Discipline: Mathematics
Originator: Sean Drake

Riverside Community College District
Integrated Course Outline of Record

Mathematics 35
MAT-35 : Intermediate Algebra
College:
Lecture Hours: 90.000
Outside-of-Class Hours: 180.000
Units: 5.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-52
Course Credit Recommendation: Degree Credit

The concepts introduced in elementary algebra are presented again, but in greater depth. In addition to basic algebraic operations and graphing, students are introduced to functions, inverse functions, exponential and logarithmic functions, complex numbers, conic sections, nonlinear systems of equations, and sequences and series. 90 hours lecture. (Letter Grade or Pass/No Pass option)
Short Description for Class Schedule
Algebra preparation for college level mathematics.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. Simplify algebraic expressions using correct mathematical symbols and language.
    • MAT-52 - Simplify algebraic expressions using correct mathematical symbols and language.
  2. Factor polynomials.
    • MAT-52 - Factor polynomials.
  3. Identify and apply appropriate methods to solve linear, quadratic, rational, and radical equations.
    • MAT-52 - Identify and apply appropriate methods to solve linear, quadratic, rational, and radical equations.
  4. Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
    • MAT-52 - Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
  5. Graph linear equations.
    • MAT-52 - Graph linear equations.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Simplify expressions using properties of exponents.
  2. Simplify expressions that involve polynomial, rational, radical, and logarithmic expressions.
  3. Divide polynomials using long division and synthetic division.
  4. Factor polynomials.
  5. Solve linear, absolute value, polynomial, rational, radical, exponential, and logarithmic equations.
  6. Solve linear systems of equations in two and three variables using substitution and elimination.
  7. Solve linear, absolute value, polynomial and rational inequalities in one variable.
  8. Solve applications using equations and systems of linear equations.
  9. Graph linear equations and inequalities in two variables.
  10. Distinguish between functions and relations.
  11. Graph functions using a table of values. Graph new functions using translations and reflections.
  12. Identify the domain of a function using its definition, equation or graph.
  13. Graph quadratic functions.
  14. Write equations of lines using the slope intercept formula and the point slope formula.
  15. Create new functions from known functions using basic operations and/or compositions of functions.
  16. Identify and graph conic sections given its equation.
  17. Solve nonlinear systems of equations.
  18. Identify the terms of a sequence and find the nth term.
  19. Find the sum of a series written in summation notation.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Simplify algebraic expressions using correct mathematical symbols and language.
    • Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
  2. Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
  3. Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
    • Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
  4. Graph linear and basic nonlinear functions.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
Course Content:
  1. Linear Equations
    1. Linear Equations
    2. Absolute Value Equations
    3. Literal Equations
    4. Applications
  2. Inequalities
    1. Interval Notation
    2. Set Notation
    3. Linear Inequalities in One Variable
    4. Compound Inequalities
    5. Absolute Value Inequalities
    6. Polynomial and Rational Inequalities
    7. Linear Inequalities in Two Variables
  3. Linear Equations in Two Variables
    1. Cartesian Coordinate System
    2. Midpoint Formula
    3. Graphs of Linear Equations in Two Variables
    4. Equations of Lines
    5. Parallel and Perpendicular Lines
  4. Systems of Linear Equations
    1. Systems with Two Variables
    2. Systems with Three Variables
    3. Substitution Method
    4. Elimination Method
    5. Applications
  5. Polynomials
    1. Algebraic Expressions with Exponents
    2. Basic Operations on Polynomials
    3. Factoring
      1. Greatest Common Factor
      2. Grouping
      3. Trinomials
      4. Difference of Squares
      5. Perfect Square Trinomials
      6. Sum and Difference of Two Cubes
    4. Polynomial Equations
    5. Applications
  6. Rational Expressions
    1. Basic Operations on Rational Expressions
    2. Complex Fractions
    3. Division of Polynomials
    4. Synthetic Division
    5. Ratios, Proportions and Variation
    6. Rational Equations
    7. Extraneous Solutions
    8. Applications
  7. Radical Expressions
    1. Basic Operations on Radical Expressions
    2. Rational Exponents
    3. Radical Equations
    4. Complex Numbers
    5. Distance Formula
    6. Applications
  8. Functions
    1. Function Notation
    2. Domain and Range
    3. Graphs of Linear Functions
    4. Graphs of Basic Nonlinear Functions
      1. Square Root Function
      2. Cube Root Function
      3. Absolute Value Function
      4. Square Function
      5. Cube Function
      6. Exponential Function
      7. Logarithmic Function
    5. Translations and Reflections of Basic Graphs
    6. Graphs of Quadratic Functions
    7. Algebra and Composition of Functions
    8. One-to-One Functions
    9. Inverse Functions
  9. Quadratic Equations
    1. Completing the Square
    2. Quadratic Formula
    3. Quadratic Forms
    4. Applications
  10. Exponential and Logarithmic Functions
    1. Exponential Functions
    2. Logarithmic Functions
    3. Properties of Logarithms
    4. Exponential and Logarithmic Equations
    5. Applications
  11. Conic Sections
    1. Parabolas
    2. Circles
    3. Ellipses
    4. Hyperbolas
    5. Nonlinear systems of equations
  12. Sequences and Series
    1. Sequences
    2. Series
    3. Summation Notation
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
  • Class lectures, discussions, and demonstrations of the four basic operations as applied to real and complex numbers, polynomial, rational, radical and logarithmic expressions and functions; solving linear and non-linear equations, inequalities or systems; graphing linear and non-linear inequalities and basic functions; identifying conic sections; recognizing and determining the distinctions between functions and relations; and calculating series and terms of sequences.
  • Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist the students in mastering the techniques involved in applying the algebraic principles and techniques to the solution of applications utilizing the four basic mathematical operations.
  • Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools, manipulatives, and worksheets in order to address multiple learning styles and to reinforce the topics of intermediate algebra.
  • Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problem solving skills at the intermediate algebra level.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
  • Evaluation of written homework assignments and/or computerized homework assignments for correct application of algebraic principles as well as the correct use of symbols and vocabulary of algebra.
  • Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of the four basic operations as applied to real and complex numbers, polynomial, rational, radical and logarithmic expressions and functions; solving linear and non-linear equations, inequalities or systems; graphing linear and non-linear inequalities and basic functions; identifying conic sections; recognizing and determining the distinctions between functions and relations; and calculating series and terms of sequences.
  • Assessment of classroom discovery activities for content knowledge and conceptual understanding of algebraic principles.

 

Sample Assignments:
Outside-of-Class Reading Assignments
  • Read and analyze text, examples and class notes covering topics such as evaluating algebraic expressions, graphing linear and quadratic functions, and solving systems of equations.
Outside-of-Class Writing Assignments
  • Use the language and symbols of algebra to solve problem sets on algebraic topics such as simplifying algebraic expressions, finding inverse functions, and solving exponential and logarithmic equations.
Other Outside-of-Class Assignments
  • Graph linear equations and inequalities, quadratic functions, and conic sections.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
  • Martin-Gay. Intermediate Algebra. 6th Pearson, 2013.
  • Turner, McKeague. Intermediate Algebra. 1st XYZ Textbooks, 2016.
  • Tussy, Gustafson. Intermediate Algebra. 5th Brooks/Cole, 2012.
  • (In addition to the textbooks listed, instructors may also choose open source textbooks which often come at little or no cost to the students.)
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: Non-Transferable (C)
CB05 NOR Transfer Status: Non-Transferable (C)
CB05 RIV Transfer Status: Non-Transferable (C)
Board of Trustees Approval Date: 11/13/2018
COR Rev Date: 11/13/2018