AP Precalculus — Free Practice Questions, Study Guides & Mock Exams
Explore the major ideas of polynomial, rational, exponential, logarithmic, trigonometric, and polar functions.
Topics covered
- Skill Drill
- True/False
- Word Bank
- MCQ
Free AP Precalculus study guides
- Function Behavior and Rates of Change — Translate among verbal descriptions, tables, graphs, and formulas while keeping direction, rate, and concavity logically separate.
- Polynomial Functions and Zeros — Use equivalent forms to connect global end behavior, local turning behavior, real zeros, multiplicity, and complex factorization.
- Rational Functions, Transformations, and Models — Classify discontinuities and asymptotes correctly, transform functions in the correct order, and defend polynomial or rational models in context.
- Sequences, Exponentials, and Model Choice — Recognize additive and multiplicative change, build exponential formulas in equivalent forms, and choose among linear, quadratic, and exponential models.
- Composition, Inverses, and Logarithmic Functions — Treat composition as a two-stage process, protect its domain, reverse one-to-one functions, and connect logarithms to exponential inverses.
- Logarithmic Properties, Equations, and Models — Rewrite logs legally, solve exponential and logarithmic equations and inequalities, and interpret logarithmic models and semilog displays.
- Periodic, Unit-Circle, and Sinusoidal Functions — Build exact trigonometric values from the unit circle, then turn amplitude, midline, period, and phase into complete sinusoidal graphs and contextual models.
- Advanced Trigonometric and Polar Functions — Analyze tangent, reciprocal and inverse functions, solve equations and inequalities, justify identities, and transfer the same exact-angle reasoning into polar coordinates and graphs.
- Parametric Functions, Motion, and Conics — Track orientation and motion through a parameter, connect parametric and implicit representations, and extract the defining features of every conic.
- Vectors, Matrices, and Transformations — Represent motion and geometry with vectors, carry out matrix operations with correct dimensions and order, and analyze matrix transformations and state-transition models.
Units
- Unit 1
- Unit 2
- Unit 3
- Unit 4