Pre-calculus

03101100 TX

Precalculus is the preparation for Calculus and is intended for the student who has successfully completed Algebra II and Geometry. The course approaches topics from a functions point of view, where appropriate, and is designed to 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. The study of Precalculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends 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.

Upon completion of this course students will be able to:

  • Explore, write, solve, graph, and perform transformations of linear, quadratic, exponential, logarithmic, trigonometric, rational, piecewise, step, polynomial, power, and inverse functions and equations.

  • Describe characteristics of functions, including behavior around asymptotes.

  • Determine values of the trigonometric functions at special angles.

  • Develop and use sinusoidal functions that model real world problems.

  • Graph and convert parametric equations into rectangular relations and vice versa.

  • Know how to graph polar coordinates and rectangular coordinates.

  • Examine conic sections, ellipses, and hyperbola.

  • Use the unit circle with radian and degree angle measure with trigonometry including Law of Sines and Law of Cosines in real world problems.

  • Apply vector and scalar operations geometrically and symbolically.

  • Evaluate, calculate, and represent (including sigma form): finite sums, geometric and arithmetic series and sequences.

  • Use the Binomial Theorem.

  • Solve polynomial and rational inequalities.

  • Simplify, generate, and solve trigonometric identities and equations using various methods.

State: Texas
Grade Level: 12
Category: Math
Course Length: Year