College Algebra (MAC 1105) Syllabus and Study Guide

Course Overview

Introduction

This syllabus outlines the structure, objectives, policies, and schedule for College Algebra (MAC 1105) at Pasco-Hernando State College. The course is designed to develop problem-solving skills, critical thinking, and computational proficiency through the study of algebraic functions and their graphs, equations and inequalities, and related topics. The content is highly relevant to Precalculus, covering foundational concepts necessary for further study in mathematics.

Main Topics Covered

1. Functions and Their Graphs

Functions are a central concept in algebra and precalculus, representing relationships between variables. Understanding their properties and graphical representations is essential for analyzing mathematical models.

• Definition: A function is a relation in which each input (domain) has exactly one output (range).

• Types of Functions: Linear, quadratic, polynomial, rational, exponential, and logarithmic.

• Graphing: Functions can be represented visually on the Cartesian plane, showing how the output changes with the input.

• Example: The function $f(x) = x^2$ is a quadratic function whose graph is a parabola opening upwards.

2. Quadratic Functions

Quadratic functions are polynomial functions of degree two and are fundamental in algebraic problem solving.

• Standard Form: $f(x) = ax^2 + bx + c$

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

• Factoring and Solving: Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula:

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

• Applications: Used in modeling projectile motion, optimization problems, and more.

3. Exponential and Logarithmic Functions

Exponential and logarithmic functions are used to model growth and decay, and to solve equations involving exponents and logarithms.

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

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

• Properties: Laws of exponents and logarithms are essential for simplifying expressions and solving equations.

• Example: Population growth can be modeled by $P(t) = P_0 e^{rt}$

4. Modeling and Curve Fitting

Mathematical modeling involves using functions to represent real-world phenomena. Curve fitting is the process of finding a function that best fits a set of data points.

• Linear Models: $y = mx + b$

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

• Applications: Used in statistics, economics, biology, and engineering to predict trends and analyze data.

5. Solving Systems of Equations and Inequalities

Systems of equations and inequalities involve finding values that satisfy multiple equations or inequalities simultaneously.

• Methods: Substitution, elimination, and graphical methods.

• Example: Solve the system:

  • $x + y = 5$

  • $x - y = 1$

  • Solution: $x = 3$, $y = 2$

• Applications: Used in business, science, and engineering to solve problems involving multiple constraints.

Course Structure and Policies

Grading Policy

• Chapter Tests: 75%

• Final Exam: 15%

• Homework Assignments: 10%

Grading Scale

Grade	Percentage
A	90 – 100%
B	80 – 89%
C	70 – 79%
D	60 – 69%
F	Below 59%

Course Schedule (Sample)

Class Day	Lecture Sections	Assignment Due Dates
1	Orientation, 5.2-7.1	All MyLab Math HW due 8:00 AM on test day
2	2.1, 2.2
3	2.3, 2.4
4	2.5, 2.6
5	2.7, 2.8
6	TEST 1 (2.1-2.8)	HW due
...	...	...

Course Policies

• Attendance: Regular attendance and participation are required.

• Homework: Assignments are given with deadlines; completion is essential for success.

• Exams: No make-up exams except for documented emergencies.

• Academic Integrity: Cheating and plagiarism are strictly prohibited.

• Use of AI: Submitting AI-generated work is not permitted.

Study Tips

• Organize your workspace and priorities.

• Use a planner and to-do lists to manage assignments.

• Break study time into manageable sessions.

• Seek help from free tutoring services if needed.

• Review notes and homework regularly to reinforce learning.

Additional Information

• Accessibility services are available for students with disabilities.

• Important college dates and withdrawal policies are outlined in the syllabus.

• Course materials include MyLab Math access code and a scientific calculator (TI-30XS recommended).

Additional info: The syllabus provides a comprehensive overview of the course structure, expectations, and resources, ensuring students are well-prepared for College Algebra and subsequent Precalculus topics.