Discipline: Mathematics
Originator: Sean Drake
Riverside Community College District
Integrated Course Outline of Record
Mathematics
35
MAT35 : Intermediate Algebra 
College:
Lecture Hours:
90.000 OutsideofClass Hours: 180.000 Units: 5.00 Grading Methods: Pass/No Pass Letter Grade 
Course Description
Prerequisite:
MAT52
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:
Simplify algebraic expressions using correct mathematical symbols and language.
 MAT52  Simplify algebraic expressions using correct mathematical symbols and language.

Factor polynomials.
 MAT52  Factor polynomials.

Identify and apply appropriate methods to solve linear, quadratic, rational, and radical equations.
 MAT52  Identify and apply appropriate methods to solve linear, quadratic, rational, and radical equations.

Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
 MAT52  Solve applications that require writing and solving equations. Communicate solution in the context of the problem.

Graph linear equations.
 MAT52  Graph linear equations.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
Simplify expressions using properties of exponents.

Simplify expressions that involve polynomial, rational, radical, and logarithmic expressions.

Divide polynomials using long division and synthetic division.
 Factor polynomials.

Solve linear, absolute value, polynomial, rational, radical, exponential, and logarithmic equations.

Solve linear systems of equations in two and three variables using substitution and elimination.

Solve linear, absolute value, polynomial and rational inequalities in one variable.

Solve applications using equations and systems of linear equations.
 Graph linear equations and inequalities in two variables.
 Distinguish between functions and relations.

Graph functions using a table of values. Graph new functions using translations and reflections.

Identify the domain of a function using its definition, equation or graph.

Graph quadratic functions.
 Write equations of lines using the slope intercept formula and the point slope formula.

Create new functions from known functions using basic operations and/or compositions of functions.

Identify and graph conic sections given its equation.
 Solve nonlinear systems of equations.
 Identify the terms of a sequence and find the nth term.
 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: 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.
 Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
 Critical Thinking: Students will be able to demonstrate higherorder 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.
 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 higherorder 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.
 Graph linear and basic nonlinear functions.
 Critical Thinking: Students will be able to demonstrate higherorder 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:
 Linear Equations
 Linear Equations
 Absolute Value Equations
 Literal Equations
 Applications
 Inequalities
 Interval Notation
 Set Notation
 Linear Inequalities in One Variable
 Compound Inequalities
 Absolute Value Inequalities
 Polynomial and Rational Inequalities
 Linear Inequalities in Two Variables
 Linear Equations in Two Variables
 Cartesian Coordinate System
 Midpoint Formula
 Graphs of Linear Equations in Two Variables
 Equations of Lines
 Parallel and Perpendicular Lines
 Systems of Linear Equations
 Systems with Two Variables
 Systems with Three Variables
 Substitution Method
 Elimination Method
 Applications
 Polynomials
 Algebraic Expressions with Exponents
 Basic Operations on Polynomials
 Factoring
 Greatest Common Factor
 Grouping
 Trinomials
 Difference of Squares
 Perfect Square Trinomials
 Sum and Difference of Two Cubes
 Polynomial Equations
 Applications
 Rational Expressions
 Basic Operations on Rational Expressions
 Complex Fractions
 Division of Polynomials
 Synthetic Division
 Ratios, Proportions and Variation
 Rational Equations
 Extraneous Solutions
 Applications
 Radical Expressions
 Basic Operations on Radical Expressions
 Rational Exponents
 Radical Equations
 Complex Numbers
 Distance Formula
 Applications
 Functions
 Function Notation
 Domain and Range
 Graphs of Linear Functions
 Graphs of Basic Nonlinear Functions
 Square Root Function
 Cube Root Function
 Absolute Value Function
 Square Function
 Cube Function
 Exponential Function
 Logarithmic Function
 Translations and Reflections of Basic Graphs
 Graphs of Quadratic Functions
 Algebra and Composition of Functions
 OnetoOne Functions
 Inverse Functions
 Quadratic Equations
 Completing the Square
 Quadratic Formula
 Quadratic Forms
 Applications
 Exponential and Logarithmic Functions
 Exponential Functions
 Logarithmic Functions
 Properties of Logarithms
 Exponential and Logarithmic Equations
 Applications
 Conic Sections
 Parabolas
 Circles
 Ellipses
 Hyperbolas
 Nonlinear systems of equations
 Sequences and Series
 Sequences
 Series
 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 nonlinear equations, inequalities or systems; graphing linear and nonlinear 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 handouts and/or computerbased 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, computerbased 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 nonlinear equations, inequalities or systems; graphing linear and nonlinear 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:
OutsideofClass 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.
OutsideofClass 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 OutsideofClass 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:
 MartinGay. 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: NonTransferable (C)
CB05 NOR Transfer Status: NonTransferable (C)
CB05 RIV Transfer Status: NonTransferable (C)
CB05 MOV Transfer Status: NonTransferable (C)
CB05 NOR Transfer Status: NonTransferable (C)
CB05 RIV Transfer Status: NonTransferable (C)
Board of Trustees Approval Date:
11/13/2018
COR Rev Date:
11/13/2018