College of the Redwoods
CURRICULUM PROPOSAL
1. Course ID and Number: Math 30
2. Course Title: College Algebra
3. Check one of the following:
New Course (If the course constitutes a new learning experience for CR students, the course is new)
Updated/revised course
If curriculum has been offered under a different discipline and/or name, identify the former course:
Should another course be inactivated? No
Title of course to be inactivated:
Yes
Inactivation date:
4. If this is an update/revision of an existing course, provide explanation of and justification for changes to this
course. Be sure to explain the reasons for any changes to class size, unit value, and prerequisites/corequisites.
Course outlines are required to be updated every five years. The revised course outline reflects changes
to the course description, outcomes, themes, concepts, issues, and skills.
5. List the faculty with which you consulted in the development and/or revision of this course outline:
Faculty Member Name(s) and Discipline(s): David Arnold (Mathematics), Tami Matsumoto
(Mathematics), Erin Wall (Mathematics), Todd Olsen (Mathematics), Michael Butler (Mathematics), Steve
Jackson (Mathematics), Kevin Yokoyama (Mathematics), Mike Haley (Mathematics)
6. If any of the features listed below have been modified in the new proposal, indicate the “old” (current) information
and proposed changes. If a feature is not changing, leave both the “old” and “new” fields blank.
FEATURES
OLD
NEW
Course Title
Catalog Description
(Please include complete text
of old and new catalog
descriptions.)
Grading Standard
A course covering first-degree and
absolute value equations and
inequalities; composite and inverse
functions; polynomial, rational,
exponential, and logarithmic
functions; systems of equations and
inequalities; matrices; sequences and
series; mathematical induction;
binomial expansion theorem; and
complex numbers.
Select
A course covering first-degree and
absolute value equations and
inequalities; composite and inverse
functions; polynomial, rational,
exponential, and logarithmic
functions; systems of equations;
matrices; sequences and series;
mathematical induction; binomial
expansion theorem; and complex
numbers.
Select
Total Units
Lecture Units
Lab Units
Prerequisites
Corequisites
Recommended Preparation
Maximum Class Size
Repeatability—
Maximum Enrollments
Other
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Page 1 of 8
College of the Redwoods
COURSE OUTLINE
1. DATE: Dec. 1, 2010
2. DIVISION: Math, Science, and Engineering
3. COURSE ID AND NUMBER: Math 30
4. COURSE TITLE (appears in catalog and schedule of classes): College Algebra
5. SHORT TITLE (appears on student transcripts; limited to 30 characters, including spaces): College Algebra
6. LOCAL ID (TOPS): 1701.00 (Taxonomy of Program codes
http://www.cccco.edu/Portals/4/AA/CP%20&%20CA3/TopTax6_rev_07.doc)
7. NATIONAL ID (CIP): 270101 (Classification of Instructional Program codes can be found in Appendix B of the TOPS code book
http://www.cccco.edu/Portals/4/AA/CP%20&%20CA3/TopTax6_rev_07.doc)
8. Discipline(s): Select from CCC System Office Minimum Qualifications for Faculty
http://www.cccco.edu/SystemOffice/Divisions/AcademicAffairs/MinimumQualifications/MQsforFacultyandAdministrators/tabid/753/Default.aspx
Course may fit more than one discipline; identify all that apply: Mathematics
9. FIRST TERM NEW OR REVISED COURSE MAY BE OFFERED: Summer 2011
10. TOTAL UNITS: 4
TOTAL HOURS: 72
[Lecture Units: 4 Lab Units: 0]
[Lecture Hours: 72
Lab Hours: 0]
(1 unit lecture=18 hours; 1 unit lab=54 hours)
11. MAXIMUM CLASS SIZE: 40
12. WILL THIS COURSE HAVE AN INSTRUCTIONAL MATERIALS FEE? No
Yes
Fee: $
(If “yes,” attach a completed “Instructional Materials Fee Request Form”—form available in Public Folders>Curriculum>Forms)
GRADING STANDARD
Letter Grade Only
Pass/No Pass Only
Is this course a repeatable lab course: No
Yes
Grade-Pass/No Pass Option
If yes, how many total enrollments?
