# ModelCourses/CollegeAlgebra

Model Courses > College Algebra Model Course

## General Description

• 2013 Contributors: Alex Basyrov, John Williams, Shumei Richman
• 2011 Contributors: Alex Basyrov, Pangyen Weng, Audrey Battrum, Shumei Richman
• Freshman level college algebra course
• Pre-requisite: Intermediate algebra or 2 years of high school algebra or high enough mathematics placement.

Possible textbooks include, but are not limited to:

• Michael Sullivan and Michael Sullivan III. College Algebra—Enhanced with Graphing Utilities, Fifth Edition. Upper Saddle River, NJ: Prentice-Hall, Inc., 2009.

## Notes on Possible Use of the Problem Sets

• There are probably more problems in the problem sets that one would want to use in a real course. The assumption was that it is easy to remove any problems that one does not want to use.
• Course topics roughly correspond to numbers (01, 02, 03, etc.) in homework sets
• Some of the larger topics are split into smaller subtopics -- in that case there is a letter attached to the number (a, b, c, etc.) to make it homework set 05a, 05b, etc.

## Topics Covered

• Linear Equations
• Lines and Circles and their graphs
• Functions and Their Graphs
• Inverse Functions
• Linear Functions, Their Properties, and Linear Models
• Quadratic Functions and Their Properties
• Polynomial and Rational Functions
• Exponential Functions
• Logarithmic Functions
• Exponential Equations
• Logarithmic Equations
• Systems of Equations and Inequalities

## (2013 Edition) Problem Sets

• Download the set-definition files and any local problems used by the course (you would be able to use File Manager to upload the file to Templates (default) directory, and then import the set-definition files)

