Strengthen your critical thinking skills in this inquiry-based Pre-calculus course

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  • Course Type CLEP
  • Subject
  • Level Introductory
  • Length 15 Weeks
  • Effort 10 hours/Week
  • Institution UTAustin

About this course

In this interactive pre-Calculus course, you will deepen and extend your knowledge of functions, graphs, and equations from high school algebra and geometry courses so you can successfully work with the concepts in a rigorous university-level calculus course. This course is designed to engage learners in the “doing” of mathematics, emphasizing conceptual understanding of mathematical definitions and student development of logical arguments in support of solutions.  The course places major emphasis on why the mathematics topics covered work within the discipline, as opposed to simply the mechanics of the mathematics.

What you’ll learn

  • How to make conjectures, construct logical arguments, and justify your reasoning
  • The concept of function in mathematics, function characteristics and properties, and rate of change of functions
  • Modeling of common relations and functions such as linear, power, exponential, and logarithmic functions using statistical regression and matrix methods
  • An exploration of algebra and geometry, and the connections between the two in analytic geometry
  • Properties and applications of exponential and logarithmic functions including exponential growth and decay and The Logistic Function
  • The development of the trigonometric functions and identities along with applications of trigonometry
  • Limits and rate of change of functions as a precursor to Calculus
  • Other Coordinates Systems – an investigation of parametrization of the plane and the polar coordinate system along with exploration and use of vectors
  • Sequences and Series including The Method of Induction
  • Basic probability and combinatorics used in an investigation and development of the Binomial Theorem and its connections to Pascal’s Triangle


This course is designed to prepare you for the CLEP Precalculus exam and cover other related topics as well.


  • Mark L. Daniels

    Mark L. Daniels is a Clinical Professor of Mathematics and The Associate Director of the UTeach Program in Natural Sciences at the University of Texas at Austin. In addition, he is an Assistant Chair in the Mathematics Department. He has developed the curriculum for and teaches multiple inquiry-based mathematics courses, some specifically designed for pre-service teachers. Dr. Daniels is also the faculty advisor for teaching options in the Mathematics Department as well as the Director of the Discovery Learning Project for the College of Natural Sciences. Moreover, he is the Co-Director of the Inquiry-based Learning Project in Mathematics working with Dr. Michael Starbird. His research interests, of late, involve the preparation of pre-service mathematics teachers and the incorporation of discovery-based instructional methodology in university undergraduate mathematics courses.

  • Jeremiah W. Lucas

    Jeremiah W. Lucas is the Precalculus Course Coordinator with the Center for Teaching and Learning at The University of Texas at Austin. He works with the OnRamps program, a dual-credit and dual-enrollment initiative designed to increase student access to rigorous, high-quality curricula that foster deep conceptual knowledge and academic skills. He earned his BS in Electrical Engineering from the University of Kentucky and his MA in Mathematics from The University of Texas. He taught high school mathematics in diverse and underprivileged schools in central Texas and is currently an Adjunct Professor at Austin Community College.

  • Karen E. Smid

    Karen E. Smid is a Project Manager with the Center for Teaching and Learning at The University of Texas at Austin. She works on a variety of course development and software adoption projects, and has a Ph.D. in Anthropology from the University of Michigan.

“You can take your entire freshman year, tuition free!”

NBA star Jalen Rose

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