Is this course to be offered as part of the Honors Program? No
Yes
If yes, explain how honors sections of the course are different from standard sections.
CATALOG DESCRIPTION -- The catalog description should clearly describe for students the scope of the course, its level, and what
kinds of student goals the course is designed to fulfill. The catalog description should begin with a sentence fragment.
A course covering first-degree and absolute value equations and inequalities; composite and inverse
functions; polynomial, rational, exponential, and logarithmic functions; systems of equations;
matrices; sequences and series; mathematical induction; binomial expansion theorem; and complex
numbers.
Special notes or advisories (e.g. field trips required, prior admission to special program required, etc.):
calculator required, TI-83 or 84 recommended.
Graphing
PREREQUISITE COURSE(S)
No
Yes
Course(s): Math 120 (or equivalent) with a grade of "C" or better or
appropriate score on the math placement exam.
Rationale for Prerequisite:
Describe representative skills without which the student would be highly unlikely to succeed. Ability to solve linear,
quadratic, polynomial, rational, radical, exponential, and logarithmic equations analytically, graphically,
numerically, and verbally in real-world settings. Ability to use technology in the study of these
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Page 2 of 8
functions.
COREQUISITE COURSE(S)
No
Yes
Rationale for Corequisite:
Course(s):
RECOMMENDED PREPARATION
No
Yes
Course(s):
Rationale for Recommended Preparation:
COURSE LEARNING OUTCOMES –This section answers the question “what will students be able to do as a result of
taking this course?” State some of the objectives in terms of specific, measurable student actions (e.g. discuss, identify,
describe, analyze, construct, compare, compose, display, report, select, etc.). For a more complete list of outcome verbs please
see Public Folders>Curriculum>Help Folder>SLO Language Chart. Each outcome should be numbered.
1. Evaluate and interpret a difference quotient symbolically, numerically, and graphically.
2. Find and interpret the real and complex roots of a polynomial symbolically, numerically, and
graphically.
3. Produce an accurate graph of a rational function by hand, and identify all salient features.
4. Demonstrate and interpret the inverse relationship between exponential and logarithmic functions.
5. Solve problems and applications involving exponential and logarithmic functions.
6. Solve 3x3 linear systems of equations using matrices and elimination, and interpret the nature of the
solution set geometrically.
7. Recognize and solve problems involving arithmetic and geometric sequences and series.
COURSE CONTENT–This section describes what the course is “about”-i.e. what it covers and what knowledge students will acquire
Concepts: What terms and ideas will students need to understand and be conversant with as they demonstrate course
outcomes? Each concept should be numbered.
1. A multiple-step problem-solving process.
2. The presentation of mathematical solutions in a logical and coherent structure, including the use of
writing skills, grammar, and punctuation.
3. The use of the graphing calculator as a problem-solving tool.
4. The connection between graphs and properties of functions.
5. Application of concepts to real-world problems.
6. Knowledge of functions to include definitions, graphs, properties, and their application to the
problem-solving process.
7. The recognition that the use of proper algebraic skills is an important tool in problem-solving
situations.
Issues: What primary tensions or problems inherent in the subject matter of the course will students engage? Each issue
should be numbered.
1. The role of the student in becoming a successful learner.
2. The importance of writing mathematics using correct notation and grammar.
3. The limitations of technology.
4. The connection between mathematics, science, and the "real world."
5. The necessity to read unfamiliar mathematics using the textbook and other resources.
Themes: What motifs, if any, are threaded throughout the course? Each theme should be numbered.
1. Functions.
2. Critical thinking.
3. Problem solving.
4. Algebraic skills.
5. Use of technology.
6. Graphing and data analysis.
7. Communication.
Skills: What abilities must students have in order to demonstrate course outcomes? (E.g. write clearly, use a scientific
calculator, read college-level texts, create a field notebook, safely use power tools, etc). Each skill should be numbered.
