College Algebra (MAC 1105) Syllabus and Study Guide

Course Overview

This syllabus outlines the structure, objectives, and policies for College Algebra (MAC 1105) at Pasco-Hernando State College. The course covers foundational algebraic concepts essential for Precalculus, including functions, equations, inequalities, and their applications.

Course Objectives and Learning Outcomes

• Develop knowledge and problem-solving skills in:

  • Functions and their graphs

  • Quadratic functions

  • Exponential and logarithmic functions

  • Modeling and curve fitting

  • Systems of equations and inequalities

Major Topics Covered

Functions and Graphs

Functions are mathematical relationships that assign each input exactly one output. Understanding their properties and graphical representations is fundamental in algebra.

• Definition: A function is a relation in which each element of the domain is paired with exactly one element of the range.

• Notation: $f(x)$ denotes a function named f with input x.

• Graphing: The graph of a function is the set of all points $(x, f(x))$ in the coordinate plane.

• Example: $f(x) = 2x + 3$ is a linear function whose graph is a straight line.

Quadratic Functions

Quadratic functions are polynomials of degree two and are central to algebraic modeling and problem-solving.

• Standard Form: $f(x) = ax^2 + bx + c$, where $a \neq 0$.

• Vertex: The vertex of the parabola is at $x = -\frac{b}{2a}$.

• Axis of Symmetry: The line $x = -\frac{b}{2a}$ divides the parabola into two mirror images.

• Example: $f(x) = x^2 - 4x + 3$ has vertex at $x = 2$.

Exponential and Logarithmic Functions

These functions model growth and decay processes and are widely used in science and finance.

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

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

• Properties: $\log_b(b^x) = x$ and $b^{\log_b(x)} = x$.

• Example: $f(x) = 2^x$ is an exponential function; $g(x) = \log_2(x)$ is its inverse.

Modeling and Curve Fitting

Mathematical models use algebraic functions to represent real-world phenomena. Curve fitting involves finding the function that best fits a set of data points.

• Linear Models: $y = mx + b$

• Quadratic Models: $y = ax^2 + bx + c$

• Exponential Models: $y = ab^x$

• Application: Predicting population growth, financial investments, or physical processes.

Systems of Equations and Inequalities

Systems involve solving for multiple variables using two or more equations or inequalities.

• Linear Systems: Two or more linear equations solved simultaneously.

• Methods: Substitution, elimination, and graphical methods.

• Example: Solve $\begin{cases} x + y = 5 \\ x - y = 1 \end{cases}$

• Inequalities: Solutions are often represented as regions on the coordinate plane.

Course Policies and Structure

Grading Policy

• Homework: 10%

• Quizzes: 10%

• Tests: 40% (4 tests, each weighted 10%)

• Final Exam (proctored): 40%

Grading Scale:

Grade	Percentage
A	95.5% - 100%
B	85.5% - 95.4%
C	75% - 84%
D	59.5% - 74%
F	Below 59.5%

Calculator Policy

• Approved scientific calculators (e.g., TI-30XS) are required.

• Graphing calculators, cell phones, and smartwatches are not allowed during assessments.

Assessment Methods

• Online homework, quizzes, and tests via MyLabMath.

• Proctored tests and final exam on campus.

• Multiple attempts allowed for quizzes; highest score counts.

Academic Integrity

• Cheating and plagiarism are strictly prohibited.

• Use of AI-generated content without permission is not allowed.

• Refer to the syllabus for detailed examples of academic dishonesty.

Course Materials

• Required Textbook: Algebra and Trigonometry (7th Edition), Robert Blitzer, Pearson, 2022.

• MyLab Math Student Access required for assignments and assessments.

Study Strategies

• Spend approximately 6-9 hours per week on coursework.

• Organize study time and use provided resources (notes, videos, tutoring).

• Complete all assignments and assessments on time.

Course Schedule (Sample)

Week	Topics	Assignments	Assessments
1	Functions and Graphs	Homework 1	Quiz 1
2	Quadratic Functions	Homework 2	Quiz 2
3	Exponential and Logarithmic Functions	Homework 3	Quiz 3
4	Modeling and Curve Fitting	Homework 4	Quiz 4
5	Systems of Equations and Inequalities	Homework 5	Quiz 5
6-7	Review and Testing	Review Assignments	Tests/Final Exam

Additional info: The actual course schedule may include more detailed weekly breakdowns and specific due dates as provided in the course management system.