System of linear equations in three variables
    4. Applications using systems of equations
  3. Linear Inequalities and Absolute Values
    1. Linear inequalities in one variable
    2. Compound inequalities
    3. Linear inequalities in two variables by graphing
    4. Equations that contain absolute values
    5. Inequalities that contain absolute values
  4. Polynomials and Polynomial Functions
    1. Multiplication of polynomials
    2. Properties of integer exponents
    3. Factor polynomials by the greatest common factors
    4. Factor polynomials by grouping
    5. Factor trinomials by trial and error and “ac” method
    6. Factor special forms (difference of squares, perfect square trinomials)
    7. Polynomial equations
    8. Applications involving polynomials
  5. Rational Equations and Rational Functions
    1. Multiply and divide rational expressions
    2. Add and subtract rational expressions
    3. Simplify complex rational expressions
    4. Problem solve using formulas and solve for a variable in a formula
    5. Solve rational equations
    6. Applications that involve rational equations
    7. Introduce vertical and horizontal asymptotes
    8. Domain and range of rational functions
    9. Graph basic reciprocal function, include translations and reflections of the reciprocal function
    10. Direct and inverse variation and combinations
    11. Applications involving direct and inverse variation
  6. Radical Expressions and Functions
    1. Properties of rational exponents
    2. Multiply and simplify radical expressions
    3. Add, subtract, and divide radical expressions
    4. Multiply with more than one term and rationalizing denominators
    5. Radical equations
    6. Basic operations with complex numbers
    7. Graph radical function and apply translations and reflections to get new graphs (only focus on square root and cube root functions)
    8. State the domain and range of radical functions
  7. Quadratic Equations and Functions
    1. The square root property and completing the square
    2. The quadratic formula
    3. Graphs of quadratic functions in standard and vertex-form
    4. Axis of symmetry and end behavior
    5. State the domain and range of radical functions
    6. Equations quadratic in form
    7. Polynomial and rational inequalities
  8. Exponential and Logarithmic Equations and Functions
    1. Composite and inverse functions
    2. Relationship of domain and range of a function and its inverse
    3. Compare graphs of a function and its inverse
    4. Logarithmic functions
    5. Properties of logarithms
    6. Exponential and logarithmic equations
    7. Graphs of exponential and logarithmic functions and apply translations and reflections to get new graphs
    8. Domains and ranges of exponential and logarithmic functions
    9. Applications of exponential growth and decay
  9. Conic Section
    1. Distance and midpoint formulas
    2. Circles
    3. Domain and range of circles
Methods of Instruction:
  1. Lecture/Discussion
  2. Group Activities
  3. Hands-on Activities
  4. Verbal explanation and demonstration.
Assignments and Methods of Evaluating Student Progress:
  1. The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to decompose?
  2. Perform an experiment with water and coffee filters and model with an exponential function.
  1. Exams/Tests
  2. Quizzes
  3. Homework
  4. Final Examination
Upon the completion of this course, the student should be able to:
  1. Critically analyze mathematical problems using a logical methodology.
  2. Communicate mathematical ideas, understand definitions, and interpret concepts.
  3. Increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Blitzer, R. (2016). Introductory and Intermediate Algebra for College Students (5th). Pearson-Prentice Hall.
  • A graphing calculator may be required.
  • Access code to an online learning system may be required.
Abbreviated Class Schedule Description:
This noncredit course is part of a noncredit certificate of competency in Preparation for College Mathematics for the Business and STEM pathway. This course is free and is intended to prepare students for the rigor of college-level mathematics coursework required in STEM fields. Students may repeat this course until mastery of the skills is met. This course covers the same content as MTH 55 Intermediate Algebra. Students who are transitioning to college, who are unsure of their abilities, or who have been out of school for while may prefer to take the noncredit MTH 255 instead of MTH 55 since it is free and may be repeated. This course covers topics of Intermediate Algebra, such as quadratic equations, parabolas and circles, functions and their graphs, systems of equations, radical equations, as well as exponential and logarithmic functions and equations. This is a great class for students interested in the Business or STEM fields who want some more preparation before transitioning to college-level math.
Discipline:
Mathematics-Basic Skills: Noncredit, Mathematics*, or