Use this as a checklist. Each unit page has the full topic list, key ideas, common mistakes and its practice test.
Unit 1 builds the language of the whole course: how inputs and outputs change together, average rates of change, and the behaviour of polynomial and rational functions, including zeros, end behaviour, asymptotes and holes. It finishes with transformations and building models from data and context.
Focus on: average rate of change is a slope; zeros, multiplicity and end behaviour; rational functions: compare degrees, then factor; transformations act on inputs or outputs.
Unit 2 contrasts additive and multiplicative change: arithmetic sequences and linear functions against geometric sequences and exponential functions. It then builds composition and inverses, which lead to logarithms, log laws, solving exponential and log equations, and modelling with semi-log plots.
Focus on: linear adds, exponential multiplies; inverses undo, and logs are inverses of exponentials; log laws turn products into sums; choose and check models.
Unit 3 models repeating patterns. It starts with the unit circle and the sine, cosine and tangent functions, then builds sinusoidal models from amplitude, period, phase shift and midline. It finishes with inverse trig, equations and identities, the reciprocal functions, and polar coordinates and polar graphs.
Focus on: the unit circle defines sine and cosine; read a sinusoid in four numbers; inverse trig has restricted outputs; polar coordinates measure angle and signed distance.
Unit 4 is part of the AP Precalculus course, but it is not tested on the AP Exam. Many schools teach it for class tests and to prepare for calculus. It covers parametric functions and motion, implicitly defined functions and conic sections, vectors, and matrices as functions and models.
Focus on: parametric functions trace motion; conic sections from equations; vectors have magnitude and direction; matrices transform and model.