College Algebra with Daniel Gryboski

Course Content from McGraw-Hill
Course Number: MAT101
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Make efficient use of your time with my guided instruction in this College Algebra course. I will help you with:

  • Timely review materials aimed directly at the concepts of each exam.
  • Office hours and individualized video tutorials.
  • Feedback on what you are doing correctly or incorrectly.
  • Suggestions on how you might use the concepts in your daily life.

This College Algebra online course provides students with a working knowledge of college-level algebra and its applications, emphasizing methods for solving linear and quadratic equations, word problems, and polynomial, rational, and radical equations and applications.

Students perform operations on real numbers and polynomials, and simplify algebraic, rational, and radical expressions.

Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities.

Students learn to graph linear, quadratic, and absolute value, and piecewise-defined functions. They solve and graph exponential and logarithmic equations. Other College Algebra online topics include solving applications using linear systems, and evaluating and finding partial sums of a series.



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3
college credits
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Self Paced
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Mathematics
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22 Reviews
Overall Rating
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  • 12/8/14 by catsgrant1
    Very difficult class
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  • 9/15/14 by jh780
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  • 9/15/14 by jh780
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  • 9/3/14 by stacysaez
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  • 8/27/14 by flt415pe
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  • 8/27/14 by flt415pe
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  • 8/12/14 by catsgrant1
    Very difficult class
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  • 8/8/14 by ashleywaage
    Easy to follow course.
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  • 8/8/14 by ashleywaage
    Easy to follow course.
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  • 7/18/14 by gregedwards.rn
    Loved it the second time
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  • 7/18/14 by gregedwards.rn
    Loved it the second time
    Content Rating
    Overall Rating
  • 6/27/14 by settingitoff07
    Yes
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  • 6/27/14 by settingitoff07
    Yes
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  • 6/6/14 by jasminelockwood
    The exams are tricky.
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  • 6/6/14 by jasminelockwood
    The exams are tricky.
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    Overall Rating
  • 3/9/14 by stacysaez
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    Overall Rating
  • 9/26/13 by gijij13
    It was good
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  • 8/23/13 by aprincess
    The course was easy to complete and had great notes
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  • 8/9/13 by jamie.miraglia
    This course was intimidating, however, the video courses really helped!
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    Overall Rating
  • 8/3/13 by lindskogxrd
    I liked the course, especially prof. Gryboski's video tutorials.
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    Overall Rating
  • 7/23/13 by jefffitz76
    Very well designed
    Content Rating
    Overall Rating
  • 7/1/13 by faith.dixon606
    good course, great examples and walk-through problems for students to view.
    Content Rating
    Overall Rating
Daniel Gryboski|MS, University of Colorado

Total students servedTotal Students Served: 1339 and counting

Dan Gryboski has been teaching math and statistics online and in the classroom since 2002. Throughout his teaching career, Dan has been recognized as a teacher who meets the students’ different learning needs. In his very first year of teaching, he was selected as the Master Teacher out of 250 other faculty members. He was nominated by his students specifically for his ability to help students apply mathematical concepts in their daily lives.

Dan made 600 tutorial videos for McGraw-Hill publishers and most recently created over 300 tutorial videos for StraighterLine. He continues making videos, as he routinely responds to students’ questions by creating tutorials that answer their specific questions.

Dan earned his Bachelor of Arts degree in Mathematics and Computer Science from Colorado College. He earned his Master of Science degree in Mechanical Engineering from the University of Colorado, Boulder. Before entering the teaching profession, he worked as an engineer modeling the passenger capacities of automated transportation systems. He was invited to present his paper, “Using a Simple Linear Regression Model to Predict the Outcome of Collegiate Football Game,” at the Hawaii International Conference on Statistics in 2004. He has presented at numerous local educational forums promoting the use of real applications in teaching mathematics and, thereby, self-reliance.

Dan enjoys spending time outside with his wife and three children, as well as riding his mountain bike and golfing.

Course Objectives

After completing this College Algebra course, students will be able to:

  • Perform operations on real numbers and polynomials.
  • Simplify algebraic, rational, and radical expressions.
  • Solve both linear and quadratic equations and inequalities.
  • Solve word problems involving linear and quadratic equations and inequalities.
  • Solve polynomial, rational, and radical equations and applications.
  • Solve and graph linear, quadratic, absolute value, and piecewise-defined functions.
  • Perform operations with functions as well as find composition and inverse functions.
  • Graph quadratic, square root, cubic, and cube root functions.
  • Graph and find zeroes of polynomial functions.
  • Perform vertical and horizontal shifts and reflections of a basic graph.
  • Perform stretches and compressions on a basic graph.
  • Transform the graph of a general function.
  • Graph quadratic functions by completing the square, using the vertex formula, and using transformations.
  • Solve and graph exponential and logarithmic equations.
  • Solve systems of linear equations and inequalities.
  • Model and solve applications using linear systems.
  • Evaluate and find partial sums of a series.
  • Evaluate and find sums of arithmetic and geometric sequences.
  • Solve application problems involving arithmetic and geometric sequences and series.
  • Solve applications involving the various types of equations and inequalities.

