Math 130 College Algebra Syllabus – Key Topics and Study Guide

Course Overview

This syllabus outlines the structure and content of a College Algebra course, which serves as a foundational component of Precalculus. The course covers essential algebraic concepts, functions, and their applications, preparing students for further study in mathematics.

Course Description and Goals

• Course Description: In-depth treatment of solving equations and inequalities, function properties and graphs, inverse functions, polynomial, rational, exponential, and logarithmic functions, and applications.

• Course Goal: Equip students with mathematical skills to model and solve real-world problems, and prepare for further coursework in mathematics and related fields.

Prerequisites

• Completion of Math 128 with a minimum grade of “C” or appropriate placement test scores.

Course Objectives

Upon completion, students should be able to:

• Solve equations and inequalities, including linear, quadratic, and rational forms.

• Analyze and graph functions, including polynomial, rational, exponential, and logarithmic functions.

• Understand and apply function operations, inverses, and compositions.

• Model and solve real-world problems using algebraic methods.

• Communicate mathematical reasoning effectively.

Major Topics and Weekly Outline

Week	Topics
1	Review of basic and literal equations
2	Linear equations and inequalities
3	Quadratic equations and inequalities
4	Functions and their properties
5	Polynomial functions and graphs
6	Rational functions
7	Exponential and logarithmic functions
8	Systems of equations
9	Sequences and series

Key Concepts and Definitions

Equations and Inequalities

• Linear Equation: An equation of the form $ax + b = 0$.

• Quadratic Equation: An equation of the form $ax^2 + bx + c = 0$.

• Rational Equation: An equation involving rational expressions.

• Inequality: A mathematical statement that relates expressions using $<, >, \leq, \geq$.

Functions and Graphs

• Function: A relation where each input has exactly one output. Notation: $f(x)$.

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

• Inverse Function: If $f(x)$ is a function, its inverse $f^{-1}(x)$ satisfies $f(f^{-1}(x)) = x$.

• Composition: $(f \circ g)(x) = f(g(x))$.

Polynomial and Rational Functions

• Polynomial Function: $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_0$.

• Rational Function: $f(x) = \frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are polynomials and $q(x) \neq 0$.

Exponential and Logarithmic Functions

• Exponential Function: $f(x) = a^x$, $a > 0$, $a \neq 1$.

• Logarithmic Function: $f(x) = \log_a x$, the inverse of the exponential function.

• Properties: $\log_a (xy) = \log_a x + \log_a y$; $\log_a (x^k) = k \log_a x$.

Systems of Equations

• System of Equations: A set of equations with the same variables, solved simultaneously.

• Methods: Substitution, elimination, and matrix methods.

Sequences and Series

• Sequence: An ordered list of numbers, often defined recursively or explicitly.

• Series: The sum of the terms of a sequence.

• Arithmetic Sequence: $a_n = a_1 + (n-1)d$.

• Geometric Sequence: $a_n = a_1 r^{n-1}$.

Assessment and Grading

• Grades are based on homework, quizzes, exams, and a final exam.

• Standard 10-point grading scale is used (A: 90–100, B: 80–89, etc.).

Additional Information

• Academic honesty is strictly enforced.

• Attendance and participation are required for success.

• Support resources include the Math Learning Center and online materials.

Additional info: This syllabus provides a comprehensive overview of College Algebra, which is a core component of Precalculus. The topics align with standard Precalculus curricula and prepare students for further mathematical study.