Precalculus

Twelve units bridging Algebra and Calculus — from advanced functions through trigonometry, analytic geometry, and an introduction to limits.

Units

12 units · Select a unit to see its lessons.

Build a rigorous foundation in function concepts: notation, domain and range, rates of change, composition, transformations, and inverses.

Deepen understanding of linear relationships, graphing, modeling, and fitting linear models to data.

Analyze polynomial and rational functions including end behavior, zeros, asymptotes, and graphing techniques.

Build and apply exponential and logarithmic models for growth, decay, and real-world data, including solving equations and fitting models.

Define the six trig functions using the unit circle, right triangles, and reference angles.

Analyze amplitude, period, phase shift, and vertical shift. Graph all six trig functions and their transformations.

Verify and apply fundamental, Pythagorean, sum/difference, double-angle, and half-angle identities. Solve trig equations.

Apply the Law of Sines and Law of Cosines. Work with vectors, polar coordinates, and parametric equations.

Solve systems of linear and nonlinear equations and inequalities. Apply matrices and Gaussian elimination.

Study conic sections — parabolas, ellipses, hyperbolas, and circles — using standard and general form equations.

Explore arithmetic and geometric sequences, series, the Binomial Theorem, permutations, combinations, and probability.

Preview limits, continuity, the derivative as a rate of change, and the connection between precalculus and calculus.

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