Precalculus

I. Introduction

Precalculus is the bridge between algebra/trigonometry and calculus. It focuses on mastering functions, graphs, and modeling so you’re ready for limits, derivatives, and integrals.

II. Outline

• Functions & Core Algebra
  • Function notation, domain/range, transformations
  • Polynomial and rational functions (zeros, asymptotes, end behavior)
  • Inverse functions and composition
  • Exponential and logarithmic functions
• Trigonometry
  • Degrees vs radians, unit circle definitions
  • Graphs of trig functions (amplitude/period/phase shift)
  • Trig identities and trig equations
  • Law of Sines / Law of Cosines and applications
• Calculus-Readiness
  • Conic sections (parabolas, ellipses, hyperbolas)
  • Systems of equations and inequalities
  • Sequences/series basics
  • Modeling and interpretation emphasis
• Vectors, Matrices, and Extras (course-dependent)
  • Vectors in 2D/3D, dot product, basic geometry
  • Intro to matrices
  • Complex numbers

III. Free Books

• Precalculus: An Investigation of Functions
• OpenStax — Precalculus 2e

IV. Video Series

• Precalculus Course - FreeCodeCamp.org Youtube
• Khan Academy — Precalculus YouTube Playlist

V. See Also

College Algebra, Trigonometry, Calculus I, Probability