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This course provides a working knowledge of college-level algebra and its applications. Emphasis is on solving linear and quadratic equations, word problems, and polynomial, rational and radical …

This course provides a working knowledge of college-level algebra and its applications. Emphasis is on 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. 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, and evaluating and finding partial sums of a series.

Includes 10 hours of 1-on-1 live, on demand instructional support from SMARTHINKING.

Introductory Algebra is a not-for-credit course which prepares students to successfully complete College Algebra.

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  • 1. College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 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: • 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.
  • 2. • 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. Course Prerequisites There are no prerequisites to take College Algebra.  Important Terms In this course, different terms are used to designate tasks: • Exercise: A non-graded assignment to assist you in practicing the skills discussed in a topic. • Exam: A graded online test.  Course Evaluation Criteria There are a total of 500 points in the course: Exam #1 100 points Exam #2 100 points Exam #3 100 points Exam #4 100 points Final Exam 100 points At the end of the course, each student will receive the number of points earned. The student’s final letter grade is determined by the corresponding institution’s grading scale. Course Topics and Objectives Topic Lesson Topic Subtopics Objectives 1 Basic Algebraic • Real Numbers and • Identify and use properties of real Operations Polynomials numbers. • Rational Expressions • Simplify algebraic expressions. • Rational Exponents • 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.
  • 3. • Multiply and divide radical expressions. 2 Linear Equations and • Linear Equations and • Use the notation of inequalities. Inequalities in One Applications • Solve linear equations by using all Variable • Linear Inequalities properties of equality and the rules. and Applications • Solve word problems using linear • Absolute Value in equations. Equations and • Solve and graph linear inequalities. Inequalities • Solve an application using inequalities. • Solve absolute value equalities and inequalities. 3 Quadratic Equations • Factoring and • Write a quadratic equation in the Solving Quadratic standard form. Equations Using • Solve quadratic equations by factoring. Factoring • Solve quadratic equations by the • Completing the square root property. Square • Solve quadratic equations by • Quadratic Formula completing the square. and Applications of • Solve quadratic equations by using the the Quadratic quadratic formula. Equations • Solve word problems involving quadratic equations. • Use the discriminant to identify the number of solutions. 4 Polynomial and Other • Polynomial Equations • Solve polynomial equations using the Equations and Applications zero factor property. • Equations Involving • Solve rational equations. Radicals and Rational • Solve radical equations. Exponents • Identify and simplify complex numbers. • Complex Numbers • Add and subtract complex numbers. • Multiply and divide complex numbers. 5 Functions and Graphs • Rectangular • Use a table of values to graph linear Coordinates and the equations. Graph of a Line • 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. 6 Operations on • The Algebra and • Compute a sum or difference of Functions Composition functions and determine the domain of Functions the result. • One-to-One and • Compose two functions and find the Inverse Functions domain. • Identify one-to-one functions. • Find inverse functions using an algebraic method. • Graph a function and its 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.
  • 4. 7 Analyzing Graphs • Piecewise-Defined • State the domain of a piecewise- Functions defined function. • Graphs and • Evaluate piecewise-defined functions. Symmetry • Graph functions that are piece-wise • Transformations 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. 8 Graphing Polynomial • Graphing General • Graph quadratic functions by Functions Quadratic Functions completing the square and using • Graphing Polynomial transformations. Functions • Graph a general quadratic function • Applications of using the vertex formula. Polynomial Functions • Solve applications involving quadratic functions. • Graph polynomial functions. • Describe the end behavior of a polynomial graph. 9 Graphing Rational • Asymptotes and • Graph the reciprocal and reciprocal Functions Rational Functions quadratic functions. • Graphing Rational • Identify horizontal and vertical Functions asymptotes. • Applications of • Use asymptotes to graph Rational Functions transformations. • Use asymptotes to determine 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. 10 Exponential and • Exponential • Evaluate an exponential function. Logarithmic Functions Functions • Graph exponential functions. • Logarithms and • Solve certain exponential equations. Logarithmic • Solve applications of exponential Functions equations. • The Exponential • Write exponential equations in Function and Natural logarithmic form. Logarithm • 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. 11 Exponential and • Exponential • Write logarithmic and exponential Logarithmic Equations Equations equations in simplified form. • Logarithmic • Solve exponential equations. Equations • Solve logarithmic equations. • Applications of • Solve applications involving Exponential and exponential and logarithmic equations. Logarithmic • Use exponential equations to find the Equations interest compounded in times per year.
  • 5. • Use exponential equations to find the interest compounded continuously. • Solve exponential growth and decay problems. 12 Systems of Linear • Solving Systems • Verify ordered pair solutions. Equations in Two Graphically and by • Solve linear systems by graphing. Variables Substitution • Solve linear systems by substitution. • Solving Systems • Solve linear systems by elimination. Using Elimination • Recognize inconsistent systems (no • Applications of Linear solutions) and dependent systems Systems (infinitely many solutions). • Use a system of equations to mathematically model and solve applications. 13 Solving Linear • Matrices • State the size of a matrix and identify Systems Using • Solving Linear entries in a specified row and column. Augmented Matrices Systems Using • Form the augmented matrix of a Matrix Equations system of equations. • More Applications of • Recognize inconsistent and dependent Linear Systems systems. • Model and solve applications using linear systems. • Solve a system of equations using row operations. 14 Sequences and Series • Sequences and • Write out the terms of a sequence Series given the general term. • Arithmetic • Determine the general term of a Sequences sequence. • Geometric • Find the partial sum of a series. Sequences • 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. 15 Review and Graded • Course Review • None Final Exam