Topic

Lesson

Subtopics

Objectives

1

Geometry and Measurement

  1. Standard Geometric Polygons and Solids
  2. Construction of Geometric Solids
  3. Perimeter, Area, and Volume
  1. Identify standard geometric polygons and solids.
  2. Construct standard solid geometry figures.
  3. Calculate perimeter, area, surface area, and volume for standard geometric figures.

2

Basic Algebraic

Operations

  1. Real Numbers and Polynomials
  2. Rational Expressions
  3. Rational Exponents and Radicals
  1. Identify and use properties of real numbers.
  2. Simplify algebraic expressions.
  3. Write rational numbers in different formats.
  4. Perform  prime factorization of natural numbers
  5. Identify and classify polynomial and Radicals expressions.
  6. Perform operations on polynomials.
  7. Factor polynomials.
  8. Write a rational expression in simplest form
  9. Compute rational expressions.
  10. Simplify radical expressions.
  11. Multiply and divide radical expressions.

3

Linear Equations and Inequalities in One 

Variable

  1. Linear Equations and Applications
  2. Linear Inequalities and Applications
  3. Absolute Value in Equations and Inequalities
  1. Solve linear equations by using all properties of equality and the rules.
  2. Solve word problems using linear equations.
  3. Solve and graph linear inequalities.
  4. Solve an application using inequalities.
  5. Solve absolute value equalities and inequalities.

4

Quadratic Equations

  1. Factoring and solving Quadratic Equations using Factoring
  2. Completing the Square
  3. Quadratic Formula and Applications of the Quadratic Equations
  1. Write a quadratic equation in the standard form.
  2. Solve quadratic equations by factoring.
  3. Solve quadratic equations by the square root property.
  4. Solve quadratic equations by completing the square.
  5. Solve quadratic equations by using the quadratic formula.
  6. Solve word problems involving quadratic equations.
  7. Use the discriminant to identify the number of solutions.

5

Polynomial and Other Equations

  1. Polynomial Equations and Applications
  2. Equations Involving Radicals and Rational Exponents
  3. Complex Numbers
  1. Solve polynomial equations using the zero factor property.
  2. Solve rational equations.
  3. Solve radical equations.
  4. Identify and simplify complex numbers.
  5. Add and subtract complex numbers.
  6. Multiply and divide complex numbers.

6

Functions and Graphs

  1. Rectangular Coordinates and the Graph of a Line
  1. Use a table of values to graph linear equations.
  2. Determine when lines are parallel or perpendicular.
  3. Use linear graphs in an applied context.
  4. Identify functions and state their domain and range.
  5. Use function notation.
  6. Write a linear equation in function form.
  7. Use function form to identify the slope.
  8. Use slope-intercept form to graph linear functions.
  9. Write a linear equation in point-intercept form.
  10. Use the function form, the slope-intercept form, and the point-intercept form to solve applications.

7

Operations and Functions

  1. The Algebra and Composition Functions
  2. One-to-One and Inverse Functions
  1. Compute a sum or difference of functions and determine the domain of the result.
  2. Compose two functions and find the domain.
  3. Identify one-to-one functions.
  4. Find inverse functions using an algebraic method.
  5. Graph a function and its inverse.
  6. Graph factorable quadratic equations.
  7. Graph the square root, cubic, and cube root functions.
  8. Compute a product or quotient of functions and determine the domain of the result.

8

Analyzing Graphs

  1. Piecewise-Defined Functions
  2. Graphs and Symmetry
  3. Tranformations
  1. State the domain of a piecewise-defined function.
  2. Evaluate piecewise-defined functions.
  3. Graph functions that are piece-wise defined.
  4. Identify different symmetry types.
  5. Use symmetry as an aid to graphing.
  6. Perform vertical and horizontal shifts of a basic graph.
  7. Perform vertical and horizontal reflections of a basic graph.
  8. Perform stretches and compressions on a basic graph.
  9. Transform the graph of a general function.

9

Graphing Polynomial Functions

  1. Graphing General Quadratic Functions 
  2. Graphing Polynomial Functions
  3. Applications of Polynomial Functions
  1. Graph quadratic functions by completing the square and using transformations.
  2. Graph a general quadratic function using the vertex formula.
  3. Solve applications involving quadratic functions.
  4. Graph polynomial functions.
  5. Describe the end behavior of a polynomial graph.

10

Graphing Rational Functions

  1. Asymptotes and Rational Functions
  2. Graphing Rational Functions
  3. Applications of Rational Functions
  1. Graph the reciprocal and reciprocal quadratic functions.
  2. Identify horizontal and vertical asymptotes.
  3. Use asymptotes to graph transformations.
  4. Use asymptotes to determine the equation of a rational function from its graph.
  5. Find the domain of a rational function.
  6. Find the intercepts of a rational function.
  7. Graph general rational functions.
  8. Solve applications involving rational functions.

