Course Description
MAC1147 – Precalculus Algebra and Trigonometry is a fast-paced lecture course that combines the content of MAC1140 (Precalculus Algebra) and MAC1114 (Trigonometry) into a single accelerated course. It is designed specifically for students intending to take MAC2311 (Calculus I) — the gateway to engineering, physics, computer science, mathematics, chemistry, and other STEM majors. Students who do not need the full calculus sequence may be better served by the slower-paced two-course sequence (MAC1140 + MAC1114) or by alternative paths such as MAC2233 (Survey of Calculus) for business majors.
The course sits within the Florida Statewide Course Numbering System (SCNS) under Mathematics > Applied Mathematics and is offered at approximately 30 Florida public institutions, including the University of Florida, Florida State University, the University of Central Florida, the University of South Florida, Florida International University, Miami Dade College, Broward College, Valencia College, St. Petersburg College, Palm Beach State College, Hillsborough Community College, and Seminole State College. It is offered both as a standard college credit course and through dual-enrollment for high school students preparing for STEM majors.
Credit value varies by institution. Most Florida institutions award 4 credit hours (UF, FAU, FIU, MDC); others award 5 credit hours (Seminole State, FSCJ, and several other state colleges) reflecting expanded contact time. Either way, MAC1147 is a heavier-than-typical course — students should expect a workload comparable to taking precalculus algebra and trigonometry simultaneously, which it effectively is.
Learning Outcomes
Required Outcomes
Upon successful completion of MAC1147, students will be able to:
- Analyze functions and their graphs, including domain, range, transformations, composition, and inverse relationships.
- Solve and analyze polynomial and rational functions, including finding zeros, identifying asymptotes, and sketching graphs.
- Solve exponential and logarithmic equations and apply them to growth, decay, and finance problems.
- Define and evaluate the six trigonometric functions using both right-triangle and unit-circle definitions.
- Graph trigonometric functions, identifying period, amplitude, phase shift, and vertical translation.
- Verify trigonometric identities and solve trigonometric equations.
- Apply the law of sines and law of cosines to solve oblique triangles.
- Work with inverse trigonometric functions, evaluating exact and approximate values.
- Apply polar coordinates and complex numbers at an introductory level.
- Solve real-world application problems across the algebraic, exponential/logarithmic, and trigonometric domains.
- Communicate mathematical reasoning and solutions clearly in both written and (where applicable) computer-graded formats.
Optional Outcomes
Depending on instructor and institutional emphasis, students may also:
- Work with matrices and determinants, including solving systems of equations.
- Analyze conic sections (parabolas, ellipses, hyperbolas) in standard and translated forms.
- Investigate sequences, series, and the binomial theorem.
- Apply mathematical induction in proof-style problems.
- Work with vectors in two dimensions, including dot products and applications.
- Use computer algebra systems or graphing technology (Desmos, GeoGebra, or graphing calculators) for visualization and verification.
Major Topics
Required Topics
- Functions and Their Graphs: Definitions, function notation, domain and range, even/odd functions, transformations (shifts, reflections, stretches), composition, one-to-one functions, inverse functions.
- Polynomial and Rational Functions: Quadratic functions and their graphs, polynomial division and the remainder theorem, rational zeros theorem, complex zeros, fundamental theorem of algebra, graphs of rational functions, vertical/horizontal/oblique asymptotes.
- Exponential and Logarithmic Functions: Exponential function properties, logarithmic function properties, change of base, properties of logarithms, exponential and logarithmic equations, applications (compound interest, exponential growth and decay, Newton's law of cooling).
- Trigonometric Functions — Right Triangle and Unit Circle: Angle measure (degrees and radians), the unit circle, the six trigonometric functions, exact values for special angles, reference angles.
- Graphs of Trigonometric Functions: Sine, cosine, tangent and their reciprocal graphs; period, amplitude, phase shift, vertical translation; sinusoidal modeling.
- Analytical Trigonometry: Fundamental identities; sum and difference formulas; double-angle, half-angle, product-to-sum identities; inverse trigonometric functions; solving trigonometric equations.
- Applications of Trigonometry: Right-triangle applications; the law of sines (including the ambiguous case); the law of cosines; the area of a triangle.
- Complex Numbers and Polar Coordinates: Complex number arithmetic; polar form of complex numbers; De Moivre's theorem; polar coordinates and graphs.
Optional Topics
- Conic Sections: Parabolas, ellipses, hyperbolas — standard form, translation, applications.
- Sequences, Series, and the Binomial Theorem: Arithmetic and geometric sequences, summation, infinite geometric series, binomial expansion.
- Matrices and Systems: Matrix algebra, Gaussian elimination, determinants, inverse matrices, applications to linear systems.
- Vectors in Two Dimensions: Vector arithmetic, dot product, vector applications.
- Mathematical Induction: Principle and applications.