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Page 3 of 8
1. Use a calculator to: graph a function, find an appropriate viewing window, trace, find intersections,
zeros, extrema, increasing/decreasing intervals, continuity and inverses; approximate solutions to
equations and inequalities; solve systems of equations. Understand the technological limits of the
calculator.
2. Be able to identify the properties of linear, quadratic, polynomial, rational, radical, exponential,
logarithmic, absolute value functions, piecewise functions, arithmetic sequences, geometric
sequences, and series.
3. Analysis of Graphs:
• Determine the domain and range of a function.
• Identify intervals of the domain for which a function is increasing/decreasing/constant.
• Identify zeros and intervals of the domain for which a function is positive/negative.
• Identify local and absolute extrema.
• Analyze functions and relations for symmetry.
• Analytically determine whether a function is even, odd, or neither.
• Identify the graph of a function or relation that has been translated by a vertical or horizontal shift.
• Identify the graph of a function that has been vertically or horizontally stretched or compressed.
• Identify the graph of a function that has been reflected across an axis.
• Evaluate and interpret the difference quotient as the slope of a secant line for a given function.
4. Solve equations and inequalities involving linear, quadratic, polynomial, rational, radical,
exponential, logarithmic, and absolute value functions.
5. Piecewise and Absolute Value Functions:
• Evaluate and graph piecewise functions.
• Express functions involving absolute value as piecewise functions, and sketch their graphs.
• Solve equations and inequalities involving absolute value functions.
• Apply absolute value to real-world situations.
6. Polynomial Functions:
• Determine the exact zeros (both real and complex) and their multiplicities of polynomial functions
by applying the Rational Zeros Theorem, Factor Theorem, Remainder Theorem, Fundamental
Theorem of Algebra, and the Conjugate Zeros Theorem.
• Use the end behavior of a polynomial function and the behavior near its zeros to sketch the graph.
• Divide polynomials by long division. Divide a polynomial by a linear factor using synthetic
division.
• Solve polynomial equations and inequalities.
7. Rational Functions:
• Identify the domain, range, vertical asymptotes, horizontal asymptotes, oblique asymptotes,
discontinuities, and zeros. Determine the end behavior and behavior near zeros and
discontinuities. Use this information to sketch the graph.
• Solve rational equations and inequalities.
• Solve applications of rational functions, including equations involving direct, inverse, and joint
variation.
8. Inverse Functions:
• Identify one-to-one functions both analytically and using the horizontal line test.
• Sketch the graph of a function and its inverse.
• Apply composition of functions to prove functions are inverses.
• Find the inverse of a function algebraically.
• Find the inverse of a function with a restricted domain.
9. Exponential Functions:
• Use the laws of exponents to simplify expressions.
• Identify the domain, range, intercepts, and asymptotes. Use this information and transformation
theory to sketch the graph.
• Compare graphs of exponential growth and decay functions, and develop exponential models for
real-world applications.
10. Logarithmic Functions:
• Use the definition of a logarithm (as the inverse of the exponential) to convert equations between
logarithmic and exponential forms.
• Identify the domain, range, intercepts, and asymptotes. Use this information and transformation
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Page 4 of 8
theory to sketch the graph.
Simplify and evaluate logarithmic expressions using the properties of logarithms.
Solve exponential and logarithmic equations.
Solve problems involving discrete and continuous compound interest.
Solve problems involving exponential growth/decay, Newton's law of cooling, logistic growth, and
logarithmic scales.
11. Systems of equations:
• Solve systems of two linear equations in two unknowns using the elimination method.
• Solve systems of three linear equations in three unknowns using the elimination method.
• Solve 3x3 linear systems using elementary row operations, row echelon and reduced row echelon
forms, and the graphing calculator.
• Compute 2x2 determinants and solve 2x2 systems using Cramer's Rule.
• Solve linear systems involving investments, mixture, rate, and work.
