MAC 1105 College Algebra – Course Syllabus and Core Topics Study Guide

Course Overview

This study guide summarizes the key information and academic content from the MAC 1105 College Algebra syllabus at Hillsborough Community College. The course provides foundational algebraic knowledge essential for further study in mathematics, engineering, business, science, and technology. The curriculum emphasizes equations, inequalities, functions, graphs, and real-world applications.

Core Course Topics

1. Equations and Inequalities

Students will learn to solve a variety of equations and inequalities using appropriate algebraic techniques.

• Quadratic Equations: Equations of the form $ax^2 + bx + c = 0$. Methods include factoring, completing the square, and the quadratic formula. Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Radical Equations: Equations involving roots, such as $\sqrt{x} = a$.

• Polynomial Equations: Equations involving polynomials of degree greater than two.

• Absolute Value Equations and Inequalities: Equations such as $|x| = a$ and inequalities like $|x| < a$.

• Systems of Linear Equations: Solving systems in three variables using elimination or substitution.

• Systems of Non-linear Inequalities: Includes quadratic and rational functions, solved graphically or analytically.

• Exponential and Logarithmic Equations: Equations involving exponents and logarithms, such as $a^x = b$ or $\log_a(x) = b$.

2. Functions and Their Properties

Understanding the definition, properties, and graphical representation of functions is central to college algebra.

• Relations and Functions: A function is a relation where each input has exactly one output.

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

• Function Notation: Expressed as $f(x)$, indicating the output for input $x$.

• Difference Quotient: Used to compute the average rate of change: $\frac{f(x+h) - f(x)}{h}$

• Linear Functions: Functions of the form $f(x) = mx + b$; applications include modeling real-world scenarios.

• Graph Characteristics: Includes symmetry, extrema (maximum and minimum points), and intervals of increase, decrease, or constancy.

• Graphing Quadratic and Polynomial Functions: Focus on end behavior and multiplicity of zeros.

• Graphing Rational Functions: Identify intercepts, vertical/horizontal asymptotes, and end behavior.

• Graphing Exponential and Logarithmic Functions: Understanding their unique shapes and properties.

3. Manipulating Functions

Students will perform operations with functions and explore new functions derived from existing ones.

• Operations with Functions: Addition, subtraction, multiplication, division, and composition of functions.

• Inverse Functions: Finding the inverse algebraically and graphically. If $f(g(x)) = x$, then $g(x)$ is the inverse of $f(x)$.

• Exponential and Logarithmic Forms: Converting between $a^x = b$ and $x = \log_a(b)$.

• Evaluating Expressions: Calculating values for logarithmic and exponential expressions.

• Properties of Logarithms: Including the change of base formula: $\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$

4. Transformations of Functions

Graphical transformations allow students to write equations for functions and graph them efficiently.

• Basic Functions: $y = c$, $y = x$, $y = |x|$, $y = x^2$, $y = x^3$, $y = \frac{1}{x}$, $y = \sqrt{x}$, $y = \sqrt[3]{x}$

• Graphical Transformations: Includes translations, reflections, stretches, and compressions.

5. Applications and Modeling

Students will apply algebraic concepts to solve real-world problems.

• Optimization Problems: Using quadratic functions to find maximum or minimum values in applied contexts.

• Rational Function Applications: Solving problems involving rates, mixtures, and proportions.

• Exponential Growth and Decay: Modeling population growth, radioactive decay, and similar phenomena.

• Systems of Equations Applications: Solving real-world problems using systems of equations.

Course Structure and Grading

Graded Assignments and Weights

The following table summarizes the assignments and their contribution to the final grade:

Assignment	Percentage of Grade	Delivery Method
Homework average (drop lowest 4 scores)	20%	MyMathLab
Quiz average (drop lowest 2 scores)	20%	MyMathLab
Exam 1	15%	Canvas using Honorlock
Exam 2	15%	Canvas using Honorlock
Exam 3	15%	Canvas using Honorlock
Exam 4	15%	Canvas using Honorlock
Total	100%
Extra credit	5%	Canvas

Grading Scale

Grade	Percentage
A	>90%
B	80%-89.99%
C	70%-79.99%
D	60%-69%
F	<60%

Course Materials and Technology

• Textbook: College Algebra Essentials (6th edition) by Blitzer

• Online Platform: MyMathLab for homework and quizzes

• Calculator: Not required; only the on-screen calculator in Honorlock is allowed during proctored exams

Academic Policies and Support

• Academic Integrity: Cheating, plagiarism, and other forms of dishonesty are prohibited.

• Withdrawal Policy: Students are responsible for understanding withdrawal deadlines and procedures.

• Disability Services: Accommodations are available through the Office of Services for Students with Disabilities (OSSD).

• Student Services: Counseling, library, and other support services are available.

Tentative Semester Schedule

The course is organized by sections from the textbook, with exams interspersed throughout the term. Key sections include:

• Sections P.5-1.5: Prerequisites and Fundamental Concepts

• Sections 1.6-1.7: Equations and Inequalities

• Sections 2.1-2.8: Functions and Graphs

• Sections 3.1-3.5: Polynomial and Rational Functions

• Sections 4.1-4.4: Exponential and Logarithmic Functions

Contact and Support

• Instructor: Diego Grilli (contact via Canvas inbox for appointments)

• Office: SMPF 121

• Email: [e-mail]

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