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General Information

Course ID (CB01A and CB01B)
MATHD031H
Course Title (CB02)
Precalculus I - HONORS
Course Credit Status
Credit - Degree Applicable
Effective Term
Fall 2023
Course Description
This course covers polynomial, rational, exponential, and logarithmic functions, graphs, solving equations, conic sections, systems of equations, and inequalities. Because this is an honors course, students will be expected to complete extra assignments to gain deeper insight into precalculus.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This is a CSU and UC transferable course that meets a general education requirement for CSU GE. It belongs on the °®¶¹´«Ã½ Liberal Arts A.A./A.S. degree. This is the first course in a sequence of two courses in precalculus mathematics intended to provide the student who has successfully completed intermediate algebra with the foundations needed for success in calculus and advanced courses in mathematics and the sciences. This part of the sequence emphasizes the theory of functions. This course is the honors version of MATH 031. and as a result, includes more advanced assignments and assessments.

Foothill Equivalency

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

Course Philosophy

Course Philosophy
The sequence of two courses in precalculus mathematics is intended to provide the student who has successfully completed intermediate algebra with the foundations needed for success in calculus and advanced courses in mathematics and the sciences. Throughout the sequence, the courses emphasize building analytical and quantitative skills and the mathematical maturity necessary for solving problems in mathematics and related fields. Specifically, the student will define variables and use them to write, analyze and graph functions and other relations which occur in modeling and other applications. The student will also develop skills in solving equations and inequalities. The material is rich in applications, both modern and classic, drawn from historical and multicultural origins of the topics and modern applications in many fields Various elementary functions are studied and used to model application problems in mathematics and science with an emphasis on developing analytical, numerical, graphical, and verbal skills as required.

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is not a basic skills course.
Grade Options
  • Letter Grade
  • Pass/No Pass
Repeat Limit
0

Transferability & Gen. Ed. Options

Transferability
Transferable to both UC and CSU
CSU GEArea(s)StatusDetails
CGB4CSU GE Area B4 - Mathematics/Quantitative ReasoningApproved
IGETCArea(s)StatusDetails
IG2XIGETC Area 2 - Mathematical Concepts and Quantitative ReasoningApproved

Units and Hours

Summary

Minimum Credit Units
5.0
Maximum Credit Units
5.0

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)

Intermediate algebra or equivalent (or higher), or appropriate placement beyond intermediate algebra

Corequisite(s)

Advisory(ies)

ESL D272. and ESL D273., or ESL D472. and ESL D473., or eligibility for EWRT D001A or EWRT D01AH or ESL D005.

Limitation(s) on Enrollment

  • (Not open to students with credit in the non-Honors related course.)
  • (Admission into this course requires consent of the Honors Program Coordinator.)

Entrance Skill(s)

General Course Statement(s)

(See general education pages for the requirements this course meets.)

Methods of Instruction

Lecture and visual aids

Discussion of assigned reading

Discussion and problem-solving performed in class

In-class exploration of internet sites

Quiz and examination review performed in class

Homework and extended projects

Guest speakers

Collaborative learning and small group exercises

Collaborative projects

Problem solving and exploration activities using applications software

Assignments

  1. Required readings from the text
  2. Problem-solving exercises, some including technology
  3. Exams and quizzes
  4. Optional project synthesizing various concepts and skills from the course content
  5. In addition, the honors project assignment should include completion of additional sets of advanced problems that require a deeper understanding of the topics and/or a written research report (10 to 15 pages). Note: The honors project will require 10 or more hours of work beyond the regular (non-honors) course requirements, and will include higher expectations for achievement in this more advanced work.

Methods of Evaluation

  1. Periodic quizzes and/or assignments from sources related to the topics listed in the curriculum are evaluated for completion and accuracy in order to assess students' comprehension and ability to communicate orally and in writing of course content and provide timely feedback to students on their progress.
  2. Projects (optional)

    Projects may be used to enhance the student's understanding of topics studied in the course in a group or individual formats where communicating their understanding orally through classroom presentation or in writing. The evaluation is to be based on completion and comprehension of course content and the students shall receive timely feedback on their progress.
  3. At least three one-hour exams without projects or at least two one-hour exams with projects are required. In these evaluations, the student is expected to provide complete and accurate solutions to problems that include both theory and applications by integrating methods and techniques studied in the course. The student shall receive timely feedback on their progress.
  4. One two-hour comprehensive final examination in which the student is expected to display comprehension of course content and be able to choose methods and techniques appropriate to the various types of problems that cover course content. The student shall have access to the final exam for review with the instructor for a period determined by college and departmental rules.
  5. The honors project will be evaluated based on the depth of understanding and mastery of advanced techniques employed within the project.

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • Graphing Calculator or computer software
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
Connally, Hughes-Hallett, Gleason, et al.Functions Modeling ChangeWiley2019 / 6th edition
LarsonPrecalculus with LimitsCengage2022 / 5th edition
Abramson, Jay, et al.PrecalculusOpenstax2021

Examples of Supporting Texts and References

AuthorTitlePublisher
Math Department Activity and Multicultural Resource Binder, available in the Math Department Office
Precalculus with Limits.
Precalculus
The Crest of the Peacock: Non-European Roots of Mathematics
Mathematical Thought from Ancient to Modern Times, Vol. 1-3
e - The Story of a Number
The MacTutor History of Mathematics Archive,