12. Sequences and Series:
• Identify the sequence as a function on the set of natural numbers.
• Generate the terms of a sequence defined by a recursive formula.
• Apply formulae for the nth term and sum of the first n terms of arithmetic and geometric
sequences and series.
• Determine whether an infinite geometric series is convergent or divergent. Find the sum of a
convergent geometric series.
• Apply sequence and series concepts to real-world problems.
13. Write proofs using the Principle of Mathematical Induction.
14. The Binomial Theorem:
• Expand a binomial using the binomial theorem.
• Find a specific term in the expansion of a binomial.
•
•
•
•
REPRESENTATIVE LEARNING ACTIVITIES –This section provides examples of things students may do to engage the
course content (e.g., listening to lectures, participating in discussions and/or group activities, attending a field trip). These
activities should relate directly to the Course Learning Outcomes. Each activity should be numbered.
1. Listening to lectures.
2. Participating in group activities or assignments.
3. Participating in in-class assignments or discussions.
4. Completing daily homework assignments.
5. Completing online activities on the computer.
ASSESSMENT TASKS –This section describes assessments instructors may use to allow students opportunities to provide
evidence of achieving the Course Learning Outcomes. Each assessment should be numbered.
Representative assessment tasks (These are examples of assessments instructors could use):
1. In-class exams.
2. Writing assignments to develop communication of mathematical concepts.
3. Quizzes.
4. Group projects or other in-class activities.
5. Portfolios.
6. Individual projects or presentations.
Required assessments for all sections (These are assessments that are required of all instructors of all sections at all
campuses/sites. Not all courses will have required assessments. Do not list here assessments that are listed as representative assessments
above.):
1. At least two proctored, closed-book examinations, plus a comprehensive final examination.
EXAMPLES OF APPROPRIATE TEXTS OR OTHER READINGS –This section lists example texts, not required texts.
Author, Title, and Date Fields are required
Author Hornsby,
Lial, Rockswold
Author Sullivan Title
Author
Title
Title
A graphical Approach to College Algebra, 5th ed.
Algebra and Trigonometry, 8th ed.
Date
Date
2011
2008
Date
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Page 5 of 8
Author
Title
Date
Other Appropriate Readings:
COURSE TYPES
1. Is the course part of a Chancellor’s Office approved CR Associate Degree?
No
Yes
If yes, specify all program codes that apply. (Codes can be found in Outlook/Public Folders/All Public Folders/ Curriculum/Degree
and Certificate Programs/choose appropriate catalog year):
Required course for degree(s)
Restricted elective for degree (s) SCI.LA.A.AA, SCI.LA.B.AA, SCI.LA.C.AA, SCI.LA.D.AA,
SCIEX.LA.A.AA, SCIEX.LA.B.AA, SCIEX.LA.C.AA, SCIEX.LA.D.AA, MS.AS, MS.CA, FNR.AS.FOR.TECH
Restricted electives are courses specifically listed (i.e. by name and number) as optional courses from which students may choose
to complete a specific number of units required for an approved degree.
2.
Is the course part of a Chancellor’s Office approved CR Certificate of Achievement?
No
Yes
If yes, specify all program codes that apply. ( Codes can be found in Outlook/Public Folders/All Public Folders/ Curriculum/Degree
and Certificate Programs/choose appropriate catalog year):
Required course for certificate(s)
Restricted elective for certificate(s) Auto.CA
Restricted electives are courses specifically listed (i.e. by name and number) as optional courses from which students may
choose to complete a specific number of units required for an approved certificate.
3.
Is the course Stand Alone?
No
Yes
(If “No” is checked for BOTH #1 & #2 above, the course is stand alone)
4.
Basic Skills: NBS Not Basic Skills
5.
Work Experience: NWE Not Coop Work Experience
6.
Course eligible Career Technical Education funding (applies to vocational and tech-prep courses only): yes
7.
Purpose: A Liberal Arts Sciences
8.
Accounting Method: W Weekly Census
9.
