College Algebra (MATH 1000) Syllabus and Topic Outline Study Guide

Course Information

Overview

This course, MATH 1000 - Algebra for College Students, is designed to provide students with a full range of algebraic skills necessary for college-level mathematics. It covers fundamental concepts, applications, and problem-solving strategies in algebra.

• Course Title: Algebra for College Students

• Credit Hours: 3.0

• Semester: Fall 2025

• Instructor: Mario Faustino Nunez

• Location: Mailman/Hollywood-311

Course Description

Purpose and Scope

This course is intended to equip students with a full range of algebraic skills. Topics include graphs of functions and relations; linear, quadratic, exponential, and radical expressions; linear, quadratic, and rational functions; absolute value and radical functions; properties and graphs of exponential and logarithmic expressions; and related applications. Pre-requisite: MyMathTest Challenge Exam Level 2 score of 80, or MATH 1000A.

• Key Topics: Linear, quadratic, exponential, and radical expressions and functions

• Applications: Real-world problem solving, graphing, and mathematical modeling

Course Objectives / Learning Outcomes

Expected Skills and Competencies

Upon successful completion of this course, students will be able to:

1. Demonstrate an ability to graph exponential, logarithmic, radical, and rational functions and/or relations.

2. Solve problems involving exponential and logarithmic equations, equations involving rational, radical, and quadratic expressions.

3. Demonstrate an ability to add, subtract, multiply, and divide rational and radical expressions, solve and graph exponential and logarithmic equations, and solve radical and quadratic equations.

4. Simplify complex expressions and solve equations using algebraic techniques.

Course Schedule and Topic Outline

Weekly Breakdown

The following is a week-by-week outline of topics covered in the course:

Week	Date	Topics
1	8/18-8/22	Syllabus, Basic Algebra, Chapter 5.1
2	8/25-8/29	Ch 5.2, Ch 5.3, Ch 5.4
3	9/02-9/05	Ch 5.5, Ch 5.6, Ch 5.8
4	9/08-9/12	Recap and Review Ch 5
5	9/15-9/19	Ch 6.1, Ch 6.2, Ch 6.3
6	9/22-9/26	Ch 6.4, Ch 6.5, Ch 6.6
7	9/29-10/03	Ch 6.7, Ch 6.8, Review Ch 6
8	10/06-10/10	Midterm Exam Ch 5 & Ch 6
9	10/13-10/17	Ch 7.1, Ch 7.2, Ch 7.3
10	10/20-10/24	Ch 7.4, Ch 7.5, Ch 7.6
11	10/27-10/31	Ch 7.7, Recap/Review Ch 7
12	11/03-11/07	Ch 8.1, Ch 8.2, Ch 8.3
13	11/10-11/14	Ch 8.4, Ch 8.5
14	11/17-11/21	Ch 8.6, Ch 8.7
15	11/24-11/28	Ch 8.8, Ch 8.9
16	Final Exam Week	Final Exam: Ch 5 - Ch 8

Detailed Topic Outline

• 5.1 Rational Expressions, Equations and Functions

• 5.2 Rational Expressions and Functions: Multiplying, Dividing and Simplifying

• 5.3 Adding, LCDs, and Subtracting

• 5.4 Simplifying Complex Expressions

• 5.5 Rational Equations

• 5.6 Applications

• 5.8 Graphs of Rational Equations and Functions

• 6.1 Radical Expressions, Equations and Functions

• 6.2 Radical Expressions and Functions: Multiplying, Dividing and Simplifying

• 6.3 Adding, LCDs, and Subtracting

• 6.4 Simplifying Complex Expressions

• 6.5 Radical Equations

• 6.6 Applications

• 6.7 Graphs of Radical Equations and Functions

• 6.8 The Radical Function

• 7.1 Quadratic Equations and Functions

• 7.2 The Quadratic Formula

• 7.3 Completing the Square

• 7.4 Graphs of Quadratic Equations and Functions

• 7.5 Applications

• 7.6 The Discriminant

• 7.7 More on Quadratic Equations

• 8.1 Exponential Functions and Logarithmic Functions

• 8.2 Properties of Exponents

• 8.3 Properties of Logarithms

• 8.4 Solving Exponential and Logarithmic Equations

• 8.5 Applications

• 8.6 Graphs of Exponential and Logarithmic Functions

• 8.7 More on Exponential and Logarithmic Functions

• 8.8 Exponential Growth and Decay

• 8.9 Applications

Assessment and Grading Criteria

Assessment Methods

• Online quizzes and assignments (via MyMathLab)

• Midterm and final exams

• Participation and learning activities

Grading Breakdown

Component	Percentage
Participation/Learning Activities	10%
Homework	20%
Quizzes	25%
Midterm Exam	20%
Final Exam	25%

Grading Scale

Score (%)	Letter Grade
93-100	A
90-92	A-
87-89	B+
83-86	B
80-82	B-
77-79	C+
73-76	C
70-72	C-
67-69	D+
63-66	D
60-62	D-
Below 60	F

Key Algebraic Concepts and Formulas

Rational Expressions and Equations

Rational expressions are fractions in which the numerator and/or denominator are polynomials. Key operations include addition, subtraction, multiplication, division, and simplification.

• Definition: A rational expression is any expression that can be written as $\frac{P(x)}{Q(x)}$, where $Q(x) \neq 0$.

• Example: $\frac{2x+3}{x^2-1}$

• Key Formula: To add rational expressions: $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$

Radical Expressions and Equations

Radical expressions involve roots, such as square roots or cube roots. Simplifying and solving radical equations are essential skills.

• Definition: A radical expression contains a root symbol, such as $\sqrt{x}$ or $\sqrt[3]{x}$.

• Example: $\sqrt{16} = 4$

• Key Formula: $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$

Quadratic Equations and Functions

Quadratic equations are second-degree polynomial equations. Their graphs are parabolas, and they can be solved by factoring, completing the square, or using the quadratic formula.

• Standard Form: $ax^2 + bx + c = 0$

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Vertex Form: $y = a(x-h)^2 + k$

• Example: Solve $x^2 - 5x + 6 = 0$ by factoring: $(x-2)(x-3) = 0$ so $x=2$ or $x=3$

Exponential and Logarithmic Functions

Exponential functions have the form $f(x) = a^x$, and logarithmic functions are their inverses. These functions model growth and decay in real-world applications.

• Exponential Function: $f(x) = a^x$

• Logarithmic Function: $f(x) = \log_a(x)$

• Properties: $\log_a(ab) = \log_a(a) + \log_a(b)$

• Example: $\log_{10}(100) = 2$

Applications

Algebraic concepts are applied in solving real-world problems, such as calculating interest, modeling population growth, and analyzing data.

• Exponential Growth: $N(t) = N_0 e^{rt}$

• Quadratic Applications: Projectile motion, area problems

Course Policies and Academic Integrity

Expectations

• Students must adhere to university policies regarding attendance, academic honesty, and use of generative AI tools.

• Plagiarism and academic dishonesty are strictly prohibited.

• Students are expected to participate actively and complete assignments on time.

Additional info:

• Some details about university policies, support services, and use of generative AI tools were inferred for completeness and context.

• Topic outline and grading scale were reconstructed from the syllabus images and may include logical groupings for clarity.