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Course Snapshot for MAT 121 - College Algebra

The information listed below is subject to change. Please review the course syllabus within your online course at the start of class.

Course Competencies

The competencies you will demonstrate in this course are as follows:

  1. Demonstrate an understanding of set notations, subsets of the real numbers and properties of real numbers.
  2. Perform algebraic manipulations including working with exponents, radicals, polynomial operations, factoring and algebraic fractions.
  3. Solve the following types of equations: linear, quadratic, rational, exponential, logarithmic equations involving radicals, equations in quadratic form and equations involving absolute value.
  4. Demonstrate an understanding of formulas including formula evaluation and solving a formula for any of the variables.
  5. Read and analyze problems in the form of word problem applications and obtain solutions using equations.
  6. Solve and graph first degree inequalities, higher degree inequalities and inequalities involving absolute value.
  7. Recognize and graph linear functions, rational functions, absolute value functions, and graph inequalities in two variables .
  8. Work with function notation and demonstrate knowledge of the meaning of a function.
  9. Demonstrate an understanding of function composition, one-to-one functions and inverse functions.
  10. Examine, evaluate and graph exponential and logarithmic functions.
  11. Use at least two of the following techniques to solve linear and non-linear systems of the equations: substitution, addition, Gaussian elimination, Cramer's rule.
  12. Perform operations with matrices and use a matrix operation.
  13. Graph systems of inequalities.
  14. Identify the conic section represented by a given second degree equation and graph conic sections including circles, parabolas, ellipses and hyperbolas.
  15. Explore various topics related to sequences and series including series notation, sequence formulas, counting principles, mathematical induction and the Binomial Theorem.
  16. Perform synthetic division.
  17. Use the Remainder Theorem and the Factor Theorem to factor and evaluate polynomials.
  18. Solve polynomial equations using the Rational Root Theorem and/or approximation techniques.
  19. Write and speak clearly and logically in presentations and essays.
  20. Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information.
Learning concepts for this course are enchanced using illustrative models, video, and online discussions.

Module Outcomes Mapped to Competencies

Module 1 Learning Outcomes

Mapped to Course Competencies (above)
Graph functions manually on paper. 7
Graph functions using a graphing calculator. 7,13
Determine x-intercepts and y-intercepts of functions. 7
State in interval notation domain and range of a function. 8
Perform the vertical line test to determine if a relation is a function. 8
Correctly write and interpret functional notation, f (x) = (some rule for x). 8
Evaluate a given function for different 'inputs' of x. 9
Manipulate and graph linear functions. 7
Calculate slope. 7
Determine if two lines are parallel, perpendicular or neither. 7
Find a linear function that best fits a set of data using linear regression techniques. 9
Find zeros of functions. 11
Solve simple and compound linear inequalities. 8
Write clearly and logically in presentations. 19

Module 2 Learning Outcomes

Mapped to Course Competencies (above)

Determine where a function increases, decreases or stays constantly analyzing its graph. 7
Describe important features of the graph of a function, including the relative maximum and minimum values. 7
Diagram, evaluate and find domain and range for piecewise functions. 7, 9
Modify operations on functions, including addition, subtraction, multiplication and division. 9
Set up and simplify a difference quotient for a function. 9
Construct and simplify composite functions and decompose composite functions. 9
Identify the type of symmetry present in a graph of a function (if it IS symmetric in any respect). 9
Order functions as even, odd or neither. 9
Convert the graphs of functions through vertical and horizontal shifts, reflections and vertical and horizontal stretchings and shrinkings. 2
Set up and solve applications involving direct, inverse and compound variation. 7?
Write clearly and logically in presentations( 19

Module 3 Learning Outcomes

Mapped to Course Competencies (above)

Define a quadratic function. 3
Identify the domain of a quadratic function. 3
Diagram and analyze the graph of a quadratic function. 6
Give the characteristics of the graph of a quadratic function by completing the square. 14
Describe a complex number and its conjugate. 1
Name the principal square root of a negative number. 1
Solve equations involving complex numbers. 1
Solve quadratics by these methods: Completing the Square, Zero Factor, and the Quadratic Formula. 18
Apply the methods of solving quadratics to solve word problems and regression problems. 5
Explain and solve equations involving radicals. 2
Solve rational equations. 3
Solve equations and inequalities with absolute value. 3
Write clearly and logically in presentations. 19

Module 4 Learning Outcomes

Mapped to Course Competencies (above)

Categorize polynomials and their degree.  
Identify the zeros of a polynomial function and their multiplicity.  
Identify major characteristics of the graph of a polynomial function.  
Write clearly and logically in presentations. 19

Module 5 Learning Outcomes

Mapped to Course Competencies (above)

