| Originator: | Brown, Clark Status: Approved Department: MAT Mathematics |
| Date Created: | 01/13/2016 Submitted: 01/19/2016 Completed: 12/27/2016 |
| Effective Semester: | Fall |
| Catalog Year: | 2017-18 |
| Course Prefix: | MAT |
| Course Number: | 121 |
| Course Full Title: | Intermediate Algebra |
| Reason for Evaluation: | Competencies Change Description Change Prerequisite Change |
| Current Credit: | 4 |
| Lecture Hours: | 4 |
| Lab Hours: | 0 |
| Clinical Hours: | 0 |
| New Credit Hours: | 0 |
| Lecture Hours: | 0 |
| If the credit hour change box has been marked, please provide the new credit hour: | |
| New Lecture Hours: | |
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| SUN Course?: | No |
| AGEC Course?: | No |
| Articulated?: | No |
| Transfer: | |
| Prerequisite(s): | Appropriate score on placement exam or completion of TRM 091 with an 'S' |
| Corequisite(s): | None |
| Catalog Course Description: | Intermediate Algebra extends and strengthens concepts covered in Beginning Algebra. Functions are introduced and integrated throughout the course where appropriate in the context of the following topics: linear equations, inequalities and graphs; absolute value equations and inequalities; operations on polynomials; rational expressions, equations and inequalities; radical expressions and equations; and quadratic equations, inequalities and graphs. |
| Course Learning Outcomes: | 1) Analyze the concepts of Beginning Algebra within the context of functions. (5)
2) Describe the differences and relationships between mathematical expressions, equations and functions. (2,3) 3) Simplify linear, absolute value, polynomial, rational, radical, and quadratic expressions using proper algebraic notation. (3) 4) Solve linear, absolute value, polynomial, rational, radical, and quadratic equations and inequalities using symbolic, graphic, and numeric operations. (3,5) 5) Model real-life situations using algebraic functions. (3,5) 6) Translate real-life problems into mathematical models that can be solved using algebra. (3,5) 7) Demonstrate appropriate use of graphing calculator technology to visualize and solve algebraic problems. (6) |
| Course Competencies: | Competency 1 Apply function concepts and notation to mathematical relationships
Objective 1.1 Explain the difference between an expression, an equation, and a function Objective 1.2 Determine if a relation is a function using the vertical line test Objective 1.3 Identify the domain and range of a function Objective 1.4 Evaluate functions using function notation for functions defined algebraically, graphically, or numerically, using both pencil/paper and a graphing calculator. Objective 1.5 Graph piecewise defined functions Objective 1.6 Describe the sum, difference, product and quotient of two functions using function notation Objective 1.7 Evaluate arithmetic combinations of functions expressed in function notation Objective 1.8 Determine the domain of an arithmetic combination of functions expressed both algebraically and graphically Competency 2 Analyze linear relationships in the context of functions Objective 2.1 Solve linear equations using algebraic and graphical techniques Objective 2.2 Graph linear functions using the intercepts and from the slope-intercept and the point-slope form of the equation Objective 2.3 Interpret slope as an average rate of change Objective 2.4 Determine the slope of a line from its graph, equation, or given two points on the line Objective 2.5 Solve problems involving parallel and perpendicular lines by applying the concepts of slope Objective 2.6 Determine the equation and graph of horizontal and vertical lines Objective 2.7 Determine the equation of a line using the slope-intercept and point-slope forms of a line Objective 2.8 Determine the equation of a line from its graph, or if given two points on the line Objective 2.9 Model linear relationships using linear functions Objective 2.10 Solve applied problems using linear functions to fit data points and interpolate or extrapolate solutions Competency 3 Solve linear inequalities and absolute value equations and inequalities Objective 3.1 Solve linear inequalities using the addition and multiplication properties of inequalities Objective 3.2 Articulate solutions to inequalities using set-builder and interval notation Objective 3.3 Translate verbal expressions of comparison using an inequality Objective 3.4 Solve applied problems using linear inequalities Objective 3.5 Solve linear equations and inequalities graphically, whether given algebraically or graphically Objective 3.6 Find intersections and unions of infinite sets Objective 3.7 Solve compound inequalities Objective 3.8 Solve conjunctions and disjunctions of linear inequalities Objective 3.9 Solve absolute value equations and inequalities Objective 3.10 Describe an interval using absolute value notation Competency 4 Analyze polynomial relationships in the context of functions Objective 4.1 Define terms associated