Precalculus Algebra

Course Description

MAC1140C – Precalculus Algebra is a 3-credit-hour course that builds on College Algebra to prepare students for trigonometry, calculus, and other calculus-based STEM coursework. The course extends students' understanding of functions and emphasizes the analytical, graphical, numerical, and verbal representations of mathematical concepts (the "rule of four"). Students develop deeper proficiency with polynomial, rational, exponential, and logarithmic functions, along with conic sections, sequences and series, and systems of equations.

The "C" indicator signals that lecture and applied problem-solving (often supported by computer algebra systems or graphing calculators) are integrated. Coursework typically includes substantial use of graphing calculators (TI-84 family) and may incorporate online homework platforms.

MAC1140C is a Florida common course offered at approximately 37 Florida institutions and satisfies general-education mathematics requirements while serving as a prerequisite for MAC1114 (Trigonometry), MAC1147 (Precalculus Algebra and Trigonometry), MAC2233 (Survey of Calculus), or MAC2311 (Calculus I) depending on the program. It transfers as the equivalent course at all Florida public postsecondary institutions per SCNS articulation policy.

Learning Outcomes

Required Outcomes

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

• Analyze functions using analytical, graphical, numerical, and verbal representations; identify domain, range, intercepts, asymptotes, intervals of increase/decrease, and extrema.
• Perform operations on functions, including arithmetic combinations, composition, and inverse functions.
• Analyze polynomial functions, including end behavior, real and complex zeros, the Fundamental Theorem of Algebra, the Rational Root Theorem, and Descartes' Rule of Signs.
• Analyze rational functions, including domain, vertical and horizontal asymptotes, holes, and graphing.
• Solve polynomial and rational equations and inequalities algebraically and graphically.
• Analyze exponential and logarithmic functions, including their graphs, transformations, and inverse relationships.
• Apply properties of logarithms to simplify and evaluate logarithmic expressions; solve exponential and logarithmic equations.
• Apply exponential and logarithmic functions to real-world problems, including compound interest, exponential growth and decay, and logarithmic scales.
• Solve systems of equations and inequalities using substitution, elimination, matrix methods (Gaussian elimination, inverse matrices, Cramer's Rule), and graphing.
• Analyze conic sections (parabolas, circles, ellipses, hyperbolas) — both centered at the origin and translated.
• Work with sequences and series, including arithmetic and geometric sequences, summation notation, and the Binomial Theorem.
• Use a graphing calculator effectively to analyze functions, solve equations, and verify results.

Optional Outcomes

• Apply partial fraction decomposition to rational expressions.
• Work with parametric equations at an introductory level.
• Apply mathematical induction to prove statements about positive integers.
• Analyze nonlinear systems of equations and inequalities in greater depth.
• Apply matrix operations beyond systems-solving (matrix algebra introduction).

Major Topics

Required Topics

• Functions and Their Graphs: Definition; function notation; domain and range; piecewise-defined functions; graphical analysis; symmetry (even/odd); transformations.
• Operations on Functions: Sum, difference, product, quotient; composition; one-to-one functions and inverses.
• Polynomial Functions: Quadratic functions and their applications; higher-degree polynomial behavior; the Division Algorithm; the Remainder and Factor Theorems; the Fundamental Theorem of Algebra; complex zeros; the Rational Root Theorem; Descartes' Rule of Signs; graphing polynomial functions.
• Rational Functions: Domain; vertical, horizontal, and slant asymptotes; holes; graphing rational functions; rational inequalities.
• Exponential and Logarithmic Functions: Exponential function definition; the natural exponential function (base e); logarithmic function definition; common and natural logarithms; properties of logarithms; change-of-base formula; exponential and logarithmic equations; applications (compound interest, growth and decay, Newton's Law of Cooling, logistic growth, pH, Richter scale, decibels).
• Systems of Equations and Inequalities: Linear and nonlinear systems; substitution and elimination; matrix representation; Gaussian elimination; reduced row-echelon form; inverse matrices; Cramer's Rule (when included); systems of inequalities and linear programming.
• Conic Sections: Parabolas (opening up/down/left/right); circles; ellipses (horizontal and vertical major axis); hyperbolas (horizontal and vertical transverse axis); identifying conics from general form; translations.
• Sequences and Series: Sequences; summation notation; arithmetic sequences and series; geometric sequences and series; sum of infinite geometric series; the Binomial Theorem; Pascal's triangle.

