COLLEGE OF THE DESERT Course Code MATH-010 Course Outline of Record 1. Course Code: MATH-010 2. a. Long Course Title: College Algebra b. Short Course Title: COLLEGE ALGEBRA 3. a. Catalog Course Description: This is a function oriented course that includes an examination of the general concept of a function and function notation, as well as an in depth investigation of polynomial, rational, exponential, and logarithmic functions, particularly their equations, graphs, and behavior. Other topics include the binomial theorem, conic sections, and matrices as they apply to systems of linear equations. b. Class Schedule Course Description: This is a function oriented course including the concept of a function and function notation. c. Semester Cycle (if applicable): Every Semester d. Name of Approved Program(s): LIBERAL ARTS with emphasis in Math and Science AA Degree and Transfer Preparation 4. Total Units: 4.00 Total Semester Hrs: 108.00 Lecture Units: 3 Semester Lecture Hrs: 54.00 Lab Units: 1 Semester Lab Hrs: 54.00 Class Size Maximum: 35 Allow Audit: No Repeatability No Repeats Allowed Justification 0 5. Prerequisite or Corequisite Courses or Advisories: Course with requisite(s) and/or advisory is required to complete Content Review Matrix (CCForm1-A) Prerequisite: MATH 040 Advisory: ENG 061 6. Textbooks, Required Reading or Software: (List in APA or MLA format.) a. Stewart, J., L. Redlin, S. Watson (2016). College Algebra (7th/e). Cengage. ISBN: 9781305115545 College Level: Yes Flesch-Kincaid reading level: N/A 7. Entrance Skills: Before entering the course students must be able: a. Demonstrate an understanding that the key characteristic of a linear model is its constant rate of change. MATH 040 - Comprehend that the key characteristic of a linear model is its constant rate of change. b. Interpret slope as a rate of change. MATH 040 - Interpret slope as a rate of change. c. Recognize when a table, graph, or equation is linear. MATH 040 - Recognize when a table, graph, or equation is linear. d. Create a linear model in the form of a table, graph, or equation. MATH 040 - Create a linear model in the form of a table, graph, or equation. e. Find the equation of a line and apply it to solve problems with a constant of change. MATH 040 - Find the equation of a line and apply it to solve problems with a constant of change. f. Solve 2x2 and 3x3 systems of linear equations. MATH 040 - Solve 2x2 and 3x3 systems of linear equations. g. Graph systems of linear inequalities in two dimensions. MATH 040 - Graph systems of linear inequalities in two dimensions. h. Graph and find the equation of a circle. MATH 040 - Graph and find the equation of a circle. 05/02/2018 1 of 6
i. Solve quadratic equations by factoring, completing the square, taking square roots or the quadratic formula. MATH 040 - Solve quadratic equations by factoring, completing the square, taking square roots or the quadratic formula. j. Solve quadratic inequalities. MATH 040 - Solve quadratic inequalities. k. Recognize when a table, graph, or equation is quadratic. MATH 040 - Recognize when a table, graph, or equation is quadratic. l. Create a quadratic model with a table, graph, or equation and solve maximum and minimum problems. MATH 040 - Create a quadratic model with a table, graph, or equation and solve maximum and minimum problems. m. Graph a parabola by finding the vertex, intercepts, and other symmetric points. MATH 040 - Graph a parabola by finding the vertex, intercepts, and other symmetric points. n. Understand and manipulate rational exponents and Nth roots. MATH 040 - Comprehend and manipulate rational exponents and Nth roots. o. Solve root equations. MATH 040 - Solve root equations. p. Demonstrate an understanding of the definition of a function including function notation and terminology (domain and range). MATH 040 - Apply the definition of a function including function notation and terminology (domain and range). q. Demonstrate an understanding that the key characteristic of an exponential function is its constant growth (decay) factor. MATH 040 - Comprehend that the key characteristic of an exponential function is its constant growth (decay) factor. r. Recognize when a table, graph, or equation is exponential and when a word problem can be modeled with an exponential function. MATH 040 - Recognize when a table, graph, or equation is exponential and when a word problem can be modeled with an exponential function. Advisory Skills: s. Demonstrate critical thinking skills when reading, composing and participating in class discussions. ENG 061 - Demonstrate the ability to think critically and express ideas using various patterns of development. t. Develop, organize and express complex ideas in both expository and research papers. ENG 061 - Use theses to organize paragraphs into coherent analyses. ENG 061 - Demonstrate the ability to use research skills including library resources such as books, periodicals, electronic databases and online resources such as the internet. u. Define, analyze, evaluate, explain, classify, compare and contrast ideas in written form. ENG 061 - Use theses to organize paragraphs into coherent analyses. ENG 061 - Recognize features of style such as purpose, audience and tone integrate these elements into academic and professional writing. ENG 061 - Demonstrate the ability to read and respond in writing beyond the literal interpretation of the text. 8. Course Content and Scope: Lecture: 1. Functions, including function-notation, domain and range, piecewise defined functions, and rates of change. 