PreCalculus

Precalculus is designed for students who intend to pursue a career in science, technology, engineering, or mathematics (STEM) that requires the study of calculus. It prepares students for calculus at the postsecondary level or AP Calculus at the high school level. Students must successfully complete Algebra II with Statistics before enrolling in Precalculus.

Precalculus builds on the study of algebra and functions in Algebra II with Statistics, adding rational functions, all trigonometric functions, and general piecewise-defined functions to the families of functions considered. In addition to focusing on the families of functions, Precalculus takes a deeper look at functions as a system, including composition of functions and inverses. Precalculus also expands on the study of trigonometry in previous courses and considers vectors and their operations. Other topics, such as statistics, that are frequently added to precalculus courses are not included because the course’s primary focus is preparing students for the study of calculus.

Precalculus Content Standards:

  • Students will perform arithmetic operations with complex numbers.

  • Students will represent complex numbers and their operations on the complex plane.

  • Students will use complex numbers in polynomial identities and equations.

  • Students will understand limits of functions.

  • Students will represent and model with vector quantities.

  • Students will perform operations on vectors.

  • Students will write expressions in equivalent forms to solve problems.

  • Students will understand the relationship between zeros and factors of polynomials.

  • Students will use polynomial identities to solve problems.

  • Students will rewrite rational expressions.

  • Students will understand solving equations as a process of reasoning and explain the reasoning.

  • Students will solve more difficult systems of equations

  • Students will interpret functions that arise in applications in terms of context.

  • Students will analyze functions using different representations.

  • Students will build a function that models a relationship between two quantities.

  • Students will build new functions from existing functions.

  • Students will recognize attributes of trigonometric functions and solve problems involving trigonometry.

  • Students will extend the domain of trigonometric functions using the unit circle.

  • Students will model periodic phenomena with trigonometric functions.

  • Students will prove and apply trigonometric identities.

*shortened from The Alabama Course of Study 2019