| 12/21/2024 6:35:33 AM |
| Changed Course |
| CATALOG INFORMATION
|
| Discipline and Nbr:
MATH 25 | Title:
PRECALCULUS ALGEBRA |
|
| Full Title:
Precalculus Algebra |
| Last Reviewed:2/8/2021 |
| Units | Course Hours per Week | | Nbr of Weeks | Course Hours Total |
| Maximum | 3.00 | Lecture Scheduled | 3.00 | 17.5 max. | Lecture Scheduled | 52.50 |
| Minimum | 3.00 | Lab Scheduled | 0 | 6 min. | Lab Scheduled | 0 |
| | Contact DHR | 0 | | Contact DHR | 0 |
| | Contact Total | 3.00 | | Contact Total | 52.50 |
| |
| | Non-contact DHR | 0 | | Non-contact DHR Total | 0 |
| | Total Out of Class Hours: 105.00 | Total Student Learning Hours: 157.50 | |
Title 5 Category:
AA Degree Applicable
Grading:
Grade Only
Repeatability:
00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:
Catalog Description:
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College algebra topics, including equations, expressions, functions, inverse functions, and graphs. Also includes parametric equations, complex numbers, sequences and series.
Prerequisites/Corequisites:
Completion of MATH 156 or MATH 154 or MATH 155 or appropriate placement based on AB 705 mandates
Recommended Preparation:
Limits on Enrollment:
Schedule of Classes Information
Description:
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College algebra topics, including equations, expressions, functions, inverse functions, and graphs. Also includes parametric equations, complex numbers, sequences and series.
(Grade Only)
Prerequisites:Completion of MATH 156 or MATH 154 or MATH 155 or appropriate placement based on AB 705 mandates
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP
ARTICULATION, MAJOR, and CERTIFICATION INFORMATION
| Associate Degree: | Effective: | Fall 1981
| Inactive: | |
| Area: | B
MC
| Communication and Analytical Thinking
Math Competency
|
| |
| CSU GE: | Transfer Area | | Effective: | Inactive: |
| | B4 | Math/Quantitative Reasoning | Fall 2006 | |
| |
| IGETC: | Transfer Area | | Effective: | Inactive: |
| | 2A | Mathematical Concepts & Quantitative Reasoning | Fall 2006 | |
| |
| CSU Transfer: | Transferable | Effective: | Fall 2006 | Inactive: | |
| |
| UC Transfer: | Transferable | Effective: | Fall 2006 | Inactive: | |
| |
| C-ID: |
Certificate/Major Applicable:
Both Certificate and Major Applicable
COURSE CONTENT
Student Learning Outcomes:
At the conclusion of this course, the student should be able to:
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1. Perform advanced operations with functions (polynomial, rational, absolute value, radical,
exponential, and logarithmic), understand the characteristics and graphs of these functions,
and apply knowledge to modeling problems.
2. Define and graph inverse functions and parametric equations.
3. Solve selected algebraic equations symbolically over the complex numbers, and solve
polynomial, rational, absolute value, radical, exponential, and logarithmic equations
graphically and symbolically over the real numbers.
Objectives:
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During this course, students will:
1. Perform advanced operations with functions (using symbolic, graphical, and numerical
representations) and apply knowledge to application and modeling problems.
2. Define and graph inverse functions.
3. Identify and interpret characteristics of functions (including intercepts, turning points, extreme
values, intervals of positive/negative, increasing/decreasing value, transformations,
symmetry, asymptotes, and holes).
4. Graph polynomial, rational, absolute value, radical, exponential, and logarithmic functions.
5. Solve equations symbolically and graphically (involving polynomial, rational, absolute value,
radical, exponential, and logarithmic functions) over the real numbers; and, as appropriate,
the complex numbers.
6. Graph piecewise-defined functions and parametric equations.
7. Perform operations with complex numbers in rectangular form.
Topics and Scope
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I. Equations and Inequalities
A. Graphical and algebraic solutions to radical and quadratic form equations
B. Graphical and algebraic solutions to absolute value equations and inequalities
C. Parametric equations
II. Complex Numbers
A. Definition
B. Operations
III. Analysis of Functions and Their Graphs
A. Definition
B. Notation
C. Domain
D. Range
E. Operations, including difference quotients and composition of functions
F. Catalog of functions
G. Symmetry (even and odd functions)
H. Transformations of graphs (shifts, scaling, reflections)
I. Modeling
IV. Polynomial and Rational Functions
A. Linear, quadratic, polynomial functions of higher degree and their graphs
B. Long division of polynomials
C. Graphs of rational functions
D. Asymptotes and holes
E. Introduction to limit concepts and notation
F. Solutions of polynomial and rational equations and inequalities, using real numbers and
complex numbers as appropriate
V. Inverse, Exponential and Logarithmic Functions
A. Definitions
B. Properties
C. Graphs
D. Equations
E. Applications
VI. Sequences and Series
A. Introduction to finite and infinite sequence and series (sigma) notation
B. Finite and infinite geometric sequences and series
C. Summation of powers of integers
D. Binomial Expansion
1. Factorial notation
2. Pascal's Triangle and/or binomial coefficients
Assignments:
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1. Reading outside of class (0-60 pages per week)
2. Problem sets (1-8 per week)
3. Quizzes (0-4 per week)
4. Projects (0-10)
5. Exams (2-6)
6. Final exam
Methods of Evaluation/Basis of Grade.
| Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing. | Writing
0 - 0% |
| None | |
| This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course. |
|
| Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills. | Problem Solving
5 - 20% |
| Problem sets | |
| Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams. | Skill Demonstrations
0 - 0% |
| None | |
| Exams: All forms of formal testing, other than skill performance exams. | Exams
70 - 95% |
| Exams and quizzes | |
| Other: Includes any assessment tools that do not logically fit into the above categories. | Other Category
0 - 10% |
| Projects | |
Representative Textbooks and Materials:
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College Algebra Enhanced with Graphing Utilities. 7th ed. Sullivan, Michael and Sullivan III, Michael. Pearson. 2016
College Algebra. 7th ed. Stewart, James and Redlin, Lothar and Watson, Saleem. Cengage L. 2015
Precalculus. 3rd corrected ed. Stitz, Carl and Zeager, Jeffrey. Open Source Text. 2013 (classic)
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