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© StraighterLine
MAT101: College Algebra

College Algebra
Course Text
Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen.
College Algebra
, 8th edition,
McGraw-Hill, 2008, ISBN: 9780072867381
[This text is available as an etextbook at purchase or students may find used, new, or rental copies at link this ]

Course Description
This course provides a working knowledge of college-level algebra and its applications.
Emphasis is placed upon the solution and the application of linear and quadratic equations, word problems, polynomials, and rational and radical equations. Students perform operations on real numbers and polynomials and simplify algebraic, rational, and radical expressions.
Arithmetic and geometric sequences are examined, and linear equations and inequalities are discussed. Students learn to graph linear, quadratic, absolute value, and piecewise-defined functions and solve and graph exponential and logarithmic equations. Other topics include solving applications using linear systems as well as evaluating and finding partial sums of a series. Course Objectives
After completing this course, students will be able to:
● Identify and then calculate perimeter, area, surface area, and volume for standard geometric figures
● 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.
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MAT101: College Algebra

● Solve application problems involving arithmetic and geometric sequences and series.
● Solve applications involving the various types of equations and inequalities.

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

Important Terms
In this course, different terms are used to designate tasks:
● Proctoring all final exams require proctoring which can be completed conveniently
:
from your home. A webcam is required.
● Tutoring memberships include online tutoring for students to access with any
:
content/subject related questions in the place of faculty. If your tutor is not able to answer your questions please contact a student advisor.
● Practice Exercise A non-graded assignment to assist you in practicing the skills
:
discussed in a topic.
● Graded Exam A graded online test.
:

Course Evaluation Criteria
StraighterLine provides a percentage score and letter grade for each course. See
Academic
Questions section in FAQ for further details on percentage scores and grading scale. A passing percentage is
70% higher. or 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 1000 points the course: in Topic

Assessment

Points Available

2

Graded Exam #1

125

5

Graded Exam #2

125

9

Graded Exam #3

125

14

Graded Exam #4

125

Review

Final Graded Exam

500

Total

1000

Course Topics and Objectives
Topic Lesson

Subtopics

Objectives

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© StraighterLine
MAT101: College Algebra

1

Geometry and Measurement





Standard Geometric
Polygons and Solids
Construction of Geometric
Solids
Perimeter, Area, and
Volume





Identify standard geometric polygons and solids.
Construct standard solid geometry figures.
Calculate perimeter, area, surface area, and volume for standard geometric figures.


2

Basic
Algebraic
Operations





Real Numbers and
Polynomials
Rational Expressions
Rational Exponents and
Radicals













3

Linear
Equations
and
Inequalities
in One
Variable





Linear Equations and
Applications
Linear Inequalities and
Applications
Absolute Value in
Equations and
Inequalities







4

Quadratic
Equations





Factoring and solving
Quadratic Equations using
Factoring
Completing the Square
Quadratic Formula and
Applications of the
Quadratic Equations







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Identify and use properties of real numbers.
Simplify algebraic expressions. Write rational numbers in different formats.
Perform prime factorization of natural numbers
Identify and classify polynomial and Radicals expressions. Perform operations on polynomials. Factor polynomials.
Write a rational expression in simplest form
Compute rational expressions. Simplify radical expressions.
Multiply and divide radical expressions. Solve linear equations by using all properties of equality and the rules.
Solve word problems using linear equations.
Solve and graph linear inequalities. Solve an application using inequalities. Solve absolute value equalities and inequalities.
Write a quadratic equation in the standard form.
Solve quadratic equations by factoring. Solve quadratic equations by the square root property.
Solve quadratic equations by completing the square.
Solve quadratic equations by

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MAT101: College Algebra




5

Polynomial and Other
Equations





Polynomial Equations and
Applications
Equations Involving
Radicals and Rational
Exponents
Complex Numbers








