Precalculus Syllabus and Study Guide: MTH 161 - V04 Spring 2026

Course Overview

Introduction to Precalculus

This Precalculus I course is designed to prepare students for further study in mathematics, including calculus. The course covers foundational algebraic concepts, functions, polynomial and rational functions, exponential and logarithmic functions, and systems of equations. Students will develop problem-solving skills and mathematical reasoning necessary for STEM and non-STEM fields.

• Course Topics:

  • Relations and Functions

  • Polynomial and Rational Functions

  • Exponential and Logarithmic Functions

  • Systems of Equations

• Course Format: Asynchronous online, 15-week session

• Prerequisites: Placement or completion of MTH 154 or equivalent

Major Topics and Subtopics

Fundamental Concepts of Algebra

Algebra forms the basis for all higher mathematics. In Precalculus, students review and expand their understanding of algebraic operations, properties, and problem-solving strategies.

• Key Point 1: Operations with real numbers, properties of equality, and solving linear equations

• Key Point 2: Manipulation and simplification of algebraic expressions

• Example: Solve $2x + 5 = 13$ for $x$ $2x = 8$ $x = 4$

Functions and Their Graphs

Functions are mathematical relationships that assign each input exactly one output. Understanding functions and their graphical representations is essential in Precalculus.

• Key Point 1: Definition of a function, domain and range

• Key Point 2: Types of functions: linear, quadratic, polynomial, rational, exponential, logarithmic

• Example: The function $f(x) = x^2$ has domain $(-18, 18)$ and range $[0, 18)$

Polynomial and Rational Functions

Polynomial functions are sums of powers of $x$ with coefficients, while rational functions are ratios of polynomials. Their properties and graphs are central to Precalculus.

• Key Point 1: Standard form of a polynomial: $f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_0$

• Key Point 2: Rational functions: $f(x) = rac{P(x)}{Q(x)}$, where $Q(x) eq 0$

• Example: $f(x) = rac{x^2 - 1}{x - 1}$ is undefined at $x = 1$

Exponential and Logarithmic Functions

Exponential functions model growth and decay, while logarithmic functions are their inverses. These functions are widely used in science and engineering.

• Key Point 1: Exponential function: $f(x) = a^x$, $a > 0$, $a eq 1$

• Key Point 2: Logarithmic function: $f(x) = ext{log}_a(x)$, inverse of $a^x$

• Example: $2^x = 8$ implies $x = ext{log}_2(8) = 3$

Systems of Equations

Systems of equations involve solving for multiple variables using multiple equations. Techniques include substitution, elimination, and matrix methods.

• Key Point 1: Linear systems can be solved by substitution or elimination

• Key Point 2: Matrix representation: $AX = B$

• Example: Solve $x + y = 5$ and $x - y = 1$ Adding: $2x = 6 ightarrow x = 3$ Substituting: $3 + y = 5 ightarrow y = 2$

Course Structure and Assessment

Grading Categories

Student performance is assessed through written problems, online assignments, tests, and a final exam. Each category contributes to the final grade as shown below.

Type of Assessment	Percent of Total Grade
Written Problems	20%
MyLab Homework Assignments	20%
Tests	30%
Final Exam	30%

Course Policies

• Late Work: Policies vary by assignment type; extensions may be granted for documented emergencies.

• Academic Honesty: Plagiarism and unauthorized collaboration are not tolerated.

• Calculator Policy: TI-83 or 84 permitted; TI-89 or equivalent not permitted.

• AI Policy: All work must be original unless otherwise directed by the instructor.

Weekly Topic Schedule

The following table summarizes the weekly topics and major assignments for the course.

Week	Topic	Assignments Due
1	Course Introduction & Syllabus, Fundamental Concepts	Get signed up, Function Notes
2	Functions: Notes, Graphs	Written Problem 1, MML 2.2 Assignment
3	Library of Functions, Transformations	MML 2.5 Assignment
4	Polynomial Functions, Graphing	MML 4.1, 4.2 Assignments
5	Rational Functions, Graphs	MML 4.3, 4.4 Assignments
6	Exponential & Logarithmic Functions	MML 5.1, 5.2 Assignments
7	Systems of Equations	MML 6.1, 6.2 Assignments
8-15	Review, Final Exam Preparation	Written Problems, Final Exam

Additional Assistance

Students are encouraged to use the tutoring center located in the library. The tutoring is free and available both in-person and online. See the syllabus for details and links.

Important Dates

• First Day of Semester: January 20

• Last Day to Drop with Refund: February 5

• Last Day to Drop without Grade Penalty: March 31

• End of Session: May 11

Required Materials

• Textbook: MyMathLab with Pearson eText for Precalculus 12th Edition

• Calculator: TI-83 or TI-84

Summary

This syllabus provides a comprehensive overview of the Precalculus I course, including major mathematical concepts, assessment methods, weekly schedule, and policies. Students should use this guide to organize their study and prepare for success in Precalculus.