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| Credit- Degree applicable | | Effective Quarter: Fall 2020 | I. Catalog Information
| MATH 114 | College Math Preparation Level 3: Intermediate Algebra | 5 Unit(s) |
| | Requisites: Prerequisite: MATH 212 or equivalent placement.
Advisory: EWRT 211 and READ 211, or ESL 272 and 273. Hours: Lec Hrs: 60.00
Out of Class Hrs: 120.00
Total Student Learning Hrs: 180.00 Description: Application of exponential, logarithmic, and rational functions. Emphasis on the development of models of real world applications and interpretation of their characteristics. |
| Student Learning Outcome Statements (SLO)
| | | • Student Learning Outcome: Evaluate real-world situations and distinguish between and apply exponential, logarithmic, rational, and discrete function models appropriately. |
| | | • Student Learning Outcome: Analyze, interpret, and communicate results of exponential, logarithmic, and rational models in a logical manner from four points of view - visual, formula, numerical, and written. |
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II. Course Objectives | A. | Develop, throughout the course as applicable, systematic problem-solving methods |
| B. | Investigate the characteristics of rational expressions |
| C. | Develop rational function models to solve problems |
| D. | Explore the concepts of inverse relation and inverse function |
| E. | Investigate the graphical and numerical characteristics of exponential relationships and describe their meaning in the context of a problem |
| F. | Explore logarithmic functions |
| G. | Develop exponential and logarithmic function models to solve problems |
| H. | Investigate distances on a number line and in a plane and develop the equation of a circle |
| J. | Explore sequences and series |
| K. | Investigate, throughout the course as applicable, how mathematics has developed as a human activity around the world |
III. Essential Student Materials IV. Essential College Facilities V. Expanded Description: Content and Form | A. | Develop, throughout the course as applicable, systematic problem-solving methods |
| 1. | Devise a strategy or plan |
| 2. | Organize information, including identification and definition of known and unknown quantities |
| 3. | Translate verbal expressions into mathematical format |
| 4. | Apply mathematical tools to formulate a solution |
| 5. | Clearly communicate the solution |
| B. | Investigate the characteristics of rational expressions |
| 1. | Identify domain restrictions on the variable |
| 3. | Simplify rational expressions involving arithmetic operations by using the least common denominator |
| 4. | Explore negative exponents and their connection to rational expressions |
| C. | Develop rational function models to solve problems |
| 1. | Develop solutions to application problems |
| 2. | Solve rational equations and check answers for reasonableness |
| 3. | Interpret the results in the context of the problem |
| D. | Explore the concepts of inverse relation and inverse function |
| 1. | Explore the intuitive concept of inverse relations |
| 2. | Identify when an inverse relation is an inverse function |
| 3. | Explore the relationship with a function and its inverse through function composition (optional) |
| E. | Investigate the graphical and numerical characteristics of exponential relationships and describe their meaning in the context of a problem |
| 1. | Graph exponential relationships |
| 2. | Identify the main characteristics of exponential functions including |
| c. | the base as it relates to whether the function is increasing or decreasing |
| f. | comparison to properties of linear functions |
| 3. | Determine domain and range of an exponential function |
| F. | Explore logarithmic functions |
| 1. | Define a logarithmic function as the inverse of an exponential function |
| 2. | Determine the domain and range of a logarithmic function |
| 3. | Identify the main characteristics of logarithmic functions including |
| c. | the base as it relates to whether the function is increasing or decreasing |
| d. | the horizontal intercept |
| 4. | Apply the laws of logarithmic functions |
| 5. | Explore natural exponential and logarithmic functions |
| G. | Develop exponential and logarithmic function models to solve problems |
| 1. | Determine the equation of an exponential function that passes through two points |
| 2. | Find values of the dependent variable by substitution |
| 3. | Solve exponential and logarithmic equations to find values of the independent variable |
| 4. | Interpret the results in the context of the problem |
| H. | Investigate distances on a number line and in a plane and develop the equation of a circle |
| 1. | Solve compound inequalities |
| a. | express solutions in interval notation |
| b. | graph solutions on the real number line |
| 2. | Define the absolute value of a number as its distance from the origin |
| 3. | Solve absolute value equations and inequalities |
| a. | express solutions in interval notation |
| b. | graph solutions on the real number line |
| 4. | Use the Pythagorean Theorem to develop the distance formula |
| a. | find the distance between points in a plane |
| b. | solve applications involving Pythagorean Theorem and/or the distance formula |
| 5. | Explore circles in a plane |
| a. | define a circle as the set of points in a plane equidistant from a fixed point |
| b. | identify the connection between the center and radius of a circle and its formula |
| 1. | Explore expressions with exponents |
| a. | define integer exponents |
| b. | utilize the properties of exponents with non-negative exponents |
| 2. | Utilize integer exponents |
| a. | define negative exponents |
| b. | apply the laws of exponents to expressions involving integer exponents |
| c. | explore scientific notation expressions including converting between scientific and standard form |
| 3. | Utilize properties of exponents |
| a. | define fractional exponents and their connection to radical expressions |
| b. | apply the laws of exponents to expressions containing fractional exponents |
