College Algebra

Course Description

MAC1105 / MAC1105C – College Algebra is a 3-credit lecture course in the Mathematics: Calculus and Pre-Calculus taxonomy of Florida's Statewide Course Numbering System (SCNS). The course is the foundational college-level mathematics course at Florida public colleges and universities and is part of the state-mandated General Education Core in Mathematics, satisfying the Gen-Ed math requirement at every Florida public institution. Students develop proficiency with linear, polynomial, rational, exponential, and logarithmic functions; their graphs and applications; the solution of equations, inequalities, and systems of equations; and the modeling of real-world situations using algebraic functions.

MAC1105 is offered at 55 Florida public institutions and transfers as equivalent across the state. The "C" suffix variant denotes integrated lecture and supplemental instruction or co-requisite support; both forms count for the same Gen-Ed core credit. The course satisfies the prerequisite for trigonometry (MAC1114), pre-calculus (MAC1140 / MAC1147), business calculus (MAC2233), and Calculus I (MAC2311) pathways. Most Florida institutions adopt Pearson MyLab Math (MyMathLab) or McGraw-Hill ALEKS as the required online homework platform.

Learning Outcomes

Required Outcomes

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

• Solve equations and inequalities in one variable, including linear, quadratic, polynomial, rational, radical, absolute value, exponential, and logarithmic equations and inequalities.
• Define and analyze functions, including identifying domain and range, evaluating functions, performing algebra of functions, finding inverses, and recognizing one-to-one functions.
• Graph functions including linear, quadratic, cubic, absolute value, radical, piecewise, polynomial, rational, exponential, and logarithmic functions.
• Apply function transformations, including vertical and horizontal shifts, reflections, and stretches/shrinks, to graph and analyze functions.
• Apply properties of exponents and logarithms to simplify expressions and solve exponential and logarithmic equations.
• Solve systems of equations and inequalities, including linear systems in two and three variables and nonlinear systems.
• Apply algebraic methods to model and solve real-world problems, including problems involving rates of change, growth and decay, and optimization.
• Find zeros and key features of polynomial functions, including identifying maxima/minima, end behavior, and rational zeros.
• Use a graphing calculator proficiently to analyze functions, find intersections, and verify analytical solutions.

Optional Outcomes

Depending on institutional emphasis, students may also:

• Operate with complex numbers, including arithmetic, conjugates, and identifying complex roots of polynomial equations.
• Apply matrix methods (Gaussian elimination, matrix inverses) to solve linear systems.
• Analyze conic sections (parabolas, circles, ellipses, hyperbolas) and write equations in standard form.
• Apply concepts of arithmetic and geometric sequences and series.
• Use computational tools (Desmos, GeoGebra) for advanced graphical analysis.

Major Topics

Required Topics

• Equations and Inequalities: Linear equations and inequalities; absolute value equations and inequalities; quadratic equations (factoring, completing the square, quadratic formula); rational equations; radical equations; interval and set-builder notation; applications.
• Functions and Graphs: Definition of function; domain and range; function notation; difference quotient; symmetry (even/odd functions); piecewise functions; algebra of functions (sum, difference, product, quotient, composition); inverse functions and one-to-one functions.
• Linear Functions: Slope and rate of change; slope-intercept and point-slope forms; parallel and perpendicular lines; modeling with linear functions; linear regression (calculator-based).
• Quadratic Functions: Standard form and vertex form; vertex, axis of symmetry, intercepts; maximum and minimum values; modeling and optimization problems.
• Polynomial Functions: End behavior; turning points; zeros (Rational Zero Theorem, Descartes' Rule of Signs); polynomial division; the Factor Theorem and the Remainder Theorem; graphing higher-degree polynomials.
• Rational Functions: Domain restrictions; vertical, horizontal, and oblique asymptotes; intercepts; graphing rational functions; rational inequalities.
• Function Transformations: Vertical and horizontal shifts; reflections across x and y axes; vertical and horizontal stretches/shrinks; combining transformations.
• Exponential Functions: Definition and graphs; the natural exponential function (e^x); compound interest formulas (discrete and continuous); exponential growth and decay applications.
• Logarithmic Functions: Definition as inverse of exponential; common and natural logarithms; properties of logarithms (product, quotient, power rules); change-of-base formula; graphing logarithmic functions.
• Exponential and Logarithmic Equations: Solving equations using logarithm properties; applications to growth, decay, pH, decibels, magnitude scales.
• Systems of Equations and Inequalities: Linear systems in two variables (substitution, elimination, graphing); linear systems in three variables; nonlinear systems; systems of linear inequalities and graphing.