2. Symmetry of functions, transformations of functions, and the algebra of functions, including composition of functions and inverses of functions. 3. Polynomial functions: roots (zeroes); factoring; polynomial division and the remainder and factor theorems; roots and complex numbers; the graphs of and behavior of polynomial functions; polynomial functions as models. 4. Rational functions: roots (zeroes); vertical asymptotes; horizontal asymptotes; oblique asymptotes; the graph of and behavior of rational functions; rational functions as models. 5. Inverse functions, their significance and the computation of an inverse function. 6. Exponential and logarithmic functions; the graphs and behavior of exponential and logarithmic functions. 7. Solving exponential and logarithmic equations. 05/02/2018 2 of 6
8. Applications of polynomial, rational, exponential and logarithmic functions, including growth and decay. 9. Matrices and the use of matrices to solve systems of linear equations, including Gauss-Jordan elimination and Cramer's Rule. 10. Conic sections: graphing conics; their behavior and characteristic properties; their use in solving application problems. 11. Linear, nonlinear and absolute value inequalities. 12. Sequences and Series Lab: (if the "Lab Hours" is greater than zero this is required) 1. Analyze and investigate properties of functions; 2. Synthesize results from the graphs and/or equations of functions; 3. Recognize the behavior of polynomial, rational, exponential, and logarithmic functions by applying transformations to the graphs of functions; 4. Recognize the relationship between functions and their inverses graphically and algebraically; 5. Solve and apply rational, linear, polynomial, radical, absolute value, exponential, and logarithmic equations and solve linear, nonlinear, and absolute value inequalities; 6. Solve linear and nonlinear systems of equations and inequalities; 7. Apply techniques for finding zeros of polynomials and roots of equations including, factoring, polynomial division, the remainder theorem, and factor theorem; 8. Solve and apply linear systems using matrices and determinants including, Gauss-Jordan elimination and Cramer s Rule; 9. Analyze conics algebraically and graphically; 10. Apply conics to model STEM applications; 11. Apply functions and other algebraic techniques to model applications in a variety of disciplines, including STEM fields, business and economics; 12. Exploration of sums of finite and infinite series. 13. Exploration of applications that involve combinations of multiple topics from lecture. 14. Demonstration of mathematical reasoning in either written work or oral presentations. 9. Course Student Learning Outcomes: 1. Demonstrate that previously learned fundamental skills and knowledge from arithmetic, algebra, and geometry prior learning have been maintained or restored. 2. Demonstrate problem solving skills in application problems, with an emphasis on the concept of function. 3. Create, analyze, and interpret graphs of functions. 4. Understand the place deductive reasoning holds in mathematics and determine appropriate usage of deductive reasoning and mathematics in human life and culture. 10. Course Objectives: Upon completion of this course, students will be able to: a. Analyze and investigate properties of functions; Represent a function graphically, numerically, and analytically and synthesize information from these representations. b. Demonstrate an understanding of function notation and operations including inverses and compositions of functions; Recognize the relationship between functions and their inverses graphically and algebraically c. Compute average rates of change and interpret as slope of a secant line. d. Recognize, graph and solve equations involving polynomial, rational, exponential, root, and logarithmic functions; Solve linear, nonlinear and absolute value inequalities. e. Recognize the behavior of polynomial, rational, exponential, and logarithmic functions; Use transformations to graph polynomial, rational, exponential, and logarithmic functions. f. Recognize and apply the appropriate function to solve problems involving tables, graphs, equations or words. g. Use matrix reduction techniques such as Gauss-Jordan elimination and Cramer's Rule to solve systems of linear equations. h. Create a system of linear equations modeling an application problem in STEM fields, Business and Economics. 05/02/2018 3 of 6