Resources & Tools
- Most-adopted textbooks at Florida institutions: Precalculus by Stewart, Redlin, and Watson (Cengage); Algebra and Trigonometry by Sullivan (Pearson); Precalculus by Larson (Cengage); Precalculus by Abramson et al., published by OpenStax (free, used at UF and an increasing number of Florida institutions as a zero-textbook-cost option).
- Online learning platforms: ALEKS (adaptive-learning system used widely at UF, MDC, and others — also used as a placement tool); WebAssign (problem-set platform); MyMathLab / MyLab Math; Pearson MathXL; Hawkes Learning.
- Visualization tools: Desmos (free graphing calculator, widely used in Florida classrooms); GeoGebra (free); Wolfram Alpha.
- Calculators: Most institutions allow scientific calculators; some allow graphing calculators (TI-83, TI-84) on certain assessments. Symbolic-algebra calculators (TI-89, TI-Nspire CAS) are typically prohibited on exams.
- Tutoring and support: Institution math labs and tutoring centers (free, walk-in); Khan Academy precalculus and trigonometry modules (free); Paul's Online Math Notes (Lamar University, free).
Career Pathways
MAC1147 is a gateway course rather than a terminal one — its primary value is as preparation for calculus and the STEM majors and careers that build on calculus. Direct downstream careers include:
- Engineer — civil, mechanical, electrical, aerospace, computer, biomedical, environmental, materials, industrial. Florida's aerospace and defense industries (the Space Coast: Kennedy Space Center, Cape Canaveral, Patrick SFB; defense contractors L3Harris, Lockheed Martin, Northrop Grumman, Boeing) are major employers.
- Computer Scientist / Software Engineer — Tampa Bay, Miami, and Orlando are growing tech hubs.
- Data Scientist / Statistician / Quantitative Analyst — finance, healthcare analytics, theme park operations research.
- Physical Scientist — physicist, chemist, geologist, atmospheric scientist; relevant to Florida's marine science (USF St. Pete, FAU Harbor Branch) and atmospheric/climate research.
- Actuary — Florida's significant insurance industry (property insurance especially).
- Mathematics Educator (secondary) — pathway through Florida math education BS degrees.
- Pre-Medicine and Pre-Health — many medical school prerequisites require calculus, which requires MAC1147.
Special Information
Articulation and Transfer
MAC1147 is part of the Florida common course numbering system. It satisfies the mathematics general education requirement and the Florida State Board of Education Rule 6A-10.030 ("Gordon Rule") math component. A grade of C or higher is required for both Gordon Rule satisfaction and articulation as a calculus prerequisite.
Important articulation note: a student who takes MAC1147 will receive credit for that course, but if they later take MAC1140 (Precalculus Algebra) and/or MAC1114 (Trigonometry), there are credit-overlap rules — typically a student may receive at most 4 credits for MAC1147 plus MAC1140, and at most 5 credits for MAC1147 plus MAC1140 plus MAC1114. Consult your registrar.
Prerequisites and Placement
The standard prerequisite is MAC1105 (College Algebra) with a minimum grade of C, or appropriate placement test scores. At many Florida institutions, placement is determined by an ALEKS PPL score (typical minimum: 50% for direct entry, with some institutions requiring 60% or higher). Miami Dade College specifically requires "A, B, or S in MAC1105" for registration.
Course Format and Workload
MAC1147 is fast-paced. Most institutions schedule 4–5 contact hours per week and expect students to spend an additional 10–15 hours per week in homework, problem sets, and study time. Students who struggled with MAC1105 (College Algebra) often find MAC1147 challenging because it covers two semesters of content in one. If you are not certain you need MAC1147 specifically (rather than the slower MAC1140 path), consult your academic advisor before enrolling.
Position in the STEM Curriculum
MAC1147 is the direct prerequisite for MAC2311 (Calculus I), which itself is the prerequisite for the calculus-based physics sequence (PHY2048C/PHY2049C), engineering courses, and most STEM major sequences. A student who completes MAC1147 with a C or higher is positioned to take MAC2311 the following term. Students considering business or non-engineering majors that need only "Calculus for Business" should consider MAC1140 (Precalculus Algebra alone) followed by MAC2233 (Survey of Calculus) — this is a less demanding path.
Honors and Dual-Enrollment Variants
An honors variant MAC1147H exists at some institutions (FAU, UF) for high-achieving students. The course is also widely offered as a dual-enrollment option for advanced high school students through Florida's Dual Enrollment program. Dual-enrolled students should confirm that their target university accepts MAC1147 dual-enrollment credit (most do, but specific articulation should be verified).
Course Code Variations
Course titles are consistent across Florida: "Precalculus Algebra and Trigonometry" or "Precalculus With Trigonometry." All refer to the same SCNS course. The credit value (4 vs. 5) is the most notable institutional variation and reflects different scheduling/pacing decisions, not different content.