### Problem Sets

• HW Set 1a – Review of Polynomials: Addition and Multiplication
• Students will be able to:
• Multiply Polynomials
• Sample pdf file
• HW Set 1b - Review of Polynomials: Factoring
• HW Set 2 – Linear and Rational equations
• Students will be able to:
• Solve Basic Linear Equations
• Solve Basic Rational Equations
• Sample pdf file
• HW Set 3 - Quadratic Equations in the Field of Real Numbers
• Students will be able to:
• Solve Quadratic Equations in the Real Domain
• Sample pdf file
• HW Set 4a – Review of Complex Numbers
• Students will be able to:
• Add and Subtract Complex Numbers
• Multiply and Divide Complex Numbers
• Sample pdf file
• HW Set 4b – Quadratic Equations in the Field of Complex Numbers (can use more problems)
• Students will be able to:
• Solve Quadratic Equations in the Complex Domain
• Sample pdf file
• HW Set 5a – Rational Equations equivalent to Quadratic Equations
• Students will be able to:
• Solve Quadratic Equations with Rational Expressions
• Sample pdf file
• HW Set 5b - Radical Equations
• HW Set 5c - Other Quadratic in Form Equations
• Students will be able to:
• Solve Equations (Degree Greater than 2) Quadratic in Form
• Sample pdf file
• HW Set 5d - Factorable Equations; Misc Equations
• Students will be able to:
• Solve Factorable Equations
• Solve Miscellaneous Equations
• Sample pdf file
• HW Set 6 – Linear Inequalities
• HW Set 7a – Absolute Value Equations
• HW Set 7b - Absolute Value Inequalities
• Students will be able to:
• Solve Absolute Value Inequalities
• Sample pdf file
• HW Set 8 – Word Problems – Total Value, Interest, Uniform Motion, Work Rate, Geometry Problems
• Students will be able to:
• Solve Basic Number/Money and Geometric Application Problems
• Solve Uniform Motion Application Problems
• Solve Simple Interest Application Problems
• Solve Mixture Application Problems
• Solve Work Rate Application Problems
• Sample pdf file
• HW Set 9 – Coordinate System, Distance Formula, Midpoints
• Students will be able to:
• Determine Distance Between Two Points
• Use Midpoint Formula
• Solve Applications Using Midpoint and Distance Formula
• Sample pdf file
• HW Set 10 – Graphs, Intercepts, Symmetry
• Students will be able to:
• Determine $$x$$-intercepts of Graph
• Determine $$y$$-intercepts of Graph
• Determine Symmetry of Graph
• Sample pdf file
• HW Set 11 – Lines and Slopes; Perpendicular and Parallel Lines
• Students will be able to:
• Determine Slope of a line between two points
• Determine Equation of a Line
• Determine Equation of a Parallel or Perpendicular Line
• Sample pdf file
• HW Set 12 – Circles
• Students will be able to:
• Determine Equation of a Circle Using Diameter and Symmetry
• Determine Equation of a Circle Using Center and Point
• Determine Standard Form of a Circle by Completing The Square
• Determine Center and Radius of a Circle Using Standard Form
• Sample pdf file
• HW Set 13 – Variation
• Students will be able to:
• Solve Direct Variation Application Problems
• Solve Inverse Variation Application problems
• Solve Joint Variation Application problems
• Sample pdf file
• HW Set 14a – Concept of a Function; Evaluation of a Function at a point
• Students will be able to:
• Identifying Functions
• Evaluating Single Functions
• Solve Functions using particular functional f(x) values
• Evaluating Arithmetic Functions
• Sample pdf file
• HW Set 14b - Concept of a Function; Domain of a Function
• Students will be able to:
• Determine Domain of a Function
• Determine Range of a Function
• Sample pdf file
• HW Set 15 – Graphs of Basic Functions (can use more problems)
• Students will be able to:
• Determine Coordinates of a Graph
• Create Table of Values for a Basic Graphs
• Analyze a Basic Graph
• Sample pdf file
• HW Set 16 – Properties of Functions: Even and Odd Functions (can use more problems)
• Students will be able to:
• Determine Increasing/Decreasing Intervals of Function
• Determine Local Maximum/Minimum Values of Function
• Identify Even and Odd Functions
• Determine Symmetry of Function
• Sample pdf file
• HW Set 17 – Library of Functions (can use more problems)
• Students will be able to:
• Identify Library Functions
• Identify Piecewise Function
• Determine Table of Value for Library Function
• Sample pdf file
• HW Set 18 – Graphing Transformations
• Students will be able to:
• Identify graphing transformations from a graph
• Apply graphing transformations to a graph
• Identify graphing transformations from a function
• Apply graphing transformations to a function
• Sample pdf file
• HW Set 19 – Math Models (can use more problems)
• Students will be able to:
• Create Mathematical Models as a Function
• Evaluate Mathematical Model as a Function
• Sample pdf file
• HW Set 20 – Linear Functions
• Students will be able to:
• Identify the graph of linear functions
• Find the slope and y-intercept of a graph of a linear function
• Find an equation of a linear function given the slope and y-intercept
• Sample pdf file
• HW Set 21 – Linear Models and Scatterplots
• Students will be able to:
• Use linear functions to model real-life situations
• Use data and technology to produce least-squares regression line, and interpret the findings
• Sample pdf file
• HW Set 22 – Quadratic Functions
• Students will be able to:
• Identify the graph of a quadratic function
• Determine a possible formula for a quadratic function based on the graph
• Find the vertex of parabola
• Bring equation of parabola into vertex form, $$a(x−h)^2+k$$
• Bring equation of parabola into standard form $$ax^2+bx+c$$
• Sample pdf file
• HW Set 23 – Quadratic Models (Max/Min Problems) and Scatterplots (can use more problems)
• Students will be able to:
• Set up quadratic function that models a real-life situation
• Determine if quadratic function has maximum or minimum
• Find the coordinates of the extreme point
• Interpret the coordinates of the extreme point in the context
• Sample pdf file
• HW Set 24 – Quadratic Inequalities
• HW Set 25 – Polynomial Functions and Properties
• Students will be able to:
• Describe the terms, degree, and coefficients of a polynomials
• Determine the $$x$$-intercepts and $$y$$-intercepts of a graph of polynomial
• Determine the end behavior of the graph of polynomial
• Evaluate polynomial at a point
• Sample pdf file
• HW Set 26 – Graph of Polynomial and Power Function
• Students will be able to:
• Find real zeros of polynomials and identify their multiplicities
• Determine end behavior of the graph of polynomial
• Determine if the graph of polynomial is above or below the $$x$$-axis to either side of the real zero
• Produce a possible formula for the polynomial based on the graph
• Sample pdf file
• HW Set 27 – Rational Function and Properties
• Students will be able to:
• Identify domain of rational functions
• Identify vertical asymptotes of rational functions
• Identify horizontal or slanted asymptotes of rational functions
• Identify any holes a graph of rational function might have
• Find the $$x$$-intercepts and $$y$$-intercepts of a graph of rational function
• Sample pdf file
• HW Set 28 – Graph of Rational Function
• Students will be able to:
• Identify domain of rational functions
• Identify vertical asymptotes of rational functions
• Identify horizontal or slanted asymptotes of rational functions
• Identify any holes a graph of rational function might have
• Find the $$x$$-intercepts and $$y$$-intercepts of a graph of rational function
• Identify the graph of rational function
• Produce a possible formula for a rational function based on the given graph
• Sample pdf file
• HW Set 29 – Polynomial and Rational Inequalities
• Students will be able to:
• Use zeros of polynomials and Intermediate Value Theorem to solve polynomial inequalities
• Use Intermediate Value Theorem to solve rational inequalities
• Sample pdf file
• HW Set 30 – Polynomial Real Zeros
• Students will be able to:
• Use Rational Zero Theorem to find zeros of polynomials
• Determine the maximum possible number of positive real zeros and negative real zeros of a polynomial
• Factor a polynomial using Factor Theorem
• Use Synthetic Division to divide polynomials
• Sample pdf file
• HW Set 31 – Polynomial Complex Zeros
• Students will be able to:
• Use Fundamental Theorem of Algebra to recover a formula for a polynomial that has given real and complex zeros
• Find all roots of a polynomial with a possible hint of the possible zeros
• Sample pdf file
• HW Set 32 – Composite Functions
• Students will be able to:
• Evaluate the sum, difference, product and quotient of functions
• Evaluate composition of functions given by their formulas
• Evaluate composition of functions given by their graphs
• Determine the domain of composition and arithmetic combination of two functions
• Decompose a function into a composition of two simpler functions
• Sample pdf file
• HW Set 33 – One-to-one and Inverse Functions
• Students will be able to:
• Identify one-to-one functions
• Find a formula for inverse function
• Identify the graph of inverse function
• Use the connection between the domain and range of the original and inverse functions
• Use inverse functions
• Sample pdf file
• HW Set 34 – Exponential Functions (Properties and Graph)
• Students will be able to:
• Identify the graphs of basic exponential functions
• Evaluate exponential functions
• Solve basic exponential equations
• Sample pdf file
• HW Set 35 – Log Functions (Basic Properties and Graph)
• Students will be able to:
• Switch exponential expressions into logarithmic form
• Switch logarithmic expressions into exponential form
• Identify graphs of basic logarithmic functions
• Determine the domain and range of simple logarithmic functions
• Evaluate expressions involving logarithmic and exponential functions
• Solve basic exponential and logarithmic equations
• Sample pdf file
• HW Set 36 – Properties of Logs
• Students will be able to:
• Use properties of logarithms to expand logarithmic expressions into a sum or difference of logarithms
• Use properties of logarithms to collapse logarithmic expressions into a single logarithm
• Sample pdf file
• HW Set 37 – Exponential Equations
• Students will be able to:
• Solve exponential equations
• Solve quadratic in form exponential equations
• Use properties of exponents to solve equations
• Sample pdf file
• HW Set 38 – Log Equations
• Students will be able to:
• Solve logarithmic equations
• Use properties of logarithms to solve logarithmic equations
• Sample pdf file
• HW Set 39a - Systems of Linear Equations 2 variables
• Students will be able to:
• Solve systems of linear equations in 2 variables
• Identify systems with unique solution, no solutions, or infinitely many solutions
• Sample pdf file
• HW Set 39b - Systems of Linear Equations 3 and more variables
• Students will be able to:
• Produce augmented matrix for a system of equations
• Perform the row operations on an augmented matrix
• Solve systems of linear equations in 3 variables
• Solve systems of linear equations in 4 variables
• Sample pdf file

