The Gateway to Advanced Mathematics and the Mathematical Tools That Power the Modern World
About This Class
Pre-Calculus bridges the gap between Algebra II and Calculus, bringing together the most powerful tools in secondary mathematics. Students who succeed here are prepared not just for Calculus, but for the mathematical rigor of any college STEM program.
We'll study trigonometry (including the unit circle and identities), advanced function analysis, polynomial and rational functions, exponential and logarithmic growth, conic sections, and an introduction to the idea of a limit. Every topic has genuine applications in fields from music and engineering to astronomy and game design.
This course moves faster and thinks harder than anything before it. The rewards match the challenge. Students who leave Pre-Calculus confident in their skills have a significant advantage in Calculus, college mathematics, and the data-driven careers of the 21st century.
Piecewise, absolute value, composition of functions, inverse functions
End behavior, zeros, synthetic division, and asymptotes
Unit circle, trig functions, identities, law of sines and cosines
Growth and decay, logarithm laws, natural log, real-world applications
Circles, parabolas, ellipses, hyperbolas, and an introduction to limit notation
Math in the Real World
Sound waves are sine waves — literally. Every note, chord, and audio effect is described by trigonometric functions. Audio engineers use Fourier analysis (built on trig) to design concert halls, tune instruments, process recordings, and build noise-canceling headphones.
Suspension bridge cables hang in parabolic curves. Road curves and tunnel cross-sections are designed with conic sections. The exponential functions we study describe how materials weaken under stress. Structural engineers use every topic in this course.
Smooth character movement, realistic physics, camera rotations, and 3D rendering all rely on trigonometric functions and function transformations. Every game engine — Unreal, Unity, Godot — is built on Pre-Calculus concepts applied at 60 frames per second.
Planetary orbits are ellipses. Calculating when a comet will return, mapping the trajectory of a spacecraft, or predicting an eclipse all require trigonometry and conic sections — exactly what we study in the second half of the year.
Lesson Plans
Click any highlighted date to jump to that lesson. Lesson plan PDFs will be linked here as they are posted — check back regularly throughout the semester.
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