Coopersmith Career Consulting | Evaluated Learning Experience
Pre-Calculus (MTH-275)
Varies; (self-study; self-paced).
June 2025 - Present.
Upon successful completion of the course, students will be able to: analyze and graph various types of functions, including linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric; apply algebraic techniques to solve equations and inequalities involving polynomials, rational expressions, exponential and logarithmic terms; interpret the properties and behaviors of functions using domain, range, composition, and inverse operations; apply trigonometric concepts by working with radian and degree measures, unit circle definitions, and fundamental identities; solve and verify trigonometric equations and identities using algebraic and graphical methods; explore and evaluate arithmetic and geometric sequences and series, including summation formulas and convergence; apply mathematical induction to prove formulas and validate patterns in sequences; analyze and graph conic sections, identifying key features of circles, ellipses, parabolas, and hyperbolas from their standard equations; and investigate the foundational concepts of limits and derivatives, understanding their role in the transition to calculus.
Pre-Calculus is a theory-based course that was designed to equip students with a strong mathematical foundation in preparation for the study of calculus. The course provides a comprehensive exploration of algebraic, trigonometric, geometric, and introductory calculus concepts without requiring formal assignments or live instruction. Learners progress through carefully sequenced topics including functions, polynomial and rational expressions, exponential and logarithmic equations, and trigonometric identities. Visual understanding and graphing skills are emphasized throughout. The course begins with a review of essential algebraic principles, focusing on equation solving, function notation, domain and range, and function composition. As students advance, they investigate polynomial and rational functions, graphing techniques, and asymptotic behavior. Exponential growth and logarithmic operations are introduced with real-life applications. Trigonometric concepts follow, with special attention to the unit circle, angle measures, identities, and solving equations. Later units guide students through advanced trigonometric identities, sequences and series, mathematical induction, and conic sections such as parabolas, ellipses, and hyperbolas. The course concludes with an introduction to limits and derivatives, offering a preview of key calculus ideas through intuitive and graphical methods.
In the lower division baccalaureate/associate degree category, 3 semester hours in Mathematics, Engineering, Computer Science, Natural Sciences, Business, or General Education (6/25).