Students will deepen and extend their knowledge of functions, graphs, and equations from their high school algebra and geometry courses so they can successfully work with the concepts in a rigorous university-level calculus course.  This course is designed to push students well beyond “drill and kill” type exercises, with an emphasis on unpacking mathematical definitions and making logical arguments to their peers. The students will strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations with algebra and trigonometry and extend their ability to make connections and apply concepts and procedures at higher levels.  Students investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems. Each unit consists of a series of explorations designed to engage students and empower them to develop their problem-solving skills alongside the teacher. In each exploration, students will create connections with prior concepts in developing the current topic. Students will experience high-quality curriculum designed by the faculty at the University of Texas at Austin. The pedagogy of the course, Inquiry-Based Learning, encourages students to take an active role in the construction of their learning. Successful completion of this course earns 3 college credits for UT M 305G and high school credit for Precalculus.