12/3/2024 8:55:38 AM	MATH 25 Course Outline as of Fall 2021	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	4.00	Lecture Scheduled	4.00		17.5 max.	Lecture Scheduled	70.00
Minimum	4.00	Lab Scheduled	0		6 min.	Lab Scheduled	0
		Contact DHR	0			Contact DHR	0
		Contact Total	4.00			Contact Total	70.00
		Non-contact DHR	0			Non-contact DHR Total	0

Total Out of Class Hours:  140.00

Total Student Learning Hours: 210.00

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:

College algebra topics, including equations, expressions, functions, inverse functions, graphs, applications, complex numbers, sequences and series.

Prerequisites/Corequisites:
Completion of MATH 156 or MATH 154 or MATH 155 or AB705 placement into Math Tier 3 or higher

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

College algebra topics, including equations, expressions, functions, inverse functions, graphs, applications, complex numbers, sequences and series.

(Grade Only)
Prerequisites:Completion of MATH 156 or MATH 154 or MATH 155 or AB705 placement into Math Tier 3 or higher
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:

1. Perform advanced operations with polynomial, rational, absolute value, radical, exponential, and logarithmic functions. Understand the characteristics and graphs of these functions and apply knowledge to modeling problems.

2. Define and graph inverse functions.

3. Solve selected algebraic equations analytically over the complex numbers, and solve polynomial, rational, absolute value, radical, exponential, and logarithmic equations graphically and analytically over the real numbers.

 

Objectives:

At the conclusion of this course, the student should be able to:

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 ( 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 (polynomial, rational, absolute value, radical, exponential, and logarithmic functions) over the real numbers; and, as appropriate, the complex numbers.

6. Graph piecewise-defined functions.

7. Perform operations with complex numbers in rectangular form.

Topics and Scope

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

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:

1. Reading outside of class (0-60 pages per week)

2. Problem sets (1-8 per week)

3. Quiz(zes) (0-4 per week)

4. Project(s) (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%
Quiz(zes), exam(s) and final exam
Other: Includes any assessment tools that do not logically fit into the above categories.		Other Category 0 - 10%
Project(s)

Representative Textbooks and Materials:

College Algebra. 11th ed. Sullivan, Michael. Pearson. 2020

 

College Algebra. 7th ed. Stewart, James and Redlin, Lothar and Watson, Saleem. Cengage L. 2016 (classic)

 

Precalculus. 3rd corrected ed. Stitz, Carl and Zeager, Jeffrey. Open Source Text. 2013 (classic)

Print PDF