Course Overview

Introduction to College Algebra Prep (MAT 114)

This course provides foundational knowledge and skills in algebra, focusing on the evaluation and manipulation of algebraic expressions, solving equations and inequalities, and understanding the properties and applications of functions. The course is designed to prepare students for further study in mathematics and related fields.

Course Competencies and Outline

1. Operations on Numbers

Understanding and performing operations with various types of numbers is essential for algebraic problem-solving.

• Integers: Whole numbers and their negatives. Operations include addition, subtraction, multiplication, and division.

• Fractions: Numbers expressed as ratios of integers. Operations include finding common denominators, simplifying, and performing arithmetic operations.

• Decimals: Numbers expressed in base 10. Includes conversion between fractions and decimals, and performing arithmetic operations.

• Exponents and Radicals: Exponents represent repeated multiplication; radicals are the inverse operation (e.g., square roots).

• Order of Operations: The standard sequence for evaluating expressions: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).

Example: Simplify . Solution: .

2. Operations on Polynomials

Polynomials are algebraic expressions consisting of variables and coefficients. Mastery of their operations is crucial for higher-level algebra.

• Evaluating Expressions: Substitute values for variables and compute the result.

• Rules of Exponents: Includes the power, product, quotient, negative, and rational exponent rules.

• Addition, Subtraction, Multiplication: Combine like terms and apply distributive property.

• Factoring: Expressing a polynomial as a product of its factors.

Key Formulas:

• Product Rule:

• Quotient Rule:

• Power Rule:

• Negative Exponent:

• Rational Exponent:

Example: Factor . Solution: .

3. Functions

Functions are mathematical relationships where each input has a unique output. Understanding functions is central to algebra.

• Definition: A function assigns each element in the domain to exactly one element in the range.

• Function Notation: denotes the output of function for input .

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

• Evaluating Functions: Substitute values into the function rule.

• Average Rate of Change: Measures how a function's output changes per unit change in input.

Key Formula:

• Average Rate of Change between and :

Example: If , find . Solution: .

4. Linear Behavior

Linear equations and functions describe relationships with constant rates of change. They are fundamental in modeling and problem-solving.

• Solving Equations: Find the value(s) of the variable that make the equation true.

• Solving Inequalities: Find the set of values that satisfy the inequality; represent solutions graphically and in interval notation.

• Key Characteristics: Intercepts, domain, range, increasing/decreasing intervals, and extrema.

• Rate of Change: The slope of a linear function, .

• Building Equations: Write equations from given information or data.

• Graphing: Plotting linear equations on the coordinate plane.

• Applications: Modeling real-world situations with linear functions.

• Solving Systems: Find the intersection point(s) of two linear equations in two variables.

Example: Solve . Solution: .

5. Quadratic Behavior

Quadratic equations and functions involve variables raised to the second power. They model parabolic relationships and have diverse applications.

• Radicals and Imaginary Numbers: Radicals involve roots; imaginary numbers arise when taking the square root of negative numbers ().

• Solving Quadratic Equations: Multiple methods are available:

  • Square Root Method:

  • Factoring: Express as a product of binomials and set each factor to zero.

  • Quadratic Formula:

  • Graphing: Find -intercepts (roots) on the graph of the quadratic function.

• Key Characteristics: Intercepts, domain, range, vertex (maximum or minimum), axis of symmetry.

• Graphing: Plotting parabolas and identifying key features.

• Applications: Modeling real-world problems with quadratic functions.

Example: Solve by factoring. Solution: .

Grading Standards

Letter Grades and Percent Ranges

The following table summarizes the grading scale for the course:

For Pass/No Pass grading:

Course Policies and Expectations

Attendance and Participation

• Attendance in all scheduled classes is mandatory.

• Three or more unexcused absences may result in withdrawal or a failing grade.

• Active participation and timely completion of assignments are expected.

Academic Integrity

• All submitted work must be original and completed without unauthorized assistance.

• Plagiarism and use of generative AI tools (unless specifically permitted) are considered academic misconduct.

Technology and Materials

• Access to a computer, internet, and a graphing calculator is required.

• Textbook: Elementary & Intermediate Algebra: Concepts (8th edition, Bittinger).

Additional Information

• Support services, including tutoring and technology help, are available to all students.

• Accommodations for students with disabilities are provided through the Disability Resources and Services Office.

• Students are expected to comply with all college policies regarding conduct, safety, and academic procedures.

Additional info: This study guide is based on the official course syllabus and competencies for MAT 114: College Algebra Prep. For detailed examples, practice problems, and further explanations, refer to the required textbook and class lectures.