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General Information

Course ID (CB01A and CB01B)
MATHD232.
Course Title (CB02)
Algebra Support for Precalculus II
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 studying the theory of trigonometric functions and their applications. Intended for majors in business, science, technology, engineering, and mathematics who are concurrently enrolled in Precalculus II.
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 trigonometric 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 D032., MATH D032H, MATH D042., or MATH D042H

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. Cengage, 2018
Barnett, Ziegler, Byleen and Sobecki. Analytic Trigonometry with Applications, 11th Edition. Wiley, 2012.
Lial, Hornsby, Schneider and Daniels. Trigonometry, 11th Edition. Pearson, 2017.

Examples of Supporting Texts and References

AuthorTitlePublisher
Blatner, David. The Joy of Pi. Walker and Co., 1997
Mathematics Multicultural Bibliography available on the °®¶¹´«Ã½ College Mathematics Resources website.
Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics, 3rd Edition. Penguin Books, 2010
Heilbron, J. L. Geometry Civilized: History, Culture and Technique. Clarendon Press, 1998
Maor, Eli. Trigonometric Delights. Princeton University Press, 1998
Nahin, Paul. An Imaginary Tale: The Story of Sqrt(-1). Princeton University Press, 1998
Historical Topics for the Mathematics Classroom. National Council of Teachers of Mathematics, Inc., 1998
Nelson, David, George Gheverghese Joseph and Julian Williams. Multicultural Mathematics: Teaching Mathematics from a Global Perspective. Oxford University Press, 1993
Rieder, John and Larry Smith, editors. Multiculturalism and Representation: Selected Essays. East-West Center, 2001
Alcoze, Thom and Miriam Barrios-Chacon. Multiculturalism in Mathematics, Science and Technology: Readings and Activities. Clarendon Press, 1999
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
Smith, Karl. Trigonometry, 4th Edition. Thomson Brooks/Cole, 2005
Connally, Hughes-Hallett, Gleason, et al. Functions Modeling Change, 4th Edition. Wiley, 2011
Sullivan, M. Trigonometry, a Unit Circle Approach, 7th Edition. Prentice-Hall, 2005
Aratari. Trigonometry, a Circular Function Approach. Addison-Wesley, 2004

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 for evaluating trigonometric functions using both degree and radian measure
  • Develop skills needed for solving oblique and right triangles
  • Develop skills needed to solve arc length and sector area problems
  • Develop skills needed to graph and analyze the six trigonometric functions
  • Develop skills needed for applying trigonometric identities to simplify and evaluate trigonometric expressions and verify other identities
  • Develop skills needed to analyze the inverse trigonometric functions
  • Develop skills needed to solve trigonometric equations
  • Develop skills needed to define the polar coordinate system and introduce polar graphs
  • Develop skills needed to examine complex numbers in the complex plane
  • Develop skills needed to perform operations with 2D vectors

CSLOs

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

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 for evaluating trigonometric functions using both degree and radian measure
    1. Reducing fractions
    2. Pythagorean theorem
    3. Simplifying square roots
    4. Rationalize denominators
    5. Special right triangles
    6. Technology support
  4. Develop skills needed for solving oblique and right triangles
    1. 180 degrees/Pi radians in a triangle
    2. Definitions of right/oblique triangles
    3. Solving proportions
  5. Develop skills needed to solve arc length and sector area problems
    1. Conversion from degrees to radians
    2. Arc length, angular velocity, linear velocity and area of a sector formulas require that the given angle be in radians
  6. Develop skills needed to graph and analyze the six trigonometric functions
    1. Period of sine, cosecant, cosine and secant are multiples of 2Pi, while tangent/cotangent are multiples of Pi
    2. Explore the phase shift and its relationship to composition of functions
  7. Develop skills needed for applying trigonometric identities to simplify and evaluate trigonometric expressions and verify other identities
    1. The unit circle and its relationship to the Pythagorean Theorem
    2. Review properties of exponents and explore their relationship to exponential powers of trigonometric terms
    3. Review algebraic simplification as it applies to combining like trigonometric terms
  8. Develop skills needed to analyze the inverse trigonometric functions
    1. Review the difference between functions and relations and how these relate to the different notions of trigonometric inverses
    2. Review the notion of domain and range and how these relate to trigonometric functions and their inverses
    3. Discuss the differences between the various inverse notations they may encounter
    4. Clarify the difference between the negative one exponent (the reciprocal function) and the negative one superscript (the inverse function)
  9. Develop skills needed to solve trigonometric equations
    1. Review techniques of factoring
    2. Apply factoring to solve quadratic equations
    3. Solve irreducible quadratic equations using the quadratic formula.
    4. Recognize the relationship between rotations and trigonometric equations involving multiple angles.
  10. Develop skills needed to define the polar coordinate system and introduce polar graphs
    1. Review the notion of distance from the origin in two dimensions.
    2. Introduce the notion of directed distance as it relates to polar coordinates
    3. Recognize multiple polar coordinate representations of a single Cartesian point
  11. Develop skills needed to examine complex numbers in the complex plane
    1. Review the definition of a complex unit
    2. Review products of binomials
    3. Recognize that the square of a binomial is neither the sum or difference of squares (The Freshman's Dream)
  12. Develop skills needed to perform operations with 2D vectors
    1. Review the difference between the absolute value of a real number and the absolute value of a complex number
    2. Investigate the relationship between the magnitude of a vector and the absolute value of a complex number
    3. Develop the connection between 2D vectors and polar coordinates
      1. Similarities between r and magnitude, between theta and direction
      2. Differences between polar coordinates and 2D vectors
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