with polynomials Objective 4.2 Evaluate polynomials at numerical values using both pencil / paper and graphing calculator technology Objective 4.3 Evaluate polynomials with binomial inputs Objective 4.4 Simplify polynomial expressions by adding, subtracting and multiplying Objective 4.5 Factor polynomial expressions by grouping and trial and error Objective 4.6 Factor quadratic polynomial expressions using the graphing calculator to identify zeros Objective 4.7 Solve polynomial equations by factoring Objective 4.8 Solve polynomial equations graphically using both the intersection and zero methods Objective 4.9 Factor complex polynomial expressions using perfect square and difference of squares techniques Objective 4.10 Factor polynomial expressions that are the sum or difference of cubes Objective 4.11 Solve applied problems that are modeled by polynomial equations Competency 5 Analyze rational expressions in the context of functions Objective 5.1 Identify vertical asymptotes of rational functions Objective 5.2 Simplify rational functions, identifying domain restrictions Objective 5.3 Combine rational functions by multiplying and / or dividing, identifying domain restrictions Objective 5.4 Combine rational functions by adding and / or subtracting, identifying domain restrictions Objective 5.5 Simplify complex rational expressions Objective 5.6 Solve rational equations Objective 5.7 Solve rational functions for an indicated output value Objective 5.8 Solve applied problems modeled using rational functions Objective 5.9 Divide polynomials by monomials, binomials, and other polynomials using the division algorithm Objective 5.10 Divide polynomials using synthetic division Objective 5.11 Evaluate polynomials using polynomial division and the Remainder Theorem Objective 5.12 Solve formulas having rational expressions for a given variable Objective 5.13 Solve problems posed using the language of direct, inverse, joint, and combined variation Competency 6 Analyze radical expressions in the context of functions Objective 6.1 Simplify odd and even roots, including correct use of the absolute value for radicands with variable expressions Objective 6.2 Evaluate radical functions for numerical values Objective 6.3 Identify domain restrictions for radical functions Objective 6.4 Express radical expressions using rational exponents Objective 6.5 Simplify expressions having both positive and negative rational exponents Objective 6.6 Simplify expressions with rational exponents by applying the rules of exponents Objective 6.7 Simplify radical expressions using rational exponents Objective 6.8 Simplify radical expressions by removing perfect power factors Objective 6.9 Simplify radical expressions to standard form by multiplying and dividing Objective 6.10 Rationalize denominators and numerators having one or two terms Objective 6.11 Simplify radical expressions involving addition and subtraction Objective 6.12 Multiply radical expressions having different indices Objective 6.13 Divide radical expressions having different indices Objective 6.14 Solve radical equations having one or two radical terms. Objective 6.15 Simplify square roots of negative numbers using the imaginary number i Objective 6.16 Categorize the Complex numbers in relation to the Natural numbers, Integers, Rational, Irrational, and Real numbers Objective 6.17 Combine complex numbers by adding, subtracting, multiplying and dividing Objective 6.18 Simplify powers of i Competency 7 Analyze quadratic expressions in the context of functions Objective 7.1 Solve quadratic equations by factoring, extracting square roots, completing the square, and the quadratic formula Objective 7.2 Approximate irrational solutions of quadratic equations to at least 3 decimals accuracy using graphing calculator technology Objective 7.3 Determine the nature of solutions to a quadratic equation by applying the discriminant Objective 7.4 Write quadratic equations having integer, rational, irrational, or complex solutions Objective 7.5 Solve applied problems modeled with quadratic functions Objective 7.6 Solve formulas for a specified variable using the quadratic formula Objective 7.7 Solve equations that are quadratic in form, including those which are quadratic in expressions that are themselves quadratic, a binomial, or involve a rational exponent or rational expression Objective 7.8 Graph quadratic functions given in vertex form f(x) = a(x-h)^2 + k Objective 7.9 Graph quadratic functions given in standard form by completing the square to rewrite in vertex form Objective 7.10 Identify the vertex of parabolas given in standard form as (-b/(2a), f(-b/(2a)) Objective 7.11 Solve applied maximization and minimization problems modeled by quadratic functions Objective 7.12 Solve quadratic, rational, and polynomial inequalities using both algebraic and graphical techniques Objective 7.13 Express solutions to nonlinear inequalities with the appropriate interval endpoint inclusion or exclusion |