Disability Status: N Not a Special Class
no
CURRENT TRANSFERABILITY STATUS
This course is currently transferable to
Neither CSU nor UC
CSU as general elective credit
CSU as a specific course equivalent (see below)
If the course transfers as a specific course equivalent, give course number(s)/ title(s) of one or more currently-active,
equivalent lower division courses from CSU.
1. Course Math 1130, Campus CSU East Bay
2. Course Math 118, Campus Cal Poly SLO
UC as general elective credit
UC as specific course equivalent
If the course transfers as a specific course equivalent, give course number(s)/ title(s) of one or more currently-active,
equivalent lower division courses from UC.
1. Course Math 2, Campus UCSC 2. Course
, Campus
PROPOSED CSU TRANSFERABILITY (If course is currently CSU transferable, go to the next section):
None
General Elective Credit
Specific Course Equivalent (see below)
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Page 6 of 8
If specific course equivalent credit is proposed, give course number(s)/ title(s) of one or more currently-active,
equivalent lower division courses from CSU.
1. Course
, Campus
2. Course
, Campus
PROPOSED UC TRANSFERABILITY (If course is currently UC transferable, go to the next section):
None
General Elective Credit OR Specific Course Equivalent (see below)
If “General Elective Credit OR Specific Course Equivalent” box above is checked, give course number(s)/ title(s) of one
or more currently-active, equivalent lower division courses from UC.
1. Course
, Campus
2. Course
, Campus
CURRENTLY APPROVED GENERAL EDUCATION
CR
CSU
IGETC
CR GE Category: D3
CSU GE Category: B4
IGETC Category: 2
PROPOSED CR GENERAL EDUCATION
Rationale for CR General Education approval (including category designation):
Natural Science
Social Science
Humanities
Language and Rationality
Writing
Oral Communications
Analytical Thinking
PROPOSED CSU GENERAL EDUCATION BREADTH (CSU GE)
A. Communications and Critical Thinking
A1 – Oral Communication
A2 – Written Communication
A3 – Critical Thinking
C. Arts, Literature, Philosophy, and Foreign Language
C1 – Arts (Art, Dance, Music, Theater)
C2 – Humanities (Literature, Philosophy, Foreign
Language)
E. Lifelong Understanding and Self-Development
E1 – Lifelong Understanding
E2 – Self-Development
B. Science and Math
B1 – Physical Science
B2 – Life Science
B3 – Laboratory Activity
B4 – Mathematics/Quantitative Reasoning
D. Social, Political, and Economic Institutions
D0 – Sociology and Criminology
D1 – Anthropology and Archeology
D2 – Economics
D3 – Ethnic Studies
D5 – Geography
D6 – History
D7 – Interdisciplinary Social or Behavioral Science
D8 – Political Science, Government and Legal Institutions
D9 – Psychology
Rationale for inclusion in this General Education category: Same as above
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Page 7 of 8
Proposed Intersegmental General Education Transfer Curriculum (IGETC)
1A – English Composition
1B – Critical Thinking-English Composition
1C – Oral Communication (CSU requirement only)
2A – Math
3A – Arts
3B – Humanities
4A – Anthropology and Archaeology
4B – Economics
4E – Geography
4F – History
4G – Interdisciplinary, Social & Behavioral Sciences
4H – Political Science, Government & Legal Institutions
4I – Psychology
4J – Sociology & Criminology
5A – Physical Science
5B – Biological Science
6A – Languages Other Than English
Rationale for inclusion in this General Education category:
Submitted by:
Bruce Wagner
Same as above
Tel. Ext.
Division Chair/Director: Rachel Anderson
4207
Date: Dec. 1, 2010
Review Date: 12/3/10
CURRICULUM COMMITTEE USE ONLY
Approved by Curriculum Committee: No
Academic Senate Approval Date: 2.4.11
Curriculum Proposal: 01/23/09 (rev.)
Academic Senate Approved: pending
Yes
Date: 01.28.11
Board of Trustees Approval Date: 3.1.11
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