College Algebra (MAC 1105) Syllabus and Topic Overview

Course Overview

This study guide summarizes the key topics, structure, and expectations for MAC 1105: College Algebra, as outlined in the course syllabus. The course focuses on foundational algebraic concepts, equations, functions, and their applications, preparing students for further study in mathematics.

Course Description and Objectives

• Algebra is the language used to describe relationships between numbers and to solve for unknowns.

• The course emphasizes formalizing algebraic reasoning, using variables, and communicating mathematical ideas efficiently.

• Students will use technology (e.g., MyMathLab) for practice and feedback.

Student Learning Outcomes

• Develop understanding of variables and their relationships.

• Distinguish between expressions and equations.

• Solve various types of equations and systems of equations.

• Define and explore functions, their graphs, and properties.

• Interpret information from graphs.

Major Topics Covered

• Equations and Inequalities

• Functions and Graphs

• Polynomial and Rational Functions

• Exponential and Logarithmic Functions

• Systems of Equations

• Applications and Mathematical Modeling

Weekly Topic Schedule (Selected Highlights)

Week	Main Topics (Blitzer Sections)
1	Functions (2.1), Functional Notation, Domain and Range
2	Graphs of Functions, Properties of Functions (2.2)
3	Graphing Techniques (2.5)
4	Piecewise Functions, Average Rate of Change
5	Quotient and Composition of Functions, Difference Quotient
6	Quadratic Functions and Their Graphs, Mathematical Models
7	Rational Functions: Domain, Asymptotes, and Graphs
8	Solving Polynomial and Rational Inequalities
9	One-to-One and Inverse Functions
10-13	Exponential and Logarithmic Functions, Properties, Equations, and Modeling
13	Midpoint and Distance Formulas, Circles
14	Systems of Non-Linear Equations, Quadratics over Imaginary Numbers

Key Concepts and Definitions

Variables and Expressions

• Variable: A symbol (often a letter) representing an unknown value.

• Expression: A mathematical phrase involving numbers, variables, and operations (e.g., $2x + 5$).

Equations and Inequalities

• Equation: A statement that two expressions are equal (e.g., $2x + 5 = 11$).

• Inequality: A statement comparing two expressions using $<, >, \leq, \geq$ (e.g., $x + 3 > 7$).

• Solving: Finding all values of the variable that make the equation or inequality true.

Functions and Graphs

• Function: A relation that assigns exactly one output to each input.

• Domain: The set of all possible input values ($x$) for a function.

• Range: The set of all possible output values ($f(x)$).

• Functional Notation: $f(x)$ denotes the value of function $f$ at input $x$.

• Graph: A visual representation of a function in the coordinate plane.

Polynomial and Rational Functions

• Polynomial Function: A function of the form $f(x) = a_n x^n + \ldots + a_1 x + a_0$.

• Rational Function: A function of the form $f(x) = \frac{P(x)}{Q(x)}$, where $P$ and $Q$ are polynomials and $Q(x) \neq 0$.

• Asymptote: A line that the graph of a function approaches but never touches.

Exponential and Logarithmic Functions

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

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

• Properties of Logarithms:

  • $\log_a (xy) = \log_a x + \log_a y$

  • $\log_a \left(\frac{x}{y}\right) = \log_a x - \log_a y$

  • $\log_a (x^r) = r \log_a x$

Systems of Equations

• System of Equations: A set of two or more equations with the same variables.

• Solution: A set of values that satisfies all equations in the system.

Assessment and Grading

Component	Weight
Final Exam	30%
Tests	40%
Math Gym	10%
MML Homework	10%
MML Quizzes	10%

Letter Grade Scale

Letter Grade	Score Range
A	93 and above
A-	89-92
B+	86-88
B	83-85
B-	79-82
C+	75-78
C	70-74
D	60-69
F	0-59

Course Materials

• Textbook: Algebra and Trigonometry (8th ed.) by Blitzer, Pearson, 2026.

• Chapters covered: 1, 2, 3, 4.

• Access to MyMathLab is required for assignments and quizzes.

Success Tips

• Stay organized: Keep notes by topic and date.

• Use all resources: Textbook, videos, instructors, and learning assistants.

• Form study groups for collaborative learning.

• Regularly review the course schedule and complete assignments on time.

Additional Info

• This course satisfies the University Core Curriculum Mathematics requirement.

• Emphasis is placed on problem-solving, critical thinking, and mathematical modeling.