Course Overview

This course, Pre-Calculus Mathematics I (SMAT-121), is designed to provide students with a comprehensive foundation in algebra and functions, preparing them for further studies in calculus and related fields. The course emphasizes both conceptual understanding and practical application, with a focus on modeling real-world scenarios and problem-solving strategies.

Course Topics and Structure

• Review of Real Numbers and Their Properties

• Operations with Complex Numbers

• Equations and Inequalities

• Polynomial, Rational, Exponential, and Logarithmic Functions and Their Graphs

• Systems of Equations and Inequalities

• Mathematical Modeling and Applications

Graphing calculators are recommended for this course.

Detailed Chapter Outline

Chapter P: Prerequisites – Fundamental Concepts of Algebra (Optional)

• Algebraic Expressions, Mathematical Models, and Real Numbers

• Exponents and Scientific Notation

• Radicals and Rational Exponents

• Polynomials

• Factoring Polynomials

• Rational Expressions

Chapter 1: Equations and Inequalities (Review)

• Graphs and Graphing Utilities

• Linear Equations and Rational Equations

• Models and Applications

• Complex Numbers

• Quadratic Equations

• Other Types of Equations

• Linear Inequalities and Absolute Value Inequalities

Chapter 2: Functions and Graphs

• Basics of Functions and Their Graphs

• More on Functions and Their Graphs

• Linear Functions and Slope

• More on Slope

• Transformations of Functions

• Combinations of Functions; Composite Functions

• Inverse Functions

• Distance and Midpoint Formulas; Circles

Chapter 3: Polynomial and Rational Functions

• Quadratic Functions

• Polynomial Functions and Their Graphs

• Dividing Polynomials; Remainder and Factor Theorems

• Zeros of Polynomial Functions

• Rational Functions and Their Graphs

• Polynomial and Rational Inequalities

• Modeling Using Variation

Chapter 4: Exponential and Logarithmic Functions

• Exponential Functions

• Logarithmic Functions

• Properties of Logarithms

• Exponential and Logarithmic Equations

• Exponential Growth and Decay; Modeling Data (Optional)

Chapter 8: Systems of Equations and Inequalities

• Systems of Linear Equations in Two Variables

Learning Objectives

• Apply multiple strategies to solve various equations and inequalities, both algebraically and graphically.

• Identify functions, relations, equations, and graphs.

• Evaluate functions, including piecewise, linear, quadratic, polynomial, rational, exponential, and logarithmic functions.

• Use functions to model data and make predictions.

• Find the slope and equation of parallel and perpendicular lines.

• Evaluate the distance and midpoint of a line, and the characteristics of a circle (center, radius, and equation).

• Solve applied problems involving quadratic and rational functions.

• Apply the Factor and Remainder Theorems.

• Solve polynomial and rational inequalities.

• Use properties of logarithms to simplify logarithmic expressions.

• Solve exponential and logarithmic equations.

• Solve linear systems.

Key Mathematical Concepts and Formulas

Equations and Inequalities

• Linear Equation:

• Quadratic Equation:

• Quadratic Formula:

• Absolute Value Inequality:

Functions and Graphs

• Function Definition: A relation where each input has exactly one output.

• Domain and Range: The set of possible inputs (domain) and outputs (range).

• Piecewise Function Example:

• Composite Function:

• Inverse Function: such that

Polynomials and Factoring

• Polynomial:

• Factoring Example:

• Remainder Theorem: If is divided by , the remainder is .

• Factor Theorem: is a factor of if and only if .

Rational, Exponential, and Logarithmic Functions

• Rational Function: , where

• Exponential Function: , ,

• Logarithmic Function: , ,

• Properties of Logarithms:

• Change of Base Formula:

Distance, Midpoint, and Circles

• Distance Formula:

• Midpoint Formula:

• Equation of a Circle:

Systems of Equations

• System of Linear Equations:

• Solution Methods: Substitution, elimination, and graphical methods.

Grading and Evaluation

Grade Scale

Course Materials

• Textbook: Algebra and Trigonometry by Blitzer, 7th Edition (Pearson)

• Calculator: TI-83 or TI-84 graphing calculator recommended

• Online Resources: MyLab and Mastering (Pearson), Canvas LMS

Student Support and Policies

• Academic integrity and plagiarism policies strictly enforced.

• Reasonable accommodations available for students with documented disabilities.

• Participation in all course activities is required for success.

• Late assignments and quizzes incur penalties as described in the syllabus.

• Mental health and counseling resources are available for all students.

Additional info:

• This syllabus provides a roadmap for the Precalculus course, outlining both the mathematical content and the expectations for student engagement and assessment.

• Students are encouraged to use all available resources, including office hours, the Math Clinic, and online support tools, to maximize their understanding and performance.