Active Outline

General Information

Course ID (CB01A and CB01B)
MATHD231.
Course Title (CB02)
Algebra Support for Precalculus I
Course Credit Status
Credit - Not Degree Applicable
Effective Term
Fall 2021
Course Description
A review of the core prerequisite skills, competencies, and concepts needed in when studying polynomial, rational, exponential and logarithmic functions. Intended for majors in business, science, technology, engineering, and mathematics who are concurrently enrolled in Precalculus I.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This is a stand-alone course designed to be AB 705 compliant by providing just-in-time instruction for students who are studying the college algebraic half of a precalculus sequence.

Foothill Equivalency

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

Course Philosophy

Course Philosophy
This course is intended to provide just-in-time instruction for students who are studying precalculus, but who may lack the intermediate algebra skills necessary to succeed in a transfer level math course. This course gives the instructor of the requisite course the opportunity to cover topics as needed to support the students' learning in precalculus. In addition to providing the algebraic skills, an emphasis should be placed on developing study skills and habits of mind that will aid the students in all of their further math courses.

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is a basic skills course.
Grade Options
  • Pass/No Pass
Repeat Limit
0

Transferability & Gen. Ed. Options

Transferability
Not transferable
°®¶¹´«Ã½ GEArea(s)StatusDetails
2SUMDA Support Course Math-CB26Approved

Units and Hours

Summary

Minimum Credit Units
2.5
Maximum Credit Units
2.5

Weekly Student Hours

TypeIn ClassOut of Class
Lecture Hours2.55.0
Laboratory Hours0.00.0

Course Student Hours

Course Duration (Weeks)
12.0
Hours per unit divisor
36.0
Course In-Class (Contact) Hours
Lecture
30.0
Laboratory
0.0
Total
30.0
Course Out-of-Class Hours
Lecture
60.0
Laboratory
0.0
NA
0.0
Total
60.0

Prerequisite(s)

Corequisite(s)

MATH D031., MATH D031H, MATH D041., or MATH D041H

Advisory(ies)

Limitation(s) on Enrollment

Entrance Skill(s)

General Course Statement(s)

Methods of Instruction

Lecture and visual aids

Discussion of assigned reading

Discussion and problem solving performed in class

Homework and extended projects

Collaborative learning and small group exercises

Collaborative projects

Quiz and examination review performed in class

Guest speakers

Assignments

  1. Required readings from text
  2. Problem-solving exercises, some involving technology
  3. Small group exercises
  4. Optional project synthesizing various concepts and skills from the course content

Methods of Evaluation

  1. Periodic quizzes and/or assignments from sources related to the topics listed in the curriculum are evaluated for completion. Feedback will be given on accuracy in order to assist the students’ comprehension.
  2. Projects may be used to enhance the students’ understanding of topics studied in the course in group or individual formats. Students will communicate their understanding orally and/or in writing. The evaluation is to be based on completion and level of participation.
  3. Small group exercises will be evaluated based on the level of engagement in the material and level of participation.
  4. Final exam or project

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • Graphing calculator and/or computer software
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
Larson , Precalculus with Limits, 4th edition. Boston: Cengage, 2018
Connally, Hughes-Hallett, Gleason, et al. Functions Modeling Change, 5th Edition. New York: Wiley, 2017

Examples of Supporting Texts and References

AuthorTitlePublisher
Aufmann, Barker, Nation. Precalculus with Limits. Boston: Houghton-Mifflin, 2000
Blitzer, Robert, Precalculus, 5th Edition, Prentice Hall, 2013
Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics, 3rd Edition, Princeton, NJ: Princeton Univ. Press, 2010
Kline, Morris, Mathematical Thought from Ancient to Modern Times, Vol. 1-3, 1972, New York and Oxford, Oxford University Press
Maor, Eli, Trigonometric Delights, Princeton, NJ, 1998 Princeton University Press
Maor, Eli, e - The Story of a Number , Princeton, NJ, 1994 Princeton University Press
The MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St. Andrews, Fife, Scotland, http://www-groups.dcs.st-and.ac.uk/~history/Indexes/HistoryTopics.html, http://www-groups.dcs.st-and.ac.uk/~history
Mathematics Multicultural Bibliography available on the °®¶¹´«Ã½ College Mathematics Resources website.