i. Recognize and graph the equations of parabolas, circles, ellipses, and hyperbolas. j. Recognize the behavior and characteristic properties of parabolas, circles, ellipses, and hyperbolas; Describe these characteristic properties in terms of how they are expressed in the standard form of the equation of a conic. k. Use linear, exponential and logarithmic equations and equations of conics to model application problems in STEM fields, Business and Economics. l. Apply studied principles and skills to new situations in addition to situations that mirror those on the homework and those shown in class m. Use formulas to find sums of finite and infinite series. n. Apply techniques for finding zeros of polynomials and roots of equations including, factoring, polynomial division, the remainder theorem, and factor theorem 11. Methods of Instruction: (Integration: Elements should validate parallel course outline elements) a. Collaborative/Team b. Demonstration, Repetition/Practice c. Discussion d. Laboratory e. Lecture Other Methods: Calculator/Computer Demonstration 12. Assignments: (List samples of specific activities/assignments students are expected to complete both in and outside of class.) In Class Hours: 108.00 Outside Class Hours: 108.00 a. Out-of-class Assignments 13. 1. Read textbooks and supplementary assignments. 2. Complete assigned homework including problem solving exercises to improve skills and mathematical understanding. b. In-class Assignments 1. Read textbooks and supplementary assignments. 2. Attend classroom lectures and take notes. 3. Participate in classroom discussions to review, analyze, diagnose and evaluate various methods of solution used in homework. 4. Complete examinations involving problems that apply studied principles to new situations. Methods of Evaluating Student Progress: The student will demonstrate proficiency by: Written homework Computational/problem solving evaluations Mid-term and final evaluations a. Chapter tests with in-class essay type exam questions; b. Comprehensive final exam with essay questions 14. Methods of Evaluating: Additional Assessment Information: 15. Need/Purpose/Rationale -- All courses must meet one or more CCC missions. IGETC Area 2: Mathematical Concepts and Quantitative Reasoning A: Mathematic CSU GE Area B: Physical and its Life Forms(mark all that apply) B4 - Mathematics/Quantitative Thinking PO-GE C4.b - Language & Rationality (Communication & Analytical Thinking) Gather, assess, and interpret relevant information. Apply logical and critical thinking to solve problems; explain conclusions; and evaluate, support, or critique the thinking of others. 05/02/2018 4 of 6
IO - Scientific Inquiry Analyze quantitative and qualitative information to make decisions, judgments, and pose questions. IO - Global Citizenship - Scientific & Technological Literacy Utilize quantitative expression in a variety of contexts. These would include units of measurement, visual representations, and scales and distributions. Synthesize, interpret, and infer, utilizing information, data, and experience to solve problems, innovate, and explore solutions. Produce oral and written information in various modes and media, using technology such as computers, the Internet, and library databases. 16. Comparable Transfer Course University System Campus Course Number Course Title Catalog Year 17. Special Materials and/or Equipment Required of Students: Graphing calculator 18. Materials Fees: Required Material? Material or Item Cost Per Unit Total Cost 19. Provide Reasons for the Substantial Modifications or New Course: Update SLOs 20. a. Cross-Listed Course (Enter Course Code): N/A b. Replacement Course (Enter original Course Code): N/A 21. Grading Method (choose one): Letter Grade Only 22. MIS Course Data Elements a. Course Control Number [CB00]: CCC000255006 b. T.O.P. Code [CB03]: 170100.00 - Mathematics, General c. Credit Status [CB04]: D - Credit - Degree Applicable d. Course Transfer Status [CB05]: A = Transfer to UC, CSU e. Basic Skills Status [CB08]: 2N = Not basic skills course f. Vocational Status [CB09]: Not Occupational g. Course Classification [CB11]: Y - Credit Course h. Special Class Status [CB13]: N - Not Special i. Course CAN Code [CB14]: N/A j. Course Prior to College Level [CB21]: Y = Not Applicable k. Course Noncredit Category [CB22]: Y - Not Applicable l. Funding Agency Category [CB23]: Y = Not Applicable m. Program Status [CB24]: 1 = Program Applicable Name of Approved Program (if program-applicable): LIBERAL ARTS with emphasis in Math and Science Attach listings of Degree and/or Certificate Programs showing this course as a required or a restricted elective.) 23. Enrollment - Estimate Enrollment First Year: 110 Third Year: 110 24. Resources - Faculty - Discipline and Other Qualifications: a. Sufficient Faculty Resources: Yes 05/02/2018 5 of 6
25. b. If No, list number of FTE needed to offer this course: N/A Additional Equipment and/or Supplies Needed and Source of Funding. N/A 26. Additional Construction or Modification of Existing Classroom Space Needed. (Explain:) N/A 27. FOR NEW OR SUBSTANTIALLY MODIFIED COURSES Library and/or Learning Resources Present in the Collection are Sufficient to Meet the Need of the Students Enrolled in the Course: Yes 28. Originator Melissa, S Flora Origination Date 10/09/17 05/02/2018 6 of 6