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General Information

Course ID (CB01A and CB01B)
MATH D314.
Course Title (CB02)
College Math Preparation Level 3: Intermediate Algebra
Course Credit Status
Non-Credit
Effective Term
Fall 2023
Course Description
This course covers the application of exponential, logarithmic and rational functions, with emphasis on the development of models of real-world applications and interpretation of their characteristics.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This is a noncredit enhance course and is a prerequisite to transfer-level mathematics courses that satisfy transfer requirements. This course covers exponential and logarithmic functions and rational functions and their applications to real-world problems.

Foothill Equivalency

Does the course have a Foothill equivalent?
No
Foothill Course ID

Course Philosophy

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is not a basic skills course.
Grade Options
  • Pass/No Pass
Repeat Limit
99

Transferability & Gen. Ed. Options

Transferability
Not transferable

Units and Hours

Summary

Minimum Credit Units
0.0
Maximum Credit Units
0.0

Weekly Student Hours

TypeIn ClassOut of Class
Lecture Hours5.010.0
Laboratory Hours0.00.0

Course Student Hours

Course Duration (Weeks)
12.0
Hours per unit divisor
36.0
Course In-Class (Contact) Hours
Lecture
60.0
Laboratory
0.0
Total
60.0
Course Out-of-Class Hours
Lecture
120.0
Laboratory
0.0
NA
0.0
Total
120.0

Prerequisite(s)

Corequisite(s)

Advisory(ies)

Elementary algebra or equivalent (or higher), or appropriate placement beyond elementary algebra

Limitation(s) on Enrollment

Entrance Skill(s)

General Course Statement(s)

NONCREDIT: (This is a noncredit enhanced course.)

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

Assignments

  1. Reading of text explanations and examples
  2. Written assignments which may include
    1. Problem solving
    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
    4. Problem journals
    5. Portfolios
  3. Class Participation which may include
    1. Collaborative activities
    2. Oral presentations

Methods of Evaluation

  1. 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 the 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.
  2. 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.
  3. Portfolios evaluated by a rubric created by the instructor
  4. Problem-solving journals assessed on completeness and accuracy of notation
  5. 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 the proper use of methods and accuracy of results.
  6. 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.

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • None.
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
Intermediate Algebra 7th Ed.; Blitzer, Prentice Hall, 2017
Lehmann, Jay. "Elementary and Intermediate Algebra, Functions and Authentic Applications". 2nd Ed. Pearson Education Inc. 2014
College Math Preparation Level 3: Intermediate Algebra, Student Workbook; Developed by Doli Bambhania, 2017
Intermediate Algebra 2nd Ed.; Clark and Anfinson, Cengage 2017.

Examples of Supporting Texts and References

AuthorTitlePublisher
Bunt, Lucas, N. H., et. al., "The Historical Roots of Elementary Mathematics." 1988, Dover Publications, New York.
Crump, Thomas, "The Anthropology of Numbers." 1990, Cambridge University Press.
Gerdes, Paulus, "Geometry from Africa, Mathematical and Educational Explorations." MAA 1999
Gerdes, Paulus, "Women, Art and Geometry in Southern Africa." 1998, Africa World Press.
Gillings, Richard J., "Mathematics in the Time of the Pharaohs." 1982, Dover Publications.
Joseph, George Gheverghese, "The Crest of the Peacock: Non-European Roots of Mathematics." 2010, Princeton University Press.
Lumpkin, Beatrice, "Algebra Activities from Many Cultures." 1997, Walch Education
McLeish, John, "Number, the History of Numbers and How They Shape Our Lives." 1991, Fawcett Columbine.
Moses, Robert P and Cobb Jr., Charles E.; "Radical Equations, Math Literacy and Civil Rights." 2001, Beacon Press.
Nahin, Paul, "An Imaginary Tale, The Story of Sqrt(-1)." 1998, Princeton University Press.
Secada, Walter G. ed., "Changing Faces of Mathematics, Perspectives on Multiculturalism and Gender Equity." 2000, NCTM.
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.
Zaslavsky, Claudia, "The Multicultural Math Classroom." 1996, Heinemann Publishers.
ALEKS Assesment & Learning System. Aleks Corporation, 2013.
See multicultural link(s) on the department resources page