Evaluate exponential functions. 2
Diagram exponential functions. 10
Define the number “e”. 10
Solve exponential equations. 10
Rewrite any exponential equation in logarithmic form and vice versa. 10
Evaluate logarithmic functions. 10
Diagram logarithmic functions. 10
Solve logarithmic equations. 10
Explain properties of logarithms. 10
Write logarithmic expressions as a sum or difference. 10
Write a logarithmic expression as a single logarithm. 10
Determine common or natural logs on a calculator and by pencil. 10
Use the change of base formula. 10
.Identify exponential and logarithmic models. 10
Use the base e and work with functions involving that base, such as f(x) = Pe0.735t 10
Set up and solve applications involving exponential and logarithmic functions. 10
Write clearly and logically in presentations. 19

Module 6 Learning Outcomes

Mapped to Course Competencies (above)

Solve a system of 2 linear equations in two unknowns by graphing, by substitution, or by elimination. 11
Solve a system of 3 or 4 linear equations in three unknowns by substitution or elimination. 11, 20
Write clearly and logically in presentations. 19
Write the augmented matrix of a system of linear equations. 19
Write the system from the augmented matrix. 19
Diagram linear inequalities and systems of linear inequalities. 19
Compute row operations on a matrix. 19
Use Gauss-Jordan Elimination to solve systems of equations. 19
Evaluate matrix operations – add, subtract, and multiply matrices. 19
Compute scalar multiples of a matrix. 19
Compute the inverse of a matrix if it has one. 19
Solve systems of linear equations using inverses of matrices. 19
Determine the value of a determinant. 19
Use Cramer’s Rule to solve linear systems of equations. 19
Solve problems by use of Linear Programming. 19

Module 7 Learning Outcomes

Mapped to Course Competencies (above)

Identify the conics. 14
Formulate and graph the equation of a parabola. 14
Solve applied problems involving parabolas. 14, 20
Find and graph the equation of an ellipse. 14
Define ellipses with center at (h,k). 14
Solve applied problems involving ellipses. 14
Determine and graph the equation of a hyperbola. 14
Characterize hyperbolas with center at (h,k). 14,20
Solve applied problems involving ellipses. 14
Convert equations to the form ax2 + by2+ cx + dy + e = 0 where possible. 14
Determine if the graph is empty, a single point, a line, a pair of intersecting lines, a circle, an ellipse, a parabola, or a hyperbola, depending on the values of a, b, c, d, & e. 14
Develop an equation of an ellipse, find the vertices, the foci, the center, and the axes and graph the figure. 14
Compose the vertices and the center, find an equation for the ellipse. 14
Describe the equation of a hyperbola, find the vertices, the foci, the center, the axes, and the asymptotes and graph the figure. 14
Identify the vertices and the center, and find an equation for a hyperbola. 14
Choose an equation of a parabola, compute the vertex, focus, directrix, and axis and diagram the figure. 14
Identify the focus and directrix of a parabola & discover an equation for the parabola. 14
Interpret Axes. 7
Solve Nonlinear Systems. 9
Identify and Generate Sequences and Series. 11
Evaluate Terms and Sums of Arithmetic Sequences. 15
Analyze Terms and Sums of Geometric Sequences. 15
Explain a Binomial Expansion. 15
Write clearly and logically in presentations. 19

Module 8 Learning Outcomes

Mapped to Course Competencies (above)

Solve, explain, or interpret problems from Modules 1-7. 19

Course Time Commitment and Expectations

For every credit hour, students should plan to spend an average of 2-3 hours per week for course-related activities in a 15-week course. For example, a 3 credit hour course would average an average 6-9 hours per week to read/listen to the online content, participate in discussion forums, complete assignments, and study the course material. For 10  and 6-week courses, the amount of time per week will be higher so all course competencies, module outcomes, and assignments will be covered.

Aside from typical reading assignments, this course has the following (Please Note: This list is subject to change based on the discretion of the instructor facilitating this course.):

AssignmentPoints
Introduction (Extra Credit) 10
Pretest (Extra Credit) 10
Scavenger Hunt Quiz (Extra Credit) 10
Discussion Posts (Best 6 of 7 @ 10 points each) 60
Dropbox Exercises (Best 4 of 5 @ 10 points each) 40
MyMathLab Homework (Best 10 of 14 @ 10 points each) 100
Module Quizzes (Best 10 of 14 @ 10 points each) 100
Module Exams (Best 6 of 7 @ 100 points each) 600
Practice Final Exam (Extra Credit)   10
Final Exam 100
TOTAL (not including extra credit)
1000

CCCOnline Course Quality Commitment

CCCOnline goes to great lengths to assure the quality of your online learning experience. You can expect the following from our courses: