Precalculus Algebra and Trigonometry: Syllabus, Competencies, and Course Structure

Course Overview

This course, Pre-Calculus Algebra/Trigonometry, is designed to prepare students for calculus by covering foundational topics in algebra, functions, trigonometry, analytic geometry, and introductory topics in sequences, series, and probability. The course emphasizes conceptual understanding, problem-solving, and mathematical modeling.

Course Structure and Policies

Instructor and Contact Information

• Instructor: Leobel Fernandez

• Email: [e-mail]

• Department Phone: [phone]

• Term: Summer 2026 (2265)

• Class Schedule: Monday-Wednesday, 5:40 PM to 8:30 PM

• Location: MD Life

Attendance Policy

• Attendance is mandatory and will be taken each class period.

• Absences include both physical/virtual absence and inactivity in MyMathLab (1 week of inactivity = 1 absence).

• Missing two or more classes may result in withdrawal from the course.

Classroom Decorum

• Arrive on time and minimize interruptions.

• Keep cell phones on silent and avoid use during class.

• Mute microphones in virtual sessions unless speaking.

Academic Integrity

• Cheating results in automatic failure of the assignment and referral to the dean.

• Refer to the Student’s Rights and Responsibilities for more details.

Grading Policy

• Grades are based on homework and four equally weighted exams.

• An optional final exam can replace the lowest test score.

• All exams are online.

Average (%)	Letter Grade
90-100	A
80-89	B
70-79	C
60-69	D
Below 60	F

Resources

• Free tutoring is available at the math lab: https://www.mdc.edu/hialeah/math/

Course Topics and Tentative Schedule

The course follows a structured schedule covering the following main topics, each corresponding to standard precalculus chapters:

• Polynomial and Rational Functions (Chapter 5)

• Exponential and Logarithmic Functions (Chapter 6)

• Trigonometric Functions and Graphs (Chapter 7)

• Analytic Trigonometry (Chapter 8)

• Applications of Trigonometric Functions (Chapter 9)

• Polar Coordinates, Complex Numbers, and Vectors (Chapter 10)

• Analytic Geometry (Conic Sections) (Chapter 11)

• Systems of Equations and Matrices (Chapter 12)

• Sequences, Series, Induction, and the Binomial Theorem (Chapter 13)

Assignments and tests are scheduled throughout the term, with late penalties applied after due dates.

Course Competencies

Piecewise-Defined Functions

• Graph advanced piecewise-defined functions.

Exponential and Logarithmic Functions

• Define and evaluate exponential and logarithmic functions and their inverses.

• Graph these functions and identify their domains and ranges.

• Apply properties of logarithms and solve related equations.

• Model exponential growth and decay.

Polynomial Functions

• Analyze and graph polynomial functions, including end behavior and zeros.

• State and apply the Fundamental Theorem of Algebra.

• Construct polynomials from given zeros and graphs.

Rational Functions

• Find and analyze asymptotes (vertical, horizontal, oblique).

• Determine domains and graph rational functions.

• Analyze behavior near discontinuities and at infinity.

Polynomial and Rational Equations and Inequalities

• Solve systems of non-linear equations and inequalities.

• Graph solution sets.

Conic Sections

• Identify and graph parabolas, ellipses, and hyperbolas.

• Write equations in standard and general forms.

• Solve application problems involving conics.

Matrices and Determinants

• Define matrices and perform algebraic operations.

• Evaluate determinants and solve linear systems.

• Identify consistent and inconsistent systems.

Sequences and Series

• Define and write terms of arithmetic and geometric sequences and series.

• Find sums and use summation notation.

Mathematical Induction

• Prove formulas using the Principle of Mathematical Induction.

Binomial Theorem

• Expand binomials and find specific terms using the Binomial Theorem.

Key Formulas and Concepts

• Polynomial Function: $f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0$

• Exponential Function: $f(x) = a b^x$

• Logarithmic Function: $f(x) = \log_b x$

• Trigonometric Functions: $\sin \theta, \cos \theta, \tan \theta, \csc \theta, \sec \theta, \cot \theta$

• Arithmetic Sequence: $a_n = a_1 + (n-1)d$

• Geometric Sequence: $a_n = a_1 r^{n-1}$

• Binomial Theorem: $(a+b)^n = \sum_{k=0}^n {n \choose k} a^{n-k} b^k$

Textbook and Materials

• Textbook: Algebra & Trigonometry, 12th Edition by Sullivan

• ISBN-13: 9780138251406

• Online Platform: MyLab Math

General Education Outcomes

• Effective communication, quantitative analysis, problem-solving, information literacy, cultural and ethical awareness, technological proficiency, and appreciation for aesthetics and the environment.