Optional Topics

• Partial Fractions: Decomposition of rational expressions for integration preparation.
• Mathematical Induction: Principle and applications to summation formulas and divisibility.
• Counting and Probability: Permutations, combinations, basic probability (when not previously covered).
• Parametric Equations: Introduction to parametric representations of curves.
• Matrix Algebra: Matrix operations beyond systems-solving.

Resources & Tools

• Common Textbooks: Precalculus (Stewart/Redlin/Watson, Larson, Sullivan, Blitzer, or Rockswold), Algebra and Trigonometry (Stewart or Sullivan), Precalculus: Mathematics for Calculus (Stewart)
• Open Educational Resources: Precalculus by OpenStax, Precalculus (Stitz/Zeager — free), Lumen Learning
• Online Platforms: MyLab Math (Pearson), MyMathLab, Connect Math (McGraw-Hill), WebAssign, ALEKS, Hawkes Learning — typically required for homework
• Calculators: Graphing calculator required (TI-84 Plus / TI-84 Plus CE most common; TI-Nspire CX accepted at most institutions); Desmos (free online graphing calculator) for in-class exploration
• Software: GeoGebra (free dynamic mathematics software), Wolfram Alpha for verification
• Reference Resources: Khan Academy, PatrickJMT (YouTube), Professor Leonard (YouTube), Paul's Online Math Notes

Career Pathways

MAC1140C is the gateway to calculus-track mathematics and is essential preparation for STEM careers. The course supports preparation for:

• Engineering: All engineering disciplines (civil, mechanical, electrical, computer, aerospace, chemical, biomedical, environmental).
• Computer Science and Information Technology: CS majors; many IT specializations.
• Physical Sciences: Physics, chemistry, geology, astronomy, atmospheric sciences.
• Mathematical Sciences: Mathematics, applied mathematics, actuarial science, statistics.
• Pre-Health Sciences (Calculus-Track): Pre-medical, pre-dental, pre-pharmacy, and pre-veterinary tracks at universities requiring calculus.
• Business (Quantitative Track): Finance, economics, business analytics, management science.
• Architecture: Often requires calculus and physics; precalculus is the bridge.
• Education (Secondary Mathematics): Future high school math teachers must complete the calculus sequence.

Florida's growing technology, aerospace (Space Coast), and engineering sectors create strong demand for graduates with strong mathematical foundations. Major employers — including Lockheed Martin, Northrop Grumman, Harris, Siemens, and the state's growing biomedical industry — recruit STEM graduates whose preparation began with strong precalculus foundations.

Special Information

General Education and Transfer

MAC1140C is a Florida common course number that satisfies general-education mathematics requirements at most Florida public colleges and universities and is required for the calculus sequence. It transfers as the equivalent course at all Florida public postsecondary institutions per SCNS articulation policy.

Course Sequence

MAC1140C fits in the calculus-preparation pathway as follows:

• Pre-MAC1140C: MAT1033 (Intermediate Algebra) → MAC1105C (College Algebra)
• MAC1140C → MAC1114C (Trigonometry): Standard sequence at institutions teaching algebra and trigonometry separately.
• Alternative — MAC1147 (Precalculus Algebra and Trigonometry): Combined 5-credit course replacing MAC1140C + MAC1114C.
• MAC1140C + MAC1114C → MAC2311C (Calculus I): Standard pathway for STEM majors.
• MAC1140C → MAC2233 (Survey of Calculus): Pathway for business and life-science majors not requiring full Calculus I.

Placement Considerations

Students entering MAC1140C should have current proficiency in College Algebra (MAC1105C) topics including factoring, function notation, equation solving, and graphing. Students returning to mathematics after extended absence should consider a refresher or placement testing before enrolling. Florida institutions accept various placement instruments (PERT, ACT, SAT, ALEKS placement) for direct entry into MAC1140C without MAC1105C.

Honors and Dual-Enrollment Considerations

MAC1140C is frequently taken by dual-enrollment students (high school students earning college credit) and is offered as an honors course at many Florida institutions. Honors sections typically cover the same content with deeper exploration of proofs and applications.