| 4. | Utilize radical expressions |
| a. | simplify radical expressions |
| b. | perform operations on radical expressions |
| c. | solve radical equations |
| J. | Explore sequences and series |
| 1. | Investigate sequences as discrete function models |
| 2. | Explore the numerical and algebraic characteristics of geometric sequences |
| a. | recognize patterns and the connections to exponential functions |
| b. | determine the formula for the general term |
| 3. | Define geometric series |
| a. | determine the sum of the first n terms |
| b. | explore infinite geometric series and their potential sum as a limit (optional) |
| K. | Investigate, throughout the course as applicable, how mathematics has developed as a human activity around the world
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| 1. | The use and development of algebraic concepts throughout history. Some possibilities are: |
| a. | explore the development and use of the number e |
| b. | investigate the development of algebra, especially as it relates to exponential, logarithmic and rational functions, in earlier times and by various cultures such as those of Egypt, India, the Arabic cultures, China and Europe |
| 2. | Algebraic applications that are of historical and/or contemporary interest. Some possibilities are: |
| a. | investigate the uses of exponential, logarithmic and rational functions in various disciplines such as the physical and biological sciences, finance and the social sciences |
| b. | investigate the uses of exponential and logarithmic functions in every day life, e.g. compound interest, spread of viral diseases, depreciation, radioactive decay, earthquakes and the Richter scale, decibels |
| c. | investigate the uses of rational functions in every day life, e.g. proportions, inverse variation |
VI. Assignments | A. | Reading of text explanations and examples |
| B. | Written assignments which may include |
| 2. | Problems requiring written explanations of key concepts, analysis of problem solving strategies and use of mathematical vocabulary |
| 3. | Projects such as labs or "big problems" that require research or data collection |
| C. | Class Participation which may include |
| 1. | Collaborative activities |
VII. Methods of Instruction | | Lecture and visual aids
Discussion and problem solving performed in class
Quiz and examination review performed in class
Collaborative learning and small group exercises
Computer lab assignments
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VIII. Methods of Evaluating Objectives | A. | Periodic quizzes and/or problem assignments from the text which will be evaluated for accuracy and completion in order to assess student’s comprehension of material covered in lecture and to provide feedback to students on their progress. Questions may also require the student to communicate ideas and conclusions in short essay format.
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| B. | Examinations will be composed of both computational and concept-based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format. |
| C. | Portfolios evaluated by a rubric created by the instructor |
| D. | Problem-solving journals assessed on completeness and accuracy of notation |
| E. | Projects/activities, group or individual, that include written descriptions of methods and results, and justification of conclusions. Projects/activities may be based upon real, simulated, or collected data, or other methods. They will be assessed on proper use of methods and accuracy of results. |
| F. | Two hour comprehensive final examination composed of both computational and concept based questions which will require the student to demonstrate ability in integrating the methods, ideas and techniques learned in class. Questions may also require the student to communicate ideas and conclusions in short essay format. |
IX. Texts and Supporting References | A. | Examples of Primary Texts and References |
| 1. | Intermediate Algebra 7th Ed.; Blitzer, Prentice Hall, 2017 |
| 2. | Lehmann, Jay. "Elementary and Intermediate Algebra, Functions and Authentic Applications". 2nd Ed. Pearson Education Inc. 2014 |
| 3. | College Math Preparation Level 3: Intermediate Algebra, Student Workbook; Developed by Doli Bambhania, 2017 |
| 4. | Intermediate Algebra 2nd Ed.; Clark and Anfinson, Cengage 2017. |
| B. | Examples of Supporting Texts and References |
| 1. | Bunt, Lucas, N. H., et. al., "The Historical Roots of Elementary Mathematics." 1988, Dover Publications, New York. |
| 2. | Crump, Thomas, "The Anthropology of Numbers." 1990, Cambridge University Press. |
| 3. | Gerdes, Paulus, "Geometry from Africa, Mathematical and Educational Explorations." MAA 1999 |
| 4. | Gerdes, Paulus, "Women, Art and Geometry in Southern Africa." 1998, Africa World Press. |
| 5. | Gillings, Richard J., "Mathematics in the Time of the Pharaohs." 1982, Dover Publications. |
| 6. | Joseph, George Gheverghese, "The Crest of the Peacock: Non-European Roots of Mathematics." 2010, Princeton University Press. |
| 7. | Lumpkin, Beatrice, "Algebra Activities from Many Cultures." 1997, Walch Education |
| 8. | McLeish, John, "Number, the History of Numbers and How They Shape Our Lives." 1991, Fawcett Columbine. |
| 9. | Moses, Robert P and Cobb Jr., Charles E.; "Radical Equations, Math Literacy and Civil Rights." 2001, Beacon Press. |
| 10. | Nahin, Paul, "An Imaginary Tale, The Story of Sqrt(-1)." 1998, Princeton University Press. |
| 11. | Secada, Walter G. ed., "Changing Faces of Mathematics, Perspectives on Multiculturalism and Gender Equity." 2000, NCTM. |
| 12. | Voolich, Erica Dakin, "A Peek into Math of the Past, Mathematical and Historical Investigations for Middle School and Pre-Algebra Students." 2001, Dale Seymour Publications. |
| 13. | Zaslavsky, Claudia, "The Multicultural Math Classroom." 1996, Heinemann Publishers. |
| 14. | ALEKS Assesment & Learning System. Aleks Corporation, 2013. |
| 15. | See multicultural link(s) on the department resources page |
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