Learning Outcomes and Objectives

Course Objectives

  • Explore topics related to developing effective learning skills
  • Develop effective skills for modeling and solving real world applications
  • Develop skills needed to graph functions and relations in rectangular coordinates
  • Develop skills needed to synthesize results from the graphs and/or equations of functions and relations
  • Develop skills needed to apply transformations to the graphs of functions and relations.
  • Develop skills needed to recognize the relationship between functions and their inverses graphically and algebraically
  • Develop skills needed to solve and apply equations including linear, quadratic, absolute value, radical, and solve linear and absolute value inequalities
  • Develop skills needed to solve and apply equations including rational, polynomial, exponential, and logarithmic, and solve nonlinear inequalities
  • Develop skills needed to solve systems of equations and inequalities.

CSLOs

  • Demonstrate sound algebraic techniques by applying proper mathematical notation to problems involving functions.

Outline

  1. Explore topics related to developing effective learning skills
    1. Learn study skills, such as but not limited to, organizational skills, time management, campus resources, peer learning, test preparation and test-taking strategies
    2. Self-assess using performance criteria to judge and improve one’s own work, such as but not limited to, analyzing and correcting exam errors
    3. Develop academic confidence and mathematical maturity
    4. Develop mathematical habits of mind
      1. Interpret contextualized problems
      2. Predict solutions
      3. Analyze different ideas
      4. Reflect on process and synthesis
  2. Develop effective skills for modeling and solving real world applications
    1. Devise a strategy or plan
    2. Apply precise mathematical notation to convey the thought process behind the work
      1. Organize algebraic and arithmetic work in a logical and neat manner
      2. Organize information, using tools such as graphs, charts, tables and diagrams
      3. Explain each step and thought process
    3. Identify and define known and unknown quantities
    4. Apply mathematical tools to formulate a solution
    5. Communicate the solution clearly
      1. State the solution
      2. Interpret the results in the context of the problem
  3. Develop skills needed to graph functions and relations in rectangular coordinates
    1. Practice graphing skills, such as, but not limited to,
      1. Plotting points
      2. Labelling units and scaling axes appropriate to the problem
    2. Determine and interpret features of graphs, such as, but not limited to,
      1. Slope of a linear function
      2. End behavior of a graph
      3. Intercepts
    3. Review domain and range
      1. Graphically
      2. Solve for domain algebraically
      3. Express using inequality and interval notation
    4. Investigate asymptotes
      1. Relate asymptotes to end behavior
      2. Use asymptotes to interpret real world problems
    5. Graph rational and polynomial equations using techniques, such as, but not limited to:
      1. Finding roots
      2. Understanding the relationship between roots, factors and horizontal intercepts
      3. Understanding end behavior
      4. Interpreting local maxima and minima
    6. Form connections between geometric notions of circles and ellipses to algebraic equations
    7. Form connections between conic sections and parent functions such as y=x^2 and y=1/x
  4. Develop skills needed to synthesize results from the graphs and/or equations of functions and relations
    1. Review properties of graphs of linear, quadratic, radical and power functions
    2. Review end behavior and relative growth, and how these concepts apply to real world problems
    3. Explore domain and range in both mathematical and real-world/practical contexts
  5. Develop skills needed to apply transformations to the graphs of functions and relations.
    1. Review arithmetic skills as they apply to real numbers and variables.
    2. Review associative, distributive and commutative properties, as they apply to real numbers and variables.
    3. Review the properties of negative numbers
    4. Explore composition of functions
    5. Compare transformations in various forms - graphs, tables, formulas, verbal
  6. Develop skills needed to recognize the relationship between functions and their inverses graphically and algebraically
    1. Identify when a function is invertible
    2. Express one variable as a function of another
    3. Find and interpret domain and range
      1. The relationship between domain and range of a function and its inverse
      2. Investigate restricting the domain to create an invertible function
  7. Develop skills needed to solve and apply equations including linear, quadratic, absolute value, radical, and solve linear and absolute value inequalities
    1. Review solving basic equations
    2. Interpret solving an equation as reversing the order of operations
    3. Review absolute value as both the distance from zero and as a piecewise function
    4. Review inequalities, such as but not limited to
      1. Inequalities in one variable
      2. Ordering properties of real numbers
      3. Graphing on a number line
      4. Interval and inequality notation
  8. Develop skills needed to solve and apply equations including rational, polynomial, exponential, and logarithmic, and solve nonlinear inequalities
    1. Practice simplifying expressions and solving equations
    2. Interpret equations graphically, including in the context of real-world applications
    3. Understand the notation of logarithmic and exponential expressions
  9. Develop skills needed to solve systems of equations and inequalities.
    1. Review the meaning of a solution to a system of equations or inequalities
    2. Review systems of linear equations in two variables
      1. Solve by graphing
      2. Solve by substitution
      3. Solve by elimination
    3. Introduce the application of linear techniques to non-linear systems
    4. Review what a solution to an inequality in two variables looks like
Back to Top