Course Overview

Introduction to Precalculus Algebra

This course, MATH 1200 - Precalculus Algebra, is designed for students with a strong background in algebra. It covers foundational algebraic concepts, equations and inequalities, functions and their graphs, polynomials, rational, exponential, and logarithmic functions, and an introduction to analytic geometry. The course prepares students for further study in calculus and related fields.

• Credit Hours: 3.0

• Prerequisite: MyMathTest Challenge Exam Level 3 score of 70 or higher or MATH 1040

• Frequency: Offered every Fall and Winter

Course Objectives and Learning Outcomes

Key Learning Goals

• Algebraic Properties: Identify properties, laws, and definitions of algebra.

• Polynomial Analysis: Factor and find real zeros of polynomials.

• Equations and Inequalities: Solve and graph linear and quadratic equations and inequalities; graph conic sections.

• Functions: Find the domain, range, and inverse of functions; graph functions including composite functions.

• Exponential and Logarithmic Functions: Solve, apply, and graph exponential and logarithmic functions.

Course Topics and Chapter Outline

Chapter 1: Graphs

This chapter introduces the concept of graphs in mathematics, focusing on plotting points, understanding the Cartesian plane, and interpreting basic graphs.

• Key Concepts: Cartesian coordinates, plotting points, intercepts, symmetry.

• Example: Plotting the graph of on the Cartesian plane.

Chapter 2: Functions and Their Graphs

This chapter explores the definition of functions, their properties, and how to represent them graphically.

• Definition: A function is a relation in which each input has exactly one output.

• Key Concepts: Domain, range, function notation, evaluating functions, graphing functions.

• Example: Determining the domain and range of .

Chapter 3: Linear and Quadratic Functions

This chapter covers the properties and graphs of linear and quadratic functions, including methods for solving related equations and inequalities.

• Linear Functions: Functions of the form .

• Quadratic Functions: Functions of the form .

• Solving Equations: Techniques include factoring, completing the square, and the quadratic formula.

• Example: Solving by factoring.

Chapter 4: Polynomial and Rational Functions

This chapter examines higher-degree polynomials and rational functions, focusing on their properties, graphs, and methods for finding zeros.

• Polynomial Functions: Functions of the form .

• Factoring: Breaking down polynomials into products of lower-degree polynomials.

• Rational Functions: Functions of the form where .

• Example: Finding the real zeros of .

Chapter 5: Exponential and Logarithmic Functions

This chapter introduces exponential and logarithmic functions, their properties, and applications in solving equations.

• Exponential Functions: Functions of the form where and .

• Logarithmic Functions: The inverse of exponential functions, .

• Applications: Growth and decay models, compound interest.

• Example: Solving using logarithms.

Chapter 10: Analytic Geometry (if time permits)

This optional chapter covers the study of geometric figures using algebraic methods, focusing on conic sections such as circles, ellipses, parabolas, and hyperbolas.

• Conic Sections: The set of curves obtained by intersecting a plane with a double-napped cone.

• Standard Equations: For example, the equation of a circle: $

• Example: Graphing the parabola .

Assessment and Grading

Evaluation Methods

• Weekly Homework & Quizzes: 25%

• Three Chapter Exams: 50%

• Cumulative Final Exam: 25%

Grading Scale

Note: +/- grades may be given depending on class statistics and averages.

Course Policies and Resources

• Textbook and Materials: MyMathLab is required for homework assignments. No calculators are allowed during exams and quizzes.

• Attendance: Regular attendance is expected. Refer to the Canvas course for detailed policies.

• University Policies: Students must adhere to all university-wide and college-wide policies, including academic integrity and code of conduct.

• Academic Resources: Tutoring, counseling, and other support services are available to aid student success.

Weekly Schedule Overview

Additional info: Chapter 10 (Analytic Geometry) will be covered if time permits.