Course description
What students will do
This is Semester I of a two-semester precalculus sequence, covering the first half of the standard curriculum: algebraic fundamentals, functions and their transformations, polynomial and rational functions, exponential and logarithmic functions, and the unit-circle approach to trigonometry.
Every unit pairs the required material with olympiad-style problem-solving. Students meet contest techniques alongside the textbook methods: Vieta's formulas and symmetric functions of roots in the polynomial unit, AM–GM and other inequality tools in the fundamentals, functional equations and involutions when studying inverses, and telescoping identities once the trigonometric functions are in hand. Problem sets draw on AMC- and AIME-style questions.
The aim is a student who reaches for structure before formula. Small-group discussion is central: students present approaches, critique each other's reasoning, and learn that a problem worth doing rarely yields on the first attempt—the productive struggle is the point, not a sign that something has gone wrong. Semester II is coming soon; the topics it covers are outlined below.
Semester I · This course
Chapters 1–5
- Fundamentals: real numbers, exponents and radicals, equations, inequalities, lines, and modeling
- Functions: graphs, rate of change, transformations, composition, and inverses
- Polynomial and rational functions: division, real and complex zeros, the Fundamental Theorem of Algebra
- Exponential and logarithmic functions: laws of logarithms, equations, and logarithmic scales
- Trigonometric functions, unit-circle approach: graphs, inverse functions, and harmonic motion
Semester II Coming soon
Chapters 6–13
- Right-triangle and analytic trigonometry: identities, addition and double-angle formulas, trigonometric equations, the Laws of Sines and Cosines
- Polar coordinates, parametric equations, and De Moivre's Theorem
- Vectors in two and three dimensions: dot and cross products, lines and planes
- Systems of equations, matrices, and conic sections
- Sequences and series: induction, the Binomial Theorem, and a preview of limits
Precalculus Semester II is coming soon. Contact Bayview to hear first when dates are announced.
Who this is for
Students taking or preparing for precalculus who want more than procedural fluency—and students who enjoy hard problems and want a route into math competition work before calculus begins.