## (2011 Edition) Problem sets

### Review

• Set 01 Real numbers, essential algebra rules
• Problem set for this unit
• Students will be able to
• evaluate algebraic expressions
• domain of a variable
• laws of exponents
• square roots
• scientific notation
• Set 07 Roots and rational exponents

### College algebra problem sets

• Set 03 Quadratic Equations with Complex Roots
• Problem set for this unit
• Students will be able to
• Solve Factorable equations
• Solve Equations with radicals (populated)
• Set 05 Inequalities
• Problem set for this unit
• Students will be able to
• Solve very simple inequalities
• Solve compound inequalities (populated, needs more)
• Set 06 Absolute value
• Problem set for this unit
• Students will be able to
• Solve equations involving absolute values
• Solve inequalities involving absolute values (populated)
• Set 07 Applications
• Problem set for this unit
• Students will be able to
• Solve word problems about interest
• Solve mixture problems
• Solve word problems about motion
• Solve word problems about constant rate jobs (populated)
• Set 08 Coordinate system
• Problem set for this unit
• Students will be able to
• Solve problems using the distance formula
• Solve problems using the midpoint formula (populated)
• Set 09 Graphs of equations in two variables
• Problem set for this unit
• Students will be able to
• Find graphs of equations in two variables
• Find intercepts
• Analyze symmetry of graphs (populated)
• Set 12 Variation
• Set 13 Functions
• Set 16 Library of functions
• Problem set for this unit
• Students will be able to
• Use several of a library of functions
• Graph piecewise-defined functions
• Evaluate piecewise-defined functions
• Set 17 Transformations of functions
• Problem set for this unit
• Students will be able to
• Use graphing techniques
• Use transformations to graph composite functions
• Set 19 Properties of Linear Functions
• Set 22 Applications of Quadratic functions
• Set 23 Inequalities with Quadratic functions
• Set 24 Polynomial functions and models
• Set 25 Properties of Rational Functions
• Set 26 Graphs of a Rational Functions
• Problem set for this unit
• Students will be able to
• Find vertical asymptotes
• Find horizontal asymptotes
• Find the domain and range of a rational function.
• Graph rational functions
• Set 27 Graphs of a Rational Functions
• Set 29 Complex zeros
• Set 31 Inverse functions
• Set 32 Conic sections
• Problem set for this unit
• Students will be able to
• Find equations for circles
• Find equations for ellipses
• Find equations for parabolas