Optional Topics

• Complex Numbers: Imaginary unit and complex arithmetic; complex conjugates; complex roots of polynomial equations; the Fundamental Theorem of Algebra.
• Matrices and Determinants: Matrix arithmetic; row operations; Gaussian and Gauss-Jordan elimination; matrix inverses; Cramer's rule.
• Conic Sections: Circles (center-radius form); parabolas; ellipses; hyperbolas.
• Sequences and Series: Arithmetic and geometric sequences; sums of finite arithmetic and geometric series; introduction to infinite geometric series.
• Mathematical Modeling: Extended applications using regression and curve-fitting on the graphing calculator.

Resources & Tools

• Standard Textbooks: College Algebra by Blitzer (Pearson, widely used statewide); College Algebra by Ratti, McWaters, and Skrzypek (Pearson); College Algebra by Stewart, Redlin, and Watson (Cengage); OpenStax College Algebra (free, openstax.org)
• Online Homework Platforms: Pearson MyLab Math (MyMathLab) — most common; McGraw-Hill ALEKS — used by some institutions, including UF; WebAssign at others. Online platforms typically include adaptive learning, video lessons, and immediate feedback.
• Required Calculator: Texas Instruments TI-83 Plus, TI-84 Plus, or TI-84 Plus CE graphing calculator (most institutions). Some institutions allow TI-89 or TI-Nspire CX CAS; some prohibit calculators with computer algebra systems on exams.
• Free Online Tools: Desmos (desmos.com) — exceptional graphing calculator with free use; GeoGebra; Wolfram Alpha (free queries) for algebraic verification
• Florida State Resources: Florida General Education Core Mathematics outcomes; Florida SCNS course descriptions
• Tutoring Resources: Free college tutoring centers at every Florida public college; Khan Academy (free, khanacademy.org); Math Tutor DVD; YouTube channels (Professor Leonard, Patrick JMT, Krista King)

Career Pathways

MAC1105 is the gateway college math course required across nearly all academic and professional pathways in Florida:

• Associate in Arts (A.A.) Transfer Pathway – Required Gen-Ed mathematics course for transfer to all Florida public universities; satisfies the math core for most baccalaureate programs.
• STEM Pathways – Prerequisite for trigonometry (MAC1114), pre-calculus (MAC1140/1147), Calculus I (MAC2311), Statistics (STA2023), and Physics (PHY2048/2053).
• Business and Economics – Prerequisite for Survey of Calculus (MAC2233) and Statistical Methods (STA2023), required for most business majors.
• Healthcare and Allied Health – Required for nursing (BSN) programs, pharmacy pre-requisites, and many allied-health pathways.
• Engineering Technology and Trades – Required for A.S. degrees in Engineering Technology, Industrial Management, and several technical pathways.
• Workforce Application – Algebraic problem-solving and quantitative reasoning are foundational skills for Florida's tech, finance, healthcare, manufacturing, and aerospace sectors.

Special Information

Gen-Ed Core Designation

MAC1105 is part of Florida's General Education Core Course Options in Mathematics, established by the Florida Department of Education and codified in Florida Statute 1007.25. All Florida public colleges and universities accept MAC1105 as fulfilling the Gen-Ed Mathematics core requirement. Students must earn a grade of C or better for the course to satisfy degree requirements.

Prerequisite and Placement

Students must demonstrate readiness for college-level algebra through one of the following: SAT Math score (typically 510+), ACT Math score (typically 21+), PERT Math score (typically 123+ for direct entry), successful completion of MAT 1033 (Intermediate Algebra) with a grade of C or better, or qualifying scores on institutional placement tests (ALEKS PPL is increasingly common). Florida's Senate Bill 1720 (2014) made developmental math optional for many students; institutions may allow direct enrollment in MAC1105 with co-requisite support (the "C" form often serves this purpose).

Course Equivalence and Variations

MAC1105 is offered as both MAC1105 (lecture-only, 3 credits) and MAC1105C (with integrated supplemental instruction or co-requisite support, 3-4 credits). The two forms are equivalent for transfer and Gen-Ed credit. Some institutions also offer MAC1105L as a separate 1-credit lab section.

Pathway Choice for Non-STEM Students

Florida's general education math pathway includes alternatives to MAC1105 that may better serve non-STEM majors: MGF1106 / MGF1107 (Mathematics for Liberal Arts) for non-STEM transfer students, and STA2023 (Elementary Statistics) for social sciences and many baccalaureate pathways. Students should consult their academic advisor before selecting MAC1105 vs. an alternative gen-ed math course.

Workload and Time Expectations

Most institutions expect 6-9 hours of weekly out-of-class work, including approximately 4-6 hours on online homework platforms (MyLab Math, ALEKS) and 2-3 hours studying notes and worked examples. Online homework completion is typically required for course credit.