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# SRJC Course Outlines

11/3/2024 2:28:27 PM | MATH 25 Course Outline as of Fall 2021
| Changed Course |

CATALOG INFORMATION |
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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 |

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 |
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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% |
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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% |
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Problem sets | |||

Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams. | Skill Demonstrations 0 - 0% |
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None | |||

Exams: All forms of formal testing, other than skill performance exams. | Exams 70 - 95% |
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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% |
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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)