11

Exponential and Logarithmic Functions

  1. Exponential Functions
  2. Logarithms and Logarithmic Functions
  3. The Exponential Function and Natural Logarithm
  1. Evaluate an exponential function.
  2. Graph exponential functions.
  3. Solve certain exponential equations.
  4. Solve applications of exponential equations.
  5. Write exponential equations in logarithmic form.
  6. Graph logarithmic functions and find their domains.
  7. Solve applications of logarithmic functions.
  8. Evaluate and graph base exponential functions.
  9. Evaluate and graph the natural logarithm functions.
  10. Apply the properties of logarithms.
  11. Use the change-of-base formula.

12

Exponential and Logarithmic Equations

  1. Exponential Equations
  2. Logarithmic Equations
  3. Applications of Exponential and Logarithmic Equations
  1. Write logarithmic and exponential equations in simplified form.
  2. Solve exponential equations.
  3. Solve logarithmic equations.
  4. Solve applications involving exponential and logarithmic equations.
  5. Use exponential equations to find the interest compounded in times per year.
  6. Use exponential equations to find the interest compounded continuously.
  7. Solve exponential growth and decay problems.

13

Systems of Equations and Inequalities

  1. Solving Systems Graphically and by Substitution
  2. Solving Systems using Elimination
  3. Applications of Linear Systems
  4. Non-linear Equations and Linear Inequalities
  1. Verify ordered pair solutions. 
  2. Solve systems of equations involving quadratic and other non-linear functions.
  3. Graph systems of linear inequalities.
  4. Solve linear systems by graphing.
  5. Solve linear systems by substitution.
  6. Solve linear systems by elimination.
  7. Recognize inconsistent systems (no solutions) and dependent systems (infinitely many solutions).
  8. Use a system of equations to mathematically model and solve applications.

14

Solving Linear Systems Using Augmented Matrices

  1. Matrices
  2. Solving Linear Systems using Matrix Equations
  3. More Applications of Linear Systems
  1. State the size of a matrix and identify entries in a specified row and column.
  2. Form the augmented matrix of a system of equations.
  3. Recognize inconsistent and dependent systems.
  4. Model and solve applications using linear systems.
  5. Solve a system of equations using row  operations.

15

Sequences and Series

  1. Sequences and Series
  2. Arithmetic Sequences
  3. Geometric Sequences
  1. Write out the terms of a sequence given the general term.
  2. Determine the general term of a sequence.
  3. Find the partial sum of a series.
  4. Use summation notation to write and  evaluate the series.
  5. Solve applications using mathematical sequences.
  6. Find the sum of a geometric series.
  7. Solve application problems involving geometric sequences and series.

16

Review and Graded Final Exam

  1. Course Review
  1. None

StraighterLine suggests, though does not require, that students take Introductory Algebra or its equivalent before enrolling in College Algebra.

Required Textbook: This course has assigned reading.

Title: College Algebra eTextbook

ISBN: 9780072867381

Our Price: $82.70

Assigned reading material as part of taking this online course.
bookshelfWith every purchase of an eTextbook through StraighterLine, students have access to their texts via the Bookshelf App which syncs to their course, provides offline access for studying on the go, and more.
-OR-
book cover

The Barnett/Ziegler/Byleen College Algebra series is designed to give students a solid grounding in pre-calculus topics in a user-friendly manner. The series emphasizes computational skills, ideas, and problem solving rather than theory. Explore/Discuss boxes integrated throughout each text encourage students to think critically about mathematical concepts. All worked examples are followed by Matched Problems that reinforce the concepts being taught. New to these editions, Technology Connections illustrate how concepts that were previously explained in an algebraic context may also be solved using a graphing calculator. Students are always shown the underlying algebraic methods first so that they do not become calculator-dependent. In addition, each text in the series contains an abundance of exercises - including numerous calculator-based and reasoning and writing exercises - and a wide variety of real-world applications illustrating how math is useful.

Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 9780072867381

StraighterLine provides a percentage score and letter grade for each course. A passing percentage is 70% or higher.

If you have chosen a Partner College to award credit for this course, your final grade will be based upon that college's grading scale. Only passing scores will be considered by Partner Colleges for an award of credit.

There are a total of 500 points in the course:

Assessment Points Available
Exam #1 75 points
Exam #2 75 points
Exam #3 75 points
Exam #4 75 points
Final Exam 200 points

Final Proctored Exam

The final exam is developed to assess the knowledge you learned taking this course. All students are required to take an online proctored final exam in order complete the course and be eligible for transfer credit.

Learn more about Proctored Exams

Make efficient use of your time with my guided instruction in this College Algebra course. I will help you with:

  • Timely review materials aimed directly at the concepts of each exam.
  • Office hours and individualized video tutorials.
  • Feedback on what you are doing correctly or incorrectly.
  • Suggestions on how you might use the concepts in your daily life.

This College Algebra online course provides students with a working knowledge of college-level algebra and its applications, emphasizing methods for solving linear and quadratic equations, word problems, and polynomial, rational, and radical equations and applications.

Students perform operations on real numbers and polynomials, and simplify algebraic, rational, and radical expressions.

Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities.

Students learn to graph linear, quadratic, and absolute value, and piecewise-defined functions. They solve and graph exponential and logarithmic equations. Other College Algebra online topics include solving applications using linear systems, and evaluating and finding partial sums of a series.



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