Learning Outcomes and Objectives

Course Objectives

  • Develop, throughout the course as applicable, systematic problem-solving methods
  • Investigate the characteristics of rational expressions
  • Develop rational function models to solve problems
  • Explore the concepts of inverse relation and inverse function
  • Investigate the graphical and numerical characteristics of exponential relationships and describe their meaning in the context of a problem
  • Explore logarithmic functions
  • Develop exponential and logarithmic function models to solve problems
  • Investigate distances on a number line and in a plane and develop the equation of a circle
  • Explore exponents
  • Explore sequences and series
  • Investigate, throughout the course as applicable, how mathematics has developed as a human activity around the world

CSLOs

  • Evaluate real-world situations and distinguish between and apply linear and exponential function models appropriately.

  • Analyze, interpret, and communicate results of linear and exponential models in a logical manner.

  • Organize sample data by constructing and/or evaluating tables, graphs, and numerical measures of characteristics of data.

Outline

  1. 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 a mathematical format
    4. Apply mathematical tools to formulate a solution
    5. Clearly communicate the solution
  2. Investigate the characteristics of rational expressions
    1. Identify domain restrictions on the variable
    2. Reduce to lowest terms
    3. Simplify rational expressions involving arithmetic operations by using the least common denominator
    4. Explore negative exponents and their connection to rational expressions
  3. 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
  4. 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)
  5. 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
      1. its algebraic form
      2. the shape of its graph
      3. the base as it relates to whether the function is increasing or decreasing
      4. the vertical intercept
      5. the asymptote
      6. comparison to properties of linear functions
    3. Determine domain and range of an exponential function
  6. 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
      1. its algebraic form
      2. the shape of its graph
      3. the base as it relates to whether the function is increasing or decreasing
      4. the horizontal intercept
      5. the asymptote
    4. Apply the laws of logarithmic functions
    5. Explore natural exponential and logarithmic functions
  7. 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
  8. Investigate distances on a number line and in a plane and develop the equation of a circle
    1. Solve compound inequalities
      1. express solutions in interval notation
      2. 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
      1. express solutions in interval notation
      2. graph solutions on the real number line
    4. Use the Pythagorean Theorem to develop the distance formula
      1. find the distance between points in a plane
      2. solve applications involving Pythagorean Theorem and/or the distance formula
    5. Explore circles in a plane
      1. define a circle as the set of points in a plane equidistant from a fixed point
      2. identify the connection between the center and radius of a circle and its formula
      3. graph a circle
  9. Explore exponents
    1. Explore expressions with exponents
      1. define integer exponents
      2. utilize the properties of exponents with non-negative exponents
    2. Utilize integer exponents
      1. define negative exponents
      2. apply the laws of exponents to expressions involving integer exponents
      3. explore scientific notation expressions including converting between scientific and standard form
    3. Utilize properties of exponents
      1. define fractional exponents and their connection to radical expressions
      2. apply the laws of exponents to expressions containing fractional exponents
    4. Utilize radical expressions
      1. simplify radical expressions
      2. perform operations on radical expressions
      3. solve radical equations
  10. Explore sequences and series
    1. Investigate sequences as discrete function models
    2. Explore the numerical and algebraic characteristics of geometric sequences
      1. recognize patterns and the connections to exponential functions
      2. determine the formula for the general term
    3. Define geometric series
      1. determine the sum of the first n terms
      2. explore infinite geometric series and their potential sum as a limit (optional)
  11. Investigate, throughout the course as applicable, how mathematics has developed as a human activity around the world
    1. The use and development of algebraic concepts throughout history. Some possibilities are:
      1. explore the development and use of the number e
      2. 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:
      1. investigate the uses of exponential, logarithmic and rational functions in various disciplines such as the physical and biological sciences, finance, and the social sciences
      2. investigate the uses of exponential and logarithmic functions in everyday life, e.g. compound interest, the spread of viral diseases, depreciation, radioactive decay, earthquakes and the Richter scale, decibels
      3. investigate the uses of rational functions in everyday life, e.g. proportions, inverse variation
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