Learning Outcomes and Objectives

Course Objectives

  • Graph functions and relations in rectangular coordinates
  • Formulate results from the graphs and/or equations of functions and relations
  • Apply transformations to the graphs of functions and relations
  • Recognize the relationship between functions and their inverses graphically and algebraically
  • Solve and apply equations including linear, quadratic, absolute value, and radical equations
  • Solve and apply equations and inequalities involving rational, polynomial, exponential, and logarithmic functions
  • Solve systems of equations and inequalities
  • Apply functions to model real-world applications
  • Apply the theory and application of precalculus through projects, extended reading, or programming and computational problems

CSLOs

    Outline

    1. Graph functions and relations in rectangular coordinates
      1. Define a function and explore its representations graphically, numerically, algebraically, and verbally
      2. Investigate linear functions
        1. Graphs and equations of linear functions
        2. Perpendicular and parallel lines
      3. Investigate quadratic functions
        1. Graph quadratic functions
        2. Express quadratic functions in general, standard, and factored form
      4. Investigate absolute value functions
      5. Investigate piecewise-defined functions
      6. Explore graphs of functions of the form y=f(x)=x^p
        1. Power functions y=f(x)=x^n
        2. Draw and recognize graphs of radical functions such as y=f(x)=x^1/2 and y=f(x)=x^1/3
        3. Draw and recognize graphs of rational functions such as y=f(x)=1/x and y=f(x)=1/(x^2)
      7. Graph logarithmic and exponential functions
      8. Graph polynomial functions
        1. Explore the graphs of polynomial functions using the relationship between intercepts and factors
        2. Explore the behavior of graphs of polynomial functions and their relationship to graphs of power functions
      9. Graph rational functions.
        1. Examine vertical, horizontal and oblique, and other non-linear asymptotes
        2. Graph functions that contain vertical, horizontal and oblique, and other non-linear asymptotes
      10. Graph conic sections in rectangular coordinates.
    2. Formulate results from the graphs and/or equations of functions and relations
      1. Investigate linear function and interpret slope as a rate of change.
      2. Investigate quadratic functions and identify relative maximum and maximum as a vertex.
      3. Investigate relative growth of power functions as x grows large
      4. Determine and interpret domain and range
      5. Evaluate sums, differences, products, and quotients of functions
      6. Explore the symmetry of functions
      7. Compare/contrast the basic properties of the transcendental functions with those of the algebraic functions
      8. Compare the growth of exponential functions to linear and power functions
      9. Investigate the Fundamental Theorem of Algebra by mathematicians such as Girard and Gauss.
        1. By using the relationship between zeros and factors.
        2. By determining the function's rational, irrational, and complex roots
        3. Historical development of the Fundamental Theorem of Algebra by mathematicians such as Girard and Gauss
    3. Apply transformations to the graphs of functions and relations
      1. Create new functions from existing functions.
      2. Explore transformations of functions
        1. Translations
        2. Stretches and compressions
        3. Reflections
      3. Investigate composite functions
      4. Write equations of conics with translated axes.
    4. Recognize the relationship between functions and their inverses graphically and algebraically
      1. Recognize one-to-one functions.
      2. Develop the concept of inverse functions
        1. Define inverse functions using composition
        2. Find inverse functions algebraically.
        3. Recognize the relationship between the graph of a function and its inverse
        4. Investigate the relationship between the domain and the range of a function and its inverse
    5. Solve and apply equations including linear, quadratic, absolute value, and radical equations
      1. Solve equations and inequalities involving linear functions
      2. Solve equations and inequalities involving quadratic functions.
      3. Solve equations and inequalities involving radical functions.
      4. Solve equations and inequalities involving absolute value functions.
    6. Solve and apply equations and inequalities involving rational, polynomial, exponential, and logarithmic functions
      1. Develop laws of logarithms
      2. Develop properties of exponents.
      3. Identify common and natural logarithms.
      4. Solve exponential equations.
      5. Solve logarithmic equations.
      6. Solve equations and inequalities involving polynomial functions
      7. Solve equations and inequalities involving rational expressions.
    7. Solve systems of equations and inequalities
      1. Solve systems of equations in 2 variables
        1. Systems of linear equations
        2. Systems of nonlinear equations
      2. Solve an inequality in 2 variables and represent the solution region graphically
      3. Solve systems of inequalities and represent solution regions graphically.
    8. Apply functions to model real-world applications
      1. Investigate linear applications such as, but not limited to
        1. Linear economic models
        2. Depreciation
      2. Investigate quadratic applications such as, but not limited to
        1. Projectile motion
        2. Freefall
        3. Area
        4. Quadratic economic models
        5. Historical contributions such as contributions by the Chinese, Babylonian, and Indian mathematicians to the solutions of quadratic equations
      3. Investigate applications involving direct and inverse variation, such as, but not limited to
        1. Hooke's law
        2. Intensity of illumination or radio waves
        3. Length and period of a pendulum
        4. Gravitational force
        5. Distance, constant velocity, and time
        6. Area or volume
      4. Investigate applications involving inverse functions, such as, but not limited to
        1. Celsius and Fahrenheit temperature
        2. Economic and business models
      5. Investigate exponential growth and decay and logarithmic applications such as, but not limited to
        1. Compound interest
        2. Exponential population models
        3. Radioactive decay
        4. pH
        5. Intensity of sound
        6. Intensity of earthquakes
        7. Frequency of musical notes
        8. Newton's law of cooling
        9. Historical contributions such as the use of exponents, and the origins of e and the logarithms
      6. Investigate polynomial applications such as, but not limited to, volume
      7. Investigate rational applications such as, but not limited to, the average cost
    9. Apply the theory and application of precalculus through projects, extended reading, or programming and computational problems
      1. Typical problem-solving topics may include convergent and divergent series
      2. Typical applied projects may include any of the following:
        1. Details and history of the proofs for some of the main theorems in precalculus.
        2. Nonlinear regression
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