The course's capstone. These topics extend the function concept beyond y = f(x): parametric and implicitly defined functions trace curves and motion, vectors carry magnitude and direction, and matrices act as functions that transform the plane. Unit 4 is not assessed on the AP Exam, but it deepens everything from Units 1–3.
Six ways to master Unit 4 — pick whichever fits how you like to study.
All 14 topics from the College Board CED, in order.
Unit 4 is not assessed on the AP Precalculus Exam. The College Board includes it as a set of additional topics that some schools teach based on state or local requirements. Everything on the exam comes from Units 1–3 — but Unit 4 extends the function concept in ways that are valuable preparation for calculus and linear algebra.
The unit widens what a "function" can be. Parametric functions give x and y each as a function of a parameter t, letting a single curve encode motion, direction, and timing — even when the curve is not a function of x. Implicitly defined functions and conic sections describe circles, ellipses, parabolas, and hyperbolas. Vectors add magnitude and direction, and vector-valued functions model position and velocity.
Finally, matrices reframe functions entirely: a matrix is a function that maps input vectors to output vectors, transforming the plane through rotation, scaling, reflection, or shear. You learn to multiply matrices, compute determinants and inverses, and use matrices — and their powers — to model change over discrete steps. The same three mathematical practices from Units 1–3 apply throughout.