6

Functions and Graphs



Rectangular Coordinates and the Graph of a Line












7

Operations and Functions




The Algebra and
Composition Functions
One-to-One and Inverse
Functions







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using the quadratic formula.
Solve word problems involving quadratic equations. Use the discriminant to identify the number of solutions. Solve polynomial equations using the zero factor property. Solve rational equations.
Solve radical equations.
Identify and simplify complex numbers. Add and subtract complex numbers. Multiply and divide complex numbers. Use a table of values to graph linear equations.
Determine when lines are parallel or perpendicular.
Use linear graphs in an applied context.
Identify functions and state their domain and range.
Use function notation.
Write a linear equation in function form.
Use function form to identify the slope.
Use slope-intercept form to graph linear functions.
Write a linear equation in point-intercept form.
Use the function form, the slope-intercept form, and the point-intercept form to solve applications. Compute a sum or difference of functions and determine the domain of the result.
Compose two functions and find the domain.
Identify one-to-one functions. Find inverse functions using an algebraic method.
Graph a function and its

© StraighterLine
MAT101: College Algebra





8

Analyzing
Graphs





Piecewise-Defined
Functions
Graphs and Symmetry
Tranformations











9

Graphing
Polynomial
Functions





Graphing General
Quadratic Functions
Graphing Polynomial
Functions
Applications of Polynomial
Functions







10

Graphing
Rational
Functions





Asymptotes and Rational
Functions
Graphing Rational
Functions
Applications of Rational
Functions






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inverse.
Graph factorable quadratic equations. Graph the square root, cubic, and cube root functions.
Compute a product or quotient of functions and determine the domain of the result. State the domain of a piecewise-defined function.
Evaluate piecewise-defined functions. Graph functions that are piece-wise defined.
Identify different symmetry types. Use symmetry as an aid to graphing. Perform vertical and horizontal shifts of a basic graph. Perform vertical and horizontal 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 and using transformations.
Graph a general quadratic function using the vertex formula. Solve applications involving quadratic functions.
Graph polynomial functions.
Describe the end behavior of a polynomial graph.
Graph the reciprocal and reciprocal quadratic functions. Identify horizontal and vertical asymptotes.
Use asymptotes to graph transformations. Use asymptotes to determine

© StraighterLine
MAT101: College Algebra





11

Exponential and Logarithmic
Functions





Exponential Functions
Logarithms and
Logarithmic Functions
The Exponential Function and Natural Logarithm













12

Exponential and Logarithmic
Equations





Exponential Equations
Logarithmic Equations
Applications of
Exponential and
Logarithmic Equations









13

Systems of
Equations



Solving Systems
Graphically and by



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the equation of a rational function from its graph.
Find the domain of a rational function. Find the intercepts of a rational function.
Graph general rational functions. Solve applications involving rational functions.
Evaluate an exponential function. Graph exponential functions.
Solve certain exponential equations. Solve applications of exponential equations.
Write exponential equations in logarithmic form.
Graph logarithmic functions and find their domains.
Solve applications of logarithmic functions.
Evaluate and graph base exponential functions.
Evaluate and graph the natural logarithm functions.
Apply the properties of logarithms. Use the change-of-base formula. Write logarithmic and exponential equations in simplified form.
Solve exponential equations.
Solve logarithmic equations.
Solve applications involving exponential and logarithmic equations. Use exponential equations to find the interest compounded in times per year.
Use exponential equations to find the interest compounded continuously. Solve exponential growth and decay problems.
Verify ordered pair solutions. © StraighterLine
MAT101: College Algebra

and
Inequalities





Substitution
Solving Systems using
Elimination
Applications of Linear
Systems
Non-linear Equations and
Linear Inequalities










14

Solving
Linear
Systems
Using
Augmented
Matrices





Matrices
Solving Linear Systems using Matrix Equations
More Applications of
Linear Systems







15

Sequences and Series





Sequences and Series
Arithmetic Sequences
Geometric Sequences









16

Review and
Graded Final
Exam



Course Review



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Solve systems of equations involving quadratic and other non-linear functions.
Graph systems of linear inequalities. Solve linear systems by graphing. Solve linear systems by substitution. Solve linear systems by elimination. Recognize inconsistent systems (no solutions) and dependent systems (infinitely many solutions).
Use a system of equations to mathematically model and solve applications.
State the size of a matrix and identify entries in a specified row and column.
Form the augmented matrix of a system of equations.
Recognize inconsistent and dependent systems.
Model and solve applications using linear systems.
Solve a system of equations using row operations.
Write out the terms of a sequence given the general term. Determine the general term of a sequence.
Find the partial sum of a series. Use summation notation to write and evaluate the series. Solve applications using mathematical sequences.
Find the sum of a geometric series. Solve application problems involving geometric sequences and series.
None

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MAT101: College Algebra

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