Course Overview

This study guide summarizes the syllabus and core learning outcomes for UNLV Math 124: College Algebra. The course covers foundational and advanced algebraic concepts, including functions, equations, inequalities, systems, matrices, conic sections, sequences, and combinatorics. The guide is structured by main textbook chapters and includes key definitions, skills, and sample applications.

Just In Time Chapter: Basic Concepts of Algebra

Algebraic Foundations

• Laws of Exponents: Rules for manipulating exponents, such as and .

• Order of Operations: PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

• Arithmetic Skills: Fluency with fractions, decimals, percentages, and integers.

• Algebraic Expressions: Simplifying and evaluating expressions using substitution and algebraic manipulation.

• Polynomials and Rational Expressions: Addition, subtraction, multiplication, division, and factoring.

• Radicals and Rational Exponents: Simplifying and solving equations involving roots and fractional exponents.

Example:

Simplify .

Chapter 1: Graphs, Functions, and Models

Lines and Their Properties

• Length of a Segment:

• Midpoint Formula:

• Graphing Lines: Using slope-intercept form or point-slope form .

• Parallel and Perpendicular Lines: Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals.

Functions and Domains

• Domain: The set of all possible input values (x-values) for a function. For rational functions, exclude values that make the denominator zero; for square roots, exclude values that make the radicand negative.

• Graphing: Plotting points and understanding the shape of functions.

Linear Inequalities

• Solving Linear Inequalities: Manipulate algebraically and represent solutions on a number line.

Example:

Find the equation of a line passing through (2, 3) and (4, 7): Slope Equation:

Chapter 2: More on Functions

Piecewise and Composite Functions

• Piecewise Functions: Functions defined by different expressions for different intervals of the domain.

• Composition: ; domain is restricted by both and .

Even and Odd Functions

• Even Function: for all in the domain.

• Odd Function: for all in the domain.

Example:

Let (even), (odd).

Chapter 3: Quadratic Functions and Equations; Inequalities

Quadratic Equations and Graphs

• Roots of Quadratic: solved by factoring, completing the square, or quadratic formula:

• Graph Characteristics: Direction (up/down), axis of symmetry , vertex , roots, y-intercept.

• Maximum/Minimum: Vertex gives max/min value depending on .

Solving Equations and Inequalities

• Rational and Radical Equations: Isolate variable, check for extraneous solutions.

• Linear Inequalities with Absolute Value: leads to two inequalities.

Example:

Solve : Factor: Roots:

Chapter 4: Polynomial Functions and Rational Functions

Polynomials: End Behavior and Division

• End Behavior: Determined by the leading term; as , .

• Long/Synthetic Division: Used to divide polynomials by binomials.

Solving Inequalities

• Polynomial Inequalities: Find zeros, test intervals.

• Rational Inequalities: Set numerator and denominator to zero, test intervals.

Example:

Divide by using synthetic division.

Chapter 5: Exponential Functions and Logarithmic Functions

Exponential and Logarithmic Equations

• Inverse Functions: reverses the effect of .

• Exponential to Logarithmic Form:

• Solving Equations: Use properties of exponents and logarithms.

• Half-Life/Doubling Time: For exponential models , half-life .

Example:

Solve :

Chapter 6: Systems of Equations and Matrices

Solving Systems

• Systems of Linear Equations: Solve using substitution, elimination, or matrix methods.

• Augmented Matrix: Row-echelon form reveals solutions.

Example:

Solve system: Solution:

Chapter 7: Conic Sections

Nonlinear Systems and Conic Sections

• Conic Sections: Circles, ellipses, parabolas, hyperbolas defined by quadratic equations.

• Solving Nonlinear Systems: Use substitution or elimination with at least one nonlinear equation.

Example:

Circle:

Chapter 8: Sequences, Series, and Combinatorics

Recursive Sequences

• Recursive Formula: Defines each term based on previous terms, e.g., for arithmetic sequence.

• Writing Terms: Use the formula to generate sequence values.

Example:

Given , , find : ,

Corequisite Material Learning Outcomes

Algebraic Manipulation and Graphs

• Exponent Laws: Apply rules for simplifying expressions.

• Arithmetic Operations: Compute with fractions, decimals, percentages, and integers.

• Polynomials: Add, subtract, multiply, divide, and factor.

• Radicals: Simplify and solve equations with roots and rational exponents.

• Graphs: Create and interpret various types; identify Cartesian components.

Evaluation and Grading

Assessment Breakdown

Letter Grade Scale

Course Policies and Resources

• Academic Integrity: Zero tolerance for dishonesty; see university policy.

• Attendance: Mandatory for all on-campus classes.

• Calculator Policy: Only non-programmable, non-graphing scientific calculators allowed during tests and exams.

• Homework and Quizzes: Assigned and graded online via Pearson MyLab and Mastering.

• Testing: Three tests and a cumulative final exam.

• Tutoring: Available through the Department of Mathematical Sciences and Academic Success Center.

Summary Table: Main College Algebra Topics

Additional info: This guide expands brief syllabus points into full academic context, including formulas, examples, and tables for clarity and completeness.