Welcome to On Ramps College Algebra

  • Here is the page for On Ramps Precalculus students. On Ramps courses are dual enrollment, meaning students are concurrently enrolled in a high school and college course. Students are able to earn credits for high school and college at the same time. On Ramps Precalculus covers several of the major topics that are covered in previous Algebra classes. However, this course goes deeper into the content than previous classes did and (most significantly) strictly limits the use of a graphing calculator.

     
    COURSE DESCRIPTION
     
    Using a creative and connected approach, students 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” exercises, emphasizing conceptual understanding of mathematical definitions and developing logical arguments with their peers. This course addresses the following three core objectives established by the Texas Higher Education Coordinating Board: communication skills, critical thinking skills, and empirical and quantitative skills. This course fulfills the University of Texas at Austin core curriculum requirement for Mathematics (Texas core code 020).
     
    Course Pre-requisites
     
    • Geometry
    • Algebra II
     
    Course Learning Outcomes
     
    • Functions, Rates, and Patterns Definition of a function, function identification, types of functions, composition of functions, inverse of a function, rates of change, function patterns, piecewise functions
    • Algebra and Geometry Transformations of functions, complex roots and polynomials, conic sections, using matrices to model functions and relations
    • Exponential and Logarithmic Functions Exponent and logarithm properties, natural logarithms, applications of logarithms and exponents, including logistic growth models
    • Trigonometry Trigonometric foundations, Unit Circle, trigonometric identities, trigonometric functions with transformations, modeling using sinusoidal functions, inverse trig functions, Law of Sines and Cosines, double angle and sum and difference identities
    • Limits and Rate of Change of Functions Rational functions, limits, average rates and instantaneous rates, derivatives and the Power Rule
    • Exploring Other Coordinate Systems Parametric equations with applications, using vector operations, Polar coordinate system with graphing
    • Sequences and Series Arithmetic and geometric sequences, convergent sequences, series and partial sums, convergent series with applications, mathematical induction, combinatorics, binomial theorem
     
    Course Format and Procedures
     
    This course uses Inquiry-Based Learning (IBL), a pedagogy designed to engage students in the educational process. Inquiry-Based Learning is a student-centered methodology, which emphasizes the importance of the active construction of learning. Therefore, students are expected to pose questions, make decisions, design plans and experiments, discuss, collaborate, communicate results, and provide justified answers and explanations when engaged in the inquiry process.
     
    Characteristics of an IBL class:
     
    • Students work together in groups to explore various mathematics concepts.
    • Instructor listens to student conversation to monitor creation of mathematical ideas.
    • Students present work to the class. This helps facilitate class discussion, closure to a problem, and allows for the Instructor to pose extension questions to the class.
    • If a misconception occurs across the class, the Instructor may choose to bring the class back together and pose leading questions to guide the discussions in the correct direction.
     
    Overall Goals:
     
    • The overall goal is to have students “do” mathematics - that is, to have students engage in thinking about the connectedness that exists between various basic areas of mathematics.
    • Students should work to provide rigorous arguments at different levels that support the development of these connections.
    • The hope is that students will more deeply understand the discipline of mathematics and the fact that if one does not ask “why” when engaging in “doing” mathematics - then the processes experienced are strictly mechanical.